The Welfare Economic Theory of Green National Accounts

Transcription

1 Environ Resource Econ DOI /s y The Welfare Economic Theory of Green Naional Accouns Parha Dasgupa Acceped: 27 June 2008 SpringerScience+BusinessMediaB.V.2008 Absrac This paper akes a criical look a he lieraure on green naional accouns. The problem sudied is o find a linear index of economic variables ha responds o perurbaions in he same direcion as social well-being. The hesis of a large lieraure, ha ne naional produc (which is a flow) is ha index in closed economies, is shown in some inerpreaions o be simply false and in ohers o suffer from deep esimaion problems. I is argued ha capial depreciaion using shadow prices should cerainly be included in naional accouns, bu ha he righ welfare index is a comprehensive measure of wealh, defined as he shadow value of an economy s sock of all capial asses. I is shown ha comprehensive wealh is usable as a crierion for policy evaluaion as well as for deermining susainable economic developmen. Keywords Naural capial Ecosysems Capial depreciaion Shadow prices Income Comprehensive wealh Ne naional produc Inergeneraional well-being Susainable developmen Populaion growh Technological uncerainy Wiener process 1Inroducion:EconomicIndicesandTheirPurposes In judging he performance of an economy, we usually ask a combinaion of four quesions: In preparing his review aricle, I have borrowed exensively from my join work wih Kenneh Arrow, Lawrence Goulder, Karl-Göran Mäler, Kevin Mumford, and Kirsen Oleson. Discussions wih hem over he years has grealy influenced my hinking on he subjec. Some of he exposiion has been aken direcly from he heoreical Secions in Arrow e al. (2008). I am mos graeful o Geir Asheim for his commens on a previous draf of his paper. P. Dasgupa (B) S. John s College, Universiy of Cambridge, Cambridge, UK parha.dasgupa@econ.cam.ac.uk

2 P. Dasgupa (A) How is he economy doing now? (B) How has is performance been in recen years? (C) How is i likely o perform under alernaive policies? (D) Wha policies should be pursued here? 1 Public economiss address quesions (C) and (D); sudens of he idea of susainable developmen are concerned wih (B), (C), and (D); while naional income saisicians respond o (A). This classificaion of ineress among he hree groups of social scieniss is no doub crude, bu i helps o dissec a large and varied lieraure ha has sudied ways o give quaniaive expression o he idea of inergeneraional well-being (well-being, for shor). Answering quesions (C) and (D) requires someone o evaluae an economy a a poin in ime before and afer a (hypoheical) perurbaion has been made o i. In conras, (B) requires he analys o evaluae when he perurbaion is he passage of ime iself. However, in order o evaluae an economy, we need a crierion wih which o do he evaluaion. We also need o jusify he choice of ha crierion in ehical erms. Ineresingly, hough perhaps no surprisingly, he same ehical calculus is involved in answers o each of quesions (B), (C), and (D). 2 We confirm ha below. Alhough i is now cusomary o regard changes in gross naional produc (GNP) as he crierion for judging he progress or regress of naions, economiss have recognized for a long ime ha, as a measure of well-being, GNP suffers from serious limiaions. I review several limiaions in Sec. 2 and conclude, as so many economis have already done, ha GNP s main weakness lies in he fac ha i is insensiive o he depreciaion of capial asses. I is hen bu naural o ask wheher ne naional produc (NNP) can serve as a measure of well-being. In Sec. 3 I review he classical argumen for NNP (or ne income ), which was ha i is he ceiling o be imposed on aggregae consumpion if he economy s wealh is no o decline. Tha argumen was pu forward by Lindahl (1933) and explored furher by Solow (1974), Harwick (1977), and Dixi e al. (1980). One of he conclusions I reach in his paper (Sec. 4) is ha, a huge conemporary lieraure on green NNP nowihsanding, here is nohing more of pracical imporance o say abou NNP s welfare properies han was uncovered by Lindahl. In racking he effec of perurbaions on well-being, i is useful o make use of shadow prices. Tha mode of analysis, which is now very well known, is developed in Sec. 4. In Secs. 4.6 and 5 6 I show ha shadow prices can be used as relaive weighs o consruc a linear index of an economy s sock of capial asses. Tha index, which we will call comprehensive wealh, moves in unison wih well-being, in ha, a perurbaion increases (resp., decreases) well-being if and only if, holding shadow prices consan, i increases (resp., decreases) comprehensive wealh (Proposiions 4 and 8, below). To be sure, comprehensive wealh isn he same as well-being, bu i responds in he same direcion o perurbaions as well-being does. As comprehensive wealh is a linear index of he socks of he economy s (comprehensive) lis of capial asses, while well-being is a non-linear funcion of is deerminans, i is a far more convenien index o use for responding o quesions (B) (D). 3 Ihen show (Proposiion 9) ha, holding shadow prices consan, comprehensive wealh increases 1 Wha we mean by an economy depends, of course, on he conex in which he quesions are asked. The economy could be a person, a household, a village or own or disric or sae or counry or region, or even he whole world. Here I assume, for concreeness, ha he economy is a counry. 2 See Dasgupa (2001a). 3 There is no seled erm ye for he linear index ha I am calling comprehensive wealh here. I am borrowing he erm from Arrow e al. (2007), bu i has been called genuine wealh (World Bank 2006), and also inclusive wealh (Dasgupa 2007). I is emping o call i green wealh o indicae ha naural capial is included in he measure, bu ha would be o downgrade such oher capial asses as healh and educaion. I am hoping ha he erm comprehensive wealh will prevail, because i is vivid.

3 The Welfare Economic Theory of Green Naional Accouns (resp., decreases) if and only if aggregae consumpion in he economy is less han (resp., greaer han) NNP. Togeher, Proposiions 8 and 9 show ha Erik Lindahl s classic definiion of NNP (Lindahl called i income ) is very closely relaed o he finding ha comprehensive wealh is a measure of well-being: one is dual o he oher. Thoseresulsnoonlyconfirm ha policy evaluaion should mean esimaing he policy s impac on comprehensive wealh (Proposiions 2 4), hey also give formal expression o he concep of susainable developmen (Definiion 2 and Proposiion 7). Secion 4 repors on an exensive recen lieraure on he welfare economics of green naional accouns ha has gone a differen roue from he one iniiaed by Lindahl. The idea here has been o find ways o redefine NNP so ha i becomes a measure of well-being. One redefiniion idenifies he feliciy of consumpion wih consumpion iself, while anoher replaces shadow prices wih price indices consruced ou of boh shadow prices and he raes a which hose prices are forecas o change over ime. I is reasonable o ask wha purpose such exercises serve in a field of enquiry ha was creaed for applicaion o pracical problems of welfare accouning, where simpliciy should be of he umos concern. Which is why I ask he quesion in Sec. 4 and repor ha he answers ha have been given are, o my mind a leas, waning. There is anoher reason why he recen lieraure on he welfare economic heory of green NNP should be found waning. The lieraure has wih bu few excepions been buil on hree assumpions: (i) populaion is consan and he economy experiences no exogenous echnological change; (ii) he economy is a a full opimum; and (iii) he commodiy ransformaion possibiliy se is convex. 4 Assumpion (ii) permis he auhors o assume no only ha all goods and services have markes, bu also ha marke prices are he shadow prices being sough. Some of he findings in he recen lieraure on green NNP remain valid if (ii) is dropped (see below). Bu as he basis of a heory of green naional accouns, where missing markes should be a dominan hough in our minds, (ii) is a paricularly bad assumpion: i encourages one o depend enirely on marke observables when applying welfare economics o policy issues. Assumpions (ii) and (iii) have proved o be aracive for anoher reason. They enable one o use he separaing hyperplane heorem in defining shadow prices. They also enable one o offer a definiion of (comprehensive) wealh ha leads o an index which, in he world we have come o know, is applicable neiher in policy evaluaion nor in he sudy of susainable developmen. (Tha index is he sum of he presen discouned values of he flow of consumpion; see Eq. 28.) The problem is ha many of he lieraure s findings are sensiive o assumpions (i) (iii). 5 Bu (i) (iii) fly in he face of evidence. Tha (i) and (ii) mus be dropped in pracical applicaions is self-eviden. Bu (iii) mus be dropped as well. In a comprehensive review of he processes ha govern he Earh Sysem, Seffen e al. (2004) have shown ha, as a near-universal rule, commodiy ransformaion possibiliy ses are non-convex because non-lineariies are a rouine feaure of Naure s processes. They summarize heir findings (p. 266) in he following erms: Non-linear behaviour is ubiquious hroughou he Earh Sysem; indeed i is much more difficul o find examples of linear han non-linear processes. Many of Naure s processes are even complex. We should conclude ha he convexiy assumpion abou he commodiy ransformaion possibiliy se should have no place in he welfare economic heory of green naional accouns. 4 Weizman (2003) isabook-lenghreamenofgreennnp,basedonassumpions(ii) (iii).seealsohe survey aricle by Heal and Krisrom (2005). 5 Brekke (1994) made a similar observaion wih regard o assumpion (i).

