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Reassessment of National Parameters for Appraisal of
Public Investment Programmes/Projects in India
NITI Aayog, Government of India
and
Indian Statistical Institute, Delhi Centre
Authors
Prof. E. Somanathan
Prof. Monisankar Bishnu
Dr. Raavi Aggarwal
October, 2026
NITI STUDY SERIES
Study No. WPS (NITI Aayog)/03/2026
Reassessment of National Parameters for Appraisal
of Public Investment Programmes/Projects in India
Prof. E. Somanathan
Prof. Monisankar Bishnu
Dr. Raavi Aggarwal
Date of Publication: 12/10/2026
Published By;
National Institution for Transforming India (NITI Aayog),
NITI Bhawan, Sansad Marg, Delhi-01
Disclaimer
1. This document is not a statement of policy by the National Institution for Transforming
India (hereinafter referred to as NITI Aayog). It has been prepared by [Prof. E.
Somanathan (Professor, ISI Delhi), Prof. Monisankar Bishnu (Professor, ISI Delhi) and
Dr. Raavi Aggarwal (Consultant, ISI Delhi)] pursuant to the support of NITI Aayog,
for the purpose of independent academic and policy-oriented research.
2. Unless otherwise stated, NITI Aayog, in this regard, has not made any representation
or warranty, express or implied, as to the completeness or reliability of the information,
data, findings, or methodology presented in this document. While due care has been
taken by the author(s) in the preparation of this publication, the content is based on
independently procured information and analysis available at the time of writing and
may not reflect the most current policy developments or datasets.
3. The assertions, interpretations, and conclusions expressed in this report are those of the
author(s) and do not necessarily reflect the views of NITI Aayog or the Government of
India, unless otherwise mentioned. As such, NITI Aayog does not endorse or validate
any of the specific views or policy suggestions made herein by the author(s).
4. NITI Aayog shall not be liable under any circumstances, in law or equity, for any loss,
damage, liability, or expense incurred or suffered as a result of the use of or reliance
upon the contents of this document. Any reference to specific organisations, products,
services, or data sources does not constitute or imply an endorsement by NITI Aayog.
Readers are encouraged to independently verify the data and conduct their analysis
before forming conclusions or taking any policy, academic, or commercial decisions.
Acknowledgements
We would like to thank Shri Ashok Kumar Lahiri, Vice Chairperson, NITI Aayog and
Shri Suman Bery, Former Vice Chairperson, NITI Aayog, Shri Anurag Jain, CEO, NITI Aayog
and Ms. Nidhi Chhibber, Former CEO, NITI Aayog, Shri B. V. R. Subrahmanyam, Former
CEO NITI Aayog, Shri Anurag Goyal, Senior Adviser, PFPA Division, NITI Aayog, Smt. Jyoti
Khattar and Smt. Esha Swaroop, Senior Research Officers, PFPA Division, NITI Aayog,
Ms. Anjali Bansal, Consultant Grade – I, NITI Aayog, Ms. Arpana Bhatt, Consultant Grade –
II, NITI Aayog, Ms. Aakriti, Young Professional, NITI Aayog and Ms. Gargi Rao, former
Research Officer, NITI Aayog for their valuable inputs in the study.
We would also like to thank Prof. Thomas Sterner, Prof. Prachi Mishra, Prof. Mudit Kapoor,
and Dr. Tanu Gupta for useful discussions. Finally, we thank Ms. K. Shreyaswini, Ms. Evelin
Treesa Jose, Mr. Raghav Modi, and Ms. Deepanshi Rai for valuable research assistance. All
errors remain our own.
Foreword
(A practice note on the use of the National Parameters)
1. Public investment decisions across infrastructure, energy, transport, urban services and
social sector programmes are generally appraised using economic cost-benefit analysis,
which requires discounting future streams of economic benefits and costs into present
values. A proposal is acceptable only if the present value of its expected benefits exceeds
the present value of its expected costs. Any such comparison, therefore, requires an
appropriate rate at which future economic benefits and costs are discounted, and that rate
is termed the Social Discount Rate (SDR).
2. Cost-benefit analysis of this kind requires adjustment of the financial or market prices,
since these are distorted by taxes, subsidies, administered wage floors, and other policy-
induced wedges that separate observed prices from the opportunity cost of resources and
the value of benefits to society. Project appraisal, therefore, requires a set of “shadow” or
accounting parameters, or conversion factors, through which market prices can be
converted into estimates of the resource cost of inputs and the economic benefits to society.
Thus, in practice, the Shadow Wage Rate Factor is used for labour, and, depending on
whether costs and benefits are expressed in domestic or world prices, either a Shadow
Exchange Rate Factor or a Standard Conversion Factor is used for traded items. An item-
specific conversion factor is estimated for the non-tradables. In addition, where a project
has material greenhouse gas impacts, a shadow price of carbon is also required.
3. The last comprehensive assessment of these parameters for the country was undertaken by
NITI Aayog through the Institute of Economic Growth (IEG) in 2018. IEG followed the
Ramsey approach to estimate the Social Rate of Time Preference (SRTP) as the Social
Discount Rate (SDR) and recommended an SDR of 8 per cent for projects with a duration
of up to 50 years, 6 per cent for projects with a duration of 50 years or more, and a rate
below 6 per cent for projects with a duration of more than 100 years. The Shadow Exchange
Rate Factor (SERF) was estimated at 1.08. The estimation of the Standard Conversion
Factor and the Shadow Wage Rate for labour was not taken up. Since these parameters are
intended to reflect prevailing economic conditions rather than remain fixed indefinitely,
they require periodic reassessment as new data become available.
4. NITI Aayog engaged the Indian Statistical Institute (ISI), Delhi, to re-estimate these
parameters. ISI has drawn on National Accounts Statistics, the Periodic Labour Force
Survey (PLFS), the Annual Survey of Industries (ASI), KLEMS, Direct Tax Statistics,
trade data and cross-country growth data, together with a review of the methodological
advances in the discounting literature, with particular attention to the Social Discount Rate.
5. Social Discount Rate: The analysis of the Social Discount Rate is particularly involved.
The literature indicates an intense debate over the appropriate method to estimate the SDR,
and whether the SDR should vary with tenure of the projects. Jenkins, Kuo, and Harberger
(2011) list four approaches for estimating the discount rate in public-sector project
evaluation.
a) The first holds that all investment projects, public and private alike, should be
discounted at the marginal productivity of capital in the private sector (Hirshleifer,
DeHaven and Milliman 1960). The rationale, as Jenkins, Kuo and Harberger present it,
is that a government seeking to maximise national output should direct funds to
wherever the return is highest, i.e. where private projects offer a higher expected
economic return than the available public projects, the funds are better left in private
hands.
b) A second approach, developed by Little and Mirrlees (1974), building on the OECD
(1969), and adapted for World Bank use by Squire and van der Tak (1975), employs an
accounting rate of interest (ARI). Jenkins, Kuo and Harberger (2011) characterise the
accounting rate approach as essentially a rationing device that allocates a fixed public
investment budget.
c) A third approach discounts costs and benefits at the Social Rate of Time Preference
(SRTP) for consumption, after converting flows that displace or augment private
investment into their consumption-equivalent values using a shadow price of
investment. Proponents include the UNIDO Guidelines (Dasgupta, Sen and Marglin
1972), Marglin (1963) and Feldstein (1964), with the formal treatment usually
attributed to Bradford (1975).
d) A fourth approach holds that the discount rate should be the Economic Opportunity
Cost of Capital (EOCK): the weighted average of the returns forgone on the sources
from which public funds are actually drawn. In its simplest closed-economy form
(Harberger 1968, reprinted 1972), this is a weighted average of the return on displaced
private investment and the rate of time preference of savers. In an open economy, a
third term is added for the marginal cost of incremental foreign capital. The premise is
that the additional government borrowing required to finance public investment
partially displaces private investment, induces additional domestic saving at the
expense of current consumption, and draws in foreign capital. The SDR is therefore
estimated as the weighted average of the returns forgone from these three sources, with
the weights derived from the interest elasticities of domestic saving, private investment,
and the foreign supply of funds.
6. This report estimates the SDR using two approaches: the SRTP approach using the
Extended Ramsey Rule (the Ramsey rule with a precautionary adjustment for uncertainty
in consumption growth), and the EOCK approach or the weighted-average approach,
following Burgess and Zerbe (2011).
a. Under the Ramsey rule, if consumption per head is expected to rise, a unit of
consumption delivered to a richer future society is worth less at the margin than the
same unit today, so a higher expected growth rate of per capita consumption implies a
higher discount rate. Calibrating that growth rate is difficult. Virmani (2024) puts real
per capita GDP growth (2017 PPP dollars) over 2020–50 at 5.9% per annum in a
conservative case, 6.4% in a median case, and 6.9% in an optimistic one. On the
conservative 5.9% path, ISI estimates an SRTP of 9.4%; and on the average per capita
growth of about 4.7% actually experienced over the past three decades, it estimates
7.3%.
b. EOCK has been calculated using the weighted-average approach, based on the
estimated rate of return to capital in the private sector from the National Accounts
Statistics (NAS) data. Estimates based on broad stock market returns – the NIFTY 500
Total Returns Index – and on ASI data have also been used as cross-checks. The risk-
free rate has been set at the real rate of return on central government securities, and the
interest rate on foreign borrowing has been estimated using annual data from India's
External Debt Status Reports. These estimates, combined with the subcomponent
weights, yield an EOCK of 9.23%.
7. This report recommends the weighted average or the EOCK approach as the basis for the
Social Discount Rate for India for projects of up to 30 years, and the SRTP approach as the
basis for the SDR applicable to longer horizons.
The report compares SDR estimates across various countries and institutions. Among the
25 countries and institutions assessed, 14 have SDR estimates based on the social
opportunity cost of capital (SOC) or weighted average (WA) approach, 9 have estimates
based on the social rate of time preference (SRTP) approach, and 2 have estimates available
under both approaches. A broadly similar pattern appears in Groom et al. (2022), which
reviews 20 countries and institutions: 12 rely on an SOC-based approach alone, 6 on the
SRTP alone, and 2 (Denmark and the United States) draw on both. On either count, the
SOC/WA approach is the more common of the two across the jurisdictions surveyed. The
middle-income jurisdictions appearing in these compilations — Chile, Mexico, Brazil,
Colombia and Peru — use SOC-based rates, most of them following the weighted-average
formulation set out in Harberger (1969); and as of the mid-2000s, most multilateral
development banks applied rates of 10–12% derived on a weighted-average basis (Zhuang
et al., 2007).
This may reflect a judgment about capital scarcity, though the rationale is not elaborated in
the sources. ADB’s 2017 Guidelines for the Economic Analysis of Projects report that the
weighted average approach has been considered the preferred method for empirically
estimating the SDR because it explicitly accounts for market imperfections and credit
constraints on investment.
Moreover, in practice, using the SRTP would require a separate shadow price of capital to
convert the investment component into its consumption equivalent, which is difficult.
Accordingly, the recommendation for the Weighted Average approach for projects with a
tenure of up to 30 years is in line with prevailing practices in comparable economies.
8. One of the terms of reference for the report was to assess whether a single constant discount
rate is appropriate for projects with widely differing life spans, such as environmental and
social sector projects, whose returns accrue over much longer periods.
By construction, discounting places greater weight on nearer-term than on more distant net
benefits. Too high a rate undervalues the long-term social benefits of public investment,
while too low a rate understates the opportunity cost of the funds committed, and so admits
projects that displace higher-yielding uses of the same resources. This matters most where
horizons differ widely: infrastructure and construction projects typically generate the bulk
of their returns within a few decades, whereas investments in education, healthcare and
climate mitigation may yield returns over much longer periods. The calibration of the
discount rate, therefore, shapes the balance of the public investment portfolio between near-
term returns and long-term value.
9. A single constant rate can therefore leave projects whose benefits accrue over several
decades unable to show a positive net present value (NPV) over their lifetime. This is
particularly relevant for the country, given its ambition to become Viksit Bharat by 2047
along with its commitment to achieving Net Zero by 2070. The Viksit Bharat vision, as a
medium-term objective, underscores the importance of prioritising high-return investments
to support higher growth and income levels. The Net Zero 2070 commitment involves
initiatives such as climate mitigation projects that may not appear economically viable due
to their capital-intensive nature and long gestation periods, even though they would deliver
long-term economic benefits.
Several methods are used to accommodate long-term benefits in cost-benefit analysis:
sensitivity analysis to account for uncertainty; differentiated rates, such as a lower rate for
health and environmental benefits; and a declining discount rate applied over the project's
tenure. The ADB Guidelines for the Economic Analysis of Projects (2017) set a minimum
required economic internal rate of return of 9% in general and permit a lower rate of 6%
for social sector projects and for projects that primarily generate environmental benefits.
One reason is that many environmental protection and conservation projects have long-
term impacts.
Thus, while practice varies across jurisdictions, the guiding principle should be that
whatever is adopted remains simple enough to apply consistently in routine cost-benefit
analysis. The 2018 assessment also adopted a declining schedule.
The current report acknowledges the difficulty of calibration and states that the choice of a
specific declining schedule is a matter of practicality rather than theory. It further states
that for very long horizons, the Ramsey approach provides a more robust and theoretically
grounded basis for the SDR. The literature points in the same direction: over long horizons,
the appropriate weighted-average rate converges on the consumption rate of interest (Li
and Pizer 2021)
3
.
3
https://www.nber.org/system/files/working_papers/w25413/revisions/w25413.rev0.pdf
Using the Ramsey rule for longer time horizons, the report recommends a declining
schedule for the social discount rate: 6.2% (30-50 years), 4.8% (50-75 years), and 3.4%
(75-100 years).
The extant practice has been to apply a single hurdle rate to all projects, together with a
sensitivity analysis for uncertainties such as inflation projections. Going forward, it is
suggested that for projects with a tenure exceeding 30 years, either of two approaches may
be adopted, depending on the project profile: the sensitivity analysis just described, as at
present, or a declining discount rate (DDR) schedule applied over the longer duration.
Where it is used, the appraisal should require that the project generate a non-negative
economic net present value under the applicable schedule over its full horizon.
10. Shadow Exchange Rate Factor (SERF), Standard Conversion Factor (SCF) &
Shadow Wage Rate Factor (SWRF):
All projects use inputs or produce outputs that can either be tradable or non-tradable. Non-
tradables are goods whose prices are primarily determined domestically, whereas the prices
of tradables are largely set internationally. Examples of tradables include importable and
exportable commodities such as steel, wood, iron, and chemicals. Examples of non-
tradables include electricity, water, all public services, construction, real estate, local
transport, hotel accommodation, and low-value/high-bulk goods such as gravel, for which
freight makes export unprofitable. For the reasons set out in para 1 above, the financial
prices at which these items are bought and sold cannot be used as such; each must be
converted to an economic value.
a) The Shadow Exchange Rate is the economic price of foreign exchange expressed in
domestic currency. The Shadow Exchange Rate Factor (SERF) is the ratio of the
Shadow Exchange Rate to the Official Exchange Rate. This is typically above unity
due to tariffs and other distortions. The value derived in this report is 1.09. This is
marginally higher than the 1.08 estimated in the 2018 study.
b) Likewise, the economic prices of tradables and non-tradables must be estimated after
removing distortions such as taxes, subsidies and price controls. For tradables, the
principal distortion is trade taxes. To simplify the analysis, a Standard Conversion
Factor (SCF) is sometimes used in place of item-specific adjustment: it converts the
financial price to its international market-price equivalent, adjusting for trade taxes. The
value estimated in this report is 0.92. Where an item accounts for a small share of total
cost, or where item-specific information is not available, the SCF is an adequate
approximation. The costs of transport and distribution between the border and the
project must, however, be added separately to arrive at the economic cost or benefit.
c) Non-tradables, when used as inputs to a project, should be valued at their marginal
economic cost of supply; and as outputs of a project, these should be valued at the
willingness to pay or at the alternative cost of supply (if the project is an alternative
source of supply of the non-tradable). For instance, in the case of power projects,
economic value is the alternative cost of generating an equivalent flow of energy by
some standard means.
This report mentions that the conversion factor for non-tradables is 1, in line with the
ADB guidelines (2017). However, it should be clarified that this conversion factor of 1
only indicates that the price is set in the domestic market. It does not state that the
domestic price is not distorted. As such, commodity-specific conversion factors are
preferred for non-tradables.
d) The shadow wage rate factor (SWRF) is the ratio of the Opportunity cost of labour to
the wage the project actually pays. Actual wages differ from the opportunity cost of
labour because of complex issues related to unemployment and labour market rigidities.
When involuntary unemployment or underemployment exists, workers are likely to
accept a lower wage rather than remain unemployed. However, it is also incorrect to
treat the opportunity cost of employing labour that would otherwise be unemployed as
nil. It is also incorrect to assume that a reduction in unemployment equals the number
employed in the project, as some of the labour is likely to be displaced from other
employment. As such, the treatment of labour costs depends on the nature of the project.
However, for simplicity, a standard wage-rate factor can be used. For scarce or skilled
labour, SWRF can normally be taken as 1.0.
This report estimates the SWRF for unskilled labour using the Periodic Labour Force
Survey (PLFS) and minimum wage notifications, disaggregated by state, sector, and
gender. The estimated SWRF is 0.86. It should be clarified, however, that where labour
is a large share of costs, or where workers are a key beneficiary group, a project-specific
SWRF based on local labour market analysis is required, and the state-specific
estimates should be used in preference to the national figure; the national value is an
approximation for simplified appraisal only.
The practical guidance on the use of the conversion factors is summarised in the table
below:
Category Treatment
Traded items valued at world prices,
converted at the official exchange rate
Multiply by SERF
Non-traded items valued at domestic prices
or WTP
Multiply by 1.00 (or use the commodity-
specific CF if there are significant
distortions like subsidies in the domestic
market)
Tariffs, indirect taxes, subsidies on the item Removed, as these are transfers
Labour — unskilled or in surplus supply
(skilled or scarce labour: 1.00)
Multiply by the applicable SWRF, using
the state-specific value where labour is a
material share of cost
11. Social cost of carbon (SCC): The social cost of carbon is used in appraisal practice to
account for the externalities associated with carbon emissions in a project. Broadly, two
distinct constructs emerge regarding what the social cost of carbon represents, i.e., whether
it measures damages or abatement costs.
The damage-based measure is the present value of future societal damages from emitting
an additional tonne of CO₂ today. This is the construct underlying the ADB, Canadian and
US guidance on cost-benefit analysis. This report also suggests a value of US$10 per tonne
of CO₂, using a damage-based measure that accounts only for damages incurred within
India.
12. The abatement-cost measure is the marginal cost of abating an additional tonne along a
least-cost path to a stated climate goal. This is the construct underlying the cost-benefit
guidance of several European countries and institutions, such as the UK, the EIB, and the
World Bank.
13. In this context, the recent launch of a Carbon Credit Trading Scheme, 2023, under the
Energy Conservation Act, 2001, as amended in 2022, is relevant. It adopts an emission-
intensity-based model for Carbon Credit Certificates (CCCs). The CERC’s 2026
regulations provide that CCCs are to be traded through power exchanges within a floor
price and a forbearance price. The CCC price should therefore serve as a proxy for the
abatement-cost measure of the social cost of carbon in the regulated sectors, once trading
matures, and the price is formed above the floor. However, it is recommended that a single
carbon shadow price be applied to all project emissions in both covered and uncovered
sectors. Accordingly, it is suggested that the same may also be used as the carbon price in
project appraisal. The report also recommends that a separate study be undertaken to
empirically determine the country-specific cost of carbon.
14. It is clarified that receipts from the sale of CCCs and payments for their purchase are cash
flows to be used in the financial analysis. These are, in effect, transfers between residents
and should not be included in the economic analysis. The project's residual emissions must
still be valued as an externality in the economic analysis.
15. To sum up, the values indicated in the table below are recommended for the national
parameters based on the current report, after rounding for practical use in cost-benefit
analysis:
Parameter Recommended Value
Social Discount Rate (< 30 years) 9.50%
Social Discount Rate (30-50 years) 6.50%
Social Discount Rate (50-75 years) 5%
Social Discount Rate (75-100 years) 3.50%
Standard Conversion Factor (SCF) 0.92
Shadow Exchange Rate Factor (SERF) 1.09
Shadow Wage Rate Factor (SWRF) - Total 0.86
Shadow Wage Rate Factor (SWRF) - Male 0.88
Shadow Wage Rate Factor (SWRF) - Female 0.82
SCC (not accounting for damages outside India) US$ 10/tCO2e
4
Where a declining discount rate is used, each year’s net flow should be discounted at the
rate applicable to the period in which it falls, rather than the whole stream being discounted
at a single rate selected by reference to the project’s total life. Applying a single lower rate
to every year of a long-lived project would create a discontinuity at the 30-year boundary
and an incentive to specify a longer appraisal period than the project warrants. In such
cases, the test of viability is a non-negative economic net present value, rather than a
comparison of an economic rate of return with a single hurdle rate.
16. In conclusion, the discount rate tests whether a project earns more than its funds could earn
elsewhere. While passing that test means the project is worth undertaking, it does not
establish that the limited budget could not have been used better elsewhere. The objective
should therefore be to select the combination of projects that yields the highest total net
present value within the available budget, rather than simply accepting every project that
clears the discount rate. In practice, ranking is difficult because projects reach appraisal at
different times and in varying states of readiness. A rough ordering can nevertheless be
built from whatever determines returns in a sector — say, projected traffic in transport —
but only where forecasts follow a common, independently set standard, since demand
forecasts prepared by project proponents tend towards optimism. Project readiness, land
availability and strategic priorities also matter and can override economic ranking; in such
cases, the specific reasons should be recorded.
The parameters estimated here — the social discount rate, in the form of the economic
opportunity cost of capital for shorter horizons and a Ramsey-based declining schedule for
longer ones; the shadow exchange rate factor and its reciprocal, the standard conversion
factor; the shadow wage rate factor; and the shadow price of carbon — help establish
whether a project is worthwhile in national economic terms and allow projects across
sectors to be compared on a common basis. Both uses require that the parameters be applied
consistently and revised as the economy changes.
(Anurag Goyal)
Sr Adviser
Public Finance & Policy Analysis Division,
NITI Aayog
4
tonne of carbon-dioxide equivalent
1
Executive Summary
Background
Public investment is a central instrument through which India advances its long-term
development objectives. Large-scale expenditures on infrastructure, energy systems, transport
networks, urban services, and social programmes require a rigorous appraisal framework that
can determine whether the present value of economic benefits from a project exceeds its
economic cost. Such appraisal cannot rely solely on financial prices, because market prices
incorporate taxes, subsidies, administered wage floors and other policy-induced distortions that
cause them to diverge from the underlying opportunity costs of resources. Economic appraisal
therefore requires translating financial magnitudes into economic values using parameters such
as discount rates, conversion factors, shadow wage rates, and the social costs of carbon which
measure climate damage valuations.
The last comprehensive national assessment of these parameters was conducted by NITI Aayog
in 2018, which provided estimates for use in public project appraisal. The study recommended
a social discount rate of 8 percent for projects with horizons up to 50 years, with a lower rate
of 6 percent for long-gestation infrastructure and environmental projects. It further suggested
rates below 6 percent for projects extending beyond 100 years. It also estimated a 10 percent
rate of return on capital, recommended as the hurdle rate for financial analysis, and identified
an 8 percent foreign-exchange premium reflecting the gap between the economic value and the
market price of foreign currency.
Since the 2018 assessment, new rounds of official data and methodologies offer a stronger
empirical foundation for revising the parameters used in economic appraisal. Since these are
intended to reflect prevailing economic conditions, the parameters require periodic
reassessments. The present study re-evaluates the parameter values for the social discount rate,
standard conversion factor and shadow prices using recent datasets and new methodological
frameworks, which build on the previous assessment by NITI Aayog conducted in 2018.
Objectives of the Study
The objectives of this study are to provide updated estimates of the five parameters required
for the economic appraisal of public-sector projects in India, which include:
2
(i) Social Discount Rate (SDR): This measures the societal trade-off between present
consumption and future consumption. It is used to discount the future stream of benefits
generated from public investments undertaken today. Projects with long timespans are
sensitive to future economic growth rates, which impact the social discount rate. Thus,
we estimate social discount rates for projects with differing lifetimes, based on the latest
methodologies in the discounting literature.
(ii) Standard Conversion Factor (SCF): It is estimated by comparing domestic market
prices of tradable goods with their border-price equivalents and is used to convert
financial costs of traded inputs into economic costs that exclude the effects of import
duties. An SCF value below 1 indicates that domestic market prices of tradable goods
exceed their economic (border-price) values, largely due to import duties. This
adjustment is relevant for costs of imported inputs in project evaluation, since this can
tilt the cost-benefit ratio for public projects that rely on imported inputs relative to
domestic inputs.
(iii) Shadow Exchange Rate Factor (SERF): It adjusts the market exchange rate to reflect
the economic cost of foreign exchange. The SERF incorporates the impact of import
tariffs and subsidies that create a wedge between domestic and border prices.
(iv) Shadow Wage Rate Factor (SWRF): It is estimated by comparing observed wages from
the PLFS with statutory minimum wages notified for unskilled labour. In many states,
minimum wages exceed prevailing market wages, causing financial labour costs to
overstate the economic opportunity cost of labour. The SWRF adjusts for this
divergence by valuing unskilled labour at market-determined wages.
(v) Social Cost of Carbon (SCC): It represents the present value of economic damages
associated with an additional tonne of CO₂ emissions and is derived from long-horizon
climate-damage modelling studies. The study compiles global SCC estimates to
provide an approximate value of the social cost of carbon for India that can be applied
in the economic appraisal of public projects.
These updated parameters aim to provide a consistent and empirically grounded basis for
evaluating the economic viability of public-sector projects.
3
Scope
The study covers the conceptual rationale, empirical estimation, and application of each
parameter within India’s cost–benefit analysis framework. It adopts the Little and Mirrlees
(1974) accounting-price approach, which recognises that market prices, which are affected by
taxes, subsidies, tariffs, and labour-market rigidities, may diverge from economic values.
The analysis relies exclusively on official Government of India datasets, including the National
Accounts Statistics, Household Consumer Expenditure Survey, Annual Survey of Industries,
Periodic Labour Force Survey, and administrative data from the Reserve Bank of India,
Ministry of Finance, and Ministry of Commerce and Industry. These datasets provide the
empirical basis for estimating the parameters in a manner consistent with India’s current
macroeconomic structure and institutional context.
Methodology
The methodological approach is parameter-specific and grounded in established economic
theory.
For the social discount rate, the study tests various approaches and applies the Ramsey rule,
which determines the discount rate by estimating the trade-off between present and future
consumption. This is based on the degree of inequality aversion and the expected future
economic growth rate for India. We estimate the inequality-aversion parameter using the equal-
sacrifice principle, and derive long-run economic growth from past trends in per-capita GDP.
The extended Ramsey rule is used to incorporate the effect of uncertainty in future economic
growth, for downward adjustment of the social discount rate for long-horizon projects.
The social discount rate is also computed based on estimated market-based rates of return such
as the social opportunity cost of capital and the weighted average approach. These methods
estimate the real returns to government securities, the private sector’s marginal product of
capital which is estimated using data from the Annual Survey of Industries, and a weighted-
average financing-cost measure that reflects domestic and external borrowing conditions. This
combined approach provides a consistent basis for determining discount rates for projects with
different time horizons.
4
The Standard Conversion Factor (SCF) is estimated by comparing domestic market prices of
traded goods with their border-price equivalents, after adjusting for import duties in import
values. Export values, already recorded at border prices, are taken as reported. These import
and export ratios are then aggregated across product categories to obtain an economy-wide
SCF. An SCF below 1 indicates that domestic market prices are higher than economic (border)
prices due to border taxes, which implies that using financial prices would overstate the true
economic costs of tradable inputs.
The Shadow Exchange Rate Factor (SERF) measures the ratio of the economic price of foreign
currency to its market price and is obtained as the reciprocal of the Standard Conversion Factor
(1/SCF). This reflects the foreign-exchange premium after removing import duties and other
trade-related distortions, based on product-level trade and tariff data.
The Shadow Wage Rate Factor (SWRF) is estimated using wage data from the Periodic Labour
Force Survey (PLFS) for unskilled workers in rural and urban areas. Since market wages reflect
the economic opportunity cost of labour, the study compares these observed wages with the
statutory minimum wages notified by the Central Government through the Chief Labour
Commissioner, for employment under the central government’s jurisdiction. For occupations
where minimum wages exceed actual market wages, common for agricultural labour in rural
areas and informal workers in urban areas, the minimum wage would overstate the economic
cost of labour, and the SWRF adjusts this downward by taking the ratio of market wages to
minimum wages. This approach yields opportunity-cost-based labour valuations suitable for
economic appraisal of public projects.
Lastly, the Social Cost of Carbon is compiled from global studies which estimate the economic
damages associated with incremental CO₂ emissions, applying discount rates that are consistent
with long-run time horizons.
Key Findings
The mean Social Discount Rate for projects with a time horizon up to 30 years is 9.23 percent
based on the weighted average approach, with various methods yielding a range of 7.3 – 11
percent. For longer project horizons, we recommend using the uncertainty-adjusted Ramsey
approach such that the social discount rate declines to 6.2 percent (30–50 years), 4.8 percent
(50–75 years), and 3.4 percent (75–100 years).
5
The Standard Conversion Factor is estimated at 0.92, indicating that domestic prices for
tradable goods exceed their economic values once duties and taxes are removed. The
corresponding Shadow Exchange Rate Factor is 1.09, implying a foreign-exchange premium
of approximately 9 percent. The Shadow Wage Rate Factor is estimated at 0.86 for unskilled
labour, with average values of 0.88 for men and 0.82 for women, reflecting wage distributions
observed in PLFS data. Lastly, the Social Cost of Carbon for India is estimated at USD 10 per
tonne of CO₂, with a broader evidence-based range of USD 9–87 per tonne.
Key Policy Extracts and Indicative Ministries
The updated parameters have implications for ministries involved in public investment
planning and appraisal. The SDR is relevant for the Ministry of Finance, NITI Aayog, and
sectoral ministries preparing long-duration project proposals for appraisal by the Public
Investment Board and Expenditure Finance Committee. It is particularly applicable to
infrastructure, energy, irrigation, and environmental projects.
The SCF and SERF provide a consistent valuation basis for traded goods and foreign-exchange
components in capital-intensive sectors, including commerce, industry, transport, ports, power,
and renewable energy. These parameters ensure that project costs reflect economic rather than
financial prices.
The SWRF is applicable to labour-intensive programmes under the Ministry of Labour and
Employment, Ministry of Rural Development, and state governments implementing public
works and construction projects.
The SCC offers an estimate of the economic damages associated with an additional tonne of
CO₂ emissions and can be used in project appraisal where valuation of climate-related
externalities is required.
Conclusion and Implications
These updated parameters provide an improved analytical foundation for public investment
decisions undertaken by the Government of India. By ensuring that project benefits and costs
are assessed at economic rather than market values, the revised estimates reinforce the
credibility of appraisal exercises and support more efficient allocation of public resources.
Their systematic use will help ensure that major public investments are evaluated on a
consistent basis, strengthening the quality of India’s development planning.
6
Table of Contents
1. Introduction .................................................................................................................. 8
1.1. Objectives .................................................................................................................... 8
1.2. Social Discount Rate ...................................................................................................... 9
1.3. Accounting (Shadow) Prices ......................................................................................... 10
1.4. Social Cost of Carbon .................................................................................................. 10
1.5. Reassessment of parameters from NITI Aayog (2018) report ............................................ 11
2. Social Discount Rate: Methods and Results .................................................................... 11
2.1. Literature Review on Social Discount Rate ..................................................................... 12
2.2. Methodologies to compute the Social Discount Rate ........................................................ 14
2.2.1. Ramsey Social Discount Rate ....................................................................................... 15
2.2.2. Market Rates of Return to Capital ................................................................................. 27
a) Real Return on Government Securities ........................................................................... 27
b) Social Opportunity Cost of Capital ................................................................................ 27
c) Weighted Average Approach ........................................................................................ 32
2.2.3. Comparison of Social Discount Rates ............................................................................ 35
3. Shadow Prices ............................................................................................................ 38
3.1. Literature Review on Shadow Prices .............................................................................. 38
3.2. Standard Conversion Factor: Methodology and Results .................................................... 39
3.3. Shadow Exchange Rate Factor: Methodology and Results ................................................ 44
3.4. Shadow Wage Rate Factor: Methodology and Results...................................................... 47
4. Social Cost of Carbon .................................................................................................. 60
4.1. Global SCC values ...................................................................................................... 61
4.2. Country-specific SCC values ........................................................................................ 64
5. Recommendations ....................................................................................................... 65
6. References .................................................................................................................. 68
A.1. Derivation of the Ramsey rule ....................................................................................... 74
A.2. Social Opportunity Cost of Capital Approach ................................................................. 76
A.3. Weighted Average Approach ........................................................................................ 79
A.4. Other approaches to estimating ................................................................................... 80
A.4.1. Euler equation approach ............................................................................................... 81
A.4.2. Frisch approach ........................................................................................................... 82
A.4.3. Subjective well-being approach ..................................................................................... 84
A.5 Shadow Exchange Rate Factor (SERF), based on alternative method ................................. 86
A.6 Synthesis of estimates for the Social Cost of Carbon ....................................................... 87
7
List of Tables
Table 1: Synthesis of parameter estimates for social discount rate....................................................... 19
Table 2: Average incomes, income taxes, average tax rates and marginal tax rates by income category,
assessment year 2023-24 ......................................................................................................... 23
Table 3: Estimate of the elasticity of the marginal utility of consumption (η) ..................................... 24
Table 4: List of countries for computing variance in the growth rate ................................................... 27
Table 5: Term structure of discount rates, with uncertainty adjustment in growth rates ...................... 29
Table 6: Estimating the Marginal Product of Capital ........................................................................... 33
Table 7: Social Discount Rate – Weighted Average Approach ............................................................ 37
Table 8: Comparison of Social Discount Rates across approaches ...................................................... 37
Table 9: Synthesis of parameter estimates for SDR across countries for various methods .................. 39
Table 10: Standard Conversion Factors, by HS 2-Digit Products ........................................................ 44
Table 11: Shadow Wage Rate Factors (SWRF) for unskilled labour, 2023-24 .................................... 52
Table 12: Average daily wage for unskilled labour, by rural and urban areas, 2023-24 ...................... 54
Table 13: Shadow wage rate factor for male unskilled workers, by States/UTs, 2023-24 ................... 55
Table 14: Shadow wage rate factor for female unskilled workers, by States/UTs, 2023-24 ................ 56
Table 15: Shadow Wage Rate Factors (SWRF) for unskilled labour (2019-2020) .............................. 58
Table 16: Shadow Wage Rate Factors (SWRF) for unskilled labour (2020-2021) .............................. 59
Table 17: Shadow Wage Rate Factors (SWRF) for unskilled labour (2021-2022) .............................. 61
Table 18: Shadow Wage Rate Factors (SWRF) for unskilled labour (2022-2023) .............................. 62
Table 19: Updating of national parameters since NITI Aayog (2018) ................................................. 71
List of Figures
Figure 1: Sector-specific SCC estimates from empirical studies vs. IAMs .......................................... 67
8
1. Introduction
This study aims to assess key parameters for appraisal of public sector investments undertaken
by the Government of India. The Government’s budget allocation towards diverse sectors of
the economy aims to maximise the present value of economic benefits, net of costs, that will
accrue to society on account of public sector investments.
1.1. Objectives
This study will extend previous analyses of parameters for project appraisal conducted by the
NITI Aayog (2018). We will estimate the following parameters used in cost-benefit analysis:
1. Appropriate Discount Rate to be used as a hurdle rate for public investments. It should
include recommendations on whether it is appropriate to use the same hurdle rate in
financial as well as economic analysis. It should also include recommendation on
whether to use different hurdle rates for projects with different lifespans over which the
returns are expected such as the large hydro power and irrigation projects, or for
projects which do not have very well-defined financial returns such as the
environmental and social sector projects.
2. Shadow exchange rate factor (SERF) - Ratio of economic price of foreign currency to
its market price.
3. Standard conversion factor (SCF) - Ratio of economic price value of all traded goods
in the economy at their border price equivalent values to their domestic market price
values.
4. Shadow wage rate factor (SWRF), for Unskilled labour, both in rural and urban areas.
5. Social cost of carbon (SCC) - net present value of climate change impacts over the next
100 years (or longer) of one additional tonne of carbon emitted.
We conduct a detailed literature review of the latest methodologies applied in estimating these
parameters and evaluate methods appropriate for estimation in the Indian context.
In estimating these parameters, we analyse several databases provided by the Ministry of
Statistics and Programme Implementation (MOSPI), Government of India, including inter alia,
9
the National Accounts Statistics, the NSSO’s Household Consumer Expenditure Survey,
several rounds of the Annual Survey of Industries and the Periodic Labour Force Survey. We
further draw on databases provided by the Reserve Bank of India (RBI), Ministry of Finance
and Ministry of Commerce and Industry, Government of India.
In the subsequent sections, we briefly describe each of the parameters for re-assessment in this
study and highlight their importance in cost-benefit analysis in the public sector.
1.2. Social Discount Rate
The social discount rate measures the rate at which individuals in society are willing to trade
present consumption against future consumption. The social discount rate is applied in project
appraisal in the public sector to evaluate the present value of net benefits that are expected to
accrue from a public sector investment over the lifespan of the project. The present value of
expected lifetime benefits from the project is compared to the current cost of incurring the
project. If the present value of expected benefits exceeds the current cost of the project, it is
economically feasible and socially beneficial to undertake the investment. In this context, the
social discount rate may be referred to simply as the “discount rate.”
The social discount rate plays a key role in cost benefit analysis (CBA) in the public sector, as
it measures the annual rate at which expected future benefits are to be discounted, to obtain
the present value of benefits from the project. The social discount rate differs from the rate of
return on investments undertaken in the private sector, as the former captures the full range of
economic costs and benefits that may accrue to all individuals in society, whereas the latter
reflects only the private rate of return to actors in the economy. When the government aims to
maximise social welfare (i.e. welfare of all individuals in society), it is the social discount rate
which ought to be applied in cost-benefit analysis in the public sector.
10
1.3.Accounting (Shadow) Prices
Measuring the costs of a public sector programme involves the financial costs and the economic
costs. While financial costs are measured at market prices (such as budget allocation towards
a project at current prices), economic costs also measure the opportunity costs of the project,
in terms of the loss in social welfare from an alternative investment. Hence, economic costs
measure the financial costs and the trade-off associated with funds being allocated to a specific
project vis-à-vis to other projects.
Cost-benefit analysis of public sector projects ought to be undertaken at the economic costs of
the factors of production, such as raw materials (produced domestically and imported), labour
costs and the cost of capital. Little and Mirrlees (1974) refer to the economic or “shadow”
prices for factors of production as “accounting prices.” These accounting prices reflect the
opportunity cost of the various factors of production, which may not necessarily be reflected
in the observed market prices (which also comprise indirect taxes on goods and services).
In this study, we compute the (i) shadow exchange rate factor, which is used to calculate the
shadow or “accounting” exchange rate, (ii) standard conversion factor, which is used to
measure tradables at accounting prices, and (iii) shadow wage rate factor for unskilled labour,
which reflects the opportunity cost of labour.
1.4. Social Cost of Carbon
The social cost of carbon (SCC) measures the monetary damage to society from an additional
ton of carbon dioxide (CO2) emission. Given high potency of greenhouse gases such as CO2,
the SCC is typically measured over long timescales of over 100 years. The expected damages
from increases in temperature associated with rising CO2 concentrations are then discounted
each year to obtain the net present value of damages from additional CO2 emissions. Rennert
et al. (2022) compute the SCC using simulations of potential damages due to higher CO2
concentrations over a 300-year timescale, applying a social discount rate of 2% per year. We
conduct a detailed literature review and provide a range of estimates for the social cost of
carbon for the Indian context.
11
1.5.Reassessment of parameters from NITI Aayog (2018) report
▪ A social discount rate of 8% was recommended for short-term projects (with a duration of
up to 50 years).
▪ For projects related to environment and infrastructure with a duration of more than 50 years,
a social discount rate of 6% was recommended.
▪ It was recommended that for projects with a duration of more than 100 years, the social
discount rate should be lower than 6%.
▪ The rate of return on capital was estimated at 10% using data from the Annual Survey of
Industries. This was the recommended internal rate of return to be used as a hurdle rate in
financial analysis.
▪ A social premium of 8% on foreign exchange was recommended.
2. Social Discount Rate: Methods and Results
The literature on cost-benefit analyses of public sector projects dates to the 1970s, where Little
and Mirrlees (1974) and Dasgupta, Marglin and Sen (1972) developed techniques for project
appraisal, specifically for developing countries. Harberger (1972) and Marglin (1967) also
provided frameworks for project appraisal for the case of India, in collaboration with the
erstwhile Planning Commission.
These frameworks discussed the key role of shadow prices, which are used to determine the
full economic costs and benefits of programmes, extending beyond the financial costs and
benefits. Dasgupta and Pearce (1972) and Drèze and Stern (1987) provided comprehensive
social welfare frameworks, within which to evaluate the optimal allocation of public sector
funds to various projects, considering their impacts on individual and social welfare.
12
2.1. Literature Review on Social Discount Rate
Policymakers face trade-offs between allocation of public funds across diverse projects.
Projects related to infrastructure and construction may yield a high rate of return, as they
generate immediate economic benefits (Little and Mirrlees 1974). On the other hand, projects
which expand access to education, healthcare and environmental services may only generate
benefits over a longer time horizon (Groom et al. 2022; Marglin 1967). Therefore,
policymakers create a portfolio of projects, with public sector investments spread across
sectors, offering different rates of return.
