Theory and Practice in the Choice of Social Discount Rate for Cost-Benefit Analysis: A Survey

8/22/2019 Theory and Practice in the Choice of Social Discount Rate for Cost-Benefit Analysis: A Survey

1/51

May 2007

ERDECONOMICS AND RESEARCH DEPARTMENT

Working PaperSERIESNo.

94

Juzhong Zhuang, Zhihong Liang,Tun Lin, and Franklin De Guzman

Theory and Practice in the Chof Social Discount Rate

for Cost-Benefit Analysis:A Survey

Theory and Practice in the Chof Social Discount Rate

for Cost-Benefit Analysis:A Survey


2/51


3/51

ERD Working Paper No. 94

Theoryand PracTiceinThe choice

of Social diScounT raTe

for coST-benefiTanalySiS: a Survey

Juzhong zhuang, zhihong liang, Tun lin, and franklin de guzman

may 2007

Juzhong Zhuang, Tun Lin, and Franklin De Guzman are Assistant Chie Economist, Economist, and Economics Ofcer,

respectively, at the Economic Analysis and Operations Support Division, Economics and Research Department, AsianDevelopment Bank (ADB); and Zhihong Liang is a Ph.D. candidate in Economics at the University o Guelph (Canada).

The authors thank Izal Ali or guidance in preparing this paper and suggestions in fnalizing it; David Dole orinitiating this work; and Anneli Lagman-Martin or research assistance. Comments rom Ramesh Adhikari, Richard

Bolt, Eunkyung Kwon, Herath Gunatilake, Muhammad Ehsan Khan, Donghyun Park, Nigel Rayner, and Hyun Hwa Son

are grateully acknowledged.


4/51

Asian Development Bank6 ADB Avenue, Mandaluyong City1550 Metro Manila, Philippines

www.adb.org/economics

2007 by Asian Development BankMay 2007

ISSN 1655-5252

The views expressed in this paper

are those o the author(s) and do notnecessarily refect the views or policies

o the Asian Development Bank.


5/51

FoREWoRD

The ERD Working Paper Series is a orum or ongoing and recently completedresearch and policy studies undertaken in the Asian Development Bank or on

its behal. The Series is a quick-disseminating, inormal publication meant tostimulate discussion and elicit eedback. Papers published under this Seriescould subsequently be revised or publication as articles in proessional journalsor chapters in books.


6/51


7/51

CoNtENts

Abstract vii

I. IntroductionI. Introduction 1

II. Theoretical oundations or the Choice o a Social Discount RateII. Theoretical oundations or the Choice o a Social Discount Rate 2

A. Approaches to Discounting uture Benets and CostsA. Approaches to Discounting uture Benets and CostsUnsettled Debate 2

B. Social Rate o Time Preerence 4 C. Marginal Social Opportunity Cost o Capital 9 D. Weighted Average Approach 10 E. Shadow Price o Capital Approach 12 . Discounting Intergenerational Projects 14

III. The Social Discount Rate in Practice around the World 1III. The Social Discount Rate in Practice around the World 16

A. Countries around the World 1A. Countries around the World 16 B. MDBs and other Supra-National Agencies 19

I. Concluding Remarks 2I. Concluding Remarks 21

Appendix Estimating the Social Discount Rate Using theAppendix Estimating the Social Discount Rate Using theWeighted Average Approach 24

Reerences 2Reerences 26


8/51


9/51

AbstRACt

The choice of an appropriate social discount rate for costbenet analysis

of public projects has long been a contentious issue and subject to intense

debate among economists. This debate has gained new impetus from the recent

discussions on the economics of climate change. The purpose of this paper is

to survey theories and practices in the choice of the social discount rate. More

specically, the paper examines economic arguments for discounting future

benets and costs and analytical approaches to the choice of the social discount

rate, including how a social discount rate can be estimated empirically undereach approach; and policy practices followed by countries around the world in

the choice of the social discount rate. This paper is intended as a reference

material on project economic analysis for ADB staff, consultants, and concerned

government ofcials in developing member countries.


10/51


11/51

I. INtRoDuCtIoN

The choice o an appropriate social discount rate1 or costbenet analysis o public investment

projects has long been a contentious issue and subject to intense debate in the economics literature.The recently released The Economics o Climate Change: The Stern Reviewhas added new impetus tothis debate (Stern 2006). The Review issued a stunning warning that ailing to invest 1 percent o

world gross domestic product (GDP) now to reduce global warming could risk a uture reduction oup to 20% in global GDP. Critics have argued that these results, dramatically dierent rom earlierstudies using the same basic data and analytical structure, depend crucially on a very low socialdiscount rate1.4%used in economic modeling. I a higher discount rate more in line with its

usual range had been applied, the estimated cost o not acting now would be reduced by an order

o magnitude (Nordhaus 2006 and Dasgupta 2006).

A social discount rate refects a societys relative valuation on todays well-being versus well-

being in the uture. Choosing an appropriate social discount rate is crucial or costbenet analysis,and has important implications or resource allocations. Setting the social discount rate too highcould preclude many socially desirable public projects rom being undertaken, while setting it too low

risks making a lot o economically inecient investments. urther, a relatively high social discountrate, by attaching less weight to benet and cost streams that occur in the distant uture, avorsprojects with benets occurring at earlier dates; while a relatively low social discount rate avorsprojects with benets occurring at later dates. Choice o the social discount rate aects not only

the ex ante decision o whether a specic public sector project deserves the unding, but also theex postevaluation o its perormance.

Economic eciency requires that the social discount rate measure the marginal social opportunity

cost o unds allocated to public investment. In a perectly competitive world without marketdistortions, the market interest rate is the appropriate social discount rate. In the real world wheremarkets are distorted, the market interest rate will no longer refect marginal social opportunitycost o public unds. Economists have proposed several alternative approaches to the choice o

the social discount rate in the presence o market distortions, but there has been no consensuson which is the most appropriate. The dierences among these approaches refect largely dieringviews on how public investment aects domestic consumption, private investment, and the cost

o international borrowing. In cases o very long-term projects with impacts lasting or more thanone generation or even hundreds o years, such as those addressing climate changes and otherenvironment problems, many have argued that the choice o the social discount rate should not

only consider economic eciency, but also intergenerational equity.

There are signicant variations in public discount rate policies practised by countries aroundthe world, with developing countries in general applying higher social discount rates (815%) thandeveloped countries (37%). These variations refect the dierent analytical approaches ollowed

by various countries in choosing the social discount rate. But more undamentally, it can be argued

1 The social discount rate is sometimes also reerred to as the cut-o economic internal rate o return (EIRR).


12/51

that the divergence refects dierences in the perceived social opportunity cost o public unds

across countries and in the extent to which the issue o intergenerational equity is taken intoconsideration in setting the social discount rate.

The purpose o this paper is to provide a survey o the vast literature on the social discount

rate that the decades o debate have generated, covering theory, estimation methods, and policypractices.2 More specically, the rest o the paper attempts to ask and answer the ollowingquestions

(i) What are the economic arguments or discounting uture benets and costs and analyticalapproaches to the choice o the social discount rate?

(ii) How can a social discount rate be estimated empirically under each approach?

(iii) What are the policy practices ollowed by countries around the world and by multilateraldevelopment banks (MDBs) in the choice o the social discount rate?

The choice o social discount rate is also an important issue or MDBs, including the AsianDevelopment Bank (ADB), and has signicant relevance or their operations. In both ex ante

project economic analysis and ex postproject perormance evaluation, most MDBs estimate andevaluate benets and costs o development projects using a uniorm cut-o discount rate, alsocalled economic internal rate o return (EIRR), o 1012 percent. This paper is intended not only toprovide a reerence material on project economic analysis or ADB sta, consultants, and concernedgovernment ocials o ADBs developing member countries (DMCs), but also to stimulate discussions

among MDBs on whether the current practice o applying a uniorm social discount rate o 1012%to all development projects in all countries is still appropriate in a changing world.

