PRINCIPLES OF COST-BENEFIT ANALYSIS

Publc Polcy Revew, 2006, Vol.2, No.1 1 PRINCIPLES OF COST-BENEFIT ANALYSIS Robn Boadway Professor, Department of Economcs, Queen's Unversty, Kngston, Canada Abstract Ths paper summarzes the procedure for the economc evaluaton of government projects and polcy reforms. It begns wth the socal welfare functon underpnnngs of cost-beneft analyss ncludng the role of dstrbutve weghts and the choce of numerare. It then turns to the conduct of a socal cost-beneft analyss usng the net present value crteron. Ths ncludes the shadow prcng of market products and nputs affected by the project, ndrect welfare effects, the opportunty cost of project fnance, the evaluaton of non-marketed nputs and outputs, and the opportunty cost of rsk. Issues nvolved n selectng a dscount rate are dscussed, especally those arsng from mperfect captal markets. Fnally, snce many publc projects have long-term consequences, the prncples that mght be used to take account of effects of projects on future generatons are outlned. Technques for accountng for these effects, such as generatonal accountng, are summarzed and ts shortcomngs hghlghted. I. INTRODUCTION : SOME FOUNDATIONS Cost-beneft analyss n ts broadest sense s the process of rankng polcy optons from an economc pont of vew, takng account of both the benefts of the polcy and ts costs. The polces range from an nvestment project that s small enough so that a partal equlbrum approach wll suffce, to a broader fscal polcy change, such as a tax, subsdy or regulaton, that wll have general equlbrum repercussons on several markets. In takng an economc pont of vew, we are concentratng on net benefts of the polcy as they affect the well beng of ndvdual households of the economy, typcally as judged by ther own preferences. We are eschewng poltcal feasblty consderatons as well as non-economc objectves, such as non-dscrmnaton, lberty, and so on. That does not mean that socal values are not nvolved. Indeed, t s mpossble to rank polcy optons wthout makng some mportant value judgments, but the ones that we make are those

2 R. Boadway / Publc Polcy Revew typcally nvolved n appled welfare economcs, and t s worth beng explct about them at the outset. There are three man ones. The frst s the precept of ndvdualsm: an ndvdual s welfare should be based on the ndvdual s own preferences. The second s the Pareto prncple: f one ndvdual s made better off and none are made worse off as a result of mplementng the polcy, socal welfare s taken to ncrease. The thrd s the prncple referred to as welfarsm: socal orderngs of alternatve polces depend only on the welfare of ndvduals and not on extraneous consderatons (lke freedom, non-dscrmnaton, etc.). These prncples lead to a set of socal preferences over allocatons of resources that can be summarzed n a Bergstrom-Samuelson Socal Welfare Functon (SWF) of the form W ( u (),u (), L,u () ) 1 2 n, whch s ncreasng n all arguments, and where u () s the utlty of household as a functon of a resource allocaton. The SWF represents a preference orderng over ndvdual utltes. As such, t s an ordnal concept, so any ncreasng functon of W ( u, u, 1 2 L, u n ) wll serve just as well. However, the SWF requres that ndvdual utltes be measurable and that they be comparable among households. There s a szeable lterature, summarzed n Boadway and Bruce (1984), on the concepts of measurablty and comparablty of ndvdual utltes functons, and how the extent of measurablty and comparablty nfluences the form of the utlty functon. We need not be detaned by that lterature. Instead, we shall adopt for llustratve purposes a partcular and commonly used form for the SWF that ncorporates some reasonable assumptons about measurablty and comparablty, and also allows us to capture socal atttudes towards equty n a sngle parameter. The SWF wll be assumed to take the followng addtve form: W 1 ρ ( u, u2,, un ) = w( u ) = u /( 1 ρ) 1 L (1) where w ( u ) s the socal utlty of ndvdual. 1 The SWF n (1) has a number of notable propertes. The socal preference orderng s symmetrc and anonymous: the same socal utlty functon w () apples to all ndvduals, and t gves rse to preference orderngs that are symmetrc around the equal utlty ponts. Thus, n the two person case, socal ndfference curves n ( u1,u 2 )-space are symmetrc around the 45-degree lne. The parameter ρ captures socety s averson to nequalty. In partcular, ρ s the elastcty of margnal socal utlty: ( u) w ρ = (2) w ( u)u We shall refer to ρ as the coeffcent of averson to nequalty, analogous to the coeffcent of relatve rsk averson n an uncertanty settng. The hgher s ρ, the more averson there s to nequalty n utltes. It may be reasonable to assume non-negatve averson to nequalty, n 1 The SWF n (1) s lnear homogeneous. Such a form s possble under the assumpton that ndvdual utlty functons are comparable and measurable up to a rato scale. That s, proportonal changes n utlty are comparable across ndvduals. Techncally, ndvdual utlty functons can be subject to multplcatve transformatons (e.g., u can be transformed to v = ku ) wthout affectng the socal orderng. See Boadway and Bruce (1984), Chapter 5.

