1997 faucheux natural capital theory

8/9/2019 1997 Faucheux Natural Capital Theory

1/26

Neoclassical Natural Capital Theory and "Weak" Indicators for SustainabilityAuthor(s): Sylvie Faucheux, Eliot Muir, Martin O'ConnorSource: Land Economics, Vol. 73, No. 4, Defining Sustainability (Nov., 1997), pp. 528-552Published by: University of Wisconsin PressStable URL: http://www.jstor.org/stable/3147244Accessed: 03/07/2010 06:09

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at

http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you

may use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at

http://www.jstor.org/action/showPublisher?publisherCode=uwisc.

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed

page of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

University of Wisconsin Press is collaborating with JSTOR to digitize, preserve and extend access toLand

Economics.

http://www.jstor.org
http://www.jstor.org/stable/3147244?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/action/showPublisher?publisherCode=uwischttp://www.jstor.org/action/showPublisher?publisherCode=uwischttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/3147244?origin=JSTOR-pdf


2/26

Neoclassical Natural Capital Theory and "Weak"Indicators for SustainabilitySylvieFaucheux,EliotMuir,and MartinO'ConnorABSTRACT.Weappraiseneoclassical heoryofgrowthwith naturalcapital or the estimationofindicatorsor sustainability. elationshipsetweenfour theoretically istinct measuresare clarified:Hicksian "changein capital stock value";theHartwick"net savings"(whichexcludescapitalgains);"sustainable ational ncome"(SNI);and"environmentally-adjustedet nationalproduct"(gNNP).An overlappingenerationsOLG)generalequilibriummodel withdepletablenaturalcapitaldemonstrateshe significance f modelparametersdeterminingechnicaleasibilityand intertemporaldistribution f consumption. rremediable ncer-taintiesn modelspecificationnd empiricalmea-surementmeanthat the neoclassical heory s notrobustor defining r estimatingndicatorsor sus-tainability.JEL011)

I. INTRODUCTIONThe classicaleconomists, n the 18thand19thcenturies, endedto regard he primaryenvironmental upportsfor economic pro-duction activityas either non-scarce(suchas air) or nondepletable (such as arableland).From this point of view, a growth nthe volume of economic output from oneyear to the next was not only a gain fromthe pointof viewof immediateconsumptionprospects, t was also a net improvementothe resourcebase upon which future eco-nomicoutputcould be achieved.Successinthe short term was thus synonymouswithaugmentation f potentialsfor consumptionand capitalaccumulationn the long term.Sustainable rowthwas simplythe continua-tion of short-termgrowth.But, if natural resourcesare depletable,and essentialenvironmental ervicescan beirreversibly mpairedthrough pollution orecosystem change, then present-dayeco-nomic activitycan have very high intertem-poral opportunitycosts. The existence of

such irreversibilitiesruptures the conso-nance between short-run performance(GNP-growth)and long-run prospects for(a) economic output and hence consump-

tion levels; and (b) the sustainingof thecyclesof resource renewal and the environ-mental life-support unctionsthat underpineconomicactivity. t is, thus,no longerpos-sible to regard GNP-growthas a signpostpointing in the direction of long-runeco-nomicprogress.The shortrunand the longrun maybe in conflict;the pursuitof rapidgrowthas a short-termobjectivemayimpairdurablythe economicwelfare prospectsoffuturegenerations.A wide rangeof proposalsand practiceshave emergedover recentyears, seekingtodefine and estimatean "environmentallyd-justed" national product,national savings,or national ncomefigure.Measuresof "netsavings" akingnaturalcapital depreciationinto account, and of an "environmentallycorrectednet nationalproduct" or "greenNNP",henceforthgNNP)havewidelybeenproposed as sustainability ndicators.Theusual recipes involve making subtractionsfromtheconventionalGNP.(We do not dis-cuss alternativemodelingapproachesn thispaper;but see de Boer,de Haan,andVoogt1994; Brouwer,O'Connor,and Raderma-cher 1996.)The key issue is how, in theoryandin measurementpractice,one can makethe jump from GNP as a measure of thisperiod's output level to "net savings"or

Faucheux s professorof economicsciences at theUniversitede Versailles and directorof the Centred'Economieet d'Ethiquepour l'Environnementt leD6veloppementC3ED) n France;Muir s a freelanceanalystand consultantandformerly esearchofficeratthe University f Aucklandn NewZealand;O'Connoris professor-associ6f economic ciencesat the Univer-sitede Versaillesandformerlyecturer n economicsatthe Universityof Auckland.The preparationof thispaperwas in partsupportedby contractEV5V-CT94-0363 on "Methodological roblemsn the Calculationof EnvironmentallydjustedNational ncomeFigures"financedbythe DG-XIIof the EuropeanCommission.Thanks o AndreaBaranzini nd RichardHowarth orhelpandadvice; esponsibilityoranyremaining rrorsis with the authors.LandEconomics * November1997 * 73(4):528-552


3/26

73(4) Faucheuxt al.: NaturalCapitalTheory 529

gNNP as an indicatorof prospectsfor sus-tainable future welfare levels relative to thecurrent level of consumption.1The usualresponse in the economics literature relieson theoretical results from neoclassicalgrowth-with-natural-capitalheory.PartII of the paperreviewskeyelementsof the neoclassical theory of economicgrowthwith natural capital. Part III thenpresents a simple overlappinggenerationsgeneralequilibriummodelwitha depletablenaturalresource,which is used to highlightthe significance or "sociallyoptimum" on-sumption timepaths of axiomatic assump-tions relatingto model structureand para-metrization, in particular presumptionsaboutsubstitutability,ime-discounting, ndrelative prices as measures of opportunitycosts. On this foundationwe assess the am-bition and limitationsof recent work,boththeoretical and applied,that has sought toassess by the "weak"criteria the "sustaina-bility" or nonsustainability of nationaleconomies. Part IV gives a syntheticoverview of the search for macroeconomicindicatorsof sustainabledevelopmentbasedon the neoclassicalnaturalcapitaltheoreti-cal approaches.Part V assesses the com-bined impactof the theoreticaland empiri-cal limits to validityof the "weak"sustain-abilityindicators.We will conclude,in PartVI, with the assessment that insurmount-able problemsof aggregationand measure-ment at both theoretical and empirical ev-els mean that the neoclassicaltheoryis notrobust-and cannot ever be maderobust--as abasis for derivingreliableindicators orsustainability.

II. NEOCLASSICAL NATURALCAPITAL THEORY ANDSUSTAINABILITYGrowthwithNaturalCapital:TheNeoclassicalConventions

It has, by now, become commonplace orefer to ecological goods and services asderiving from existing stocks of "naturalcapital" (cf. Daly 1994). The biosphere as ahabitat and life support system is a finite,and in many respects destructible, reservoir

of naturalcapital.Estimating he severityoftrade-offs, and the redistributionsof eco-nomic opportunities,access to environmen-tal benefits, financialand ecological costs,and burdensof risks,becomes a majortaskof economicsas a policyscience.Our concern in this paper is with oneclass of theoreticaland empiricalproblemsin the estimation of such trade-offs. Wefocus on the definition,estimation,and in-terpretation f "indicatorsorsustainability"pertainingto neoclassical models that as-sume substitutabilitybetween natural andproducedcapitalsas (i) inputsfor economiccapital accumulationand/or (ii) elementsof consumption.These models characterizesustainabilityas nondecreasingsocial wel-fare over time, the socialwelfarebeing de-fined by an aggregate utility function orconsumption evel. The mathematicalmod-els are of two mainforms. On the one handare those in the lineage of growththeory,with an aggregateoutput that can be usedin consumption or invested in economiccapitalaccumulationsee Pezzey1989,1992,1996; Toman, Pezzey, and Krautkraemer1995; and papers in this volume). On theother hand are intertemporalequilibriummodelsthat considerutilityas a functionofconsumption evels and agents'preferences(as pioneered by Howarth and Norgaard1990, 1992, 1993; also Muir 1995 gives agood overview).We can think of these models as express-ing "socialchoices,"as signifiedby popula-tion growth, ndividuals' referencesandin-stitutionalarrangementsgoverningendow-ment or income distribution, ubjectto thedefined technical and resourceconstraints.In modeling,populationchange is usuallytreated as exogenous, so the emphasis isplaced on production feasibility (the in-tertemporalproductionpossibilityfrontier)and on the social determinantsof invest-ment and consumptionover time.

1Thedistinctionsbetween GDP and GNP,and be-tween NDP and NNP, do not matterfor this paper.Most(thoughnot all)of the models n thisdomainare"closed"economies,so it is most convenient o writeGNP andgNNP.


4/26

530 LandEconomics November997

On the feasibility ide,the growthand/orsustainabilitypotentials for a model econ-omy depend on the specific assumptionsmade about natural capital renewal rates,about elasticities of substitution betweennatural and produced capitals, and abouttechnical progress augmentingproductivityof capitals. Where "technical progress"and/or elasticities of substitutionbetweennaturalandproducedcapitalsaremadehighenough,the value of the economy'scapitalstock maygrowwithoutlimit, and thus the"sustainable ational ncome" hat is attain-able "in the long run" is correspondinglyunbounded. In such instances, achievingsustainability ppearsas a problemof sav-ings. In any particular period there is atrade-off between consumptionand capitalaccumulation.High consumption n a givenperiodmeans"livingoff capital"duringtheperiodin question,but no permanentdam-age to "sustainable rowth"prospects f thisis just a transitoryphenomenon.The feature of the modelingworkin the1970s was the introductionof depletable"naturalcapital."Analyses focused on theimportanceof substitutability nd technicalprogress orrelievinggrowthconstraintsdueto the depletabilityof the natural capital.Three articles appearing just after the1973/ 74 OPEC oil crisis,by DasguptaandHeal (1974), Solow (1974), and Stiglitz(1974), are among the seminal contribu-tions;muchof the morerecent work followsdirectly n their line. As an illustration,weoutline featuresof the model developedbyStiglitz 1974),some of whichare preservedin our own model to be presentedin PartIII.