II. thEoREtICAl FouNDAtIoNs FoR thE ChoICE oF A soCIAl DIsCouNt RAtE

A. Apprace Dicnin Fre benef and C: uneed Deae

A public investment project typically incurs costs and generates benets at dierent points

o time. A common practice in costbenet analysis, called discounting, is to express all costs andbenets in terms o their present value by assigning smaller weights to those that occur urtheraway in the uture than to those occurring more recently. Discounting, a critical step in determiningwhether or not a public project is socially desirable, makes costs and benets with dierent time

paths comparable.3

There are two arguments why costs and benets with dierent time proles may not be

comparable i not properly discounted. The rst is that consumers (or savers) preer to receivethe same amount o goods and services sooner rather than later. There are two standard textbookexplanations or this time preerence (Dasgupta and Pearce 1972). The rst is that individuals expect

their level o consumption to increase in the uture, hence, marginal utility o consumption willdiminish. With this expectation, individuals would have to be paid more than one unit in the utureto compensate or sacricing (saving) one unit o consumption now. The second explanation, which

2 There have been a number o surveys and reviews o this subject in the literature (Stiglitz 1994, Spackman 2004, Evans2005). Most o these ocus either on theory, empirical estimation, or policy practices; not many look at all the three

aspects at the same time.3 Discounting is also required in investment decision making in the private sector where the present value o nancial

benets o a project is compared with that o nancial costs.

May2007

Theoryand PracTiceinThechoiceofSocial diScounTraTefor coSTBenefiTanalySiS: a Survey

Juzhongzhuang, zhihongliang, Tunlin, and franklindeguzMan


13/51

SecTion ii

TheoreTical foundaTionSforThechoiceofa Social diScounTraTe

has been a subject o great controversy (see Box 1), is that individuals have a positive pure time

preerence, that is, even i levels o uture consumption are not expected to change, they would stilldiscount the uture. Two reasons are oten quoted in explaining the pure time preerence. One isthat consumers are generally impatient or myopic. The other is the risk o not being alive in the

uture. According to these lines o reasoning, the rate to discount uture benets and costs shouldbe the marginal social rate o time preerence (SRTP), that is, the rate at which society is willingto postpone a marginal unit o current consumption in exchange or more uture consumption.4

The second argument or discounting uture costs and benets takes the perspective o a producer(or an investor). According to this, capital is productive and resources acquired or a particularproject can be invested elsewhere, generate returns, and so have an opportunity cost. Thereore,to persuade an investor to invest in a project, the expected return rom the investment should be

at least as high as the opportunity cost o unding, which is the expected return rom the nextbest investment alternative. ollowing this logic, the rate the investor should use in discountingbenets and costs o a project is the marginal rate o return on investment in the private sector.

In the absence o market distortions, this is equivalent to the marginal social rate o return onprivate investment, also termed marginal social opportunity cost o capital (SOC).

In a perectly competitive economy without distortions, prices o inputs and outputs would

refect their economic or social values. The supply and demand prices o investible unds are givenby SRTP and SOC, respectively. The capital market clears at an interest rate that equates the supplyo and demand or investible unds. Both SRTP and SOC are equal to the market interest rate. Themarket interest rate refects marginal social opportunity cost o investible unds, which is then the

appropriate social discount rate to achieve an ecient allocation o resources in the economy.

In reality, the market is oten distorted due to various imperections. A typical example oimperection is the taxes imposed on corporate incomes and individuals interest earnings. Other

examples are risks, inormation asymmetry, and externalities. These imperections create a wedgebetween SRTP and SOC (with the ormer generally lower than the latter), and make both deviate

rom the market interest rate. Under such circumstances, the market interest rate will not refectthe marginal social opportunity cost o public unds, and the latter will vary depending on whetherit is measured in terms o SRTP or SOC. What rate then should be used to discount uture benetsand costs in costbenet analysis? The debate on this has been ongoing or many decades. ouralternative approaches have been put orward (i) SRTP, (ii) SOC, (iii) weighted average approach,

and (iv) shadow price o capital (SPC) approach. However, there has been no consensus on whichis the most appropriate (Boardman et al. 2001). In essence, these dierent approaches refectdiering views on how public projects aect domestic consumption, private investment, and costo international borrowing.

Earlier discussions on public sector discounting coincided with the rise o costbenet analysisin the 1960s and 1970s. In the 1990s, the choice o the social discount rate was brought up again

in the context o nding a rate to discount the long-term environmental benets and costs, such asthose related to addressing climate changes and global warming. Here, the problem o choosing anappropriate discount rate is urther complicated by the consideration o intergenerational equity. Inthe ollowing subsections, we review in some detail how the social discount rate can be estimated

under each o the our approaches, and the latest debate on how to choose a discount rate orvery long-lived environmental projects.

4 Here we disregard the issues involved in aggregating individual preerences into the social preerence. See Dasgupta

and Pearce (1972) or discussions on these issues.

erd WorkingPaPer SerieSno. 94


14/51

b. scia Rae time Preerence

The social rate o time preerence is the rate at which a society is willing to postpone a unito current consumption in exchange or more uture consumption. The use o SRTP as the socialdiscount rate, supported by Sen (1961), Marglin (1963a and b), Diamond (1968), and Kay (1972),

is based on the argument that public projects displace current consumption, and streams o costsand benets to be discounted are essentially streams o consumption goods either postponed orgained. Two alternative methods have been suggested or empirical estimation o SRTP. One is to

approximate it by the ater-tax rate o return on government bonds or other low-risk marketablesecurities. Although this is straightorward, a major concern is that individuals may not express alltheir preerences concerning the uture in the marketplace and, even i they do, their preerencesexpressed as individuals may not be the same as their preerences expressed when they see

themselves as part o a society. Society as a whole would have a lower rate o discount in itscollective attitude than the observed market rates, which could refect individuals myopia (Dasguptaand Pearce 1972).

The other method is to use a ormula named ater the renowned British economist rank P.

Ramsey. According to Ramseys ormula derived rom a growth model, SRTP is the sum o two termsthe rst is a utility discount rate refecting the pure time preerence and the second is the producto two parametersthe elasticity o the marginal utility o consumption5 and the annual rate o

growth o per capita real consumption (Ramsey 1928). The second term o the ormula refectsthe act that, when consumption is expected to grow in the uture, people will be less willing tosave in the current period to obtain more in the uture, because o diminishing marginal utility o

consumption. Using the Ramsey ormula to empirically estimate SRTP requires inormation on theutility discount rate (), elasticity o marginal utility o consumption (), and annual rate o percapita real consumption growth (g). The choice og is relatively straightorward while the choiceo and is more dicult, as it involves normative value judgments, and has been a subject o

intense debate, as discussed in Box 1.

The utility discount rate, , is conceptually considered as consisting o two components, onerelated to individuals impatience or myopia and the other related to the risk o death or human

race extinction.6 Many empirical studies set the rst component to zero oten on the ethical ground(see, or example, Kula 1984, 1987, and 2004; Cline 1992; Stern 2006). It has also been arguedthat considering myopia in estimating SRTP implies introducing irrationality into the decision-

making process, which is inconsistent with the principle o costbenet analysis, i.e., to bringrationality into investment decisions (Kula 1984). The diculty in empirically estimating this rstcomponent o pure time preerence could also be a reason why many studies have ignored it. Onthe other hand, setting this to zero does lead to some paradoxical results (see Box 1). Among

empirical studies that consider this to be positive, the suggested range is 00.5% (OXERA 2002).Scott (1977 and 1989) argues that the long-run savings behavior in the United Kingdom (UK) is

consistent with a value o 0.30.5% or this component o.

Table 1 provides a survey o someo the empirical studies on the utility discount rate including both o its two components. The

suggested range is 13 percent.

5 The elasticity o marginal utility o consumption is the percentage change in individuals marginal utility correspondingto each percentage change in consumption.

6 In the literature, some authors relate the pure time preerence only to the rst component while most relate it to

both. In this paper, we ollow the convention used by most authors pure time preerence refects both individualsimpatience and risk o not being alive in the uture.