R. Boadway / Publc Polcy Revew 3 whch case ρ 0. Ths s equvalent to assumng that the SWF W () s quas-concave. The two lmtng cases are the utltaran SWF, where ρ = 0 (so socal welfare s just the sum of utltes), and the maxmn (or Rawlsan) SWF, where ρ = (where socal welfare s the utlty of the least well-off ndvdual). The value of the coeffcent of averson to nequalty ncorporates a value judgment that reasonable people may dffer on, and ths poses enormous problems for cost-beneft analyss snce vrtually all polcy alternatves have dfferent relatve effects on dfferent ndvduals. It s not possble to rank such alternatves unless one makes an explct comparson of utltes of dfferent households. Unless one alternatve s Pareto superor to another, rankngs depend upon the SWF that one has n mnd. In fact, there are really two levels of value judgment nvolved n arrvng at (1). Gven ndvdual preference orderngs, one frst has to measure the utlty assocated wth each outcome, that s, formulate the ndvdual utlty functon u (), and then one has to decde on the socal utlty functon w ( u) to apply to ndvdual utlty. As we shall see a common procedure for measurng welfare levels n appled welfare economcs s to use a money metrc measure of utlty, that s, to measure welfare levels usng the values of expendtures requred to acheve dfferent welfare levels gven a set of reference prces. Formally, defne the real ncome of household, denoted y, by the expendture functon at a set of reference prces r p, or: r r ( p u ) { p x u( x) u } y = e, mn (3) x where x s a vector of commodtes. Then, the utlty functon for household can be wrtten u ( y), where u reflects the rate at whch the margnal utlty of ncome declnes. If the α household utlty functon also takes the constant elastcty form, u ( y) = y /( 1 α ), the socal utlty functon w( u( y) ) can be transformed nto: 1 σ ( ) = y /( 1 σ ) ν y (4) whereσ = ρ + α + ρα. Thus, σ now becomes the coeffcent of averson to nequalty n real ncome. Note, however, whereas the same socal utlty functon w ( u) may be used to convert ndvdual utlty nto socal utlty, t may well be the case that convertng real ncome to ndvdual utlty may requre an ndvdual-specfc utlty functon u ( y). For example, dfferent households may have dfferent abltes to convert real ncome to utlty f they dffer n needs or dsablng crcumstances. Moreover, they may dffer n preferences as well, whch causes even more vexng problems for constructng comparable utlty functons. These conceptual problems cause nevtable dffcultes for cost-beneft analyss. There are two standard ways of proceedng, assumng there s no consensus about the approprate SWF to use. One procedure s to rank polcy alternatves usng a SWF wth an explct assumpton about averson to nequalty, and to conduct senstvty analyss wth respect to the weghts. In ths way, the decson-maker can be gven a menu of rankngs dependng on the weghts used and be

4 R. Boadway / Publc Polcy Revew responsble for choosng among them. For ths purpose, t s typcally convenent to roll the judgments about measurablty of ndvdual utlty and averson to nequalty n utlty nto one, and apply the followng SWF: W 1 σ ( y, y2,, y n ) = y /( 1 σ ) 1 L (5) The other procedure, most commonly used, s to gnore redstrbutve concerns and smple aggregate real ncome changes yen by yen regardless of to whom they accrue. Ths s the procedure advocated by Harberger (1971a), and s effectvely equvalent to assumng the coeffcent of averson to ncome nequalty σ n (5) s zero. Alternatvely, f the SWF n (1) s used, the utltaran form s assumed (so ρ = 0 ), and the ndvdual utlty functon s assumed to be quaslnear n some consumpton good (e.g., u ( x) x + g( x x, ) =,, 0 1 2 L x n, so the margnal utlty of ncome s constant. Though ths procedure s most frequently used n practce, the general theoretcal case for t s dsputed n the lterature unless one s prepared to assume σ = 0. 2 The argument n favor reles on beng able to separate effcency and equty consderatons n cost-beneft analyss. Three sorts of arguments can be used for gnorng redstrbutve concerns. The frst s related to the classc separaton of effcency and redstrbuton functons of government proposed by Musgrave (1959). The government has wde-rangng polcy nstruments avalable for redstrbuton, ncludng the progressve tax system, transfer programs, socal nsurance and n-knd transfers. If t s usng them effectvely, equty consequences of other polces should be gnored, t beng presumed that account wll be taken of them elsewhere. Although ths s a seductve argument, ts lmtatons are evdent. For one, the argument does not apply for polces that have explct redstrbutve ntent. For another, even f redstrbutve polces are set optmally, because these polces are dstortonary, they cannot succeed n achevng the frst-best socal optmum. In these second-best crcumstances, one cannot really gnore the redstrbutve consequences of polces except n specal crcumstances. The famous Damond-Mrrlees (1971) producton effcency theorem ndcates one such set of crcumstances. If taxes are set optmally, there should be producton effcency n the economy, mplyng that the government should evaluate ts own producton plans accordng to the crteron of the value of output measured n producer prces. A smlar argument can be adduced n evaluatng projects nvolvng traded goods: ther shadow prces should be world prces uncorrected for equty concerns (Boadway, 1976; Drèze and Stern, 1987). The second argument s that f the aggregate change n real ncome s postve ( y > 0 ), ths ndcates that those who gan from the polcy should be able to compensate those who lose and stll be better off. There are three problems wth ths hypothetcal compensaton argument. The frst s that the compensaton wll not actually be pad, even f t hypothetcally could be. In 2 A comprehensve summary of the arguments aganst usng ths procedure may be found n Blackorby and Donaldson (1990).