In evaluating these trade-offs, the social discount rate becomes highly pertinent (Dasgupta
2008). An excessively high social discount rate would underestimate the long-run social
benefits of public investments and lead to sub-optimal investment in public programmes. On
the other hand, a relatively low social discount rate would understate the benefits of
consumption in the immediate future and lead to inefficient public spending. Investments in
high-return projects could generate immediate revenues for the public sector which could be
invested in generating long-term societal gains. The level of the social discount rate is therefore
key to generating an optimal portfolio of public sector investments.
Accumulation of human capital via investments in healthcare and education would not only
generate welfare gains to individuals, but also confer benefits to society through positive
externalities (Aghion and Howitt 2008). An example is knowledge spill-overs through R&D
investments, which can stimulate economic growth and create productive jobs in the economy.
Non-optimal human capital may also result from consumption externalities, i.e. when one’s
consumption is affected by the consumption level of others in society (Bishnu 2013). The latest
advances in macroeconomic theory highlight the importance of technological progress in
bringing about economic growth, particularly in the context of developing countries, which
typically exhibit sub-optimal levels of investment (Aghion and Howitt 2008). Hence, research
and development activity requires government subsidies to ensure optimal levels of knowledge
creation and economic progress.
In contrast to the discount rate, the hurdle rate is applied in financial analysis as the minimum
rate of return on investments by private firms. As the OECD recommends, governments ought
to apply the social discount rate for project evaluation and for selection of projects (Coleman
2021). While governments may conduct financial analysis to evaluate certain investments by
13
the private sector, such as in public-private partnerships, governments are advised to apply the
social discount rate for project selection and evaluation (Perkins 1995).
The social discount rate can be computed based on two broad approaches. The first approach
is based on the Ramsey rule, which is derived by asking what is the optimal saving rate for
society each year, accounting for the future expected economic growth rate of consumption
and the degree of inequality aversion in society (NITI Aayog 2018; Ramsey 1928; Dasgupta
2008). This is explained further in Section 2.2.1.
The second approach to calculating the social discount rate is based on market rates of return
to capital. This can further be sub-divided into three methods. The first method measures the
social discount rate as the real rate of return on government securities which are relevant for
consumers’ savings decisions. This method is used by the United States’ Office of Management
and Budget (OMB) to calculate social discount rates for the U.S. economy (US OMB 2023).
The second method measures the real rate of return to capital in the economy, which is also
known as the social opportunity cost of capital (SOC) (Harberger 1972). The social opportunity
cost of capital can be measured as the real interest rate on loans. It can also be measured as the
productivity of capital, or the marginal addition to output from an incremental rise in the capital
stock in firms. The third method calculates the social discount rate as a weighted average of
the discount rates obtained in the above two methods – (i) the rate of return to government
deposits and (ii) the market rate of return to capital), and (iii) the cost of foreign borrowing by
the Government (Harberger 1972; ADB 2017; Zhuang et al. 2007).
In the previous assessment, the recommended real social discount rate of 8% was based on the
Ramsey rule (NITI Aayog 2018). Sensitivity checks using different methods had been
conducted to ensure robustness of the proposed discount rate. A recent assessment by
NABARD finds a relatively lower value of the social discount rate of 4.5% in real terms
(Dholakia et al. 2024).
In this study, we review the NITI Aayog’s (2018) assessment and recent studies conducted for
India, to identify the most appropriate methods that ought to be used in computing the social
discount rate by the Government of India. In so doing, we also review the academic and policy
literature for high-income and middle-income countries to draw on the latest guidance by
various country governments.
14
2.2. Methodologies to compute the Social Discount Rate
In this section, we present the two approaches to estimating the social discount rate (sections
2.2.1 and 2.2.2).
The first approach uses the Ramsey rule as the social discount rate for public sector projects.
This is the rate at which individuals trade present consumption against future consumption in
society. This is based on the rate of time preference, the degree of inequality aversion and the
expected future economic growth rate of consumption (Dasgupta 2008; Dholakia et al. 2024;
NITI Aayog 2018; Ramsey 1928). This approach requires an estimate for the inequality
aversion parameter, to compute the social discount rate.
The second approach measures the social discount rate as the real rate of return to capital. This
can be measured in three ways. First, the discount rate can be measured as the long-term real
rate of return on government securities, which reflects a safe rate of return on household
savings. The United States’ Office of Management and Budget (OMB)’s latest guidance
recommends using the real rate of return on government bonds as the social discount rate (US
OMB 2023). The United States has recently revised its social discount rate downward to 2%.
Second, the social discount rate can be measured as the social opportunity cost of capital
(SOC), which reflects the market rate of return to capital (Harberger 1972). This can be
measured as the minimum real lending rate by the Reserve Bank of India to commercial banks,
which reflects the cost of loans to capital owners and thus the rate of return to capital.
The real rate of return to capital can also be measured via a broad stock market index (e.g.
NIFTY 500) over a 30-year time horizon, to reflect the real rate of return on private investments
in the economy. Alternatively, the marginal product of capital measured using firm-level
survey data may best reflect the productivity of capital use in the economy (Burgess and Zerbe
2011). Third, the social discount rate can be measured as a weighted average of the (i) rate of
return on government securities, (ii) the market rate of return to capital (social opportunity cost
of capital) and (iii) the real interest rate on the government’s external borrowing (Harberger
1972; ADB 2017; Zhuang 2007).
15
In this study, we will apply each of the aforementioned methods to provide a range of values
for the social discount rate for short-term projects. In addition to computing the short-term
social discount rate, we will compute the social discount rate for longer-term projects (greater
than 30 years), following the extended Ramsey rule (Gollier 2024; Gollier and Hammitt 2014).
Further, we will adjust for uncertainty in future economic growth and compute the risk-adjusted
social discount rate, which has been adopted in policy guidance in several European countries,
including France, Denmark and Sweden (Groom et al. 2022).
2.2.1. Ramsey Social Discount Rate
The Ramsey rule has been extensively applied as a benchmark method in project appraisal in
several countries (Groom et al. 2022; Dasgupta 2008; Gollier and Hammitt 2014; NITI Aayog
2018). The previous report on project appraisal of the NITI Aayog also used the Ramsey rule
to calculate the social discount rate for cost-benefit analysis in public sector projects (NITI
Aayog 2018). We derive the Ramsey social discount rate from a social welfare maximisation
problem, following Dasgupta (2008).
Approximate Ramsey Rule
Consider a representative consumer who gets utility �(
�), from consuming an amount
� in
period �. The government that seeks to maximise the welfare of the representative consumer
may discount utility from consumption in future periods at rate, δ. This is known as the social
rate of time preference (Dasgupta 2008). The government then seeks to maximise the present
value of lifetime utility, �
0, as follows:
�
0=�(
0)+
�(�1)
(1+�)
+⋯+
�(�
)
(1+�)
+⋯=∑
∞
�=0
�(�)
(1+�)
(1)
From the government’s maximisation problem in equation (1), we can derive the approximate
simple Ramsey rule for the social discount rate.
5
This is stated as follows:
�
≈�+�
� (2)
5
The derivation in presented in Appendix A.
16
The social discount rate,
�
, depends on the (i) growth rate of consumption, �
�, (ii) the social
rate of time preference, � and (iii) the elasticity of the marginal utility of consumption, which
is assumed to be a constant . The elasticity of the marginal utility of consumption measures
the percentage increase in marginal utility from a 1 percent increase in consumption. The utility
function is assumed to be concave, with marginal utility diminishing in consumption, which
are standard assumptions in the economics literature (Mas-Colell et al. 1995). This means that
additional consumption is considered more valuable for individuals who are consuming very
little compared to those who are already consuming a lot. The parameter measures the
curvature of the utility function and the degree of inequality aversion of the government. A
high value for suggests a high degree of inequality aversion. In this case, the government will
discount future consumption at a high rate if it expects positive economic growth, because it
then expects consumption to be higher in the future, so that additional units of consumption in
the future add less to utility than they do for poorer present consumers. Drupp et al. (2018)
conduct a survey of 180 experts on discounting and find the most common reported value of η
= 1.
The social rate of time preference measures the rate at which future utility (not consumption),
is discounted relative to present utility. Since this report is concerned with social cost-benefit
analysis, it is the social rate of time preference that is relevant, not the rate of time preference
used by individuals. For example, older individuals may have a high rate of time preference,
but this is not relevant for social decision-making since they will be replaced by younger
individuals. The Intergovernmental Panel on Climate Change (IPCC) which made a
comprehensive and authoritative assessment of the literature, noted in its 2014 report that there
is “a broad consensus for a zero or near-zero pure rate of time preference” (IPCC 2014).
However, Drupp et al. (2018) reported a median value of the pure rate of time preference, δ =
0.5% in their survey of 180 economic experts on discounting. We thus apply this value to
compute the Ramsey social discount rate for short- and long-term projects.
6
We present
syntheses of estimates of the social discount rate based on the simple Ramsey rule in Table 1
based on Gollier and Hammitt (2014).
6
Some prominent economists (Dasgupta 2008 and Stern 2006) have suggested a value of δ very close to zero,
with Stern (2006) recommending δ = 0.1%. Stern (2006) justifies a positive, rather than zero, value based on the
assumption that there is a very small probability in each period that humanity will cease to exist. Another survey
of 14 philosophers with value judgements on climate policy yields a median value of δ of zero (Nesje et al. 2023).
17
To determine the per capita consumption growth rate, we use estimates of annual per capita
GDP growth rates at constant prices for the period 1993-94 to 2022-23, from the National
Accounts Statistics, Ministry of Statistics and Programme Implementation.
7
We compute the
average annual real GDP per capita growth rate over the last 30 years and apply �=4.7%, as
a minimum annual rate of per capita GDP growth that may be expected over the next 30 years.
Finally, we require an estimate of the elasticity of marginal utility of consumption. We follow
Groom and Maddison (2019) and test various methods to estimate .
Table 1: Synthesis of parameter estimates for social discount rate
Author Inequality aversion, η Growth rate, g Discount rate, ηg
Stern (1977) 2
Cline (1992) 1.5 1% 1.5%
IPCC (1995) 1.5–2 1.6–8% 2.4–16%
Arrow (1999) 2 2% 4%
HM Treasury (2003) 1 2% 2%
Lebègue (2005) 2 2% 4%
Arrow (2007) 2–3
Dasgupta (2007) 2–4
Stern (2007) 1 1.3% 1.3%
Weitzman (2007a) 2 2% 4%
Nordhaus (2008) 2 2% 4%
Pindyck (2013) 1–3
Source: Gollier and Hammitt (2014). Note: These estimates are based on the approximate
Ramsey rule with social rate of time preference, � = 0.
Estimating the elasticity of marginal utility of consumption (η)
Groom et al. (2022) and Gollier and Hammitt (2014) review parameter values for inequality
aversion (η) across countries based on the Ramsey rule. Most of the studies report values of the
inequality aversion parameter around 1, with a consensus around 1.5, based on different
methods of estimation across countries (Groom and Maddison 2019; Del Campo et al. 2024).
7
We apply the growth rate in GDP per capita rather than private consumption expenditure as a better metric for
individuals’ standard of living given lower annual fluctuations in GDP compared to consumption expenditure.
18
Groom and Maddison (2019) outline five different methods which may be used to compute the
elasticity of marginal utility of consumption (η). These are the (i) equal sacrifice approach, (ii)
Euler equation approach, (iii) risk-aversion approach, (iv) Frisch approach and the (v)
subjective well-being approach. Groom and Maddison (2019) test each of these methods and
apply them to the context of the United Kingdom.
We test four of these five methods and compare our results with those from contemporary
studies such as by NABARD (Dholakia et al. 2024) and NITI Aayog (2018). While the study
by NABARD applied the Frisch approach to estimate the discount rate, the previous study by
NITI Aayog applied the equal sacrifice and Euler equation approaches to estimating the social
discount rate. We omit the risk aversion approach due to lack of data in the Indian context to
apply that approach.
In this chapter, we outline and present results from the equal sacrifice approach, which yields
reliable estimates of the elasticity of marginal utility of consumption. The other approaches do
not yield reliable estimates. In particular, we do not recommend the use of the Frisch approach
in computing the social discount rate for public sector projects by the Government of India,
due to unreliable estimates.
We test these approaches using data for the Indian economy and consistent with the literature
(Groom and Maddison 2019), find negative values for in some cases. We also do not
recommend the subjective well-being approach to calculate as this method relies on
assumptions about the individual’s utility function and uses subjective information, rather than
objective data. Lastly, we do not apply the Euler equation approach for project evaluation as it
generates implausibly large estimates from our datasets. This is likely due to sparse data points
available for time series regressions which we use for estimation. We present results from these
other approaches in Appendix A.
Equal sacrifice approach
The equal sacrifice approach to estimating η assumes that the government distributes the
burden of income taxation among people so that each bears the same utility loss as a result of
the tax, given a system of progressive income taxation.
19
Consider a representative individual with income �
and utility from income, �(�
). Define the
tax function, �(�
), as the direct tax paid by individual on income, �
. The equal sacrifice
principle states that the difference in the individual’s utility levels between the pre-tax income,
�(�
), and the post-tax income, �(�
−�(�
)), is equal to a constant, � (Evans 2004). This
holds for all individuals in society where a progressive income tax system is in place. Formally,
the principle states:
�(�
)−�(�
−�(�
))=� ∀ (4)
Following Evans (2004), a formulation can be derived for the elasticity of marginal utility of
consumption, :
=
��(1−��)
��(1−��)
(5)
where �� is the average tax rate, defined as
�(
)
and ��� is the marginal tax rate, defined
as
��(
)
. Intuitively, reflects the degree of inequality aversion. A high average tax rate and
relatively low marginal tax rate, i.e. >1, suggests a high degree of inequality aversion, where
the marginal utility of consumption declines sharply with increasing consumption levels.
Data Sources
To estimate the elasticity of marginal utility of consumption, , we use annual data on “Direct
Tax Statistics” from the Income Tax Department (ITD), for the assessment years, 2012-13 to
2023-24. We use data on average incomes (“Average Salary Income (in lakh INR)”) for each
income category from the annual reports of the “Direct Tax Statistics.”
Next, we obtain information on marginal tax rates (and surcharges) for each tax slab, by year,
from the Annual Finance Bill Memoranda, Union Budgets, for the years 2011-12 to 2022-23.
The assessment years (AY) for the income tax returns follow the financial years (FY), such
that FY 2012-13 corresponds to the AY 2013-14. We apply the marginal tax schedules to the
average incomes reported in each income category to calculate the corresponding tax paid in
20
each category, by year.
8
Subsequently, we calculate average tax rates for each income category,
by year.
Results
In this section, we present results from the equal sacrifice approach. In Table 2, we present
average incomes, average taxes paid, average tax rates (ATR) and the marginal tax rates (MTR)
for all income categories for the assessment year 2023-24, as an illustration.
Based on data for average tax rates and marginal tax rates for each of 22 income categories and
11 years of data, we estimate the elasticity of marginal utility of consumption (). We estimate
a pooled Ordinary Least Squares (OLS) regression, with the constant term suppressed. We
apply frequency weights with the number of returns filed in each income category as weights
for each category.
In this case, a fixed effects estimator is not required since the income categories do not
represent a source of unobserved individual heterogeneity. Further, we cannot include time
controls in the regression as the entire variation in the data used to estimate arises from annual
changes in tax rates.
Table 2: Average incomes, income taxes, average tax rates and marginal tax rates by income
category, assessment year 2023-24
Income Category
Average Income
(INR)
Average tax paid
(INR)
ATR MTR
>0 and <=1,50,000 66,000 - 0.00 0.00
>1,50,000 and <= 2,00,000 1,76,000 - 0.00 0.00
>2,00,000 and <=2,50,000 2,33,000 - 0.00 0.00
>2,50,000 and <= 3,50,000 3,03,000 150 0.00 0.05
>3,50,000 and <= 4,00,000 3,75,000 3,750 0.01 0.05
8
Sample calculation: Consider an average income level of INR 12,05,000. Based on the marginal tax schedule
for the assessment year 2012-13, we apply a zero marginal tax rate for income up to INR 1,80,000, and then
marginal tax rates of 10% for income between INR 1,80,001 – 5,00,000, 20% for income between INR 5,00,001
– 8,00,000 and 30% on income between INR 8,00,001 – 12,05,000. Hence, taxes paid on an average income of
INR 12,05,000 = INR 2,13,500. Thus, the average tax rate is 18%, while the marginal tax rate (on incomes above
INR 8,00,000) is 30%.
21
>4,00,000 and <= 4,50,000 4,26,000 6,300 0.01 0.05
>4,50,000 and <= 5,00,000 4,81,000 9,050 0.02 0.05
>5,00,000 and <= 5,50,000 5,22,000 22,200 0.04 0.10
>5,50,000 and <= 9,50,000 6,99,000 24,900 0.04 0.10
>9,50,000 and <= 10,00,000 9,75,000 56,250 0.06 0.15
>10,00,000 and <=15,00,000 12,06,000 91,200 0.08 0.20
>15,00,000 and <= 20,00,000 17,17,000 2,15,100 0.13 0.30
>20,00,000 and <= 25,00,000 22,25,000 3,67,500 0.17 0.30
>25,00,000 and <= 50,00,000 33,95,000 7,18,500 0.21 0.30
>50,00,000 and <= 1,00,00,000 68,06,000 19,15,980 0.28 0.30
>1,00,00,000 and <=5,00,00,000 1,89,53,000 64,63,080 0.34 0.30
>5,00,00,000 and <=10,00,00,000 6,94,46,000 2,66,93,940 0.38 0.30
>10,00,00,000 and <=25,00,00,000 15,46,05,000 5,99,05,950 0.39 0.30
>25,00,00,000 and <=50,00,00,000 34,95,84,000 13,59,47,760 0.39 0.30
>50,00,00,000 and <=100,00,00,000 69,73,89,000 27,15,91,710 0.39 0.30
>100,00,00,000 and <=500,00,00,000 2,05,81,72,000 80,22,97,080 0.39 0.30
>500,00,00,000 23,81,85,11,000 9,28,88,29,290 0.39 0.30
Overall average 1,23,57,39,318 48,15,98,168 0.17 0.18
Source: Data on average income are from the Direct Tax Statistics, Income Tax Department, and data on
marginal tax rates (MTR) are from the Annual Finance Bill, Union Budget, Government of India. Average
taxes paid and average tax rates (ATR) are calculated for average incomes in each income category.
The regression results are displayed in Table 3, which show an estimate of = 1.8, for the
main specification. Column (2) of Table 3 presents a robustness check using only the last three
years of data on income tax assessments (2021-22 to 2023-24).
Table 3: Estimate of the elasticity of the marginal utility of consumption (η)
ln(1-MTR) (1) (2)
ln(1-ATR) 1.81*** 1.86***
(0.078) (0.158)
Observations 242 66
R
2
0.827 0.833
Robust standard errors in parentheses.
Constant term suppressed.
*
p < 0.10,
**
p < 0.05,
***
p < 0.01
22
Based on parameter values, �=0.5%, =1.8 and �=4.7%, the Ramsey rule yields a social
discount rate (in real terms) of 8.9%. In nearly all studies that apply social discount rates based
on the Ramsey rule (displayed in Table 1), the inequality aversion parameter () takes a value
greater than one. In its 2018 report to NITI Aayog, the Institute of Economic Growth (IEG)
reported an average value of =1.2, based on the equal sacrifice principle and the Euler
equation approach. A recent study by NABARD applies a value of =0.8, based on the Frisch
approach (Dholakia et al. 2024). However, our application of the Frisch approach yields a
negative value for , which is consistent with results from other studies (Groom and Maddison
2019). Thus, we recommend the equal sacrifice approach to estimate and the social discount
rate based on the Ramsey rule.
The expected growth rate of 4.7% is based on historical annual growth rates observed in India
over the last 30 years. Alternatively, we may compute the social discount rate using the
Government of India’s Viksit Bharat targets for 2047, applied to the simple Ramsey rule.
According to NITI Aayog (2024), the Indian economy may be reasonably expected to grow at
5.9% per year in real terms in a conservative scenario. A projected annual growth rate of 5.9%
yields a social discount rate (based on the simple Ramsey rule) of 11.1%. However, the report
mentions a caveat based on observations from other countries’ past growth rates:
“Sustained fast growth is extremely rare; Virmani (2012) showed that there were only a dozen
non-resource rich countries, which had a per capita GDP growth rate of 7% or higher for
more than a decade, of which half sustained it for less than two decades.”
Therefore, we consider the high, Viksit Bharat target growth rate as an upper bound estimate
for a 30-year period and consider a lower average annual growth rate of 4.7% for projects
which last more than 30 years.
Social Discount Rate with uncertainty adjustment (Extended Ramsey Rule)
Public sector investments would also be subject to uncertainty in the future rate of growth of
consumption. External shocks to the economy, for instance due to pandemics, wars or climate
crises, may unexpectedly reduce future GDP and per capita income. To account for uncertainty
in the future rate of economic growth, policymakers ought to consider a risk-adjusted social
23
discount rate for project appraisal. The latest economic research recommends adjusting the
discount rate for uncertainty and volatility in consumption growth, based on the extended
Ramsey rule (Groom et al. 2022; Gollier and Hammitt 2014; Gollier 2024). This is more
important for developing countries that have high and more uncertain growth rates than
developed countries. As uncertainty in the future level of consumption compounds over time,
projects with longer time spans may need to be discounted at lower rates, due to the uncertainty
in future economic growth. A lower social discount rate allows social planners to invest in risk
mitigation measures such as emission abatement technologies (which would reduce economic
damages from climate change) in a cost-effective manner, and thereby insure society against
future risk in consumption.
As an example, consider a pensioner who faces uncertainty in the expected future pension,
which depends on government revenue as a result of future economic growth. If the pensioner
were to receive a certain pension of say, INR 1,00,000 per month, they would experience higher
utility levels than in the uncertain case, where they may receive a pension of INR 50,000 with
probability 0.5 and a pension of INR 1,50,000 with probability 0.5. The second case represents
uncertain future economic growth and in turn, government expenditure. In the latter case, the
policymaker is inclined to apply a lower discount rate for precautionary savings in the event of
lower economic growth and consumption levels in the future, compared to the case of high
economic growth with certainty. This result relies on the convexity of the marginal utility of
consumption, a standard assumption in macroeconomics, which stems from the expected utility
theory (Caballero 1990; Rabin 2000).
The extended Ramsey rule, derived in Gollier (2024), is expressed as follows:
�
≈�+
�−0.5
2
�
�
2
Where
�
is the uncertainty-adjusted social discount rate, � is the social rate of time preference,
is the degree of inequality aversion,
�
is the expected rate of future economic growth
between �=0 and �, and
�
2
is the variance in the expected growth rate.
9
The extended Ramsey
rule assumes that consumption growth (or equivalently, economic growth), over the next t
9
This follows Equation 20 in Gollier (2024). Gollier takes to be zero and has another term accounting for
a possible correlation between future consumption and the returns to a particular public investment
project. Since we are interested in a single discount rate for public projects and it is unclear what the
correlation with future consumption, if any, will be for different classes of projects, we ignore this term.
24
years, follows a normal distribution, so that �
�=
1
�
���� (
�
�0
) ~�(
�,
�
2
). Further, � is the
lifetime duration of the public project, which allows the social planner to compute discount
rates for different project timespans. This results in a term structure for discount rates (Gollier
and Hammitt 2014). This is because for a given level of uncertainty
�
2
in the growth rate
between now and t, the uncertainty in consumption at time t relative to today (
�
0
), is increasing
in t due to compounding. The precautionary motive pushes us to save more, leading to a lower
discount rate. This is less of a problem for developed countries that have a lower variance in
their growth rates.
We compute the term structure for discount rates, accounting for uncertainty in the growth rate.
Existing studies typically use the historical time series of growth rates for a particular country
to estimate the variance in the growth rate (Gollier 2012). However, the observed variance in
a country’s economic growth over the past 30 years is likely to substantially understate the
potential variance in future economic growth. Instead, we draw on other countries’ experiences
to predict potential variance in India’s expected economic growth over the next 30 years.
10
We draw on country-level data on annual real GDP per capita levels and growth rates for 266
countries from the World Bank’s World Development Indicators (WDI) database for the 1960-
2023 period. We construct a comparison group of countries for India based on similarity of per
capita income levels and past economic growth rates. In 2023, India’s per capita GDP stood at
US$ 2,239 (in US$ 2015 constant prices). Further, India exhibited an average annual growth
rate of real GDP per capita of 4.7% between 1993-2023.
We construct the comparison group of countries based on two measures. First, we restrict the
sample to countries that exhibited real GDP per capita levels (in US$ 2015 constant prices) in
the range of India’s GDP per capita +/- 50%, i.e. between US$ 1,120 and US$ 3,359, between
the 1970-1993 period. This large band of per capita incomes ensures a sizeable number of
countries which exhibited similar per capita incomes in the past to India’s present income.
Second, we restrict the sample to countries which also exhibited similar growth rates to India’s
average growth rate +/- 50%, over the preceding 30 years. Specifically, we consider countries
which exhibited average annual growth rates between 2.35% and 7.05% in the preceding time
10
The necessary adjustment for uncertainty in computing the discount rate is smaller for developed countries that
have a lower variance in their growth rates.
25
period, i.e. until 1993. Hence, we observe a sample of 20 countries which exhibited similar per
capita incomes as India’s current income, prior to 1993 and similar economic growth rates as
India’s recent average growth rate, prior to 1993. The list of countries is presented in Table 4.
11
Table 4: List of countries for computing variance in the growth rate
S. No. Country
Initial GDP per capita
(2015 US$, Constant
Prices)
Past GDP per capita
growth rate, % (till
1993)
Subsequent GDP
per capita growth
rate, %
1 Belize 3,233 2.7 1.9
2 China 1,239 5.0 7.6
3 Dominica 3,288 2.9 2.9
4 Dominican Republic 3,179 2.5 3.4
5 Ecuador 3,337 2.4 1.0
6 Egypt, Arab Rep. 2,040 3.0 2.4
7 Eswatini 2,110 3.5 2.3
8 Grenada 3,243 5.7 3.1
9 Indonesia 1,707 3.2 3.0
10 Kyrgyz Republic 1,203 4.1 -0.2
11 Malaysia 3,292 4.5 3.1
12 Maldives 3,275 5.1 3.5
13 Malta 3,212 2.4 5.5
14 Mauritius 3,256 3.1 3.8
15 Morocco 1,668 2.6 2.3
16 Paraguay 3,274 4.1 1.2
17 Sri Lanka 1,488 2.6 3.3
18 Syrian Arab Republic 1,122 2.7 -1.1
19 Thailand 3,167 5.1 2.3
20 Turkey 3,274 2.7 2.3
Source: World Development Indicators, World Bank Group.
Note: Initial GDP per capita (constant 2015 US$) refers to the 1970-1993 period.
11
We select this range of GDP as the minimum range of GDP required to ensure a sufficient sample size of
comparison countries to predict the potential variance in the future economic growth rate for India. We also
conducted this analysis for the interquartile range of GDP. However, that resulted in a very limited set of
comparison countries, which were insufficient to predict the variance in future economic growth for India.
26
Next, we compute the economic growth rates for each of these 20 countries over the subsequent
30-year period from 1993-2023 and record the observed variance in growth rates across
countries. We use this observed variance in growth rates as a reasonable prediction for potential
variance in India’s future economic growth. We observe a range of expected future growth
rates between -1.1% in Syria to 7.6% in China. The resulting term structure of discount rates
is presented in Table 5.
The simple Ramsey social discount rate is 11.1% for an expected economic growth rate of
5.9% over the next 30 years based on the Viksit Bharat 2047 growth projection (NITI Aayog
2024). When this growth rate is adjusted for future uncertainty, the social discount rate is
revised downward to 9.4%. Similarly, for an expected growth rate of 4.7% based on past
performance, the social discount rate for a 30-year time horizon is estimated at 8.9%, based on
the Ramsey rule. Adjusting for future uncertainty reduces this discount rate to 7.3%.
Table 5: Term structure of discount rates, with uncertainty adjustment in growth rates
Social rate
of time
preference
Inequality
aversion
Mean
growth
rate
(India)
Project
Term
Variance in
30-year
growth rates
of other
countries
Simple
Ramsey
discount rate
(%)
Uncertainty
term (%)
Extended
Ramsey
discount
rate (%)
(1) (2) (3) (4) (5) (6) (7) (8)
δ η
� t
�
2
δ+ η
� 0.5
2
t
�
2
�
0.5 1.8 0.059
*
30 0.000344 11.1 1.7 9.4
0.5 1.8 0.047 30 0.000344 8.9 1.7 7.3
0.5 1.8 0.047 50 0.000344 8.9 2.8 6.2
0.5 1.8 0.047 75 0.000344 8.9 4.2 4.8
0.5 1.8 0.047 100 0.000344 8.9 5.6 3.4
Note:
*
This refers to the conservative growth rate scenario over the next 30 years, according to NITI Aayog (2024).
Based on an expected annual economic growth rate of 4.7% and adjusting for future uncertainty
yields the following term structure of social discount rates (corresponding project terms): 7.3%
(< 30 years), 6.2% (30-50 years), 4.8% (50-75 years) and 3.4% (75-100 years). Given potential
uncertainty in future economic growth, we recommend applying the extended Ramsey rule to
compute social discount rates (adjusted for uncertainty), for varying time horizons.
27
2.2.2. Market Rates of Return to Capital
a) Real Return on Government Securities
The real rate of return on government bonds reflects the risk-free rate at which individuals
might trade present consumption against future consumption (e.g. see US OMB 2023). We
calculate the real rate of return on central government securities, using data on nominal interest
rates and the Consumer Price Index (CPI)-based inflation rates, which are available at annual
frequency, published by the Reserve Bank of India, for the period 1993-94 to 2022-2023.
12
Government securities provide households a safe, risk-free option to invest their savings over
the long term. Hence, the rate of return on these securities provides households a risk-free
interest rate to use in intertemporal consumption and savings decisions.
We find an average annual, pre-tax real rate of return of 3.46% on central government
securities using annual data for the 1993-94 to 2022-23 period. We take this to be a lower
bound value for the social discount rate.
b) Social Opportunity Cost of Capital
The second approach to calculating the short-run discount rate (for projects with lifetimes of
30 years or less) is to measure the social opportunity cost of capital in the economy. The
productivity of capital deployed in production yields the rate of return to capital, which is a
measure of its opportunity cost (or its next best use). The social discount rate would equal the
social opportunity cost of capital (SOC) in an economy without financial market imperfections
or externalities. The social opportunity cost of capital should thus be reflected in the market
interest rate, as the market interest rate equals the marginal product of capital in an economy
at equilibrium. Thus, we estimate the marginal product of capital deployed in manufacturing
sector production in private firms.
Studies by Poterba (1998) and Jenkins et al. (2011) compute the rate of return to capital using
country-level national accounts. However, this method may lead to significant overestimation
of the marginal return to capital and is likely to generate an upward bias in the calculated
12
In addition to central government securities, we also analysed data on real interest rates for fixed deposits with
maturities over 5 years and the real rate of return on gold, for the 1993-2023 period. We selected central
government securities as these yielded the highest rates of return compared to the other savings instruments.
28
discount rate, as discussed in Poterba (1998).
13
Here, the rate of return to capital, measured as
the ratio of income from capital to the stock of capital for a given year, can be estimated using
data from the National Accounts Statistics on an annual basis, following the approach outlined
in Jenkins et al. (2011). We find the average real rate of return to capital to be 10.6% over the
2012-13 to 2022-23 period. The detailed calculations for this method are presented in Appendix
A.
Next, we outline a robust econometric method to estimate the marginal return to capital, using
annual firm-level data from the Government of India’s Annual Survey of Industries. The
drawback of this approach, however, is that it only applies to the formal, organised
manufacturing sector and omits the informal sector from analysis, which accounts for a sizeable
share of the economy.
Estimating the marginal product of capital
We estimate a production function at the firm-level, following Levinsohn and Petrin (2003).
Consider a firm-level production function, �=�(�,�,�), where firms produce output �,
using capital (�), labour (�) and other raw materials (�) as inputs in production. We estimate
the marginal product of capital, or regression coefficient, � in the regression equation below.
�
�=�
+�
�+� �
�+ �
�+��
�+�
�
where and � specify the firm and year, respectively. The regression includes firm-level fixed
effects �
and year fixed effects �
�
.
Estimating � requires an external source of variation in the capital input that is uncorrelated
with the firm’s unobserved productivity. Since changes in the capital stock are likely to be
correlated with firms’ unobserved productivity levels, Levinsohn and Petrin (2003)
recommend using alternative input purchases, such as raw materials or fuels like electricity as
a proxy variable. The proxy variable is used as an instrumental variable for changes in the
capital stock. In this analysis, we use electricity input costs as the proxy variable given that we
13
Economic theory suggests the average rate of return (calculated as the ratio of income from capital to the capital
stock) overestimates the rate of return to capital on the marginal project (Poterba 1998). The marginal rate of
return to capital accurately measures the expected rate of return to investment in an additional project
commissioned by the government.
29
observe expenditure on electricity incurred by each firm in the survey. This relies on the
assumption that electricity usage, which complements capital use, is likely to be uncorrelated
with unobserved firm-level technology shocks or other productivity changes which may be
linked to capital usage.
Electricity use also varies at a higher frequency than changes in the firm’s capital stock. In
other words, we expect changes in electricity use to respond more flexibly than changes in the
capital stock of the firm. We find this assumption to be validated in the empirical literature
(Allcott et al. 2016). Further, we use data on electricity expenditures rather than electricity
consumed to be consistent with the Levinsohn-Petrin approach, which uses data on inputs
expressed in value terms, rather than quantities. Also, electricity prices charged to firms have
remained relatively stable across firms as the firm-level reported prices are highly correlated
with the state-level tariffs charged to firms by the distribution companies. Hence, we do not
expect large fluctuations in electricity prices over the timeframe observed.
Data Sources
We draw on firm-level panel data from the Annual Survey of Industries, conducted by the
Ministry of Statistics and Programme Implementation (MOSPI), for the period 2009-10 to
2019-20. The ASI is a nationally representative survey of registered firms. The survey data
contain detailed information on input use and output production. We compute real gross value
added (GVA), following the ASI tabulation programme and deflating GVA by the Wholesale
Price Index (WPI). Next, we compute the real capital stock at the firm-level, which comprises
both fixed capital and working capital. Then, we calculate employment at the firm as the
“average persons worked,” provided in the ASI survey. We also compute material and fuel
costs (excluding electricity), in real terms, as other inputs in production. The cost of electricity
purchases is used as the proxy variable. We exclude Public Sector Enterprises (PSEs) from this
analysis.
Results
The results are displayed in Table 6. The estimated elasticity of output with respect to capital
is 0.22. We compute the median ratio of output to capital,
, across the distribution of firms in
30
our sample, which equals 0.46. The derived marginal product of capital, or the real annual rate
of return to capital is 10%.
14
We also find similar rates of return to capital if we utilise data on
“number of man-days worked” at the firm.
Table 6: Estimating the Marginal Product of Capital
ln (Real GVA) (1)
ln (Capital) 0.217
***
(0.007)
ln (Labour) 0.625
***
(0.004)
ln (Materials) 0.0725
***
(0.002)
Observations 148,394
Wald test (Chi-sq.) 163.65
Median Ratio: Real GVA/Real Capital 0.46
Real return to capital 10.0%
Standard errors in parentheses.
*
p < 0.05,
**
p < 0.01,
***
p < 0.001
The third method to compute the rate of return to capital is based on a broad stock market
index, which reflects the return on private investments. We calculate the annual real rate of
return on the NIFTY 500 Total Returns Index, which comprises price appreciation and
dividend payments, for the 1999-2025 period.
15
We find an annual, pre-tax real rate of return
of 11% over this period.
16
The NIFTY 500 index comprises the top 500 publicly-listed companies on the National Stock
Exchange, based on market capitalisation. Thus, it includes approximately 250 companies with
relatively low market capitalisation, 150 companies with medium market capitalisation and
100 companies with large market capitalisation. Thus, the real rate of return would not need to
14
This can be derived as follows: ln Y ln K =β. The marginal product of capital, ∂Y∂K=βYK .
15
Data for the NIFTY 500 Total Returns Index are only available online from 1996.
16
This estimate can be contrasted with the real interest rate for loans set by the Reserve Bank of India for
Scheduled Commercial Banks. Analysing the minimum lending rate by commercial banks for the 1993-2023
period, using data published by the RBI, we find an average minimum real lending rate of 4.3%, which may be
considered a minimum safe rate of return on investment in the long run.
31
be adjusted further for size premiums, which often accrue to companies with small market
capitalisation. While the literature on corporate finance shows that private equity firms tend to
observe higher rates of return on investment than publicly-listed firms on the stock market,
empirical research in the context of India shows that these higher rates of return to private
equity are on account of a selection effect, whereby investments are targeted towards more
productive firms, but unproductive firms do not gain in productivity due to private investments
(Smith 2015; Officer 2007).
Therefore, the higher rate of return accruing to the private equity firms should not be applied
as the social opportunity cost of capital for public project evaluation. The rate of return to
investment observed in the stock market can be considered an appropriate real rate of return to
private investment in the Indian economy. This is particularly so for the Total Returns Index
which accounts for both price appreciation of the stock and dividend payments made to
investors, which have an outsized impact on the total return on the stock market (Golez and
Koudijs 2018). The stock market return represents the opportunity cost of capital used in the
public sector under the assumption that this capital would otherwise have been invested in a
listed private sector firm.
The first method to estimating the rate of return to capital, using the national accounts,
measures an average return but captures the whole economy, and yields 10.6% for the 2012-
13 to 2022-23 period. The second method measures the marginal rate of return and yields 10%,
but only captures the formal sector in the economy. The third method measures the rate of
return on the stock market and yields 11%, but only measures the return in privately listed
companies. In what follows, we apply a rate of return to capital of 10.6% derived from the
national accounts.
The estimated figures broadly represent the return on domestic capital in the economy.
However, they may not strictly correspond to the return on private capital, which is likely to
be higher, as the estimates are based on aggregate national accounts data that include both
private and government sectors. In principle, one approach would be to adjust the estimates by
deducting components that relate to the government sector in order to approximate the return
on private capital. However, such adjustments are constrained by limitations in the available
data, as a clear and precise segregation of the relevant components is not always possible.
Accordingly, the estimates should be interpreted as providing an indicative measure of the
32
overall return to capital in the economy, rather than a precise estimate of the return to private
capital alone.
c) Weighted Average Approach
The weighted average approach, proposed by Harberger (1972) and widely adopted in cost-
benefit analysis (Burgess and Zerbe 2011; ADB 2017), is premised on the assumption that
additional government borrowing undertaken to finance public sector projects is likely to
displace, in part, household consumption, private investment, and foreign borrowing. As
government borrowing raises the demand for funds in the market, the interest rate rises in the
short-run, which leads to reductions in household consumption, private investment, and the
government’s external borrowing. The social discount rate based on the weighted average
approach can be expressed as follows (Harberger 1972; Zhuang et al. 2007):
=��
�+�
+(1−�−�)
�
where �
� is the net of tax real interest rate on government securities,
is the social opportunity
cost of capital and
� is the real interest rate on the government’s external borrowing. The
weights, � and � measure the marginal displacement of private consumption and private
investment due to an increase in the government’s borrowing to finance public sector
expenditure.
Burgess and Zerbe (2011) derive a tractable formula to estimate these weights and compute the
social discount rate, as follows:
=
−(
�
�
)(
�
)�
�+((
1
��
)−1)
�
−(
�
�
)(
�
)+
1
��
where (
�
) is the ratio of domestic savings to private investment in the economy and �� is the
savings retention coefficient, which measures the association between the domestic savings
rate and the investment rate (i.e. investment as a proportion of GDP associated with savings as
33
a proportion of GDP), following Feldstein and Horioka (1980).
17
The parameters, � and �,
respectively measure the sensitivity of savings to the interest rate and the sensitivity of
investment to the interest rate. In Appendix A, we decompose the above formula to display the
weights attached to each of the three parameters,
, �
� and
�, expressed in terms of the
remaining parameters.
Results
We estimated the real rate of return on central government securities as 3.46% (section 2.2.2a).
To calculate the net of tax rate of return, we use data on marginal tax rates for different income
slabs for the latest assessment year (2023-24) and compute a weighted average marginal tax
rate. The marginal tax rate in each slab is weighted by the number of ITR filers in the
corresponding slab. We obtain a weighted average marginal tax rate of 10%. Hence, the net of
tax rate of return on government securities, �
�, is 3.1%. We obtained an estimate for the
marginal product of capital,
, of 10.6%, as the average real return from the National
Accounts Statistics (Section 2.2.2b).
Next, we analyse data on the Government of India’s external borrowing, drawing on annual
status reports of “India’s External Debt Position,” published by the Ministry of Finance. We
obtain an average real interest rate,
�, over the 2016-17 to 2023-24 period of 4.9%.
18
Further,
we compute the savings-investment ratio from the National Accounts Statistics for the latest
year available, 2023-24, (
�
)=0.95. We estimate the savings retention coefficient as the
correlation coefficient between the savings-GDP ratio, (
�
�
) and the investment-GDP ratio, (
�
),
and find ��=0.95.
Finally, we estimate the interest elasticities of investment and savings, � and �, respectively.
We estimate � using panel data on investments by firms from the Annual Survey of Industries,
for the period, 2011-12 to 2019-20. We use data on minimum real lending rates published by
the RBI (adjusted by CPI-inflation rates) to estimate �=−0.3, with a 95% confidence interval
17
The savings retention coefficient measures the proportion of incremental savings invested domestically relative
to the proportion of incremental savings invested abroad.
18
To calculate the real interest rate from the nominal interest rate reported in the annual status reports, we compute
the annual percentage change in the reciprocal of the real effective exchange rate (REER). Then, the real interest
rate is the nominal interest rate less the percentage change in REER.