4 May2007




15/51

or the component o the utility discount rate related to the risk o not being alive in the

uture, the controversy is not on whether it should be considered; rather, it is on how to measurethis risk. Some attempt to estimate individuals survival probability and risk o death using deathrate statistics (Kula 1984, 1987, 2004). Others argue that individuals risk o death is not relevant

to the derivation o the social time preerence; what is relevant is the changing lie chance orwhole generations (Pearce and Ulph 1999).

box 1

The debaTeon Pure Time Preference

Many argue that the positive pure time preerence, which implies valuing utility o uture

generations less than the present generation, is ethically indeensible (Ramsey 1928, Pigou 1932,Harrod 1948, Solow 1974). Others, while admitting that ethically all generations should be treated alike,

point out that a zero rate o pure time preerence implies a savings rate excessively higher than what wenormally observe and contradicts real world savings behavior, leading also to other paradoxical results

(Arrow 1995). There are also those who argue that the risk o death, or mortality, is a rational enough

reason or positive pure time preerence (Eckstein 1961). This argument, although more amenable toempirical investigation and less prone to undamental disputes about value judgments, is also subject

to disagreement about what precise risks are being discussed (Pearce and Ulph 1999). Dasgupta andPearce (1972) highlight the problem o considering risk-o-death time preerence in calculating the

social discount rate, because the social time preerence relates to society, and not to an aggregate oindividuals; although individuals are mortal and society is not. Among more recent empirical studies,

some authors look at the increasing risk o death, or changing survival probability, or an individualas one gets older (Kula 1985, 1987, 2004; Evans and Sezer 2004). Pearce and Ulph (1999) highlightproblems o this approach, and argue that when dealing with very long-lived projects, the appropriate

risks are not so much the increasing probability o death o a single individual, but what is happeningto the lie chances o whole generations. Newbery (1992) attempts to measure this risk by estimating

the perceived risk o the end o mankind in 100 years. The Green Booko the UK HM Treasury reers tothis as a catastrophe risk, that is, the likelihood that there will be some events so devastating that

all returns rom policies, programs, or projects are eliminated, or at least radically and unpredictablyaltered (HM Treasury 2003). The Stern Review denes this as the risk o extinction o the human raceand argues that such risks could arise rom possible shocks such as a meteorite, a nuclear war, or a

devastating outbreak o some diseases.

Empirical estimates o the elasticity o marginal utility o consumption () also vary rom

one study to another. Three dierent approaches have been used direct survey methods; indirectbehavioral evidence; and revealed social values (see a recent review by Evans 2005). The surveymethods ocus on measuring risk and inequality aversion7 rom responses to specially designedsurvey questions. The indirect behavioral evidence is based on observed consumption behaviors

rom empirically estimated consumer demand models. The third approach in estimating involves

inerence rom government behavior revealed through spending and tax policies. A survey oempirical estimates o based on the three approaches indicates that its values mostly all within

the range rom 1 to 2%, except or a ew outliers (Table 2). The dierences suggest that the results

7 Risk aversion measures the reluctance o an individual to accept a bargain with an uncertain payo rather thanRisk aversion measures the reluctance o an individual to accept a bargain with an uncertain payo rather than

another bargain with a more certain but possibly lower expected payo. Inequality aversion measures an individuals

tolerance to income inequality. Risk aversion is closely related to inequality aversion, and both are closely related tothe elasticity o marginal utility o consumption.

SecTion ii




16/51

are sensitive to model specication, level o aggregation in the data, choice o estimators, sample

size, and the length o sample periods.

Table 1

emPirical eSTimaTeSofThe uTiliTy diScounTraTe

Source emPirical eSTimaTeS TheoreTical baSiS

Scott (1977) 1.5% Component refecting myopia is 0.5%, and

that refecting the changing lie chance dueto the risk o total destruction o a society is1.0%

Kula (1985) 2.2% Refecting average annual survival probabilityin the UK during 19001975

Kula (1987) 1.2% Refecting average annual probability o

death in the UK in 1975

Scott (1989) 1.3% Component refecting myopia is 0.3%, and

that refecting the changing lie chance dueto the risk o total destruction o a society is1.0%

Newbery (1992) 1.0% Perceived risk o the end o mankind in 100years

Dynamic Integrated

Model o Climate and theEconomy (DICE) model(Nordhaus 1993)

3% per year Utility discount rate refecting pure social

time preerence, determined by calibratingthe DICE model to match actual data

Pearce and Ulph (1995) 1.1% Refecting the average annual probability o death in the UK in 1991

Arrow (1995) 1% Utility discount rate refecting pure social

time preerence, and matching the observedsavings behavior

OXERA (2002) Myopia = 0-0.5%

Risk o death = 1.1% witha projected change in the

near uture to 1.0%

Based on previous studies and projected and

recent average annual death rates in the UK

Evans and Sezer (2004) 1.01.5% 1% or EU countries and 1.5% or non-EUcountries, refecting catastrophe risks

Kula (2004) 1.3% Refecting the average annual death rate inIndia during 19651995

Evans (2006) 1% Based on the approximate average annual

death rate in 20022004 in 15 countries othe European Union

Stern Review (2006) 0.1% Probability o human race extinction per year

Sources Compiled by authors.

May2007




17/51

Table 2

emPirical eSTimaTeSofThe elaSTiciTyof marginal uTiliTyof conSumPTion

Source emPirical eSTimaTeS daTeS

A. srvey Med

Barsky et al. (1995)

Amiel et al. (1999)

Approximately 4.0

0.20.8

Refecting risk aversion o

the US middle-aged whowere surveyed

Relecting inequali tyaversion o US students

who were surveyed

b. Indirec beavira Evidence

Constant elasticity demand models

Kula (1984)Kula (1984)Evans and Sezer (2002)Evans (2004a)

Kula (2004)Evans et al. (2005)

Percoco (2006)

Almost ideal demand system

Blundell (1988)Evans (2004b)

Lifetime consumption model

Blundell et al. (1994)

Quadratic almost ideal demand system

Blundell et al. (1993)

Banks et al. (1997)

1.561.891.64

1.61.64

1.61.28

1.97

1.33

1.21.4

1.06

1.061.371.07

Canada 19541976 dataUS 19541976 dataUK 19671997 data

UK 19652001 dataIndia 19651995 data

UK 19632002 dataItaly 19802004 data

UK 19701984 data

rance 19702001 data

UK 19701986 data

UK 19701984 dataAggregate model

Micro modelsUK 1970-1986 data

C. Reveaed scia Vae

Cowell and Gardiner (1999)Evans and Sezer (2004)

Evans (2005)

1.28-1.411.5

1.25-1.45

UK 19992000 dataUK 20012002 data

ive major OECD countries(rance, Germany, Japan,

UK, US) 20022003 data

Sources Evans (2005); compiled by authors.

SecTion ii




18/51

With estimates o, , and g, SRTP can be calculated using the Ramsey ormula. Box 2 provides

an illustration.

box 2

eSTimaTing SrTP uSingThe ramSey formula

Consider the ollowing Ramsey growth model where the representative agent maximizes its lie-time

welare subject to intertemporal constraints (Ramsey 1928)

Maximize U c e dt tt( )

0

(1)

subject to k k c t t t= ( ) (2)

where U(.) represents a time-invariant utility unction with properties oU(.)>0(the marginal utility

o consumption is positive) and U(.)


19/51

A major criticism on using SRTP as the social discount rate is that it is purely a measure

o the social opportunity cost in terms o oregone consumption and ignores the act that publicprojects could displace or crowd out private sector investment i they cause the market interestrate to rise (Baumol 1968 and Harberger 1972). I additional public investment is made at the

cost o displacing private investment, its marginal social opportunity cost should also refect whatthe displaced private investment would otherwise bring to the society, which can be measuredby the marginal social rate o return on private sector investment (SOC).8 Since SRTP is generallylower than SOC because o the wedge created by market distortions such as taxes, this raises the

possibility that too many low-return investments in the public sector would be undertaken whenSRTP is used as the social discount rate.

C. Marina scia opprniy C Capia

The proposal or using the marginal social opportunity cost o capital (SOC) as the social

discount rate, advocated by Mishan (1967), Baumol (1968), and Diamond and Mirrlees (1971aand b), among others, is based on the argument that resources in any economy are scarce; that

government and private sector compete or the same pool o unds; that public investment displacesprivate investment dollar by dollar; and those devoted to public sector projects could be invested

in the private sector. Thereore, public investment should yield at least the same return as privateinvestment. I not, total social welare can be increased by reallocating resources to the privatesector, which yields higher returns.

It has been suggested that SOC could be approximated by the marginal pretax rate o returnon riskless private investments. A good proxy or this is the real pretax rate on top-rated corporatebonds (Moore et al. 2004). Box 3 provides an illustration o estimating the marginal rate o return

based on Moodys AAA bonds. Some have argued that SOC, as estimated in Box 3 should be adjusteddownward or a number o reasons (Lind 1982, Boardman et al. 2001). irst, in theory, the marginalpretax rate o return, rather than the average rate, should be used in estimating SOC. The marginal

rate o return will be lower than the average rate as rational businessmen will make their best dealrst. Second, the rate o return on private investment includes premiums to compensate investorsor risks that are generally higher than those or public sector investment. Third, returns on privateinvestment as social opportunity cost o capital may also be contaminated by market distortions

such as externalities and monopolistic pricing.

box 3

eSTimaTing Soc from yieldSon corPoraTe bondS

Based on the method used by Boardman et al. (2001), the average annual yield on Moodys AAAlong-term corporate bonds was estimated at 6.81% rom January 1947 to December 2005 in the United

States (US). Applying the 2004 corporate tax rate o 40% (KPMG 2004), the nominal pre-tax return onbonds was calculated at [0.0681 / (1- 0.38)] = 11.35 percent. A proxy or the expected rate o infation

is the average annual infation rate, which was 3.78% between 1947 and 2005 in the United States.Thereore, the real pretax rate o return on top-rated corporate bonds in the US is [(0.1135 0.0378) /

(1+0.0378)] = 7.29%, which approximates SOC.