4 P. Dasgupa So as o develop a heory of green naional accouns ha is applicable in he world we have come o know, I follow an approach ha assumes neiher ha he economy is a a full welfare opimum nor ha commodiy ransformaion possibiliies define a convex se. In Secs. 4 and 5 i is assumed ha populaion is consan and ha he processes he economy is subjec o are ime-auonomous. In Sec. 6 I exend he analysis of Sec. 5 by dropping hose wo assumpions. Secion 7 concludes and poins o he many problems ha are now urgenly in need of sudy. 2GNPandNaionalIncome Quesion (A) sands apar from quesions (B) (D), a leas if convenional pracice among naional income saisicians is any guide. I is now common o summarize he sae of an economy by is gross domesic produc (or GDP). For simpliciy of exposiion, we will consider a closed economy. There, GDP is he same as GNP. In a closed economy, GNP is he value of all he final goods ha are produced here. Bu when a commodiy is produced and sold, he price paid for he purchase finds is way ino someone s pocke in he economy. So GNP can be measured also by adding up everyone s incomes wages, salaries, ineress, profis, and governmen income. The sum oal of all he incomes is called (gross) naional income. As GNP and gross naional income are wo sides of he same coin, we use he erms inerchangeably in wha follows. The concep of GNP was developed originally for marke economies, which is why he values impued o goods and services were marke prices. Bu by a clever consrucion of shadow prices, economiss have adaped GNP even for economies where much economic aciviy is underaken in non-marke insiuions. The empirical lieraure on rural household incomes drawn from common propery resources in poor counries offers a good illusraion of he use of shadow prices (Jodha 1986; Cavendish 2000). Two poins should be noed a once: (1) GNP doesn measure wealh. GNP is a flow (dollars per year, say), whereas wealh is a sock (dollars period). Similarly, naional income is aflow,nosock. 6 (2) Alhough i has become a commonplace o regard GNP as a welfare index, i is an aggregae measure of he oupu of final goods and services, nohing more. A good hisory of he conceps of GNP and naional income was provided by Richard Sone in his Nobel Lecure, which is available on he home page of he Nobel Foundaion. 6 Heal and Krisrom (2008) referohepresendiscounedsumofheflowofaneconomy saggregaeconsumpion (which is a sock; see Eq. 25) as naionalincome.anameisbuaname,buheheal-krisrom move does lile o clarify a large and varied lieraure on he welfare economics of green naional accouns. The move confuses maers especially when i is placed nex o Brekke (1994, p.242),heal (1998), Heal and Krisrom (2005), and World Bank (2006), who define wealh o be wha Heal and Krisrom (2008) call naional income. Conflaing socks wih flows has become a commonplace. In giving expression o heir moral ourage over he enormous inequaliy in oday s world, auhors of UNDP (1998, p. 30) wroe: New esimaes show ha he world s 225 riches people have a combined wealh of over 1 rillion US dollars, equal o he annual income of he poores 47% of he world s people (2.5 billion). As wealh and income differ in dimension, hey can be compared. The sock has o be convered ino an equivalen flow (or vice versa) before comparisons can be made. (The auhors of UNDP 1999, repeaed he misake.) If we were o pursue UNDP s reasoning, we could follow he sandard pracice of convering wealh ino a figure for permanen income by using a 5% annual ineres rae, ha is, divide wealh by 20. When his conversion is made on he daa, my calculaions, albei hey are very crude, ell me ha he world s riches 225 people, having a combined annual income of over 50 billion US dollars, earn more han he combined annual incomes of people in he world s welve poores counries, or abou 7% of he world s populaion (385 million). This is sill a sobering saisic.

5 The Welfare Economic Theory of Green Naional Accouns Bu even a cursory sudy ells us ha GNP rose o prominence during he 1930s, when advanced indusrial counries were suffering from a deep economic depression. A ha ime here was need for an index ha refleced aggregae economic aciviy. GNP filled ha need. Bu, somehow, during he pos-war years GNP came o be regarded as a welfare index. Tha inerpreaion is now so ingrained in us, ha growh in GNP is regarded oday as he mos significan indicaor of economic progress. If someone alks of economic growh, he lisener doesn need o ask, Growh in wha? ; he will know ha he speaker means growh in GNP. However, inerpreing naional income as a measure of well-being has problems. Three are superficial, bu one is deep. Le us begin wih he former. (1) Because a dollar in he hands of he poor is awarded he same weigh as a dollar in he hands of he rich, GNP doesn reflec concerns abou income inequaliy. There is a simple way ou of he problem, hough. I is o apply income disribuional weighs, whereby a dollar s worh of income going o a poor household is awarded a greaer weigh han a dollar going o a rich household. The resuling GNP, being a weighed sum of household incomes, would reflec disribuional concerns. 7 (2) Following Sen (1987) anddreze and Sen (1990), Anand and Ravallion (1993) and UNDP (1994, pp ) have criicized hose who regard GNP o be a welfare index on grounds ha i is insead a measure of a counry s opulence, and hey remark ha opulence is no he same as well-being. The criicism is fauly in wo ways. Firs, opulence is a sock concep, and GNP is no a reurn on any index of opulence ha I am aware of. Secondly, and more imporanly, i isn a misake o seek o measure well-being in erms of an index of opulence. The poin isn ha opulence misleads, bu raher ha we should search for he righ measure of opulence. Below we show ha he righ measure of opulence is comprehensive wealh. (3) An educaed populaion produces greaer oupu (Schulz 1961; Becker 1983)asdoes ahealhypopulaion(dasgupa and Ray 1986, 1987; Fogel 1994, 2004; Dasgupa 1997). So i would seem ha GNP responds o improvemens in educaion and healh. I has been counered hough ha, as hey reflec mere insrumenal virues of human capial, GNP doesn adequaely reflec he well-being people enjoy from becoming educaed (Sen 1987, 1999), or from being in good healh (Bauer 1971). The way o mee his paricular criicism is he same as he one we noed for meeing problem (1), which is o make use of shadow prices for valuing healh and educaion. Healh and educaion are simulaneously aspecs of human well-being and facors ha produce human well-being. As each possesses wo ses of values, healh and educaion should each be couned wice. UNDP (1990) made a sep oward including healh and educaion as aspecs of human well-being, by consrucing is Human Developmen Index (HDI), which is an aggregae of GNP per capia, life expecancy a birh, and lieracy. However, even while adverising he index vigorously over he years, UNDP has offered no ehical jusificaion for he relaive weighs hey aach o he hree componens of HDI, nor for why he sae of he environmen should be missing from i. The deep problem wih GNP lies in he fac ha he index mismanages ineremporal issues badly. (We confirm below ha HDI suffers from ha same weakness.) GNP is he acronym for gross naional produc. The word gross means ha GNP ignores he depreciaion of capial asses. Among naural resources, ha depreciaion can range from a full 100% of he services drawn from oil and naural gas, o he depreciaion experienced by ecosysems from mismanagemen. As environmenal resources are paricularly vulnerable o depreciaion hrough overuse, serious criicisms of GNP were firs made in he conex of 7 Dasgupa e al. (1972)appliedhisechniqueinheirworkonsocialcos-benefianalysisinpoorcounries. On he use of disribuional weighs in naional accouns and on heir relaionship o he shadow prices of goods and services in imperfec economies, see Mirrlees (1969), Sen (1976), and Aronsson and Löfgren (1999).