34
of (-0.48, -0.12).
19
Lastly, we estimate � as the product of the reciprocal of the elasticity of
marginal utility (
1
) and the consumption-wealth ratio (
�
), as explained in Burgess and Zerbe
(2011). We estimated =1.8 (section 2.2.1) and obtain the consumption-wealth ratio as
(
�
)=0.1, from Bharti et al. (2024) and the World Inequality Database. Hence, we obtain an
interest elasticity of savings, �=0.06.
In Table 7, we present calculations of the social discount rate, with sensitivity checks. The
social discount rate varies from 8.1% to 9.6%, with a mean estimate of 9.23%. The range of
discount rates is based on the 95% confidence interval for the interest elasticity of investment,
which provides a range of estimates for n.
Table 7: Social Discount Rate – Weighted Average Approach
Rate of
return
on
capital
Rate of
return to
household
savings
Interest
rate on
external
borrowing
Savings-
Investment
Ratio
Savings
Retention
Coefficient
Interest
elasticity
of
savings
Interest
elasticity
of
investment
Social
Discount
Rate (%)
Remarks
on Interest
elasticity
of
investment
�
�
� (
�
) �� � �
10.6 3.1 4.9 0.95 0.95 0.06 -0.30 9.23
Mean
estimate
10. 6 3.1 4.9 0.95 0.95 0.06 -0.48 9.59
Upper
bound
10. 6 3.1 4.9 0.95 0.95 0.06 -0.12 8.12
Lower
bound
Note: The lower and upper bound values are based on the 95% confidence interval of the interest elasticity of
investment.
19
We estimate the following regression equation:
ln
�=+�+�
�+�
�
where
� is investment by firm i in year t and �
� is the real interest rate on loans by commercial banks. The panel
regression includes firm and year fixed effects, i and t.
35
2.2.3. Comparison of Social Discount Rates
We compare the estimates of the short-run social discount rate obtained from these approaches
in Table 8. These discount rates pertain to projects with lifetimes of less than 30 years. Our
estimates of the short-run social discount rate range from 6.8% to 11% with mean estimates of
6.8% and 9.23% from the Ramsey rule and weighted average methods, respectively.
The long-term social discount rates, with varying project maturities and accounting for
potential uncertainty in future consumption growth, are presented in Table 5 in preceding
section 2.2.1. To compare our estimates for India with those for other developed and
developing countries, we present estimates of social discount rates from several countries
surveyed by Groom et al. (2022) in Table 9. These studies synthesize guidance on discounting
for project appraisal across national governments in different countries and across empirical
studies.
Table 8: Comparison of Social Discount Rates across approaches
Approach Method δ
Expectation of g Variance of g SDR
Ramsey
Rule
Equal sacrifice
principle
0.5 1.8 0.047 0.000344 7.3
SOC
Real rate of return to
capital
- 10.6
Weighted
Average
Lower bound - 8.12
Mean estimate - 9.23
Upper bound - 9.59
The social opportunity cost of capital (SOC) and weighted average (WA) methods are being
adopted around the world. Social discount rates based on these approaches are typically
upwards of 8% in middle-income countries such as Mexico, China, and Colombia, which may
provide a reasonable benchmark for India in terms of future public investment and expected
future economic growth. Discount rates based on the Ramsey approach are typically lower in
the range of 1-5% in real terms for European countries. Given high rates of economic growth
observed in developing countries, the Ramsey approach yields higher discount rates of 8% and
above in the case of China and India (ADB 2017).
36
Table 9: Synthesis of parameter estimates for SDR across countries for various methods
Country/
Institution
Year Social Discount Rate
SOC/STP/Weighted
Average (WA)
Social rate of time
preference
Inequality
Aversion
Uncertainty Nonmarket effects
ADB 2017 9% STP 1% 1.5
6% SDR for environmental or
social benefits
Australia 2020 7% SOC
Sensitivity with 3% and 10%,
DDR to 3.7% (> 300 years),
lower risk premium for
nonmarket benefits
4% SDR for nonmarket
benefits
Brazil
a
2020 8.5% WA
Canada 2020 8% SOC
3% SDR may be used for
health and environmental
goods
Chile 2021 6% SOC
China 2021
8% for short- and
medium-term projects;
less than 8% for long-
term projects
WA
Colombia
a
2019 9% WA
Denmark 2021 3.5% Both STP & SOC
0.1% to
3%
1.25
1.5% systematic risk premium,
falling to 0% (>70 years).
DDR to 1.5%
(>70 years)
European Union 2021 3% STP DDR for >50 years
France 2017 4.5% STP
Risk-free SDR from 2.5% to
1.5% and risk premium from
2% to 3% (> 2070)
RPA for environmental goods
Germany 2018 1% STP 0% 1
37
IDB 2021 12% SOC
Ireland 2019 4% STP 1% 1–1.5
DDR to 1.5%
(>275 years)
Japan 2015 4% SOC
Mexico
a
2014 10% WA
The
Netherlands
2020 2.25% SOC
1% RPA for environmental
goods
New Zealand 2020 5% SOC
Norway 2021 4% SOC
DDR from 4% to 2%
(>75 years); 1.5% risk premium
OECD Countries 2018
Average rate of 4.78%
for energy and 4.64% for
transport
STP
Peru
a
2021 8% WA
DDR from 8% to 1%
(>200 years)
The Philippines 2020 10% SOC
Poland 2021 5% STP
Sweden 2020 3.5% STP 0.5% 1 1% catastrophic risk premium
United
Kingdom
2020
3.5% for 0-30 years, 3%
for 31–75 years, and
2.5% for 76 years or
more
STP 1
1% catastrophic risk premium;
DDR to 2.14% (>75 years)
SDR for health (1.5% for 0-
30 years; 1.29% for 31-75
years and 1.07% for 76 years
or more); 2% RPA for air
pollution damages
USA 2023 2% Both STP & SOC
Source: Groom et al. (2022) and from the authors’ collection based on governmental guidelines. Abbreviations: ADB, Asian Development Bank; DDR, declining discount rate;
IDB, Inter-American Development Bank; RPA, relative price adjustment; SCC, social cost of carbon; SDR, social discount rate; SOC, social opportunity cost of capital; STP,
social time preference (or Ramsey approach).
38
3. Shadow Prices
The frameworks developed by Little and Mirrlees (1974) and Dasgupta, Marglin and Sen
(1972) for project appraisal highlight the role of “accounting” or “shadow” prices for labour
and tradeable commodities, in estimating the social costs of public sector projects. We follow
the approach outlined by Little and Mirrlees (1974) to estimate shadow or “accounting” prices
used in cost-benefit analysis. Here, we estimate the (i) standard conversion factor (SCF), (ii)
shadow exchange rate factor (SERF) and (iii) shadow wage rate factor (SWRF). These
conversion factors are applied to evaluate financial costs and benefits in economic terms for
public sector projects.
3.1. Literature Review on Shadow Prices
The shadow exchange rate measures the economic value of foreign currency, whereas the
market exchange rate measures the financial value of foreign currency. To compute the shadow
exchange rate, we require the standard conversion factor. The standard conversion factor is a
measure of the economic value of traded commodities relative to their market or financial
value. While market prices for tradables would include import duties and other indirect taxes,
the “accounting” prices for tradables reflect the border prices of imports, exclusive of import
duties and taxes. The shadow exchange rate is obtained as the product of the standard
conversion factor and the market exchange rate. It is measured as the ratio of the value of
tradable goods and services in domestic prices relative to world prices (in foreign currency)
(ADB 2017).
The standard conversion factor is typically less than one, which suggests that tradables have
higher social value than what is reflected in the observed market prices. The standard
conversion factor helps adjust costs of imports at market prices to economic prices (or border
prices, excluding import tariffs), while the shadow exchange rate adjusts the official exchange
rate to the economic price of foreign currency, accounting for border duties (ADB 2017; Little
and Mirrlees 1974).
The shadow wage for unskilled labour is relevant when evaluating the economic costs of labour
in public sector projects and the prospect of employment creation from public investments.
Shadow wage rates for unskilled labour, typically available in large numbers and drawn from
39
agriculture, may be below market wage rates if there is involuntary unemployment (Little and
Mirrlees 1974). Several studies compute the shadow wage rate as the economic opportunity
cost of labour (Jenkins et al. 2011; Dinwiddy and Teal 1994; Curry and Weiss 2023). Since
involuntary unemployment among unskilled labour is less prevalent in the Indian context
(Dhingra and Kondirolli 2022), the market wage rate is likely to best represent the opportunity
cost of workers’ time (Jenkins et al. 2011), particularly for unskilled labour.
Thus, from the policymaker’s perspective, for government projects, the shadow wage rate
ought to reflect the divergence between the government’s stipulated minimum wage rate and
the prevailing market wage rate for agricultural workers in rural areas and the market wage rate
for informal sector workers in urban areas (Gupta 1986).
The Government of India stipulates minimum wage rates for unskilled labour for some sectors
on a bi-annual basis. The observed market wage rates for unskilled labour likely differ from
the stipulated minimum wages. If the market wage rates exceed the minimum wage rates
stipulated by the Central Government, the shadow wage rate factor may be taken as ‘1’ for
unskilled workers. In this case, minimum wage costs may be used to evaluate the costs and
benefits for public sector projects.
3.2. Standard Conversion Factor: Methodology and Results
First, we compute the standard conversion factor (SCF), which measures the accounting price
or factor costs of tradables relative to their market price. The market costs of imported inputs
largely comprise import duties. Since import duties differ across commodities, we compute a
weighted average standard conversion factor, following the Asian Development Bank
(Lagman-Martin 2004):
��=
������
��+�������
���
������
��+��� ����� ����+�������
���+��� ������ ����
where import values are recorded at border prices (cost, insurance, and freight), export values
are recorded at border prices (free on board) and net import and net export taxes are included.
Since net export taxes and subsidies on exports are zero (due to the Government of India’s
RODTEP scheme), we measure exports at market prices. To compute import values at border
40
prices, we deduct the import tariff for each tradable good and service from its market price to
generate its accounting price.
20
We draw on trade data for 2023-24 from the Ministry of Commerce and Industry, Government
of India, and product-level data on import tariffs for 2023 from the World Trade Organisation
(WTO). Data on quantities and purchase values at the Harmonised System (HS) 8-digit product
level are drawn from the Export-Import Data Bank (Ministry of Commerce and Industry),
while corresponding data on 8-digit level import tariffs (as percentage of the product price) are
from the WTO.
We merge the two databases at the 8-digit product level to compute the standard conversion
factor. Then, we generate average standard conversion factors at the HS 2-digit product level
and an overall SCF across all products. The results are presented in Table 10.
We observe an average standard conversion factor of 0.92, with a range from 0.24 to 1.00
across products. The standard conversion factor does not apply to non-tradable sectors and
commodities such as electricity, local construction, local transportation services etc, since the
domestic market prices reflect the economic costs of these inputs. Since import tariffs will not
apply to non-tradable goods and services, the market prices of these commodities reflect their
economic costs. Since their “shadow prices” equal their market prices, the implicit conversion
factor for non-tradable commodities is 1.
Table 10: Standard Conversion Factors, by HS 2-Digit Products
HS Code (2-
digit)
Industry description SCF
01 Live animals 0.82
02 Meat and edible meat offal 1.00
03 Fish and crustaceans, molluscs and other aquatic invertebrates 0.99
04
Dairy produce; birds' eggs; natural honey; edible products of animal origin,
not elsewhere specified or included
0.97
05 Products of animal origin, not elsewhere specified or included 0.96
20
Alternatively, SCF=Imports1-τ+ExportsImports+Exports where import and export values are recorded at
market prices and is the product-level import tariff.
41
06
Live trees and other plants; bulbs, roots and the like; cut flowers and
ornamental foliage
0.92
07 Edible vegetables and certain roots and tubers 0.79
08 Edible fruit and nuts; peel of citrus fruit or melons 0.73
09 Coffee, tea, mate and spices 0.90
10 Cereals 0.99
11 Products of the milling industry; malt; starches; inulin; wheat gluten 0.96
12
Oil seeds and oleaginous fruits; miscellaneous grains, seeds and fruit;
industrial or medicinal plants; straw and fodder
0.87
13 Lac; gums, resins and other vegetable saps and extracts 0.92
14
Vegetable plaiting materials; vegetable products not elsewhere specified or
included
0.79
15
Animal or vegetable fats and oils and their cleavage products; prepared
edible fats; animal or vegetable waxes
0.47
16
Preparations of meat, of fish or of crustaceans, molluscs or other aquatic
invertebrates
0.99
17 Sugars and sugar confectionery 0.80
18 Cocoa and cocoa preparations 0.78
19 Preparations of cereals, flour, starch or milk; pastrycooks' products 0.94
20 Preparations of vegetables, fruit, nuts or other parts of plants 0.96
21 Miscellaneous edible preparations 0.95
22 Beverages, spirits and vinegar 0.24
23 Residues and waste from the food industries; prepared animal fodder 0.94
24 Tobacco and manufactured tobacco substitutes 0.98
25 Salt; sulphur; earths and stone; plastering materials, lime and cement 0.93
26 Ores, slag and ash 0.97
27
Mineral fuels, mineral oils and products of their distillation; bituminous
substances; mineral waxes
0.93
28
Inorganic chemicals; organic or inorganic compounds of precious metals, of
rare- earth metals, of radioactive elements or of isotopes
0.93
29 Organic chemicals 0.94
30 Pharmaceutical products 0.99
31 Fertilisers 0.92
32
Tanning or dyeing extracts; tannins and their derivatives; dyes, pigments and
other colouring matter; paints and varnishes; putty and other mastics; inks
0.95
33 Essential oils and resinoids; perfumery, cosmetic or toilet preparations 0.89
42
34
Soap, organic surface-active agents, washing preparations, lubricating
preparations, artificial waxes, prepared waxes, polishing or scouring
preparations, candles and similar articles, modelling pastes, "dental waxes"
and dental preparations with a basis of plaster
0.93
35 Albuminoidal substances; modified starches; glues; enzymes 0.82
36
Explosives; pyrotechnic products; matches; pyrophoric alloys; certain
combustible preparations
0.99
37 Photographic or cinematographic goods 0.91
38 Miscellaneous chemical products 0.94
39 Plastics and articles thereof 0.92
40 Rubber and articles thereof 0.95
41 Raw hides and skins (other than furskins) and leather 0.97
42
Articles of leather; saddlery and harness; travel goods, handbags and similar
containers; articles of animal gut (other than silk- worm gut)
0.98
43 Furskins and artificial fur; manufactures thereof 0.96
44 Wood and articles of wood; wood charcoal 0.93
45 Cork and articles of cork 0.93
46
Manufactures of straw, of esparto or of other plaiting materials; basketware
and wickerwork
0.99
47
Pulp of wood or of other fibrous cellulosic material; recovered (waste and
scrap) paper and paperboard
0.94
48 Paper and paperboard; articles of paper pulp, of paper or of paperboard 0.95
49
Printed books, newspapers, pictures and other products of the printing
industry; manuscripts, typescripts and plans
0.97
50 Silk 0.86
51 Wool, fine or coarse animal hair; horsehair yarn and woven fabric 0.90
52 Cotton 0.98
53 Other vegetable textile fibres; paper yarn and woven fabrics of paper yarn 0.89
54 Man-made filaments; strip and the like of man-made textile materials 0.93
55 Man- made staple fibres 0.95
56
Wadding, felt and nonwovens; special yarns; twine, cordage, ropes and
cables and articles thereof
0.93
57 Carpets and other textile floor coverings 0.98
58
Special woven fabrics; tufted textile fabrics; lace; tapestries; trimmings;
embroidery
0.94
43
59
Impregnated, coated, covered or laminated textile fabrics; textile articles of a
kind suitable for industrial use
0.88
60 Knitted or crocheted fabrics 0.88
61 Articles of apparel and clothing accessories, knitted or crocheted 0.98
62 Articles of apparel and clothing accessories, not knitted or crocheted 0.98
63
Other made up textile articles; sets; worn clothing and worn textile articles;
rags
0.98
64 Footwear, gaiters and the like; parts of such articles 0.93
65 Headgear and parts thereof 0.97
66
Umbrellas, sun umbrellas, walking- sticks, seat- sticks, whips, riding- crops
and parts thereof
0.89
67
Prepared feathers and down and articles made of feathers or of down;
artificial flowers; articles of human hair
0.99
68 Articles of stone, plaster, cement, asbestos, mica or similar materials 0.96
69 Ceramic products 0.97
70 Glass and glassware 0.93
71
Natural or cultured pearls, precious or semi- precious stones, precious metals,
metals clad with precious metal, and articles thereof; imitation jewellery;
coin
0.91
72 Iron and steel 0.91
73 Articles of iron or steel 0.95
74 Copper and articles thereof 0.94
75 Nickel and articles thereof 0.96
76 Aluminium and articles thereof 0.96
78 Lead and articles thereof 0.96
79 Zinc and articles thereof 0.97
80 Tin and articles thereof 0.94
81 Other base metals; cermets; articles thereof 0.94
82
Tools, implements, cutlery, spoons and forks, of base metal; parts thereof of
base metal
0.94
83 Miscellaneous articles of base metal 0.91
84 Nuclear reactors, boilers, machinery and mechanical appliances; parts thereof 0.95
85
Electrical machinery and equipment and parts thereof; sound recorders and
reproducers, television image and sound recorders and reproducers, and parts
and accessories of such articles
0.93
44
86
Railway or tramway locomotives, rolling- stock and parts thereof; railway or
tramway track fixtures and fittings and parts thereof; mechanical (including
electro- mechanical) traffic signalling equipment of all kinds
0.93
87
Vehicles other than railway or tramway rolling- stock, and parts and
accessories thereof
0.92
88 Aircraft, spacecraft, and parts thereof 0.93
89 Ships, boats and floating structures 0.94
90
Optical, photographic, cinematographic, measuring, checking, precision,
medical or surgical instruments and apparatus; parts and accessories thereof
0.94
91 Clocks and watches and parts thereof 0.89
92 Musical instruments; parts and accessories of such articles 0.94
93 Arms and ammunition; parts and accessories thereof 0.97
94
Furniture; bedding, mattresses, mattress supports, cushions and similar
stuffed furnishings; lamps and lighting fittings, not elsewhere specified or
included; illuminated signs, illuminated name- plates and the like;
prefabricated buildings
0.92
95 Toys, games and sports requisites; parts and accessories thereof 0.86
96 Miscellaneous manufactured articles 0.93
97 Works of art, collectors' pieces and antiques 0.95
Overall Average 0.92
3.3. Shadow Exchange Rate Factor: Methodology and Results
The shadow exchange rate factor (SERF) measures the economic cost of foreign exchange
relative to its market price and is used to adjust foreign exchange earnings and costs incurred
in public projects to obtain their economic values. The shadow exchange rate (SER) can be
obtained as a product of the official market exchange rate and the shadow exchange rate factor
(SERF) to obtain the economic value of foreign exchange (as opposed to its market value).
Little and Mirrlees (1974) formulate the shadow exchange rate factor as the reciprocal of the
standard conversion factor, i.e. ����=1/��.
The Standard Conversion Factor (SCF) is applied to the market value of imports to obtain their
economic value. Since import tariffs create a distortion between the market price of the
imported product and its economic price, it is important to undertake a downward adjustment
45
of the market price of imports (by applying the standard conversion factor) to obtain the
economic cost of imports. Since import tariffs (and export subsidies) distort the economic value
of foreign products relative to domestically produced goods, it is key to adjust for taxes and
subsidies in evaluating the economic costs and benefits of public sector projects that entail
imports and exports. As the Standard Conversion Factor (SCF) is estimated at 0.92, the
����=
1
��
=1.09, which reflects a 9% premium on foreign exchange.
Jenkins et al. (2011) provide an alternative method to compute the economic price of foreign
exchange as functions of import demand and export supply elasticities, following theory
developed in Balassa (1974) and Bacha and Taylor (1971). Balassa (1974) discusses the
theoretical conditions under which these formulae simplify such that the standard conversion
factor and the shadow exchange rate factor are inversely related, as outlined in Little and
Mirrlees (1974).
21
The previous assessment conducted by NITI Aayog followed a simplified formulation to derive
the shadow exchange rate factor, applying the average import demand and export supply
elasticities across all traded products, rather than product-specific elasticities (NITI Aayog
2018). We present calculations of the shadow exchange rate factor using this approach for the
last five years in the Appendix. This approach yields substantially different values for the
shadow exchange rate factor, primarily due to the lack of updated estimates in the literature on
import demand and export supply elasticities. We apply available estimates of these trade
elasticities from an IMF study for the 2001-2004 period (Tokarick 2010). Since there are no
recent estimates, this method does not yield updated and accurate estimates of the shadow
exchange rate factor for the Indian context.
Pending further updates to methodology and estimation of trade elasticities for more recent
data, we would recommend relying on the methodology suggested by the ADB (2004) to
estimate the shadow exchange rate factor as the reciprocal of the standard conversion factor.
This methodology yields an estimate of the SERF of 1.09, which reflects a foreign exchange
premium of approximately 9% for the year 2023-24. This estimate of SERF is only marginally
higher than the previously computed value by NITI Aayog (2018) of 1.08 for 2015-16.
21
The theoretical conditions depend on symmetry between import demand and export supply elasticities (Balassa
1974).
46
The difficulty in measurement of trade elasticities has been noted in the literature (Devarajan
et al. 2023; Kee et al. 2008). Several complex econometric approaches have been followed to
circumvent problems of endogeneity in naïve OLS-based estimation of trade elasticities. Given
the difficulty in precise estimation of trade elasticities, we would not recommend following
this approach for the Indian economy. The accurate implementation of this approach would
require precise estimates of trade elasticities at the HS 2-digit product level for the recent
period. To the best of our knowledge, these estimates are not available for the Indian economy.
Therefore, we would recommend calculating the shadow exchange rate factor as the reciprocal
of the standard conversion factor (ADB 2004). Following this method, we obtain a shadow
exchange rate factor of 1.09, which suggests a 9% premium on foreign exchange.
Export subsidies are not applicable in this analysis for India as the government does not provide
an explicit subsidy to boost exports, in compliance with WTO regulations. The Government of
India launched the Remission of Duties and Taxes on Exported Products (RoDTEP) scheme in
2021 to provide tax rebates to exporters. However, these rebates are on taxes paid to the
government, but are not explicit subsidies for exported products. Hence, export prices received
by producers (net of taxes) remain unaffected by this scheme.
22
Similarly, the government launched the Production-linked Incentive (PLI) scheme to boost
domestic manufacturing. While the scheme provides incentives to producers (as a fraction of
the revenue from sales), which could indirectly boost exports, these incentives nevertheless are
not a form of export subsidies as they do not alter the prices of exports received by producers.
Hence, the introduction of the RODTEP and PLI schemes does not impact our calculation of
the shadow exchange rate factor. Since import tariffs are updated annually, the standard
conversion factor and the shadow exchange rate factor can be revised on an annual basis, using
readily available data on import volumes and tariffs at the product level, published by the
Ministry of Commerce and Industry.
22
In addition, the average rate of tax rebate under the RODTEP scheme across products is 1.1%, which would
have a negligible impact on the calculation for the shadow exchange rate factor, given import tariffs are an order
of magnitude higher than tax rebates under the RODTEP export promotion scheme.
47
3.4. Shadow Wage Rate Factor: Methodology and Results
We compute the shadow wage rate factor (SWRF) for unskilled labour. The market wage
reflects the opportunity cost of labour and thus the market valuation of time (Little and Mirrlees
1974). The shadow wage rate factor, which we measure as the ratio of market wages to
minimum wages for specific occupations, is used to adjust the cost of labour in project cost-
benefit analyses. A market wage which falls short of the minimum wage for workers in rural
or urban areas would imply that minimum wages overstate the opportunity cost of labour in
those sectors. Insofar as projects funded by the government are aimed at generating
employment, the shadow wage rate which equals the market wage rate, can be utilised for
project evaluation.
We obtain individual-specific data on weekly hours worked and wages earned for the principal
and subsidiary activities of employment from the nationally representative Periodic Labour
Force Survey (PLFS), 2023-24. We compute the daily wage rate for all individuals employed
in mining and construction for urban areas and agriculture for rural areas. To compute the
SWRF for unskilled labour, we exclude individuals with college degrees and diplomas from
analysis. This yields a sample of 6,905 individuals in rural areas and 3,170 individuals in urban
areas. In both cases, we assume an 8-hour work day to compute the daily wage.
23
We further
compute the shadow wage rate factor by gender to account for gender-specific differences in
observed average wages for unskilled labour.
24
Next, we use the latest data available on minimum wages, which are set on a bi-annual basis
by the Chief Labour Commissioner (Central), Ministry of Labour and Employment. As
minimum wages are set at the district-level, we match minimum wages for unskilled labour
employed in agriculture (for rural areas) and construction (for urban areas), across regional
areas A, B and C, to districts in the PLFS survey. We select the construction sector (NCO
occupation code – 931) for urban areas since this is the third most commonly reported
23
The Factories Act, 1948 prohibits manual work for more than 40 hours per week.
24
We compute the annual shadow wage rate factor which accounts for seasonal differences in wage rates,
particularly in the agriculture sector.
48
occupation in the PLFS and is relevant for project evaluation. For rural areas, we use data on
reported market wage rates in the agricultural sector (occupation code – 921).
25
Finally, we compute the shadow wage rate factor as the ratio of observed market wages to
minimum wages for unskilled workers, i.e. ����=
����� ���
���� ���
. We compute the SWRF
for rural and urban areas, by State and Union Territory (UT), applying survey weights from
PLFS, which ensure population-representative statistics at the state-level. To obtain the
combined shadow wage rate factor for each state/UT, we also compute a weighted average of
the corresponding shadow wage rate factors for rural and urban areas, weighted by the shares
of the working population residing in each of these areas, reported in the PLFS survey. The
results are presented in Table 11. Table 12 also presents the average annual wages obtained
from the PLFS, used to compute the shadow wage rate factors. Finally, Table 13 and Table 14
present average wages and shadow wage rate factors for male and female unskilled workers by
States/UTs, respectively.
Table 11: Shadow Wage Rate Factors (SWRF) for unskilled labour, 2023-24
State/UT
Rural
SWRF
% Rural %
population
Urban
SWRF
% Urban
Population
Total
Andaman & Nicobar
Islands
1.00 55.59 1.00 44.41 1.00
Arunachal Pradesh 1.00 70.64 1.00 29.36 1.00
Assam 0.80 89.07 0.94 10.93 0.82
Bihar 0.95 90.9 0.85 9.1 0.94
Chandigarh - 0 0.65 100 0.65
Chhattisgarh 0.49 80.57 0.47 19.43 0.49
Dadra & Nagar
Haveli
- - - - -
Daman & Diu 0.83 42.53 - 57.47 0.83
Delhi 0.93 2.44 0.68 97.56 0.69
Goa 1.00 41.59 1.00 58.41 1.00
Gujarat 0.63 58.55 0.75 41.45 0.68
25
The minimum daily wage rates are applied based on the Minimum Wage Notifications by the Chief Labour
Commissioner, Ministry of Labour and Employment, available at a bi-annual frequency. Minimum wage rates are
matched to individual data in the PLFS based on quarter of the survey.
49
Haryana 0.95 61.87 0.91 38.13 0.93
Himachal Pradesh 0.98 87.63 0.97 12.37 0.98
Jammu & Kashmir 0.36 81.01 0.96 18.99 0.47
Jharkhand 0.84 81.57 0.68 18.43 0.81
Karnataka 0.86 62.78 0.88 37.22 0.87
Kerala 1.00 52.38 1.00 47.62 1.00
Lakshadweep - 28.5 1.00 71.5 1.00
Madhya Pradesh 0.61 74.46 0.74 25.54 0.64
Maharashtra 0.75 57.72 0.92 42.28 0.82
Manipur 0.86 71.23 1.00 28.77 0.90
Meghalaya 0.90 85.69 0.87 14.31 0.90
Mizoram 0.94 54.79 0.98 45.21 0.96
Nagaland 1.00 71.97 1.00 28.03 1.00
Odisha 0.62 85.05 0.72 14.95 0.63
Puducherry 1.00 37.33 1.00 62.67 1.00
Punjab 0.90 61.81 0.80 38.19 0.86
Rajasthan 0.83 73.23 0.84 26.77 0.83
Sikkim - 76.86 1.00 23.14 1.00
Tamil Nadu 0.91 54.22 1.00 45.78 0.95
Telangana 0.94 60.31 1.00 39.69 0.96
Tripura 1.00 82.37 0.99 17.63 1.00
Uttar Pradesh 0.79 79.26 0.74 20.74 0.78
Uttarakhand 1.00 74.6 0.90 25.4 0.97
West Bengal 0.75 70.94 0.82 29.06 0.77
Overall Average 0.85 63.51 0.88 36.49 0.86
Note:
States with insufficient data in the PLFS to compute the shadow wage rate factor are marked with ‘-’.
We observe shadow wage rate factors in the range of 0.36 – 1.00 for unskilled labour employed
in agriculture in rural areas and between 0.47 – 1.00 for unskilled workers employed in the
construction sector in urban areas, across states and UTs. Overall, the average SWRF is 0.86
for unskilled labour in both rural and urban areas. Thus, the combined shadow wage rate factor
across rural and urban areas is 0.86. Shadow wage rate factors significantly below one suggests
that minimum wages might be considerably overstating the opportunity costs of workers’ time.
50
Applying these shadow wage rate factors can lower the costs of labour in project evaluation.
However, in some states and UTs, shadow wage rate factors that exceed one have been replaced
with “1.00” in Table 11. These reflect average market wages which exceed minimum wage
rates, even for unskilled labour. In these cases, we recommend the use of ����=1, for
unskilled labour, similar to that for skilled labour (ADB 2017).
Table 12: Average daily wage for unskilled labour, by rural and urban areas, 2023-24
State/UT
Average daily wage (INR) -
Rural
Average daily wage (INR) -
Urban
Andaman & Nicobar Islands 712 684
Arunachal Pradesh 434 585
Assam 350 500
Bihar 411 442
Chandigarh - 409
Chhattisgarh 215 272
Dadra & Nagar Haveli - -
Daman & Diu 356 -
Delhi 444 509
Goa 527 885
Gujarat 274 455
Haryana 413 502
Himachal Pradesh 424 496
Jammu & Kashmir 162 554
Jharkhand 369 394
Karnataka 374 519
Kerala 597 876
Lakshadweep - 883
Madhya Pradesh 267 389
Maharashtra 330 529
Manipur 377 555
Meghalaya 394 480
Mizoram 400 495
Nagaland 501 722
51
Odisha 268 401
Puducherry 481 676
Punjab 391 440
Rajasthan 359 472
Sikkim - 671
Tamil Nadu 396 637
Telangana 411 717
Tripura 469 500
Uttar Pradesh 344 419
Uttarakhand 440 479
West Bengal 327 427
Overall Average 394.10 544.67
Note: States with insufficient data in the PLFS to compute the shadow
wage rate factor are marked as ‘-’.
Table 13: Shadow wage rate factor for male unskilled workers, by States/UTs, 2023-24
State/UT
Average
daily wage
(INR) -
Rural
Rural
SWRF
% Rural
Populatio
n
Average
daily wage
(INR) -
Urban
Urban
SWR
F
% Urban
Populatio
n
Tota
l
Andaman &
Nicobar
Islands
712 1.00 56.15 684 1.00 43.85 1.00
Arunachal
Pradesh
491 1.00 71.13 596 1.00 28.87 1.00
Assam 379 0.87 89.13 497 0.96 10.87 0.88
Bihar 418 0.96 90.68 436 0.83 9.32 0.95
Chandigarh - 0 400 0.64 100 0.64
Chhattisgarh 231 0.53 79.97 299 0.45 20.03 0.51
Dadra &
Nagar Haveli
- - - - - - -
Daman &
Diu
- - 40.18 - - 59.82 -
Delhi 444 0.93 2.63 482 0.64 97.37 0.65
52
Goa 506 1.00 41.99 - - 58.01 1.00
Gujarat 277 0.64 58.11 438 0.74 41.89 0.68
Haryana 419 0.97 61.9 505 0.93 38.1 0.95
Himachal
Pradesh
424 0.98 86.35 508 0.97 13.65 0.98
Jammu &
Kashmir
162 0.36 81.01 564 0.96 18.99 0.47
Jharkhand 397 0.89 81.28 409 0.69 18.72 0.85
Karnataka 421 0.97 62.39 505 0.81 37.61 0.91
Kerala 747 1.00 52.82 895 1.00 47.18 1.00
Lakshadwee
p
- 1.00 28.79 - 71.21 1.00
Madhya
Pradesh
277 0.63 74.88 426 0.77 25.12 0.67
Maharashtra 376 0.86 57.06 492 0.88 42.94 0.87
Manipur 376 0.90 71.44 539 1.00 28.56 0.93
Meghalaya 401 0.91 85.93 415 0.72 14.07 0.88
Mizoram 400 0.94 55.85 480 0.94 44.15 0.94
Nagaland 501 1.00 71.08 800 1.00 28.92 1.00
Odisha 329 0.77 84.47 396 0.68 15.53 0.76
Puducherry 655 1.00 39.26 - 60.74 1.00
Punjab 409 0.94 61.42 438 0.82 38.58 0.89
Rajasthan 382 0.88 72.15 515 0.84 27.85 0.87
Sikkim - 75.74 690 1.00 24.26 1.00
Tamil Nadu 497 1.00 54.7 636 1.00 45.3 1.00
Telangana 453 1.00 59.04 771 1.00 40.96 1.00
Tripura 490 1.00 82.61 509 1.00 17.39 1.00
Uttar
Pradesh
364 0.84 78.71 413 0.70 21.29 0.81
Uttarakhand 436 0.99 74.62 489 0.94 25.38 0.98
West Bengal 335 0.77 71.04 422 0.81 28.96 0.78
Overall
Average
423.63 0.89 63.37 521.63 0.86 36.63 0.88
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
53
Table 14: Shadow wage rate factor for female unskilled workers, by States/UTs, 2023-24
State/UT
Average
daily wage
(INR) -
Rural
Rural
SWRF
% Rural
Population
Average
daily wage
(INR) -
Urban
Urban
SWR
F
Urban
Populatio
n Share
Tota
l
Andaman &
Nicobar Islands
- - 54.98 519 1.00 45.02 1.00
Arunachal
Pradesh
388 0.89 70.17 561 1.00 29.83 0.92
Assam 307 0.71 89 451 0.96 11 0.74
Bihar 401 0.93 91.12 414 0.83 8.88 0.92
Chandigarh - 0 409 0.64 100 0.64
Chhattisgarh 203 0.47 81.18 221 0.45 18.82 0.47
Dadra & Nagar
Haveli
- - - - - - -
Daman & Diu 356 0.83 45.41 287 - 54.59 0.83
Delhi 444 0.93 2.22 370 0.64 97.78 0.65
Goa 576 1.00 41.19 646 - 58.81 1.00
Gujarat 275 0.63 59.03 348 0.74 40.97 0.68
Haryana 397 0.91 61.84 468 0.93 38.16 0.92
Himachal
Pradesh
428 1.00 88.9 260 0.97 11.1 1.00
Jammu &
Kashmir
343 0.78 81.01 498 0.96 18.99 0.81
Jharkhand 347 0.80 81.89 318 0.69 18.11 0.78
Karnataka 326 0.75 63.19 499 0.81 36.81 0.77
Kerala 391 0.90 52 771 1.00 48 0.95
Lakshadweep - - 28.19 811 - 71.81 0.00
Madhya
Pradesh
253 0.58 74 321 0.77 26 0.63
Maharashtra 284 0.65 58.42 419 0.88 41.58 0.75
Manipur 383 0.88 71.03 574 1.00 28.97 0.91
Meghalaya 383 0.87 85.46 392 0.72 14.54 0.85
54
Mizoram 400 0.94 53.71 503 0.94 46.29 0.94
Nagaland - - 72.85 632 1.00 27.15 1.00
Odisha 235 0.54 85.61 268 0.68 14.39 0.56
Puducherry 293 0.67 35.55 627 - 64.45 0.67
Punjab 348 0.80 62.22 406 0.82 37.78 0.81
Rajasthan 338 0.78 74.31 367 0.84 25.69 0.80
Sikkim - - 78.17 587 1.00 21.83 1.00
Tamil Nadu 329 0.75 53.78 520 1.00 46.22 0.87
Telangana 384 0.88 61.55 590 1.00 38.45 0.93
Tripura 440 1.00 82.15 426 1.00 17.85 1.00
Uttar Pradesh 297 0.68 79.83 383 0.70 20.17 0.68
Uttarakhand 459 1.00 74.58 440 0.94 25.42 0.98
West Bengal 304 0.70 70.83 399 0.81 29.17 0.73
Overall
Average
355.59 0.80 63.69 491.91 0.86 36.31 0.82
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
The following tables present time trends of shadow wage rate factors computed for the
preceding four years, 2019-20 to 2022-23, at the state-level.