Suppose a productionfunction with la-bor,economiccapital,and naturalcapital(adepletableresource)as inputs,and a singlehomogenousoutput:Q = f(M, L, R, t) = MclLa2Ra3ext,where Q is the output;M is manufacturedcapital,L is labor,R is naturalcapitalusedin production; nd h is the rate of technicalprogress assumed o be time-invariant). heoutputcan be used either for consumption

(C) or for investment o augmentthe stockof manufactured apital (dM/dt), so: Q =C + dM/dt. Dividingby Q, andwritingx =C/Q for the fractionpf output consumed,and a = (dM/dt)/Q for the fractionsaved,we obtain:1 = C/Q + (dM/dt)/Q =: x = 1 - a.Assume that labor supplygrows at a con-stant rate, n = (dL/dt)/L, and that thereare constantreturnsto scale, so ao + a 2+a3 = 1. The parameters ao, 2,3 thendesignate the respective output elasticitiesof manufactured apital,labor,and naturalcapital. With all these assumptions,it isshownby Stiglitz 1974)that a timepathwitha positiverate of growth n per capitacon-sumption, that is, gc = (L/C)d/dt(C/L)= (dC/dt)/C - n > 0, requires that X >a 3n. The rate of technicalprogressmust berelatively high comparedwith the popula-tion growth rate and the factor share ofnaturalcapital.For the Cobb-Douglas orm of produc-tion function, the elasticityof substitutionfor naturalcapitalby other inputsis alwaysequal to unity.While some inputof naturalcapitalis necessary or nonzeroproduction,both the marginaland the average produc-tivityof naturalcapitalare unbounded,andindeedwill rise withoutlimitas the ratio ofnaturalto economiccapital input tends to-wardszero. This substitutionropertys thusa key underlyingcondition-also identifiedby Solow(1974)-under whicha nondeclin-ingpositive evel of output/consumption anbe sustained ndefinitelydespitedependencyof productionon the nonrenewablenaturalcapital.Considernow the case where populationgrowthandtechnicalprogressarezero(X =n = 0), so that the significanceof substi-tutability s isolated. Stiglitzshowed that atimepathwith constantconsumption s ob-tained by setting c = a3. We recall thatwith Cobb-Douglas production functions,the output elasticities a, a 2, a3 indicate,respectively,he relative mportanceof eco-nomic capital,labor,and naturalcapital inproduction, s measuredbyfactor share.So,this condition or nonnegativechangein per


5/26

73(4) Faucheux t al.:NaturalCapitalTheory 531

capitaconsumptionwhentechnicalprogressand populationgrowthare zero, is that theshare of economicproduct hat is saved(a)is at least as large as the natural capitalfactor share (a,). This illustrates he resultnow knownas "Hartwick'sRule"(Hartwick1977,1978).Necessaryconditions or a non-negative per capita consumption n a Cobb-Douglas (unit elasticity of substitution)economywith a constantpopulationare:

* that manufacturedcapital is relativelymore important han naturalcapitalinproduction a1 > a 3),meaning hatthefactor share receivedby economiccapi-tal (share to profits,al ) is largerthanthat going to naturalcapital (share torents,a 3);and* thatsavingsaresufficientlyhigh-moreparticularly, hat for each moment intime there is investment in manufac-tured capital stock formation(savings)of at least the equivalentof the valueof the resourcerents.

SustainabilityndIntertemporalistribution ulesBy now a variety of models have beenconstructed n which there exists the tech-

nological capability or unlimitedgrowthinthe value of economic capital over timeby substitutingaway from a renewable ornonrenewable natural capital, but whereachievementor not of consumption ustain-ability s a social choice.Typically, olutionsare obtainedin these models using the cri-terion of maximizing he present value of"society's utility" as defined by some in-tertemporal"social welfare function." Thegeneric result is now well known: wherethere is a sufficientlyhigh time-preferencefor present consumptionover future con-sumption, the intertemporal equilibriumpath will be characterized,rom the outsetor after a peak is obtained,by monotoni-cally decliningvalues for total capitalstockand, correspondingly, er capital utility orconsumption levels (see notably Howarthand Norgaard1990, 1992, 1993; Norgaard

and Howarth1991;Mourmouras 993;Ash-eim 1994;Toman,Pezzey,and Krautkraem-er 1995;Pezzey1994,1997).The determinants f the distribution vertime of consumption include consumers'preferencesin two respects,alongwith the"social distributionrule" that is applied.First,wheremorethan one good enters intoindividuals'utilityfunctions at a given mo-ment andthese goodshavedifferingnaturalcapitalrequirementsor theirproductionorsupply,the relativeintensityof preferencesfor one good over another influences thepressure on natural capital. We will notfurther consider this feature here. Second,individuals'and society's consumptionaredistributedover time, and this is partly atime-preferencephenomenon.We use theterm "subjective ime preference"o meanthe waythat a consumercompares he value(in welfare terms to her or himself)of con-sumptionat one moment(or period) n timecomparedwith other moments(or periods).In an overlapping generations model,each class andgenerationof consumerswillhave a distinctive"preferenceunction,"andeach consumer'srate of time discounting sdetermined by their particular preferencefunction in conjunctionwith the consump-tion opportunityset. In an intertemporalgeneral equilibrium,each individual's ub-jective rate of time discountingwill, at agiven momentin time or period,be equal-ized to the interest rate (whichmayitself bea function of time) characteristic of themodel solutiontimepath.2Consumers'pref-erences may be taken as a "datum"(or,alternatively,pecifiedas a sociologicalvari-able) while the interest rate measuringop-portunity ost of capital s influencedby the"social distribution rule" that determines(in conjunctionwith technologicalparame-ters, initial stock levels, and preferences)the particularmodelequilibriumattained.The role of savings s nowseen to be oneof influencingthe distributionacross con-

2The consumer'smarginalrate of intertemporalsubstitution s madeequalto the marginalproductofcapital.


6/26

532 LandEconomics November 997

sumers (successive generations, for exam-ple) of endowmentsandof consumptionop-portunities.Thus, as Dixit, Hammond,andHoel (1980) observed,followinga programof investmentrespecting he HartwickRuleamounts to a policy choice in favor of in-tertemporalequity.The problemof recon-ciling criteria of economic efficiencywithintertemporalequity concerns had alreadybeen identifiedbySolow(1974),whoconsid-ered the timepathof naturalresource de-pletionunder the assumptionof a maximinsocial choice function. Dasguptaand Heal(1979) noted that a timepath for present-value-of-utility maximization with eithernonrenewable or renewable natural re-sources (for example, coal or fish, respec-tively)couldbe strongly nequitable owardsfuture generations.3 The issues involvedhere, discussedearly by Page (1977), havebeen most clearly brought out by modelsreframinghe optimalresourceuse problemas one of intertemporal eneral equilibriumwith utility maximizingconsumers,notablybyHowarth 1991,1992,1996),andHowarthand Norgaard 1990, 1992,1993).These au-thors' usual model form is a closed econ-omy,and the questionof time preference sstructuredby assumingoverlapping enera-tions. Our model in Part III is adapteddirectly romHowarth 1991),so we give theformulation n detail. Each generation ivesfor two time periods(say n and n + 1), andthe nth generationmaximizesutility Un=Un(Cn,y, Cn + 1,o), whereCn,y isconsumptionduringperiod n when the nth generation syoung, and C, 1,o is consumption duringperiod n + 1 when the generation is old.Within each generation,all individualsareidenticalso we can treat them as one, andthe emphasisis on aggregate consumptioneach period; no questions of intragenera-tional equity are addressed.4Markets fornaturalcapital(resourcesor environmentalamenity), consumer goods, and labor areassumed o be "competitive"n the sense ofequalizationof opportunity osts on all mar-gins. Labor is an initial endowment dis-tributedequallyacrossall generations; ach

generation"owns" andthussupplies) aboronly while young. Intergenerational rans-fers are possible through exchange of in-come for naturalcapital held as initial en-dowments.Technicalparametersand initialstock levels determine the intertemporalproductionpossibilitiesfrontier (IPPF) forthe economy, and the "optimal"point onthis frontier s then selected as either:

(i) the equilibriumoutcome of utility-maximizingconsumers' choices sub-ject to a specifiedendowmentdistri-bution,or(ii) the optimumof a social welfare func-tion, the latter being formulatedinterms of consumptionor utility evelsthrough ime.

A number of importantresults emerge.First, sustainability n the sense of indefi-nitely nondecliningconsumptionfrom onegenerationto the next, is not guaranteedbythe "competitive"rule of maximizingpre-sent-valueof total consumptionover time.On the contrary,when the propertyrightsover naturalcapital are tipped in favor ofthe "present" generation (still able to beexchangedbetween generations to enable

3The converse is also true. Dasgupta and Heal(1979), for example,showed that under some condi-tionsan investmentprogram ssuringnondeclining ercapita consumptionwhilenaturalcapitalwas depletedcould be achievedthroughan income tax combinedwithgovernmentnvestment-a policyregime nvolvinga "trade-off' betweenefficiencyand intergenerationalequity.4Workby Muir 1996)drawsattention o the signif-icance of groupshavingdivergentpreferenceswithinagiven generation.If income distributions shiftedto-wardsgroupswhosepreferencesare forgoodsthat areless demandingof naturalcapital exploitationor who"caremore about the future," his will tend to favorsustainabilityf the model equilibrium.This result isimplicit n HowarthandNorgaard'swork,and can beinferredfrom Pezzey'sresults,but was not systemati-callybroughtout.


7/26


the old of each period to consume opti-mally), the typical result is monotonicallydecliningutility levels beyond some periodinto the future.5Second and conversely, achieving anequilibriumwith nondecreasing consump-tion levels requires that, one way or an-other, present generations "care enough"about future generations.This "caringforthe future"can be expressed hrougha vari-ety of mechanisms,notably:

* the impositionof a maximin ocialwel-fare function;or impositionof a crite-rion of intertemporal social-welfaremaximizationsubject to nonnegativechange in representative individuals'welfarefrom one periodto next;* the assumptionof a sufficientlyhighlevel of individualaltruismof eachgen-erationtowards he generation mmedi-ately following;* the assumptionof an "obligation"onthe part of each generationto providefor a utilitylevel of the generation m-mediatelyfollowingat least as high asits own,resulting n a "chainof obliga-tion"indefinitely nto the future;* the explicit award of propertyrightsover naturalcapitalor the benefits ob-tainable from it as initial endowmentsdistributed"equitably" o all genera-tions.

Third,the possiblemodel equilibria or agiven model are each characterizedby dis-tinctive trajectories, not just for capitalstocks and consumption,but also for rela-tive pricesincludingthe time discount rate.It is often said that, for intertemporal ffi-ciency, the price of naturalcapital such asminerals or energyresources or fish or for-est products,should "correctly" eflect theintertemporal opportunity cost (viz., the"usercost").If sustainabilitys an objective,we must add the conditionthat this has tobe the opportunity osts as evaluatedalongan intertemporal fficientpaththat also sat-isfies the sustainability riterion.6

III. A SIMPLEOLG MODELWITHNATURALCAPITALPresentationf theModel

We now specify a multi-periodoverlap-ping generations(OLG) model which hasthe same production unctionas in Stiglitz's(1974)originalproblem:hreeinputs-man-ufacturedcapital M, humancapital L, andnonrenewable natural capital R-to aCobb-Douglas production function whichproduces manufacturedcapital as its soleoutput. The manufacturedcapital can beused in consumptionC or savedfor invest-ment S.The model problem is to maximizeanintertemporal ocial welfarefunction,or inother words an intertemporaldistributionrule, subjectto a numberof constraints.Asin the earlier Howarth-Norgaardmodels,each generationlives two periods.The nthgeneration s youngin period n, and old inperiod n + 1, and obtainsutilityfrom con-sumption specified by the Cobb-Douglasfunction of the form Un= ln(Cn,) +ln(Cn+ ,o).We have set N = 20 periods, which issufficiently"long"to showthe rangeof so-lution properties in question.' There are

5Thus, Pareto-efficiencyndsustainabilityandeq-uityconsiderationsmoregenerally)mustbe consideredas distinct,andcomplementary,riteria orcharacteriz-ing model solutionsand policy possibilities see alsoDasguptaand Mitra1983;Dubourgand Pearce1996;Toman,Pezzey,and Krautkraemer995;Baranzini ndBourguignon 995).6Thisresult also appliesto the "correct" aluationof environmentalmenityandto the size of a "correc-tive tax"for internalizing n externaleffect relatedtoeconomic productionor naturalcapital exploitation.HowarthandNorgaard1992)showthat,for a situationof cumulativepollution,both the "efficient"ax leveland the interestrate arefunctionsof the incomedistri-bution between generations(as determined n theirmodel by the choice of social welfarefunction).Forfurthertheoreticaldiscussionof "endowment ffects"on valuation, ee Martinez-Alier ndO'Connor1996),O'Connorand Muir(1995),and Muir 1996).The number of periods can be varied betweenN = 3 and N = any large (finite) number, limited onlyby computational apacityof the software and hard-ware.


