Stefano Bartolini* and Luigi Bonatti** ENDOGENOUS GROWTH AND NEGATIVE EXTERNALITIES **

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1 Sefano Barolini* and Luigi Bonai** ENDOGENOUS GROWTH AND NEGATIVE EXTERNALITIES ** ABSTRACT: In his paper, he expansion of privae producion erodes he qualiy of commonly owned goods, hereby forcing individuals o rely increasingly on privae goods o saisfy heir needs. In he face of his deerioraion, households keep heir labor supplies and saving raes relaively high in spie of heir increasing privae wealh. By so doing, each household conribues o an increase in producion and hus has a derimenal--hough negligible--impac on commonly owned goods. Perpeual growh is he oucome of his self-fuelling process. Since long-run growh resuls from a coordinaion failure, i may be higher han socially desirable. KEY WORDS: Common propery, Defensive expendiure, Coordinaion failure, Undesirable growh, Environmenal asses, Social asses, Subsiuion process, Self-fuelling process. JEL CLASSIFICATION NUMBERS: O40, Q20. *Diparimeno di Economia Poliica, Universià di Siena Piazza S: Francesco 7 I, 53100, Siena **Diparimeno di Economia, Universià di Treno Via Inama TRENTO ** This paper resuls from long-sanding research which has benefied from numerous commens and suggesions made a seminars and workshops, as well as in conversaions. We are especially indebed o L. Punzo and A. Leijonhufvud, whose commens a an iniial sage of his work were decisive for is progress. We are also graeful for heir useful commens o G. Becaini, E. Bonai, L. Bosco, E. Cresa, M. Dardi, V. Ferrane, A. Gay, D. Heymann, F. Luna, L. Marengo, G. Mondello, U. Pagano, R. Palma, M. Pugno, P. L. Sacco, A. Vercelli. The usual caveas apply. Barolini hanks Eu CompEcs and he Economics Deparmen of he Universiy of Treno for heir financial suppor.

2 The aim of his paper is o presen a view on growh which differs from he dominan paradigm, wih is insisence ha self-susained growh is fuelled by posiive exernaliies. We insead emphasise he role played in he growh process by negaive exernaliies: 1 he expansion of privae producion erodes he qualiy and reduces he endowmen of resources o which all individuals have free access, hereby forcing hem o increase heir consumpion of privae goods in order o saisfy heir needs. This furher erodes he free resources, giving rise o a self-fuelling process. A coordinaion failure is a he origin of his process. Acing enirely auonomously, households seek o defend heir welfare agains he deerioraion of commonly owned resources by keeping boh heir labor supplies and saving raes relaively high, despie heir increasing privae wealh. By so doing, each household conribues o an increase in curren and fuure producion, wih a derimenal--hough negligible- -impac on he fuure qualiy or quaniy of he free resources. In he absence of incenives for he full inernalizaion of hese exernaliies, individual aciviies have a subsanial aggregae effec on free resources. Perpeual growh is he oucome of his self-fuelling process. Since growh resuls from a coordinaion failure, i ends o be excessive, and seady-sae raes of growh may be higher han socially desirable. Legiimae inerpreaions of he mechanism described in his paper can be formulaed boh in erms of he damage wrough o environmenal asses by producive aciviies, and in erms of he undermining of he insiuional and non-maerial bases of communal modes of life by he enlargemen of he sphere of acion dominaed by privae enerprise. In boh cases, individuals mus increasingly rely on privaely produced goods in order o aver a drasic decline in heir well-being. This paper is based on ideas wih a long and inerdisciplinary hisory behind hem. Obviously, i would be beyond is scope o conduc a horough survey of he conribuions made o his hisory by anhropologiss, sociologiss, psychologiss, philosophers, economic geographers, economic hisorians, and economiss economiss of developmen in paricular. 2 However, of he wenieh-cenury economiss who 1 As an ample variey of posiive exernaliies have revealed fruiful o explain imporan mechanisms generaing endogenous growh, we sugges ha a wide range of negaive exernaliies should be considered for heir role in he growh process. 2 Among sudies relaed o his research projec see Anoci and Barolini (1999), which derives some of he resuls of his paper in he conex of an evoluionary game. 1