6 P. Dasgupa environmenal and naural resource problems. 8 I is cerainly possible for a counry s overall producive base (i.e., he base upon which all economic aciviy depends) o grow while is GNP increases, which is no doub a pah of economic developmen we all would like o follow; bu i is also possible for a counry s overall producive base o shrink during a period when GNP grows. 9 The problem is ha no one would noice he shrinking if everyone s eyes were riveed o GNP. If he economy s overall producive base coninues o shrink, economic growh will sooner or laer sop and reverse sign. GNP will hen decline, as will he sandard of living, bu no one would suspec ha a fall was in sore. So, growh in GNP per head can encourage us o hink ha all is well, when i isn. In ha regard, HDI is no beer: i is possible for a counry s HDI o increase even while is overall producive base shrinks. This means ha HDI oo can mislead (for illusraions based on inernaional daa, see Dasgupa 2001b). The resuls jus menioned show ha he enormous empirical lieraure on he sources of economic growh, admirably surveyed by Barro (1997) and Helpman (2004), misdirecs. I seems o me we economiss should have ried insead o discover hose feaures of economies ha proec and promoe growh in comprehensive wealh (suiably adjused for demographic rends). The equaions ha define cross-counry growh regressions have GNP growh on he lef hand side. The welfare economic heory of green naional accouns says ha GNP growh should be replaced by growh in comprehensive wealh. We should wan o know for example, wheher, oher hings being equal, poliical and civil liberies or rade liberalizaion or any one of he many oher feaures of economies people ake ineres in promoe he accumulaion of comprehensive wealh. To he bes of my knowledge, no one has sudied such quesions empirically. So as o sudy a number of subsanive issues in wha follows, we inerpre naural resources in a very broad way. Included on our lis of resources are asses ha provide he many and varied ecosysem services upon which life is based. We also add minerals and fossil fuels o he lis. Frequenly hough, environmenal problems are idenified in erms of polluion, no he depleion of naural resources. In fac environmenal polluans are he reverse side of naural resources. In some cases he emission of polluans amouns direcly o a degradaion of ecosysems (he effec of acid rains on foress). In ohers, i means a reducion in environmenal qualiy (deerioraion of waer qualiy), which also amouns o degradaion of ecosysems (waersheds). For analyical purposes here is no reason o disinguish resource economics from environmenal economics, nor resource managemen problems from polluion managemen problems, nor resource accouning from environmenal accouning. Roughly speaking, resources are goods, while polluans (he degrader of resources) are bads. Polluion is he reverse of conservaion. 10 Some economiss oday conflae environmenal and resource economics by calling i ecological economics. 8 See Nordhaus and Tobin (1972), Mäler and Wyzga (1976), Dasgupa and Heal (1979), Harwick (1990), and Luz (1993), among ohers. Harwick (2000)is a fine heoreical reaise onways o esimae shadow prices for green naional accouns. Mäler (1991), and Weale (1997) provide oulines of a complee sysem of naional accouns inclusive of environmenal naural resources. Perrings and Vincen (2003) conains applied sudies on he subjec. 9 Tha boh are heoreically possible is easy o demonsrae, and I do ha below (Sec. 5). For illusraions of hose possibiliies using crude daa from conemporary naional accouns, see Dasgupa (2001b),Dasgupa (2007)andArrow e al. (2007), Arrow e al. (2008). 10 This poin of view was explored in Dasgupa (1982).

7 The Welfare Economic Theory of Green Naional Accouns 3GreenNNPasMaximumConsanConsumpion As GNP doesn recognize real capial depreciaion, why no deduc depreciaion from i and use NNP as he welfare measure? Because his looks like a soluion o wha I have called he deep problem wih GNP, an exensive conemporary lieraure has advocaed he use of NNP as a measure of well-being. I canno be doubed ha real capial depreciaion should be included in naional accouns (see Repeo e al. 1989,andVincen e al. 1997a, 1997b, on esimaes of he depreciaion of fores resources in Indonesia and Malaysia, respecively, and on mehods for embedding hem in naional accouns), bu he claim ha i is GNP from which ha depreciaion should be deduced in order o obain a measure of (inergeneraional) well-being requires jusificaion. Ineresingly, a jusificaion was provided long ago. The simples way o describe is o sudy he consumpion-saving decisions of a dynasy of consan populaion size, operaing in a deerminisic, compeiive marke economy. Le ( 0) denoe ime, assumed o be coninuous. Suppose r(>0) is he marke rae of ineres on capial, which means ha r is ne of capial depreciaion. We wrie W () for wealh a, wherew () 0. Imagine ha a = 0 he dynasy owns asses worh W (0) in marke value. If C() is he dynasy s consumpion rae, wealh changes according o he equaion, dw ()/d = rw() C(). (1) Equaion 1 says ha if he dynasy is deermined ha is wealh doesn ever decline, consumpion (C()) mus never exceed income (rw()). Erik Lindahl s definiion of income, as he maximum consumpion rae ha mainains wealh is a generalizaion of his observaion. 11 Solow (1974)and Harwick (1977) deepened he conen of Lindahl s income when hey sudied an economy where producion involves reproducible capial and exhausible naural resources. Assuming no echnological progress, Solow idenified condiions on producion possibiliies under which consumpion can be mainained above zero forever. He, and Harwick subsequenly wih greaer generaliy, showed ha in order o consume a he maximum consan rae, ne invesmen in reproducible capial a each momen would have o equal he value of he rae of depleion of naural resources. This resul, which was dubbed Harwick s Rule in Dixi e al. (1980), formalizes Lindahl s suggesion ha an economy s income should be defined as he ceiling ha mus be placed on consumpion if i is required ha comprehensive wealh never declines. Of course, if subsiuion possibiliies are limied, i could be ha susainable developmen simply isn possible. While making a relaed poin, Asheim (1994, p. 262) pu i nicely: Harwick s rule characerizes a susainable developmen; i is no a prescripive rule for susainable developmen. In he following wo secions I argue ha, a huge conemporary lieraure on green NNP nowihsanding, here is nohing more of pracical imporance o say abou NNP s welfare properies han was unearhed by Lindahl. 4WelfareIndices:SocksVersusFlows In a much noed paper, Weizman (1976) claimed o show ha NNP,measured in shadow prices, is proporional o inergeneraional well-being. Tha claim has been widely acceped 11 See Lindahl (1933). Alhough in he English-speaking world Lindahl s noion of income has come o be called Hicksian income, prioriy belongs o Lindahl.