R. Boadway / Publc Polcy Revew 5 these crcumstances, gnorng equty consequences seems partcularly arbtrary. Second, even f one accepts the hypothetcal compensaton crteron as a vald one, the aggregate change n real ncome turns out not to be a perfect ndcator: postve aggregate real ncome changes need not be suffcent to satsfy the hypothetcal compensaton crteron (Boadway, 1974). Thrd, the hypothetcal compensaton crteron can take varous forms dependng on what one assumes to be the mechansm, and none of them yelds a complete orderng of outcomes. The thrd argument s that f there are many polces beng undertaken over tme, the redstrbutve consequences of them should roughly cancel out, so gnorng them for any one polcy evaluaton s nnocuous. Ths s especally true f, followng argument one, there are polces n place to address redstrbutve concerns. Ths argument seems to be no more convncng than the others. Perhaps all these arguments are smply ratonalzatons for the more practcal one. That s that t s very dffcult to take account of the redstrbutve consequences of polces. Most often, only aggregate data that do not dstngush among ndvduals of dfferent real ncome levels are avalable, so measurng aggregate real ncome changes s the only feasble procedure. Ths mght be supplemented by some mperfect ndcaton of the dstrbutve consequences of the polcy. Much of our dscusson wll focus on the use of real ncome measures of costs and benefts wthout redstrbutve weghts explctly ncorporated. The general prncples can best be llustrated ths way. Whatever vew we take of the redstrbutve consequences of varous polces, a basc ngredent s what we have referred to as the real ncome of ndvduals n the economy. To repeat, ths s a money metrc of utlty (preference) levels of the household under dfferent polces. Conceptually, n the smple case of utlty n two goods, a money metrc measure of utlty change s the dstance between two ndfference curves measured n monetary terms. Of course, there are an ndefnte number of ways of measurng the dstance between two ndfference curves, so the conventon followed s to measure the dstance usng a budget lne wth gven relatve prces. Thus, our money metrc utlty measure s just the expendture functon: the value of expendtures requred to reach a gven ndfference curve at some reference set of prces. It can be nterpreted as the wllngness to pay for the bundle of goods n a gven stuaton. (Ths s a useful nterpretaton when t comes to evaluatng non-marketed commodtes as dscussed later.) Of course, even ths s not wthout ambguty snce the expendture functon dffers accordng to the reference prces used. Two common examples when consderng the effect of movng from polcy zero to polcy one are the compensatng varaton (CV) and equvalent varaton (EV). The CV uses prces n the new stuaton to obtan a monetary measure of welfare change: CV = e 1 1 1 0 ( p, u ) e( p, u ) where superscrpts 1 and 0 refer to the prces and utltes after and before the change

6 R. Boadway / Publc Polcy Revew respectvely. Thus, p 1 represents the vector of prces of both goods demanded and factors suppled n the new stuaton, and e( p 1,u 1 ) level of the new stuaton at the prces EV = e 0 1 0 0 ( p, u ) e( p, u ) s the net expendture requred to acheve the utlty 1 p. Alternatvely, the EV uses the old prces: In general, CV and EV wll dffer even though both are equally legtmate measures of changes n utlty levels. More generally, any set of reference prces would serve as well. In prncple, the choce of reference prces can have consequences for relatve utlty changes across households, for example, f they have dfferent preferences for goods. But, n practce, gven measurement problems that are lkely to exst, any set of reference prces would serve as well. Before leavng ths secton on the foundatons, t s worth brefly turnng to the practcal ssue of how one mght ncorporate dstrbutve weghts nto cost-beneft analyss gven the data constrants that are lkely to apply. Dstrbutve weghts should take account of the fact that one yen of real ncome s of dfferent socal value to dfferent ndvduals (e.g., Boadway, 1976; Drèze and Stern, 1987; Ahmad and Stern, 1991). Suppose we take as gven the coeffcent of averson to real ncome nequalty, σ, n the SWF gven n (5). Then, changes n real ncome accrung to ndvdual should be weghted by the margnal socal utlty of ncome β defned by: W β = y y j j σ Note that (6) smplfes to β = 1 for the case where σ = 0, so no welfare weghts are used. Apart from the ssue of determnng the correct value of σ to use, mplementng (6) for evaluatng polces s dffcult snce t wll not generally be possble to attrbute costs and benefts to ndvduals accordng to ther real ncome levels. Often, only market-wde data wll be avalable. There may be some exceptons. For example, wage payments for ndvdual workers mght be avalable n whch case they could be weghted usng β, but generally that wll not be possble for other cost tems. A less demandng procedure that has been proposed by Feldsten (1972b) n the context of publc sector prcng s to assgn socal weghts to commodtes accordng to estmates of the proportons n whch they are consumed by ndvduals wth dfferent real ncomes. The procedure s as follows. From basc consumer theory, the change n ndvdual s real ncome of from a change n a the prce of commodty j s gven (usng Hotellng s lemma) by: y e () = = x j p p where x j s the demand for commodty j by ndvdual. Then, the change n real ncome from a change n all commodty prces becomes: dy = j x dp j j (6)

R. Boadway / Publc Polcy Revew 7 Usng ths and (6), the change n socal welfare from a change n consumer prces may be wrtten: where dw = dy = β x jdp j = β R X dp (7) j j j j j X = s aggregate demand for commodty j and: j x j β x j R j X j s defned as the dstrbuton characterstc of good j. It s a weghted average of β s, where the weghts are the proportons of commodty consumed by ndvdual j. Gven that β falls wth real ncome, R j wll be hgher for commodtes wth lower ncome elastctes of demand snce these wll be dsproportonately consumer by lower ncome persons. More generally, costs and benefts of a polcy can be weghted by ther dstrbutve characterstcs n evaluatng a polcy (see Boadway, 1976). Ths s clearly a procedure that s less demandng emprcally than calculatng real ncome changes for each ndvdual and weghtng them by β. Consder, for example, the followng llustratve applcaton of the welfare effects of an excse tax, drawn from Harberger (1978). Gven that the tax s on a sngle good, a partal equlbrum can be taken. Denote the aggregate output for the good smply by X, whose market s depcted n Fgure 1. The mposton of a tax at the per unt rate t causes market output to fall from X 0 to X 1, and consumer prce to rse from p 0 to p 1. If dstrbutve effects were gnored, the standard measure of welfare loss would be the trangular area ABC, whch s the dfference between the losses n consumer and producer surplus (FABE and EBCD) and the gan n government revenue FACD. If dstrbutve weghts are attached to these losses and gans, the change n socal welfare wll be: W = RD FABE RS EBCD + R G FACD where R D, R S, and R G are the dstrbutve characterstcs assocated wth consumers surplus, producers surplus and government revenue, respectvely. In the case of the frst two, these reflect the shares of ndvduals of dfferent ncome groups n the demand and supply of the good n queston. The dstrbutve weght on government revenue reflects the shares of government revenue rased from dfferent ncome groups. In prncple, ths knd of methodology can be appled to any polcy change. Fnally, before movng to the specfcs of cost-beneft analyss of polces, t s worth drawng specal attenton to the problems assocated wth evaluatng the net benefts of projects, as opposed to fscal polces. A natural queston that arses s why we cannot smply use fnancal proftablty measures such as are used n the prvate sector, and must nstead rely on cost-beneft analyss. In other words, what are the sources of dfferences between socal proftablty and prvate proftablty?