3 have helped o shape hese ideas, menion should a leas be made of Polanyi (1968) and Hirsch (1976). The work of hese auhors has srenghened he view ha economic developmen and growh are boh he effecs and causes of he erosion of radiional insiuions and culures, he decline of which releases he energies ha fuel he growh process, wih is desrucive impac on such insiuions. This erosion plays a crucial role in he mobilizaion of human resources and in he formaion of he aiudes oward hrif essenial for a populaion s saving propensiy and capial formaion. 3 The model presened below explores he explanaory and predicive poenialiies of hese ideas in he simples possible way. Is focus is on he deerminans of labor supply and hrif, and is implicaions and predicions are ofen complemenary o hose of curren growh models. In oher insances, i may shed ligh on sylized facs which modern growh heory canno easily explained or has somehow overlooked. We share wih he lieraure on susainable growh is concern for he poenial impac ha curren economic aciviies may have by depleing social and environmenal asses on long-erm growh performances and fuure well-being. The emphasis in he lieraure, however, is on wheher unbounded growh is possible in he presence of naural resources negaively affeced by he growh process, 4 and no on he role as he engine of growh played by he progressive degradaion of hese asses. In oher words, he lieraure does no seem enirely aware of he exen o which he declining endowmen of free resources is able o boos economic growh. By conras, we focus precisely on he manner in which work aiudes, 3 A recen example of he crucial role played in growh episodes by human resource mobilizaion and rising saving raes is provided by he Asian Tigers, where in many cases, raes of aciviy and dependen employmen have doubled in he space of en years (see e.g. Krugman,1995). While he modelling radiion has concenraed on pull facors (in Lewis, 1954, and in Todaro, 1969, he pull facor is he wage differenial beween he modern and he radiional secor), a large body of lieraure has sressed push facors. Among hem, he decline of radiional insiuions of he rural secor is considered a major deerminan of hose migraion flows ino urban areas ha make possible he formaion of an indusrial workforce. 4 In Musu (1994), susainable growh is consisen wih a modified AK model, assuming ha here is no increase in polluion as producion increases because of higher capial sock. In he absence of a lower limi, below which environmenal qualiy canno fall wihou enailing irreversible caasrophe, Marin and Roillon (1996) analyse under wha condiions on he uiliy funcion he AK model is able o generae susainable growh. In he presence of such a limi, Aghion and Howi (1998) show ha growh is no susainable wih a AK producion funcion. 2

4 saving propensiy and consumpion habis become more favourable o growh as access o free resources diminishes. The paper is organized as i follows. Secion 1 discusses some of he poins ha moivae he model. Secion 2 presens he model and derives he opimizing behavior of he agens. Secion 3 characerizes he equilibrium pahs of he economy, showing ha i is only in he presence of negaive exernaliies ha perpeual growh is possible. Secion 4 dwells on cerain implicaions and possible exensions of he model. The appendix gives anoher example of an economy which can exhibi a sricly posiive long-run growh rae only in he presence of negaive exernaliies, ogeher wih characerizaion of he pah seleced by a benevolen planner under hese circumsances. 1. Moivaions Growh and working ime in he long run By endogenizing he decision on he ime spen working, our model makes i possible o deal wih a crucial issue in long-erm growh: he allocaion of produciviy gains beween leisure and consumpion. Growh models in which he labor supply is exogenous assume precisely wha hey should explain: ha increases in produciviy are uilized mainly o augmen oupu, and only marginally o reduce working ime. If he reverse occurs, growh (in he sense of increased per-capia oupu) may no ake place. Curren endogenous growh models find i difficul o preserve perpeual growh when he possibiliy of a labor/leisure choice is explicily considered. 5 We show in his paper ha if a Ramsey-Rebelo AK model is augmened by reaing he unis of ime devoed o work, h, ( capial operaing ime ) as a choice variable, he resuling Akh model does no generae endogenous growh in he absence of negaive exernaliies. 6 In 5 Baldassarri e al. (1992) show ha he models of Romer (1986) and Lucas (1988) admi endogenous growh only if leisure is no a choice variable (see also Solow, 1995). 6 In Rebelo s (1991) AK model, he absence of diminishing reurns o capial can be made plausible by inerpreing K in a broad sense o include human capial (see also Barro and Sala-i-Marin, 1995). I is even more plausible o le labor ener he producion funcion boh as a reproducible facor whose qualiy depends on previous invesmen and as an inpu whose quaniy depends on demand and supply. In oher words, physical capial ends o increase ogeher wih he qualiy of he working populaion, bu no necessarily wih he ime ha his populaion devoes o work: in our model, h can be inerpreed as he capial (in he broad sense inclusive of human capial) operaing ime. 3