Table 15: Shadow Wage Rate Factors (SWRF) for unskilled labour (2019-2020)
State/UT
Average daily
wage (INR) -
Rural
Rural
SWR
F
% Rural
Population
Average daily
wage (INR) -
Urban
Urban
SWR
F
% Urban
Populatio
n
Total
Andaman &
Nicobar Islands
- - 58.93 - - 41.07 -
Arunachal
Pradesh
285 0.82 68.45 464 0.77 31.55 0.80
Assam 281 0.8 88 485 0.68 12 0.79
Bihar 274 0.79 89.31 498 0.7 10.69 0.78
Chandigarh - - 4.74 503 0.61 95.26 0.61
Chhattisgarh 152 0.44 81.96 465 0.48 18.04 0.45
Dadra & Nagar
Haveli
- - 43.59 - - 56.41 -
55
Daman & Diu 166 0.46 21.7 - - 78.3 0.46
Delhi 272 0.71 3.83 606 0.64 96.17 0.64
Goa 450 1.00 38.47 - - 61.53 1.00
Gujarat 200 0.57 57.43 534 0.6 42.57 0.58
Haryana 319 0.91 64.81 474 0.78 35.19 0.86
Himachal
Pradesh
313 0.9 86.94 403 0.66 13.06 0.87
Jammu &
Kashmir
410 1.0 80.35 497 0.87 19.65 0.97
Jharkhand 164 0.47 79.29 495 0.62 20.71 0.50
Karnataka 226 0.65 59.3 543 0.66 40.7 0.65
Kerala 524 1.0 50.67 518 1.0 49.33 1.00
Lakshadweep - - 20.1 448 1.0 79.9 1.00
Madhya Pradesh 189 0.55 73.11 467 0.55 26.89 0.55
Maharashtra 200 0.57 58.12 551 0.61 41.88 0.59
Manipur 286 0.83 72.13 431 0.93 27.87 0.86
Meghalaya 225 0.64 83.28 501 0.62 16.72 0.64
Mizoram - - 52.55 443 0.82 47.45 0.82
Nagaland 302 0.84 69.22 - - 30.78 0.84
Odisha 252 0.73 84.8 469 0.52 15.2 0.70
Puducherry 183 0.52 32.75 603 0.75 67.25 0.67
Punjab 282 0.81 62.35 498 0.66 37.65 0.75
Rajasthan 262 0.75 74.55 492 0.65 25.45 0.72
Sikkim 500 1.0 74.75 433 1.0 25.25 1.00
Tamil Nadu 273 0.78 53.21 540 0.71 46.79 0.75
Telangana 263 0.75 59.58 447 1.0 40.42 0.85
Tripura 345 0.99 79.78 467 0.82 20.22 0.96
Uttar Pradesh 224 0.63 77.8 524 0.63 22.2 0.63
Uttarakhand 266 0.76 72.89 439 0.78 27.11 0.77
West Bengal 232 0.67 70.14 476 0.66 29.86 0.67
Overall
Average
277.33 0.74 61.40 490.47 0.73 38.60 0.74
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
56
Table 16: Shadow Wage Rate Factors (SWRF) for unskilled labour (2020-2021)
State/UT
Average
daily wage
(INR) -
Rural
Rural
SWRF
% Rural
Population
Average
daily wage
(INR) -
Urban
Urban
SWRF
% Urban
Population
Total
Andaman &
Nicobar Islands
679 1.0 56.73 - - 43.27 1.00
Arunachal
Pradesh
310 0.84 67.54 446 0.96 32.46 0.88
Assam 285 0.77 87.8 592 1.0 12.2 0.80
Bihar 285 0.78 90.57 392 0.83 9.43 0.78
Chandigarh - - 4.47 280 0.52 95.53 0.52
Chhattisgarh 172 0.47 80.85 228 0.53 19.15 0.48
Dadra & Nagar
Haveli
200 0.54 56.38 - - 43.62 0.54
Daman & Diu - - 20.56 - - 79.44 -
Delhi - - 2.85 440 0.69 97.15 0.69
Goa 529 1.0 39.59 - - 60.41 1.00
Gujarat 201 0.54 59.27 296 0.65 40.73 0.58
Haryana 349 0.95 66.67 397 0.92 33.33 0.94
Himachal
Pradesh
359 0.97 90.67 428 1.0 9.33 0.97
Jammu &
Kashmir
356 0.96 80.36 478 1.0 19.64 0.97
Jharkhand 176 0.48 79.6 288 0.56 20.4 0.50
Karnataka 255 0.69 63.07 415 0.86 36.93 0.75
Kerala 526 1.0 53.11 798 1.0 46.89 1.00
Lakshadweep - - 27.76 - - 72.24 -
Madhya Pradesh 192 0.52 73.05 291 0.65 26.95 0.56
Maharashtra 230 0.62 60.34 372 0.74 39.66 0.67
Manipur 409 1.0 71.71 481 1.0 28.29 1.00
Meghalaya 218 0.59 82.3 309 0.61 17.7 0.59
Mizoram 329 0.9 51.53 338 0.79 48.47 0.85
Nagaland 429 1.0 71.29 - - 28.71 1.00
Odisha 233 0.63 84.88 274 0.64 15.12 0.63
57
Puducherry 250 0.67 40.62 - - 59.38 0.67
Punjab 300 0.82 61.99 349 0.75 38.01 0.79
Rajasthan 271 0.74 77.83 351 0.75 22.17 0.74
Sikkim - - 72.29 478 1.0 27.71 1.00
Tamil Nadu 296 0.8 54.32 492 1.0 45.68 0.89
Telangana 320 0.86 59.33 474 1.0 40.67 0.92
Tripura 326 0.89 80.35 366 0.86 19.65 0.88
Uttar Pradesh 263 0.71 79.72 321 0.68 20.28 0.70
Uttarakhand 302 0.82 71.04 379 0.78 28.96 0.81
West Bengal 256 0.7 71.72 301 0.7 28.28 0.70
Overall Average 310.20 0.78 62.63 394.79 0.80 37.37 0.79
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
Table 17: Shadow Wage Rate Factors (SWRF) for unskilled labour (2021-2022)
State/UT
Average
daily
wage
(INR) -
Rural
Average
daily wage
(INR) -
Urban
Rural
SWRF
% Rural
Populatio
n
Urban
SWRF
% Urban
Population
Total
Andaman &
Nicobar Islands
705 584 1.0 51.63 1.0 48.37 1.00
Arunachal
Pradesh
376 474 1.0 69.97 1.0 30.03 1.00
Assam 348 392 0.92 89.74 0.89 10.26 0.92
Bihar 365 387 0.97 91.88 0.88 8.12 0.96
Chandigarh 413 - 4.87 0.75 95.13 0.75
Chhattisgarh 210 182 0.55 81.31 0.41 18.69 0.52
Dadra & Nagar
Haveli
- - - - - - -
Daman & Diu 391 178 1.0 38.46 0.41 61.54 0.64
Delhi 191 - 3.45 0.29 96.55 0.29
Goa 404 514 1.0 38.82 0.94 61.18 0.96
Gujarat 233 275 0.62 57.09 0.59 42.91 0.61
Haryana 396 417 1.0 65.57 0.94 34.43 0.98
58
Himachal
Pradesh
428 232 1.0 90.3 0.53 9.7 0.95
Jammu &
Kashmir
309 457 0.81 80.88 1.0 19.12 0.85
Jharkhand 307 266 0.82 80.19 0.58 19.81 0.77
Karnataka 311 453 0.82 64.31 0.95 35.69 0.87
Kerala 527 785 1.0 50.06 1.0 49.94 1.00
Lakshadweep - 793 - 27.5 1.0 72.5 1.00
Madhya Pradesh 219 280 0.58 75.67 0.63 24.33 0.59
Maharashtra 270 384 0.71 56.94 0.75 43.06 0.73
Manipur 477 443 1.0 73.38 1.0 26.62 1.00
Meghalaya 326 261 0.86 85.67 0.56 14.33 0.82
Mizoram 400 359 1.0 53.96 0.82 46.04 0.92
Nagaland 442 456 1.0 75.1 1.0 24.9 1.00
Odisha 259 303 0.69 85.96 0.67 14.04 0.69
Puducherry 301 489 0.79 37.08 0.96 62.92 0.90
Punjab 346 357 0.91 65.8 0.77 34.2 0.86
Rajasthan 361 332 0.96 74.21 0.73 25.79 0.90
Sikkim - 220 - 79.03 0.5 20.97 0.50
Tamil Nadu 375 460 0.99 56.4 0.98 43.6 0.99
Telangana 382 457 1.0 65.04 1.0 34.96 1.00
Tripura 439 389 1.0 82.16 0.89 17.84 0.98
Uttar Pradesh 328 348 0.86 80.33 0.75 19.67 0.84
Uttarakhand 413 432 1.0 74.95 0.98 25.05 0.99
West Bengal 316 373 0.84 72.57 0.84 27.43 0.84
Overall
Average
365.47 392.24 0.89 64.13 0.79 35.87 0.86
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
59
Table 18: Shadow Wage Rate Factors (SWRF) for unskilled labour (2022-2023)
State/UT
Average
daily wage
(INR) -
Rural
Rural
SWRF
% Rural
Populatio
n
Average
daily wage
(INR) -
Urban
Urban
SWRF
% Urban
Population
Total
Andaman &
Nicobar Islands
571 1.0 56.75 676 1.0 43.25 1.00
Arunachal
Pradesh
412 1 70.49 533 1.0 29.51 1.00
Assam 421 1 96.69 468 0.94 3.31 1.00
Bihar 364 0.91 92.17 419 0.85 7.83 0.91
Chandigarh - 5.08 418 0.68 94.92 0.68
Chhattisgarh 204 0.5 81.27 248 0.47 18.73 0.49
Dadra & Nagar
Haveli
- - - - - - -
Daman & Diu 337 0.83 35.81 - - 64.19 0.83
Delhi - - 2.67 512 0.68 97.33 0.68
Goa 428 1.0 41.16 839 1.0 58.84 1.00
Gujarat 242 0.59 56.73 405 0.77 43.27 0.67
Haryana 425 1.0 66.15 468 0.79 33.85 0.93
Himachal
Pradesh
397 0.97 90 417 0.87 10 0.96
Jammu &
Kashmir
475 1.0 82.92 529 1.0 17.08 1.00
Jharkhand 208 0.51 82.69 386 0.72 17.31 0.55
Karnataka 337 0.83 63.84 490 0.88 36.16 0.85
Kerala 525 1.0 53.38 850 1.0 46.62 1.00
Lakshadweep - - 23.98 783 1.0 76.02 1.00
Madhya
Pradesh
243 0.6 74.99 352 0.69 25.01 0.62
Maharashtra 305 0.74 58.19 484 0.82 41.81 0.77
Manipur 460 1.0 72.43 519 1.0 27.57 1.00
Meghalaya 387 0.95 84.86 390 0.74 15.14 0.92
Mizoram 400 0.99 53.69 455 0.97 46.31 0.98
Nagaland 461 1.0 74.33 512 1.0 25.67 1.00
60
Odisha 297 0.73 85.78 393 0.78 14.22 0.74
Puducherry 282 0.68 36.19 527 1.0 63.81 0.88
Punjab 371 0.91 64.4 416 0.84 35.6 0.89
Rajasthan 368 0.9 76.09 429 0.84 23.91 0.89
Sikkim 566 1.0 79.07 541 1.0 20.93 1.00
Tamil Nadu 380 0.94 57.25 566 1.0 42.75 0.97
Telangana 383 0.94 62.87 580 1.0 37.13 0.96
Tripura 437 1.0 82.73 472 1.0 17.27 1.00
Uttar Pradesh 339 0.82 80.24 409 0.77 19.76 0.81
Uttarakhand 411 1.0 74 477 0.98 26 0.99
West Bengal 322 0.79 71.47 418 0.87 28.53 0.81
Overall
Average
379.29 0.88 64.42 496.39 0.88 35.58 0.88
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
4. Social Cost of Carbon
The social cost of carbon (SCC) is a measure of the present discounted value of the societal
damages associated with an additional ton of CO2 emissions incurred today. It reflects the
global economic damages due to rise in temperature associated with increasing CO2
concentrations in the atmosphere. Since carbon dioxide remains in the atmosphere for more
than 300 years, the SCC measures the continuum of economic damages incurred over this
timeframe (Rennert et al. 2022). The SCC integrates climate science, economics, and social
welfare considerations to provide a single monetary figure useful for cost-benefit analyses of
climate policies.
Estimating the SCC proceeds in seven steps using Integrated Assessment Models (IAMs)
(Carleton and Greenstone 2022). First, the model entails future projections of CO2
concentrations in response to various socioeconomic pathways, which include business-as-
usual, ambitious climate policy and so on. Second, the climate science module relates rise in
CO2 concentrations to probable increases in mean surface temperature, termed climate
sensitivity. Third, the model accounts for future economic damages due to higher temperatures,
associated with a rise in CO2 emissions. Fourth, the model converts future economic damages
61
to present value terms, applying an appropriate social discount rate for a long timescale. The
remaining three steps are normative in nature and involve value judgements to be made by the
policymaker. Here, the model assesses whether to evaluate only domestic or local damages or
also global damages. Subsequently, the model accounts for potential uncertainty in future
consumption. Finally, the model considers integrating inequality aversion in evaluating the
SCC (Carleton and Greenstone 2022).
The existing literature has analysed a range of IAMs, with incremental improvements made to
various aspects of IAMs over the last few decades. Nordhaus’ foundational work with the
Dynamic Integrated Climate-Economy (DICE) Model evaluated the optimal transition path to
mitigating the rise in greenhouse gas concentrations while maximising social welfare
(Nordhaus 1993a; Nordhaus 1993b). Nordhaus (1993b) proposed a modest carbon tax as an
effective policy instrument to mitigate the rise in CO2 emissions, while ensuring steady
economic growth over a long-time horizon.
4.1. Global SCC values
In the most recent update of the DICE model (DICE-2023), Barrage and Nordhaus (2024) find
SCC values ranging from US$ 37 – 571 per tonne of CO2 for 2025 (at 2019 US$ prices), for
constant social discount rates, ranging from 5% to 1% per year respectively. Higher social
discount rates generate lower values for the social cost of carbon. They find an SCC which
maximizes global welfare of $59 in 2025 (in 2019 US$ prices). The associated social discount
rate declines over time due to adjustment for uncertainty in the long-run future growth rate of
world GDP. This optimal path is associated with a temperature increase of 2.6
o
C in 2100 in
their model.
In contrast, a recent study by Rennert et al. (2022) uses the open-source model, Greenhouse
Gas Impact Value Estimator (GIVE), following recommendations by the US National
Academies of Science, Engineering and Medicine (NASEM), to update the latest models in
evaluating the SCC. Rennert et al. (2022) apply a risk-free social discount rate of 2% and find
a mean SCC estimate of US$ 185/ton CO2 in real terms (at 2020 US$ prices), with a 5%-95%
confidence interval of US$ 44 – 413/ton CO2.
62
Higher SCC estimates reported by Rennert et al. (2022) reflect a lower social discount rate as
well as an improved understanding of long-term economic risks to climate change via the GIVE
model, which integrates probabilistic climate projections and updated socio-economic data. In
particular, the model accounts for the potential rise in energy consumption due to temperature
rise based on work by Clarke et al. (2018), premature mortality due to heat stress from high
temperature based on Cromar et al. (2022) and economic damages in agriculture due to high
temperatures and drought based on Moore et al. (2017).
Importantly, Hänsel et al. (2020) update the DICE model to integrate damage functions from
Howard and Sterner (2017), which leads to substantially higher damages from climate change.
They revise the social discount rate used to evaluate the present value of damages, based on
the Ramsey rule, applying an expert elicitation survey by Drupp et al. (2018), which finds a
median social rate of time preference (δ) and lower degree of inequality aversion (η) of 0.5%
and 1 respectively, compared to δ = 1.5% and =1.45 used in the DICE-2016R model by
Nordhaus (2017).
26
These revisions lower the social discount rate used to evaluate climate
damages and increase the social cost of carbon to US$ 101/ton CO2.
Moore et al. (2024) synthesize evidence on the social cost of carbon by combining 1,823 SCC
estimates from 147 studies and conduct an expert elicitation survey of authors of the reviewed
studies. From these studies which cover over three IAMs including DICE, FUND and PAGE,
the authors find a mean SCC estimate of US$ 132/ton CO2 (at 2020 US$ prices). In contrast
to published estimates, their expert elicitation survey and a random forest-trained model results
in a synthetic distribution with higher SCC estimates. The synthetic distribution results in a
mean SCC value of US$ 185/ton CO2 (at 2020 US$ prices), with an interquartile range of US$
97-369/ton CO2.
In addition to global SCC estimates, recent studies provide sector-specific estimates of the
social damage associated with rising temperatures. Rode et al. (2021) develop the Data-driven
Spatial Climate Model (DSCIM) of the Climate Impact Lab, at the University of Chicago, to
estimate the impact of rising temperature on the global energy demand for heating and cooling.
Estimating econometric regression models for 146 countries over the 1971-2020 period, the
authors find that while higher temperatures increase energy consumption from air conditioning,
26
The modal value of the social rate of time preference in the survey was zero.
63
particularly in India and other tropical countries, the rise in temperature is associated with a
decline in demand for residential heating from other fuels such as oil and gas, which outweighs
the rise in demand for cooling. Overall, rising temperatures from higher CO2 concentrations
lead to a net decline in energy consumption from all fuels combined, resulting in negative SCC
estimates for the energy sector (Rode et al. 2021). Rode et al. (2021) present a significant
methodological advance in computing the social cost of carbon, based on empirical estimates,
compared to modelled estimates used in previous studies.
Similar to the energy sector, Carleton et al. (2022) estimate excess mortality due to climate-
induced increases in temperature at the subnational level for 40 countries, accounting for the
projected increase in incomes and adaptation to climate change. The authors estimate the mean
‘partial SCC’ for temperature-induced mortality at US$ 37/ton CO2, with an interquartile range
of US$ -8 to 73/ton CO2. Analogously, Moore et al. (2017) present partial SCC estimates for
the agriculture sector, ranging from US$ 3.5/ton CO2 to US$ 8.5/ton CO2.
Estimates from empirical studies for energy consumption and mortality differ significantly
from sector-wise estimates from integrated assessment models, as displayed in Figure 1 (Rode
et al. 2021; Carleton et al. 2022). While the SCC associated with energy consumption is
significantly smaller than that used in IAM-based modelling studies, the partial SCC for
mortality costs due to temperature rise are an order of magnitude larger than costs presumed in
modelling studies. The nascent empirical literature critically informs debates on the aggregate,
global value of the social cost of carbon (Carleton and Greenstone 2022; US EPA 2023).
Figure 1: Sector-specific SCC estimates from empirical studies vs. IAMs
Source: Carleton and Greenstone (2022)
64
4.2. Country-specific SCC values
While most studies present global aggregate estimates of the social cost of carbon, some studies
analyse country-specific economic damages in response to rising temperatures. Global
damages then equal the sum of country-specific damages, aggregated across all countries.
Ricke et al. (2018) combine climate-economic estimates to compute the country-specific social
cost of carbon for several countries. Their results show that India is particularly vulnerable to
climate change and economic damages incurred in India account for 21% of global damages
from climate change.
Ricke et al. (2018) apply the empirical model of Burke, Hsiang and Miguel (2015), who analyse
the global non-linear impact of temperature rise on economic output. Ricke et al. (2018)
estimate a mean country social cost of carbon (CSCC) for India of US$ 86/ton CO2, with a
range from US$ 49-157/ton CO2. The study applies simplified functions of the economic
response to increases in temperature, which are drawn from cross-country or global studies,
rather than empirical estimates specifically from the Indian context.
The recent study by Moore et al. (2024) provides a synthesis of the evidence on the global
social cost of carbon, reviewing nearly 150 studies to provide a range of estimates of the SCC.
Similarly, Rennert et al. (2022) utilise updated damage functions and climate sensitivity
relationships to estimate the global SCC. A synthesis of estimates for the social cost of carbon
from the literature is presented in Appendix Table A.6.A.
As Ricke et al. (2018) provides evidence to suggest that India accounts for around one-fifth of
global damages from climate change, we utilise the estimates from the studies by Moore et al.
(2024) and Rennert et al. (2022) to estimate a plausible range of values for the SCC for India.
We find a mean CSCC for India of US$ 39/ton CO2 with a range of US$ 9 – 87/ton CO2, by
using the assumption that damages to India are one-fifth of global damages. This would need
a further downward adjustment since the social discount rate for India will be higher, at least
in the short-term, than the rate used in the global analyses cited above.
Global analyses typically apply a near-term discount rate of 2%, whereas the present study
estimates a higher social discount rate of 7% for India. Since previous studies do not provide
65
estimates for the social cost of carbon corresponding to higher discount rates, it is beyond the
scope of this report to estimate the precise social cost of carbon. However, based on earlier
studies, we estimate a lower-bound value for the social cost of carbon for India. Hence, we
would recommend a minimum social cost of carbon of US$10 per ton of CO2 to be applied in
project evaluation for public sector projects by the Government of India. Further research is
needed to analyse the relationship between temperature rise and economic output for the Indian
context, which would inform estimates for the social cost of carbon for India.
5. Recommendations
This study reassessed key parameters for cost-benefit analysis in public sector projects
undertaken by the Government of India. We evaluated short-run and long-run social discount
rates, following several state-of-the-art methods in the academic and policy literature. We also
computed conversion factors for foreign exchange, traded commodities, and labour usage in
production. Finally, we synthesized the literature to present a range of plausible estimates for
the social cost of carbon for cost-benefit analysis. In this section, we summarise our key
recommendations on parameters for use in cost-benefit analyses for public sector projects.
5.1. Social Discount Rate
The social discount rate or “discount rate” measures the trade-off between present and future
consumption. It is used to obtain the present value of the future benefits of a public investment
project. We computed the social discount rate based on two broad approaches, including (i) the
Ramsey approach, that gives a discount rate of 7.3% for a time horizon up to 30 years and (ii)
market rates of return, which gave a range of discount rates from 8.1% to 11%, across methods
(Table 5). These discount rates pertain to projects with lifetimes of less than 30 years. Our
estimates of the short-run social discount rate range from 7.3% to 11% with mean estimates of
7.3% and 9.23% from the Ramsey rule and weighted average methods, respectively (Table 8).
We recommend using the weighted average method for projects with time horizons up to 30
years, since this method accounts for consumers’ savings decisions and societal trade-offs
between present and future consumption, while also accounting for displacement of private
66
investment and government borrowing. This suggests an upward revision of the social discount
rate from 8% in the previous assessment (NITI Aayog 2018) to 9.23% in real terms, for short-
term projects with maturities up to 30 years.
For longer horizons, however, we suggest using the uncertainty-adjusted Ramsey approach to
calculate the social discount rate, since this approach accounts for uncertainty about future
growth rates, which can be substantial in the case of a developing country like India. Lower
social discount rates over longer time horizons would also place higher value on socially
beneficial projects whose benefits only accrue after a few decades (such as those in health,
education, or for environmental protection). Thus, for longer term projects, we recommend
applying a term structure of discount rates, adjusting for uncertainty in future economic growth
(Table 5).
Further, we recommend the use of a social discount rate for selection and evaluation for public
projects, instead of the hurdle rate. The hurdle rate is applied in evaluation of private sector
investments by private companies. Hence, the social discount rate is the appropriate metric to
apply in the context of public project evaluation by the Government.
5.2. Shadow Prices
We computed conversion factors for foreign exchange, imports, and labour costs in production.
We obtained standard conversion factors at the Harmonised System 2-digit product code level
for all traded commodities, with an average standard conversion factor (SCF) of 0.92. We also
obtained a shadow exchange rate factor (SERF) of 1.09. This reflects a 9% premium on foreign
exchange. This exceeds the foreign exchange premium of 8% calculated in the previous
assessment report (NITI Aayog 2018). Finally, we computed shadow wage rate factors for
unskilled labour for rural and urban areas across states and UTs (Table 11), with an average
shadow wage rate factor of 0.86. These are to be applied when minimum wages, rather than
market wages, are used for calculating labour costs in project evaluation.
5.3. Social Cost of Carbon
We synthesized the latest advances in science to reflect on the global social cost of carbon,
which measures the present value of the monetary social damage due to an incremental ton of
67
CO2 emissions. Based on our review of the literature, a country social cost of carbon for India
incorporating only damages to India rather than global damages, may be about US$ 10/ton
CO2, with a range of US$ 9 – 87/ton CO2, based on recent global studies. Further research is
needed to improve the calculation of the SCC for the Indian context, in particular, to
incorporate economic damages for India into global damage functions and to reconcile
empirical estimates with those from modelling studies. In this respect, we recommend that a
research study be conducted by the Government of India to estimate the appropriate social cost
of carbon for India.
5.4. Comparison of parameters
We compare our recommendations on parameter values with those applied in the previous
assessment by NITI Aayog (2018) in Table 19.
Table 19: Updating of national parameters since NITI Aayog (2018)
Parameter NITI Report (2018) NITI Report (2026)
Social Discount Rate (< 30 years) 8% 9.23%
Social Discount Rate (30-50 years) 8% 6.2%
Social Discount Rate (50-75 years) 6% 4.8%
Social Discount Rate (75-100 years) < 6% 3.4%
Standard Conversion Factor (SCF) - 0.92
Shadow Exchange Rate Factor (SERF) 1.08 1.09
Shadow Wage Rate Factor (SWRF) - Total - 0.86
Shadow Wage Rate Factor (SWRF) - Male - 0.88
Shadow Wage Rate Factor (SWRF) - Female - 0.82
SCC (not accounting for damages outside India) -
US$ 10/ton CO2
68
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74
Appendix
A.1. Derivation of the Ramsey rule
We follow Dasgupta (2008) to derive the social discount rate based on the Ramsey rule.
Consider a representative consumer who maximises lifetime utility, �(
�), where
� represents
consumption in period �, with �=0 to �= ∞. The utility function, �(
�), is strictly quasi-
concave, with marginal utility of consumption, �
′
(
�)>0. The utility function exhibits
diminishing marginal utility of consumption, i.e. �
′′
(
�)<0. The present value of lifetime
utility, �
0, discounted at rate δ, is given by:
�
0=�(
0)+
�(�1)
(1+�)
+⋯+
�(�
)
(1+�)
+⋯=∑
∞
�=0
�(�)
(1+�)
(A.1)
Next, we define parameters, η - the elasticity of marginal utility of consumption, and �
� - the
growth rate of private household consumption:
=−
�
′
(�)
�
�
�
′(�)
=−
� �′′(�)
�′(�)
(A.2)
�
�=
�+1
�
−1 (A.3)
We assume a constant relative risk aversion (CRRA) utility function to ensure the elasticity of
marginal utility , is constant (i.e. it does not vary with the level of consumption). The CRRA
utility function is defined as follows:
�(
�)={
�
(1−)
1−
,>0; ≠1 ����
� ,=1
Note that for any t, �
′
(
�)=
�
−
for >0 and ≠1. Further, assume there are small
changes in consumption growth rates between two consecutive time periods, such that
variations in
� and
�+1 leave the individual’s present value of lifetime utility, �
0,
unchanged.
Next, take the differential of �
0, as follows:
75
�
0=
�′(
1)
(1+�)
1+⋯+
�′(
�)
(1+�)
�
�+
�′(
�+1)
(1+�)
�+1
�+1=0
The previous assumption implies that for any pair of consecutive changes in consumption
growth rates,
� and
�+1, �
0=0. This leads to the following equation:
�′(�
)
(1+�)
�+
�′(�+1
)
(1+�)
+1
�+1=0 (A.4)
Next, we multiply the above equation by (
(1+�)
�
�
):
�′(
�)+
�′(
�+1)
(1+�)
�+1
�
=0
Subsequently, we substitute the values of �′(
�) and �
� in the above equation, as follows:
�
−
+
�+1
−
(1+�)
�+1
�
=0 (A.5)
Next, we define the social discount rate, following Dasgupta (2008), as follows:
�
=−
�+1
�
−1 (A.6)
We substitute equation (A.6) into (A.5), as follows:
1
�
−
1
�+1
(1+�)
(1+
�)=0 (A.7)
Lastly, we substitute the growth rate of consumption, �
�, in the above equation, as follows:
(
�+1
�
)
−
(1+
�
)
(1+�)
=(1+�
�
)
−
(1+
�
)
(1+�)
=0 (A.8)
This leads to the approximate Ramsey rule for the social discount rate,
�
:
�
≈ �+�
� (A.9)
76
A.2. Social Opportunity Cost of Capital Approach
We apply the methodology derived in Poterba (1998) and explained in Jenkins et al. (2011) to
estimate the rate of return to capital from the National Accounts Statistics. The rate of return
to capital is measured as the ratio of the national income derived from capital and the capital
stock in the economy, i.e. �
=
. Theoretically, the average rate of return (or average product
of capital) would intersect the marginal rate of return (or marginal product of capital) when the
average product of capital is at its highest value in the production function. To calculate income
from capital (which is not directly reported in the national accounts), we apply the methodology
outlined in Jenkins et al. (2011). The calculations are presented below in Table A.2.1. We find
an average rate of return to capital of 10.6% over the 2012-13 to 2022-23 period, with this
approach.
Specifically, we estimate the rate of return to capital using the National Accounts Statistics
(NAS), following the methodology of Jenkins et al. (2011). Capital income is derived by
applying the capital share of Gross Value Added (GVA) to aggregate GVA (in constant prices)
and deducting depreciation (consumption of fixed capital – CFC, in constant prices). The rate
of return is then computed as the ratio of capital income net of depreciation to the net capital
stock at the beginning of the accounting year, as reported by NAS. The net capital stock is
available only in current prices in the NAS database. To derive this in constant price terms, we
derive the capital stock deflator as the ratio of gross capital formation (GCF) in current prices
to the GCF in constant prices, both of which are reported in the NAS.
27
Thus, we derive the
real rate of return to capital, as follows:
�
=
(��
�.
�)−�
�
��� ��� ����
�−1
We apply capital shares of GVA using the RBI KLEMS database, for the 2012-13 to 2022-23
period. These capital shares are reported at the sector-level. To derive an economy-wide capital
share of GVA for year t,
�, we compute a weighted average across sectors, using the sector-
level contributions to national GVA as weights. This calculation is conducted as follows:
27
Net Capital Stockt-1=Net Capital Stockt-1, Current PricesCapital Stock Deflatort-1, where Capital Stock
Deflator=GCFCurrent pricesGCFConstant prices.
77
�=∑�
���
��
�
The economy-wide capital share of GVA for year t,
�, is a weighted average of sectoral capital
shares of GVA, �
��, weighted by sector-level weights, �
��. The weights, �
��, in turn, are
derived as follows:
�
��=
��
��
∑��
���
However, the Jenkins et al. (2011) approach requires modification for the Indian context,
because it derives capital income from GDP as the residual of labour, land income from
agriculture and resource income. The NAS does not separately report operating surplus and
mixed income, preventing accurate decomposition of mixed income/ operating surplus into
labour and capital components. Since mixed income includes substantial labour earnings of
self-employed households, particularly in the informal sector, which is typically underreported,
capital income is likely to be overestimated. In addition, land income from agriculture is not
estimated separately in the KLEMS database. As a result, the estimated capital income and rate
of return are likely to overstate the true economy-wide rate of return to capital, since this is an
average return to capital, rather than the marginal return.
78
Table A.2.1. Average rate of return to capital estimated from National Accounts Statistics
Year
GVA (constant
prices, INR
crores)
Capital
share of
GVA
Capital income
(INR Crores)
Consumption of fixed capital
(Depreciation, constant prices,
INR Crores)
Net capital stock
(constant prices, INR
crores)
Rate of return to
capital, in real
terms (%)
(1) (2) (3) (4) (5) (6) (7)
2012-13 85,46,275 0.50 42,90,426 10,10,661 2,66,76,772 12.3%
2013-14 90,63,649 0.50 45,17,051 11,00,610 2,96,88,120 11.5%
2014-15 97,12,133 0.50 48,27,952 11,78,644 3,20,75,086 11.4%
2015-16 1,04,91,870 0.50 52,48,999 12,70,890 3,58,53,477 11.1%
2016-17 1,13,28,285 0.49 55,87,142 13,81,526 3,75,40,296 11.2%
2017-18 1,20,34,171 0.49 58,88,773 14,89,921 3,95,77,694 11.1%
2018-19 1,27,33,798 0.49 61,83,330 16,14,455 4,24,24,566 10.8%
2019-20 1,32,36,100 0.48 63,27,168 17,31,178 4,69,73,698 9.8%
2020-21 1,26,87,345 0.48 60,96,735 18,32,759 4,95,49,369 8.6%
2021-22 1,38,76,840 0.48 66,63,430 19,55,788 4,89,10,789 9.6%
2022-23 1,48,78,028 0.48 70,92,668 20,87,964 5,14,45,594 9.7%
Average 10.6%
Note: The formulae applied are: Col. (4) = Col. [(2)*(3)]. Then, Col. (7) = Col. [(4) – (5)/ (6)].
79
A.3. Weighted Average Approach
The weighted average approach computes the social discount rate as a weighted average of the
social rate of time preference (�
�), marginal product of capital (
) and the real interest rate on
foreign borrowings (
�):
=��
�+�
+(1−�−�)
�.
Burgess and Zerbe (2011) provide a tractable formulation of the weighted average discount
rate, as follows:
=
−(
�
)(
�
)��+((
1
��
)−1)
�
−(
�
)(
�
)+
1
��
(A.11)
We decompose this formula to derive the weights placed on each of the three discount rates, as
follows:
�=
−(
�
)(
�
)
−(
�
)(
�
)+
1
��
(A.12)
�=
1
−(
�
)(
�
)+
1
��
(A.13)
(1−�−�)=
(
1
��
)−1
−(
�
)(
�
)+
1
��
(A.14)
We estimate parameter values for each of the parameters in the above equations to estimate the
weights, � and �, as follows:
- Interest elasticity of savings: According to Burgess and Zerbe (2011), the interest
elasticity of savings is calculated as the product of the elasticity of inter-temporal
substitution and the proportion of wealth that is consumed in the economy. Since the
elasticity of inter-temporal substitution is the reciprocal of the elasticity of the marginal
utility of consumption, we obtain this as the reciprocal of estimated earlier. Next, we
calculate the proportion of national wealth that is consumed based on recent work by
Bharti et al. (2024). Thus, we estimate �=0.06.
80
- Interest elasticity of investment: We estimate this parameter using firm-level data on
annual investment from the Annual Survey of Industries and data on the real interest
rate from the RBI. We estimate a linear regression model and obtain a mean estimate
for. We also conduct a sensitivity check to estimate the range of values for based on the
confidence interval of the regression estimate. This leads to a range for n from - 0.48 to
-0.12.
- Savings to Investment Ratio: This is obtained from the National Accounts Statistics,
2024, as 0.95.
- Savings Retention Coefficient (SRC): This is calculated as a ratio of the savings-
output ratio on the investment-output ratio from the National Accounts Statistics, to
assess the fraction of national savings that are retained domestically in the form of
investment. We obtain the SRC as 0.95.
Table A.3.1. displays the calculated weights for the weighted average approach, corresponding
to the mean estimate and the lower and upper bound estimates presented in Table 7.
Table A.3.1. Weights on private consumption, investment, and foreign borrowing:
WA approach
Remarks on regression
coefficient (interest
elasticity of investment)
Weight
(Private
Consumption)
Weight
(Private
Investment)
Weight
(Foreign Borrowing)
SDR
α β 1-α-β
Mean estimate 0.15 0.81 0.04 9.23
Upper bound 0.10 0.85 0.04 9.59
Lower bound 0.30 0.66 0.03 8.12
A.4. Other approaches to estimating
The first approach proposed by Groom and Maddison (2019) to estimate the elasticity of
marginal utility of consumption, , is the equal sacrifice principle, which is applied in this
report and examined in section 2.2.1. Groom and Maddison (2019) outline four other
approaches to estimate . We investigate three of these four approaches, finding imprecise
81
estimates of , with only the equal sacrifice approach yielding plausible results for and hence
the social discount rate, based on the Ramsey rule. We present results from these methods
below. We omit the risk aversion approach due to lack of data on insurance premiums in the
Indian context.
A.4.1. Euler equation approach
Groom and Maddison (2019) propose the Euler equation approach to estimate the elasticity of
marginal utility of consumption, , drawing on a lifecycle model, where consumers maximise
lifetime discounted utility, subject to a lifetime wealth constraint. The optimisation problem
leads to the Euler consumption equation, defined as follows:
�
′
(
�)=�(1+�
�)�
′
(
�+1) (A.15)
where �
� is the real interest rate prevailing in the financial market.
The Euler consumption equation leads to the following estimating equation for the elasticity of
marginal felicity, :
���� (
�+1
�
) =
1
���� � +
1
���� (1+�
�)
(A.16)
where is the elasticity of marginal felicity.
Results
We draw on annual data on private final consumption expenditure (PFCE) at constant prices
from the National Accounts Statistics, MOSPI, for 1950-51 to 2022-23 and real interest rates
(nominal bank rate less the annual inflation rate) from the Reserve Bank of India for the
corresponding period. We estimate an OLS regression (applying the Newey-West standard
errors to correct for heteroscedasticity and ergodicity) to estimate the elasticity of intertemporal
substitution, =
1
, and correspondingly, . We find ranges from 2.2 to 2.9 across
82
specifications, which significantly exceeds the plausible range of estimates of observed in
the literature.
Table A.4.1. Regression estimates of the Euler equation and elasticity of the
marginal felicity of consumption,
���� (
�+2
�
)
(1) (2)
Compound Real Bank
Rate (over two years)
0.34
*
(0.185)
Compound Real Deposit
Rate (over two years)
0.45
**
(0.215)
Constant -0.39 -0.54
*
(0.258) (0.298)
Observations 33 26
F-Statistic 3.39 4.46
η 2.94 2.2
Newey-West standard errors in parentheses.
*
p < 0.10,
**
p < 0.05,
***
p < 0.01
A.4.2. Frisch approach
The next approach is based on the Frisch formula, which assumes commodities satisfy additive
separability, to estimate the elasticity of marginal felicity (Groom and Maddison 2019):
=
(1−
)
�
(A.18)
where
is the income (budget) elasticity of demand for good i, �
is the budget share and �
is the own-price compensated elasticity of demand for good i. For parameters to be consistent
with consumer theory, �
<0. Hence, for >0 requires
<0 or (1−�
)<0.
83
Results
We use household-level data from the NSS Household Consumer Expenditure Survey, 2022-
23, to estimate the price and income elasticities of demand for food items, with results
displayed in Table A.4.2. Regression estimates based on the Frisch Approach yield negative
estimates of the elasticity of the marginal felicity of consumption (=−0.21), and hence,
negative discount rates. Groom and Maddison (2019) implement this approach on data for the
UK and find =−3.57. However, NABARD (2024) estimate a positive compensated own-
price elasticity of demand, which is inconsistent with economic theory, finding a value for =
0.8. Given the inconsistency of our estimates with economic theory, we do not recommend use
of this method for calculation of the social discount rate by the Government of India. Groom
and Maddison (2019) also acknowledge the limitations of this approach and do not recommend
this method for calculation of the social discount rate for government projects.
Table A.4.2. Estimates of risk aversion parameter from NSS HCES data, 2022-23
(1) (2)
Budget Share (Food) ln (Food Exp.)
ln (Food Exp.) -0.07
***
(0.001)
ln (Price, Food) -0.04
***
(0.002)
ln (Price, Other Nondurable) -0.03
***
(0.001)
HH. Size 0.01
***
0.11
***
(0.000) (0.001)
Urban 0.01
***
0.04
***
(0.000) (0.002)
ln (Total HH. Exp.) 0.43
***
(0.002)
Constant 1.35
***
3.88
***
(0.010) (0.026)
Observations 224,555 228,284
84
R
2
0.371 0.522
0.26
�
-1.10
�
0.40
-0.21
Note: Robust standard errors in parentheses. Regression includes categorical variables
for state code.
*
p < 0.10,
**
p < 0.05,
***
p < 0.01
A.4.3. Subjective well-being approach
The subjective well-being approach measures the association between consumption and utility
from directly observable household-level data on self-reported well-being and levels of
household consumption (Groom and Maddison 2019). In the absence of these data, we rely on
the World Values Survey, which conducted a longitudinal survey of 1,700 individuals from
1989-2022, across six waves, for India. The survey contains subjective questions on
individual’s self-reported “general satisfaction with life” on a ten-point scale
28
and questions
on the individual’s range of incomes, such as “Less than Rs 500 per month”, “501 - 1000 per
month” etc. However, data are missing for this question for majority of the sample.
Specifically, this question was not posed to respondents after the 1999-2000 survey wave.
To estimate the elasticity of the marginal felicity of consumption (), we require an additional
assumption of the functional form for utility. For consistency with preceding analyses, we
assume the utility function is of the constant relative risk aversion (CRRA) form, as follows:
�(
�)={
�
(1−)
1−
,>0; ≠1 ����
� ,=1
Hence, the marginal utility of consumption, �
′
(
�)=
�
−
for >0 and ≠1. For an
average level of individual consumption (or earnings),
�, we compute the coefficient of
relative risk aversion, , from our point estimate of the marginal utility of consumption, �
′
(
�).
28
The specific question is: “All things considered, how satisfied are you with your life as a whole these days?
Using this card on which 1 means you are “completely dissatisfied” and 10 means you are “completely satisfied”
where would you put your satisfaction with your life as a whole?”
85
Results
We use longitudinal data for approximately 1,700 individuals, for 1989-2022, from the World
Values Survey to estimate the marginal utility of consumption, �
�
′
=
−
for a CRRA utility
function, and calculate the value of . We find ranges from 0.3 to 0.4 (Table A.4.3.). We
conduct a robustness check using income ranges, provided in the data for the 1999-2004 survey
wave. We find a similar point estimate of 0.23, which suggests = 0.26.
The relatively low values observed for appear inconsistent with the literature, which finds
estimates approximately close to 1 or greater than 1. This is potentially due to the subjective
nature of questions asked in the survey, which may not yield consistent quantitative estimates
for . Hence, we do not recommend this approach to calculating and the social discount rate.
Table A.4.3. Association between individual’s income category and life satisfaction
Life
Happiness
Life
Happiness
Life
Satisfaction
Life
Satisfaction
Income Scale 0.10
***
0.21
***
0.13
***
0.23
***
(Estimate of �
�
′
) (0.004) (0.040) (0.005) (0.008)
Age -0.01
***
-0.01
***
-0.00
***
-0.01
***
(0.001) (0.003) (0.001) (0.001)
Female -0.04
*
-0.08
*
-0.05
**
-0.07
**
(0.021) (0.047) (0.019) (0.032)
Observations 11,794 11,794 11,665 11,665
Average Daily Consumption
(INR), 2022
270 270 270 270
0.41 0.29 0.36 0.27
Note: Robust standard errors in parentheses. Regressions include language categorical variables. The average
daily consumption is based on a provisional estimate of annual national income per capita of INR 98,374 for
2022-23, published by the Ministry of Statistics and Programme Implementation.
*
p < 0.10,
**
p < 0.05,
***
p < 0.01
86
A.5 Shadow Exchange Rate Factor (SERF), based on alternative method
The NITI Aayog (2018) reported calculated the shadow exchange rate factor using the
following formula:
����=
�
��+
��
�
�
�
(1+�)
+
�
�
(1+)
where �
� is the price elasticity of export supply,
�
is the price elasticity of import demand, �
is the average export subsidy across products, is the average import tariff across products, �
is the total value of exports and � is the total value of imports under protection. We also
calculate the SERF using this alternative method (as applied in NITI Aayog 2018). To do so,
we apply an average import demand elasticity (
�
) and average export supply elasticity (�
�),
estimated by the International Monetary Fund for India and several other countries, using
annual trade data over the 2001-2004 period (Tokarick 2010). Next, we obtain data on the total
values of imports and exports for 2023-24 from the Ministry of Commerce and Industry,
Government of India. We also present the SERF values using this method for the last five years,
i.e. 2019-20 to 2023-24. The results are presented in Table A.5.A below.
Table A.5.A: Shadow Exchange Rate Factor (Alternative Method), 2019-20 to 2023-24
Year
Value of
Imports (INR
Crores)
Value of
Exports (INR
Crores)
Average
Import
tariff (%)
Import
demand
elasticity
Export
supply
elasticity
Average
Subsidy
Rate (%)
SER
F
2019-20 33,60,954 22,19,854 11.2 -1.16 1.21 0 1.5
2020-21 29,15,958 21,59,043 12.6 -1.16 1.21 0 2.0
2021-22 45,72,775 31,47,021 11.3 -1.16 1.21 0 1.6
2022-23 57,49,801 36,21,550 12.0 -1.16 1.21 0 1.5
2023-24 56,16,042 36,18,952 12.0 -1.16 1.21 0 1.5
This method suggests a shadow exchange rate factor of 1.48, which is significantly higher than
the previously calculated value of 1.09, based on the ADB method. An exchange rate factor of
87
1.48 suggests an average foreign exchange premium of 48%, which is inconsistent with the
observed average import tariff of 12% across tradables for India. It is to be noted that this
calculation relies on import demand and export supply elasticities estimated for the 2001-2004
period by the IMF. Since these elasticity values have not been updated over the last two
decades, we would not recommend applying this method to compute the shadow exchange rate
factor for the Indian economy.
A.6 Synthesis of estimates for the Social Cost of Carbon
Table A.6.A: Synthesis of estimates for the Social Cost of Carbon
Study Model / Method Key Assumptions
Social Cost of Carbon
(SCC) (USD/ton CO₂)
Price Base
Moore et al.
(2024)
Meta-analysis (1,823
estimates from 147
studies; includes
DICE, FUND, PAGE)
Parameter values
from expert elicitation
surveys and random
forest synthesis
Mean: $132; synthetic
mean $185 (Interquartile
Range: $97–$369)
2020 US$
Barrage &
Nordhaus
(2024)
DICE-2023 (Dynamic
Integrated Climate–
Economy Model)
Constant discount
rates (1–5%)
$37–$571 (range by
discount rate); $59
(welfare-maximizing
value)
2019 US$
Rennert et al.
(2022)
GIVE (Greenhouse
Gas Impact Value
Estimator)
Risk-free social
discount rate of 2%
Mean: $185 (95%
Confidence Interval: $44–
$413)
2020 US$
Ricke et al.