8/26


N - 1 = 19 generations who each live twoperiods.Also we add an "old"generationwho consumesin the firstperiod only;butno new "young"generationis born in thefinal Nth period. For our exposition,twosocial welfare distributionrules will be ap-plied.The first rule is to maximize he presentvalue of utility(henceforthPVU-max),dis-countingeach generation'sutilityby a con-stant factor 8, where 0 < 8 < 1, relative tothe previousgeneration.The problem o besolved is:Maximize:Y61U,

where the sum is over n = 1to n = N, [1]subjectto:M LMLa2Rn--l-a2=S2 + Cn,y Cn,o

Vn= 1... (N- 1) [2]Mn+, = Sn Vn= 1... (N - 1) [31M1= Mini, [4]L, = 1 Vn = 1... N [5]SN =0 [6]CN,y= 0 [7]IR, = RTOT

where the sum is overn = 1to n = N. [8]Un= ln(Cn,) + ln(Cn+1,o). [9]The constraints have the following mean-ings:[2]represents he marketclearingcon-dition combined with the production unc-tion; [3] is a device to propagatesavings,analytically onvenientbut not strictlynec-essary;[4] sets the initial level of manufac-tured capital in the first period, owned bythe firstgeneration; 5] specifiesa constantendowmentof labor for each generation ntheir "young"period;[6] specifiesthat theNth generation young do not save anythingbecause they are not born; [7] specifies thatthe Nth generation young do not consumeanything because they are not born; [8] is

the natural resource constraint conditionstating that the entire stock of nonrenew-able naturalcapital is used up by the Nthperiod; [9] is the nth generation's utility.The symbolsare as follows:Rn is the amount of natural resourcesused in periodn,RToris the total amount of natural re-sources,Cn, yis the amountconsumedby the younggeneration n periodn,C, o is the amount consumed by theold-the (n - 1)th generation-in

periodn,U = ln(C y) + ln(C +1,o) is the Cobb-Douglas utility function of the nthgeneration,8 is the utilitydiscountfactor,Mn is the economic capital of the nthgeneration,Ln is the labor endowment of the nthgenerationof young,S, is the savingsof the nth generationof young,Minit is the initial level of economiccapitalin the firstperiod.

From [9], each generation gives equalweight to its own consumptionas "young"as it does to its own consumptionas "old."There is thus no "subjective"discountingwithin a generation'slife. The social dis-count parameter8 dictatesthe strengthoftime-preference impatience)for the econ-omy overall. If 8 = 1 all generationscountequally; f 8 < 1 the successivegenerationscountprogressivelyess. Conventionally,hesocial discountrate between generationsisgivenby p definedby 1/(1 + p) - * p -(1 - 8)/B; note that this is not the interestrate.The second social distributionrule con-sists of a "sustainability"equirementover-laid on the PVU-maximizationobjective,representing he intergenerationalquityre-quirement hat each generationbe at leastas well off as the immediately precedingone:Un+1 > U,, for n = 1to n = N- 1. [10]


9/26


Further, and more complicated specifica-tions would be possible, but would notchange the essential demonstration harac-ter of our results. The optimization prob-lems have been solved numericallywith astandard olver underEXCEL 5.0. It is nec-essary to choose with some care the initial"guess" o avoidnon-convergence.Once anequilibriumhas been obtained it is possibleto vary all parametersgraduallyto obtaincomparative quilibria.The ratherprimitivespecification of the boundary conditions,with abruptcutoff at the N = 20th periodwith the death of the (N - 1)thgeneration,is obviouslyan artifice;what matters is thequalitative behavior of solutions up toaroundthe 18thperiod.QualitativeTypology f PVU-maximizingolutions

The nowlarge bodyof work on models ofgrowth-with-natural-capitalas shown thatat least four qualitativelydifferent sorts ofPVU-maximizing timepaths may be ob-tained, depending on initial capital stocklevels and renewal properties,the techno-logical determinantsof production easibil-ity,andthe socialdeterminants f the distri-butionthroughtime of consumption.Theseare:

(a) monotonic decrease in utility overtime: path of decline,clearlynonsus-tained;(b) increase of utilityfor a while, then aturningpointwith monotonic declineafter that: nonsustainable conomicgrowth;(c) exactlyconstantutilitythroughtime:sustainabilityas intertemporaleco-nomicequality;(d) monotonic increase in utilitythroughtime: sustainable conomicgrowth.

Our focus will be on category(b) solutionsas comparedwith categories(a) and (d). Abrief comment about category (c) is war-ranted.In continuous-time rowthmodels,aconstant-utility ath can be obtainedby ap-plyingHartwick'sRule;butasAsheim(1994)and others have discussed(see also Svens-son 1986;Pezzey1997), f this resultis to be

obtained as an otherwise unconstrainedPVU-maxsolution then the social discountrate p(t) must be positive but decreasingover time, dp/dt < 0 for t > 0. A similarresult might be expected to hold for anOLG model, but we have not investigatedthis mathematically.8 ur OLG modelsetupprovidesfor direct investigationof the sig-nificanceof varying hree parameters:

* the initialstock of naturalcapitalRTorin comparison with initial economicstock Mini,and labor endowmentL =1;* the constant ntergenerational iscountrate parameter8, where we can writep- (1- 8)/0;* the relative mportanceof naturalcapi-tal in productionas indicatedby theoutput elasticity coefficient (p-(1 -

a1 - a12).In the examplespresentedbelow,we haveselectedcapitalstock levelscompatiblewiththe possibilityof obtaining olutions n all ofcategories(a), (b), and (d). For demonstra-tion purposes:(a) Let RTor = 16; Einit= 0.3;Ln = 1. [11](b) To see the significanceof varying heimportanceof naturalcapitalrelativeto economiccapital n production,wefix a2 = 0.15 for labor,and considerthe two cases a, = 0.7 and ao = 0.3.(c) At the same time, we may vary thesocialdiscountrate:we takethe cases:8= .10 p - (1 - 8)/B = 1/9 and8 = .30 p - (1 - 0)/8 = 3/7.8An analogue to a "Hartwick path" having Un,? =U,, for n = 1... N - 1, couldpresumably e obtainedas a PVU-maxsolutionfor onlyoneparticular et ofintergenerationalime-discountparametersB, whichvaried from one generationto the next. It mightbethought hatthis set of parametershouldsatisfy81


10/26

536 LandEconomics November 997TABLE 1

PARAMETERS NDPROPERTIES OR MODELEQUILIBRIUM CENARIOS8 = .10 * p (1 - 8)/8 = 1/9 8 = .30 * p (1 - 8)/8 = 3/7

-(1-otz - o2) =0.15 (A) sustainedgrowth (B)single-peak rowthanddecline0.55 (C)single-peak rowthanddecline (D) monotonicdecline

ConsumptionLevels2,5

1.5YoungConsumpoonOld Consumption

05 -M-, ..'.......50 1 3 5 7 9 11 13 15 17 19

FIGURE 1(A)CONSUMPTIONEVELSOVERTIME:

PVU-MAX SCENARIO)(nat capital 0 = 0.15; econ capital al = 0.55; labor a2 =0.30; PVU-max with intergenerationalutilitydiscount fac-tor 8 = 0.90)

ConsumptionLevels0,7

06

K..,5- 0-iYoung Consumption...OlOdConsumption

0 2

oo r01 3 5 7 9 11 3 5 7 9FIGURE 1(B)

CONSUMPTION EVELSOVERTIME:PVU-MAX (SCENARIOB)(nat capital (p= 0.15; econ capital al = 0.55; labor a2 =0.30; PVU-maxwith intergenerationalutilitydiscount fac-tor 8 = 0.70)

ConsumptionLevels0,60,s03 --+Young Consumption-... OldConsumption

0,2

1 3 5 7 9 11 3 5 7 9FIGURE 1(C)

CONSUMPTIONEVELSOVERTIME:PVU-MAX SCENARIO)(nat capital p = 0.55; econ capitalal = 0.15; labor a2 =0.30; PVU-max with intergenerationalutilitydiscountfac-tor 8 = 0.90)

This givesus four"scenarios,"or whichwecompare he timepaths or consumption, eeTable 1 and Figure1. The graphsshow theconsumptionlevels of the "old" and the"young" n each period.The utilityof eachgeneration, Un -= ln(C, y) +C 1), fol-lows the same trend as the consumptioncurves.9Solution[11-A] s sustained rowth;the output elasticityof economiccapital ishighandthe societyis sufficientlypatienttoallowfuturegenerations o enjoya progres-sively greater utility level. Solutions [11-B]and [11-C] are nonsustainablegrowth pathswith a boom-and-declineorm. In case (B)the culpritis the high social discount rate

9Extension of the model to a larger number ofperiods (say N = 50) does not alter the qualitativefeatures of the four cases chosen. Note in particularthat cases (A) and (B) have the substitution elasticityand output elasticity properties identified by Stiglitz,Solow, Hartwick, and others as capable of supporting afinite nondecreasing consumption indefinitely.


11/26

73(4) Faucheux t al.: NaturalCapitalTheory 537

ConsumptionLevels1,20,8

-4-Young ConsumptonOld Conuumpdion

0,4

0.2

1 3 5 7 9 11 13 15 17 19

FIGURE 1(D)CONSUMPTION EVELSOVERTIME:PVU-MAX SCENARIO)(nat capital (p= 0.55; econ capital cal = 0.15; labor ca2=0.30; PVU-maxwith intergenerationalutilitydiscount fac-tor 8 = 0.70)

p = 43 percent per generation; n case (C)the mainculprit s the heavy dependenceofproductionon depletablenaturalcapital (p= 0.55, notwithstanding the lower p = 11percent. Solution [11-D] is monotoniceco-nomicdecline,due to heavy dependenceonthe depletablenaturalcapitaland highcon-sumption mpatience.PathswithNon-decreasing tilityacrossGenerations

Now look at the significanceof the inter-generational equity requirement[10] as asupplementaryconstraint.In this case weget the timepaths or consumption howninFigure2. The case (A/S) is unaltered,be-cause the growth s alreadysustainableoverthe 20-period horizon. At the other ex-treme, in case (D/S) the requirementtohold future generations'utility at "equita-ble" levels means that consumption s dra-matically reduced for early periods com-pared with the non-constrainedPVU-maxcase.10 In cases (B/S) and (C/S) there isslight reductionin early period'sconsump-tion levels,andinsteadof boom-and-declinethe consumptionrises more slowlythan forthe PVU-max path and then stays on aplateau until the end of the time horizon.