8 This can be approximated by the pretax rate o return on private investment. See discussions in the nextsubsection.

SecTion ii


erd WorkingPaPer SerieSno. 94 9


20/51

Dasgupta, Marglin, and Sen (1972), on the other hand, note that the argument or using SOC

as the social discount rate is only justied in the context o a two-period model where the totalamount o capital available or investment is xed independently o project choice in the publicsector. In this case, the public investment displaces (or crowds out) private investment dollar

or dollar, and the marginal rate o return on private investment (inclusive o taxes) provides anadequate measure o SOC. But when either assumption (two-period model or xed amount o capital)is dropped, the argument would not hold anymore. I capital needed or nancing public projectsis partially satised by consumers postponing their current consumption, the return required by

consumers usually is less than the marginal rate o return on private investment; hence, the socialdiscount rate should be lower than SOC.

D. Weied Averae Apprac

Previous discussions suggest that using SRTP to discount uture costs and beneits is

problematic since it does not take into account impacts o public projects on unds available orprivate investment. Using SOC as the social discount rate, on the other hand, assumes that public

investment only displaces private investment and not private consumption, which is also not alwaystrue in reality. The weighted average approach, associated with contributions by, among others,

Harberger (1972), Sandmo and Drze (1971), and Burgess (1988), attempts to reconcile the SRTPapproach with that o SOC.

Proponents o the weighted average approach recognize that sources o unds available to

public projects may come rom displacing private investment, inducing consumers to postpone currentconsumption, and, in the case o an open economy, borrowing rom international capital markets.The social opportunity costs o unds rom these various sources are dierent because o market

distortions such as taxes. Thus, the social discount rate should be the weighted average o SOC,SRTP, and the cost o oreign borrowing, with weights refecting proportions o unds obtained romtheir respective sources. Harberger (1972) argues that SOC may dier rom one productive sector to

another and SRTP could also vary among dierent groups o savers (refecting, or instance, dierenttax brackets); thereore, SOC and SRTP themselves should be the weighted average o those o variousproductive sectors or saver groups. Burgess (1988) suggests that the weights depend also on thedegree o complementarity or substitutability between public and private investment, but points out

that the positive externalities o public investment due to its complementarity can be consideredas part o benet streams and, in that case, no adjustments to the weights are necessary.

or a closed economy, i the supply o unds is perectly inelastic, a public sector project will

displace only private investment, so the weight or SRTP will be zero and the social discount ratewill be equal to SOC. I, on the other hand, the demand or unds is perectly inelastic, a publicproject will only displace current consumption, the weight or SOC will be zero, and the socialdiscount rate will be equal to SRTP. In general, it is believed that both the supply and demand o

investible unds respond to changes in the market interest rate, so the social discount rate willlie somewhere between the two extremes. Harberger (1972), however, argues that the accumulatedeconometric evidence on investment unctions clearly shows that many categories o investmentare quite sensitive to changes in the interest rate, while evidence that savings are responsive to

interest rate changes is only scanty. Hence, there is a reasonable presumption that the relevantweighted average will be reasonably close, i not precisely equal, to SOC.

10 May2007




21/51

or an open economy where capital is mobile across countries, it is expected that the domestic

interest rate will be related in some way to the interest rate at which the country can borrow inthe world capital market (Sandmo and Drze 1971, Edwards 1986, Lind 1990). In the extreme caseo a small open economy with perect capital mobility, risk neutrality, pegged exchange rate (with

zero expected devaluation), and an innitely elastic supply o oreign capital, public projects willdisplace neither domestic consumption nor private investment. The weights or SOC and SRTP will,thereore, both be zero and the social discount rate will be equal to the international borrowingrate. However, Edwards (1986) argues that even a small economy with perect capital mobility will

ace an upward-sloping supply curve o oreign capital. One justication is that a higher level ooreign indebtedness could be related to a higher probability o deault as perceived by lenders, andto a higher cost at which this particular country can borrow rom the international capital market.In this case, a public project that is (partially) nanced with additional oreign debt will result in

a higher rate charged on oreign loans, and perhaps, higher domestic interest rates as well sincethe two are linked. Thereore, a public project will be nanced partially by an increase in oreigndebt, and partially by an increase in private savings and a reduction in private investment. Then,

in the presence o country risk premiums, the social discount rate will be a weighted average o

SOC, SRTP, and the international borrowing rate inclusive o risk premiums. 9 In another extreme,i a country aces credit rationing rom abroad, the new demand or public unds will be met ullyby additional domestic private savings and displaced private investment. Then, the social discount

rate will be a weighted average o only SOC and SRTP.

A key challenge in the empirical estimation o the social discount rate using the weightedaverage approach is to determine the weights attached to SRTP, SOC, and the international borrowing

rate, as well as weights or SRTPs o various saver groups and or SOCs o various productive sectors.Harberger (1972) provides a ormula or calculating the social discount rate using the weightedaverage approach in the case o a closed economy, where the weights are estimated rom interest

derivatives (the responses o private investment and savings to changes in market interest rates),which can also be expressed in terms o elasticities. Sandmo and Drze (1971) expands the ormula

to an open economy context by incorporating the international borrowing rate, with weights beingestimated rom the interest derivatives o the domestic and oreign supplies o unds. Based on

Harberger and Jenkins (2002), Box 4 provides an example using the weighted average approach toestimate the social discount rate, assuming varying SRTP among saver groups, varying SOC amongproductive sectors, taxation on interest earnings (including withholding tax or oreign savers) andon investment returns, and an upward-sloping supply curve o oreign capital.

A major criticism on the weighted average approach is that, while it recognizes that costso public investment can displace private investment, it assumes that benets will be consumed

immediately and ignores the act that they could also be reinvested in the private sector, generateuture consumption, and bring more social value than i they were consumed immediately. Recognizinghigher social cost o displaced private investment than displaced consumption, while ignoring the

higher social value o project benets that are reinvested than immediately consumed, leads tooverdiscounting o project benets. This overdiscounting will be higher the arther in the uture

9 Edwards (1986) argued that whether this higher interest rate should be considered as a higher cost o borrowing

will depend on the relationship between the probability o deault as perceived by the lenders and by borrowers. Ithe perceived probability o deault is the same or lenders and borrowers, the higher interest rate charged to the

developing country will not represent a higher economic cost o oreign unds. But in general, the perceived probability

o deault is dierent between lenders and borrowers (the ormer is mostly greater than the latter); the risk premiumdoes constitute economic cost or a borrowing country.

SecTion ii




22/51

the benets occur. Thereore, compared to SRTP, the weighted average approach could be biased

against long-term projects (Zerbe and Dively 1994).

box 4

eSTimaTingThe Social diScounTraTe uSingThe WeighTed average aPProach

According to the weighted average approach, also known as Harberger approach, the social

discount rate can be expressed as

= + +SOC i SRTP ( )1 (1)wheredenotes the social discount rate, ifis the governments real long-term oreign borrowing rate, is the proportion o unds or public investment obtained at the expense o private investment, is theproportion o unds obtained at the expense o current consumption, and (1 ) is the proportion

o unds rom oreign borrowing. SRTP and SOC are measured, respectively, by the rate o real return onsavings exclusive o (ii) and investments inclusive o (rj). Expressing the weights attached to dierent

unding sources in terms o elasticities o demand and supply o unds with respect to changes in

interest rates, equation (1) becomes

=

( ) + ( ) ( )

( ) + ( )

i i t i i

t j j t jj

i i ti

t

S S i S S i I I r

S S S S j j tj

I I( )(2)

where i j, , are respectively elasticities o savings, supply o oreign capital, and private investmentwith respect to the interest rate. Si/Stand S/Stare the shares to the total savings by various groups odomestic savers and oreign savers. Ij/It is the investment share o various business sectors.