8 R. Boadway / Publc Polcy Revew Fgure 1 S(p - t) p 1 F A p 0 E B p 1 - t D C D(p) X 1 X 0 X The most fundamental dfferences arse because of the fact that n a second-best settng-when prvate markets are dstorted-market prces typcally devate from socal values. These dstortons arse from several sources. One s that some markets may exhbt non-compettve behavor ether on the supply or the demand sdes. Ths arses because of the fact that scale economes lead to a relatvely small number of market partcpants. In these crcumstances, a dstorton arses between the demand prce (reflectng the margnal beneft) and the margnal cost. Another s that a commodty may emt an externalty that accrues to thrd partes and that, f not prced, causes margnal socal benefts to devate from margnal socal costs. Thrd, n some markets agents nvolved n transactons may be mperfectly nformed about relevant characterstcs or hdden actons of those on the other sde of the market. Well-known examples nclude frms nablty to observe ether the productvty or the work effort of ther employees, and consumers nablty to observe the qualty of products before they purchase them. Ths gves rse to neffcent market outcomes. Fnally, government polces, such as taxes, subsdes and regulatons, themselves ntroduce dstortons n market economes. If these dstortons must be taken as gven by the analyst (even though n some cases, polces could be taken that mght mtgate them), they wll affect the evaluaton of the net benefts of the project. As we shall see, one way to take market dstortons nto account s to devse shadow prces to measure the socal value of commodtes sold on dstorted markets rather than usng the prces set on markets. Ths may be a dffcult task because n many cases, the nformaton needed to calculate shadow prces (such as the magntude of externaltes) may not be readly avalable from observed market data. Related to ths problem of evaluatng project nputs and outputs when there markets are dstorted s the fact that projects may have ndrect effects on dstorted markets elsewhere n

R. Boadway / Publc Polcy Revew 9 the economy. As emphaszed by Harberger (1971a), f a market has a postve tax dstorton, the amount transacted wll be too low n equlbrum. Equvalently, the last unt sold wll have a greater value to purchasers than to sellers. In these crcumstances, f a project ndrectly ncreases the output of ths product because of complementarty relatonshps, there wll be a net beneft on that account. Ths should be treated as a beneft of the project. A thrd reason why prvate proftablty mght not adequately reflect socal values s that some of the outputs produced or nputs used n a project may have no explct market prce attached to them. Examples nclude the benefts of new nformaton produced by research and development, the value of tme saved on a publc transportaton faclty, the value of mprovements n health and longevty, and the value of envronmental amentes. Moreover, the government may decde to make the project s output avalable free of charge, as mght be the case wth a recreaton of transportaton faclty. Evaluatng the benefts of any of these thngs nvolves resortng to technques to elct the wllngness to pay for the benefts by households or frms. Fourth, and related to the last case, projects undertaken by the publc sector may not be fnancally self-suffcent but must rely on publc funds to cover ther costs. In a second-best economy, the costs of rasng publc revenue wll nvolve a margnal deadweght loss from the dstortons of the tax system. Ths wll be the case whether tax or debt fnance s nvolved. Note that ths cost s over and above the value of resources used n the project. The two are often aggregated nto a margnal cost of publc funds (MCPF) that reflects the full cost of rasng an addtonal yen of publc revenues. 3 The excess burden of project fnancng must be ncluded as a socal cost of the project. Prvate proftablty calculatons gnore ths cost. Fnally, projects are typcally ntertemporal n nature, so the benefts and costs occur over a number of perods. In arrvng at a measure of the net beneft of the project, a dscount rate must be used. The dscount rate used on publc projects-the socal dscount rate-may dffer from the dscount rate used for prvate projects. Ths wll occur because of ether dstortons on captal markets (e.g., captal ncome taxes) or because of externaltes assocated wth savng for future consumpton, perhaps for hers. Of course, to the extent that benefts or costs accrue to ndvduals of dfferent generatons or brth cohorts, addtonal equty ssues would arse. How should we wegh real ncome changes of future generatons relatve to those of current generatons? Should we dscount them, or gve them the same weght as n the statc SWF of (5). All of these ssues wll be taken nto account n what follows. We begn wth a dscusson of the decson rule for aggregatng project or polcy costs and benefts, and then turn to the evaluaton of the varous elements of costs and benefts. 3 On the MCPF, see Brownng (1976), Wldasn (1984), Usher (1986) and Sandmo (1998).