(2018)
Empirical climate–
economic model
(Burke–Hsiang–
Miguel 2015
framework)
Country-level SCC
(CSCC) using non-
linear temperature-
output link
Global SCC: $417; India
= $86 (range $49–157)
2010 US$
88
Public Investment Programmes/Projects in India
NITI Aayog, Government of India
and
Indian Statistical Institute, Delhi Centre
Authors
Prof. E. Somanathan
Prof. Monisankar Bishnu
Dr. Raavi Aggarwal
October, 2026
NITI STUDY SERIES
Study No. WPS (NITI Aayog)/03/2026
Reassessment of National Parameters for Appraisal
of Public Investment Programmes/Projects in India
Prof. E. Somanathan
Prof. Monisankar Bishnu
Dr. Raavi Aggarwal
Date of Publication: 12/10/2026
Published By;
National Institution for Transforming India (NITI Aayog),
NITI Bhawan, Sansad Marg, Delhi-01
Disclaimer
1. This document is not a statement of policy by the National Institution for Transforming
India (hereinafter referred to as NITI Aayog). It has been prepared by [Prof. E.
Somanathan (Professor, ISI Delhi), Prof. Monisankar Bishnu (Professor, ISI Delhi) and
Dr. Raavi Aggarwal (Consultant, ISI Delhi)] pursuant to the support of NITI Aayog,
for the purpose of independent academic and policy-oriented research.
2. Unless otherwise stated, NITI Aayog, in this regard, has not made any representation
or warranty, express or implied, as to the completeness or reliability of the information,
data, findings, or methodology presented in this document. While due care has been
taken by the author(s) in the preparation of this publication, the content is based on
independently procured information and analysis available at the time of writing and
may not reflect the most current policy developments or datasets.
3. The assertions, interpretations, and conclusions expressed in this report are those of the
author(s) and do not necessarily reflect the views of NITI Aayog or the Government of
India, unless otherwise mentioned. As such, NITI Aayog does not endorse or validate
any of the specific views or policy suggestions made herein by the author(s).
4. NITI Aayog shall not be liable under any circumstances, in law or equity, for any loss,
damage, liability, or expense incurred or suffered as a result of the use of or reliance
upon the contents of this document. Any reference to specific organisations, products,
services, or data sources does not constitute or imply an endorsement by NITI Aayog.
Readers are encouraged to independently verify the data and conduct their analysis
before forming conclusions or taking any policy, academic, or commercial decisions.
Acknowledgements
We would like to thank Shri Ashok Kumar Lahiri, Vice Chairperson, NITI Aayog and
Shri Suman Bery, Former Vice Chairperson, NITI Aayog, Shri Anurag Jain, CEO, NITI Aayog
and Ms. Nidhi Chhibber, Former CEO, NITI Aayog, Shri B. V. R. Subrahmanyam, Former
CEO NITI Aayog, Shri Anurag Goyal, Senior Adviser, PFPA Division, NITI Aayog, Smt. Jyoti
Khattar and Smt. Esha Swaroop, Senior Research Officers, PFPA Division, NITI Aayog,
Ms. Anjali Bansal, Consultant Grade – I, NITI Aayog, Ms. Arpana Bhatt, Consultant Grade –
II, NITI Aayog, Ms. Aakriti, Young Professional, NITI Aayog and Ms. Gargi Rao, former
Research Officer, NITI Aayog for their valuable inputs in the study.
We would also like to thank Prof. Thomas Sterner, Prof. Prachi Mishra, Prof. Mudit Kapoor,
and Dr. Tanu Gupta for useful discussions. Finally, we thank Ms. K. Shreyaswini, Ms. Evelin
Treesa Jose, Mr. Raghav Modi, and Ms. Deepanshi Rai for valuable research assistance. All
errors remain our own.
Foreword
(A practice note on the use of the National Parameters)
1. Public investment decisions across infrastructure, energy, transport, urban services and
social sector programmes are generally appraised using economic cost-benefit analysis,
which requires discounting future streams of economic benefits and costs into present
values. A proposal is acceptable only if the present value of its expected benefits exceeds
the present value of its expected costs. Any such comparison, therefore, requires an
appropriate rate at which future economic benefits and costs are discounted, and that rate
is termed the Social Discount Rate (SDR).
2. Cost-benefit analysis of this kind requires adjustment of the financial or market prices,
since these are distorted by taxes, subsidies, administered wage floors, and other policy-
induced wedges that separate observed prices from the opportunity cost of resources and
the value of benefits to society. Project appraisal, therefore, requires a set of “shadow” or
accounting parameters, or conversion factors, through which market prices can be
converted into estimates of the resource cost of inputs and the economic benefits to society.
Thus, in practice, the Shadow Wage Rate Factor is used for labour, and, depending on
whether costs and benefits are expressed in domestic or world prices, either a Shadow
Exchange Rate Factor or a Standard Conversion Factor is used for traded items. An item-
specific conversion factor is estimated for the non-tradables. In addition, where a project
has material greenhouse gas impacts, a shadow price of carbon is also required.
3. The last comprehensive assessment of these parameters for the country was undertaken by
NITI Aayog through the Institute of Economic Growth (IEG) in 2018. IEG followed the
Ramsey approach to estimate the Social Rate of Time Preference (SRTP) as the Social
Discount Rate (SDR) and recommended an SDR of 8 per cent for projects with a duration
of up to 50 years, 6 per cent for projects with a duration of 50 years or more, and a rate
below 6 per cent for projects with a duration of more than 100 years. The Shadow Exchange
Rate Factor (SERF) was estimated at 1.08. The estimation of the Standard Conversion
Factor and the Shadow Wage Rate for labour was not taken up. Since these parameters are
intended to reflect prevailing economic conditions rather than remain fixed indefinitely,
they require periodic reassessment as new data become available.
4. NITI Aayog engaged the Indian Statistical Institute (ISI), Delhi, to re-estimate these
parameters. ISI has drawn on National Accounts Statistics, the Periodic Labour Force
Survey (PLFS), the Annual Survey of Industries (ASI), KLEMS, Direct Tax Statistics,
trade data and cross-country growth data, together with a review of the methodological
advances in the discounting literature, with particular attention to the Social Discount Rate.
5. Social Discount Rate: The analysis of the Social Discount Rate is particularly involved.
The literature indicates an intense debate over the appropriate method to estimate the SDR,
and whether the SDR should vary with tenure of the projects. Jenkins, Kuo, and Harberger
(2011) list four approaches for estimating the discount rate in public-sector project
evaluation.
a) The first holds that all investment projects, public and private alike, should be
discounted at the marginal productivity of capital in the private sector (Hirshleifer,
DeHaven and Milliman 1960). The rationale, as Jenkins, Kuo and Harberger present it,
is that a government seeking to maximise national output should direct funds to
wherever the return is highest, i.e. where private projects offer a higher expected
economic return than the available public projects, the funds are better left in private
hands.
b) A second approach, developed by Little and Mirrlees (1974), building on the OECD
(1969), and adapted for World Bank use by Squire and van der Tak (1975), employs an
accounting rate of interest (ARI). Jenkins, Kuo and Harberger (2011) characterise the
accounting rate approach as essentially a rationing device that allocates a fixed public
investment budget.
c) A third approach discounts costs and benefits at the Social Rate of Time Preference
(SRTP) for consumption, after converting flows that displace or augment private
investment into their consumption-equivalent values using a shadow price of
investment. Proponents include the UNIDO Guidelines (Dasgupta, Sen and Marglin
1972), Marglin (1963) and Feldstein (1964), with the formal treatment usually
attributed to Bradford (1975).
d) A fourth approach holds that the discount rate should be the Economic Opportunity
Cost of Capital (EOCK): the weighted average of the returns forgone on the sources
from which public funds are actually drawn. In its simplest closed-economy form
(Harberger 1968, reprinted 1972), this is a weighted average of the return on displaced
private investment and the rate of time preference of savers. In an open economy, a
third term is added for the marginal cost of incremental foreign capital. The premise is
that the additional government borrowing required to finance public investment
partially displaces private investment, induces additional domestic saving at the
expense of current consumption, and draws in foreign capital. The SDR is therefore
estimated as the weighted average of the returns forgone from these three sources, with
the weights derived from the interest elasticities of domestic saving, private investment,
and the foreign supply of funds.
6. This report estimates the SDR using two approaches: the SRTP approach using the
Extended Ramsey Rule (the Ramsey rule with a precautionary adjustment for uncertainty
in consumption growth), and the EOCK approach or the weighted-average approach,
following Burgess and Zerbe (2011).
a. Under the Ramsey rule, if consumption per head is expected to rise, a unit of
consumption delivered to a richer future society is worth less at the margin than the
same unit today, so a higher expected growth rate of per capita consumption implies a
higher discount rate. Calibrating that growth rate is difficult. Virmani (2024) puts real
per capita GDP growth (2017 PPP dollars) over 2020–50 at 5.9% per annum in a
conservative case, 6.4% in a median case, and 6.9% in an optimistic one. On the
conservative 5.9% path, ISI estimates an SRTP of 9.4%; and on the average per capita
growth of about 4.7% actually experienced over the past three decades, it estimates
7.3%.
b. EOCK has been calculated using the weighted-average approach, based on the
estimated rate of return to capital in the private sector from the National Accounts
Statistics (NAS) data. Estimates based on broad stock market returns – the NIFTY 500
Total Returns Index – and on ASI data have also been used as cross-checks. The risk-
free rate has been set at the real rate of return on central government securities, and the
interest rate on foreign borrowing has been estimated using annual data from India's
External Debt Status Reports. These estimates, combined with the subcomponent
weights, yield an EOCK of 9.23%.
7. This report recommends the weighted average or the EOCK approach as the basis for the
Social Discount Rate for India for projects of up to 30 years, and the SRTP approach as the
basis for the SDR applicable to longer horizons.
The report compares SDR estimates across various countries and institutions. Among the
25 countries and institutions assessed, 14 have SDR estimates based on the social
opportunity cost of capital (SOC) or weighted average (WA) approach, 9 have estimates
based on the social rate of time preference (SRTP) approach, and 2 have estimates available
under both approaches. A broadly similar pattern appears in Groom et al. (2022), which
reviews 20 countries and institutions: 12 rely on an SOC-based approach alone, 6 on the
SRTP alone, and 2 (Denmark and the United States) draw on both. On either count, the
SOC/WA approach is the more common of the two across the jurisdictions surveyed. The
middle-income jurisdictions appearing in these compilations — Chile, Mexico, Brazil,
Colombia and Peru — use SOC-based rates, most of them following the weighted-average
formulation set out in Harberger (1969); and as of the mid-2000s, most multilateral
development banks applied rates of 10–12% derived on a weighted-average basis (Zhuang
et al., 2007).
This may reflect a judgment about capital scarcity, though the rationale is not elaborated in
the sources. ADB’s 2017 Guidelines for the Economic Analysis of Projects report that the
weighted average approach has been considered the preferred method for empirically
estimating the SDR because it explicitly accounts for market imperfections and credit
constraints on investment.
Moreover, in practice, using the SRTP would require a separate shadow price of capital to
convert the investment component into its consumption equivalent, which is difficult.
Accordingly, the recommendation for the Weighted Average approach for projects with a
tenure of up to 30 years is in line with prevailing practices in comparable economies.
8. One of the terms of reference for the report was to assess whether a single constant discount
rate is appropriate for projects with widely differing life spans, such as environmental and
social sector projects, whose returns accrue over much longer periods.
By construction, discounting places greater weight on nearer-term than on more distant net
benefits. Too high a rate undervalues the long-term social benefits of public investment,
while too low a rate understates the opportunity cost of the funds committed, and so admits
projects that displace higher-yielding uses of the same resources. This matters most where
horizons differ widely: infrastructure and construction projects typically generate the bulk
of their returns within a few decades, whereas investments in education, healthcare and
climate mitigation may yield returns over much longer periods. The calibration of the
discount rate, therefore, shapes the balance of the public investment portfolio between near-
term returns and long-term value.
9. A single constant rate can therefore leave projects whose benefits accrue over several
decades unable to show a positive net present value (NPV) over their lifetime. This is
particularly relevant for the country, given its ambition to become Viksit Bharat by 2047
along with its commitment to achieving Net Zero by 2070. The Viksit Bharat vision, as a
medium-term objective, underscores the importance of prioritising high-return investments
to support higher growth and income levels. The Net Zero 2070 commitment involves
initiatives such as climate mitigation projects that may not appear economically viable due
to their capital-intensive nature and long gestation periods, even though they would deliver
long-term economic benefits.
Several methods are used to accommodate long-term benefits in cost-benefit analysis:
sensitivity analysis to account for uncertainty; differentiated rates, such as a lower rate for
health and environmental benefits; and a declining discount rate applied over the project's
tenure. The ADB Guidelines for the Economic Analysis of Projects (2017) set a minimum
required economic internal rate of return of 9% in general and permit a lower rate of 6%
for social sector projects and for projects that primarily generate environmental benefits.
One reason is that many environmental protection and conservation projects have long-
term impacts.
Thus, while practice varies across jurisdictions, the guiding principle should be that
whatever is adopted remains simple enough to apply consistently in routine cost-benefit
analysis. The 2018 assessment also adopted a declining schedule.
The current report acknowledges the difficulty of calibration and states that the choice of a
specific declining schedule is a matter of practicality rather than theory. It further states
that for very long horizons, the Ramsey approach provides a more robust and theoretically
grounded basis for the SDR. The literature points in the same direction: over long horizons,
the appropriate weighted-average rate converges on the consumption rate of interest (Li
and Pizer 2021)
3
.
3
https://www.nber.org/system/files/working_papers/w25413/revisions/w25413.rev0.pdf
Using the Ramsey rule for longer time horizons, the report recommends a declining
schedule for the social discount rate: 6.2% (30-50 years), 4.8% (50-75 years), and 3.4%
(75-100 years).
The extant practice has been to apply a single hurdle rate to all projects, together with a
sensitivity analysis for uncertainties such as inflation projections. Going forward, it is
suggested that for projects with a tenure exceeding 30 years, either of two approaches may
be adopted, depending on the project profile: the sensitivity analysis just described, as at
present, or a declining discount rate (DDR) schedule applied over the longer duration.
Where it is used, the appraisal should require that the project generate a non-negative
economic net present value under the applicable schedule over its full horizon.
10. Shadow Exchange Rate Factor (SERF), Standard Conversion Factor (SCF) &
Shadow Wage Rate Factor (SWRF):
All projects use inputs or produce outputs that can either be tradable or non-tradable. Non-
tradables are goods whose prices are primarily determined domestically, whereas the prices
of tradables are largely set internationally. Examples of tradables include importable and
exportable commodities such as steel, wood, iron, and chemicals. Examples of non-
tradables include electricity, water, all public services, construction, real estate, local
transport, hotel accommodation, and low-value/high-bulk goods such as gravel, for which
freight makes export unprofitable. For the reasons set out in para 1 above, the financial
prices at which these items are bought and sold cannot be used as such; each must be
converted to an economic value.
a) The Shadow Exchange Rate is the economic price of foreign exchange expressed in
domestic currency. The Shadow Exchange Rate Factor (SERF) is the ratio of the
Shadow Exchange Rate to the Official Exchange Rate. This is typically above unity
due to tariffs and other distortions. The value derived in this report is 1.09. This is
marginally higher than the 1.08 estimated in the 2018 study.
b) Likewise, the economic prices of tradables and non-tradables must be estimated after
removing distortions such as taxes, subsidies and price controls. For tradables, the
principal distortion is trade taxes. To simplify the analysis, a Standard Conversion
Factor (SCF) is sometimes used in place of item-specific adjustment: it converts the
financial price to its international market-price equivalent, adjusting for trade taxes. The
value estimated in this report is 0.92. Where an item accounts for a small share of total
cost, or where item-specific information is not available, the SCF is an adequate
approximation. The costs of transport and distribution between the border and the
project must, however, be added separately to arrive at the economic cost or benefit.
c) Non-tradables, when used as inputs to a project, should be valued at their marginal
economic cost of supply; and as outputs of a project, these should be valued at the
willingness to pay or at the alternative cost of supply (if the project is an alternative
source of supply of the non-tradable). For instance, in the case of power projects,
economic value is the alternative cost of generating an equivalent flow of energy by
some standard means.
This report mentions that the conversion factor for non-tradables is 1, in line with the
ADB guidelines (2017). However, it should be clarified that this conversion factor of 1
only indicates that the price is set in the domestic market. It does not state that the
domestic price is not distorted. As such, commodity-specific conversion factors are
preferred for non-tradables.
d) The shadow wage rate factor (SWRF) is the ratio of the Opportunity cost of labour to
the wage the project actually pays. Actual wages differ from the opportunity cost of
labour because of complex issues related to unemployment and labour market rigidities.
When involuntary unemployment or underemployment exists, workers are likely to
accept a lower wage rather than remain unemployed. However, it is also incorrect to
treat the opportunity cost of employing labour that would otherwise be unemployed as
nil. It is also incorrect to assume that a reduction in unemployment equals the number
employed in the project, as some of the labour is likely to be displaced from other
employment. As such, the treatment of labour costs depends on the nature of the project.
However, for simplicity, a standard wage-rate factor can be used. For scarce or skilled
labour, SWRF can normally be taken as 1.0.
This report estimates the SWRF for unskilled labour using the Periodic Labour Force
Survey (PLFS) and minimum wage notifications, disaggregated by state, sector, and
gender. The estimated SWRF is 0.86. It should be clarified, however, that where labour
is a large share of costs, or where workers are a key beneficiary group, a project-specific
SWRF based on local labour market analysis is required, and the state-specific
estimates should be used in preference to the national figure; the national value is an
approximation for simplified appraisal only.
The practical guidance on the use of the conversion factors is summarised in the table
below:
Category Treatment
Traded items valued at world prices,
converted at the official exchange rate
Multiply by SERF
Non-traded items valued at domestic prices
or WTP
Multiply by 1.00 (or use the commodity-
specific CF if there are significant
distortions like subsidies in the domestic
market)
Tariffs, indirect taxes, subsidies on the item Removed, as these are transfers
Labour — unskilled or in surplus supply
(skilled or scarce labour: 1.00)
Multiply by the applicable SWRF, using
the state-specific value where labour is a
material share of cost
11. Social cost of carbon (SCC): The social cost of carbon is used in appraisal practice to
account for the externalities associated with carbon emissions in a project. Broadly, two
distinct constructs emerge regarding what the social cost of carbon represents, i.e., whether
it measures damages or abatement costs.
The damage-based measure is the present value of future societal damages from emitting
an additional tonne of CO₂ today. This is the construct underlying the ADB, Canadian and
US guidance on cost-benefit analysis. This report also suggests a value of US$10 per tonne
of CO₂, using a damage-based measure that accounts only for damages incurred within
India.
12. The abatement-cost measure is the marginal cost of abating an additional tonne along a
least-cost path to a stated climate goal. This is the construct underlying the cost-benefit
guidance of several European countries and institutions, such as the UK, the EIB, and the
World Bank.
13. In this context, the recent launch of a Carbon Credit Trading Scheme, 2023, under the
Energy Conservation Act, 2001, as amended in 2022, is relevant. It adopts an emission-
intensity-based model for Carbon Credit Certificates (CCCs). The CERC’s 2026
regulations provide that CCCs are to be traded through power exchanges within a floor
price and a forbearance price. The CCC price should therefore serve as a proxy for the
abatement-cost measure of the social cost of carbon in the regulated sectors, once trading
matures, and the price is formed above the floor. However, it is recommended that a single
carbon shadow price be applied to all project emissions in both covered and uncovered
sectors. Accordingly, it is suggested that the same may also be used as the carbon price in
project appraisal. The report also recommends that a separate study be undertaken to
empirically determine the country-specific cost of carbon.
14. It is clarified that receipts from the sale of CCCs and payments for their purchase are cash
flows to be used in the financial analysis. These are, in effect, transfers between residents
and should not be included in the economic analysis. The project's residual emissions must
still be valued as an externality in the economic analysis.
15. To sum up, the values indicated in the table below are recommended for the national
parameters based on the current report, after rounding for practical use in cost-benefit
analysis:
Parameter Recommended Value
Social Discount Rate (< 30 years) 9.50%
Social Discount Rate (30-50 years) 6.50%
Social Discount Rate (50-75 years) 5%
Social Discount Rate (75-100 years) 3.50%
Standard Conversion Factor (SCF) 0.92
Shadow Exchange Rate Factor (SERF) 1.09
Shadow Wage Rate Factor (SWRF) - Total 0.86
Shadow Wage Rate Factor (SWRF) - Male 0.88
Shadow Wage Rate Factor (SWRF) - Female 0.82
SCC (not accounting for damages outside India) US$ 10/tCO2e
4
Where a declining discount rate is used, each year’s net flow should be discounted at the
rate applicable to the period in which it falls, rather than the whole stream being discounted
at a single rate selected by reference to the project’s total life. Applying a single lower rate
to every year of a long-lived project would create a discontinuity at the 30-year boundary
and an incentive to specify a longer appraisal period than the project warrants. In such
cases, the test of viability is a non-negative economic net present value, rather than a
comparison of an economic rate of return with a single hurdle rate.
16. In conclusion, the discount rate tests whether a project earns more than its funds could earn
elsewhere. While passing that test means the project is worth undertaking, it does not
establish that the limited budget could not have been used better elsewhere. The objective
should therefore be to select the combination of projects that yields the highest total net
present value within the available budget, rather than simply accepting every project that
clears the discount rate. In practice, ranking is difficult because projects reach appraisal at
different times and in varying states of readiness. A rough ordering can nevertheless be
built from whatever determines returns in a sector — say, projected traffic in transport —
but only where forecasts follow a common, independently set standard, since demand
forecasts prepared by project proponents tend towards optimism. Project readiness, land
availability and strategic priorities also matter and can override economic ranking; in such
cases, the specific reasons should be recorded.
The parameters estimated here — the social discount rate, in the form of the economic
opportunity cost of capital for shorter horizons and a Ramsey-based declining schedule for
longer ones; the shadow exchange rate factor and its reciprocal, the standard conversion
factor; the shadow wage rate factor; and the shadow price of carbon — help establish
whether a project is worthwhile in national economic terms and allow projects across
sectors to be compared on a common basis. Both uses require that the parameters be applied
consistently and revised as the economy changes.
(Anurag Goyal)
Sr Adviser
Public Finance & Policy Analysis Division,
NITI Aayog
4
tonne of carbon-dioxide equivalent
1
Executive Summary
Background
Public investment is a central instrument through which India advances its long-term
development objectives. Large-scale expenditures on infrastructure, energy systems, transport
networks, urban services, and social programmes require a rigorous appraisal framework that
can determine whether the present value of economic benefits from a project exceeds its
economic cost. Such appraisal cannot rely solely on financial prices, because market prices
incorporate taxes, subsidies, administered wage floors and other policy-induced distortions that
cause them to diverge from the underlying opportunity costs of resources. Economic appraisal
therefore requires translating financial magnitudes into economic values using parameters such
as discount rates, conversion factors, shadow wage rates, and the social costs of carbon which
measure climate damage valuations.
The last comprehensive national assessment of these parameters was conducted by NITI Aayog
in 2018, which provided estimates for use in public project appraisal. The study recommended
a social discount rate of 8 percent for projects with horizons up to 50 years, with a lower rate
of 6 percent for long-gestation infrastructure and environmental projects. It further suggested
rates below 6 percent for projects extending beyond 100 years. It also estimated a 10 percent
rate of return on capital, recommended as the hurdle rate for financial analysis, and identified
an 8 percent foreign-exchange premium reflecting the gap between the economic value and the
market price of foreign currency.
Since the 2018 assessment, new rounds of official data and methodologies offer a stronger
empirical foundation for revising the parameters used in economic appraisal. Since these are
intended to reflect prevailing economic conditions, the parameters require periodic
reassessments. The present study re-evaluates the parameter values for the social discount rate,
standard conversion factor and shadow prices using recent datasets and new methodological
frameworks, which build on the previous assessment by NITI Aayog conducted in 2018.
Objectives of the Study
The objectives of this study are to provide updated estimates of the five parameters required
for the economic appraisal of public-sector projects in India, which include:
2
(i) Social Discount Rate (SDR): This measures the societal trade-off between present
consumption and future consumption. It is used to discount the future stream of benefits
generated from public investments undertaken today. Projects with long timespans are
sensitive to future economic growth rates, which impact the social discount rate. Thus,
we estimate social discount rates for projects with differing lifetimes, based on the latest
methodologies in the discounting literature.
(ii) Standard Conversion Factor (SCF): It is estimated by comparing domestic market
prices of tradable goods with their border-price equivalents and is used to convert
financial costs of traded inputs into economic costs that exclude the effects of import
duties. An SCF value below 1 indicates that domestic market prices of tradable goods
exceed their economic (border-price) values, largely due to import duties. This
adjustment is relevant for costs of imported inputs in project evaluation, since this can
tilt the cost-benefit ratio for public projects that rely on imported inputs relative to
domestic inputs.
(iii) Shadow Exchange Rate Factor (SERF): It adjusts the market exchange rate to reflect
the economic cost of foreign exchange. The SERF incorporates the impact of import
tariffs and subsidies that create a wedge between domestic and border prices.
(iv) Shadow Wage Rate Factor (SWRF): It is estimated by comparing observed wages from
the PLFS with statutory minimum wages notified for unskilled labour. In many states,
minimum wages exceed prevailing market wages, causing financial labour costs to
overstate the economic opportunity cost of labour. The SWRF adjusts for this
divergence by valuing unskilled labour at market-determined wages.
(v) Social Cost of Carbon (SCC): It represents the present value of economic damages
associated with an additional tonne of CO₂ emissions and is derived from long-horizon
climate-damage modelling studies. The study compiles global SCC estimates to
provide an approximate value of the social cost of carbon for India that can be applied
in the economic appraisal of public projects.
These updated parameters aim to provide a consistent and empirically grounded basis for
evaluating the economic viability of public-sector projects.
3
Scope
The study covers the conceptual rationale, empirical estimation, and application of each
parameter within India’s cost–benefit analysis framework. It adopts the Little and Mirrlees
(1974) accounting-price approach, which recognises that market prices, which are affected by
taxes, subsidies, tariffs, and labour-market rigidities, may diverge from economic values.
The analysis relies exclusively on official Government of India datasets, including the National
Accounts Statistics, Household Consumer Expenditure Survey, Annual Survey of Industries,
Periodic Labour Force Survey, and administrative data from the Reserve Bank of India,
Ministry of Finance, and Ministry of Commerce and Industry. These datasets provide the
empirical basis for estimating the parameters in a manner consistent with India’s current
macroeconomic structure and institutional context.
Methodology
The methodological approach is parameter-specific and grounded in established economic
theory.
For the social discount rate, the study tests various approaches and applies the Ramsey rule,
which determines the discount rate by estimating the trade-off between present and future
consumption. This is based on the degree of inequality aversion and the expected future
economic growth rate for India. We estimate the inequality-aversion parameter using the equal-
sacrifice principle, and derive long-run economic growth from past trends in per-capita GDP.
The extended Ramsey rule is used to incorporate the effect of uncertainty in future economic
growth, for downward adjustment of the social discount rate for long-horizon projects.
The social discount rate is also computed based on estimated market-based rates of return such
as the social opportunity cost of capital and the weighted average approach. These methods
estimate the real returns to government securities, the private sector’s marginal product of
capital which is estimated using data from the Annual Survey of Industries, and a weighted-
average financing-cost measure that reflects domestic and external borrowing conditions. This
combined approach provides a consistent basis for determining discount rates for projects with
different time horizons.
4
The Standard Conversion Factor (SCF) is estimated by comparing domestic market prices of
traded goods with their border-price equivalents, after adjusting for import duties in import
values. Export values, already recorded at border prices, are taken as reported. These import
and export ratios are then aggregated across product categories to obtain an economy-wide
SCF. An SCF below 1 indicates that domestic market prices are higher than economic (border)
prices due to border taxes, which implies that using financial prices would overstate the true
economic costs of tradable inputs.
The Shadow Exchange Rate Factor (SERF) measures the ratio of the economic price of foreign
currency to its market price and is obtained as the reciprocal of the Standard Conversion Factor
(1/SCF). This reflects the foreign-exchange premium after removing import duties and other
trade-related distortions, based on product-level trade and tariff data.
The Shadow Wage Rate Factor (SWRF) is estimated using wage data from the Periodic Labour
Force Survey (PLFS) for unskilled workers in rural and urban areas. Since market wages reflect
the economic opportunity cost of labour, the study compares these observed wages with the
statutory minimum wages notified by the Central Government through the Chief Labour
Commissioner, for employment under the central government’s jurisdiction. For occupations
where minimum wages exceed actual market wages, common for agricultural labour in rural
areas and informal workers in urban areas, the minimum wage would overstate the economic
cost of labour, and the SWRF adjusts this downward by taking the ratio of market wages to
minimum wages. This approach yields opportunity-cost-based labour valuations suitable for
economic appraisal of public projects.
Lastly, the Social Cost of Carbon is compiled from global studies which estimate the economic
damages associated with incremental CO₂ emissions, applying discount rates that are consistent
with long-run time horizons.
Key Findings
The mean Social Discount Rate for projects with a time horizon up to 30 years is 9.23 percent
based on the weighted average approach, with various methods yielding a range of 7.3 – 11
percent. For longer project horizons, we recommend using the uncertainty-adjusted Ramsey
approach such that the social discount rate declines to 6.2 percent (30–50 years), 4.8 percent
(50–75 years), and 3.4 percent (75–100 years).
5
The Standard Conversion Factor is estimated at 0.92, indicating that domestic prices for
tradable goods exceed their economic values once duties and taxes are removed. The
corresponding Shadow Exchange Rate Factor is 1.09, implying a foreign-exchange premium
of approximately 9 percent. The Shadow Wage Rate Factor is estimated at 0.86 for unskilled
labour, with average values of 0.88 for men and 0.82 for women, reflecting wage distributions
observed in PLFS data. Lastly, the Social Cost of Carbon for India is estimated at USD 10 per
tonne of CO₂, with a broader evidence-based range of USD 9–87 per tonne.
Key Policy Extracts and Indicative Ministries
The updated parameters have implications for ministries involved in public investment
planning and appraisal. The SDR is relevant for the Ministry of Finance, NITI Aayog, and
sectoral ministries preparing long-duration project proposals for appraisal by the Public
Investment Board and Expenditure Finance Committee. It is particularly applicable to
infrastructure, energy, irrigation, and environmental projects.
The SCF and SERF provide a consistent valuation basis for traded goods and foreign-exchange
components in capital-intensive sectors, including commerce, industry, transport, ports, power,
and renewable energy. These parameters ensure that project costs reflect economic rather than
financial prices.
The SWRF is applicable to labour-intensive programmes under the Ministry of Labour and
Employment, Ministry of Rural Development, and state governments implementing public
works and construction projects.
The SCC offers an estimate of the economic damages associated with an additional tonne of
CO₂ emissions and can be used in project appraisal where valuation of climate-related
externalities is required.
Conclusion and Implications
These updated parameters provide an improved analytical foundation for public investment
decisions undertaken by the Government of India. By ensuring that project benefits and costs
are assessed at economic rather than market values, the revised estimates reinforce the
credibility of appraisal exercises and support more efficient allocation of public resources.
Their systematic use will help ensure that major public investments are evaluated on a
consistent basis, strengthening the quality of India’s development planning.
6
Table of Contents
1. Introduction .................................................................................................................. 8
1.1. Objectives .................................................................................................................... 8
1.2. Social Discount Rate ...................................................................................................... 9
1.3. Accounting (Shadow) Prices ......................................................................................... 10
1.4. Social Cost of Carbon .................................................................................................. 10
1.5. Reassessment of parameters from NITI Aayog (2018) report ............................................ 11
2. Social Discount Rate: Methods and Results .................................................................... 11
2.1. Literature Review on Social Discount Rate ..................................................................... 12
2.2. Methodologies to compute the Social Discount Rate ........................................................ 14
2.2.1. Ramsey Social Discount Rate ....................................................................................... 15
2.2.2. Market Rates of Return to Capital ................................................................................. 27
a) Real Return on Government Securities ........................................................................... 27
b) Social Opportunity Cost of Capital ................................................................................ 27
c) Weighted Average Approach ........................................................................................ 32
2.2.3. Comparison of Social Discount Rates ............................................................................ 35
3. Shadow Prices ............................................................................................................ 38
3.1. Literature Review on Shadow Prices .............................................................................. 38
3.2. Standard Conversion Factor: Methodology and Results .................................................... 39
3.3. Shadow Exchange Rate Factor: Methodology and Results ................................................ 44
3.4. Shadow Wage Rate Factor: Methodology and Results...................................................... 47
4. Social Cost of Carbon .................................................................................................. 60
4.1. Global SCC values ...................................................................................................... 61
4.2. Country-specific SCC values ........................................................................................ 64
5. Recommendations ....................................................................................................... 65
6. References .................................................................................................................. 68
A.1. Derivation of the Ramsey rule ....................................................................................... 74
A.2. Social Opportunity Cost of Capital Approach ................................................................. 76
A.3. Weighted Average Approach ........................................................................................ 79
A.4. Other approaches to estimating ................................................................................... 80
A.4.1. Euler equation approach ............................................................................................... 81
A.4.2. Frisch approach ........................................................................................................... 82
A.4.3. Subjective well-being approach ..................................................................................... 84
A.5 Shadow Exchange Rate Factor (SERF), based on alternative method ................................. 86
A.6 Synthesis of estimates for the Social Cost of Carbon ....................................................... 87
7
List of Tables
Table 1: Synthesis of parameter estimates for social discount rate....................................................... 19
Table 2: Average incomes, income taxes, average tax rates and marginal tax rates by income category,
assessment year 2023-24 ......................................................................................................... 23
Table 3: Estimate of the elasticity of the marginal utility of consumption (η) ..................................... 24
Table 4: List of countries for computing variance in the growth rate ................................................... 27
Table 5: Term structure of discount rates, with uncertainty adjustment in growth rates ...................... 29
Table 6: Estimating the Marginal Product of Capital ........................................................................... 33
Table 7: Social Discount Rate – Weighted Average Approach ............................................................ 37
Table 8: Comparison of Social Discount Rates across approaches ...................................................... 37
Table 9: Synthesis of parameter estimates for SDR across countries for various methods .................. 39
Table 10: Standard Conversion Factors, by HS 2-Digit Products ........................................................ 44
Table 11: Shadow Wage Rate Factors (SWRF) for unskilled labour, 2023-24 .................................... 52
Table 12: Average daily wage for unskilled labour, by rural and urban areas, 2023-24 ...................... 54
Table 13: Shadow wage rate factor for male unskilled workers, by States/UTs, 2023-24 ................... 55
Table 14: Shadow wage rate factor for female unskilled workers, by States/UTs, 2023-24 ................ 56
Table 15: Shadow Wage Rate Factors (SWRF) for unskilled labour (2019-2020) .............................. 58
Table 16: Shadow Wage Rate Factors (SWRF) for unskilled labour (2020-2021) .............................. 59
Table 17: Shadow Wage Rate Factors (SWRF) for unskilled labour (2021-2022) .............................. 61
Table 18: Shadow Wage Rate Factors (SWRF) for unskilled labour (2022-2023) .............................. 62
Table 19: Updating of national parameters since NITI Aayog (2018) ................................................. 71
List of Figures
Figure 1: Sector-specific SCC estimates from empirical studies vs. IAMs .......................................... 67
8
1. Introduction
This study aims to assess key parameters for appraisal of public sector investments undertaken
by the Government of India. The Government’s budget allocation towards diverse sectors of
the economy aims to maximise the present value of economic benefits, net of costs, that will
accrue to society on account of public sector investments.
1.1. Objectives
This study will extend previous analyses of parameters for project appraisal conducted by the
NITI Aayog (2018). We will estimate the following parameters used in cost-benefit analysis:
1. Appropriate Discount Rate to be used as a hurdle rate for public investments. It should
include recommendations on whether it is appropriate to use the same hurdle rate in
financial as well as economic analysis. It should also include recommendation on
whether to use different hurdle rates for projects with different lifespans over which the
returns are expected such as the large hydro power and irrigation projects, or for
projects which do not have very well-defined financial returns such as the
environmental and social sector projects.
2. Shadow exchange rate factor (SERF) - Ratio of economic price of foreign currency to
its market price.
3. Standard conversion factor (SCF) - Ratio of economic price value of all traded goods
in the economy at their border price equivalent values to their domestic market price
values.
4. Shadow wage rate factor (SWRF), for Unskilled labour, both in rural and urban areas.
5. Social cost of carbon (SCC) - net present value of climate change impacts over the next
100 years (or longer) of one additional tonne of carbon emitted.
We conduct a detailed literature review of the latest methodologies applied in estimating these
parameters and evaluate methods appropriate for estimation in the Indian context.
In estimating these parameters, we analyse several databases provided by the Ministry of
Statistics and Programme Implementation (MOSPI), Government of India, including inter alia,
9
the National Accounts Statistics, the NSSO’s Household Consumer Expenditure Survey,
several rounds of the Annual Survey of Industries and the Periodic Labour Force Survey. We
further draw on databases provided by the Reserve Bank of India (RBI), Ministry of Finance
and Ministry of Commerce and Industry, Government of India.
In the subsequent sections, we briefly describe each of the parameters for re-assessment in this
study and highlight their importance in cost-benefit analysis in the public sector.
1.2. Social Discount Rate
The social discount rate measures the rate at which individuals in society are willing to trade
present consumption against future consumption. The social discount rate is applied in project
appraisal in the public sector to evaluate the present value of net benefits that are expected to
accrue from a public sector investment over the lifespan of the project. The present value of
expected lifetime benefits from the project is compared to the current cost of incurring the
project. If the present value of expected benefits exceeds the current cost of the project, it is
economically feasible and socially beneficial to undertake the investment. In this context, the
social discount rate may be referred to simply as the “discount rate.”
The social discount rate plays a key role in cost benefit analysis (CBA) in the public sector, as
it measures the annual rate at which expected future benefits are to be discounted, to obtain
the present value of benefits from the project. The social discount rate differs from the rate of
return on investments undertaken in the private sector, as the former captures the full range of
economic costs and benefits that may accrue to all individuals in society, whereas the latter
reflects only the private rate of return to actors in the economy. When the government aims to
maximise social welfare (i.e. welfare of all individuals in society), it is the social discount rate
which ought to be applied in cost-benefit analysis in the public sector.
10
1.3.Accounting (Shadow) Prices
Measuring the costs of a public sector programme involves the financial costs and the economic
costs. While financial costs are measured at market prices (such as budget allocation towards
a project at current prices), economic costs also measure the opportunity costs of the project,
in terms of the loss in social welfare from an alternative investment. Hence, economic costs
measure the financial costs and the trade-off associated with funds being allocated to a specific
project vis-à-vis to other projects.
Cost-benefit analysis of public sector projects ought to be undertaken at the economic costs of
the factors of production, such as raw materials (produced domestically and imported), labour
costs and the cost of capital. Little and Mirrlees (1974) refer to the economic or “shadow”
prices for factors of production as “accounting prices.” These accounting prices reflect the
opportunity cost of the various factors of production, which may not necessarily be reflected
in the observed market prices (which also comprise indirect taxes on goods and services).
In this study, we compute the (i) shadow exchange rate factor, which is used to calculate the
shadow or “accounting” exchange rate, (ii) standard conversion factor, which is used to
measure tradables at accounting prices, and (iii) shadow wage rate factor for unskilled labour,
which reflects the opportunity cost of labour.
1.4. Social Cost of Carbon
The social cost of carbon (SCC) measures the monetary damage to society from an additional
ton of carbon dioxide (CO2) emission. Given high potency of greenhouse gases such as CO2,
the SCC is typically measured over long timescales of over 100 years. The expected damages
from increases in temperature associated with rising CO2 concentrations are then discounted
each year to obtain the net present value of damages from additional CO2 emissions. Rennert
et al. (2022) compute the SCC using simulations of potential damages due to higher CO2
concentrations over a 300-year timescale, applying a social discount rate of 2% per year. We
conduct a detailed literature review and provide a range of estimates for the social cost of
carbon for the Indian context.
11
1.5.Reassessment of parameters from NITI Aayog (2018) report
▪ A social discount rate of 8% was recommended for short-term projects (with a duration of
up to 50 years).
▪ For projects related to environment and infrastructure with a duration of more than 50 years,
a social discount rate of 6% was recommended.
▪ It was recommended that for projects with a duration of more than 100 years, the social
discount rate should be lower than 6%.
▪ The rate of return on capital was estimated at 10% using data from the Annual Survey of
Industries. This was the recommended internal rate of return to be used as a hurdle rate in
financial analysis.
▪ A social premium of 8% on foreign exchange was recommended.
2. Social Discount Rate: Methods and Results
The literature on cost-benefit analyses of public sector projects dates to the 1970s, where Little
and Mirrlees (1974) and Dasgupta, Marglin and Sen (1972) developed techniques for project
appraisal, specifically for developing countries. Harberger (1972) and Marglin (1967) also
provided frameworks for project appraisal for the case of India, in collaboration with the
erstwhile Planning Commission.
These frameworks discussed the key role of shadow prices, which are used to determine the
full economic costs and benefits of programmes, extending beyond the financial costs and
benefits. Dasgupta and Pearce (1972) and Drèze and Stern (1987) provided comprehensive
social welfare frameworks, within which to evaluate the optimal allocation of public sector
funds to various projects, considering their impacts on individual and social welfare.
12
2.1. Literature Review on Social Discount Rate
Policymakers face trade-offs between allocation of public funds across diverse projects.
Projects related to infrastructure and construction may yield a high rate of return, as they
generate immediate economic benefits (Little and Mirrlees 1974). On the other hand, projects
which expand access to education, healthcare and environmental services may only generate
benefits over a longer time horizon (Groom et al. 2022; Marglin 1967). Therefore,
policymakers create a portfolio of projects, with public sector investments spread across
sectors, offering different rates of return.