Using Equation (2) and 19881989 data or Papua New Guinea, Harberger and Jenkins (2002)

present an example o calculating the social discount rate, which they call economic opportunity costo capital. The example assumes that there are our savers groups households, business, government,

and oreign. or each saver group, the real rate o return on savings was calculated rom the nominalmarket interest rate by taking out the respective taxes and infation. In estimating the real marginalcost o oreign borrowing, urther adjustment was made by taking into consideration the eects o

new borrowing on the countrys oreign borrowing rate. In the case o investors or demanders o unds,they were classied into the ollowing sectors housing, agriculture, manuacturing, government, and

mining. The nominal pre-tax rate o return on investment or each sector was again calculated rom thenormal market interest rate by adding respective tax rates.

These rates, together with the estimated saving shares and elasticities o various saver andinvestor groups, yield an estimated economic cost o capital, or the social discount rate, o 11.76percent. Detailed calculations are in the Appendix.

Source Harberger and Jenkins (2002).

E. sadw Price Capia Apprac

The shadow price o capital (SPC) approach, associated with contributions by eldstein (1972),Bradord (1975), and Lind (1982) among others, also attempts to reconcile the SRTP approach withthat o SOC and, at the same time, addresses the limitation o the weighted average approach. The

1 May2007




23/51

SPC approach recognizes that while costs o a public project can displace private investment, its

benets can also be reinvested in the private sector. In terms o generated uture consumptionstreams, these benets are worth more to society than i they are consumed immediately. Thus, thetotal cost o a public project is the sum o the current consumption that is directly displaced and

those uture consumption streams that are oregone due to the displacement o private investment.Similarly, the total benet o a public project is the sum o those immediately consumed and thoseuture consumption streams generated rom reinvestment.

The SPC approach involves our steps. The rst is estimating SPC, which is the present valueo streams o uture consumption oregone arising rom displacing one unit o private investmentor the present value o uture consumption streams generated rom reinvesting one unit o projectbenets in the private sector. The second step involves, or each time period, converting all the

costs and benets that either displace or generate private investment into consumption equivalentsby multiplying them by SPC. The third step is adding these costs and benets to the other portionso costs (in the orm o directly displaced consumption) and o benets (in the orm o immediate

consumption), respectively. inally, discount the total cost and benet streams at SRTP to calculatethe net present value (NP) (see Box 5).

Zerbe and Dively (1994) discussed a number o situations where costs and benets need not

be adjusted by SPC

(i) or a closed economy, i the raction o benets that return to private capital is equal to theraction o costs that displace private investment, adjusting the costs and benets by SPC

does not change the sign o the NP o a project. In this case, a project is socially desirable ithe NP is positive when applying SRTP as a discount rate to the ordinary costs and benets.This is likely the case or many environmental projects where benets are costs avoided whosenancing is similar to initial costs.

(ii) or an open economy, i the supply o capital is highly or perectly elastic, the displaced andgenerated private investment will be small and be similar in size, or both, will be zero, and it

is then sucient to discount benets and costs by the international borrowing rate withoutadjusting them by SPC.

(iii) or least-cost analysis (also reerred to as cost-eectiveness analysis), the goal is to compare

the costs o alternative methods o producing the same output. As long as the nancing othe various alternatives is similar, adjustment by SPC is not warranted.

When project costs and benets need to be adjusted by SPC, empirical estimation o SPC is

warranted, which requires inormation on the ollowing parameters SOC, SRTP, depreciation rate,and marginal propensity to save. Lyon (1990) provides two alternative ormulas to calculate SPC.One applies when the savings rate is expressed in terms o the gross return, and the other applieswhen the savings rate is expressed in terms o the return net o depreciation. Box 5 provides

these ormulas. The application o the SPC approach requires urther inormation on proportions odisplaced consumption and private investment due to project costs, and proportions o generatedconsumption and reinvestment due to project benets.

The SPC approach, although theoretically attractive (see eldstein 1972, Bradord 1975, Lind1982) is dicult to implement. The value o SPC is very sensitive to the values o SRTP and SOC,to how depreciation and reinvestment are assumed, and to the length o lie o a project. Lyon

(1990) shows that the value o SPC could vary rom about one to innity, depending on dierent

SecTion ii




24/51

assumptions on the values o the various parameters. Harberger and Jenkins (2002) argue that i

the SPC approach is employed, a dierent shadow price o capital has to be estimated or everyproject according to the length o lie o the project. This could be very conusing or policymakersin the government decision-making process, many o whom are noneconomists.

box 5

The ShadoW Priceof caPiTal aPProach

Consider a project with a liespan on years, benet streams, Bt, and cost streams, Ct. The netpresent value o the project will be

NP =B C

i

B V C V

i

t tt

t

nt b b t c c

t

* *

( ) ( )

+=

+ ( ) + ( ) +=

1

1 1

10

tt

n

=

0(1)

where Bt* is the consumption equivalents o benets at time t; Ct

* is the consumption equivalents o

costs at time t; b is the raction o benets that return to the private sector or investment; cis the

raction o costs that displace private investment; iis SRTP; and Vis SPC. Lyon (1990) provides twoalternative ormulas to calculate V

Vr sr

i d sr =

+ (2)

where ris the gross rate o return on private investment prior to depreciation, dis the depreciation rate,ands is the rate o savings rom the gross return; and

Vi

=

(3)

where is the rate o return rom private investment net o depreciation, and is the rate o savingrom the net return.

Source Zerbe and Dively (1994).

F. Dicnin Inereneraina Prjec

rom the mid-1990s, with the growing concerns over climate changes, global warming, andother environmental problems, there has been a renewed interest on whether and how discountingshould be applied to long-term projects, the eects o which spread over more than one generation(more than 3040 years) or even hundreds o years, and whose present values are extremely

sensitive to the choice o the discount rate. In evaluating intragenerational projects, it could beargued that the main issue is to achieve ecient allocation o scarce resources, thus the discount

rate should refect the economic opportunity cost o capital. When evaluating intergenerationalprojects, identiying an appropriate discount rate involves an additional challenge o considering

intergenerational equity.

What is common to the our approaches described above is that the discount rate, whatever

it is, is time-invariant, implying that discounting would be exponential. With a constant discountrate, benets and costs that occur in the distant uture will become very small in terms o their

14 May2007




25/51

present value. Thus, it seems not worth investing even a little to avoid potential catastrophic

consequences o some environment problems i they will occur only ar into the uture. Sincebeneciaries o projects dealing with such type o problems will be uture generations, attachingvery small weights to uture benets implied by exponential discounting does pose a question o

whether it is ethically indeensible. Put simply why should the well-being derived rom the samelevel o consumption o any uture generation be given less weight than or the current generationon the grounds o individuals being impatient? Many believe that this is not ethical, and the purerate o time preerence should be zero. Others argue that weighting generations equally leads to

paradoxical and even nonsensical results (see Box 1). Apart rom the ethical issue, exponentialdiscounting implies that the importance o a cataclysmic event happening our centuries rom nowis much less signicant relative to that o a cataclysmic event occurring, say, three centuries romnow. Weitzman (1998) argues that almost no one really eels this way about the distant uture.

Some have proposed a solution to the problem, which involves using a declining discount rate,namely, hyperbolic discounting (Weitzman 1994, 1998, 2001; Henderson and Langord 1998; Cropper

and Laibson 1998). Hyperbolic discounting hypothesizes that the discount unction with regard totime is shaped like a hyperbola, thus allowing the discount rate to decline with time according tosome predetermined trajectory and raising the weight attached to the welare o uture generations.According to Weitzman (1998), near uture and ar uture should be viewed dierently because

o dierent levels o uncertainties involved. Compared to the near uture, the ar distant uturehas much greater uncertainties about economic growth, rate o capital accumulation, state o theenvironment, pace o technological progress, rate o pure time preerence, etc. As a result, thereis a wide range o possible discount rates or the ar uture, and a certainty equivalent discount

rate should be calculated as a weighted average o these possible discount rates. He shows thatthe certainty equivalent discount rate equals the lowest possible discount rate.10 This way heexplains why dierent discount rates should be used or near uture projects and ar distant uture

ones. Over the past decades, there has also been increasing evidence rom experiments conductedby economists and psychologists, which suggests that people do use a declining discount rate in

making intertemporal choices (Weitzman 2001).