8 P. Dasgupa as being rue, alhough a imes i has been advanced in a more specialized version, as in (S. Dasgupa e al. 2008,p.7),whowrie: Weizman...proved ha he presen value of curren NNP (held consan) is jus equal o he presen value of consumpion along he opimal growh pah for he economy. Even if he claim in S. Dasgupa e al. (2008) were rue, i would be of no ineres, because well-being is no he same hing as consumpion. If, however, Weizman s claim were rue, NNP would be usable as a welfare measure. I is shown in Sec. 5.1 ha, exceping in cases where he direc deerminans of well-being are consan over ime (a case of no pracical ineres whasoever), neiher claim is rue. I develop Weizman s argumen in he conex of an aggregae model of he economy. The model incorporaes he concerns many people oday express abou he naure of economic progress in a world wih depleable naural resources. The resuls we obain are self-evidenly valid for disaggregaed producion srucures, involving inermediae goods. Bu concreeness has is uses: i reminds us ha he moivaion behind he welfare economic heory of green accouning should be pracical applicaion. 4.1 A Simple Model Economy A ime, lek () be a numerical index of he economy s se of reproducible capial asses (buildings, roads, machines) and le L() be he quaniy of human capial (healh and educaion) per person. For simpliciy, we imagine a populaion of idenical individuals. Populaion is assumed o remain consan, which we normalize o be 1. So L() is he oal quaniy of human capial a ime. There are many ways in which Naure eners human aciviies. Habia desrucion, occasioned by he ransformaion of naural ecosysems ino bricks, glass, seel, and concree, would be one way o model environmenal concerns. Dobson e al. (1997), among ohers, have consruced such a model. In conras, I consider he case where Naure s services are exraced for use in producion. So le R() be a numerical index of hose exracion raes. We could imagine ha R is measured in biomass unis. Le A() be a combined index of publicly known ideas and he effeciveness of he economy s insiuions. We inerpre A() o be oal facor produciviy a.now le Y () denoe he economy s aggregae oupu, or GNP. We express Y () by means of he producion funcion Y () = A()F(K (), L(), R()), (2) where F is a non-decreasing, wice differeniable funcion of each of is argumens, and F = 0 if any of is argumens is zero. IdonoassumehaFisconcave. We now describe he evoluion of he economy over ime. Reproducible capial depreciaes a he rae λ( > 0). Ou of GNP, he amoun consumed is C() and he amoun spen in he accumulaion of human capial is J(). C() is an aggregae of he raes of consumpion of many goods and services, including environmenal services. In measuring C, Nordhaus and Tobin (1972) added leisure, direc consumpion services from he naural environmen, and negaive consumpions arising from polluion o he lis of markeed consumpion goods and services. In conras, he lieraure on green naional accouns being reviewed here has focussed on he amendmens ha need o be made for esimaing invesmen. Here I follow he laer lieraure; which is why I inroduce aggregae consumpion in he model wihou specifying how ha aggregaion is achieved. None of he resuls ha follow depends on he way consumpion is aggregaed.

9 The Welfare Economic Theory of Green Naional Accouns We don need o suppose ha ex-ane and ex-pos savings are equal. Wheher hey are or no, he ne accumulaion of reproducible capial, ex-pos, saisfies he equaion, dk ()/d = A()F(K (), L(), R()) J() C() λk. (3) As people die, human capial depreciaes. Le µ(> 0) be he proporional rae a which L depreciaes. I follows ha dl()/d = J() µl(). (4) I remains o describe he evoluion of naural resources. Le N() be he (aggregae) sock of naural capial and M(N) he naural growh rae. The dynamics of naural capial is hen dn()/d = M(N()) R(). (5) A simple way o hink abou he dynamics of naural capial is o suppose ha M(N) is quadraic. Here we inroduce hresholds in he produciviy of naural capial. Le m, b, and Q be posiive consans. We assume ha M(N()) = b + mn() 1 N()/Q], for N() >0, and. (6) M(N()) = 0, for N() = 0 As Naure is producive, we mus assume oo ha Q > 4b/m (oherwise, he righ hand side of he firs par of Eq. 6 isn posiive for any N). Maximum susainable yield from Naure is (mq/4 b) >0. Moreover, Naure s carrying capaciy is Q1 + (1 4b/mQ) 1/2 ] and is hreshold is Q1 (1 4b/mQ) 1/2 ].IfN were o decline o he hreshold level, he economy would be doomed (as F(K, P, 0) = 0, oupu would evenually decline o zero). Noe ha M(N) in Expression 6 is no a concave funcion. 12 Modern heories of economic growh assume ha oal facor produciviy A increases wih invesmen in research and developmen. In some models A is aken o be an increasing funcion of cumulaive oupu (a case of learning by doing ). For our purposes here would be no advanages in making any of he assumpions paricular o endogenous growh heory. So I ake i ha A() is exogenous. The sae of he economy is defined by he vecor (K, L, N). WewrieS = (K, L, N). Assume ha feliciy (insananeous well-being) a depends solely on consumpion a. Wriing U for feliciy, we have U() = U(C()). WesupposehaU (C) >0andU (C) <0 (where U (C) and U (C) are he firs wo derivaives of U wih respec o C, respecively). The assumpion, U (C) <0, could appear innocuous, even self-evidenly rue in welfare economics, bu we see below ha i became cusomary in he lieraure on green naional accouns ha followed Weizman (1976), o drop i and assume insead ha U (C) = 0. Tha U is a funcion only of C rules ou any influence on feliciy of habiual consumpion or he average consumpion of a person s peer group. 13 Moreover, he specificaion assumes ha feliciy doesn depend explicily on naural capial as socks (e.g. sacred groves or places of scenic beauy). To inroduce such facors in he feliciy funcion would leave he 12 The specificaion in Eq. 6 is aken from Dasgupa (1982). 13 Inergeneraional welfare economics when habiual consumpion is an argumen of feliciy has been sudied by Ryder and Heal (1973) and Aronsson and Löfgren (2008). On he welfare implicaions of he influence of he consumpion of ohers on an individual s feliciy, see Layard (1980, 2005) and Arrow and Dasgupa (2007), among ohers.

10 P. Dasgupa proposiions we prove below unaffeced; i would only affec he srucure of shadow prices (Equaions 10a c below). 14 Le V () denoe inergeneraional well-being a. V () is aken o be of he form V () = U(C(τ))e δ(τ )] dτ, (7) where δ(>0) is he rae of ime discoun. We assume ha he inegral exiss. Expression 7 gives us an ehical calculus wih which we address quesions (A) (D). The expression for V in Eq. 7 has a srong srucure. A more general form for V would have a recursive srucure, now familiar in conemporary macroeconomics. However, he Proposiions on susainable developmen ha we prove below (Proposiions 7 11) would remain unchanged if we were o work wih a more general, recursive srucure han Expression 7. Because of is familiariy, we shall resric our discussion o he case where V saisfies Eq. 7. A now-enormous lieraure has consruced he welfare economics of green naional accouns in an economy a a full opimum. Moreover, he lieraure has been buil on he backs of economic models in which non-convexiies in commodiy ransformaion possibiliies are ou of sigh. 15 So as o develop a heory of green naional accouns ha is applicable, I repor an approach ha assumes neiher ha he economy is a a full welfare opimum nor ha producion possibiliies define a convex se. The approach, which has been developed wih increasing generaliy in Dasgupa and Mäler (2000) and Arrow e al. (2003a,b), bases he welfare economics of green naional accouns on economic forecass. 16 I is assumed ha he forecas is no mere guesswork, bu is based on a heory abou he economy (which no doub has guesswork buil ino i). This means ha he evaluaor is able o prepare a forecas no only on he basis of he sae he economy happens o be a oday, bu also from saes a which i could conceivably have been oday. 4.2 Resource Allocaion Mechanisms 17 Imagine ha he economy faces no only echnological and ecological consrains, bu also insiuional consrains (someimes called ransacion and informaion consrains). By he economy s insiuions I mean marke srucures, he srucure of propery righs, ax raes, non-marke insiuions (for credi, insurance, and common propery resources), he characer of various levels of governmen, and so forh. We do no assume ha he governmen is ben on maximizing V subjec o consrains. I could be ha he governmen is predaory, or is a bes neglecful, and has objecives of is own ha are no congruen wih inergeneraional well-being. Nor do we assume insiuions o be unchanging over ime. Wha I do assume is ha insiuions co-evolve wih he sae of he economy in ways ha are considered by he evaluaor. I is no doub a ruism ha social and poliical insiuions influence he evoluion of he sae of an economy, bu i has also been argued ha he sae of an economy influences 14 Such echniques as hose ha measure coningen values (CVM), ravel cos, and hedonic prices, were developed in order ha he shadow prices of ameniies could be esimaed. Freeman (1993) is an excellen reaise on he subjec. 15 For book-lengh reamens, see Heal (1998), Harwick (1990), and Weizman (2003). 16 Dasgupa (2001b) provides a book-lengh reamen of he approach, including a very crude aemp o apply i o daa from a seleced se of counries. Arrow e al. (2004, 2007, 2008) have obained improved (bu sill woefully crude!) esimaes of susainable developmen from recen hisory. 17 Here I draw on Dasgupa and Mäler (2000).