10 R. Boadway / Publc Polcy Revew II. THE DECISION RULE The rankng of projects nvolves aggregatng the socal benefts and costs nto a sngle measure. In what follows, we neglect dstrbutonal weghts and proceed by summng up all real ncome changes for ndvduals n the economy. In the absence of dstrbutonal weghts, a yen s worth of real ncome s worth the same to all ndvduals, whch smplfes our analyss consderably. We can aggregate net benefts and costs wthout regard to whom they accrue. In an ntertemporal context, the approprate decson rule s the present value crteron. In the smplest case where the socal dscount rate s constant over tme and denoted r, the present value of a project or polcy s wrtten: T B C PV = (8) t t t t= 0 ( 1+ r) where B t and C t are the benefts and costs of the project n perod t, whch goes from 0 untl the termnaton date of the project T. If ths PV s postve, the project s socally proftable. More generally, polces can be ranked accordng to ther PV, and that determnes whch one(s) should be undertaken. 4 Varous choce stuatons are possble. If the choce s smply whether to undertake a gven project, then the project should be undertaken f ts PV s postve. If the polcymaker s faced wth a choce between two or more mutually exclusve projects or sets of projects, the one wth the hghest PV should be undertaken. These may be gven types of projects of dfferent scales, of dfferent startng tmes, or of dfferent lengths of lfe. A slghtly more complcated case s when there s a fxed captal budget avalable to allocate to a chosen set of projects. In ths case, the best opton s the set of projects that satsfes the captal budget and has the hghest summaton of PVs. Ths may well nvolve excludng projects wth hgher PVs f, for example, they are relatvely large n sze. Care must be taken to nclude any welfare consequences of unused funds n evaluatng among optons. In partcular, unused funds that revert to general revenues wll avod excess burdens of taxaton that would otherwse arse. As well, care must be taken to account both for captal budgets that cover several perods, and for future captal expendtures that mght be needed as the project contnues over tme. There are some other specfc ssues that must be dealt wth n applyng PV formula (8). One has to do wth the fact that when the project s expected to termnate at tme T, there may well be some assets stll on hand. Whatever scrap value they have must be treated as a beneft and evaluated approprately. That evaluaton may be problematc, dependng on whether the 4 There are alternatves to the PV that use the same basc nformaton. One s the beneft-cost rato, whch s the raton of the PV of benefts to the PV of costs. Whle t wll ndcate whether a gven project s worth undertakng, t can gve a msleadng rankng of mutually exclusve projects of dfferent scales. Another s the nternal-rate-of-return (IRR) crteron, whch calculates the dscount rate that makes the PV of benefts equal to the PV of costs. If the IRR exceeds the socal dscount rate, the project has a postve PV and s worth undertakng. However, the IRR may not be unque, and t may also rank mutually exclusve projects ncorrectly f the tme profle of benefts and costs dffer.

R. Boadway / Publc Polcy Revew 11 termnal captal can be put to alternatve uses. If so, the present value of ts subsequent benefts must be estmated. There may also be some negatve assets (future labltes) at the termnal date. For example, there may be some ste clearng requrements, f there are hazardous waste materals. The cost of dsposng of these must be treated as a cost, assumng that the project s responsble for creatng them n the frst place. A very mportant ssue that must be decded s the unt of measurement of costs and benefts to be used n applyng (8), or equvalently the numerare. In prncple, the choce of numerare wll not affect the rankng of projects, but t wll gve rse to numerare-specfc procedures for evaluatng benefts and costs. The ssue s complcated by the fact that markets are dstorted, and some numerare choces may themselves face dstortons. As well, benefts and costs occur over tme, and the measurng rod must take that nto account. The standard approach s to use consumpton n the present perod as a numerare, where consumpton can be thought of as a composte of the consumpton of all goods and servces measured by the real ncome requred to purchase them as dscussed earler. There are several conceptual ssues that are nvolved n evaluatng all benefts and costs n terms of current consumpton, some of whch nvolve convertng benefts and costs nto consumpton n the current perod, and others nvolvng dscountng benefts and costs accrung n dfferent perods. Wth respect to measurng benefts and costs n terms of consumpton n any gven perod, several ssues arse, whch are treated n more detal n the followng sectons. The frst s how to evaluate project nputs and outputs n terms of current consumpton when these are traded domestcally on dstorted markets. As we shall see, shadow-prcng technques can be used for ths purpose. A specal case s that of labor used on the project, gven that labor markets not only face tax dstortons, but may be characterzed by unemployment and the adjustment costs assocated wth changng employment. Specal technques that exst for shadow prcng labor must be appled. Related to ths n the evaluaton of nputs and outputs for whch there s no market prce. Here shadow prcng nvolves estmatng the wllngness-to-pay for these tems n terms of current consumpton. A further ssue s how to evaluate commodtes that are traded so that ther fnancal benefts or costs ultmately nvolve a supply or demand for foregn exchange. Here, the evaluaton nvolves convertng foregn exchange amounts to domestc consumpton values usng a shadow prce of foregn exchange that takes account of dstortons that mght exst n foregn exchange markets. Next, projects or polces typcally are not self-fnancng but have effects on government revenues. If there are dstortons nvolved n rasng revenues, a yen n the hands of the government wll be worth more than a yen n the hands of consumers: the MCPF, whch s the opportunty cost of convertng a unt of consumer ncome to government revenue, wll exceed unty. Ths premum on government revenues must be accounted for n evaluatng the benefts and costs of the project n terms of current consumpton. Fnally, f dstrbutonal consderatons are an ssue, the value of current consumpton wll dffer accordng to whom t accrues. One approach that can be taken s to treat as the numerare consumpton n