ConsumptionLeves2,51,50,5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

FIGURE 2(A/S)CONSUMPTIONEVELS:"OP-SUS"(PVU-MAX WITHSUSTAINABILITYULE)(SCENARIO / S)(nat cap (p = 0.15; econ cap al = 0.55; labor a2 = 0.30;"Op-Sus"with intergenerationaldiscount factor 8 = 0.90;PVU-max, ubject o (nonbinding)nondecreasing tilityrule)

ConsumptionLevels

o0,

--

Young

Conunpoon

o0.3Old Consumpio02

01 2 3 4 5 6 7 8 10 11 12 13 14 15 17 18 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1920

FIGURE 2(B/S)CONSUMPTION EVELS:"OP-Sus"(PVU-MAX WITHSUSTAINABILITYULE)

(SCENARIOB / S)(nat cap p = 0.15; econ cap al = 0.55; labor a2 = 0.30;"Op-Sus"with intergenerationaldiscount factor 8 = 0.70;PVU-max ubject o nondecreasing tility onstraint)

10For case (D/S), the "old" generation in period 1has a curiously high consumption. This seems to be anartifact of the way the solution conditions were speci-fied for this "old," in conjunction with the nondecliningutility condition. We have not smoothed the blip away;it is a reminder that inevitably there are some arbitraryelements in the way that initial and final periods aredealt with in an OLG model.


12/26


ConsumptionLevels

0.4!-4Young Consumption0,3 1*--Ol-Ol Consumpbon

02

0,1

123456789101234567890FIGURE2(C/S)CONSUMPTIONEVELS:OP-SUS"(PVU-MAXWITHUSTAINABILITYULE)(SCENARIO/ S)(nat cap 9p= 0.55; econ cap aol = 0.15; labor ao2 = 0.30;"Op-Sus"with intergenerationaldiscount factor 8 = 0.90;PVU-max subject to nondecreasing utility constraint)

ConsumptionLevels

1,2---Young Conswnpbon-*-8Old C1nsp2on

0.2

1 2 3 4 5 6 7 8 9 1011 12 131415 1617 18 1920

FIGURE2(D/S)CONSUMPTIONEVELS:"OP-Sus"(PVU-MAXWITH USTAINABILITYULE)(SCENARIO / S)(nat cap (? = 0.55; econ cap al = 0.15; labor a2 = 0.30;"Op-Sus"with intergenerationaldiscount factor 8 = 0.70;PVU-max subject to nondecreasing utility constraint)

Whilethe PVU-maxcriterion s still appliedfor solutionpurposes, he nondecreasingtil-ity constraint is dominant in determiningthe allocationthroughtime of naturalcapi-tal for productionand of economiccapitalsavings rom one periodto the next.

IV. INDICATORSFOR PROSPECTSOF "WEAK"SUSTAINABILITYSustainable ational ncomeand "Savings" ulesfor Sustainability

We now review he problemof measuringthe requirements or "savings" o providefor sustainability.Let us providesome defi-nitions that pertain, n the firstinstance,tomodelswith an infinitetime horizon.Sustainableationalncome.The sustainablenational income (henceforth SNI) for aneconomy may be defined,in theory,as thequantityof goods and services,say C*, thatmay be consumed ratherthan conserved/reinvested) n a given periodwhile the econ-omy-system till furnishes the capitalstockas the basis for providingat least)the samelevel of real consumptionC* in everype-riod throughthe future. At least two some-what differentdefinitionscan be offeredfora SNI:

(i) Immediatelyand thereafterperpetu-allyobtainable ncome:SNI(i).SNI(i),is the highest level of "income" hatcan be attained immediately, romsome givenvector of stocksV(t = 0),subjectto the constraint hat the in-come level during t > 0 is perma-nently nondecreasing.This is a maxi-minutility ath.(ii) Later but thereafterperpetuallyob-tainable ncome:SNI(ii).SNI(ii) s thehighest level of "income" that theeconomy can continuouslyattain atand aftera finite time, startingfromsome givenvector of stocksV(t = 0),subjectto the constraint hat the in-come level is permanentlynonde-creasing.

SNI(ii) is an importantreference pointfor anyreal or modeleconomythat permitsgrowth of the total capital stock throughtime, as it will be possible to increase the"sustainablenational income" for the fu-ture,by, provisionally, estraining onsump-tion below the currentsustainableincome


13/26

73(4) Faucheux tal.: NaturalCapitalTheory 539

-the SNI(i)-so that the manufacturedcapitalstockis built up. This is, indeed,thepresumptionbehind traditional macroeco-nomic modeling that discusses the "trade-off' between current consumption andgrowth rate-the so-called "golden-rule"literature;and as Pezzey (1994, 1997) dis-cusses, the concept of SNI(ii) seems verypertinentwhere naturalcapitalscarcitycon-strainslong-runmanufactured apitalaccu-mulation.11Hicksianncome.The Hicksiandefinition faperson's or nation's) ncome s the amounthe/she (or it) can consumeduringa speci-fied period, while ensuring that his/herwealth at the end of the period is no lessthan his/her wealth at the outset (Hicks1946).Assume that the valueof total capitalstocks is K, measured n moneyunits,so letus write:K - X,whereX = (M, L, R) is the vector of stocks inphysicalunits,and7r= (Pi, P2,P3) is the vector of relativeprices.Then the Hicksiannational ncome will beassociated with the rule: dK/dt = 0. Thechangein value of capitalstockmay, gener-ally, be written:dK/dt = d/dt(7r -X), andthis can be split into two parts:the currentvalue of savings: -rrdX/dtand the "capitalgains"term: X- drr/dt.

Hartwick'savingsrule.Using the above no-tation, Hartwick's ule is written:-7rdX/dt? 0. For a model with constantpopulationwe have dL/dt = 0, so this becomesp, dM/dt + P3 dR/dt ? 0. The first termrefers to the value, in currentprices,of thechange in manufacturedcapital stock; thesecond term refers to the value, in currentprices,of the changein naturalcapitalstock.Green net national product.Suppose theeconomy maximizespresent value of con-sumption. Then the net national product(henceforth NNP) is defined as value of

consumptionplusnet change n the value ofcapital stocks. If naturalcapital stocks areincluded,we call it a "greenNNP,"definedas: gNNP = p1C + (' -dX/dt) where, asbefore, C is the physicalquantityof con-sumption,p, is the currentprice of manu-facturedcapital(whichcan be savedor con-sumed)and 7r-dX/dt is the Hartwick"netsavings"measured n currentprices(Solow1986;Miiler1991).BecauseHartwick's ule does not includethe "capital gains" term, the respect ofHartwick's ule at anymomentin time doesnot necessarily mplynonnegativechangeinthe value of total capital stocks. So theHicksian national income and the net na-tional product (gNNP) are not the samething.12Furthermore,the gNNP and theSNI(i)are not the samething.As the recentworkbyAsheim(1994)andbyPezzey(1994,1997)has madeplain,the gNNP and SNI(i)will coincide only if highlyrestrictive heo-reticalconditionsare fulfilled.TheReasoningor the "Weak"ndicatorsforSustainability

The earlyworkby Solow, Hartwick,andothers showed that, for a closed economyobeyingthe PVU-maxcriterion,a propertyof the SNI(i) "maximin" onsumptionpathis that Hartwick's rule is satisfied at alltimes.However t was not initiallyremarkedthat respect of Hartwick's ule in this con-text was a necessary but not a sufficientcondition. In effect, the problems of (1)changesin relativepricesalonga PVU-maxpath through time-showing up in, amongother places,the "capitalgains"term-andof (2) different relative prices associatedwith each distinct PVU-maxsolution,were

"Apart from Pezzey'swork and our own resultsreportedhere, relativelylittle neoclassical modelingworkalongthese lines seems to havebeen done. Thisreflects past computationalobstacles(which are nolongeras severe),andperhapsalso modelers'addictionto PVU-maxcriteria?12See also JohanssonandL6fgren 1996),who lookat the way that price changesmake welfarecompar-isons for alternativeinvestment/consumptionime-pathsa hazardous usiness.


14/26


not fully appreciated.13 Consider,with thisin mind,the resultsthat we mayobtainif wesimplyneglectpricechanges.* As above, write gNNP = pC + ?r*dX/dt.* According to the Hartwick-Solow e-sults, along a path of constant con-

sumption dC/dt = 0, Hartwick's rule isnecessarilyrespectedin equalityform:,r- dX/dt = 0 for all t. Under theseconditions we obtain: gNNP = pC, andthis is the SNI(i).* Now, if it were that the prices do notchange,the capitalgainsterm would bezero and we could write: dK/dt=u.=dX/dt.* Thus along a PVU-max path whereHartwick's rule is respectedat all timesand also there are no capital gains (ifsuch a path can be found), the net na-tional productgNNP is a measure ofthe immediatelyand perpetuallysus-tainable welfare deliverypotential,theSNI(i),for the economyand its naturalcapitalstock,andthis would also be the"Hicksiannational ncome"at all times.

This is the reasoningthat has motivatedthe estimation of (r.- dX/dt) and gNNP assustainability ndicators.If the above rea-soningwere valid:* The gNNP = SNI(i) and so the gNNP

could be interpretedas an estimateforlevel of consumption in moneyterms)that may, in principle,be maintainedfrom the present onwards,on a long-term basis, while also maintaining n-tact the valueof the total stockof capi-tal.* A positivevalue of the Hartwick erm(,u dX/dt > 0) would signal that the"net savings"of economicplus naturalcapital, measured in money units, ispositive during the period. A negativevalue (r . dX/dt < 0) would signal thatthe "net savings"is negative, or there is

"net depreciation"during the period.This yields the Hartwick-Solow WeakSustainability Indicator" or "savingsrule" as proposed by Solow (1986),quickly followed by others such asMiiler(1991) and Pearce and Warford(1993).