11 The Welfare Economic Theory of Green Naional Accouns he evoluion of social and poliical insiuions (Lipse 1959; Acemoglu and Robinson 2006). The heory developed below accommodaes his muual influence. We sudy he economy a ( 0). Leτ. Thesaeofheeconomya is S() = (K (), L(), N()).Le{E(τ)} {C(τ), R(τ), J(τ), K (τ), L(τ), N(τ)} denoe an economic programme saisfying Eqs. 3 6 from o, wihs() as he iniial condiion. Definiion 1 A resource allocaion mechanism, α, isamany-onemapping α :{S(), } {E(τ)}. (8) We are no assuming ha α maps {S(), } ino a full opimum a, nor even ha i maps {S(), } ino an efficien programme a.i may be haα is riddled wih economic disorions and inequiies. We noe again ha if insiuions and he sae of he economy were known o co-evolve, ha co-evoluion would be refleced in α. Noe finally ha in our model economy commodiy ransformaion possibiliies do no define a convex se. Taking α as a given, Eq. 7 can be wrien as V (S(), ) U(C(S(), τ))e δ(τ )] dτ. (9) V (S(), ) is he value funcion a. In Expression 9, V is assumed o depend explicily on because we allow for he possibiliy ha he economy experiences changes ha are exogenous o i (e.g., ha A() is no consan), a maer o which we reurn below. Before puing he concep of resource allocaion mechanism o work, i is as well o discuss examples. Imagine firs ha all capial asses are privae propery and ha here is a complee se of compeiive forward markes capable of susaining a unique equilibrium. In our model here, α would map {S(), } ino he full opimum (earlier we assumed, for exposiional ease, ha households are idenical). Much modern macroeconomics is founded on his mechanism, as are many wriings on he welfare economics of he environmen. 18 Of paricular ineres are siuaions where some of he asses are no privae propery. Consider he case where K and L are privae propery, bu N is common propery. I may be ha N is a local common propery resource, no open o ousiders. If asses are managed efficienly, we are back o he case of an opimum allocaion, albei one no enirely suppored by marke prices, bu in par by, say, social norms. On he oher hand, i may be ha local insiuions are no funcioning well (e.g., because social norms are breaking down and privae benefis from using environmenal naural resources exceed social benefis). Suppose in addiion ha decisions bearing on he accumulaion of K and L are guided by he profi moive. Then hese behavioural rules ogeher help o deermine α. In a similar manner, we could characerize α for he case where environmenal naural resources are open o free access (Arrow e al. 2003a). Assumpions abou insiuions are embedded in he noion of resource allocaion mechanism. Aspecs of he concep of social capial (Punam eal. 1993) appear in our framework as par of he defining characerisics of α, as do ideas relaing o social capabiliy (Adelman and Morris 1965; Abramoviz 1986), and social infrasrucure (Hall and Jones 1999). The prevalence (or absence) of rus and honesy are embodied in α, whereas oher aspecs of he concep of social capial such as personal neworks ener as componens of human capial (Dasgupa 2000). 18 Heal (1998) conains an accoun of he laer lieraure.

12 P. Dasgupa 4.3 Differeniabiliy of he Value Funcion V is aken o be differeniable. Unaided inuiion is of lile help in judging wheher his is srong assumpion. The mahemaical properies of V depend on he mahemaical properies of α. Problems are compounded because household behaviour and producion and subsiuion possibiliies among he facors of producion are embedded in α, as is he economy s evolving insiuional srucure. Moreover, here are no obvious limis o he kinds of insiuions one can imagine. In many pars of he world he Sae has been known o ac in bizarre and horrible ways. So one looks a wha migh be ermed canonical insiuions. Analyically, he mos well undersood are hose ha suppor opimum economic programmes. Wha do we know abou hem? 19 If U is concave and he commodiy ransformaion possibiliy se is convex, V is concave and is herefore differeniable almos everywhere in each componen of S. This propery holds even in hose circumsances where opimum programmes are chaoic. Thus, chaoic αs don rule ou differeniable V s(almoseverywhere). 20 If he commodiy ransformaion possibiliy se is no convex, opimum economic programmes can have jumps a cerain poins on he space of Ss known as Skiba poins (Brock and Sarre 2003). Skiba (1978)showedhaa hose values of S where V is non-differeniable wih respec o S (such poins are, however, non-generic), V is coninuous. Bu if V possesses righ- and lef-parial derivaives (and i does in every example I have sudied), he analysis ha follows goes hrough. The same could be expeced o be rue for he case of marke economies subjec o fixed disorions, such as hose considered by Lile and Mirrlees (1974) in heir reaise on social cos-benefi analysis. Experience wih dynamical sysems ells us ha if α is non-opimal, V can be disconinuous a cerain values of S. Shadowpriceswouldnobedefinableasuchpoins(see Eqs. 10a c below). For hose αs hahavebeensudiedinhelieraure,disconinuiiesare however non-generic. So, unless he economy is by fluke a a poin of disconinuiy, V would be differeniable wihin a sufficienly small neighbourhood of he iniial sae. Now, shadow prices would exis if V possessed righ- and lef-parial derivaives a poins a which i is disconinuous. Moreover, if he locaion of he poins of disconinuiy on he space of capial socks are uncerain and he uncerainy is a smooh probabiliy disribuion, he expeced value of V would be coninuous. I would seem hen ha he demand ha V be differeniable does no rule ou much of pracical significance. The accoun ha follows is valid for a subsanially more general se of environmens han is usual in wriings on inergeneraional welfare economics. 4.4 Shadow Prices Define p(s, ) = V (S, )/ K (), (10a) q(s, ) = V (S, )/ L(), and (10b) n(s, ) = V (S, )/ N(). (10c) 19 Differeniabiliy everywhere is a srong assumpion. For pracical purposes, however, i would suffice o assume ha V is differeniable in S almos everywhere. The laer would appear o be a reasonable assumpion even when commodiy ransformaion possibiliy ses display non-convexiies. See below in he ex. 20 See Majumdar and Mira (2000) for a fine accoun. I am graeful o Mukul Majumdar for discussions on his poin.