In evaluating these trade-offs, the social discount rate becomes highly pertinent (Dasgupta
2008). An excessively high social discount rate would underestimate the long-run social
benefits of public investments and lead to sub-optimal investment in public programmes. On
the other hand, a relatively low social discount rate would understate the benefits of
consumption in the immediate future and lead to inefficient public spending. Investments in
high-return projects could generate immediate revenues for the public sector which could be
invested in generating long-term societal gains. The level of the social discount rate is therefore
key to generating an optimal portfolio of public sector investments.
Accumulation of human capital via investments in healthcare and education would not only
generate welfare gains to individuals, but also confer benefits to society through positive
externalities (Aghion and Howitt 2008). An example is knowledge spill-overs through R&D
investments, which can stimulate economic growth and create productive jobs in the economy.
Non-optimal human capital may also result from consumption externalities, i.e. when one’s
consumption is affected by the consumption level of others in society (Bishnu 2013). The latest
advances in macroeconomic theory highlight the importance of technological progress in
bringing about economic growth, particularly in the context of developing countries, which
typically exhibit sub-optimal levels of investment (Aghion and Howitt 2008). Hence, research
and development activity requires government subsidies to ensure optimal levels of knowledge
creation and economic progress.
In contrast to the discount rate, the hurdle rate is applied in financial analysis as the minimum
rate of return on investments by private firms. As the OECD recommends, governments ought
to apply the social discount rate for project evaluation and for selection of projects (Coleman
2021). While governments may conduct financial analysis to evaluate certain investments by
13
the private sector, such as in public-private partnerships, governments are advised to apply the
social discount rate for project selection and evaluation (Perkins 1995).
The social discount rate can be computed based on two broad approaches. The first approach
is based on the Ramsey rule, which is derived by asking what is the optimal saving rate for
society each year, accounting for the future expected economic growth rate of consumption
and the degree of inequality aversion in society (NITI Aayog 2018; Ramsey 1928; Dasgupta
2008). This is explained further in Section 2.2.1.
The second approach to calculating the social discount rate is based on market rates of return
to capital. This can further be sub-divided into three methods. The first method measures the
social discount rate as the real rate of return on government securities which are relevant for
consumers’ savings decisions. This method is used by the United States’ Office of Management
and Budget (OMB) to calculate social discount rates for the U.S. economy (US OMB 2023).
The second method measures the real rate of return to capital in the economy, which is also
known as the social opportunity cost of capital (SOC) (Harberger 1972). The social opportunity
cost of capital can be measured as the real interest rate on loans. It can also be measured as the
productivity of capital, or the marginal addition to output from an incremental rise in the capital
stock in firms. The third method calculates the social discount rate as a weighted average of
the discount rates obtained in the above two methods – (i) the rate of return to government
deposits and (ii) the market rate of return to capital), and (iii) the cost of foreign borrowing by
the Government (Harberger 1972; ADB 2017; Zhuang et al. 2007).
In the previous assessment, the recommended real social discount rate of 8% was based on the
Ramsey rule (NITI Aayog 2018). Sensitivity checks using different methods had been
conducted to ensure robustness of the proposed discount rate. A recent assessment by
NABARD finds a relatively lower value of the social discount rate of 4.5% in real terms
(Dholakia et al. 2024).
In this study, we review the NITI Aayog’s (2018) assessment and recent studies conducted for
India, to identify the most appropriate methods that ought to be used in computing the social
discount rate by the Government of India. In so doing, we also review the academic and policy
literature for high-income and middle-income countries to draw on the latest guidance by
various country governments.
14
2.2. Methodologies to compute the Social Discount Rate
In this section, we present the two approaches to estimating the social discount rate (sections
2.2.1 and 2.2.2).
The first approach uses the Ramsey rule as the social discount rate for public sector projects.
This is the rate at which individuals trade present consumption against future consumption in
society. This is based on the rate of time preference, the degree of inequality aversion and the
expected future economic growth rate of consumption (Dasgupta 2008; Dholakia et al. 2024;
NITI Aayog 2018; Ramsey 1928). This approach requires an estimate for the inequality
aversion parameter, to compute the social discount rate.
The second approach measures the social discount rate as the real rate of return to capital. This
can be measured in three ways. First, the discount rate can be measured as the long-term real
rate of return on government securities, which reflects a safe rate of return on household
savings. The United States’ Office of Management and Budget (OMB)’s latest guidance
recommends using the real rate of return on government bonds as the social discount rate (US
OMB 2023). The United States has recently revised its social discount rate downward to 2%.
Second, the social discount rate can be measured as the social opportunity cost of capital
(SOC), which reflects the market rate of return to capital (Harberger 1972). This can be
measured as the minimum real lending rate by the Reserve Bank of India to commercial banks,
which reflects the cost of loans to capital owners and thus the rate of return to capital.
The real rate of return to capital can also be measured via a broad stock market index (e.g.
NIFTY 500) over a 30-year time horizon, to reflect the real rate of return on private investments
in the economy. Alternatively, the marginal product of capital measured using firm-level
survey data may best reflect the productivity of capital use in the economy (Burgess and Zerbe
2011). Third, the social discount rate can be measured as a weighted average of the (i) rate of
return on government securities, (ii) the market rate of return to capital (social opportunity cost
of capital) and (iii) the real interest rate on the government’s external borrowing (Harberger
1972; ADB 2017; Zhuang 2007).
15
In this study, we will apply each of the aforementioned methods to provide a range of values
for the social discount rate for short-term projects. In addition to computing the short-term
social discount rate, we will compute the social discount rate for longer-term projects (greater
than 30 years), following the extended Ramsey rule (Gollier 2024; Gollier and Hammitt 2014).
Further, we will adjust for uncertainty in future economic growth and compute the risk-adjusted
social discount rate, which has been adopted in policy guidance in several European countries,
including France, Denmark and Sweden (Groom et al. 2022).
2.2.1. Ramsey Social Discount Rate
The Ramsey rule has been extensively applied as a benchmark method in project appraisal in
several countries (Groom et al. 2022; Dasgupta 2008; Gollier and Hammitt 2014; NITI Aayog
2018). The previous report on project appraisal of the NITI Aayog also used the Ramsey rule
to calculate the social discount rate for cost-benefit analysis in public sector projects (NITI
Aayog 2018). We derive the Ramsey social discount rate from a social welfare maximisation
problem, following Dasgupta (2008).
Approximate Ramsey Rule
Consider a representative consumer who gets utility �(
�), from consuming an amount
� in
period �. The government that seeks to maximise the welfare of the representative consumer
may discount utility from consumption in future periods at rate, δ. This is known as the social
rate of time preference (Dasgupta 2008). The government then seeks to maximise the present
value of lifetime utility, �
0, as follows:
�
0=�(
0)+
�(�1)
(1+�)
+⋯+
�(�
)
(1+�)
+⋯=∑
∞
�=0
�(�)
(1+�)
(1)
From the government’s maximisation problem in equation (1), we can derive the approximate
simple Ramsey rule for the social discount rate.
5
This is stated as follows:
�
≈�+�
� (2)
5
The derivation in presented in Appendix A.
16
The social discount rate,
�
, depends on the (i) growth rate of consumption, �
�, (ii) the social
rate of time preference, � and (iii) the elasticity of the marginal utility of consumption, which
is assumed to be a constant . The elasticity of the marginal utility of consumption measures
the percentage increase in marginal utility from a 1 percent increase in consumption. The utility
function is assumed to be concave, with marginal utility diminishing in consumption, which
are standard assumptions in the economics literature (Mas-Colell et al. 1995). This means that
additional consumption is considered more valuable for individuals who are consuming very
little compared to those who are already consuming a lot. The parameter measures the
curvature of the utility function and the degree of inequality aversion of the government. A
high value for suggests a high degree of inequality aversion. In this case, the government will
discount future consumption at a high rate if it expects positive economic growth, because it
then expects consumption to be higher in the future, so that additional units of consumption in
the future add less to utility than they do for poorer present consumers. Drupp et al. (2018)
conduct a survey of 180 experts on discounting and find the most common reported value of η
= 1.
The social rate of time preference measures the rate at which future utility (not consumption),
is discounted relative to present utility. Since this report is concerned with social cost-benefit
analysis, it is the social rate of time preference that is relevant, not the rate of time preference
used by individuals. For example, older individuals may have a high rate of time preference,
but this is not relevant for social decision-making since they will be replaced by younger
individuals. The Intergovernmental Panel on Climate Change (IPCC) which made a
comprehensive and authoritative assessment of the literature, noted in its 2014 report that there
is “a broad consensus for a zero or near-zero pure rate of time preference” (IPCC 2014).
However, Drupp et al. (2018) reported a median value of the pure rate of time preference, δ =
0.5% in their survey of 180 economic experts on discounting. We thus apply this value to
compute the Ramsey social discount rate for short- and long-term projects.
6
We present
syntheses of estimates of the social discount rate based on the simple Ramsey rule in Table 1
based on Gollier and Hammitt (2014).
6
Some prominent economists (Dasgupta 2008 and Stern 2006) have suggested a value of δ very close to zero,
with Stern (2006) recommending δ = 0.1%. Stern (2006) justifies a positive, rather than zero, value based on the
assumption that there is a very small probability in each period that humanity will cease to exist. Another survey
of 14 philosophers with value judgements on climate policy yields a median value of δ of zero (Nesje et al. 2023).
17
To determine the per capita consumption growth rate, we use estimates of annual per capita
GDP growth rates at constant prices for the period 1993-94 to 2022-23, from the National
Accounts Statistics, Ministry of Statistics and Programme Implementation.
7
We compute the
average annual real GDP per capita growth rate over the last 30 years and apply �=4.7%, as
a minimum annual rate of per capita GDP growth that may be expected over the next 30 years.
Finally, we require an estimate of the elasticity of marginal utility of consumption. We follow
Groom and Maddison (2019) and test various methods to estimate .
Table 1: Synthesis of parameter estimates for social discount rate
Author Inequality aversion, η Growth rate, g Discount rate, ηg
Stern (1977) 2
Cline (1992) 1.5 1% 1.5%
IPCC (1995) 1.5–2 1.6–8% 2.4–16%
Arrow (1999) 2 2% 4%
HM Treasury (2003) 1 2% 2%
Lebègue (2005) 2 2% 4%
Arrow (2007) 2–3
Dasgupta (2007) 2–4
Stern (2007) 1 1.3% 1.3%
Weitzman (2007a) 2 2% 4%
Nordhaus (2008) 2 2% 4%
Pindyck (2013) 1–3
Source: Gollier and Hammitt (2014). Note: These estimates are based on the approximate
Ramsey rule with social rate of time preference, � = 0.
Estimating the elasticity of marginal utility of consumption (η)
Groom et al. (2022) and Gollier and Hammitt (2014) review parameter values for inequality
aversion (η) across countries based on the Ramsey rule. Most of the studies report values of the
inequality aversion parameter around 1, with a consensus around 1.5, based on different
methods of estimation across countries (Groom and Maddison 2019; Del Campo et al. 2024).
7
We apply the growth rate in GDP per capita rather than private consumption expenditure as a better metric for
individuals’ standard of living given lower annual fluctuations in GDP compared to consumption expenditure.
18
Groom and Maddison (2019) outline five different methods which may be used to compute the
elasticity of marginal utility of consumption (η). These are the (i) equal sacrifice approach, (ii)
Euler equation approach, (iii) risk-aversion approach, (iv) Frisch approach and the (v)
subjective well-being approach. Groom and Maddison (2019) test each of these methods and
apply them to the context of the United Kingdom.
We test four of these five methods and compare our results with those from contemporary
studies such as by NABARD (Dholakia et al. 2024) and NITI Aayog (2018). While the study
by NABARD applied the Frisch approach to estimate the discount rate, the previous study by
NITI Aayog applied the equal sacrifice and Euler equation approaches to estimating the social
discount rate. We omit the risk aversion approach due to lack of data in the Indian context to
apply that approach.
In this chapter, we outline and present results from the equal sacrifice approach, which yields
reliable estimates of the elasticity of marginal utility of consumption. The other approaches do
not yield reliable estimates. In particular, we do not recommend the use of the Frisch approach
in computing the social discount rate for public sector projects by the Government of India,
due to unreliable estimates.
We test these approaches using data for the Indian economy and consistent with the literature
(Groom and Maddison 2019), find negative values for in some cases. We also do not
recommend the subjective well-being approach to calculate as this method relies on
assumptions about the individual’s utility function and uses subjective information, rather than
objective data. Lastly, we do not apply the Euler equation approach for project evaluation as it
generates implausibly large estimates from our datasets. This is likely due to sparse data points
available for time series regressions which we use for estimation. We present results from these
other approaches in Appendix A.
Equal sacrifice approach
The equal sacrifice approach to estimating η assumes that the government distributes the
burden of income taxation among people so that each bears the same utility loss as a result of
the tax, given a system of progressive income taxation.
19
Consider a representative individual with income �
and utility from income, �(�
). Define the
tax function, �(�
), as the direct tax paid by individual on income, �
. The equal sacrifice
principle states that the difference in the individual’s utility levels between the pre-tax income,
�(�
), and the post-tax income, �(�
−�(�
)), is equal to a constant, � (Evans 2004). This
holds for all individuals in society where a progressive income tax system is in place. Formally,
the principle states:
�(�
)−�(�
−�(�
))=� ∀ (4)
Following Evans (2004), a formulation can be derived for the elasticity of marginal utility of
consumption, :
=
��(1−��)
��(1−��)
(5)
where �� is the average tax rate, defined as
�(
)
and ��� is the marginal tax rate, defined
as
��(
)
. Intuitively, reflects the degree of inequality aversion. A high average tax rate and
relatively low marginal tax rate, i.e. >1, suggests a high degree of inequality aversion, where
the marginal utility of consumption declines sharply with increasing consumption levels.
Data Sources
To estimate the elasticity of marginal utility of consumption, , we use annual data on “Direct
Tax Statistics” from the Income Tax Department (ITD), for the assessment years, 2012-13 to
2023-24. We use data on average incomes (“Average Salary Income (in lakh INR)”) for each
income category from the annual reports of the “Direct Tax Statistics.”
Next, we obtain information on marginal tax rates (and surcharges) for each tax slab, by year,
from the Annual Finance Bill Memoranda, Union Budgets, for the years 2011-12 to 2022-23.
The assessment years (AY) for the income tax returns follow the financial years (FY), such
that FY 2012-13 corresponds to the AY 2013-14. We apply the marginal tax schedules to the
average incomes reported in each income category to calculate the corresponding tax paid in
20
each category, by year.
8
Subsequently, we calculate average tax rates for each income category,
by year.
Results
In this section, we present results from the equal sacrifice approach. In Table 2, we present
average incomes, average taxes paid, average tax rates (ATR) and the marginal tax rates (MTR)
for all income categories for the assessment year 2023-24, as an illustration.
Based on data for average tax rates and marginal tax rates for each of 22 income categories and
11 years of data, we estimate the elasticity of marginal utility of consumption (). We estimate
a pooled Ordinary Least Squares (OLS) regression, with the constant term suppressed. We
apply frequency weights with the number of returns filed in each income category as weights
for each category.
In this case, a fixed effects estimator is not required since the income categories do not
represent a source of unobserved individual heterogeneity. Further, we cannot include time
controls in the regression as the entire variation in the data used to estimate arises from annual
changes in tax rates.
Table 2: Average incomes, income taxes, average tax rates and marginal tax rates by income
category, assessment year 2023-24
Income Category
Average Income
(INR)
Average tax paid
(INR)
ATR MTR
>0 and <=1,50,000 66,000 - 0.00 0.00
>1,50,000 and <= 2,00,000 1,76,000 - 0.00 0.00
>2,00,000 and <=2,50,000 2,33,000 - 0.00 0.00
>2,50,000 and <= 3,50,000 3,03,000 150 0.00 0.05
>3,50,000 and <= 4,00,000 3,75,000 3,750 0.01 0.05
8
Sample calculation: Consider an average income level of INR 12,05,000. Based on the marginal tax schedule
for the assessment year 2012-13, we apply a zero marginal tax rate for income up to INR 1,80,000, and then
marginal tax rates of 10% for income between INR 1,80,001 – 5,00,000, 20% for income between INR 5,00,001
– 8,00,000 and 30% on income between INR 8,00,001 – 12,05,000. Hence, taxes paid on an average income of
INR 12,05,000 = INR 2,13,500. Thus, the average tax rate is 18%, while the marginal tax rate (on incomes above
INR 8,00,000) is 30%.
21
>4,00,000 and <= 4,50,000 4,26,000 6,300 0.01 0.05
>4,50,000 and <= 5,00,000 4,81,000 9,050 0.02 0.05
>5,00,000 and <= 5,50,000 5,22,000 22,200 0.04 0.10
>5,50,000 and <= 9,50,000 6,99,000 24,900 0.04 0.10
>9,50,000 and <= 10,00,000 9,75,000 56,250 0.06 0.15
>10,00,000 and <=15,00,000 12,06,000 91,200 0.08 0.20
>15,00,000 and <= 20,00,000 17,17,000 2,15,100 0.13 0.30
>20,00,000 and <= 25,00,000 22,25,000 3,67,500 0.17 0.30
>25,00,000 and <= 50,00,000 33,95,000 7,18,500 0.21 0.30
>50,00,000 and <= 1,00,00,000 68,06,000 19,15,980 0.28 0.30
>1,00,00,000 and <=5,00,00,000 1,89,53,000 64,63,080 0.34 0.30
>5,00,00,000 and <=10,00,00,000 6,94,46,000 2,66,93,940 0.38 0.30
>10,00,00,000 and <=25,00,00,000 15,46,05,000 5,99,05,950 0.39 0.30
>25,00,00,000 and <=50,00,00,000 34,95,84,000 13,59,47,760 0.39 0.30
>50,00,00,000 and <=100,00,00,000 69,73,89,000 27,15,91,710 0.39 0.30
>100,00,00,000 and <=500,00,00,000 2,05,81,72,000 80,22,97,080 0.39 0.30
>500,00,00,000 23,81,85,11,000 9,28,88,29,290 0.39 0.30
Overall average 1,23,57,39,318 48,15,98,168 0.17 0.18
Source: Data on average income are from the Direct Tax Statistics, Income Tax Department, and data on
marginal tax rates (MTR) are from the Annual Finance Bill, Union Budget, Government of India. Average
taxes paid and average tax rates (ATR) are calculated for average incomes in each income category.
The regression results are displayed in Table 3, which show an estimate of = 1.8, for the
main specification. Column (2) of Table 3 presents a robustness check using only the last three
years of data on income tax assessments (2021-22 to 2023-24).
Table 3: Estimate of the elasticity of the marginal utility of consumption (η)
ln(1-MTR) (1) (2)
ln(1-ATR) 1.81*** 1.86***
(0.078) (0.158)
Observations 242 66
R
2
0.827 0.833
Robust standard errors in parentheses.
Constant term suppressed.
*
p < 0.10,
**
p < 0.05,
***
p < 0.01
22
Based on parameter values, �=0.5%, =1.8 and �=4.7%, the Ramsey rule yields a social
discount rate (in real terms) of 8.9%. In nearly all studies that apply social discount rates based
on the Ramsey rule (displayed in Table 1), the inequality aversion parameter () takes a value
greater than one. In its 2018 report to NITI Aayog, the Institute of Economic Growth (IEG)
reported an average value of =1.2, based on the equal sacrifice principle and the Euler
equation approach. A recent study by NABARD applies a value of =0.8, based on the Frisch
approach (Dholakia et al. 2024). However, our application of the Frisch approach yields a
negative value for , which is consistent with results from other studies (Groom and Maddison
2019). Thus, we recommend the equal sacrifice approach to estimate and the social discount
rate based on the Ramsey rule.
The expected growth rate of 4.7% is based on historical annual growth rates observed in India
over the last 30 years. Alternatively, we may compute the social discount rate using the
Government of India’s Viksit Bharat targets for 2047, applied to the simple Ramsey rule.
According to NITI Aayog (2024), the Indian economy may be reasonably expected to grow at
5.9% per year in real terms in a conservative scenario. A projected annual growth rate of 5.9%
yields a social discount rate (based on the simple Ramsey rule) of 11.1%. However, the report
mentions a caveat based on observations from other countries’ past growth rates:
“Sustained fast growth is extremely rare; Virmani (2012) showed that there were only a dozen
non-resource rich countries, which had a per capita GDP growth rate of 7% or higher for
more than a decade, of which half sustained it for less than two decades.”
Therefore, we consider the high, Viksit Bharat target growth rate as an upper bound estimate
for a 30-year period and consider a lower average annual growth rate of 4.7% for projects
which last more than 30 years.
Social Discount Rate with uncertainty adjustment (Extended Ramsey Rule)
Public sector investments would also be subject to uncertainty in the future rate of growth of
consumption. External shocks to the economy, for instance due to pandemics, wars or climate
crises, may unexpectedly reduce future GDP and per capita income. To account for uncertainty
in the future rate of economic growth, policymakers ought to consider a risk-adjusted social
23
discount rate for project appraisal. The latest economic research recommends adjusting the
discount rate for uncertainty and volatility in consumption growth, based on the extended
Ramsey rule (Groom et al. 2022; Gollier and Hammitt 2014; Gollier 2024). This is more
important for developing countries that have high and more uncertain growth rates than
developed countries. As uncertainty in the future level of consumption compounds over time,
projects with longer time spans may need to be discounted at lower rates, due to the uncertainty
in future economic growth. A lower social discount rate allows social planners to invest in risk
mitigation measures such as emission abatement technologies (which would reduce economic
damages from climate change) in a cost-effective manner, and thereby insure society against
future risk in consumption.
As an example, consider a pensioner who faces uncertainty in the expected future pension,
which depends on government revenue as a result of future economic growth. If the pensioner
were to receive a certain pension of say, INR 1,00,000 per month, they would experience higher
utility levels than in the uncertain case, where they may receive a pension of INR 50,000 with
probability 0.5 and a pension of INR 1,50,000 with probability 0.5. The second case represents
uncertain future economic growth and in turn, government expenditure. In the latter case, the
policymaker is inclined to apply a lower discount rate for precautionary savings in the event of
lower economic growth and consumption levels in the future, compared to the case of high
economic growth with certainty. This result relies on the convexity of the marginal utility of
consumption, a standard assumption in macroeconomics, which stems from the expected utility
theory (Caballero 1990; Rabin 2000).
The extended Ramsey rule, derived in Gollier (2024), is expressed as follows:
�
≈�+
�−0.5
2
�
�
2
Where
�
is the uncertainty-adjusted social discount rate, � is the social rate of time preference,
is the degree of inequality aversion,
�
is the expected rate of future economic growth
between �=0 and �, and
�
2
is the variance in the expected growth rate.
9
The extended Ramsey
rule assumes that consumption growth (or equivalently, economic growth), over the next t
9
This follows Equation 20 in Gollier (2024). Gollier takes to be zero and has another term accounting for
a possible correlation between future consumption and the returns to a particular public investment
project. Since we are interested in a single discount rate for public projects and it is unclear what the
correlation with future consumption, if any, will be for different classes of projects, we ignore this term.
24
years, follows a normal distribution, so that �
�=
1
�
���� (
�
�0
) ~�(
�,
�
2
). Further, � is the
lifetime duration of the public project, which allows the social planner to compute discount
rates for different project timespans. This results in a term structure for discount rates (Gollier
and Hammitt 2014). This is because for a given level of uncertainty
�
2
in the growth rate
between now and t, the uncertainty in consumption at time t relative to today (
�
0
), is increasing
in t due to compounding. The precautionary motive pushes us to save more, leading to a lower
discount rate. This is less of a problem for developed countries that have a lower variance in
their growth rates.
We compute the term structure for discount rates, accounting for uncertainty in the growth rate.
Existing studies typically use the historical time series of growth rates for a particular country
to estimate the variance in the growth rate (Gollier 2012). However, the observed variance in
a country’s economic growth over the past 30 years is likely to substantially understate the
potential variance in future economic growth. Instead, we draw on other countries’ experiences
to predict potential variance in India’s expected economic growth over the next 30 years.
10
We draw on country-level data on annual real GDP per capita levels and growth rates for 266
countries from the World Bank’s World Development Indicators (WDI) database for the 1960-
2023 period. We construct a comparison group of countries for India based on similarity of per
capita income levels and past economic growth rates. In 2023, India’s per capita GDP stood at
US$ 2,239 (in US$ 2015 constant prices). Further, India exhibited an average annual growth
rate of real GDP per capita of 4.7% between 1993-2023.
We construct the comparison group of countries based on two measures. First, we restrict the
sample to countries that exhibited real GDP per capita levels (in US$ 2015 constant prices) in
the range of India’s GDP per capita +/- 50%, i.e. between US$ 1,120 and US$ 3,359, between
the 1970-1993 period. This large band of per capita incomes ensures a sizeable number of
countries which exhibited similar per capita incomes in the past to India’s present income.
Second, we restrict the sample to countries which also exhibited similar growth rates to India’s
average growth rate +/- 50%, over the preceding 30 years. Specifically, we consider countries
which exhibited average annual growth rates between 2.35% and 7.05% in the preceding time
10
The necessary adjustment for uncertainty in computing the discount rate is smaller for developed countries that
have a lower variance in their growth rates.
25
period, i.e. until 1993. Hence, we observe a sample of 20 countries which exhibited similar per
capita incomes as India’s current income, prior to 1993 and similar economic growth rates as
India’s recent average growth rate, prior to 1993. The list of countries is presented in Table 4.
11
Table 4: List of countries for computing variance in the growth rate
S. No. Country
Initial GDP per capita
(2015 US$, Constant
Prices)
Past GDP per capita
growth rate, % (till
1993)
Subsequent GDP
per capita growth
rate, %
1 Belize 3,233 2.7 1.9
2 China 1,239 5.0 7.6
3 Dominica 3,288 2.9 2.9
4 Dominican Republic 3,179 2.5 3.4
5 Ecuador 3,337 2.4 1.0
6 Egypt, Arab Rep. 2,040 3.0 2.4
7 Eswatini 2,110 3.5 2.3
8 Grenada 3,243 5.7 3.1
9 Indonesia 1,707 3.2 3.0
10 Kyrgyz Republic 1,203 4.1 -0.2
11 Malaysia 3,292 4.5 3.1
12 Maldives 3,275 5.1 3.5
13 Malta 3,212 2.4 5.5
14 Mauritius 3,256 3.1 3.8
15 Morocco 1,668 2.6 2.3
16 Paraguay 3,274 4.1 1.2
17 Sri Lanka 1,488 2.6 3.3
18 Syrian Arab Republic 1,122 2.7 -1.1
19 Thailand 3,167 5.1 2.3
20 Turkey 3,274 2.7 2.3
Source: World Development Indicators, World Bank Group.
Note: Initial GDP per capita (constant 2015 US$) refers to the 1970-1993 period.
11
We select this range of GDP as the minimum range of GDP required to ensure a sufficient sample size of
comparison countries to predict the potential variance in the future economic growth rate for India. We also
conducted this analysis for the interquartile range of GDP. However, that resulted in a very limited set of
comparison countries, which were insufficient to predict the variance in future economic growth for India.
26
Next, we compute the economic growth rates for each of these 20 countries over the subsequent
30-year period from 1993-2023 and record the observed variance in growth rates across
countries. We use this observed variance in growth rates as a reasonable prediction for potential
variance in India’s future economic growth. We observe a range of expected future growth
rates between -1.1% in Syria to 7.6% in China. The resulting term structure of discount rates
is presented in Table 5.
The simple Ramsey social discount rate is 11.1% for an expected economic growth rate of
5.9% over the next 30 years based on the Viksit Bharat 2047 growth projection (NITI Aayog
2024). When this growth rate is adjusted for future uncertainty, the social discount rate is
revised downward to 9.4%. Similarly, for an expected growth rate of 4.7% based on past
performance, the social discount rate for a 30-year time horizon is estimated at 8.9%, based on
the Ramsey rule. Adjusting for future uncertainty reduces this discount rate to 7.3%.
Table 5: Term structure of discount rates, with uncertainty adjustment in growth rates
Social rate
of time
preference
Inequality
aversion
Mean
growth
rate
(India)
Project
Term
Variance in
30-year
growth rates
of other
countries
Simple
Ramsey
discount rate
(%)
Uncertainty
term (%)
Extended
Ramsey
discount
rate (%)
(1) (2) (3) (4) (5) (6) (7) (8)
δ η
� t
�
2
δ+ η
� 0.5
2
t
�
2
�
0.5 1.8 0.059
*
30 0.000344 11.1 1.7 9.4
0.5 1.8 0.047 30 0.000344 8.9 1.7 7.3
0.5 1.8 0.047 50 0.000344 8.9 2.8 6.2
0.5 1.8 0.047 75 0.000344 8.9 4.2 4.8
0.5 1.8 0.047 100 0.000344 8.9 5.6 3.4
Note:
*
This refers to the conservative growth rate scenario over the next 30 years, according to NITI Aayog (2024).
Based on an expected annual economic growth rate of 4.7% and adjusting for future uncertainty
yields the following term structure of social discount rates (corresponding project terms): 7.3%
(< 30 years), 6.2% (30-50 years), 4.8% (50-75 years) and 3.4% (75-100 years). Given potential
uncertainty in future economic growth, we recommend applying the extended Ramsey rule to
compute social discount rates (adjusted for uncertainty), for varying time horizons.
27
2.2.2. Market Rates of Return to Capital
a) Real Return on Government Securities
The real rate of return on government bonds reflects the risk-free rate at which individuals
might trade present consumption against future consumption (e.g. see US OMB 2023). We
calculate the real rate of return on central government securities, using data on nominal interest
rates and the Consumer Price Index (CPI)-based inflation rates, which are available at annual
frequency, published by the Reserve Bank of India, for the period 1993-94 to 2022-2023.
12
Government securities provide households a safe, risk-free option to invest their savings over
the long term. Hence, the rate of return on these securities provides households a risk-free
interest rate to use in intertemporal consumption and savings decisions.
We find an average annual, pre-tax real rate of return of 3.46% on central government
securities using annual data for the 1993-94 to 2022-23 period. We take this to be a lower
bound value for the social discount rate.
b) Social Opportunity Cost of Capital
The second approach to calculating the short-run discount rate (for projects with lifetimes of
30 years or less) is to measure the social opportunity cost of capital in the economy. The
productivity of capital deployed in production yields the rate of return to capital, which is a
measure of its opportunity cost (or its next best use). The social discount rate would equal the
social opportunity cost of capital (SOC) in an economy without financial market imperfections
or externalities. The social opportunity cost of capital should thus be reflected in the market
interest rate, as the market interest rate equals the marginal product of capital in an economy
at equilibrium. Thus, we estimate the marginal product of capital deployed in manufacturing
sector production in private firms.
Studies by Poterba (1998) and Jenkins et al. (2011) compute the rate of return to capital using
country-level national accounts. However, this method may lead to significant overestimation
of the marginal return to capital and is likely to generate an upward bias in the calculated
12
In addition to central government securities, we also analysed data on real interest rates for fixed deposits with
maturities over 5 years and the real rate of return on gold, for the 1993-2023 period. We selected central
government securities as these yielded the highest rates of return compared to the other savings instruments.
28
discount rate, as discussed in Poterba (1998).
13
Here, the rate of return to capital, measured as
the ratio of income from capital to the stock of capital for a given year, can be estimated using
data from the National Accounts Statistics on an annual basis, following the approach outlined
in Jenkins et al. (2011). We find the average real rate of return to capital to be 10.6% over the
2012-13 to 2022-23 period. The detailed calculations for this method are presented in Appendix
A.
Next, we outline a robust econometric method to estimate the marginal return to capital, using
annual firm-level data from the Government of India’s Annual Survey of Industries. The
drawback of this approach, however, is that it only applies to the formal, organised
manufacturing sector and omits the informal sector from analysis, which accounts for a sizeable
share of the economy.
Estimating the marginal product of capital
We estimate a production function at the firm-level, following Levinsohn and Petrin (2003).
Consider a firm-level production function, �=�(�,�,�), where firms produce output �,
using capital (�), labour (�) and other raw materials (�) as inputs in production. We estimate
the marginal product of capital, or regression coefficient, � in the regression equation below.
�
�=�
+�
�+� �
�+ �
�+��
�+�
�
where and � specify the firm and year, respectively. The regression includes firm-level fixed
effects �
and year fixed effects �
�
.
Estimating � requires an external source of variation in the capital input that is uncorrelated
with the firm’s unobserved productivity. Since changes in the capital stock are likely to be
correlated with firms’ unobserved productivity levels, Levinsohn and Petrin (2003)
recommend using alternative input purchases, such as raw materials or fuels like electricity as
a proxy variable. The proxy variable is used as an instrumental variable for changes in the
capital stock. In this analysis, we use electricity input costs as the proxy variable given that we
13
Economic theory suggests the average rate of return (calculated as the ratio of income from capital to the capital
stock) overestimates the rate of return to capital on the marginal project (Poterba 1998). The marginal rate of
return to capital accurately measures the expected rate of return to investment in an additional project
commissioned by the government.
29
observe expenditure on electricity incurred by each firm in the survey. This relies on the
assumption that electricity usage, which complements capital use, is likely to be uncorrelated
with unobserved firm-level technology shocks or other productivity changes which may be
linked to capital usage.
Electricity use also varies at a higher frequency than changes in the firm’s capital stock. In
other words, we expect changes in electricity use to respond more flexibly than changes in the
capital stock of the firm. We find this assumption to be validated in the empirical literature
(Allcott et al. 2016). Further, we use data on electricity expenditures rather than electricity
consumed to be consistent with the Levinsohn-Petrin approach, which uses data on inputs
expressed in value terms, rather than quantities. Also, electricity prices charged to firms have
remained relatively stable across firms as the firm-level reported prices are highly correlated
with the state-level tariffs charged to firms by the distribution companies. Hence, we do not
expect large fluctuations in electricity prices over the timeframe observed.
Data Sources
We draw on firm-level panel data from the Annual Survey of Industries, conducted by the
Ministry of Statistics and Programme Implementation (MOSPI), for the period 2009-10 to
2019-20. The ASI is a nationally representative survey of registered firms. The survey data
contain detailed information on input use and output production. We compute real gross value
added (GVA), following the ASI tabulation programme and deflating GVA by the Wholesale
Price Index (WPI). Next, we compute the real capital stock at the firm-level, which comprises
both fixed capital and working capital. Then, we calculate employment at the firm as the
“average persons worked,” provided in the ASI survey. We also compute material and fuel
costs (excluding electricity), in real terms, as other inputs in production. The cost of electricity
purchases is used as the proxy variable. We exclude Public Sector Enterprises (PSEs) from this
analysis.
Results
The results are displayed in Table 6. The estimated elasticity of output with respect to capital
is 0.22. We compute the median ratio of output to capital,
, across the distribution of firms in
30
our sample, which equals 0.46. The derived marginal product of capital, or the real annual rate
of return to capital is 10%.
14
We also find similar rates of return to capital if we utilise data on
“number of man-days worked” at the firm.
Table 6: Estimating the Marginal Product of Capital
ln (Real GVA) (1)
ln (Capital) 0.217
***
(0.007)
ln (Labour) 0.625
***
(0.004)
ln (Materials) 0.0725
***
(0.002)
Observations 148,394
Wald test (Chi-sq.) 163.65
Median Ratio: Real GVA/Real Capital 0.46
Real return to capital 10.0%
Standard errors in parentheses.
*
p < 0.05,
**
p < 0.01,
***
p < 0.001
The third method to compute the rate of return to capital is based on a broad stock market
index, which reflects the return on private investments. We calculate the annual real rate of
return on the NIFTY 500 Total Returns Index, which comprises price appreciation and
dividend payments, for the 1999-2025 period.
15
We find an annual, pre-tax real rate of return
of 11% over this period.
16
The NIFTY 500 index comprises the top 500 publicly-listed companies on the National Stock
Exchange, based on market capitalisation. Thus, it includes approximately 250 companies with
relatively low market capitalisation, 150 companies with medium market capitalisation and
100 companies with large market capitalisation. Thus, the real rate of return would not need to
14
This can be derived as follows: ln Y ln K =β. The marginal product of capital, ∂Y∂K=βYK .
15
Data for the NIFTY 500 Total Returns Index are only available online from 1996.
16
This estimate can be contrasted with the real interest rate for loans set by the Reserve Bank of India for
Scheduled Commercial Banks. Analysing the minimum lending rate by commercial banks for the 1993-2023
period, using data published by the RBI, we find an average minimum real lending rate of 4.3%, which may be
considered a minimum safe rate of return on investment in the long run.
31
be adjusted further for size premiums, which often accrue to companies with small market
capitalisation. While the literature on corporate finance shows that private equity firms tend to
observe higher rates of return on investment than publicly-listed firms on the stock market,
empirical research in the context of India shows that these higher rates of return to private
equity are on account of a selection effect, whereby investments are targeted towards more
productive firms, but unproductive firms do not gain in productivity due to private investments
(Smith 2015; Officer 2007).
Therefore, the higher rate of return accruing to the private equity firms should not be applied
as the social opportunity cost of capital for public project evaluation. The rate of return to
investment observed in the stock market can be considered an appropriate real rate of return to
private investment in the Indian economy. This is particularly so for the Total Returns Index
which accounts for both price appreciation of the stock and dividend payments made to
investors, which have an outsized impact on the total return on the stock market (Golez and
Koudijs 2018). The stock market return represents the opportunity cost of capital used in the
public sector under the assumption that this capital would otherwise have been invested in a
listed private sector firm.
The first method to estimating the rate of return to capital, using the national accounts,
measures an average return but captures the whole economy, and yields 10.6% for the 2012-
13 to 2022-23 period. The second method measures the marginal rate of return and yields 10%,
but only captures the formal sector in the economy. The third method measures the rate of
return on the stock market and yields 11%, but only measures the return in privately listed
companies. In what follows, we apply a rate of return to capital of 10.6% derived from the
national accounts.
The estimated figures broadly represent the return on domestic capital in the economy.
However, they may not strictly correspond to the return on private capital, which is likely to
be higher, as the estimates are based on aggregate national accounts data that include both
private and government sectors. In principle, one approach would be to adjust the estimates by
deducting components that relate to the government sector in order to approximate the return
on private capital. However, such adjustments are constrained by limitations in the available
data, as a clear and precise segregation of the relevant components is not always possible.
Accordingly, the estimates should be interpreted as providing an indicative measure of the
32
overall return to capital in the economy, rather than a precise estimate of the return to private
capital alone.
c) Weighted Average Approach
The weighted average approach, proposed by Harberger (1972) and widely adopted in cost-
benefit analysis (Burgess and Zerbe 2011; ADB 2017), is premised on the assumption that
additional government borrowing undertaken to finance public sector projects is likely to
displace, in part, household consumption, private investment, and foreign borrowing. As
government borrowing raises the demand for funds in the market, the interest rate rises in the
short-run, which leads to reductions in household consumption, private investment, and the
government’s external borrowing. The social discount rate based on the weighted average
approach can be expressed as follows (Harberger 1972; Zhuang et al. 2007):
=��
�+�
+(1−�−�)
�
where �
� is the net of tax real interest rate on government securities,
is the social opportunity
cost of capital and
� is the real interest rate on the government’s external borrowing. The
weights, � and � measure the marginal displacement of private consumption and private
investment due to an increase in the government’s borrowing to finance public sector
expenditure.
Burgess and Zerbe (2011) derive a tractable formula to estimate these weights and compute the
social discount rate, as follows:
=
−(
�
�
)(
�
)�
�+((
1
��
)−1)
�
−(
�
�
)(
�
)+
1
��
where (
�
) is the ratio of domestic savings to private investment in the economy and �� is the
savings retention coefficient, which measures the association between the domestic savings
rate and the investment rate (i.e. investment as a proportion of GDP associated with savings as
33
a proportion of GDP), following Feldstein and Horioka (1980).
17
The parameters, � and �,
respectively measure the sensitivity of savings to the interest rate and the sensitivity of
investment to the interest rate. In Appendix A, we decompose the above formula to display the
weights attached to each of the three parameters,
, �
� and
�, expressed in terms of the
remaining parameters.
Results
We estimated the real rate of return on central government securities as 3.46% (section 2.2.2a).
To calculate the net of tax rate of return, we use data on marginal tax rates for different income
slabs for the latest assessment year (2023-24) and compute a weighted average marginal tax
rate. The marginal tax rate in each slab is weighted by the number of ITR filers in the
corresponding slab. We obtain a weighted average marginal tax rate of 10%. Hence, the net of
tax rate of return on government securities, �
�, is 3.1%. We obtained an estimate for the
marginal product of capital,
, of 10.6%, as the average real return from the National
Accounts Statistics (Section 2.2.2b).
Next, we analyse data on the Government of India’s external borrowing, drawing on annual
status reports of “India’s External Debt Position,” published by the Ministry of Finance. We
obtain an average real interest rate,
�, over the 2016-17 to 2023-24 period of 4.9%.
18
Further,
we compute the savings-investment ratio from the National Accounts Statistics for the latest
year available, 2023-24, (
�
)=0.95. We estimate the savings retention coefficient as the
correlation coefficient between the savings-GDP ratio, (
�
�
) and the investment-GDP ratio, (
�
),
and find ��=0.95.
Finally, we estimate the interest elasticities of investment and savings, � and �, respectively.
We estimate � using panel data on investments by firms from the Annual Survey of Industries,
for the period, 2011-12 to 2019-20. We use data on minimum real lending rates published by
the RBI (adjusted by CPI-inflation rates) to estimate �=−0.3, with a 95% confidence interval
17
The savings retention coefficient measures the proportion of incremental savings invested domestically relative
to the proportion of incremental savings invested abroad.
18
To calculate the real interest rate from the nominal interest rate reported in the annual status reports, we compute
the annual percentage change in the reciprocal of the real effective exchange rate (REER). Then, the real interest
rate is the nominal interest rate less the percentage change in REER.
34
of (-0.48, -0.12).