12 R. Boadway / Publc Polcy Revew the hands of a gven ncome class, such as the lowest. Then, to the extent that benefts accrue to ndvduals n other ncome classes, those must be dscounted usng the relatve values of β defned above. Of course, t may well be decded to avod ncorporatng dstrbutonal concerns drectly nto the analyss, and reportng dstrbutonal effects separately nstead. Once n-perod benefts and costs have been estmated, they must be converted to current consumpton values. The approprate dscount rate s the consumpton dscount rate, that s the rate at whch ndvduals actually dscount future versus present consumpton. A number of ssues arse here as well. An obvous one s the choce of dscount rate. A natural canddate mght be the after-tax nterest rate faced by ndvduals n the economy. However, f there are externaltes assocated wth savng (e.g., altrusm toward future generatons, or externaltes assocated wth captal accumulaton), these ought to be taken nto account. Smlarly, f captal market constrants restrct the ablty of ndvduals to borrow and lend, or f there s uncertanty about the future that cannot be shed on captal markets, market nterest rates may not reflect true consumpton dscount rates. Another ssue s that projects may affect the level of nvestment elsewhere n the economy. If, for example, some nvestments are crowded out, the opportunty cost of that wll be the present value of forgone consumpton that would have been generated by the nvestment, whch n the presence of captal market dstortons, wll be greater than one per yen of forgone nvestment. The crowdng out of prvate nvestment may come about from the way a project s fnanced, for example, whether by tax or debt fnance. Fnally, to the extent that the consumpton of future generatons s affected, the queston arses as to what weght should be attrbuted to t when evaluated aganst current consumpton. In other words, what dstrbutve weght should be attached to the consumpton of future generatons. Ths wll be mportant wth respect to long-lved projects as well as wth respect to fscal polcy changes that have ntergeneratonal mpacts, such as major tax reforms or reforms of socal transfers. Another ssue that arses n aggregatng benefts and costs over tme s the manner of accountng for prce level nflaton. Here, what s mportant s consstency. Two alternatve-and equvalent-procedures exst. One s to use nomnal prces n each perod, that s, the prces that obtan on markets. In ths case, the dscount rate that must be used s the nomnal nterest rate, whch ncorporates the effect of nflaton. The other s to use constant-yen prces, whch are obtaned by deflatng nomnal prces by a prce ndex that reflect the rate of nflaton. Followng ether procedure wll generate the same results. To see ths, consder the PV formula gven by (8). Suppose that benefts and costs are measured n nomnal terms, and that the nterest rate r s a nomnal one. If the nflaton rate s π per perod (assumed constant here), convertng nomnal benefts and costs to real ones n terms of perod 0 prces nvolves the followng transformatons: b t = B t, c = C t t ( 1+ π ) ( 1+ π ) t t

R. Boadway / Publc Polcy Revew 13 As well, f we denote the real nterest rate by, t must satsfy: ( 1+ ) = ( 1+ r)( 1+ π ) Then, t can be seen that the PV formula (8) can equvalently be expressed n real terms as follows: T c c PV = ( 8 ) t t t t= 0 ( 1+ ) Of course, ether approach nvolves predctng values nto the future, whether they be constantor current-yen values. All cost-beneft analyses face ths problem. Some accountng ssues also arse n the costng of captal nputs because of ther durable nature. Ther costs are ncurred up front, but ther use s spread over the future. Standard accountng prncples suggest two alternatve approaches to account for captal costs, cash-flow accountng and accrual accountng. Under cash-flow accountng, all outlays and nflows are costed as they occur. Captal expendtures are fully expensed when they are made. These nclude all nvestment expendtures - addtons to a project s captal stock, replacement and deprecaton spendng, and scrap value salvaged when the project termnates. Costs of fnancng and ongong deprecaton are not ncluded snce that would be double countng, except to the extent that deprecated captal s replaced. Accrual accountng costs captal as t s used rather than when t s acqured. Two costs are ncluded, deprecaton and fnancng costs. Deprecaton ncludes the amount of captal value that s used up each perod, and comprses obsolescence, wear and tear, and changes n the relatvely prce of the captal. Fnancng costs reflect the forgone nterest assocated wth holdng captal rather than nvestng the funds nto fnancal assets. Cash and accrual accountng for captal costs are alternatve ways of presentng the same nformaton, and ought not to be mxed: otherwse, double-countng or under-countng wll occur. If properly done, the present value of the accrual costs of an nvestment should equal ts cash flow. Accrual accountng s by ts nature more dffcult snce t requres knowledge of deprecaton, whch cannot readly be observed from market prces. As well, the prncples of shadow prcng dscussed below are much less transparent under accrual accountng. Hence, cash accountng s typcally used for cost-beneft analyss, contrary to the practce n the prvate sector. Accrual accountng s the norm for prvate frms snce t conveys more nformaton to shareholders of the current proftablty of the frm. The above dscusson summarzes the ssues that arse when current perod consumpton s chosen as the numerare. Shadow prces for nputs purchases and outputs sold must take account of dstortons on domestc markets; net foregn exchange earned from transactons nvolvng tradables must be converted to consumpton equvalents usng a shadow prce of foregn exchange; changes n government revenue must be converted to consumpton equvalents usng a MCPF; and future net benefts, ncludng those affected by crowded-out nvestment,

14 R. Boadway / Publc Polcy Revew must be dscounted usng a consumpton dscount rate. The result s the PV of a project measured n terms of consumpton or real ncome of domestc ndvduals, wth or wthout dstrbutonal consderatons havng been ncorporated. There are other optons for the numerare. One that has been promnent n the development lterature s foregn exchange n the hand of the government. Ths was the choce proposed by Lttle and Mrrlees (1968), and developed further by Ray (1984). In ths case, the value of all nputs and outputs are converted nto equvalent values of foregn exchange usng converson factors that are analogous to the above shadow prces. Traded commodtes can be evaluated at ther foregn exchange costs (so-called world prces). Non-traded commodtes are then converted nto equvalent values n terms of foregn exchange usng the nverse of a shadow prce of foregn exchange. The use of ths numerare entals the use of analogous converson factors as above, but the converson s typcally done n the reverse drecton. Thus, any changes n output or use of non-traded commodtes must be converted nto foregn exchange usng effectvely the recprocal of the shadow prce of foregn exchange. Changes n domestc consumpton changes are dscounted relatve to foregn exchange n the hand of the government because of the MCPF factor already mentoned. It was argued that ths MCPF exceeds unty not just because of tax dstortons, but also because n a developng country context, government funds mght be an mportant source of fnance for nvestment, whch has hgher value than consumpton because of captal market dstortons. The Lttle-Mrrlees approach also recommended ncorporatng dstrbutonal weghts nto the cost-beneft evaluaton, t beng the case that polcy nstruments were not as readly avalable n developng countres for addressng equty concerns drectly. But n the end, nothng of real substance s nvolved n choosng between current consumpton and foregn exchange n the hand of the government as the numerare. If used consstently, both should yeld the same project rankngs. In what follows, we follow the conventon of takng current consumpton as the numerare. We take up some of the ssues nvolved n measurng costs and benefts n terms of current consumpton n more detal. III. VALUING MARKETABLE INPUTS AND OUTPUTS Cost-beneft analyss nvolves puttng socal values on the net benefts of projects or polces n dstorted economes. Before turnng to the specfc of partcular types of costs and benefts, t s useful to put thngs nto context by outlnng a general expresson for welfare change measures n a dstorted economy. The expresson we develop was proposed by Harberger (1971a), so we refer to t as Harberger s measure of welfare change. It s a measure that gnores the dstrbutve effects of polces, so we can base our dscusson on an economy consstng of a representatve household. Let the representatve consumer have a utlty functon u( x,x,x, L ) 0 1 2,x n where x s the