5 his case, an economy wih he prospec of becoming richer by accumulaing capial ends o reduce he saving rae, even if he producion funcion is such ha for given levels of echnology and labor effor he marginal produciviy of capial is no decreasing in K. This is because he reurn on capial invesmen is reduced by he less ime devoed by individuals o work as he capial sock grows larger and he economy becomes more producive. As well as ruling ou he possibiliy of unbounded growh, inclusion of he labor/leisure choice in a AK model which ignores he negaive exernaliies generaed by economic growh yields he counerfacual predicion ha working ime will be highly responsive in he long run o echnological advances. Indeed, he endency for labor inpu o decrease is weak, and i displays very imporan excepions. 7 Obviously, saisfacory assessmen of he exen o which oal working ime reacs o produciviy improvemens also requires analysis of how produciviy changes affec home work (see Greenwood and Hercowiz, 1991; Benhabib e al., 1991). This is especially rue in he ligh of he hisorical rend oward increased female labor-marke paricipaion disincive of he advanced counries during he wenieh cenury. However, he fac ha he producion of cerain services is no longer confined o he family is par of he general and progressive weakening of communiarian modes of life ha has accompanied modern economic growh. Furhermore, widespread in conemporary socieies is he percepion ha people suffer from a shorage of ime in he mids of affluence. 8 Growh models which include he labor/leisure choice as a conrol variable (see, for example, Barro and Sala-i-Marin, 1995) explain he low long-erm elasiciy of per-capia working ime wih respec o produciviy advances by assuming ha in he long run he income effec only weakly predominaes over he subsiuion effec induced by he increased remuneraion of labor. Tha is o say, sandard explanaions rely on he peculiariies of individual preferences. The sympoms of widespread disconen wih he excessive role played by work in people s lives should promp a search for complemenary explanaions as o why produciviy gains are no massively ransformed ino leisure increases. 7 In he USA, labor inpu per head of populaion (hours) was 710 and labor produciviy (GDP per hour worked) was 8.64 in Analogous figures were 756 and in 1950, and 741 and in 1992 (see Maddison,1995). According o Schor (1993), in 1987 Americans worked for around one monh per year more han hey did in 1969 (+163 hours). 8 Among he aemps o explain his famine of ime, see Linder (1970), Hirschmann (1973), Cross (1993). 4

6 The explanaion proposed in his paper ress on he need of individuals o subsiue for diminishing free resources. In response o echnological progress, he same individual ases are consisen wih a drasic long-erm fall in working ime when negaive exernaliies are ignored, while hey do no generae any significan working ime reducion once hese exernaliies have been aken ino accoun. Observed longerm reacions of per-capia working ime o produciviy advances depend on a coordinaion failure and no on he ases of individuals, who would prefer lower levels of marke aciviy in exchange for more free ime and more resources. The presence of negaive exernaliies caused by he growh process is an incenive for individuals o devoe produciviy increases mainly o he producion of subsiues (o he poin of increasing he labor supply) because heir uncoordinaed effors do no ake accoun of he social cos of increased producion, hus fuelling he mechanism whereby increases in oupu cause a deerioraion in he free resources which simulaes increases in oupu. As he economy grows and free resources deeriorae, he value of privae consumpion for households increases relaively o he value of ime, and he reurn on capial invesmen is no depressed by households willingness o work less. The growing labor produciviy brough abou by he rising capial sock is no used o reduce he ime devoed o work, because he deerioraion of free resources makes i more urgen o increase privae consumpion. 9 Growh and hrif in he long run An economy ha has he prospec of increasing is privae wealh by accumulaing capial ends o keep he saving rae consan as households anicipae ha he fuure endowmen of he free resource will be negaively affeced by he growh process, and herefore increasingly subsiue privae goods for free resources in heir consumpion aciviy. Indeed, social wealh also includes hose commonly owned asses whose progressive degradaion accompanies he growh of capial sock. In our model, he impoverishmen due o he declining qualiy of free resources ends o offse he negaive effec on he saving rae due o he increase in privae wealh. As an example of how he gradual erosion of communal insiuions in favour of more individualisic lifesyles may keep he saving rae high, one may cie he major effec on saving 9 I is precisely in order o focus on his poin ha a mechanism generaing endogenous echnological progress is no included in he model, he inenion being o analyse how negaive exernaliies influence decisions concerning labor supply and capial accumulaion in he presence of echnological progress, regardless of he mechanism ha generaes i. 5