A conceptual problem with time-decliningdiscounting is that it leads to time-inconsistentplanning a person who applies a hyperbolic discount rate will not carry out the consumption plansmade today and reverse the decisions in the uture even though no new inormation emerges (Cropperand Laibson 1998). Due to this type o problem, some have suggested that intergenerational equity

should be treated directly rather than through adjusting the discount rate (Lesser and Zerbe 1995,Schelling 1995). More specically, some argue that in the context o global warming mitigation, oneshould not simply lower the discount rate used to evaluate costs and benets o projects; in cases

where there may be signicant irreversibility and potential questions o intergenerational equity,one should not rely on the project discount rate alone. Instead, a ull analysis o all these concernsand options should be carried out separately and explicitly or inormed choice and decision-making

(Lind 1997, Nordhaus 1999, Kopp and Portney 1999, and Toman 1999). Henderson and Bateman(1995) suggest that discount rate sensitivity analysis may include hyperbolic discount rate results

10 This is best illustrated through an example (Spackman 2004). Suppose in the long term that the discount rate is believedto be either 2% or 4%, with equal likelihood. The project benets are worth $1 million in 500 years. The present value

o the $1 million in 500 years would be $50 using 2% discount rate, and almost $0 using 4% discount rate. Since two

discount rates have an equal likelihood to occur, the expected present value o the project is about $25, the averageo $50 and $0. This gives an eective discount rate o 2.1%, close to the lower end o two possibilities.

SecTion ii




26/51

along with classical constant discount rate results or intergenerational projects. There is also a

suggestion that the dilemma in the choice o the social discount rate or intergenerational projectscould be resolved by realizing that the problem is one o concern over missing values to ignoringethical values. This deciency could be overcome by incorporating moral values directly into the

costbenet analysis and, inter alia, recognizing all values or which there is a willingness to pay(Zerbe 2005).

Despite the debates, there appears a general agreement that the SRTP should be used in

discounting intergenerational projects. The Stern Review applies an SRTP o 1.4% to discountdamages o global warming, estimated using the Ramsey ormula. It is the sum o two numbers0.1%, which is the rate o pure time preerence refecting solely the assumed risk o human raceextinction,11 and 1.3%, which is the product o a unity elasticity o marginal utility o consumption

and an expected annual growth rate o per capita real consumption refecting the diminishingmarginal utility o consumption. Nordhaus (2006), in his critique o the Stern Review, argues thatthe near-zero rate o pure time preerence combined with the unity elasticity o the marginal utility

o consumption is inconsistent with key economic variables observable in the real world such asthe real interest rate and saving rate. To match the observed values o these variables, either ahigher rate o pure time preerence or higher elasticity o marginal utility o consumption has to beassumed, implying a much higher social discount. Using the Dynamic Integrated Model o Climate

and the Economy (DICE), he shows that i the rate o pure time preerence is raised rom 0.1%(as assumed by the Stern Review) to 3% at the beginning, then declining slowly to about 1% in300 years (matching key economic variables observable in the real world), the optimal base year(2005) carbon price would decrease rom $159 to $1720 per ton. 12 He concluded that the radical

revision o the economics o climate change proposed by the Stern Review depends decisively onthe assumption o a near-zero rate o social time preerence.

III. thE soCIAl DIsCouNt RAtE IN PRACtICE ARouND thE WoRlD

Since there is no consensus as to which approach is the most appropriate or the choice oa social discount rate, it is not surprising that there are signicant variations in public discountrate policies in dierent countries around the world. This section provides a survey o the socialdiscount rate policies in practice used by countries around the world and by multilateral development

banks.

A. Cnrie arnd e Wrd

A survey o social discount rate policies o individual countries around the world show signicantvariations. Even within a country, dierent government agencies may have their own policy. Table4 summarizes the discount approaches and rates adopted in selected countries.

11 The Stern Review thereore disregards the impatience related argument or discounting.12 Developed by William D. Nordhaus, the DICE model is one o the economic models widely used to estimate costs and

benets o dierent paths or slowing climate change and or analyzing the impact o control strategies over time

(Nordhaus 1994). The optimal carbon price, or carbon tax, sometimes also called the social cost o carbon, is the

calculated price o carbon emissions that will balance the incremental costs o reducing carbon emissions with theincremental benets o reducing climate damages.

1 May2007




27/51

SecTion iii

TheSocial diScounTraTeinPracTicearoundTheWorld

Table 4

Social diScounTraTeSin SelecTed counTrieS

counTry/ agency diScounTraTe TheoreTicalbaSiS

Australia 1991 8%; current SOC rate annuallyreviewed

SOC approach

Canada 10% SOC approach

Peoples Republic oChina

8% or short and medium term projects;lower than 8% rate or long-term projects

Weighted average approach

rance Real discount rate set since 1960; set at 8%

in 1985 and 4% in 2005

1985 To keep a balance between

public and private sectorinvestment

2005 SRTP approach

Germany 1999 4%2004 3%

Based on ederal renancing rate,which over the late 1990s was

6% nominal; average GDP defator(2%) was subtracted giving 4%

real

India 12% SOC approach

Italy 5% SRTP approach

New Zealand

(Treasury)

10% as a standard rate whenever there is no

other agreed sector discount rate

SOC approach

Norway 1978 7%1998 3.5%

Government borrowing rate inreal terms

Pakistan 12% SOC approach

Philippines 15% SOC approach

Spain 6% or transport; 4% or water SRTP approachUnited Kingdom 1967 8%

1969 10%1978 5%

1989 6%2003 3.5%Dierent rates lower than 3.5% or long-

term projects over 30 years

SOC approach until early 1980s;

thereater SRTP approach

continued.



28/51

US (Oce oManagement and

Budget)

Beore 1992 10%; ater 1992 7% Mainly SOC approach withthe rate being derived rom

pretax return to private sectorinvestment

Other approaches (SPC, Treasuryborrowing rates) are also

mentioned

US (CongressionalBudget Oce and

General AccountingOce)

Rate o marketable Treasury debt withmaturity comparable to project span

SRTP approach

US (Environmental

Protection Agency)

Intragenerational discounting 23% subject

to sensitivity analysis in the range o 23%

and at 7%, as well as presentation oundiscounted cost and benet streams

Intergenerational discounting presentationo undiscounted cost and benet streamssubject to sensitivity analysis in the range

o 0.53% and at 7%

SRTP approach

Sources Compiled by ADB sta.

In North America, Canada uses a rate o 10% based on the SOC approach, while in the US,

the situation is more complicated. The US Oce o Management and Budget (OMB) uses a discount

rate that approximates the marginal pretax rate o return on private investment, thus ollowing theSOC approach. In the 1970s and 1980s, it was specied at 10 percent. In 1992, OMB revised the

discount rate to 7% (OMB 2003). The OMB also takes the view that the SPC discounting is theanalytically preerred means o capturing the eects o government projects on resource allocation inthe private sector. In its Circular A-94, OMB indicates that the Treasury borrowing rates should beused as the discount rate in cost-eectiveness analysis, lease-purchase analysis, internal government

investments, and asset sale analysis.

The US Congressional Budget Oce and the General Accounting Oce (1991) avor the use odiscount rates based on government bond rates (Lyon 1990, Hartman 1990). They use the interest

rate or marketable Treasury debt with maturity comparable to the program being evaluated as abase case discount rate or cost benet analysis, thus avoring the SRTP approach.

The US Environmental Protection Agency supports using the SRTP approach in evaluating

environmental projects (EPA 2000). It recommends that or intragenerational discounting, a rate o23% be used, which is reckoned to be the market interest rate ater tax. The EPA urther recommendsundertaking sensitivity analysis o alternative discount rates in the range o 23% as well as at

7% (prescribed by OMB), as this may provide useul inormation to decisionmakers. In addition,all analyses are required to present undiscounted benet and cost streams. or intergenerational

Table 4. conTinued.

1 May2007




29/51

projects or policies with intergenerational eects, the EPA prescribes that economic analyses shouldgenerally include a no discounting scenario by displaying undiscounted cost and benet streams

over time. The economic analysis should also present a sensitivity analysis o alternative discount

rates, including discounting at 23% and 7% as in the intragenerational case, as well as scenariosusing rates in the range o 0.53% as prescribed by optimal growth models. The discussion o thesensitivity analysis is required to include appropriate caveats regarding the state o the literature

with respect to discounting or very long time horizons.

In Europe, there is now a near convergence among ocial social discount rates (Evans 2006).

Germany uses 3%, based on values o real long-term government bond rate. Norway has beenusing a 3.5% discount rate ater 1998also based on real government borrowing rate. rancesCommissariat General du Plan in 2005 lowered its project discount rate to 4% based on the SRTPapproach. Italy uses the SRTP approach to derive a 5% discount rate, while Spain adopts 46%

or dierent sectors.