19
Lastly, we estimate � as the product of the reciprocal of the elasticity of
marginal utility (
1
) and the consumption-wealth ratio (
�
), as explained in Burgess and Zerbe
(2011). We estimated =1.8 (section 2.2.1) and obtain the consumption-wealth ratio as
(
�
)=0.1, from Bharti et al. (2024) and the World Inequality Database. Hence, we obtain an
interest elasticity of savings, �=0.06.
In Table 7, we present calculations of the social discount rate, with sensitivity checks. The
social discount rate varies from 8.1% to 9.6%, with a mean estimate of 9.23%. The range of
discount rates is based on the 95% confidence interval for the interest elasticity of investment,
which provides a range of estimates for n.
Table 7: Social Discount Rate – Weighted Average Approach
Rate of
return
on
capital
Rate of
return to
household
savings
Interest
rate on
external
borrowing
Savings-
Investment
Ratio
Savings
Retention
Coefficient
Interest
elasticity
of
savings
Interest
elasticity
of
investment
Social
Discount
Rate (%)
Remarks
on Interest
elasticity
of
investment
�
�
� (
�
) �� � �
10.6 3.1 4.9 0.95 0.95 0.06 -0.30 9.23
Mean
estimate
10. 6 3.1 4.9 0.95 0.95 0.06 -0.48 9.59
Upper
bound
10. 6 3.1 4.9 0.95 0.95 0.06 -0.12 8.12
Lower
bound
Note: The lower and upper bound values are based on the 95% confidence interval of the interest elasticity of
investment.
19
We estimate the following regression equation:
ln
�=+�+�
�+�
�
where
� is investment by firm i in year t and �
� is the real interest rate on loans by commercial banks. The panel
regression includes firm and year fixed effects, i and t.
35
2.2.3. Comparison of Social Discount Rates
We compare the estimates of the short-run social discount rate obtained from these approaches
in Table 8. These discount rates pertain to projects with lifetimes of less than 30 years. Our
estimates of the short-run social discount rate range from 6.8% to 11% with mean estimates of
6.8% and 9.23% from the Ramsey rule and weighted average methods, respectively.
The long-term social discount rates, with varying project maturities and accounting for
potential uncertainty in future consumption growth, are presented in Table 5 in preceding
section 2.2.1. To compare our estimates for India with those for other developed and
developing countries, we present estimates of social discount rates from several countries
surveyed by Groom et al. (2022) in Table 9. These studies synthesize guidance on discounting
for project appraisal across national governments in different countries and across empirical
studies.
Table 8: Comparison of Social Discount Rates across approaches
Approach Method δ
Expectation of g Variance of g SDR
Ramsey
Rule
Equal sacrifice
principle
0.5 1.8 0.047 0.000344 7.3
SOC
Real rate of return to
capital
- 10.6
Weighted
Average
Lower bound - 8.12
Mean estimate - 9.23
Upper bound - 9.59
The social opportunity cost of capital (SOC) and weighted average (WA) methods are being
adopted around the world. Social discount rates based on these approaches are typically
upwards of 8% in middle-income countries such as Mexico, China, and Colombia, which may
provide a reasonable benchmark for India in terms of future public investment and expected
future economic growth. Discount rates based on the Ramsey approach are typically lower in
the range of 1-5% in real terms for European countries. Given high rates of economic growth
observed in developing countries, the Ramsey approach yields higher discount rates of 8% and
above in the case of China and India (ADB 2017).
36
Table 9: Synthesis of parameter estimates for SDR across countries for various methods
Country/
Institution
Year Social Discount Rate
SOC/STP/Weighted
Average (WA)
Social rate of time
preference
Inequality
Aversion
Uncertainty Nonmarket effects
ADB 2017 9% STP 1% 1.5
6% SDR for environmental or
social benefits
Australia 2020 7% SOC
Sensitivity with 3% and 10%,
DDR to 3.7% (> 300 years),
lower risk premium for
nonmarket benefits
4% SDR for nonmarket
benefits
Brazil
a
2020 8.5% WA
Canada 2020 8% SOC
3% SDR may be used for
health and environmental
goods
Chile 2021 6% SOC
China 2021
8% for short- and
medium-term projects;
less than 8% for long-
term projects
WA
Colombia
a
2019 9% WA
Denmark 2021 3.5% Both STP & SOC
0.1% to
3%
1.25
1.5% systematic risk premium,
falling to 0% (>70 years).
DDR to 1.5%
(>70 years)
European Union 2021 3% STP DDR for >50 years
France 2017 4.5% STP
Risk-free SDR from 2.5% to
1.5% and risk premium from
2% to 3% (> 2070)
RPA for environmental goods
Germany 2018 1% STP 0% 1
37
IDB 2021 12% SOC
Ireland 2019 4% STP 1% 1–1.5
DDR to 1.5%
(>275 years)
Japan 2015 4% SOC
Mexico
a
2014 10% WA
The
Netherlands
2020 2.25% SOC
1% RPA for environmental
goods
New Zealand 2020 5% SOC
Norway 2021 4% SOC
DDR from 4% to 2%
(>75 years); 1.5% risk premium
OECD Countries 2018
Average rate of 4.78%
for energy and 4.64% for
transport
STP
Peru
a
2021 8% WA
DDR from 8% to 1%
(>200 years)
The Philippines 2020 10% SOC
Poland 2021 5% STP
Sweden 2020 3.5% STP 0.5% 1 1% catastrophic risk premium
United
Kingdom
2020
3.5% for 0-30 years, 3%
for 31–75 years, and
2.5% for 76 years or
more
STP 1
1% catastrophic risk premium;
DDR to 2.14% (>75 years)
SDR for health (1.5% for 0-
30 years; 1.29% for 31-75
years and 1.07% for 76 years
or more); 2% RPA for air
pollution damages
USA 2023 2% Both STP & SOC
Source: Groom et al. (2022) and from the authors’ collection based on governmental guidelines. Abbreviations: ADB, Asian Development Bank; DDR, declining discount rate;
IDB, Inter-American Development Bank; RPA, relative price adjustment; SCC, social cost of carbon; SDR, social discount rate; SOC, social opportunity cost of capital; STP,
social time preference (or Ramsey approach).
38
3. Shadow Prices
The frameworks developed by Little and Mirrlees (1974) and Dasgupta, Marglin and Sen
(1972) for project appraisal highlight the role of “accounting” or “shadow” prices for labour
and tradeable commodities, in estimating the social costs of public sector projects. We follow
the approach outlined by Little and Mirrlees (1974) to estimate shadow or “accounting” prices
used in cost-benefit analysis. Here, we estimate the (i) standard conversion factor (SCF), (ii)
shadow exchange rate factor (SERF) and (iii) shadow wage rate factor (SWRF). These
conversion factors are applied to evaluate financial costs and benefits in economic terms for
public sector projects.
3.1. Literature Review on Shadow Prices
The shadow exchange rate measures the economic value of foreign currency, whereas the
market exchange rate measures the financial value of foreign currency. To compute the shadow
exchange rate, we require the standard conversion factor. The standard conversion factor is a
measure of the economic value of traded commodities relative to their market or financial
value. While market prices for tradables would include import duties and other indirect taxes,
the “accounting” prices for tradables reflect the border prices of imports, exclusive of import
duties and taxes. The shadow exchange rate is obtained as the product of the standard
conversion factor and the market exchange rate. It is measured as the ratio of the value of
tradable goods and services in domestic prices relative to world prices (in foreign currency)
(ADB 2017).
The standard conversion factor is typically less than one, which suggests that tradables have
higher social value than what is reflected in the observed market prices. The standard
conversion factor helps adjust costs of imports at market prices to economic prices (or border
prices, excluding import tariffs), while the shadow exchange rate adjusts the official exchange
rate to the economic price of foreign currency, accounting for border duties (ADB 2017; Little
and Mirrlees 1974).
The shadow wage for unskilled labour is relevant when evaluating the economic costs of labour
in public sector projects and the prospect of employment creation from public investments.
Shadow wage rates for unskilled labour, typically available in large numbers and drawn from
39
agriculture, may be below market wage rates if there is involuntary unemployment (Little and
Mirrlees 1974). Several studies compute the shadow wage rate as the economic opportunity
cost of labour (Jenkins et al. 2011; Dinwiddy and Teal 1994; Curry and Weiss 2023). Since
involuntary unemployment among unskilled labour is less prevalent in the Indian context
(Dhingra and Kondirolli 2022), the market wage rate is likely to best represent the opportunity
cost of workers’ time (Jenkins et al. 2011), particularly for unskilled labour.
Thus, from the policymaker’s perspective, for government projects, the shadow wage rate
ought to reflect the divergence between the government’s stipulated minimum wage rate and
the prevailing market wage rate for agricultural workers in rural areas and the market wage rate
for informal sector workers in urban areas (Gupta 1986).
The Government of India stipulates minimum wage rates for unskilled labour for some sectors
on a bi-annual basis. The observed market wage rates for unskilled labour likely differ from
the stipulated minimum wages. If the market wage rates exceed the minimum wage rates
stipulated by the Central Government, the shadow wage rate factor may be taken as ‘1’ for
unskilled workers. In this case, minimum wage costs may be used to evaluate the costs and
benefits for public sector projects.
3.2. Standard Conversion Factor: Methodology and Results
First, we compute the standard conversion factor (SCF), which measures the accounting price
or factor costs of tradables relative to their market price. The market costs of imported inputs
largely comprise import duties. Since import duties differ across commodities, we compute a
weighted average standard conversion factor, following the Asian Development Bank
(Lagman-Martin 2004):
��=
������
��+�������
���
������
��+��� ����� ����+�������
���+��� ������ ����
where import values are recorded at border prices (cost, insurance, and freight), export values
are recorded at border prices (free on board) and net import and net export taxes are included.
Since net export taxes and subsidies on exports are zero (due to the Government of India’s
RODTEP scheme), we measure exports at market prices. To compute import values at border
40
prices, we deduct the import tariff for each tradable good and service from its market price to
generate its accounting price.
20
We draw on trade data for 2023-24 from the Ministry of Commerce and Industry, Government
of India, and product-level data on import tariffs for 2023 from the World Trade Organisation
(WTO). Data on quantities and purchase values at the Harmonised System (HS) 8-digit product
level are drawn from the Export-Import Data Bank (Ministry of Commerce and Industry),
while corresponding data on 8-digit level import tariffs (as percentage of the product price) are
from the WTO.
We merge the two databases at the 8-digit product level to compute the standard conversion
factor. Then, we generate average standard conversion factors at the HS 2-digit product level
and an overall SCF across all products. The results are presented in Table 10.
We observe an average standard conversion factor of 0.92, with a range from 0.24 to 1.00
across products. The standard conversion factor does not apply to non-tradable sectors and
commodities such as electricity, local construction, local transportation services etc, since the
domestic market prices reflect the economic costs of these inputs. Since import tariffs will not
apply to non-tradable goods and services, the market prices of these commodities reflect their
economic costs. Since their “shadow prices” equal their market prices, the implicit conversion
factor for non-tradable commodities is 1.
Table 10: Standard Conversion Factors, by HS 2-Digit Products
HS Code (2-
digit)
Industry description SCF
01 Live animals 0.82
02 Meat and edible meat offal 1.00
03 Fish and crustaceans, molluscs and other aquatic invertebrates 0.99
04
Dairy produce; birds' eggs; natural honey; edible products of animal origin,
not elsewhere specified or included
0.97
05 Products of animal origin, not elsewhere specified or included 0.96
20
Alternatively, SCF=Imports1-τ+ExportsImports+Exports where import and export values are recorded at
market prices and is the product-level import tariff.
41
06
Live trees and other plants; bulbs, roots and the like; cut flowers and
ornamental foliage
0.92
07 Edible vegetables and certain roots and tubers 0.79
08 Edible fruit and nuts; peel of citrus fruit or melons 0.73
09 Coffee, tea, mate and spices 0.90
10 Cereals 0.99
11 Products of the milling industry; malt; starches; inulin; wheat gluten 0.96
12
Oil seeds and oleaginous fruits; miscellaneous grains, seeds and fruit;
industrial or medicinal plants; straw and fodder
0.87
13 Lac; gums, resins and other vegetable saps and extracts 0.92
14
Vegetable plaiting materials; vegetable products not elsewhere specified or
included
0.79
15
Animal or vegetable fats and oils and their cleavage products; prepared
edible fats; animal or vegetable waxes
0.47
16
Preparations of meat, of fish or of crustaceans, molluscs or other aquatic
invertebrates
0.99
17 Sugars and sugar confectionery 0.80
18 Cocoa and cocoa preparations 0.78
19 Preparations of cereals, flour, starch or milk; pastrycooks' products 0.94
20 Preparations of vegetables, fruit, nuts or other parts of plants 0.96
21 Miscellaneous edible preparations 0.95
22 Beverages, spirits and vinegar 0.24
23 Residues and waste from the food industries; prepared animal fodder 0.94
24 Tobacco and manufactured tobacco substitutes 0.98
25 Salt; sulphur; earths and stone; plastering materials, lime and cement 0.93
26 Ores, slag and ash 0.97
27
Mineral fuels, mineral oils and products of their distillation; bituminous
substances; mineral waxes
0.93
28
Inorganic chemicals; organic or inorganic compounds of precious metals, of
rare- earth metals, of radioactive elements or of isotopes
0.93
29 Organic chemicals 0.94
30 Pharmaceutical products 0.99
31 Fertilisers 0.92
32
Tanning or dyeing extracts; tannins and their derivatives; dyes, pigments and
other colouring matter; paints and varnishes; putty and other mastics; inks
0.95
33 Essential oils and resinoids; perfumery, cosmetic or toilet preparations 0.89
42
34
Soap, organic surface-active agents, washing preparations, lubricating
preparations, artificial waxes, prepared waxes, polishing or scouring
preparations, candles and similar articles, modelling pastes, "dental waxes"
and dental preparations with a basis of plaster
0.93
35 Albuminoidal substances; modified starches; glues; enzymes 0.82
36
Explosives; pyrotechnic products; matches; pyrophoric alloys; certain
combustible preparations
0.99
37 Photographic or cinematographic goods 0.91
38 Miscellaneous chemical products 0.94
39 Plastics and articles thereof 0.92
40 Rubber and articles thereof 0.95
41 Raw hides and skins (other than furskins) and leather 0.97
42
Articles of leather; saddlery and harness; travel goods, handbags and similar
containers; articles of animal gut (other than silk- worm gut)
0.98
43 Furskins and artificial fur; manufactures thereof 0.96
44 Wood and articles of wood; wood charcoal 0.93
45 Cork and articles of cork 0.93
46
Manufactures of straw, of esparto or of other plaiting materials; basketware
and wickerwork
0.99
47
Pulp of wood or of other fibrous cellulosic material; recovered (waste and
scrap) paper and paperboard
0.94
48 Paper and paperboard; articles of paper pulp, of paper or of paperboard 0.95
49
Printed books, newspapers, pictures and other products of the printing
industry; manuscripts, typescripts and plans
0.97
50 Silk 0.86
51 Wool, fine or coarse animal hair; horsehair yarn and woven fabric 0.90
52 Cotton 0.98
53 Other vegetable textile fibres; paper yarn and woven fabrics of paper yarn 0.89
54 Man-made filaments; strip and the like of man-made textile materials 0.93
55 Man- made staple fibres 0.95
56
Wadding, felt and nonwovens; special yarns; twine, cordage, ropes and
cables and articles thereof
0.93
57 Carpets and other textile floor coverings 0.98
58
Special woven fabrics; tufted textile fabrics; lace; tapestries; trimmings;
embroidery
0.94
43
59
Impregnated, coated, covered or laminated textile fabrics; textile articles of a
kind suitable for industrial use
0.88
60 Knitted or crocheted fabrics 0.88
61 Articles of apparel and clothing accessories, knitted or crocheted 0.98
62 Articles of apparel and clothing accessories, not knitted or crocheted 0.98
63
Other made up textile articles; sets; worn clothing and worn textile articles;
rags
0.98
64 Footwear, gaiters and the like; parts of such articles 0.93
65 Headgear and parts thereof 0.97
66
Umbrellas, sun umbrellas, walking- sticks, seat- sticks, whips, riding- crops
and parts thereof
0.89
67
Prepared feathers and down and articles made of feathers or of down;
artificial flowers; articles of human hair
0.99
68 Articles of stone, plaster, cement, asbestos, mica or similar materials 0.96
69 Ceramic products 0.97
70 Glass and glassware 0.93
71
Natural or cultured pearls, precious or semi- precious stones, precious metals,
metals clad with precious metal, and articles thereof; imitation jewellery;
coin
0.91
72 Iron and steel 0.91
73 Articles of iron or steel 0.95
74 Copper and articles thereof 0.94
75 Nickel and articles thereof 0.96
76 Aluminium and articles thereof 0.96
78 Lead and articles thereof 0.96
79 Zinc and articles thereof 0.97
80 Tin and articles thereof 0.94
81 Other base metals; cermets; articles thereof 0.94
82
Tools, implements, cutlery, spoons and forks, of base metal; parts thereof of
base metal
0.94
83 Miscellaneous articles of base metal 0.91
84 Nuclear reactors, boilers, machinery and mechanical appliances; parts thereof 0.95
85
Electrical machinery and equipment and parts thereof; sound recorders and
reproducers, television image and sound recorders and reproducers, and parts
and accessories of such articles
0.93
44
86
Railway or tramway locomotives, rolling- stock and parts thereof; railway or
tramway track fixtures and fittings and parts thereof; mechanical (including
electro- mechanical) traffic signalling equipment of all kinds
0.93
87
Vehicles other than railway or tramway rolling- stock, and parts and
accessories thereof
0.92
88 Aircraft, spacecraft, and parts thereof 0.93
89 Ships, boats and floating structures 0.94
90
Optical, photographic, cinematographic, measuring, checking, precision,
medical or surgical instruments and apparatus; parts and accessories thereof
0.94
91 Clocks and watches and parts thereof 0.89
92 Musical instruments; parts and accessories of such articles 0.94
93 Arms and ammunition; parts and accessories thereof 0.97
94
Furniture; bedding, mattresses, mattress supports, cushions and similar
stuffed furnishings; lamps and lighting fittings, not elsewhere specified or
included; illuminated signs, illuminated name- plates and the like;
prefabricated buildings
0.92
95 Toys, games and sports requisites; parts and accessories thereof 0.86
96 Miscellaneous manufactured articles 0.93
97 Works of art, collectors' pieces and antiques 0.95
Overall Average 0.92
3.3. Shadow Exchange Rate Factor: Methodology and Results
The shadow exchange rate factor (SERF) measures the economic cost of foreign exchange
relative to its market price and is used to adjust foreign exchange earnings and costs incurred
in public projects to obtain their economic values. The shadow exchange rate (SER) can be
obtained as a product of the official market exchange rate and the shadow exchange rate factor
(SERF) to obtain the economic value of foreign exchange (as opposed to its market value).
Little and Mirrlees (1974) formulate the shadow exchange rate factor as the reciprocal of the
standard conversion factor, i.e. ����=1/��.
The Standard Conversion Factor (SCF) is applied to the market value of imports to obtain their
economic value. Since import tariffs create a distortion between the market price of the
imported product and its economic price, it is important to undertake a downward adjustment
45
of the market price of imports (by applying the standard conversion factor) to obtain the
economic cost of imports. Since import tariffs (and export subsidies) distort the economic value
of foreign products relative to domestically produced goods, it is key to adjust for taxes and
subsidies in evaluating the economic costs and benefits of public sector projects that entail
imports and exports. As the Standard Conversion Factor (SCF) is estimated at 0.92, the
����=
1
��
=1.09, which reflects a 9% premium on foreign exchange.
Jenkins et al. (2011) provide an alternative method to compute the economic price of foreign
exchange as functions of import demand and export supply elasticities, following theory
developed in Balassa (1974) and Bacha and Taylor (1971). Balassa (1974) discusses the
theoretical conditions under which these formulae simplify such that the standard conversion
factor and the shadow exchange rate factor are inversely related, as outlined in Little and
Mirrlees (1974).
21
The previous assessment conducted by NITI Aayog followed a simplified formulation to derive
the shadow exchange rate factor, applying the average import demand and export supply
elasticities across all traded products, rather than product-specific elasticities (NITI Aayog
2018). We present calculations of the shadow exchange rate factor using this approach for the
last five years in the Appendix. This approach yields substantially different values for the
shadow exchange rate factor, primarily due to the lack of updated estimates in the literature on
import demand and export supply elasticities. We apply available estimates of these trade
elasticities from an IMF study for the 2001-2004 period (Tokarick 2010). Since there are no
recent estimates, this method does not yield updated and accurate estimates of the shadow
exchange rate factor for the Indian context.
Pending further updates to methodology and estimation of trade elasticities for more recent
data, we would recommend relying on the methodology suggested by the ADB (2004) to
estimate the shadow exchange rate factor as the reciprocal of the standard conversion factor.
This methodology yields an estimate of the SERF of 1.09, which reflects a foreign exchange
premium of approximately 9% for the year 2023-24. This estimate of SERF is only marginally
higher than the previously computed value by NITI Aayog (2018) of 1.08 for 2015-16.
21
The theoretical conditions depend on symmetry between import demand and export supply elasticities (Balassa
1974).
46
The difficulty in measurement of trade elasticities has been noted in the literature (Devarajan
et al. 2023; Kee et al. 2008). Several complex econometric approaches have been followed to
circumvent problems of endogeneity in naïve OLS-based estimation of trade elasticities. Given
the difficulty in precise estimation of trade elasticities, we would not recommend following
this approach for the Indian economy. The accurate implementation of this approach would
require precise estimates of trade elasticities at the HS 2-digit product level for the recent
period. To the best of our knowledge, these estimates are not available for the Indian economy.
Therefore, we would recommend calculating the shadow exchange rate factor as the reciprocal
of the standard conversion factor (ADB 2004). Following this method, we obtain a shadow
exchange rate factor of 1.09, which suggests a 9% premium on foreign exchange.
Export subsidies are not applicable in this analysis for India as the government does not provide
an explicit subsidy to boost exports, in compliance with WTO regulations. The Government of
India launched the Remission of Duties and Taxes on Exported Products (RoDTEP) scheme in
2021 to provide tax rebates to exporters. However, these rebates are on taxes paid to the
government, but are not explicit subsidies for exported products. Hence, export prices received
by producers (net of taxes) remain unaffected by this scheme.
22
Similarly, the government launched the Production-linked Incentive (PLI) scheme to boost
domestic manufacturing. While the scheme provides incentives to producers (as a fraction of
the revenue from sales), which could indirectly boost exports, these incentives nevertheless are
not a form of export subsidies as they do not alter the prices of exports received by producers.
Hence, the introduction of the RODTEP and PLI schemes does not impact our calculation of
the shadow exchange rate factor. Since import tariffs are updated annually, the standard
conversion factor and the shadow exchange rate factor can be revised on an annual basis, using
readily available data on import volumes and tariffs at the product level, published by the
Ministry of Commerce and Industry.
22
In addition, the average rate of tax rebate under the RODTEP scheme across products is 1.1%, which would
have a negligible impact on the calculation for the shadow exchange rate factor, given import tariffs are an order
of magnitude higher than tax rebates under the RODTEP export promotion scheme.
47
3.4. Shadow Wage Rate Factor: Methodology and Results
We compute the shadow wage rate factor (SWRF) for unskilled labour. The market wage
reflects the opportunity cost of labour and thus the market valuation of time (Little and Mirrlees
1974). The shadow wage rate factor, which we measure as the ratio of market wages to
minimum wages for specific occupations, is used to adjust the cost of labour in project cost-
benefit analyses. A market wage which falls short of the minimum wage for workers in rural
or urban areas would imply that minimum wages overstate the opportunity cost of labour in
those sectors. Insofar as projects funded by the government are aimed at generating
employment, the shadow wage rate which equals the market wage rate, can be utilised for
project evaluation.
We obtain individual-specific data on weekly hours worked and wages earned for the principal
and subsidiary activities of employment from the nationally representative Periodic Labour
Force Survey (PLFS), 2023-24. We compute the daily wage rate for all individuals employed
in mining and construction for urban areas and agriculture for rural areas. To compute the
SWRF for unskilled labour, we exclude individuals with college degrees and diplomas from
analysis. This yields a sample of 6,905 individuals in rural areas and 3,170 individuals in urban
areas. In both cases, we assume an 8-hour work day to compute the daily wage.
23
We further
compute the shadow wage rate factor by gender to account for gender-specific differences in
observed average wages for unskilled labour.
24
Next, we use the latest data available on minimum wages, which are set on a bi-annual basis
by the Chief Labour Commissioner (Central), Ministry of Labour and Employment. As
minimum wages are set at the district-level, we match minimum wages for unskilled labour
employed in agriculture (for rural areas) and construction (for urban areas), across regional
areas A, B and C, to districts in the PLFS survey. We select the construction sector (NCO
occupation code – 931) for urban areas since this is the third most commonly reported
23
The Factories Act, 1948 prohibits manual work for more than 40 hours per week.
24
We compute the annual shadow wage rate factor which accounts for seasonal differences in wage rates,
particularly in the agriculture sector.
48
occupation in the PLFS and is relevant for project evaluation. For rural areas, we use data on
reported market wage rates in the agricultural sector (occupation code – 921).
25
Finally, we compute the shadow wage rate factor as the ratio of observed market wages to
minimum wages for unskilled workers, i.e. ����=
����� ���
���� ���
. We compute the SWRF
for rural and urban areas, by State and Union Territory (UT), applying survey weights from
PLFS, which ensure population-representative statistics at the state-level. To obtain the
combined shadow wage rate factor for each state/UT, we also compute a weighted average of
the corresponding shadow wage rate factors for rural and urban areas, weighted by the shares
of the working population residing in each of these areas, reported in the PLFS survey. The
results are presented in Table 11. Table 12 also presents the average annual wages obtained
from the PLFS, used to compute the shadow wage rate factors. Finally, Table 13 and Table 14
present average wages and shadow wage rate factors for male and female unskilled workers by
States/UTs, respectively.
Table 11: Shadow Wage Rate Factors (SWRF) for unskilled labour, 2023-24
State/UT
Rural
SWRF
% Rural %
population
Urban
SWRF
% Urban
Population
Total
Andaman & Nicobar
Islands
1.00 55.59 1.00 44.41 1.00
Arunachal Pradesh 1.00 70.64 1.00 29.36 1.00
Assam 0.80 89.07 0.94 10.93 0.82
Bihar 0.95 90.9 0.85 9.1 0.94
Chandigarh - 0 0.65 100 0.65
Chhattisgarh 0.49 80.57 0.47 19.43 0.49
Dadra & Nagar
Haveli
- - - - -
Daman & Diu 0.83 42.53 - 57.47 0.83
Delhi 0.93 2.44 0.68 97.56 0.69
Goa 1.00 41.59 1.00 58.41 1.00
Gujarat 0.63 58.55 0.75 41.45 0.68
25
The minimum daily wage rates are applied based on the Minimum Wage Notifications by the Chief Labour
Commissioner, Ministry of Labour and Employment, available at a bi-annual frequency. Minimum wage rates are
matched to individual data in the PLFS based on quarter of the survey.
49
Haryana 0.95 61.87 0.91 38.13 0.93
Himachal Pradesh 0.98 87.63 0.97 12.37 0.98
Jammu & Kashmir 0.36 81.01 0.96 18.99 0.47
Jharkhand 0.84 81.57 0.68 18.43 0.81
Karnataka 0.86 62.78 0.88 37.22 0.87
Kerala 1.00 52.38 1.00 47.62 1.00
Lakshadweep - 28.5 1.00 71.5 1.00
Madhya Pradesh 0.61 74.46 0.74 25.54 0.64
Maharashtra 0.75 57.72 0.92 42.28 0.82
Manipur 0.86 71.23 1.00 28.77 0.90
Meghalaya 0.90 85.69 0.87 14.31 0.90
Mizoram 0.94 54.79 0.98 45.21 0.96
Nagaland 1.00 71.97 1.00 28.03 1.00
Odisha 0.62 85.05 0.72 14.95 0.63
Puducherry 1.00 37.33 1.00 62.67 1.00
Punjab 0.90 61.81 0.80 38.19 0.86
Rajasthan 0.83 73.23 0.84 26.77 0.83
Sikkim - 76.86 1.00 23.14 1.00
Tamil Nadu 0.91 54.22 1.00 45.78 0.95
Telangana 0.94 60.31 1.00 39.69 0.96
Tripura 1.00 82.37 0.99 17.63 1.00
Uttar Pradesh 0.79 79.26 0.74 20.74 0.78
Uttarakhand 1.00 74.6 0.90 25.4 0.97
West Bengal 0.75 70.94 0.82 29.06 0.77
Overall Average 0.85 63.51 0.88 36.49 0.86
Note:
States with insufficient data in the PLFS to compute the shadow wage rate factor are marked with ‘-’.
We observe shadow wage rate factors in the range of 0.36 – 1.00 for unskilled labour employed
in agriculture in rural areas and between 0.47 – 1.00 for unskilled workers employed in the
construction sector in urban areas, across states and UTs. Overall, the average SWRF is 0.86
for unskilled labour in both rural and urban areas. Thus, the combined shadow wage rate factor
across rural and urban areas is 0.86. Shadow wage rate factors significantly below one suggests
that minimum wages might be considerably overstating the opportunity costs of workers’ time.
50
Applying these shadow wage rate factors can lower the costs of labour in project evaluation.
However, in some states and UTs, shadow wage rate factors that exceed one have been replaced
with “1.00” in Table 11. These reflect average market wages which exceed minimum wage
rates, even for unskilled labour. In these cases, we recommend the use of ����=1, for
unskilled labour, similar to that for skilled labour (ADB 2017).
Table 12: Average daily wage for unskilled labour, by rural and urban areas, 2023-24
State/UT
Average daily wage (INR) -
Rural
Average daily wage (INR) -
Urban
Andaman & Nicobar Islands 712 684
Arunachal Pradesh 434 585
Assam 350 500
Bihar 411 442
Chandigarh - 409
Chhattisgarh 215 272
Dadra & Nagar Haveli - -
Daman & Diu 356 -
Delhi 444 509
Goa 527 885
Gujarat 274 455
Haryana 413 502
Himachal Pradesh 424 496
Jammu & Kashmir 162 554
Jharkhand 369 394
Karnataka 374 519
Kerala 597 876
Lakshadweep - 883
Madhya Pradesh 267 389
Maharashtra 330 529
Manipur 377 555
Meghalaya 394 480
Mizoram 400 495
Nagaland 501 722
51
Odisha 268 401
Puducherry 481 676
Punjab 391 440
Rajasthan 359 472
Sikkim - 671
Tamil Nadu 396 637
Telangana 411 717
Tripura 469 500
Uttar Pradesh 344 419
Uttarakhand 440 479
West Bengal 327 427
Overall Average 394.10 544.67
Note: States with insufficient data in the PLFS to compute the shadow
wage rate factor are marked as ‘-’.
Table 13: Shadow wage rate factor for male unskilled workers, by States/UTs, 2023-24
State/UT
Average
daily wage
(INR) -
Rural
Rural
SWRF
% Rural
Populatio
n
Average
daily wage
(INR) -
Urban
Urban
SWR
F
% Urban
Populatio
n
Tota
l
Andaman &
Nicobar
Islands
712 1.00 56.15 684 1.00 43.85 1.00
Arunachal
Pradesh
491 1.00 71.13 596 1.00 28.87 1.00
Assam 379 0.87 89.13 497 0.96 10.87 0.88
Bihar 418 0.96 90.68 436 0.83 9.32 0.95
Chandigarh - 0 400 0.64 100 0.64
Chhattisgarh 231 0.53 79.97 299 0.45 20.03 0.51
Dadra &
Nagar Haveli
- - - - - - -
Daman &
Diu
- - 40.18 - - 59.82 -
Delhi 444 0.93 2.63 482 0.64 97.37 0.65
52
Goa 506 1.00 41.99 - - 58.01 1.00
Gujarat 277 0.64 58.11 438 0.74 41.89 0.68
Haryana 419 0.97 61.9 505 0.93 38.1 0.95
Himachal
Pradesh
424 0.98 86.35 508 0.97 13.65 0.98
Jammu &
Kashmir
162 0.36 81.01 564 0.96 18.99 0.47
Jharkhand 397 0.89 81.28 409 0.69 18.72 0.85
Karnataka 421 0.97 62.39 505 0.81 37.61 0.91
Kerala 747 1.00 52.82 895 1.00 47.18 1.00
Lakshadwee
p
- 1.00 28.79 - 71.21 1.00
Madhya
Pradesh
277 0.63 74.88 426 0.77 25.12 0.67
Maharashtra 376 0.86 57.06 492 0.88 42.94 0.87
Manipur 376 0.90 71.44 539 1.00 28.56 0.93
Meghalaya 401 0.91 85.93 415 0.72 14.07 0.88
Mizoram 400 0.94 55.85 480 0.94 44.15 0.94
Nagaland 501 1.00 71.08 800 1.00 28.92 1.00
Odisha 329 0.77 84.47 396 0.68 15.53 0.76
Puducherry 655 1.00 39.26 - 60.74 1.00
Punjab 409 0.94 61.42 438 0.82 38.58 0.89
Rajasthan 382 0.88 72.15 515 0.84 27.85 0.87
Sikkim - 75.74 690 1.00 24.26 1.00
Tamil Nadu 497 1.00 54.7 636 1.00 45.3 1.00
Telangana 453 1.00 59.04 771 1.00 40.96 1.00
Tripura 490 1.00 82.61 509 1.00 17.39 1.00
Uttar
Pradesh
364 0.84 78.71 413 0.70 21.29 0.81
Uttarakhand 436 0.99 74.62 489 0.94 25.38 0.98
West Bengal 335 0.77 71.04 422 0.81 28.96 0.78
Overall
Average
423.63 0.89 63.37 521.63 0.86 36.63 0.88
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
53
Table 14: Shadow wage rate factor for female unskilled workers, by States/UTs, 2023-24
State/UT
Average
daily wage
(INR) -
Rural
Rural
SWRF
% Rural
Population
Average
daily wage
(INR) -
Urban
Urban
SWR
F
Urban
Populatio
n Share
Tota
l
Andaman &
Nicobar Islands
- - 54.98 519 1.00 45.02 1.00
Arunachal
Pradesh
388 0.89 70.17 561 1.00 29.83 0.92
Assam 307 0.71 89 451 0.96 11 0.74
Bihar 401 0.93 91.12 414 0.83 8.88 0.92
Chandigarh - 0 409 0.64 100 0.64
Chhattisgarh 203 0.47 81.18 221 0.45 18.82 0.47
Dadra & Nagar
Haveli
- - - - - - -
Daman & Diu 356 0.83 45.41 287 - 54.59 0.83
Delhi 444 0.93 2.22 370 0.64 97.78 0.65
Goa 576 1.00 41.19 646 - 58.81 1.00
Gujarat 275 0.63 59.03 348 0.74 40.97 0.68
Haryana 397 0.91 61.84 468 0.93 38.16 0.92
Himachal
Pradesh
428 1.00 88.9 260 0.97 11.1 1.00
Jammu &
Kashmir
343 0.78 81.01 498 0.96 18.99 0.81
Jharkhand 347 0.80 81.89 318 0.69 18.11 0.78
Karnataka 326 0.75 63.19 499 0.81 36.81 0.77
Kerala 391 0.90 52 771 1.00 48 0.95
Lakshadweep - - 28.19 811 - 71.81 0.00
Madhya
Pradesh
253 0.58 74 321 0.77 26 0.63
Maharashtra 284 0.65 58.42 419 0.88 41.58 0.75
Manipur 383 0.88 71.03 574 1.00 28.97 0.91
Meghalaya 383 0.87 85.46 392 0.72 14.54 0.85
54
Mizoram 400 0.94 53.71 503 0.94 46.29 0.94
Nagaland - - 72.85 632 1.00 27.15 1.00
Odisha 235 0.54 85.61 268 0.68 14.39 0.56
Puducherry 293 0.67 35.55 627 - 64.45 0.67
Punjab 348 0.80 62.22 406 0.82 37.78 0.81
Rajasthan 338 0.78 74.31 367 0.84 25.69 0.80
Sikkim - - 78.17 587 1.00 21.83 1.00
Tamil Nadu 329 0.75 53.78 520 1.00 46.22 0.87
Telangana 384 0.88 61.55 590 1.00 38.45 0.93
Tripura 440 1.00 82.15 426 1.00 17.85 1.00
Uttar Pradesh 297 0.68 79.83 383 0.70 20.17 0.68
Uttarakhand 459 1.00 74.58 440 0.94 25.42 0.98
West Bengal 304 0.70 70.83 399 0.81 29.17 0.73
Overall
Average
355.59 0.80 63.69 491.91 0.86 36.31 0.82
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
The following tables present time trends of shadow wage rate factors computed for the
preceding four years, 2019-20 to 2022-23, at the state-level.