13 The Welfare Economic Theory of Green Naional Accouns Expressions 10a c are he (spo) shadow prices a of reproducible capial, human capial, and naural capial, respecively. The uni of accoun in Eqs. 10a c is feliciy a. So as o develop a sysem of accouns ha is neural among he facors of producion, I shall hroughou use feliciy as numeraire. 21 Using Eqs. 7 and 10a c, he dynamics of he shadow prices of capial asses can be shown o be, dp()/d = δp() U (C()) C()/ K () p() (dk ()/d)/ K () q() (dl()/d)/ L() n() (dn()/d)/ N(), dq()/d = δq() U (C()) C()/ L() p() (dk ()/d)/ K () (11a) q() (dl()/d)/ L() n() (dn()/d)/ N(), and (11b) dn()/d = δn() U (C()) C()/ N() p() (dk ()/d)/ K () q() (dl()/d)/ L() n() (dn()/d)/ N(). 22 (11c) A he iniial dae S(0) is given. α deermines he iniial shadow prices: p(0), q(0), and n(0). ThedynamicalsysemdefinedbyEqs.3 7 and 10a c o 11a c hen allows one o deermine he fuure hisory of he economy in erms boh of quaniies and shadow prices. For ease of noaion we have defined one shadow price for each ype of capial asse: reproducible, human, and naural. For imperfec αs, his is an awkward move. Consider for example he ype of reproducible capial asse ha goes by he name, lahe. I can be ha,when α is imperfec, a lahe deployed in an auomobile facory has a differen shadow price from ha of a lahe deployed in a facory making racors. By lumping all capial asses ino a single aggregae, Eq. 10a misses ha fac. When, in Sec. 4.6, we show ha he welfare crierion ha should be used in policy evaluaion is comprehensive wealh, we will find i useful o remember ha Eq. 10a c are overly aggregaive and ha we need o relax hem by defining a separae shadow price for each capial asse, in each economic aciviy in which he asse is deployed. Shadow prices equal marke prices in hose compeiive marke economies where he se of axes and subsidies ha are required o suppor a full opimum is in place. In imperfec economies, however, marke prices are good approximaions for shadow prices in he case of only cerain commodiies (Lile and Mirrlees 1969, 1974; Dasgupa e al. 1972). Environmenal naural resources are among he many goods and services whose marke prices don approximae heir shadow prices. There is now a large body of applied work ha has sudied ways o esimae he shadow prices of environmenal ameniies (Freeman 1993). In comparison, he lieraure on ways o esimae he shadow prices of ecosysem services remains small. 23 The mehods ha have been developed for esimaing he shadow prices of human capial are applicable mainly in rich counries wih a well developed se of markes. Broadly 21 Dasgupa e al. (1972)andLile and Mirrlees (1974), respecively, developed heir accouns of social cosbenefi analysis wih consumpion and governmen income as numeraire. Which numeraire one chooses is, ulimaely, no a maer of principle, bu one of pracical convenience. 22 I am mos graeful o Geir Asheim for correcing he wrong accoun of shadow-price dynamics in Dasgupa and Mäler (2000). 23 Daily (1997)isheclassiconhewaysinwhicheconomicaciviymakesuseofecosysemservices.Daily and Ellison (2002) is an excellen overview of he scienific lieraure. Among a growing number of valuaion sudies, see Gren e al. (1994), Barbier and Srand (1998), Chichilnisky and Heal (1998), Turner e al. (2000), Boyer and Polasky (2004), Rickes e al. (2004), Sekercioglu e al. (2004), Bin and Polasky (2005), Naidoo and Adamowicz (2005), Goldsein e al. (2006), and Turner and Daily (2008).

14 P. Dasgupa speaking, economiss have used wo ways o measure improvemens in human capial. To illusrae, consider he value of a marginal increase in life expecancy. Some economiss have measured he (social) cos of bringing abou ha increase, while ohers have esimaed he value of he increase iself. The wo would lead o he same number a a full opimum, bu no in imperfec economies, where he laer is he righ way o go abou he maer Eq. 10b. Bu as i requires one o esimae he value of a saisical life (Viscusi and Aldy 2003), he mehod has proved o be conroversial, especially when deployed for making cross counry comparisons. Arrow e al. (2004) used figures for public healh expendiure as esimaes of he shadow price of healh improvemens in poor counries, while Arrow e al. (2008) have combined age-specific moraliy ables wih values of saisical life years so as o esimae he shadow price of increases in life expecancy. The laer esimaes have been found o be subsanially higher han he former, implying ha he economies in quesion are highly imperfec. Shadow prices a depend on he exen o which various capial asses are subsiuable for one anoher, no only a, bu beyond as well. For example, imagine ha pas profligacy has mean ha he sock of naural capial, N, has come perilously close o Naure s hreshold, Q1 (1 4b/mQ) 1/2 ], (see Expression 6). A small furher nudge would ip he economy ino a basin of aracion ha spells d-o-o-m-s-d-a-y. Now inroduce a furher dose of realism ino he model by acknowledging ha he hreshold level is no known wih cerainy and ha he exracion rae R() will never urn ou o be exacly as forecas. The shadow price of naural capial, n, would hen be very large, signalling ha Naure s scarciy value is huge. Even a small furher damage o Naure would be recorded as a large negaive number. Tha large figure would be included in esimaes of comprehensive invesmen (defined formally in Eq. 13). A recen suggesion by Mäler e al. (2007) andwalker e al. (2007) ha an ecosysem s resilience (which, in he presen conex, is he disance beween N and he hreshold, namely, {N Q1 (1 4b/mQ) 1/2 ]}) should be regarded as a capial asse, is an imporan pracical move oward he creaion of a sysem of naional accouns ha akes Naure s non-lineariies seriously. 24 Shadow prices of privae goods can be negaive if propery righs are dysfuncional, such as hose ha lead o he ragedy of he commons. All fuure effecs on he economy of changes in he srucure of asses are refleced in shadow prices. Shadow prices do an awful lo of work for us. Tha is why hey are useful objecs Comprehensive Invesmen I has been common in he lieraure on green naional accouns o assume ha he resource allocaion mechanism, α, is auonomous, by which we mean ha V (S(), ) is no an explici funcion of.thawould beimplied in ourmodeleconomyif oalfacor produciviy (A) in Expression 2 were a consan. For he momen, le us assume ha i is a consan. 24 See Mäler (2008) for an inroducion o he economics of resilience. 25 Marin Weizman (in conversaion) has made he enirely valid poin ha he machinery of welfare opimizaion heory can equally be brough o bear on he formulaion I am advancing here. He observed ha he economic forecas we are sudying in he ex can be inerpreed o be he opimum economic programme subjec o he consrain ha he programme is he forecas iself. True enough; alhough an opimizaion exercise involving a feasible se ha conains a single objec canno invoke he non-empy inerior assumpion in opimizaion heory. Tha said, one can ask wha purpose would be served by inroducing he heory of dynamic opimizaion when he forecas is available. Why no work round he forecas, as I am doing in he ex?

15 The Welfare Economic Theory of Green Naional Accouns So we have V () = V (S()).DiffereniaingV wih respec o and using Eq. 10a c yields, Wrie dv (S())/d = p()dk ()/d + q()dl()/d + n()dn()/d. (12) I () = p()dk ()/d + q()dl()/d + n()dn()/d. (13) I () is comprehensive invesmen a. Equaions (12 13)giveus So we have dv (S())/d = I (). (14) Proposiion 1 Comprehensive invesmen measures he rae a which inergeneraional wellbeing changes wih ime. Hamilon and Clemens (1999) and Dasgupa and Mäler (2000) noed and sressed ha Proposiion 1 offers a simple crierion ha can be applied by naional income saisicians o sudy susainable developmen, an idea ha we sudy in deail in Sec. 5. I argue in Sec. 6 ha exensions of Eq. 14 o cases where α is no auonomous will prove o be fundamenal in applied sudies of quesions (B) (D). Comprehensive invesmen (or invesmen, for shor)has a well-known welfare inerpreaion. Imagine ha he vecor of capial asses a is no S() bu S() + S(),where is an operaor denoing a small difference. In he obvious noaion, V (S() + S()) V (S()) U (C(τ)) C(τ)e δ(τ )] dτ. (15) Now suppose ha a here is a small change in α which akes he form of an increase in invesmen, bu only for a brief momen,. We wrie he change in he vecor of capial asses a + consequen upon he brief increase in invesmen as S().So S() is he consequence of he increase in invesmen a,and(s() + S()) is he resuling vecor of capial asses a +. Le end o zero. From Eq. 15 we obain Proposiion 2 Comprehensive invesmen measures he presen discouned value of he changes in consumpion brough abou by i. I am unable o say who firs proved Proposiion 2. IisimpliciinRamsey (1928), who sudied he case where α is he full opimum. Marglin (1963) proved he proposiion for a simple imperfec economy and used i o develop a heory of social cos-benefi analysis (Dasgupa e al. 1972). Our formulaion here shows ha Proposiion 2 is very general. I forms he welfare basis for responding o quesions (C) (D). We confirm ha nex. 4.6 Policy Evaluaion Imagine ha even hough he governmen does no opimize, i is able o bring abou small changes o he economy by alering he exising resource allocaion mechanism, α. The perurbaion in quesion could be small adjusmens o he prevailing srucure of axes, i could be aleraions o he exising se of propery righs, or i could be a small public invesmen projec. Call any such perurbaion a policy reform.