There is, or wouldbe, one final step for"operationalizing"he procedures.Thisis toestimate the components of the formulagNNP = pC + T'- dX/dt on the basis ofcurrentperiod prices and quantities. The"sustainablenational ncome"SNI(i)is thusestimatedby makingdeductions n . dX/dt)from current GNP (pC) representing de-preciation of capital stocks, including manu-factured capital and naturalcapital.Theoretical reconditionsor WeakIndicatorValidity

The procedures described above havewidespread appeal, because they seem toresolve objectionsmade on environmentalgroundsto the use of GNP as an indicatorof macroeconomicperformance.But theserecipes are theoreticallyflawed as well asbeing difficult to implement in statisticalpractice.The Hicksian ncome. Consider the notionthat sustainabilitys achieved f the value ofthe nation'scapitalstockremains ntactfromone generationto the next,meaning dK/dt= 0, whileprovidinghe Hicksian ncome asthe consumptionat any given time. Thereare two inaccuracies here. First, as seenabove, dK/dt = 0 is not the condition for amaximinSNI(i) timepathin a closed econ-omy. Second, and more important,observ-ing dK/dt > 0 in a closed economy at agiven moment in time does not guarantee

13Thisstill seems to be the case with some recentliterature,for example,Hartwick 1991) and Pearce,Hamilton,and Atkinson(1996).On the other hand,several recent authorscorrectlyexpressedmisgivingsabout the correct nterpretationnd robustnessof thededuction-basedndicators,without dentifyinghe the-oretical "wrong prices" problems as such (e.g.,FaucheuxandFroger1994;AaheimandNyborg1995).


15/26

73(4) Faucheux t al.: NaturalCapitalTheory 541that the economyis capableof sustaininganondecreasingHicksian ncome.We do not provethis secondresultmath-ematically.The reason can be seen intu-itivelyfrom ourmodelresults as follows.Ona "single-peak"PVU-max timepath, thevalue of total capital stock rises initially.There is a portion of the timepathwhereconsumptionrises beyondthe long-runsus-tainable evel while dK/dt ? 0. Forour dis-crete-timemodelthe "Hicksianndicator" sthe change in the value of the total stockfrom the nth to the (n + 1)th period, sayAK,n.Figure3 shows,for our scenarios(B)and (C) of single-peakPVU-maxconsump-tion, the associatedtimepathsfor the valueof the stock of eachcapital,and the value oftotal capital stock, measuredusing the pricescurrent at each point along the PVU-maxtimepath.

Case (B) has high outputelasticitybuta boom-and-declinepath for PVU-maxconsumptions obtainedbecauseof im-patience.The comparisonwith the cor-respondinggraphs(B) in Figure 1 and(B/S) in Figure2 shows that from the4th to the 10th periodconsumptionbyyoungand old in each periodis signifi-cantlyhigherthan the plateaulevel at-tained in the case (B/S) where thesustained-utility onstraint is imposed.The rapid exploitation of the de-pletable naturalcapital combinedwithinadequate savings of manufacturedcapital compromises future genera-tions'economicchances.We observe ngraph(B) of Figure3 that the sign ofAKn is positiveuntil the end of the 5thperiod. Thus, by the time a negativeAKn is observed, he consumptionevelhas already, or two periods,trespassedbeyondthe sustainable evel.The Hick-sian indicator AK 2 0, signalling anonnegative change in value of totalcapital stocks from one period to thenext, provides a too-weak signal as towhether or not the consumption in theperiod is compatible or not with the

TotrlValueof Rource

P-TV rod Cap0 TV Nat Cap-ATV LabourX TV Resources

0,4

0,.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1819s 20

FIGURE3(B)VALUE FCAPITALTOCKS:VU-MAX"BOOMANDBUST"SCENARIO)(nat capital(p = 0.15; econ capitalt = 0.55; labor ar2=0.30; PVU-maxwith intergenerationalutilitydiscountfac-tor 8 = 0.70)

TotalValue f Resources

---TV ProdCapTV Not Cap

S-TV Labour-*-TV Resorces

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

FIGURE3(C)VALUE OFCAPITALSTOCKS:PVU-MAX

"BOOMAND BUST"(SCENARIOC)(nat capital cp= 0.55; econ capital al = 0.15; labor a2 =0.30; PVU-maxwith intergenerationalutilitydiscountfac-tor 8 = 0.90)

sustainabilitycriterion of nondecreas-ing utility.For case (C), the comparisonwith thesustainability-constrained ase (C/S)shows that consumption"overshoots"the sustainableplateaulevel at the 2ndperiod.FromFigure3 case (C), we seethat the sign of the AK, is positiveonly for the change between the 1stand 2nd periods.So the Hicksian ndi-


16/26


cator AK > 0 tells us,withone period'sdelay, that the consumptionhas tres-passedbeyond he levelcompatiblewiththe sustainabilitycriterion of nonde-creasingutility.

The Hicksian Rule dK/dt > 0 is "tooweak" as a sustainabilityndicator.Along asingle-peakpath, by the time that the signof the indicatorAKn changesfrompositiveto negative, significant(and possibly irre-versible)damagehas alreadybeen done tosustainability rospects.The Hartwick rule. Now consider thepropositionthat a nondecreasingconsump-tion is assuredby respect of the Hartwickrule, WT. X/dt = 0. The reasoning is that apositive sign of the Hartwickian"net sav-ings" t.- dX/dt) > 0 for a PVU-maxecon-omy means that pC < gNNP. If it is as-sumed that gNNP = SNI(i), then the cur-rent consumptionwould be lower than themaximin ncome and hence the economyisnot violating requirementsfor sustainableconsumption.But as Asheim (1994) andPezzey(1994, 1997)have demonstrated:

* the "Hartwick ncome" definedby thegNNP when w -dX/dt = 0, is not (gen-erally)the SNI(i);* the equalitybetweengNNP and SNI(i)holds only for a PVU-maxpath wherethe Hartwickrule is respectedat everypoint in time;* the gNNP for a PVU-max timepaththereforewill not, in general, coincidewith SNI(i), nor for that matter withSNI(ii). This statement holds even if,for a particularmoment in time, it hap-pens that C = gNNP is the PVU-maxconsumption;* therefore a positive sign of the Hart-wickian "net savings" 7-rdX/dt) for aPVU-max economy is not a reliableindicator hat the currentconsumptionpC is lower than the SNI(i), and hencethat the economy is not violating re-quirements for sustainable consump-tion.

The measurementroblems n theoryand inpractice.Figures that have, in recent years,been actually produced as putative esti-mates for a "greenGNP" in this perspec-tive, are generallyadmitted to involve"in-complete" adjustments e.g., Repetto 1989;El Serafy 1989; Peskin 1991; Pearce andAtkinson 1993; Pearce and Warford1993;and others since). Yet, there has been atendencyto let it be presumedthat these"preliminary"calculations can somehowfunction as "first approximations," ervingthe same policy relevance as the theoreticallyspecified measures.14 This presumption isdifficult to defend, partly because of therestrictedvalidityin theory,and partlybe-cause of problemsof indeterminacy,ncom-pleteness, and systematicmeasurementbi-ases at the empirical evel.The monetizationof environmentaldete-rioration, n neoclassicalperspective,relieson the abilityto estimateopportunity ostsassociatedwith resourceuse alternatives neconomic production,pollution treatment,waste disposal,and environmentalmanage-ment. Strictly speaking, these opportunitycosts are definableonlywithin the theoreti-cal frameworkof an intertemporalgeneralequilibriummodel.Forvalid indicator pec-ificationestimation,three related theoreti-cal points thus arise.First,the role of capi-

'4In workreporting stimationsof performance c-cordingto the "weaksustainability"riterion,Pearceand Atkinson(1993, 104) stated:"We beginwith anintuitiverule for determiningwhether a country s onor off a sustainabledevelopmentpath.To do this,weadopta neoclassical tance and assume the possibilityof substitution etween natural'and 'man-made' api-tal...." They presentedempirical alculationsuppos-edlyas estimatesof the value of the "weaksustainabil-ity indicator" or 22 countries,of whichonly 8 do notfulfill henonnegativityondition.Proopsand Atkinson(1997) present similar sets of results,making adjust-ments for international radesuchthatnaturalcapitaldepreciations attributed o the countryof finalgoodsconsumptionatherthanproduction.Somechanges nmagnitudesare observable,but the basic patternre-mains he same,and the underlying ssumptionsf theapproachare the same whetheror not the figuresare"corrected"or international rade.The evidentdefectof this work s that the depreciationoversonlya verysmall number of categoriesof marketednatural re-sources and environmental egradation,usingcurrentpricesor inferences romcurrentprices.


17/26

73(4) Faucheuxt al.:Natural apital heory 543tal gains in indicator definition and mea-surement must be dealt with correctly.Second,the measurementsof dK/dt, or ofthe gNNP and the related Hartwickian av-ings (wrr X/dt), must be specified n termsof prices (or, as the case may be) shadowpricesfor the particularmoment(or period)in timealongthe particular quilibrium athbeing considered. But this leads to a thirdproblem, of "chicken and egg." Take thecase of the closed economy.The relevantindicatorsaregNNPandHartwick"netsav-ings."Estimateswillhave reliable and trans-parent "sustainability"ndicatorproperties-those correspondingo a maximinSNI(i)timepath-only if the calculationsuse theconsumptionevels, prices, and stock varia-tionscorrespondingo an economyon a PVU-maxintertemporalquilibriumath character-ized by constantnational.But, as Norgaard(1990)has observed, f the purposeof indi-cator constructions to learn whetheror notan economyis far from a "sustainable" ra-jectory,we cannot assume the propertiesofa sustainable trajectory n the process ofmaking he calculations."5

V. EMPIRICALMEASUREMENTSAND THE INTERMEDIATION FMODELSThe Arrow-Debreuquilibriums veryusefulwhen or nstance ne comes o arguewith ome-one whomaintainshatwe neednotworry boutexhaustible esources ecause heywill alwayshavepriceswhich nsure heir"proper"se. Ofcoursethere are many hingswrongwith thiscontention ut a quickwayof disposing f theclaim s to note thatan Arrow-Debreuquilib-riummustbe the assumptione is makingortheeconomy,nd hen o showwhy heeconomycannotbe in thisstate. Hahn1973,14)Gettingthe Model Right?

The basic idea of the "savings"ndicator-not generallyvalid,as we haveseen-wasthat if Hartwick's ule is respected, hen theeconomy s "operatingwithin the bounds ofsustainability"n the sense that currentcon-sumptionplC is less than the sustainablenational ncome(presumed, omewhaterro-neously,to be indicatedby gNNP).