The UK government indicates in the Green Book, Appraisal and Evaluation in Central Government

(HM Treasury 2003) that an SRTP o 3.5% should be used to discount uture benets and costs opublic projects with a liespan below 30 years. This gure is calculated on the basis o the estimateso the ollowing three parameters (i) the rate o pure time preerence at 1.5%; (ii) the elasticityo the marginal utility o consumption at around 1; and (iii) the output growth per capita overthe period 19501998 in the UK at 2.1 percent. or projects with very long-term impacts (over

30 years), the discount rate will depend on the length o their liespan 3.0% or projects with aliespan o 3175 years; 2.5% with 76125 years; 2.0% with 126200 years; 1.5% with 201300years; and 1.0% with 301 years and beyond.

In Asia, the social discount rates adopted are generally higher. The Philippines and Pakistanuse 15% and 12%, respectively, both based on the SOC approach. India currently uses 12 percent.In the PRC, according to National Development and Reorm Commission and Ministry o Construction

(2006), the economic cost o capital is a weighted average o social time preerence and returnson capital. The ormer is estimated to be around 4.56% and the latter around 911 percent. Thesuggested social discount rate is 8% or short- and medium-term projects. The document alsorecommends that a lower than 8% discount rate be adopted or projects with a long time horizon.

In Australia, the mandated discount rate was 8% beore 1991 and, since then, there has been noprescribed benchmark social discount rate on the basis that the appropriate discount rate may varyrom one year to another, and should be under continuous review. The New Zealand Treasury has a

long-standing discount rate o 10%, which was rearmed in its 2005 Cost Beneft Analysis primer(Rose 2006).

b. MDb and er spra-Naina Aencie

The World Banks Handbook on Economic Analysis o Investment Operations provides guidance on

how to calculate the social discount rate (Belli et al. 1998). The handbook states that the discountrate used should refect not only the likely returns o unds in their best relevant alternative use(i.e., the opportunity cost o capital or investment rate o interest), but also the marginal rateat which savers are willing to save in the country (i.e., the rate at which the value o consumption

alls over time, or consumption rate o interest). Thereore, the World Bank prescribes the weighted

SecTion iii

TheSocial diScounTraTeinPracTicearoundTheWorld



30/51

average approach. The World Bank traditionally has not calculated a discount rate but has used

1012% as a notional gure or costbenet analysis. The handbook urther advises that taskmanagers may use a dierent discount rate as long as departures rom the 1012% rate have been

justied in the Country Assistance Strategy.

ADBs policy on the social discount rate, specied in its Guidelines or the Economic Analysiso Projects (ADB 1997), ollows the World Bank approach. Although the Guidelines state thateconomic rates o return dier considerably between sectors and countries, and rom time to

time, an appropriate discount rate or economic analysis should be calculated or each country tocompare with the existing practice, in practice, a single minimum rate o 1012% has been usedto calculate the net present value o a project, or to compare with the internal rate o return, oreconomic analysis or all countries and all projects all the time. ADB would expect to

(i) accept all independent projects and subprojects with an EIRR o at least 12%;

(ii) accept independent projects and subprojects with an EIRR between 10 and 12% or which

additional unvalued benets can be demonstrated, and where they are expected to exceedunvalued costs;

(iii) reject independent projects and subprojects with an EIRR between 10 and 12% or which

no additional unvalued benets can be demonstrated, or where unvalued costs are expectedto be signicant; and

(iv) reject independent projects and subprojects with an EIRR below 10 percent.

Other MDBs have chosen a social discount rate more or less in the range similar to those othe World Bank and ADB. In the case o the Inter-American Development Bank, a 12% discount

rate is being used as a measure o the economic opportunity cost o capital while the EuropeanBank or Reconstruction and Development uses 10 percent. The Arican Development Bank, basedon a review o various project appraisal reports, also uses a project discount rate ranging rom 10to 12 percent.

Among supranational governmental agencies, the European Commission advocates a benchmarkdiscount rate o 5% in real terms or costbenet analysis in the case o member countries o theEuropean Union. This is a compromise gure based on market interest rate, cost o capital, and

time preerence considerations. However, the European Commission encourages member states toprovide their own benchmark or the project discount rate, which must then be applied consistentlyto all projects (see Evans 2006 and European Commission 2006).

In sum, there are signicant variations in the social discount rate policy around the world.Most MDBs apply a rate o 1012%, ollowing the weighted average approach. Among individualcountries, most developed countries ollow the SRTP approach and apply much lower discount rates,

mostly in the range o 37%, with many revising the rates downward in recent years. On the otherhand, the three Asian developing countries surveyed (India, Pakistan, and Philippines) ollow theSOC approach, and apply a much higher rate, in the range o 1215%, and the PRC uses 8 percent.As shown in Table 4, these dierences in the social discount rate policies in practice are due to

dierent analytical approaches ollowed. The various approaches refect diering views on how publicinvestment aects domestic consumption, private investment, and cost o international borrowing.At a deeper level, however, the divergence refects the dierences in the perceived marginal socialopportunity cost o public unds, and in the extent to which the issue o intergenerational equity

0 May2007


http://www.adb.org/Documents/Guidelines/Eco_Analysis/default.asphttp://www.adb.org/Documents/Guidelines/Eco_Analysis/default.asphttp://www.adb.org/Documents/Guidelines/Eco_Analysis/default.asphttp://www.adb.org/Documents/Guidelines/Eco_Analysis/default.asp


31/51

SecTion iv

concludingreMarkS

is taken into consideration in setting the social discount rate. Public unds, in general, have a

higher marginal social opportunity cost in developing countries than in developed countries or anumber o reasons, such as more scarcity o capital, poorer nancial intermediation, greater marketdistortions, and greater impediments in accessing international capital markets. Intergenerational

equity is a newer issue in the public domain o developing countries than that o developedcountries. Thereore, it is not surprising to see that developing countries generally use a highersocial discount rate than developed countries.

IV. CoNCluDINg REMARks

The choice o the social discount rate plays a critical role in costbenet analysis and projectevaluation, and has been a subject o intense debate or the last several decades. In a perectlycompetitive world without market distortions, the market interest rate is the appropriate socialdiscount rate. In the real world where markets are distorted, there are our alternative approaches

in the choice o the social discount rate SRTP, SOC, weighted average o SRTP and SOC, and SPC.Economists have not reached a consensus as to which is the most appropriate.

The dierence among the our approaches refects largely the dierent views on how publicprojects aect the domestic economy whether public investment displaces current consumption, orprivate investment, or both, and whether benets o projects are consumed immediately, or reinvestedto generate more uture consumption (see Table 5 or a summary). In cases o very long-termprojects, an additional consideration is intergenerational equity, where the debate has centered on

whether or not one should assume a positive pure time preerence on the grounds that individualsare impatient, and whether a declining discount rate should be used to avoid problems associatedwith exponential discounting as implied by a constant discount rate. The recent controversy over

the Stern Review ocuses largely on what discount rate should be used in costbenet analysis opolicies to control global warming, which impacts on uture generations.

There are signicant variations in public discount rate policies in practice around the world, with

developed countries applying lower rates (37%) than the developing countries surveyed (815%).These variations largely refect dierent theoretical approaches to the choice o the discount rateollowed by various countries. At a deeper level, however, the divergence also refects dierencesin the perceived marginal social opportunity cost o public unds that the social discount rate tries

to measure in order to ensure ecient allocation o resources, and dierences in the extent towhich the issue o intergenerational equity is considered.

What conclusion can we draw rom this survey? irst, there is no one-size-ts-all solution to

the choice o the social discount rate. Countries dier in economic structure, capital scarcity, stageo nancial development, eciency o nancial intermediation, impediments aced in accessing theinternational capital market, and social time preerence. All these actors together determine a countrys

social opportunity cost o capital, and should be taken into consideration in the choice o the social

discount rate. Second, there is need or each country to regularly review the appropriateness o itssocial discount rate policy in light o changing domestic economic circumstances and internationalcapital market conditions, and to adjust the social discount rate as necessary. Third, there is a

strong case or considering the equity issue in discounting benets and costs o intergenerationalprojects (e.g., those designed to address climate changes and other environmental problems) inaddition to the economic eciency issue, as opposed to intragenerational projects where eciency

should be the primary concern. inally, or MDBs that provide development assistance to developing



32/51

countries through capital investment, there could be a case or reviewing their decades-old practice

o applying a uniorm discount rate o 1012% to all projects to see whether this practice is stillappropriate in a changing world.