R. Boadway / Publc Polcy Revew 15 consumer s purchase of commodty (whch wll be negatve for factors suppled). The consumer s prce for commodty s p, where p = 0 1 for the numerare good x 0. Dfferentatng the utlty functon and usng the frst-order condtons for the consumer s utlty maxmzaton problem, u / u0 = p / p0 = p, we obtan an expresson for the change n utlty from a change n consumpton measured n terms of the numerare good: du udx dw = = = p dx (9) u0 uo Next, suppose consumpton s suppled from ether the prvate market, y, or from publc sector projects, z, so that market clearng mples x = y + z. Prvate sector producton s mplctly determned by a transformaton functon f ( y0, y1, y2, L.y n ) = 0. Assumng there s producton effcency, the producer prce for commodty n terms of the numerare good can be expressed as f / f 0 = p t, where t s the dstorton n market. We can thnk of ths as a tax dstorton, but t could also be an externalty or a dstorton due to monopoly power. Dfferentatng the transformaton functon, and usng the expressons for relatve producer prces, we obtan: ( t ) p dy = 0 (10) Then, combnng (9) and (10) and usng the market clearng condton, we obtan: tdx + ( p t ) dw = dz (11) Ths s the general expresson for the change n welfare arsng from any small change n consumer demands and project producton. The former are evaluated at the sze of the dstorton, whle project nputs and outputs are evaluated at ther producer prces. It s useful for what follows to recognze that projects wll only operate n some markets. Let k ndex the markets on whch a project under consderaton operates and j ndex all other markets. Then, (11) may be wrtten: t kdxk + ( pk tk ) dz + dw = t jdx j (12) k k k j Thus, f we are evaluatng a project that nvolves a change n the z k s, (12) ndcates that we must take account of the drect opportunty cost of the project s nputs and outputs, ndrect changes n welfare on the markets on whch those nputs and outputs are traded and welfare changes n other markets. In the followng we frst consder frst the welfare effects arsng from changes n outputs on the markets n whch the project operates-the frst two terms n (12)-and then the ndrect effects-the thrd term. We then look at ssues that arse n partcular markets. III.1. DIRECT WELFARE EFFECTS ON MARKET INPUTS AND OUTPUTS We consder here the welfare effects assocated wth the purchase of a commodty on a

16 R. Boadway / Publc Polcy Revew dstorted market, where the welfare effect ncludes both the value of the resources transferred to the publc sector and changes n the cost of the dstorton tself. The technque used s to construct a shadow prce that takes account of both of these effects. In terms of the general welfare change measure (12), the effect of a change n the output of a commodty z k by a project can be expressed as: w x x k j = pk tk + t k + t j k j zk zk z (13) k 144 2443 14243 drect effect ndrect effect Here we consder what s labeled the drect effect, whch we can thnk of as the shadow prce of commodty k, denoted s k. We can obtan a smplfed expresson for ths shadow prce by adoptng a partal equlbrum approach and supposng that market supples and demands depend only on own-prces. Then, the market clearng condton can be wrtten x k ( pk ) = yk ( pk tk ) + z k. Dfferentatng ths, we obtan: 1 pk xk y k = = ( x ' y ') 1 k k zk pk pk Then, snce xk / z k = xk' pk / zk, the shadow prce of z k (correspondng to the drect effect above) s: ( p t ) k k yk' pk xk' sk = (14) yk' xk' Ths s known as Harberger s shadow prcng rule, followng Harberger (1969). It stpulates that the shadow prce s a weghted average of the supply and demand prces, where the weghts are the proportons n whch an ncrease n z k comes from ncreased supply and reduced demand. For dscrete changes n project demand, t can be wrtten n the followng approxmate form: 5 s ( p t ) y x k k k = k k pk (15) zk zk To llustrate the meanng of ths shadow prce, refer to Fgure 2. Suppose before the project 0 0 0 s ntroduced, market output s x k = y k, wth the assocated consumer prce p k and producer 0 1 prce pk tk. The project demand s zk, whch causes supply to rse to y k and demand to fall 1 to x k. The opportunty cost of the project demand conssts of loss n value to consumers of the area beneath the demand curve x 1 abx 0 p 0 x, whle the opportunty cost to producers s the 0 1 0 relevant area under the supply curve yk cdyk ( pk tk ) yk k k k k. Thus, the opportunty cost per unt of z k, that s, ts shadow prce, s gven by (15). Notce that f the supply curve s horzontal, the shadow prce s the supply prce pk tk, whle f the demand curve s horzontal, the shadow prce s the demand prce p k. The former case mght be thought to be relevant where the commodty s tradable and the supply prce s dctated by the world prce. However, n ths case, an ncrement n project supply results n an ncrement of foregn exchange earnngs. To the extent that there are dstortons n trade (tarffs, ex post subsdes, quotas, etc.), the converson 5 If dstrbuton s an ssue, the weghts n ths shadow prcng rule could be augmented by dstrbutve weghts n a manner dscussed earler.