To appreciate ullythe theoretical imita-tions of this procedure,we mustpose againthe question:what is involved,theoretically,in defininghepassage roman actualGNP toan estimateor an SNI? Far more thanjustsome arithmeticwith some categoriesof thenational accounts and monetized satelliteaccounts. Both in theory and in fact, thespecificationof a "sustainablenational in-come" is highlyspeculative.It dependsonthe underlyingmodel, and also on assump-tions about investment and consumptionchoices madethrough ime.First, ora givenmodel:

* The maximinSNI(i) and the Pezzey-path SNI(ii)will generallynot coincide.As our own model resultsshow,in Fig-ure 2 cases(B/S) and(C/S), theremaybe the possibilitythat a judicious in-vestmentprogram n the directions ofnaturalresourceconservation, nti-pol-lution, environmentalquality improve-ments, etc., could permitthe economyto attain a value for SNI(ii) that ishigher than the SNI(i) that would beimmediately easible.* Attainmentof SNI(ii) does not gener-allycoincidewith a PVU-maxpath.Re-sults presented by Pezzey (1997) andalso with our own model, as shown inFigure2, suggestthat pathsthat attainSNI(ii) will usually not be PVU-maxpaths-except in cases where C(t) in-creaseswithoutboundsand thusSNI(ii)is also unbounded n the long run.e The values for SNI(i) and for SNI(ii)will each be a function of (inter alia)the initialcapitalstock vector. That is,values for SNI(i) and SNI(ii) can, in

15Inthecase of an openeconomy, he specificationsfor sustainedconsumptionwill be somewhatdifferent(see the contribution yBrekke1997, n thisissue),andunder certainassumptionshe HickscriteriondK/dt= 0 is the relevantone. But still, the same "chicken-and-egg"problemwill remain, hat the indicator's a-lidity s not assuredunlessone is alreadyon a sustain-able path, and this is preciselywhat one wants theindicator or, in order to findout.


18/26


principle,be determinedas functionsofan initialstock vectorwithinthe analyt-ical frameworkof a particularmodel(subject to algebraic tractabilityandnumericalsolution convergenceobsta-cles).

So the mathematicalpassage from a valueof gNNPobtainedempirically r for a pointon a model timepath,to either version ofSNI, is model specificand dependson sce-narioparameters.* Thetransformationrom GNP to gNNPfor the currentperiodcan be made onthe basis of currentprices, neglectingfor the momentwhetheror not these

pricesarePVU-optimalbutsee below).* The transformationrom currentgNNPto SNI(i) or SNI(ii) is, by contrast,strongly model-specific.It requires acomplicated algebraic transformationthat assumesknowledge, or the entiretime-horizonof interest, of the socialdiscountrate or rates-the p(t) or thepn-that characterize he existingeco-nomic equilibrium,of the substitutionandproductivity arameters or all sec-tors(includinganyso-called echnologi-cal progress),of demographictrends,andof consumerpreferences.

The values obtainable for SNI(i) andSNI(ii) dependmore heavilyon the choiceof model and the parameterspecificationsthan on the empirical price/quantity dataobtainable from the real world (see alsoCommon1993 and Vanoli 1996).But sincewe do not know what the "rightmodel"is,and we cannot deduce this reliably fromempiricallyavailable nformation,we are ina "chickenand egg"situation."LetUsSuppose PVU-maxEquilibrium..."

We can highlight the significance ofmodel uncertainty or indicatorestimation,with the help of our OLG model. Our sus-tainabilitycriterionleads to solutions that

are finite-time-horizonnaloguesof SNI(ii).It is already hown n Figure2 that the levelof consumptionper periodattainable n thelong run (that is, throughuntil at least the20th period) under the sustainabilitycon-straint varies considerably-from 0.4 to> 1.5 units for each generation livingin agiven period, dependingon our choice ofscenarioparameters.The initialstock levelsare identical in all cases. Our problemofindicatorreliability an be phrased:

* Is it possible to deduce whichof thesetimepaths A/S, B/S, C/S, or D/S) isthe best representationof the econo-my's welfare-deliveryprospects,basedsolely on past and currentprice infor-mation?* Can we use indicatormeasures o gaugehow far the economyis from sustain-abilityif, at the same time,we need toknowhow far the economy s from sus-tainabililityn order to gaugethe valid-ity of the indicators?

The short answersare, no and no. This isserious, because, even in our (probably ic-titious) PVU-maxworld,applying he indi-cator recipes blindlycan give perversere-sults. Take the situations,such as our sce-narios(B) and(C),wherea model economyhas a nonsustainable VU-maxequilibriumpath alongwhich nationalconsumption irstrises to nonsustainable levels then fallsmonotonically.As discussedby Pezzey 1994)and Asheim(1994),such "singlepeak"con-sumptionpathswill necessarilyhave a por-tion alongwhichthe aggregatewealth-thevalue of total capitalstocks-is rising,priorto a subsequentmonotonicdecline. Alongthe rising-aggregate-stockortionof such apath, the weak sustainabilityndicatorswillfail to signal the consumption"overshoot"and thus do not signalthat the resourceuseand savingsregimeis impairingdurably heeconomy's sustainabilityprospects. Theseauthors'results establishthat:* the use of equilibriumprices to esti-mate the naturalcapitaldepreciations


19/26

73(4) Faucheux tal.: NaturalCapitalTheory 545

a systematicunderestimate,n the sensethat a positive Hartwick"net savings"7

dX/dt 2 0 can be obtained despitethe fact that the currentconsumptionlevel is plC > SNI(i)and,as such,can-not be sustained ndefinitely.the gNNP obtained from the formulagNNP = pjC + 7r dX/dt is higherthan the SNI(i), which means that anestimatefor gNNP obtainedby deduct-ing net capital depreciation rom GNPwill not correctly ndicatethe extent towhich currentconsumptionovershootssustainability.Bycorollary,a hypotheti-cal reallocation of economic resourcesaway from consumptionto investmentequalin magnitude o the currentvalueof capital depreciation (wr dX/dt)would not be sufficient to reduce theconsumption o the SNI(i) as would berequired to put the economy onto asustainablepath.

By the time that aggregate wealth hasstoppedrising(that is, dK/dt becomesnon-positive), and by the time the sign of theHartwick"net savings"7 *-dX/dt changesfrompositiveto negative,it is too late. Sig-nificant,andperhaps rreversible, amage osustainabilityprospects has already beendone. (We have alreadyseen the same sortof defect with applicationof the "Hicksian"indicator.)The source of the systematicerrorscan,indeed, readilybe identified in the frame-work of our model. On the "boom"portionof a single-peakPVU-maxpath, the price/quantityinformation is giving "wrong sig-nals" from the point of view of resourceallocationfor sustainability.n Figure4, weshow the flows of resourcenputs oproduc-tion for the scenarios(C) and (C/S). Thesecorrespondrespectively o Figure 1(C)withboom-and-declinepath for PVU-max con-sumptiondue to the time-discounting f fu-ture generations'utility,and Figure2(C/S)withsustained-utility,lose to the "maximin"form. Comparison shows that high earlyconsumption under PVU-max involvingrapid exploitationof the depletablenatural

capital compromises future generations'economic chances. From the 2ndthrough othe 9th period consumptionby young andold in each period is significantlyhigherthan the plateau level maintained in thecase (C/S) where the sustainabilitycon-straint s imposed.The corollary s that naturalcapitalis, inearly periods, being used relatively morequicklyfor the nonsustainablegrowththanis the case along the sustainability-con-strained path, and also the manufacturedcapital stock grows relativelymore quicklyin the unconstrainedPVU-maxcase than inthe sustainability-constrainedase. This im-mediately mpliesmis-valuation.Recall thatwith a Cobb-Douglasproductionfunction,the factor shares are constant and so therelative price p3/pl is inversely propor-tional to the input proportions.So, relativeto the sustainability-constrainedath, theearly periodsof the PVU-maxpath is char-acterized by lower p3/pl than along thesustained-utility ath.These prices "under-value"each unit of naturalcapital depletedand "overvalue" ach unit of the savingsofmanufacturedcapital compared with thesustained-utility ath prices.16EmpiricalMeasurementssing ncompleteInventories nd "StronglyWrong"rices

Real trends of economic activityare exhypothesiar fromsustainability. ven if oneallows the doubtfulpropositionof a PVU-max interpretationof economicreality,thefar-from-sustainabilityrices and quantitiesfor capital stock variations are systemati-cally wrong for the estimation purposeswantedof them. Worse,there is no reasonto believe that currentprices and patterns

16The Hartwicknet savingsfor a period can bewritten:PI AM + p3 AR. In each of the earlyperiods,the priceandquantitybiasesfor manufacturedapitalsavingsreinforceeachother,so as to bias upwardshefirsttermin the Hartwick"netsavings"measurecom-paredwith the sustained-utilityath. For the naturalcapital"depreciation",he pricebias (-) is offset bythe quantitybias(+) due to the morerapiddepletionin each period,but this offsettingis not enough to"correct" he indicatorproperly.The mathematics etsverymessy; ee the seminalworkbyAsheimandPezzey.


20/26


CapitalStock Flows3

2,5-4-Produced Capital1,5 - - NaturalCapita

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

FIGURE 4(C)FLOWSOF CAPITALSNTOPRODUCTION: VU-MAX "BOOMANDBUST"

(SCENARIOC)(nat capital p= 0.55;econ capital o I = 0.15;laborot2= 0.30;PVU-maxwithintergenerationalutilitydiscount factor 8= 0.90)

C o r p i t a l S t o c k F l o w s32.52 -n-:::~::::::u:~:-ae~:~....E:~:::s:::::~::Xf "Mz~???~ss~:?..f?............s...i?:~::'~~:::::-iK::*:.:.:RIM,?::-:ji ---rdcef~i:z.:~~. . .........::~~::~j::~:~;?:~:::i~%.....x MM. g -gk?..:::~:~:~:i:M A?.~s~i, ~~~"~K"":~::~:5~':":KOX *f::%ffi;:~'f'5:~:~:~i::i~Ii~:?:~-:;~;?:;?55S~??-,:::"':..:.:::::i~j~:~"i -*gMm ~::::::;;:g:;;:gX.I:~,,, *%...............-??::~:"~:::ii~j:,~i:.0,5? ,-,31 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 0

FIGURE 4(C/S)FLOWSOF CAPITALS NTOPRODUCTION:OP-SUS WITHNONDECREASING TILITY(SCENARIO / S)(nat cap p= 0.55;econ cap alt = 0.15;labora 2= 0.30;"Op-Sus"withintergenerationalutilitydiscount factor8 = 0.90)

of resource utilization conform to a PVU-max path, and a lot of reasons exist tobelieve the contrary, notably the prevalenceof market power, force majeure, and otherforms of non-Pareto-efficient competition(e.g., oligopoly market power, high commer-cial discount rates, strategic behavior, gratu-

itous and cynical disposal of toxic wastes,state interventions to furnish low-cost ac-cess by commercial interests to forest, wa-ter, fisheries, and agriculturalresources, andso on). Many environmental services (in-cluding waste disposal) and scarce naturalresources (including fish, water, forests) are


21/26


obtained virtuallygratis simplybecause ofmarketpower and outrightcoercion, evenwhen it is knownthat high opportunity osts(including uncompensated environmentaldamages)are involved.Most non-commodifiednatural capitalssuchas the atmosphereandoceans,and thegreat diversityof marine, freshwater,andterrestrialecosystems,are, in effect, treatedby users as "free gifts of nature."Access isdeterminedby social power relations,withor without regardfor the future (Arnoux,Dawson, and O'Connor 1993; Martinez-Alier and O'Connor1996). In the case ofirreversibilities,he marginalcost of degra-dationbecomesveryhighor infinite(Pearce1976).Sometimesthe use of marketpriceshas been defended as pragmatism citing,amongother reasons,the difficultyof "cor-rect"valuation!),and as a matter of makinga step in the rightdirection.This is hardlyaconvincing defense of systematic error.Moreover,as Victor, Hanna, and Kubursihave commented,