Table 5

alTernaTive aPProacheSToThe choiceofThe Social diScounTraTe

aPProach imPlied aSSumPTion Who uSeS iT meThodof emPirical

eSTimaTion

maJor criTiciSm

Social Rate

o TimePreerence

(SRTP)

Time-invariant

Public projects only

displace currentconsumption

Mostly

developedcountries

Apply Ramsey ormula

with the ollowingparameters

(i) utility discount rate,(ii) elasticity o marginal

utility o consumption,

and (iii) growth rateo real per capita

consumption

Approximated by ater-

tax rate o return ongovernment bonds

Ignores the act that

public investmentcould displace private

investment

Choice o utility discount

rate involves normativevalue judgment, and

estimation o the

elasticity o marginalutility o consumption

is sensitive to data andmethodology

Time-declining

Public projects only

displace currentconsumption, and

discount rate declinesover time as uncertainty

increases. There is need to

consider intergenerationalequity.

Mostlyacademic

and policy

researchers

Typically estimatedthrough experiments

Leads to time-inconsistent planning

SocialOpportunity

Cost o

Capital(SOC)

Public projects onlydisplace current private

investment

Mostlydeveloping

countries

Approximated by pretaxrate o return on riskless

private investments, such

as top-rated corporatebonds

Ignores the act thatpublic investment

also displaces current

consumption

continued.

May2007




33/51

WeightedAverage

Closed economy or openeconomy with oreign

capital rationing

Public projects displace

current consumption andprivate investment

Mostly MDBs Weighted average o SRTPand SOC

Ignores the possibilitythat project benets

could be reinvested

Determining the weights

attached to SRTP,SOC, and international

borrowing rate could bedicult

Open economy with

upward sloping supplycurve o oreign capital

Public projects unded

by displaced currentdomestic consumption,displaced domestic private

investment, and oreignborrowings

Weighted average o

SRTP, SOC, and oreignborrowing rate

Open economy with

perectly elastic supply ooreign capital

Displacement odomestic consumption

and investments wouldbe small or negligible;

the weighted averageapproach uses a discount

rate equal to oreign

borrowing rate

International borrowing

rate

Shadow

Price oCapital

Appropriate when public

investments displacecurrent consumption

and investment and

generate not only utureconsumption, but also

uture investment

Converts all costs

and benets intoconsumption equivalents

using the SPC. Discount

total cost and benetfows with SRTP to

calculate NP

When the eects o

displacement and

generation o investmentsare the same, the SPCapproach is equivalent

to using SRTP as the

discount rate

Although considered as

theoretically the mostattractive approach,

practical application

could be dicult

SecTion iv

concludingreMarkS

Table 5. conTinued.

aPProach imPlied aSSumPTion Who uSeS iT meThodof emPirical

eSTimaTion

maJor criTiciSm



34/51

APPENDIx

EstIMAtINg thE soCIAl DIsCouNt RAtE

usINg thE WEIghtED AVERAgE APPRoACh1

According to the weighted average approach, also known as Harberger approach, the social discountrate can be expressed as

= + +SOC i SRTP f( )1 (1)

where denotes the social discount rate, i is the governments real long-term oreign borrowing rate,

is the proportion o unds or public investment obtained at the expense o private investment, is the

proportion o unds obtained at the expense o current consumption, and (1 ) is the proportion o

unds rom oreign borrowing. SRTP and SOC are measured, respectively, by the rate o real return on savings

exclusive o (ii) and investments inclusive o (rj). Expressing the weights attached to dierent unding sources

in terms o elasticities o demand and supply o unds with respect to changes in interest rates, equation

(1) becomes

=

( ) + ( ) ( )( ) + ( )

i i t i i

f f t f j j t jj

i i ti

f f t

S S i S S i I I r

S S S S j j tj

I I( )(2)

where i, f, jare respectively elasticities o savings, supply o oreign capital, and private investment with

respect to the interest rate. Si /Stand S/Stare the shares to the total savings by various groups o domestic

savers and oreign savers.Ij /Itis the investment share o various business sectors.

Using Equation (2) and 19881989 data or Papua New Guinea, Harberger and Jenkins (2002) present

an example o calculating the social discount rate, which they call economic opportunity cost o capital.

The example assumes that there are our savers groups households, business, government, and oreign. The

assumptions and results o calculations are given in Appendix Table 1 below

aPPendix Table 1

SaverS

assumpTions houSeholdS buSineSS governmenT foreign

Share (Si/St) 33.70% 44.90% 7.80% 13.60%

Elasticity (s, ) 0.5 0.5 0 2

Nominal market interest rate (im) 14.50% 14.50% 14.50%

Nominal cost o oreign borrowing (i) 18.00%

Tax rate (ti, t

w) 9.30% 30.00% 0% 17.00%

Rate o infation (g) 5.00% 5.00% 5.00% 5.00%

Real return on savings(ii) 7.76% 4.90% 9.05%

Real marginal cost o oreign borrowing 12.31%

13 This Appendix draws rom Harberger and Jenkins (2002).

4 May2007

Theoryand PracTiceinThechoiceof Social diScounT raTefor coSTBenefiT analySiS: a Survey

Juzhong zhuang, zhihong liang, Tun lin, and franklin de guzMan


35/51

aPPendix

The real return on savings or each domestic saver group is calculated by removing the respective tax

rates rom the nominal market interest rate and then removing infation

Real return on savings (ii

) = [im

* (1 ti) g] / (1 + g).

or the oreign savers group, the same procedure is applied as or domestic savers, but with a urther

adjustment to refect the eect o additional oreign borrowing on the countrys overall borrowing costs.

The adjustment involves the elasticity o supply o oreign unds () as well as the rate o change in the

oreign borrowing cost as the country becomes more indebtedwhich is assumed to be 0.6 by Harberger

and Jenkins.

Real marginal cost o oreign borrowing (i) = {[i* (1 tw) g] / (1 + g)} * [1 + 0.6 * (1 /)]

The example urther assumes that there are ve groups o investors or demanders o unds housing,

agriculture, manuacturing, government, and mining. See Appendix Table 2 or the assumptions and

calculations.

aPPendix Table 2inveSTorSor demanderSof fundS

houSing agriculTure manufacTuring governmenT1 mining

Share (Ij/It)Elasticity (j)Nominal Market Interest

Rate (im)

Tax rate (ti)Rate o infation

Real return on investment

(rj)

14.40%1

14.50%

15.00%5.00%

11.43%

17.70%1

14.50%

0.00%5.00%

9.05%

65.80%1

14.50%

30.00%5.00%

14.95%

0%0

0%

0%0%

0%

2.10%1

14.50%

35.00%5.00%

16.48%1No data was available on the governments share o investment in Papua New Guinea.

The real return on investment is calculated by adjusting the nominal pretax rate o return on investment

or each sector (i.e., the nominal market interest rate) with tax rates and then taking out infation, using

the ollowing ormula

Real return on investment (rj)= [im * (1 tj) g] / (1 + g)

ollowing equation (2), the social discount rate, which is the economic cost o capital, or Papua New

Guinea is estimated at

=

( ) + ( ) ( )

( ) + ( )

i i t i i

f f t f j j t jj

i i ti

f f t

S S i S S i I I r

S S S S j j tj

I I( )=

11 76. %



36/51

REFERENCEs

Amiel, Y., J. Creedy, and S. Hurn, S. 1999. Measuring Attitudes Towards Inequality. Scandinavian Journal

o Economics 1018396.

Arrow, K. 1995. Intergenerational Equity and the Rate o Discount in Long-Term Social Investment. Paper

presented at the IEA World Congress, December, Tunis, Tunisia.

Asian Development Bank. 1997. Guidelines or the Economic Analysis o Projects. Manila.

Banks, J., R. Blundell, and A. Lewbell. 1997. Quadratic Engel Curves and Consumer Demand. Review o

Economics and Statistics 79(4)52740.

Barsky, R., M. Kimball, T. Juster, and M. Shapiro. 1995. Preerence Parameters and Behavioral Heterogeneity

An Experimental Approach in the Health and Retirement Survey. NBER Working Paper No. 5213, National

Bureau o Economic Research, Massachusetts.

Baumol, W. 1968. On the Socia

Theory and Practice in the Choice of Social Discount Rate for Cost-Benefit Analysis: A Survey

Documents

Transcript of Theory and Practice in the Choice of Social Discount Rate for Cost-Benefit Analysis: A Survey