7 propensiy exered by he declining imporance of he family in providing suppor o he elderly which ypically accompanies he evoluion of an advanced sociey. 10 Growh as a subsiuion process As growh proceeds, agens increasingly derive welfare from privae raher han common consumpions. This conclusion may srike sociologiss as familiar, since hey ofen associae growh wih he creaion of new needs and wih a change in paerns of consumpion. These expressions end o be inerpreed in erms of an endogenous change in preferences. In our model, he creaion of new needs and change in consumpion paerns consiue he engine of growh, bu in a conex of invarian preferences. This is because new needs are viewed as increases in demand for subsiue goods generaed by a diminuion in free consumpions, while changes in paerns of consumpion concerns he passage from common (free) goods o privae (cosly) ones. Consequenly, he radiional view ha increasing quaniies of goods become available as growh proceeds may be incomplee. The image conveyed is one of luxury goods which become sandard goods for he nex generaion, and absolue needs for he one ha follows hereafer. Our model suggess ha his is only parially rue, since also involved are free goods whose endowmen and qualiy are progressively reduced. The poin is an obvious one in an environmenal inerpreaion of he concep of free resource : meadows, woods, clean beaches, unpollued air and waer, silence, and so on, are all examples of free goods which may deeriorae or become scarce. I is ofen he case in advanced economies is ha, in order o enjoy wha could be obained for free hiry or fory years ago, agens mus now purchase a house in an exclusive area in he counryside or a he seaside, or buy an expensive holiday in some ropical paradise, ec. However, a sociological inerpreaion of free goods is also possible, given ha many of hem relae o social relaions and seemingly grow scarcer wih growh. Wih his broader inerpreaion in mind, he concep of subsiue may help o explain changes in lifesyles, as well as in paerns of consumpion. According o Hirsch (1976), growh in advanced economies is largely due o an increase in defensive consumpion: ha is, consumpion induced by he negaive exernaliies produced by growh, 10 Pay-as-you-go pension schemes which have replaced he family as he principal source of suppor for he elderly in mos Wesern socieies sill incorporae an imporan solidarisic elemen, since hey are widely used o perform inrageneraional and inergeneraional ranfers. The curren rend oward reducing heir role in favour of more individualisic ways o provide for he elderly could be inerpreed as anoher sep in he erosion of communal insiuions. Those who advocae his reducion expec i o boos aggregae saving. 6

8 which is similar o he concep used here of subsiue consumpion. Afer Hirsch, he noion of defensive consumpion was aken up by he debae on correcions o GNP in order o improve i as a index of welfare. The lieraure on defensive consumpion conains a large number of ineresing examples, bu he idea ha seems o inspire all auhors, and Hirsch in paricular, is ha reacions o a siuaion of general decay may be very general. 11 Individuals may compensae for he deerioraion in everyhing ha is public wih a concern for everyhing ha is privae, giving rise o he conras ypical of "affluen socieies" (Galbraih's wellknown observaion). Growh and increased pressure on environmenal and social resources The model predics ha a larger populaion size and a greaer impac of a given level of producion on free resources end o boos long-run per capia growh, bu a he cos of a declining seady-sae level of households welfare. In fac, everyhing ha exers greaer pressure on he free resource and acceleraes is decline induces individuals o reac by working and saving more. Thus, according o he model, policies ha reduce populaion growh and he environmenal impac of producive aciviies resrain he long-erm per capia growh rae of he economy. I is also worh noing ha he predicion ha populaion increase will raise he rae of growh of per capia income is enirely consisen wih he predicions made by models of endogenous echnological 11 The empirical lieraure on defensive consumpion displays a number of concepual difficulies--evidenced, for example, by he variey of definiions of defensive expendiure--which derive in par from a failure o undersand ha he concep of defensive expendiure is a sub-case of he concep of subsiued good (which is clearly codified). In he se of subsiues i is he sub-se of subsiues for environmenal goods (i.e. for he free goods subjec o negaive exernaliies). In he opinion of hese auhors, however, i is difficul o give plausible saisical subsance o he concep, owing o he difficuly of idenifying spending for defensive reasons among he iems in he GNP, consruced on oher crieria. The sraegy followed is generally highly resricive, in ha only classified as defensive is spending which is cerainly and wholly such: spending on environmenal purificaion, on land reclamaion, on polluion-relaed diseases. The esimaes obained are no negligible, bu on he admission of he auhors hemselves hey are enormously under-esimaed. For a growh model including defensive expendiure, see Belrai (1996). In his model, however, he presence of defensive expendiures canno generae a self-propelled process of growh, since (i) a rise in defensive expendiures does no increase he level of economic aciviy by inducing individuals o work harder, and (ii) he flow of use of he environmenal asse is fixed (i is no affeced by he level of producion). 7