By emphasizingn theirempiricalworkthoseaspectsof naturalcapital or whicheconomicmeasuresare more readilyavailable i.e., forresources old through he marketand a fewmeasures f pollutiondamages),ar more hasbeen left out thanhas beenincluded.17Victor,Hanna, ndKubursi997, orthcoming).The errors and omissions are thus twofold-first of all the exclusion altogether ofmanyecologicalassetsandservices rom theaccountingscheme, and second the use ofmarketprices that are probably systemati-cally"wrong"rom the pointof intertempo-ral opportunity osts. These impose system-atic biases in the same direction beingdue,generallyspeaking,to the habit of "self-in-terested"producersand consumers o treatnatureas a "free gift"and to the predomi-nance of present-day market power andpurchasing power over, inter alia, futuregenerations' nterests).The omissions-tan-tamount to employinga zero-price in thecorrection calculations-are sufficientlylarge that it becomes preposterousto sug-gest that these empirical figures give anyindication of sustainabilitypotential. The

"pragmatic" estimation procedures cur-rentlyin use are proneto give, in the situa-tions of greatest policyneed, a positive signfor the putative indicator(whether this isHartwickian net savings or the Hicksianchange in value of capital stock) while infact the economy s movingon a nonsustain-able trajectory.This is not a reliablesort ofpolicyindicator.In reality,we can only observepast andpresentquantity-price ariations. n the ab-sence of independentknowledge of theeconomy'skey technicaland social parame-ters (stock levels, output and substitutionelasticities, social discount rate) it is notpossibleto inferbyhowmuch the pricesare"wrong." f we do not knowwhat the "cor-rect"parameterspecificationsof, interalia,substitution and output elasticities shouldbe used as the basis for estimatingopportu-nity costs,we are not justified n presumingthat they are "revealed" n marketprices!This is whywe are notjustified o inferfroma positive sign of net savings ,a dX/dt) orAKn whether or not consumptionin thenth period is respectfulof a sustainabilityintergenerational quitynorm.For example, the strikingdifference inposition of the curve for value of naturalcapitalstock in Figure3(B) comparedwithFigure3(C)shows how significantlyhe esti-mate of the relative importanceof naturalcapital comparedwith economiccapitalandlabordependson modelparameters-in thiscase the relativeoutputelasticities.Thereisno reliable basis for deducingthe "correct"value of such parametersfrom price andquantity nformation urnishedby"the mar-ket."Which model should be selected as the"right"one for the purpose of inferringshadowprices?Because there is no consen-sus on this, any indicator estimation resultwill be controversial.Underlying disagree-mentson scientificandpoliticalmatterswill

17Theresults reportedby Pearce and Atkinson(1993) and by Proops and Atkinson (1997), involveestimates of naturalcapital depreciationusingmarketvaluesfor a verylimitedrangeof items such as forestproducts,petroleum,andminerals.


22/26


end up reframedin the arcane languageof modeling,without necessarily being re-solved.TheImpossibilityf Estimation fModelParameters

Knowingthe "correct" shadow relativepricesand the associatedquantities or cal-culatingthe gNNP dependson knowing heintertemporal roductionpossibility rontierfor economicproductionandenvironmentalfunction(ipsofacto the elasticitiesof substi-tution and the technological hangesfor thetimespanof analysis),and knowing-or, atleast, placing bounds around-the patternof "demand" or economicgoods and envi-ronmental functions on the part of futuregenerations.Norgaard 1990)has pointedout that theuse of existing market prices in order togaugeresourcescarcity and,by implication,gaugesubstitution lasticities)and, thus,thecritical values for model price variables,would involvea fallacyof circular easoning.Similarly,Cabeza(1996) concludesthat, inmodelsof endogenous echnological hange,in order for market orces to induce naturalresource productivity-augmentingechno-logical change,the relative nput priceshaveto signalthe relativescarcityof these inputscorrectly. f pricesfail in this role, then thetheory itself tells us we can hardlyexpectthe technologicalchangeto follow the "ap-propriate"path.Thisbringsus to the finalquestion:whatempirical evidence might we be able toamass concerning key model parameterssuch as output elasticitiesor elasticitiesofsubstitution?The short answer is: ambigu-ous at best. A numberof studieshave beencarriedout to obtain estimatesof elasticitiesof substitution or inputsto manufacturing.These have yielded widely varyingresults.Artus and Perroux 1981),makinguse of aTranslog production function form, ob-tainedelasticityestimatesvaryingrom -6.9to + 1.8. Brown and Field (1979) reportelasticities of substitutionfor several min-eral inputs (iron, aluminium,copper) and

woodpulp,in relationto manufacturedap-ital inputs, ranging from +0.6 to + 15.Kiimmel 1989)has investigated he estima-tion of productivitymprovements ased ona productionfunction with manufacturedcapital, labor,and primaryenergy,but theresults are inconclusive. Although thesesorts of econometricestimationsmay haveworthfor individual ectoralanalyses, hereare severalreasons to doubt theirrelevanceas indications for overall sustainabilityprospects.First, these estimates are sensi-tive to the form of production unctionas-sumedandto the estimation echniquesem-ployed (see Faucheux1993; FaucheuxandNoe*l 995;Stern1994a,1994b).Second,andmoreimportant,hese resultspertain o veryspecific production nputs,not to the broadspectrumof environmentalgoods and ser-vices. We cannot infer much about substi-tutabilitybetween life support,pollutionas-similation, and biological stock renewalfunctions,and economiccapital, rom exam-ination of elasticitiesfor a few minerals.Asauthors such as Daly (1994),Victor(1991),and Victor, Hanna,and Kubursi 1997) ar-gue, knowledgefrom physicaland life sci-ences suggests hatreadysubstitutabilitye-tween natural and manufacturedcapitalsshould not be presumed,and that casualaggregations a ratherchancybusiness.Forexample, thermodynamic rreversibilitym-plies the impossibilityof substituting,be-yond certainwell-defined imits, awayfromenvironmental ources of "free energy"asproduction nputs.Substitutionmaybe rea-sonably easy betweenenergy types,but thisrelativeease appliesonlywithin the class ofenergy sources, not between energy andother production nputs(Slesser 1978;Peet1992).Ecologicalsystemshavecomplexspa-tial structures, nd are interlockedwithgeo-physicalprocesses(such as hydrological y-cles) that extend over large (sometimesplanetary)distances. These systemscannotbe fragmentedand transportedn the sameway as minerals and manufacturedcapitalinputs.There is a strongcomplementarityf"inputs"in the processes of reproductionand renewalof ecologicalsystems hat works


23/26


against the applicationof the concept ofsubstitutionon the margin.VI. CONCLUSIONS:UNSUSTAINABILITYF THE"WEAK" NDICATORS

Estimatesfor SNI(i), presumed equal togNNP, and for Hartwick "net savings"assustainabilityndicatorsobtainedby deduc-tions of naturalcapital "depreciation"romconventionalGNP using currentprices,areboth logically invalid and empiricallysus-pect for the situations in which they aremost urgently needed. The estimates ofchanges ntotalcapitalstock areoftenmade,in practice,on the basis of currentpriceswithout enquiring into the conditions for"correctness" f these valuations.But also-and more crucially-there is no way ofbeing able to gauge,from marketpriceandquantity information,the extent to whichthey might be "incorrect."The validityofthe estimates cannot be gauged withoutknowingin advance the values of all keytechnicaland socialparametersdeterminingactual and possible economicperformance,and this is impossible.So the realvalueof the neoclassicalnatu-ral capital theory, properlyunderstood,ismerelydidactic. t allowsthe construction fparables o alertus:

* first, to the likelihood of "failure" ofexisting prices to signal intertemporalopportunitycosts of natural resourceuse andenvironmentaldegradation;* second, to the fact that, even if pricesare assumedto be PVU-optimal,theyalmost certainlydo not correspond oanything near a sustainable resourceuse timepath;andif not,then the "weakcriterion"for sustainability nonnega-tive "net savings") s logically invalidandwhollyunreliableas an indicatoroflong-run economic performancepros-pects.

All is not lost, however.The explicituse ofscenario-typeanalyses introducingdiffering

hypothesesaboutkeyparameterse.g.,com-plementarily or substitutability, savingsrules,technological hange)can,we suggest,serve to help decision makers understandbetter the difficulties nherentin evaluatingsustainabilityprospects,and the nature ofthe judgmentsabout uncertaintyand bur-den-sharing nvolvedin resource conserva-tion and investmentpolicies (see also daMotta 1997).But,goingbeyondthe didacticvalue, empiricalquantification f the sever-ity of the risks and "trade-offs"associatedwith naturalcapitaluse requires quite dif-ferent forms of decision-supportanalysisfrom what the neoclassical optimizationanalysiscan provide.

ReferencesAaheim,A.,andK.Nyborg.995."On he Inter-pretation ndApplicabilityf a 'GreenNa-tional Product'."Reviewof IncomeandWealth41(1):57-71.Arnoux,R.,R.Dawson, ndM.O'Connor.993."TheLogicsof Death and Sacrificen the

ResourceManagementawReforms f Aot-earoa/NewZealand." ournal f EconomicIssues27:1059-96.Artus,P., andC. Perroux. 981."FonctionseProductionvecFacteur nergie: stimationspour es Grands aysdeI'OCDE."nnales eI'INSEE44:3-38.Asheim,GeirB. 1994."NetNational roduct san Indicator f Sustainability."candanavianJournal f Economics96:257-65.Baranzini, ndrea,and FranqoisBourguignon.1995."Is Sustainable rowthOptimal?"n-ternational axand PublicFinance 2:341-56.Brekke,KjellArne.1997."Hicksianncome romResourceExtractionn an OpenEconomy."LandEconomics73 (Nov.):516-27.Brown,G. M., and B. C. Field 1979."The Ade-quacy f MeasuresorSignalinghe Scarcityof NaturalResources."n Scarcitynd GrowthRevisited,d. V. K. Smith.Baltimore: ohnHopkinsUniversityress.Brouwer,R., M. O'Connor,nd W. Raderma-cher. 1996. "Defining Cost-Effective Re-sponsesto EnvironmentalDeterioration n aPeriodicAccountingSystem." n Proceedingsof the 3rd Meetingof the London GrouponNaturalResource nd Environmental ccount-ing, 397-422 (Stockholm,28-31 May).Stock-holm:StatisticsSweden.


