Discounting and welfare evaluation of policies

• Published date: 01 October 2017
• DOI: http://doi.org/10.1111/jpet.12266
• Author: Anna Rubinchik,Jean‐François Mertens
• Date: 01 October 2017

Received: 27 May2016 Accepted: 2 August 2017

DOI: 10.1111/jpet.12266

ARTICLE

Discounting and welfare evaluation of policies

Jean-François Mertens1Anna Rubinchik2

1CORE,Université Catholique de Louvain

2Departmentof Economics, University of Haifa

Theauthors wish to thank the seminar partici-

pantsat Bar-Ilan University, participants of the

conferenceorganized by the Society for Benefit-

CostAnalysis in Washington, DC, and the two

anonymousreferees for their useful comments;

S.Coate and L. Kotlikoff for insightful discussions,

aswell as S. BenYosef.The paper has been sub-

stantiallyrevised since the first author passed

away.The scientific responsibility rests with the

secondauthor.

Jean-FrançoisMertens, CORE, Université

Catholiquede Louvain, 34, Voie du Roman-

Pays,B-1348 Louvain-la-Neuve, Belgique

(jfm@core.ucl.ac.be).

AnnaRubinchik, Department of Economics,

Universityof Haifa, Mount Carmel, Haifa 31905,

Israel(arubinchik@econ.haifa.ac.il).

We start with the premise that if policy discounting is to have any

welfare relevance, one has to accept it being a derivative of a social

welfare function (SWF). We show that if that derivative is to have

a net present value (NPV) form, then the baseline allocation must

be stationary. In addition, we show that at a stationary baseline in

an overlappinggenerations growth economy, the intergenerationally

fair discount rate equals the growth rate of per-capita consump-

tion, which is, roughly, 2% for the United States. This differs from

the interest rate, even in the golden rule equilibrium, unless popu-

lation growth is null. The last result is based on the main theorem in

Mertensand Rubinchik (2012) and is demonstrated for a policy space

that might naturally arise in applications.

1INTRODUCTION

Our main goal is to reconcile two approaches to policy evaluation.One is the benefit-cost analysis used by practitioners

and the other is the welfare-based criterion commonly used by academic economists. We show that the two might be

consistent, and when they are the latter yields a clear choice of parameters for the former.

“Benefit-cost analysis is a primary tool used for regulatory analysis.” This statement appears in Circular A-4 of the

U.S. Office of Management and Budget (OMB; 2003, p. 2), which was developed to reviewand coordinate regulatory

programs of the U.S.Federal agencies.1

As is well-known (cf. Mishan, 1976), the classical “efficiency” rationale used in cost-benefit analysis (CBA) is the

Kaldor–Hicks criterion, which is based on the total monetized net benefit, and thus is seemingly independent of dis-

tribution of benefits. The same applies to projects that span several years, in which case the regulators are to use a

discounted value of future net benefits, and hence to evaluate the net present value (NPV) of the monetized benefits

using the interest rate for discounting.2

CBA has a major advantage over manyother possible ways to evaluate merits of a public project: it provides a clear

quantifiable criterion for policy evaluation (whenever full monetization is feasible) that is based on willingness to pay

(WTP) and cost of resources, which are fundamental to determining an optimal allocation in a classical sense. There are

1Inaccordance with sect. 2(b) of Executive Order 12866, “Regulatory Planning and Review.”

2U.S.Office of Management and Budget, 2003, p. 31–36.

Journal of Public Economic Theory.2017;19:903–920. wileyonlinelibrary.com/journal/jpet c

2017 Wiley Periodicals,Inc. 903

904 MERTENSAND RUBINCHIK

some caveats, however,that make us want to come back to the welfare foundations, i.e., evaluating policies based on a

well-defined (or evenaxiomatized) societal objective. As Hammond (1985) puts it,

The compensation test compares different individuals'monetary gains and losses by treating all incre-

mental dollars equally. …There is no denyingthat such comparisons are actually very specific interper-

sonal comparisons of utility,with utility effectively measured in monetary units, and all individuals'incre-

mental dollars being regarded as equally valuable, no matter what the distribution of income may be.

One might want to be more careful about such interpersonal comparisons, when the losers and winners belong

to different generations. Even the OMB Circular encourages the regulators to analyze the distributional effects of

the proposed action in addition to the standard CBA, as “[b]enefits and costs of a regulation may also be distributed

unevenly overtime, perhaps spanning several generations.”

This is where the classical welfare foundations could help to identify the underlying “trade-offs” and evaluate them

in a systematic way.

The merits of using an explicit welfare function for policy analysis havebeen advocated by Drèze and Stern (1987).

Our ability to meaningfully argue about choosing such a function dates back to the seminal contribution of Harsanyi

(1955).3

Let us now illustrateHammond's claim that any policy evaluation based on the Kaldor–Hicks criterion embeds some

distributional judgment. If we takethe utilitarian view, it pins down welfare weights, which are equilibrium-dependent,

known as Negishi weights (Negishi, 1960). Such weights are not always easy to justify,especially when any agent can

consume only a subset of all goods in the economy, as is true in an overlapping generations (OG)world. The latter

assumption is crucial to express the passage of time: all consumer goods are dated goods; not all of them are available

at the same point in time.

Example (A toy OG model). There are three different private goods: apples (c1), pheasants (c2) and salt (s), and one public

good (g). There are three agents standing for generations A, B, C (B overlaps with A and C). Toavoid dealing with infinite past

and future and to prevent autarchic (inefficient) equilibria, we let salt play the role of money. The first generation is endowed

with salt; none of the first two generations derives utility from it, but the last generation enjoys it, which representsthe value

of salt “in future transactions” that are cut off from this model. As for the public good, the first generationlikes it, the second

generation does not carefor it, but the last generation hates it. To be specific, assume:

uA(c1A,g)= c1Ag

g+c1A

,(1)

uB(c1B,c

2B)=𝜗c1B+c2B,(2)

uC(c2C,s

C,g)=c2C−2g+sC.(3)

A owns all the salt (𝜔s),B owns all the apples (𝜔1>𝜔s

𝜗), and C owns all the pheasants (𝜔2>𝜔

s). All agents act as price takers

(replicate the economyif needed). Only private goods are traded. Then the markets should clear at prices p1=𝜗for apples and

p2=ps=1for pheasants and salt. Indeed, then the demand for apples is c1A=𝜔s

𝜗from agent A, while agent B is indifferent

between any bundle on his budget line, hence c1B=𝜔1−1

𝜗c2B; therefore, market clearing in the apple market implies that

c2B=𝜔s. At these prices, agent C is also indifferent between any bundle on his budget line so c2C=𝜔2−sC;hence,market

clearing in the pheasant market yields sC=𝜔s. Thus, the marketallocation is (for some fixed initial g)

(c1A,c

2A,s

A)=𝜔s

𝜗,0,0,

(c1B,c

2B,s

B)=𝜔1−𝜔s

𝜗,𝜔s,0,

(c1C,c

2C,s

C)=(0,𝜔2−𝜔s,𝜔s).

3Foran overview of the related literature, please refer to Mertens and Rubinchik (2012). Here, let us mention one of the most recent relevant contributions,

Fleurbaeyand Zuber (2015), who analyze the implications of equity considerations on social discounting.