16 P. Dasgupa As all policy reforms involve a change in resource allocaions, hey can be inerpreed as invesmen projecs. So consider an invesmen projec ha sars a = 0 and erminaes a = T. The projec can be viewed as a perurbaion o α. Alhoughheprojec s formal life is of lengh T,iseffecsarefelindefiniely.Weconsiderprojecshaaresmallrelaive o he size of he economy. For concreeness, suppose ha he projec s oupu a ε0, T ] is Y () and ha Y () is obained by displacing K () and L() unis, respecively, of reproducible capial and human capial from he res of he economy and by increasing he exracion rae of naural capial by R(). Howshouldheprojecbeevaluaed? 26 The projec s accepance would perurb C() over he enire fuure ( 0). Le ha perurbaion be C(). The corresponding perurbaion o U() would be U (C()) C().Bu ha perurbaion includes no only he direc bu also all indirec effecs, exending beyond T. I would be iresome for he projec evaluaor o esimae C() for every projec ha came up for consideraion. Shadow prices are useful because hey enable he evaluaor o esimae C() indirecly by valuing (i) he projec s oupu, (ii) he addiional exracion of naural capial, and (iii) he reallocaions of reproducible and human capial. All shadow prices are esimaed along α because he projec is small. 27 I is mos unlikely ha consumpion and he wo forms of invesmen in he economy have he same shadow price in an imperfec economy. Moreover, if he evaluaor knows α, she knows he way Y () will be divided ino addiional consumpion and invesmen in reproducible capial and human capial, respecively. U (C()) is he shadow price of C(). In Sec. 4.4 we wroe p() for he shadow price of reproducible capial. Tha s far oo aggregaive for our purpose here. Le p() be he shadow price of reproducible capial in he aciviy from which K () is o be displaced for deploymen in he projec a ; andleξ() be he shadow renal on reproducible capial in ha aciviy. I follows ha ξ() = δ + λ (d p()/d)/ p()). 28 Similarly, le ( q)() be he shadow price of human capial in he aciviy from which L() is o be displaced for employmen in he projec; and le θ() be he shadow wage rae (i.e., he shadow renal on human capial) in ha aciviy. Then θ() = δ + µ (d( q)()/d)/( q)()). Finally, suppose ha R() is o be obained by addiional exracion. From Eqs. 5, 6 and 10c, weknowha he shadow price of R() is n(). Knowing α and he shadow prices, our projec evaluaor can calculae he shadow price of Y (), which we denoe by y(). Bu he conribuion he projec makes o well-being is 0 U (C()) C()e δ] d. Weconcludeha U (C()) C()e δ] d 0 = T 0 (y() Y () θ() L() ξ() K () n() R())e δ ] d. (16) 26 If he projec has been designed efficienly, we would have: Y () = (A F/ K ) K () + (A F/ L) L() + (A F/ R) R(). The analysis ha follows in he ex does no require he projec o have been designed efficienly. 27 Of course, if he projec is large relaive o he size of he economy, shadow prices alone would no do, and he evaluaor would have o esimae he consumer s surpluses ha would resul from i. These are familiar maers. 28 ( p)() could be disconinuous a if K () displaced reproducible capial from a differen aciviy from he one i had been rened in a period ha ended a. Ifiis,helef-andrigh-handderivaivesof( p)() would be used on he wo sides of.

17 The Welfare Economic Theory of Green Naional Accouns The righ hand side of Eq. 16 is he presen discouned value of social profis from he projec. And he lef hand side of Eq. 16 equals V (0), he laer being he change in well-being a = 0hawouldbebroughaboubyheprojec.So,Eq.16 can be re-expressed as V (0) = T 0 (y() Y () θ() L() ξ() K () n() R())e δ ] d. (17) Equaion 17 leads o he well-known crierion for projec evaluaion: Proposiion 3 A projec should be acceped if and only if he presen discouned value of is social profis is posiive. Noice ha Proposiions 2 and 3 in effec say he same hing. Define comprehensive wealh a o behe shadowvalueofhe economy scomprehensive lis of capial asses (see Eq. 27, below). Our invesmen projec reallocaes capial asses. The presen discouned value of social profis appearing on he righ hand side of Eq. 17 is he change he projec would bring abou o comprehensive wealh a = 0 by he marginal reallocaion of capial asses in he economy. Proposiion 3 can herefore be re-saed as Proposiion 4 Aprojecshouldbeaccepedifandonlyifisaccepancewouldincreasehe economy s comprehensive wealh. In Sec. 5.1 we show ha wealh also plays a key role in he analysis of susainable developmen. Policy evaluaion and he economics of susainable developmen involve he same welfare crierion: comprehensive wealh. Now imagine for simpliciy ha he economy is viable, in he sense ha i is feasible for he governmen o embark on an indefinie sequence of policy reforms, where wellbeing increases a each sep. We would imagine ha he sequence converges. In view of he non-convexiy of he commodiy ransformaion possibiliy se, he economy would be expeced o move asympoically o a locally opimum resource allocaion mechanism. Tha increase occurs in real ime. In conras, an earlier lieraure derived âonnemon-like planning mechanisms (wih or wihou prices as coordinaing device) ha were assumed o be operaing in imaginary ime (Malinvaud 1967; Heal 1973). The objec ha changes a each sep under he sequence of policy reforms we have formulaed here is he resource allocaion mechanism; whereas, wha changes a each sep in âonnemon-like planning mechanisms is he resource allocaion iself. 4.7 Green NNP and he Curren-value Hamilonian In deriving Eq. 14, he key mahemaical objec was he value funcion, V.FollowingWeizman (1976), he lieraure on green NNP has insead focussed on he economic sysem s curren value Hamilonian. Using Eqs. 10a c, he curren-value Hamilonian associaed wih α can be expressed as H () = U(C()) + p()dk ()/d + q()dl()/d + n()dn()/d. 29 (18) Combining Eqs. 13 and 18, H() = U(C()) + I (). (19) 29 As elsewhere (barring Sec. 4.6), I have suppressed α because i is a given.