24/26


Cabeza,Maite. 1996. "On the Conceptof WeakSustainability." Ecological Economics. 17(3):147-56.Common,Mick. 1993. "A Cost Effective Envi-ronmentallyAdjustedPerformance ndicator."Discussion Papers in Environmental Eco-nomics and EnvironmentalManagementNo.9307, Universityof York, Heslington,Eng-land.da Motta,R. Serba.1997."Sustainability rinci-ples and DepreciationEstimates of NaturalCapital in Brazil."In SustainableDevelop-ment:Concepts,Rationalities,trategies,ds. S.Faucheux,M. O'Connor,J. van der Straaten.Dordrecht:Kluwer, orthcoming.Daly, Herman. 1994."Operationalizingustain-able Developmentby Investing in NaturalCapital." n Investingn NaturalCapital:TheEcologicalEconomicsApproacho Sustainabil-ity,eds.A.-M.Jansson,M. Hammer,C. Folke,and R. Costanza,22-37. Washington,DC:IslandPress.Dasgupta,P., and M. G. Heal. 1974. "TheOpti-malDepletionof ExhaustibleResources."Re-viewof EconomicStudies41 (1):1-23.. 1979. EconomicTheory nd ExhaustibleResources. London: Cambridge UniversityPress.Dasgupta,S., and T. Mitra. 1983."Intergenera-tional Equityand Efficient Allocation of Ex-haustible Resources." nternational conomicReview24 (1):133-53.de Boer, B., M. de Haan, and M. Voogt. 1994."What Would Net Domestic Product HaveBeen in an EnvironmentallySustainableEconomy?PreliminaryViews and Results."Paperfor the Meetingon NationalAccountsand the Environment,London,16-18 March.Dixit,A., P. Hammond,and M. Hoel. 1980."OnHartwick'sRule for RegularMaximinPaths

of CapitalAccumulationand Resource De-pletion." Review of Economic Studies 47(3):551-56.Dubourg,R., and D. Pearce. 1996. "Paradigmsfor EnvironmentalChoice:Sustainabilityer-sus Optimality."n Modelsof SustainableDe-velopment,ds. S. Faucheux,D. Pearce,andJ.Proops,21-36. Cheltenham,UK: EdwardEl-gar.El Serafy,S. 1991."Sustainability,ncomeMea-surement and Growth."In EnvironmentallySustainableEconomicDevelopment:Building

on Brundtland,ds. R. Goodlandet al. Paris:Unesco.Faucheux,Sylvie.1993."The Role of EnergyinProduction Functions."Internationalournal

of GlobalEnergy ssues (special issue on en-ergyanalysis)15 (1):45-55.Faucheux,S., and G. Froger.1994. "Le RevenuNationalSoutenable," st-il un IndicateurdeSoutenabilit6?" evueFranqaise 'Economie(2):3-37.Faucheux,S., and J.-F. Noil. 1995. L'Economiedes RessourcesNaturelleset de l'Environne-ment. Paris:ArmandColin.Hahn, Frank.1973. "On the Notion of Equilib-riumin Economics." nauguralLecture,Cam-bridgeUniversityPress,Cambridge,UK.Hartwick,J. M. 1977."Intergenerational quityand the Investingof Rents fromExhaustibleResources."AmericanEconomic Review 67(5):972-74.

. 1978. "SubstitutionAmongExhaustibleResourcesandIntergenerational quity."Re-viewof EconomicStudies45 (2):347-54.- . 1991. "Degradationof EnvironmentalCapitalandNationalAccountingProcedures."EuropeanEconomicReview35 (2-3):642-49.Hicks,J. R. 1946. Valueand Capital.2d ed. Ox-ford:OxfordUniversityPress.Howarth,Richard.1991."Intertemporal quilib-ria and ExhaustibleResources."EcologicalEconomics43:237-52.. 1992."Intergenerationalustice and theChain of Obligation."EnvironmentalValues12:133-40.1996. "An OverlappingGenerationsModel of ClimateChange."Paperto the 4thConference of the InternationalSociety forEcologicalEconomics,Boston,4-7 August.Howarth,R. B., and R. B. Norgaard.1990."In-tergenerationalResource Rights, Efficiency,and Social Optimality."Land Economics 66(Feb.):1-11.1992. "EnvironmentalValuation underSustainable Development." AmericanEco-nomicReview,Papersand Proceedings 0 (2):473-77.. 1993. "Intergenerational ransfersandthe Social DiscountRate."EnvironmentalndResourceEconomics3:337-58.Johansson,P.-O., and K.-G.L6fgren.1996. "Onthe Interpretation f 'Green'NNP Measuresas Cost-BenefitRules." Environmentnd Re-sourceEconomics7:243-50.Kiimmel,R. 1989."Energyas a Factor of Pro-duction and Entropyas a Pollutant Indicat-or in MacroeconomicModelling."EcologicalEconomics1:161-80.

Lupi, F., and T. Tomasi.1994. "CanEconomicGrowth hatDepletesResourcesBe Intergen-erationallyEquitable?"Nota di Lavoro80-94,FondazioneEni EnricoMattei,Milan.


25/26


Miller,K.-G. 1991."NationalAccountsandEnvi-ronmentalResources."EnvironmentalndRe-sourceEconomics1 (1):1-15.Martinez-Alier, ., and M. O'Connor.1996. "Dis-tributionalIssues in EcologicalEconomics."In GettingDown to Earth:PracticalApplica-tionsof EcologicalEconomics,eds. R. Costan-za, O. Segura,andJ. Martinez-Alier, 53-84.Washington,DC: Island Press.Mourmouras,A. 1993. "ConservationistGovern-ment PoliciesandIntergenerational quity nan OverlappingGenerationsModel with Re-newable Resources."Journalof PublicEco-nomics 51 (1):249-68.Muir,Eliot. 1995. "TheQuestionof Value:Price

and OutputDistributionSensitivities n Gen-eral Equilibrium."M.Sc. thesis. Departmentof Economics/EnvironmentalScience, Uni-versityof Auckland.. 1996. "Intra-GenerationalWealth Dis-tributionalEffects on Global WarmingCostBenefitAnalysis."Journalof IncomeDistribu-tion 6 (2):193-212.Norgaard,R. B. 1990. "Economic IndicatorsofResourceScarcity:A CriticalEssay."Journalof EnvironmentalconomicsandManagement19 (1):19-25.Norgaard,R. B., andR. B. Howarth.1991."Sus-tainabilityand Discountingthe Future."InEcologicalEconomics:The Scienceand Man-agementof Sustainability, d. R. Costanza,88-101. New York/Oxford: ColumbiaUni-versityPress.O'Connor,M., and E. Muir.1995."EndowmentEffects in CompetitiveGeneral Equilibrium:A Primerfor PolicyAnalysts."Journalof In-comeDistribution:145-75.Page, Talbot. 1977. Conservationnd EconomicEfficiency.Baltimore:John Hopkins Univer-

sityPress.Pearce,David.1976."The Limitsof Cost-BenefitAnalysisas a Guideto Environmental olicy."Kyklos29:97-112.Pearce,D. W.,andG. D. Atkinson.1993."CapitalTheoryand the Measurementof SustainableDevelopment:An Indicatorof "Weak"Sus-tainability."EcologicalEconomics8:85-103.Pearce, D., K. Hamilton,and G. D. Atkinson.1996. "MeasuringSustainableDevelopment:Progresson Indicators."EnvironmentndDe-velopment conomics1:85-101.Pearce,D. W.,andJ. Warford.1993.WorldWith-out End:EconomicsEnvironment nd Sustain-able Development.Oxford:OxfordUniversityPress,for the WorldBank.

Peet, John. 1992.Energy nd theEcologicalEco-nomicsof Sustainability.Washington,DC: Is-land Press.Peskin,H. M. 1991. "AlternativeEnvironmentaland Resource AccountingApproaches."InEcologicalEconomics,The Science and Man-agement f Sustainability,d. R. Costanza.NewYork:ColumbiaUniversityPress.Pezzey,John. 1989. "EconomicAnalysisof Sus-tainable Growth and Sustainable Develop-ment." Environment Department WorkingPaperNo. 15, the WorldBank,Washington,DC. 1992. "Sustainability:An Interdisci-plinary Guide." EnvironmentalValues 14:

321-62.-. 1994. "The OptimalSustainableDeple-tion of Non-renewable Resources." Paperpresented to the 5th Annual conference ofthe EAERE,22-24 June,Dublin.. 1997."SustainabilityConstraintsversus'Optimality'versus IntertemporalConcern,and AxiomsversusData."LandEconomics73(4):448-66.Proops,John L.R., andG. D. Atkinson.1997."APracticalSustainabilityCriterionWhenThereis InternationalTrade."In SustainableDevel-opment:Concepts,Rationalities nd Strategies,eds. S. Faucheux,M. O'Connor,J. van derStraaten.Dordrecht:Kluwer, orthcoming.Repetto, R. 1989. "NationalAccounts and theEnvironment."OCDE, Joint Seminaron theEconomicsof Environmentalssues,October.Slesser,Malcolm.1978. Energyn the Economy.London:Macmillan.Solow, R. M. 1974. "IntergenerationalEquityand ExhaustibleResources."Reviewof Eco-nomicStudies41:29-46.-- . 1986. "On the IntertemporalAllocationof NaturalResources."Scandanavianournalof Economics88:141-49.Stern, David. 1994a."The CapitalTheoryAp-proach o Sustainability: CriticalAppraisal."Discussion Paper in EnvironmentalEco-nomics and EnvironmentalManagementNo.9411,YorkUniversity,UK, December.-- . 1994b."NaturalResourcesas FactorsofProduction:Three EmpiricalStudies."Ph.D.diss.,BostonUniversity.Stiglitz,J. 1974. "GrowthwithExhaustibleNatu-

ral Resources: The CompetitiveEconomy."Reviewof EconomicStudies,Symposiumonthe Economics of Exhaustible Resources,41:123-37.


26/26


Svensson,L. E. 0. 1986. "Commenton R. M.Solow." Scandanavian ournalof Economics88:153-55.Toman,M.,J. Pezzey,andJ. Krautkraemer.995."L'EconomieNeoclassiqueFacea la Souten-abilit6." Economie Appliqu&e 8 (2):25-58.Englishversion:1995."EconomicTheoryandSustainability."n Handbookof Environmen-tal Economics,ed. D. W. Bromley.Oxford:Blackwell.Vanoli,Andre.1996."ModellingandAccountingWork in National Accounts."Paper to the

SpecialIARIWConferenceon IntegratedEn-vironmental and Economic Accounting inTheoryandPractice,Tokyo,5-8 March.Victor, Peter. 1991. "Indicatorsof SustainableDevelopment: Some Lessons from CapitalTheory."EcologicalEconomics4:191-213.Victor,P. A., J. E. Hanna,andA. Kubursi.1997."HowStrong s WeakSustainability?"n Sus-tainableDevelopment:Concepts,Rationalities,Strategies,ds. S. Faucheux,M. O'Connor,J.van der Straaten. Dordrecht:Kluwer,forth-coming.

1997 faucheux natural capital theory

Documents