R. Boadway / Publc Polcy Revew 17 of foregn exchange earnngs to domestc consumpton values wll tself nvolve some shadow prcng. We return to that ssue below. Fgure 2 S(p k ) p k 1 a S(p k - t k ) p k 0 b p 1 k - t k p 0 k - t k c d D(p k ) + z k D(p k ) x k 1 x k 0 y k 1 x k III.2. INDIRECT WELFARE EFFECTS ON RELATED MARKETS To the extent that the change n project demand for commodty k nduces changes n the market output of commodtes n other dstorted markets, an ndrect welfare effect must be taken nto account. Ths ndrect effect s captured n the last term n (13), whch can be approxmated for dscrete changes to: x j rk = j k t j (16) z k The augmented shadow prce of z k would then be the sum of the drect and ndrect effects, s k + r k, where s k s gven by (15). Ths ndrect effect can be depcted geometrcally for the case of one of the related markets n Fgure 3. Here, the market for the related commodty x j has a negatve dstorton, so t j < 0. Ths could be a subsdy or a negatve externalty causng the margnal value to consumers to be less than the margnal cost on the supply sde (the margnal socal cost n the case of an 0 externalty). In the ntal equlbrum wthout the project n place, output s x j and demand 0 0 0 and supply prces are p j and p j t j > p j, respectvely. The margnal dstorton-the dfference between the opportunty cost to supplers and the value to demanders-s gven by t j. Snce the margnal dstorton s constant, the welfare gan from any change n x j s gven by t j x j, as (16) mples. In Fgure 3, the supply prce s assumed to be constant for smplcty, and the change n project demand zk s assumed to cause the demand curve for x j to shft rght. Thus,

18 R. Boadway / Publc Polcy Revew f z k > 0, so x k < 0, t would be the case that x j > 0 f the two commodtes were substtutes 1 n demand. The equlbrum output of good j rses to x j. The welfare change n the market for x j conssts of two components: the ncrease n the costs of provdng the extra x j gven by 0 1 area x bcx and the ncrease n the value of the addtons output to consumers, x 0 adx 1. The j j j j dfference between these s the area abcd, whch corresponds wth the ndrect effect t j x j that appears n (16), n ths case an addtonal welfare cost. The augmented shadow prce would have to nclude the analogous ndrect effects from all dstorted markets that are affected. Fgure 3 p j - t j p j a c d D 1 (p j ) D 0 (p j ) x j 0 x j 1 x j Indrect effects of ths sort have been mportant n the evaluaton of transportaton projects, such as a subway system, an arport, or a major brdge or tunnel. One of the man effects of these knds of projects, n addton to creatng new demand, s to dvert traffc from other modes of transport, and often these other forms have dstorted prces. For example, publc transport projects may dvert traffc from road travel, where prce (the cost of a trp on the road) wll be less than socal cost, whch ncludes the congeston mposed on other travelers. In ths case, the ndrect effect would be a beneft assocated wth the reducton n traffc on congested roadways. These ndrect benefts can be among the most mportant benefts of transportaton projects. Moreover, the exstence of ndrect benefts arsng from dverted traffc can lead to arguments for subsdzng publc transt usage as a way of ncreasng the amount of traffc dverted. Ths s a classc second-best prcng argument. III.3. SHADOW PRICING OF PARTICULAR INPUTS The above dscusson of the shadow prcng of nputs and outputs apples n general to any

R. Boadway / Publc Polcy Revew 19 commodtes. There are a few specal examples that tend to be of partcular mportance. Here, we consder two specal cases: labor and foregn exchange. When we turn to ntertemporal ssues below, the weghted average methodology wll reappear. III.3.1. The Shadow Wage Rate Vrtually all projects employ labor as a major nput, and labor markets are typcally dstorted. Taxes of varous sorts-both drect and ndrect-wll drve a wedge between the prce frms pay workers and the after-tax wage that workers receve. There may also be unemployment n labor markets, and there may be rgdtes that preclude costless movement of labor from one locaton or occupaton to another. Shadow prcng of labor should take all these factors nto account. If the only dstorton were taxaton, the weghted-average prncple would apply drectly. The shadow wage rate would be a weghted average of the before-tax wage rate and the after-tax wage rate, where the weghts are the proportons n whch the project labor comes from workers prevously employed elsewhere (forgone demand) and workers nduced to enter the labor force (ncreased supply). More generally, where there are other sources of dstortons, these would need to be taken nto account. Begn wth the case of nvoluntary unemployment. If ths exsts, workers hred by a project can come from three sources: those who would be employed elsewhere, those who are attracted nto the workforce from voluntary unemployment, and those who are nvoluntarly unemployed. The shadow wage wll be a weghted average of the opportunty cost of each of these. In the case of workers employed elsewhere, the opportunty cost s the before-tax wage rate, and for those voluntarly unemployed, t s the after-tax wage rate, as above. For the nvoluntarly unemployed, they would have been wllng to work for the gong wage rate but are unable to fnd a job. Ther opportunty cost s less that the after-tax wage rate (snce they would be wllng to work at the gong wage), but greater than the value of lesure (dscussed further below). Snce the true opportunty costs dffers for dfferent workers, and snce t s not observed on the market, some arbtrary choce must be made, perhaps mdway between the before-tax wage and an estmated value of lesure tme, whch s presumably above zero. Matters are more complcated once one takes account of the fact that nvoluntary unemployment mght be an equlbrum phenomenon. Consder the followng smple example, taken from the lterature on cost-beneft analyss n a developng country context. Suppose there are two sectors n the economy, a rural one and an urban one, and a wage dfferental exsts between them. In partcular, the urban wage rate w u exceeds the rural wage, w r. There mght, for example, by severe underemployment n the rural sector because of, say, technologcal mprovement makng labor redundant, but nonetheless famles contnue to employ famly members at subsstence wage rates. A naïve applcaton of shadow prcng mght take the shadow wage rate to be a weghted average of w u and w r, wth the weghts beng the