18 P. Dasgupa The feliciy price of consumpion is U (C).IfollowshainfeliciyunisNNPa (which we wrie as NNP()), a leas as naional income saisicians conceive i, is NNP() = U (C)C() + I (). (20) Equaions19 and 20 say ha he curren-value Hamilonian is NNP plus consumers surplus. Tha imporan difference beween he Hamilonian and NNP has been obscured in he lieraure ha has aken is lead from Weizman (1976). So i is ineresing o speculae why ha was allowed o happen. 30 The curren-value Hamilonian possesses an ineresing welfare propery. To find i, I follow Weizman (1976) and exend his analysis o imperfec resource allocaion mechanisms. Inegraing Eq. 19 over ime and using Eqs. 9 and 14 yields, H(τ)e δ(τ )] dτ = = V () + = V () + (U(C(τ)) + I (τ))e δ(τ )] dτ I (τ)e δ(τ )] dτ dv (τ)/dτ)e δ(τ )] dτ. (21) Now inegrae he second erm on he righ hand side of Eq. 21 by pars. Tha yields H(τ)e δ(τ )] dτ = δ V (τ)e δ(τ )] dτ. (22) Because Eq. 22 holds for all, We have herefore proved. H() = δv (). (23) Proposiion 5 The curren-value Hamilonian is he reurn on inergeneraional well-being. 30 The lieraure following Weizman (1976) ishuge.hulen (1992), Luz (1993), Asheim (1994), Asheim (2007), Brekke (1994), Harwick (1994), and Heal and Krisrom (2005) conain exposiions of he Weizman argumen and derive some exensions and noe a few of is limiaions. Early criicisms of he pracice of inerpreing he Hamilonian as NNP are in Dasgupa and Mäler (1991), Dasgupa and Mäler (2000). Weizman (2001)noes hahe Hamilonian is NNP plushe sumofconsumers surpluses and hen observes ha he surplus has o be measured by inegraing under he demand funcions. Li and Löfgren (2006)havealsonoedhaheHamilonianisNNPplushesumofconsumers surpluses;bu hen have re-named i uiliy NNP. Harwick (1994, p.254)calledhehamilonian NNPinuils,having assumed ha U (C) <0. Asheim (1994, p. 260) suggesed ha... a naural candidae for a concep of NNP in uiliy erms is (he Hamilonian). And Asheim and Weizman (2001)sayhahe...curren-value Hamilonian is essenially comprehensive NNP expressed in uiliy unis. See also Aronsson and Löfgren (1998)forrecommendingheuseofheHamilonianashebasisforgreenaccouninginimperfececonomies. Those re-namings, however, don make he Hamilonian any easier o esimae in pracical applicaions. In any even, I hazard he guess ha, if asked, naional income saisicians would inerpre NNP in uils o be Expression 20 in he ex, no Expression 19.

19 The Welfare Economic Theory of Green Naional Accouns Now, δ{ e δ(τ ) ] dτ} =1. So Eq. 23 can be wrien as H() = δ H()e δ(τ )] dτ = δv (), from which, H() e δ(τ )] dτ = Equaion 24 can be summarized as = H()e δ(τ )] dτ = V () U(C(τ))e δ(τ )] dτ. (24) Proposiion 6 The curren-value Hamilonian a of an economic programme {E(τ)} equals he consan-equivalen feliciy associaed wih {E(τ)}. Weizman (1976) proved Proposiions 5 and 6 for opimum economies, while assuming ha U is linear (i.e., U (C) = 0) in Expression 7.NowEqs.19 and 20 say ha if U is linear, he Hamilonian H() equals NNP, NNP(). So i has become a commonplace o say ha NNP() is he consan-equivalen feliciy a. Agains all evidence, boh from observed human behaviour wih regard o consumpion smoohing and from ehical concerns over inequaliy, why did Weizman (1976) assume U(C) o be a linear funcion? Weizman (1998, pp. 1,583) has offered he following accoun:...i is assumed ha, in effec, here is jus one composie consumpion good. I migh be calculaed as an index number wih given price weighs, or as a muliple of some fixed baske of goods, or, more generally, as a cardinal uiliy-like aggregaor funcion. The imporan hing is ha he consumpion level in period can always be regisered unambiguously by he single number C(). (Emphasis added). 31 Dasgupa and Mäler (1991, 2000) noed a problem wih Weizman s reasoning. Measuring non-linear feliciy funcions for an enire economy would involve esimaing economy-wide consumer surpluses. The pracical appeal of such indices as NNP and wealh is ha hey are linear funcions of quaniies. We are being asked, however, o abandon pracical advanages in order o accommodae a paricular inerpreaion of he Hamilonian. And we are asked o do i by simply renaming he feliciy of consumpion as consumpion. I would be ineresing o know how naional income saisicians would reac o a proposal ha henceforh hey should esimae heir economy s curren-value Hamilonian Earlier, in a very clear discussion of Weizman (1976), Brekke (1994, p. 242) assumed ha...(shadow) prices are... normalized so ha an exra dollar of consumpion a any poin in ime adds he same amoun o uiliy. Harwick (1994, p. 254) inerpreed Proposiion 5 o be saying,... curren NNP(), in uils, is ineres on pas accumulaions of invesmen, valued a curren prices. By curren NNP() Harwick mean he curren-value Hamilonian a. 32 If U is homogeneous of degree h(0 < h < 1), onecanconsrucameasurehalookslikennpandis proporional o he Hamilonian. However, i involves using prices ha do no reflec social scarciy values. To see how his can be done, noice ha for he case in hand, Eq. 19 can be wrien as H() = hdu(c())/dc() + I ().

20 P. Dasgupa In response, Weizman (2000), following a suggesion in Sefon and Weale (1996), has argued ha a simple recalibraion of U enables one o inerpre NNP as he consan-equivalen feliciy rae. His argumen is as follows: Recall ha he ehical ordering of consumpion pahs is invarian under posiive affine ransformaions of U.So,ifU is a feliciy funcion, one could as well use (au + b),where a and b are consans, and a > 0. This means here are wo degrees of freedom when U is calibraed. Le us assume ha U (C) >0andU (C) <0, and le C(0) be consumpion a = 0. Choose a and b so ha au (C(0)) = 1and(aU(C(0)) + b) = C(0). Theidea herefore is o so calibrae U ha iniial feliciy equals iniial consumpion (expressed in feliciy numeraire) and iniial marginal feliciy equals one. This makes he Hamilonian a = 0 equal o NNP a = 0. I follows from Eq.24 ha a = 0, NNP can be inerpreed as he consan-equivalen feliciy associaed wih α. There is a problem hough. A high or low value of U in iself carries no significance (a and b are freely chooseable, remember). So, o be old ha oday s NNP, expressed in feliciy numeraire, is high (or low) because he consan-equivalen U is high (or low), in iself has no meaning. Wha would have meaning are comparisons of U (equivalenly, V ); across ime, or space, or groups of people. I would cerainly be informaive if we could be old, say, ha because NNP is expeced o be greaer omorrow han i is oday, omorrow s consan-equivalen U can be expeced o be greaer han wha i is oday. If we were o be old ha, we would deduce ha V omorrow should be expeced o be higher han V oday. Unforunaely, we canno in general be old ha. The reason is ha once U has been calibraed a = 0, i mus no be recalibraed, ever again. To do so would be o aler he underlying ehical ordering of economic programmes, which would make ineremporal comparisons of V meaningless. Bu unless U is consan over ime (i.e., unless C is consan), i would have o be recalibraed coninuously if Weizman s inerpreaion of NNP were o be preserved a each dae. We should conclude ha Proposiions 5 and 6 do no offer a normaive inerpreaion of NNP. There is anoher, seemingly plausible, way o jusify he use of a linear feliciy funcion in discussions of susainable developmen. Assume ha he commodiy ransformaion possibiliy se is convex. Assume oo ha he value funcion is Expression 7,whereU (C) <0, and ha α is he full opimum. Consider an arbirary dae 0. For τ, lec (τ) maximize V () in Expression 7. By he separaing hyperplane heorem, among all feasible consumpion pahs, C (τ) also maximizes V () = In Eq. 25, V () is linear in C(τ). The curren-value Hamilonian corresponding o V *() is U (C (τ))c(τ)e δ(τ )] dτ. (25) H () = U (C ())C() + I (), (26) where I () is (comprehensive) invesmen in he linearized maximizaion problem. So H () can be inerpreed as NNP() in feliciy unis. Foonoe 32 coninued Then NNP() = H()/h = du(c())/dc()] C() + I ()/h. Noice hough ha in his expression he prices of invesmen goods relaive o hose of consumpion goods do no reflec social scarciy values. This is why he resul should be of lile ineres.