Table 15: Shadow Wage Rate Factors (SWRF) for unskilled labour (2019-2020)
State/UT
Average daily
wage (INR) -
Rural
Rural
SWR
F
% Rural
Population
Average daily
wage (INR) -
Urban
Urban
SWR
F
% Urban
Populatio
n
Total
Andaman &
Nicobar Islands
- - 58.93 - - 41.07 -
Arunachal
Pradesh
285 0.82 68.45 464 0.77 31.55 0.80
Assam 281 0.8 88 485 0.68 12 0.79
Bihar 274 0.79 89.31 498 0.7 10.69 0.78
Chandigarh - - 4.74 503 0.61 95.26 0.61
Chhattisgarh 152 0.44 81.96 465 0.48 18.04 0.45
Dadra & Nagar
Haveli
- - 43.59 - - 56.41 -
55
Daman & Diu 166 0.46 21.7 - - 78.3 0.46
Delhi 272 0.71 3.83 606 0.64 96.17 0.64
Goa 450 1.00 38.47 - - 61.53 1.00
Gujarat 200 0.57 57.43 534 0.6 42.57 0.58
Haryana 319 0.91 64.81 474 0.78 35.19 0.86
Himachal
Pradesh
313 0.9 86.94 403 0.66 13.06 0.87
Jammu &
Kashmir
410 1.0 80.35 497 0.87 19.65 0.97
Jharkhand 164 0.47 79.29 495 0.62 20.71 0.50
Karnataka 226 0.65 59.3 543 0.66 40.7 0.65
Kerala 524 1.0 50.67 518 1.0 49.33 1.00
Lakshadweep - - 20.1 448 1.0 79.9 1.00
Madhya Pradesh 189 0.55 73.11 467 0.55 26.89 0.55
Maharashtra 200 0.57 58.12 551 0.61 41.88 0.59
Manipur 286 0.83 72.13 431 0.93 27.87 0.86
Meghalaya 225 0.64 83.28 501 0.62 16.72 0.64
Mizoram - - 52.55 443 0.82 47.45 0.82
Nagaland 302 0.84 69.22 - - 30.78 0.84
Odisha 252 0.73 84.8 469 0.52 15.2 0.70
Puducherry 183 0.52 32.75 603 0.75 67.25 0.67
Punjab 282 0.81 62.35 498 0.66 37.65 0.75
Rajasthan 262 0.75 74.55 492 0.65 25.45 0.72
Sikkim 500 1.0 74.75 433 1.0 25.25 1.00
Tamil Nadu 273 0.78 53.21 540 0.71 46.79 0.75
Telangana 263 0.75 59.58 447 1.0 40.42 0.85
Tripura 345 0.99 79.78 467 0.82 20.22 0.96
Uttar Pradesh 224 0.63 77.8 524 0.63 22.2 0.63
Uttarakhand 266 0.76 72.89 439 0.78 27.11 0.77
West Bengal 232 0.67 70.14 476 0.66 29.86 0.67
Overall
Average
277.33 0.74 61.40 490.47 0.73 38.60 0.74
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
56
Table 16: Shadow Wage Rate Factors (SWRF) for unskilled labour (2020-2021)
State/UT
Average
daily wage
(INR) -
Rural
Rural
SWRF
% Rural
Population
Average
daily wage
(INR) -
Urban
Urban
SWRF
% Urban
Population
Total
Andaman &
Nicobar Islands
679 1.0 56.73 - - 43.27 1.00
Arunachal
Pradesh
310 0.84 67.54 446 0.96 32.46 0.88
Assam 285 0.77 87.8 592 1.0 12.2 0.80
Bihar 285 0.78 90.57 392 0.83 9.43 0.78
Chandigarh - - 4.47 280 0.52 95.53 0.52
Chhattisgarh 172 0.47 80.85 228 0.53 19.15 0.48
Dadra & Nagar
Haveli
200 0.54 56.38 - - 43.62 0.54
Daman & Diu - - 20.56 - - 79.44 -
Delhi - - 2.85 440 0.69 97.15 0.69
Goa 529 1.0 39.59 - - 60.41 1.00
Gujarat 201 0.54 59.27 296 0.65 40.73 0.58
Haryana 349 0.95 66.67 397 0.92 33.33 0.94
Himachal
Pradesh
359 0.97 90.67 428 1.0 9.33 0.97
Jammu &
Kashmir
356 0.96 80.36 478 1.0 19.64 0.97
Jharkhand 176 0.48 79.6 288 0.56 20.4 0.50
Karnataka 255 0.69 63.07 415 0.86 36.93 0.75
Kerala 526 1.0 53.11 798 1.0 46.89 1.00
Lakshadweep - - 27.76 - - 72.24 -
Madhya Pradesh 192 0.52 73.05 291 0.65 26.95 0.56
Maharashtra 230 0.62 60.34 372 0.74 39.66 0.67
Manipur 409 1.0 71.71 481 1.0 28.29 1.00
Meghalaya 218 0.59 82.3 309 0.61 17.7 0.59
Mizoram 329 0.9 51.53 338 0.79 48.47 0.85
Nagaland 429 1.0 71.29 - - 28.71 1.00
Odisha 233 0.63 84.88 274 0.64 15.12 0.63
57
Puducherry 250 0.67 40.62 - - 59.38 0.67
Punjab 300 0.82 61.99 349 0.75 38.01 0.79
Rajasthan 271 0.74 77.83 351 0.75 22.17 0.74
Sikkim - - 72.29 478 1.0 27.71 1.00
Tamil Nadu 296 0.8 54.32 492 1.0 45.68 0.89
Telangana 320 0.86 59.33 474 1.0 40.67 0.92
Tripura 326 0.89 80.35 366 0.86 19.65 0.88
Uttar Pradesh 263 0.71 79.72 321 0.68 20.28 0.70
Uttarakhand 302 0.82 71.04 379 0.78 28.96 0.81
West Bengal 256 0.7 71.72 301 0.7 28.28 0.70
Overall Average 310.20 0.78 62.63 394.79 0.80 37.37 0.79
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
Table 17: Shadow Wage Rate Factors (SWRF) for unskilled labour (2021-2022)
State/UT
Average
daily
wage
(INR) -
Rural
Average
daily wage
(INR) -
Urban
Rural
SWRF
% Rural
Populatio
n
Urban
SWRF
% Urban
Population
Total
Andaman &
Nicobar Islands
705 584 1.0 51.63 1.0 48.37 1.00
Arunachal
Pradesh
376 474 1.0 69.97 1.0 30.03 1.00
Assam 348 392 0.92 89.74 0.89 10.26 0.92
Bihar 365 387 0.97 91.88 0.88 8.12 0.96
Chandigarh 413 - 4.87 0.75 95.13 0.75
Chhattisgarh 210 182 0.55 81.31 0.41 18.69 0.52
Dadra & Nagar
Haveli
- - - - - - -
Daman & Diu 391 178 1.0 38.46 0.41 61.54 0.64
Delhi 191 - 3.45 0.29 96.55 0.29
Goa 404 514 1.0 38.82 0.94 61.18 0.96
Gujarat 233 275 0.62 57.09 0.59 42.91 0.61
Haryana 396 417 1.0 65.57 0.94 34.43 0.98
58
Himachal
Pradesh
428 232 1.0 90.3 0.53 9.7 0.95
Jammu &
Kashmir
309 457 0.81 80.88 1.0 19.12 0.85
Jharkhand 307 266 0.82 80.19 0.58 19.81 0.77
Karnataka 311 453 0.82 64.31 0.95 35.69 0.87
Kerala 527 785 1.0 50.06 1.0 49.94 1.00
Lakshadweep - 793 - 27.5 1.0 72.5 1.00
Madhya Pradesh 219 280 0.58 75.67 0.63 24.33 0.59
Maharashtra 270 384 0.71 56.94 0.75 43.06 0.73
Manipur 477 443 1.0 73.38 1.0 26.62 1.00
Meghalaya 326 261 0.86 85.67 0.56 14.33 0.82
Mizoram 400 359 1.0 53.96 0.82 46.04 0.92
Nagaland 442 456 1.0 75.1 1.0 24.9 1.00
Odisha 259 303 0.69 85.96 0.67 14.04 0.69
Puducherry 301 489 0.79 37.08 0.96 62.92 0.90
Punjab 346 357 0.91 65.8 0.77 34.2 0.86
Rajasthan 361 332 0.96 74.21 0.73 25.79 0.90
Sikkim - 220 - 79.03 0.5 20.97 0.50
Tamil Nadu 375 460 0.99 56.4 0.98 43.6 0.99
Telangana 382 457 1.0 65.04 1.0 34.96 1.00
Tripura 439 389 1.0 82.16 0.89 17.84 0.98
Uttar Pradesh 328 348 0.86 80.33 0.75 19.67 0.84
Uttarakhand 413 432 1.0 74.95 0.98 25.05 0.99
West Bengal 316 373 0.84 72.57 0.84 27.43 0.84
Overall
Average
365.47 392.24 0.89 64.13 0.79 35.87 0.86
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
59
Table 18: Shadow Wage Rate Factors (SWRF) for unskilled labour (2022-2023)
State/UT
Average
daily wage
(INR) -
Rural
Rural
SWRF
% Rural
Populatio
n
Average
daily wage
(INR) -
Urban
Urban
SWRF
% Urban
Population
Total
Andaman &
Nicobar Islands
571 1.0 56.75 676 1.0 43.25 1.00
Arunachal
Pradesh
412 1 70.49 533 1.0 29.51 1.00
Assam 421 1 96.69 468 0.94 3.31 1.00
Bihar 364 0.91 92.17 419 0.85 7.83 0.91
Chandigarh - 5.08 418 0.68 94.92 0.68
Chhattisgarh 204 0.5 81.27 248 0.47 18.73 0.49
Dadra & Nagar
Haveli
- - - - - - -
Daman & Diu 337 0.83 35.81 - - 64.19 0.83
Delhi - - 2.67 512 0.68 97.33 0.68
Goa 428 1.0 41.16 839 1.0 58.84 1.00
Gujarat 242 0.59 56.73 405 0.77 43.27 0.67
Haryana 425 1.0 66.15 468 0.79 33.85 0.93
Himachal
Pradesh
397 0.97 90 417 0.87 10 0.96
Jammu &
Kashmir
475 1.0 82.92 529 1.0 17.08 1.00
Jharkhand 208 0.51 82.69 386 0.72 17.31 0.55
Karnataka 337 0.83 63.84 490 0.88 36.16 0.85
Kerala 525 1.0 53.38 850 1.0 46.62 1.00
Lakshadweep - - 23.98 783 1.0 76.02 1.00
Madhya
Pradesh
243 0.6 74.99 352 0.69 25.01 0.62
Maharashtra 305 0.74 58.19 484 0.82 41.81 0.77
Manipur 460 1.0 72.43 519 1.0 27.57 1.00
Meghalaya 387 0.95 84.86 390 0.74 15.14 0.92
Mizoram 400 0.99 53.69 455 0.97 46.31 0.98
Nagaland 461 1.0 74.33 512 1.0 25.67 1.00
60
Odisha 297 0.73 85.78 393 0.78 14.22 0.74
Puducherry 282 0.68 36.19 527 1.0 63.81 0.88
Punjab 371 0.91 64.4 416 0.84 35.6 0.89
Rajasthan 368 0.9 76.09 429 0.84 23.91 0.89
Sikkim 566 1.0 79.07 541 1.0 20.93 1.00
Tamil Nadu 380 0.94 57.25 566 1.0 42.75 0.97
Telangana 383 0.94 62.87 580 1.0 37.13 0.96
Tripura 437 1.0 82.73 472 1.0 17.27 1.00
Uttar Pradesh 339 0.82 80.24 409 0.77 19.76 0.81
Uttarakhand 411 1.0 74 477 0.98 26 0.99
West Bengal 322 0.79 71.47 418 0.87 28.53 0.81
Overall
Average
379.29 0.88 64.42 496.39 0.88 35.58 0.88
Note: States/UTs marked ‘-’ did not have sufficient data in the PLFS survey to generate shadow wage rate
factors.
4. Social Cost of Carbon
The social cost of carbon (SCC) is a measure of the present discounted value of the societal
damages associated with an additional ton of CO2 emissions incurred today. It reflects the
global economic damages due to rise in temperature associated with increasing CO2
concentrations in the atmosphere. Since carbon dioxide remains in the atmosphere for more
than 300 years, the SCC measures the continuum of economic damages incurred over this
timeframe (Rennert et al. 2022). The SCC integrates climate science, economics, and social
welfare considerations to provide a single monetary figure useful for cost-benefit analyses of
climate policies.
Estimating the SCC proceeds in seven steps using Integrated Assessment Models (IAMs)
(Carleton and Greenstone 2022). First, the model entails future projections of CO2
concentrations in response to various socioeconomic pathways, which include business-as-
usual, ambitious climate policy and so on. Second, the climate science module relates rise in
CO2 concentrations to probable increases in mean surface temperature, termed climate
sensitivity. Third, the model accounts for future economic damages due to higher temperatures,
associated with a rise in CO2 emissions. Fourth, the model converts future economic damages
61
to present value terms, applying an appropriate social discount rate for a long timescale. The
remaining three steps are normative in nature and involve value judgements to be made by the
policymaker. Here, the model assesses whether to evaluate only domestic or local damages or
also global damages. Subsequently, the model accounts for potential uncertainty in future
consumption. Finally, the model considers integrating inequality aversion in evaluating the
SCC (Carleton and Greenstone 2022).
The existing literature has analysed a range of IAMs, with incremental improvements made to
various aspects of IAMs over the last few decades. Nordhaus’ foundational work with the
Dynamic Integrated Climate-Economy (DICE) Model evaluated the optimal transition path to
mitigating the rise in greenhouse gas concentrations while maximising social welfare
(Nordhaus 1993a; Nordhaus 1993b). Nordhaus (1993b) proposed a modest carbon tax as an
effective policy instrument to mitigate the rise in CO2 emissions, while ensuring steady
economic growth over a long-time horizon.
4.1. Global SCC values
In the most recent update of the DICE model (DICE-2023), Barrage and Nordhaus (2024) find
SCC values ranging from US$ 37 – 571 per tonne of CO2 for 2025 (at 2019 US$ prices), for
constant social discount rates, ranging from 5% to 1% per year respectively. Higher social
discount rates generate lower values for the social cost of carbon. They find an SCC which
maximizes global welfare of $59 in 2025 (in 2019 US$ prices). The associated social discount
rate declines over time due to adjustment for uncertainty in the long-run future growth rate of
world GDP. This optimal path is associated with a temperature increase of 2.6
o
C in 2100 in
their model.
In contrast, a recent study by Rennert et al. (2022) uses the open-source model, Greenhouse
Gas Impact Value Estimator (GIVE), following recommendations by the US National
Academies of Science, Engineering and Medicine (NASEM), to update the latest models in
evaluating the SCC. Rennert et al. (2022) apply a risk-free social discount rate of 2% and find
a mean SCC estimate of US$ 185/ton CO2 in real terms (at 2020 US$ prices), with a 5%-95%
confidence interval of US$ 44 – 413/ton CO2.
62
Higher SCC estimates reported by Rennert et al. (2022) reflect a lower social discount rate as
well as an improved understanding of long-term economic risks to climate change via the GIVE
model, which integrates probabilistic climate projections and updated socio-economic data. In
particular, the model accounts for the potential rise in energy consumption due to temperature
rise based on work by Clarke et al. (2018), premature mortality due to heat stress from high
temperature based on Cromar et al. (2022) and economic damages in agriculture due to high
temperatures and drought based on Moore et al. (2017).
Importantly, Hänsel et al. (2020) update the DICE model to integrate damage functions from
Howard and Sterner (2017), which leads to substantially higher damages from climate change.
They revise the social discount rate used to evaluate the present value of damages, based on
the Ramsey rule, applying an expert elicitation survey by Drupp et al. (2018), which finds a
median social rate of time preference (δ) and lower degree of inequality aversion (η) of 0.5%
and 1 respectively, compared to δ = 1.5% and =1.45 used in the DICE-2016R model by
Nordhaus (2017).
26
These revisions lower the social discount rate used to evaluate climate
damages and increase the social cost of carbon to US$ 101/ton CO2.
Moore et al. (2024) synthesize evidence on the social cost of carbon by combining 1,823 SCC
estimates from 147 studies and conduct an expert elicitation survey of authors of the reviewed
studies. From these studies which cover over three IAMs including DICE, FUND and PAGE,
the authors find a mean SCC estimate of US$ 132/ton CO2 (at 2020 US$ prices). In contrast
to published estimates, their expert elicitation survey and a random forest-trained model results
in a synthetic distribution with higher SCC estimates. The synthetic distribution results in a
mean SCC value of US$ 185/ton CO2 (at 2020 US$ prices), with an interquartile range of US$
97-369/ton CO2.
In addition to global SCC estimates, recent studies provide sector-specific estimates of the
social damage associated with rising temperatures. Rode et al. (2021) develop the Data-driven
Spatial Climate Model (DSCIM) of the Climate Impact Lab, at the University of Chicago, to
estimate the impact of rising temperature on the global energy demand for heating and cooling.
Estimating econometric regression models for 146 countries over the 1971-2020 period, the
authors find that while higher temperatures increase energy consumption from air conditioning,
26
The modal value of the social rate of time preference in the survey was zero.
63
particularly in India and other tropical countries, the rise in temperature is associated with a
decline in demand for residential heating from other fuels such as oil and gas, which outweighs
the rise in demand for cooling. Overall, rising temperatures from higher CO2 concentrations
lead to a net decline in energy consumption from all fuels combined, resulting in negative SCC
estimates for the energy sector (Rode et al. 2021). Rode et al. (2021) present a significant
methodological advance in computing the social cost of carbon, based on empirical estimates,
compared to modelled estimates used in previous studies.
Similar to the energy sector, Carleton et al. (2022) estimate excess mortality due to climate-
induced increases in temperature at the subnational level for 40 countries, accounting for the
projected increase in incomes and adaptation to climate change. The authors estimate the mean
‘partial SCC’ for temperature-induced mortality at US$ 37/ton CO2, with an interquartile range
of US$ -8 to 73/ton CO2. Analogously, Moore et al. (2017) present partial SCC estimates for
the agriculture sector, ranging from US$ 3.5/ton CO2 to US$ 8.5/ton CO2.
Estimates from empirical studies for energy consumption and mortality differ significantly
from sector-wise estimates from integrated assessment models, as displayed in Figure 1 (Rode
et al. 2021; Carleton et al. 2022). While the SCC associated with energy consumption is
significantly smaller than that used in IAM-based modelling studies, the partial SCC for
mortality costs due to temperature rise are an order of magnitude larger than costs presumed in
modelling studies. The nascent empirical literature critically informs debates on the aggregate,
global value of the social cost of carbon (Carleton and Greenstone 2022; US EPA 2023).
Figure 1: Sector-specific SCC estimates from empirical studies vs. IAMs
Source: Carleton and Greenstone (2022)
64
4.2. Country-specific SCC values
While most studies present global aggregate estimates of the social cost of carbon, some studies
analyse country-specific economic damages in response to rising temperatures. Global
damages then equal the sum of country-specific damages, aggregated across all countries.
Ricke et al. (2018) combine climate-economic estimates to compute the country-specific social
cost of carbon for several countries. Their results show that India is particularly vulnerable to
climate change and economic damages incurred in India account for 21% of global damages
from climate change.
Ricke et al. (2018) apply the empirical model of Burke, Hsiang and Miguel (2015), who analyse
the global non-linear impact of temperature rise on economic output. Ricke et al. (2018)
estimate a mean country social cost of carbon (CSCC) for India of US$ 86/ton CO2, with a
range from US$ 49-157/ton CO2. The study applies simplified functions of the economic
response to increases in temperature, which are drawn from cross-country or global studies,
rather than empirical estimates specifically from the Indian context.
The recent study by Moore et al. (2024) provides a synthesis of the evidence on the global
social cost of carbon, reviewing nearly 150 studies to provide a range of estimates of the SCC.
Similarly, Rennert et al. (2022) utilise updated damage functions and climate sensitivity
relationships to estimate the global SCC. A synthesis of estimates for the social cost of carbon
from the literature is presented in Appendix Table A.6.A.
As Ricke et al. (2018) provides evidence to suggest that India accounts for around one-fifth of
global damages from climate change, we utilise the estimates from the studies by Moore et al.
(2024) and Rennert et al. (2022) to estimate a plausible range of values for the SCC for India.
We find a mean CSCC for India of US$ 39/ton CO2 with a range of US$ 9 – 87/ton CO2, by
using the assumption that damages to India are one-fifth of global damages. This would need
a further downward adjustment since the social discount rate for India will be higher, at least
in the short-term, than the rate used in the global analyses cited above.
Global analyses typically apply a near-term discount rate of 2%, whereas the present study
estimates a higher social discount rate of 7% for India. Since previous studies do not provide
65
estimates for the social cost of carbon corresponding to higher discount rates, it is beyond the
scope of this report to estimate the precise social cost of carbon. However, based on earlier
studies, we estimate a lower-bound value for the social cost of carbon for India. Hence, we
would recommend a minimum social cost of carbon of US$10 per ton of CO2 to be applied in
project evaluation for public sector projects by the Government of India. Further research is
needed to analyse the relationship between temperature rise and economic output for the Indian
context, which would inform estimates for the social cost of carbon for India.
5. Recommendations
This study reassessed key parameters for cost-benefit analysis in public sector projects
undertaken by the Government of India. We evaluated short-run and long-run social discount
rates, following several state-of-the-art methods in the academic and policy literature. We also
computed conversion factors for foreign exchange, traded commodities, and labour usage in
production. Finally, we synthesized the literature to present a range of plausible estimates for
the social cost of carbon for cost-benefit analysis. In this section, we summarise our key
recommendations on parameters for use in cost-benefit analyses for public sector projects.
5.1. Social Discount Rate
The social discount rate or “discount rate” measures the trade-off between present and future
consumption. It is used to obtain the present value of the future benefits of a public investment
project. We computed the social discount rate based on two broad approaches, including (i) the
Ramsey approach, that gives a discount rate of 7.3% for a time horizon up to 30 years and (ii)
market rates of return, which gave a range of discount rates from 8.1% to 11%, across methods
(Table 5). These discount rates pertain to projects with lifetimes of less than 30 years. Our
estimates of the short-run social discount rate range from 7.3% to 11% with mean estimates of
7.3% and 9.23% from the Ramsey rule and weighted average methods, respectively (Table 8).
We recommend using the weighted average method for projects with time horizons up to 30
years, since this method accounts for consumers’ savings decisions and societal trade-offs
between present and future consumption, while also accounting for displacement of private
66
investment and government borrowing. This suggests an upward revision of the social discount
rate from 8% in the previous assessment (NITI Aayog 2018) to 9.23% in real terms, for short-
term projects with maturities up to 30 years.
For longer horizons, however, we suggest using the uncertainty-adjusted Ramsey approach to
calculate the social discount rate, since this approach accounts for uncertainty about future
growth rates, which can be substantial in the case of a developing country like India. Lower
social discount rates over longer time horizons would also place higher value on socially
beneficial projects whose benefits only accrue after a few decades (such as those in health,
education, or for environmental protection). Thus, for longer term projects, we recommend
applying a term structure of discount rates, adjusting for uncertainty in future economic growth
(Table 5).
Further, we recommend the use of a social discount rate for selection and evaluation for public
projects, instead of the hurdle rate. The hurdle rate is applied in evaluation of private sector
investments by private companies. Hence, the social discount rate is the appropriate metric to
apply in the context of public project evaluation by the Government.
5.2. Shadow Prices
We computed conversion factors for foreign exchange, imports, and labour costs in production.
We obtained standard conversion factors at the Harmonised System 2-digit product code level
for all traded commodities, with an average standard conversion factor (SCF) of 0.92. We also
obtained a shadow exchange rate factor (SERF) of 1.09. This reflects a 9% premium on foreign
exchange. This exceeds the foreign exchange premium of 8% calculated in the previous
assessment report (NITI Aayog 2018). Finally, we computed shadow wage rate factors for
unskilled labour for rural and urban areas across states and UTs (Table 11), with an average
shadow wage rate factor of 0.86. These are to be applied when minimum wages, rather than
market wages, are used for calculating labour costs in project evaluation.
5.3. Social Cost of Carbon
We synthesized the latest advances in science to reflect on the global social cost of carbon,
which measures the present value of the monetary social damage due to an incremental ton of
67
CO2 emissions. Based on our review of the literature, a country social cost of carbon for India
incorporating only damages to India rather than global damages, may be about US$ 10/ton
CO2, with a range of US$ 9 – 87/ton CO2, based on recent global studies. Further research is
needed to improve the calculation of the SCC for the Indian context, in particular, to
incorporate economic damages for India into global damage functions and to reconcile
empirical estimates with those from modelling studies. In this respect, we recommend that a
research study be conducted by the Government of India to estimate the appropriate social cost
of carbon for India.
5.4. Comparison of parameters
We compare our recommendations on parameter values with those applied in the previous
assessment by NITI Aayog (2018) in Table 19.
Table 19: Updating of national parameters since NITI Aayog (2018)
Parameter NITI Report (2018) NITI Report (2026)
Social Discount Rate (< 30 years) 8% 9.23%
Social Discount Rate (30-50 years) 8% 6.2%
Social Discount Rate (50-75 years) 6% 4.8%
Social Discount Rate (75-100 years) < 6% 3.4%
Standard Conversion Factor (SCF) - 0.92
Shadow Exchange Rate Factor (SERF) 1.08 1.09
Shadow Wage Rate Factor (SWRF) - Total - 0.86
Shadow Wage Rate Factor (SWRF) - Male - 0.88
Shadow Wage Rate Factor (SWRF) - Female - 0.82
SCC (not accounting for damages outside India) -
US$ 10/ton CO2
68
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74
Appendix
A.1. Derivation of the Ramsey rule
We follow Dasgupta (2008) to derive the social discount rate based on the Ramsey rule.
Consider a representative consumer who maximises lifetime utility, �(
�), where
� represents
consumption in period �, with �=0 to �= ∞. The utility function, �(
�), is strictly quasi-
concave, with marginal utility of consumption, �
′
(
�)>0. The utility function exhibits
diminishing marginal utility of consumption, i.e. �
′′
(
�)<0. The present value of lifetime
utility, �
0, discounted at rate δ, is given by:
�
0=�(
0)+
�(�1)
(1+�)
+⋯+
�(�
)
(1+�)
+⋯=∑
∞
�=0
�(�)
(1+�)
(A.1)
Next, we define parameters, η - the elasticity of marginal utility of consumption, and �
� - the
growth rate of private household consumption:
=−
�
′
(�)
�
�
�
′(�)
=−
� �′′(�)
�′(�)
(A.2)
�
�=
�+1
�
−1 (A.3)
We assume a constant relative risk aversion (CRRA) utility function to ensure the elasticity of
marginal utility , is constant (i.e. it does not vary with the level of consumption). The CRRA
utility function is defined as follows:
�(
�)={
�
(1−)
1−
,>0; ≠1 ����
� ,=1
Note that for any t, �
′
(
�)=
�
−
for >0 and ≠1. Further, assume there are small
changes in consumption growth rates between two consecutive time periods, such that
variations in
� and
�+1 leave the individual’s present value of lifetime utility, �
0,
unchanged.
Next, take the differential of �
0, as follows:
75
�
0=
�′(
1)
(1+�)
1+⋯+
�′(
�)
(1+�)
�
�+
�′(
�+1)
(1+�)
�+1
�+1=0
The previous assumption implies that for any pair of consecutive changes in consumption
growth rates,
� and
�+1, �
0=0. This leads to the following equation:
�′(�
)
(1+�)
�+
�′(�+1
)
(1+�)
+1
�+1=0 (A.4)
Next, we multiply the above equation by (
(1+�)
�
�
):
�′(
�)+
�′(
�+1)
(1+�)
�+1
�
=0
Subsequently, we substitute the values of �′(
�) and �
� in the above equation, as follows:
�
−
+
�+1
−
(1+�)
�+1
�
=0 (A.5)
Next, we define the social discount rate, following Dasgupta (2008), as follows:
�
=−
�+1
�
−1 (A.6)
We substitute equation (A.6) into (A.5), as follows:
1
�
−
1
�+1
(1+�)
(1+
�)=0 (A.7)
Lastly, we substitute the growth rate of consumption, �
�, in the above equation, as follows:
(
�+1
�
)
−
(1+
�
)
(1+�)
=(1+�
�
)
−
(1+
�
)
(1+�)
=0 (A.8)
This leads to the approximate Ramsey rule for the social discount rate,
�
:
�
≈ �+�
� (A.9)
76
A.2. Social Opportunity Cost of Capital Approach
We apply the methodology derived in Poterba (1998) and explained in Jenkins et al. (2011) to
estimate the rate of return to capital from the National Accounts Statistics. The rate of return
to capital is measured as the ratio of the national income derived from capital and the capital
stock in the economy, i.e. �
=
. Theoretically, the average rate of return (or average product
of capital) would intersect the marginal rate of return (or marginal product of capital) when the
average product of capital is at its highest value in the production function. To calculate income
from capital (which is not directly reported in the national accounts), we apply the methodology
outlined in Jenkins et al. (2011). The calculations are presented below in Table A.2.1. We find
an average rate of return to capital of 10.6% over the 2012-13 to 2022-23 period, with this
approach.
Specifically, we estimate the rate of return to capital using the National Accounts Statistics
(NAS), following the methodology of Jenkins et al. (2011). Capital income is derived by
applying the capital share of Gross Value Added (GVA) to aggregate GVA (in constant prices)
and deducting depreciation (consumption of fixed capital – CFC, in constant prices). The rate
of return is then computed as the ratio of capital income net of depreciation to the net capital
stock at the beginning of the accounting year, as reported by NAS. The net capital stock is
available only in current prices in the NAS database. To derive this in constant price terms, we
derive the capital stock deflator as the ratio of gross capital formation (GCF) in current prices
to the GCF in constant prices, both of which are reported in the NAS.
27
Thus, we derive the
real rate of return to capital, as follows:
�
=
(��
�.
�)−�
�
��� ��� ����
�−1
We apply capital shares of GVA using the RBI KLEMS database, for the 2012-13 to 2022-23
period. These capital shares are reported at the sector-level. To derive an economy-wide capital
share of GVA for year t,
�, we compute a weighted average across sectors, using the sector-
level contributions to national GVA as weights. This calculation is conducted as follows:
27
Net Capital Stockt-1=Net Capital Stockt-1, Current PricesCapital Stock Deflatort-1, where Capital Stock
Deflator=GCFCurrent pricesGCFConstant prices.
77
�=∑�
���
��
�
The economy-wide capital share of GVA for year t,
�, is a weighted average of sectoral capital
shares of GVA, �
��, weighted by sector-level weights, �
��. The weights, �
��, in turn, are
derived as follows:
�
��=
��
��
∑��
���
However, the Jenkins et al. (2011) approach requires modification for the Indian context,
because it derives capital income from GDP as the residual of labour, land income from
agriculture and resource income. The NAS does not separately report operating surplus and
mixed income, preventing accurate decomposition of mixed income/ operating surplus into
labour and capital components. Since mixed income includes substantial labour earnings of
self-employed households, particularly in the informal sector, which is typically underreported,
capital income is likely to be overestimated. In addition, land income from agriculture is not
estimated separately in the KLEMS database. As a result, the estimated capital income and rate
of return are likely to overstate the true economy-wide rate of return to capital, since this is an
average return to capital, rather than the marginal return.
78
Table A.2.1. Average rate of return to capital estimated from National Accounts Statistics
Year
GVA (constant
prices, INR
crores)
Capital
share of
GVA
Capital income
(INR Crores)
Consumption of fixed capital
(Depreciation, constant prices,
INR Crores)
Net capital stock
(constant prices, INR
crores)
Rate of return to
capital, in real
terms (%)
(1) (2) (3) (4) (5) (6) (7)
2012-13 85,46,275 0.50 42,90,426 10,10,661 2,66,76,772 12.3%
2013-14 90,63,649 0.50 45,17,051 11,00,610 2,96,88,120 11.5%
2014-15 97,12,133 0.50 48,27,952 11,78,644 3,20,75,086 11.4%
2015-16 1,04,91,870 0.50 52,48,999 12,70,890 3,58,53,477 11.1%
2016-17 1,13,28,285 0.49 55,87,142 13,81,526 3,75,40,296 11.2%
2017-18 1,20,34,171 0.49 58,88,773 14,89,921 3,95,77,694 11.1%
2018-19 1,27,33,798 0.49 61,83,330 16,14,455 4,24,24,566 10.8%
2019-20 1,32,36,100 0.48 63,27,168 17,31,178 4,69,73,698 9.8%
2020-21 1,26,87,345 0.48 60,96,735 18,32,759 4,95,49,369 8.6%
2021-22 1,38,76,840 0.48 66,63,430 19,55,788 4,89,10,789 9.6%
2022-23 1,48,78,028 0.48 70,92,668 20,87,964 5,14,45,594 9.7%
Average 10.6%
Note: The formulae applied are: Col. (4) = Col. [(2)*(3)]. Then, Col. (7) = Col. [(4) – (5)/ (6)].
79
A.3. Weighted Average Approach
The weighted average approach computes the social discount rate as a weighted average of the
social rate of time preference (�
�), marginal product of capital (
) and the real interest rate on
foreign borrowings (
�):
=��
�+�
+(1−�−�)
�.
Burgess and Zerbe (2011) provide a tractable formulation of the weighted average discount
rate, as follows:
=
−(
�
)(
�
)��+((
1
��
)−1)
�
−(
�
)(
�
)+
1
��
(A.11)
We decompose this formula to derive the weights placed on each of the three discount rates, as
follows:
�=
−(
�
)(
�
)
−(
�
)(
�
)+
1
��
(A.12)
�=
1
−(
�
)(
�
)+
1
��
(A.13)
(1−�−�)=
(
1
��
)−1
−(
�
)(
�
)+
1
��
(A.14)
We estimate parameter values for each of the parameters in the above equations to estimate the
weights, � and �, as follows:
- Interest elasticity of savings: According to Burgess and Zerbe (2011), the interest
elasticity of savings is calculated as the product of the elasticity of inter-temporal
substitution and the proportion of wealth that is consumed in the economy. Since the
elasticity of inter-temporal substitution is the reciprocal of the elasticity of the marginal
utility of consumption, we obtain this as the reciprocal of estimated earlier. Next, we
calculate the proportion of national wealth that is consumed based on recent work by
Bharti et al. (2024). Thus, we estimate �=0.06.
80
- Interest elasticity of investment: We estimate this parameter using firm-level data on
annual investment from the Annual Survey of Industries and data on the real interest
rate from the RBI. We estimate a linear regression model and obtain a mean estimate
for. We also conduct a sensitivity check to estimate the range of values for based on the
confidence interval of the regression estimate. This leads to a range for n from - 0.48 to
-0.12.
- Savings to Investment Ratio: This is obtained from the National Accounts Statistics,
2024, as 0.95.
- Savings Retention Coefficient (SRC): This is calculated as a ratio of the savings-
output ratio on the investment-output ratio from the National Accounts Statistics, to
assess the fraction of national savings that are retained domestically in the form of
investment. We obtain the SRC as 0.95.
Table A.3.1. displays the calculated weights for the weighted average approach, corresponding
to the mean estimate and the lower and upper bound estimates presented in Table 7.
Table A.3.1. Weights on private consumption, investment, and foreign borrowing:
WA approach
Remarks on regression
coefficient (interest
elasticity of investment)
Weight
(Private
Consumption)
Weight
(Private
Investment)
Weight
(Foreign Borrowing)
SDR
α β 1-α-β
Mean estimate 0.15 0.81 0.04 9.23
Upper bound 0.10 0.85 0.04 9.59
Lower bound 0.30 0.66 0.03 8.12
A.4. Other approaches to estimating
The first approach proposed by Groom and Maddison (2019) to estimate the elasticity of
marginal utility of consumption, , is the equal sacrifice principle, which is applied in this
report and examined in section 2.2.1. Groom and Maddison (2019) outline four other
approaches to estimate . We investigate three of these four approaches, finding imprecise
81
estimates of , with only the equal sacrifice approach yielding plausible results for and hence
the social discount rate, based on the Ramsey rule. We present results from these methods
below. We omit the risk aversion approach due to lack of data on insurance premiums in the
Indian context.
A.4.1. Euler equation approach
Groom and Maddison (2019) propose the Euler equation approach to estimate the elasticity of
marginal utility of consumption, , drawing on a lifecycle model, where consumers maximise
lifetime discounted utility, subject to a lifetime wealth constraint. The optimisation problem
leads to the Euler consumption equation, defined as follows:
�
′
(
�)=�(1+�
�)�
′
(
�+1) (A.15)
where �
� is the real interest rate prevailing in the financial market.
The Euler consumption equation leads to the following estimating equation for the elasticity of
marginal felicity, :
���� (
�+1
�
) =
1
���� � +
1
���� (1+�
�)
(A.16)
where is the elasticity of marginal felicity.
Results
We draw on annual data on private final consumption expenditure (PFCE) at constant prices
from the National Accounts Statistics, MOSPI, for 1950-51 to 2022-23 and real interest rates
(nominal bank rate less the annual inflation rate) from the Reserve Bank of India for the
corresponding period. We estimate an OLS regression (applying the Newey-West standard
errors to correct for heteroscedasticity and ergodicity) to estimate the elasticity of intertemporal
substitution, =
1
, and correspondingly, . We find ranges from 2.2 to 2.9 across
82
specifications, which significantly exceeds the plausible range of estimates of observed in
the literature.
Table A.4.1. Regression estimates of the Euler equation and elasticity of the
marginal felicity of consumption,
���� (
�+2
�
)
(1) (2)
Compound Real Bank
Rate (over two years)
0.34
*
(0.185)
Compound Real Deposit
Rate (over two years)
0.45
**
(0.215)
Constant -0.39 -0.54
*
(0.258) (0.298)
Observations 33 26
F-Statistic 3.39 4.46
η 2.94 2.2
Newey-West standard errors in parentheses.
*
p < 0.10,
**
p < 0.05,
***
p < 0.01
A.4.2. Frisch approach
The next approach is based on the Frisch formula, which assumes commodities satisfy additive
separability, to estimate the elasticity of marginal felicity (Groom and Maddison 2019):
=
(1−
)
�
(A.18)
where
is the income (budget) elasticity of demand for good i, �
is the budget share and �
is the own-price compensated elasticity of demand for good i. For parameters to be consistent
with consumer theory, �
<0. Hence, for >0 requires
<0 or (1−�
)<0.
83
Results
We use household-level data from the NSS Household Consumer Expenditure Survey, 2022-
23, to estimate the price and income elasticities of demand for food items, with results
displayed in Table A.4.2. Regression estimates based on the Frisch Approach yield negative
estimates of the elasticity of the marginal felicity of consumption (=−0.21), and hence,
negative discount rates. Groom and Maddison (2019) implement this approach on data for the
UK and find =−3.57. However, NABARD (2024) estimate a positive compensated own-
price elasticity of demand, which is inconsistent with economic theory, finding a value for =
0.8. Given the inconsistency of our estimates with economic theory, we do not recommend use
of this method for calculation of the social discount rate by the Government of India. Groom
and Maddison (2019) also acknowledge the limitations of this approach and do not recommend
this method for calculation of the social discount rate for government projects.
Table A.4.2. Estimates of risk aversion parameter from NSS HCES data, 2022-23
(1) (2)
Budget Share (Food) ln (Food Exp.)
ln (Food Exp.) -0.07
***
(0.001)
ln (Price, Food) -0.04
***
(0.002)
ln (Price, Other Nondurable) -0.03
***
(0.001)
HH. Size 0.01
***
0.11
***
(0.000) (0.001)
Urban 0.01
***
0.04
***
(0.000) (0.002)
ln (Total HH. Exp.) 0.43
***
(0.002)
Constant 1.35
***
3.88
***
(0.010) (0.026)
Observations 224,555 228,284
84
R
2
0.371 0.522
0.26
�
-1.10
�
0.40
-0.21
Note: Robust standard errors in parentheses. Regression includes categorical variables
for state code.
*
p < 0.10,
**
p < 0.05,
***
p < 0.01
A.4.3. Subjective well-being approach
The subjective well-being approach measures the association between consumption and utility
from directly observable household-level data on self-reported well-being and levels of
household consumption (Groom and Maddison 2019). In the absence of these data, we rely on
the World Values Survey, which conducted a longitudinal survey of 1,700 individuals from
1989-2022, across six waves, for India. The survey contains subjective questions on
individual’s self-reported “general satisfaction with life” on a ten-point scale
28
and questions
on the individual’s range of incomes, such as “Less than Rs 500 per month”, “501 - 1000 per
month” etc. However, data are missing for this question for majority of the sample.
Specifically, this question was not posed to respondents after the 1999-2000 survey wave.
To estimate the elasticity of the marginal felicity of consumption (), we require an additional
assumption of the functional form for utility. For consistency with preceding analyses, we
assume the utility function is of the constant relative risk aversion (CRRA) form, as follows:
�(
�)={
�
(1−)
1−
,>0; ≠1 ����
� ,=1
Hence, the marginal utility of consumption, �
′
(
�)=
�
−
for >0 and ≠1. For an
average level of individual consumption (or earnings),
�, we compute the coefficient of
relative risk aversion, , from our point estimate of the marginal utility of consumption, �
′
(
�).
28
The specific question is: “All things considered, how satisfied are you with your life as a whole these days?
Using this card on which 1 means you are “completely dissatisfied” and 10 means you are “completely satisfied”
where would you put your satisfaction with your life as a whole?”
85
Results
We use longitudinal data for approximately 1,700 individuals, for 1989-2022, from the World
Values Survey to estimate the marginal utility of consumption, �
�
′
=
−
for a CRRA utility
function, and calculate the value of . We find ranges from 0.3 to 0.4 (Table A.4.3.). We
conduct a robustness check using income ranges, provided in the data for the 1999-2004 survey
wave. We find a similar point estimate of 0.23, which suggests = 0.26.
The relatively low values observed for appear inconsistent with the literature, which finds
estimates approximately close to 1 or greater than 1. This is potentially due to the subjective
nature of questions asked in the survey, which may not yield consistent quantitative estimates
for . Hence, we do not recommend this approach to calculating and the social discount rate.
Table A.4.3. Association between individual’s income category and life satisfaction
Life
Happiness
Life
Happiness
Life
Satisfaction
Life
Satisfaction
Income Scale 0.10
***
0.21
***
0.13
***
0.23
***
(Estimate of �
�
′
) (0.004) (0.040) (0.005) (0.008)
Age -0.01
***
-0.01
***
-0.00
***
-0.01
***
(0.001) (0.003) (0.001) (0.001)
Female -0.04
*
-0.08
*
-0.05
**
-0.07
**
(0.021) (0.047) (0.019) (0.032)
Observations 11,794 11,794 11,665 11,665
Average Daily Consumption
(INR), 2022
270 270 270 270
0.41 0.29 0.36 0.27
Note: Robust standard errors in parentheses. Regressions include language categorical variables. The average
daily consumption is based on a provisional estimate of annual national income per capita of INR 98,374 for
2022-23, published by the Ministry of Statistics and Programme Implementation.
*
p < 0.10,
**
p < 0.05,
***
p < 0.01
86
A.5 Shadow Exchange Rate Factor (SERF), based on alternative method
The NITI Aayog (2018) reported calculated the shadow exchange rate factor using the
following formula:
����=
�
��+
��
�
�
�
(1+�)
+
�
�
(1+)
where �
� is the price elasticity of export supply,
�
is the price elasticity of import demand, �
is the average export subsidy across products, is the average import tariff across products, �
is the total value of exports and � is the total value of imports under protection. We also
calculate the SERF using this alternative method (as applied in NITI Aayog 2018). To do so,
we apply an average import demand elasticity (
�
) and average export supply elasticity (�
�),
estimated by the International Monetary Fund for India and several other countries, using
annual trade data over the 2001-2004 period (Tokarick 2010). Next, we obtain data on the total
values of imports and exports for 2023-24 from the Ministry of Commerce and Industry,
Government of India. We also present the SERF values using this method for the last five years,
i.e. 2019-20 to 2023-24. The results are presented in Table A.5.A below.
Table A.5.A: Shadow Exchange Rate Factor (Alternative Method), 2019-20 to 2023-24
Year
Value of
Imports (INR
Crores)
Value of
Exports (INR
Crores)
Average
Import
tariff (%)
Import
demand
elasticity
Export
supply
elasticity
Average
Subsidy
Rate (%)
SER
F
2019-20 33,60,954 22,19,854 11.2 -1.16 1.21 0 1.5
2020-21 29,15,958 21,59,043 12.6 -1.16 1.21 0 2.0
2021-22 45,72,775 31,47,021 11.3 -1.16 1.21 0 1.6
2022-23 57,49,801 36,21,550 12.0 -1.16 1.21 0 1.5
2023-24 56,16,042 36,18,952 12.0 -1.16 1.21 0 1.5
This method suggests a shadow exchange rate factor of 1.48, which is significantly higher than
the previously calculated value of 1.09, based on the ADB method. An exchange rate factor of
87
1.48 suggests an average foreign exchange premium of 48%, which is inconsistent with the
observed average import tariff of 12% across tradables for India. It is to be noted that this
calculation relies on import demand and export supply elasticities estimated for the 2001-2004
period by the IMF. Since these elasticity values have not been updated over the last two
decades, we would not recommend applying this method to compute the shadow exchange rate
factor for the Indian economy.
A.6 Synthesis of estimates for the Social Cost of Carbon
Table A.6.A: Synthesis of estimates for the Social Cost of Carbon
Study Model / Method Key Assumptions
Social Cost of Carbon
(SCC) (USD/ton CO₂)
Price Base
Moore et al.
(2024)
Meta-analysis (1,823
estimates from 147
studies; includes
DICE, FUND, PAGE)
Parameter values
from expert elicitation
surveys and random
forest synthesis
Mean: $132; synthetic
mean $185 (Interquartile
Range: $97–$369)
2020 US$
Barrage &
Nordhaus
(2024)
DICE-2023 (Dynamic
Integrated Climate–
Economy Model)
Constant discount
rates (1–5%)
$37–$571 (range by
discount rate); $59
(welfare-maximizing
value)
2019 US$
Rennert et al.
(2022)
GIVE (Greenhouse
Gas Impact Value
Estimator)
Risk-free social
discount rate of 2%
Mean: $185 (95%
Confidence Interval: $44–
$413)
2020 US$
Ricke et al.
(2018)
Empirical climate–
economic model
(Burke–Hsiang–
Miguel 2015
framework)
Country-level SCC
(CSCC) using non-
linear temperature-
output link
Global SCC: $417; India
= $86 (range $49–157)
2010 US$
88