9 change (see Grossman and Helpman, 1991; Aghion and Howi, 1992; Kremer, 1993). However, our model has normaive implicaions regarding he desirabiliy of populaion increases which are a odds wih hose sressed by models of endogenous echnological change, since our predicion depends on he increase in negaive exernaliies due o congesion (increased pressure on environmenal and social asses), raher han on posiive exernaliies due o scale effecs. 12 Growh and insiuional shocks The model predics ha an insiuional shock which causes a collapse of free resources will accelerae growh. This acceleraion is only ransiory and in he long run he economy will resume he seady-sae per capia rae of growh deermined by is srucural feaures. As a permanen effec of his acceleraion, he economy ends o be endowed wih a higher capial sock a any fuure poin in ime. However, he ne expeced impac of such a shock on households lifeime well-being is negaive, since as he economy moves back o seady sae, people suffer from he welfare decline due o he fall-off in he endowmen of environmenal and social asses. More han one hisorical episode could be cied as examples of insiuional shocks of his kind. Perhaps he bes known example, however, is provided by he enclosures, he process whereby he privae ownership of land was exended in Briain. The enclosures broke up he communal insiuions of land use and deprived vas numbers of he rural populaion of heir means of subsisance, uprooing hem from agriculural under-employmen and forcing hem ino urbanizaion or vagabondage. In our erms, he enclosures consiued a collapse of free consumpion, 13 and hisorians widely recognize ha hey were a pre-condiion for he formaion of an indusrial labor supply. Explanaions à la Polanyi of he role of insiuional shocks in deermining growh accep he neoinsiuionalis emphasis on he imporance of he exension of privae propery. Bu hey give an explanaion 12 In models of echnological change an increase in populaion spurs echnological change and economic growh by increasing he size of he marke, because he cos of invening a new echnology is independen of he number of people who use i. According o Kuznes (1960) an increase in populaion booss echnological progress by favouring inellecual conacs among people and labor specializaion. In his way, greaer populaion densiy can explain he disproporionally larger number of innovaions in ciies. 13 Transiion since he end of sae socialism in Eas Europe can be inerpreed as anoher social experimen in growh se in rain by he collapse of insiuions allowing he free consumpion of (low qualiy) goods and services. 8

10 of is role in deermining growh which differs enirely from ha couched in erms of he increased efficiency, accumulaion and echnical progress brough abou by he inernalizaion of exernaliies. 14 In Polanyi's conex, which we shall aemp o formalize, he exension of exclusion righs may rigger growh because i resrics righs of free access o resources. The wo explanaions are no incompaible: he explanaion in erms of a decline in free consumpion may poin o a furher reason why privae propery generaes growh. Afer all, he mechanism à la Polanyi may be considered o be he reverse side of he neoinsiuionalis mechanism: he aribuion of exclusion righs o someone, alers his/her decisions concerning he use of he resource, which becomes subjec o his/her righ bu also reduces someone else s righ of access o ha resource. Polanyi emphasises he general equilibrium reacion o his reducion: increased paricipaion in he labour and produc markes. Growh, discoun rae and long-erm welfare One predicion of he model is ha he long-erm welfare of individuals ends o decline as hey discoun he fuure less heavily: he greaer he concern of living individuals abou he fuure, he more hey will worsen he prospecs of fuure generaions. This apparen paradox depends on he fac ha raional individuals more anxious abou he fuure are inclined o save more in order o safeguard heir welfare (or he welfare of heir descendans) in anicipaion of a deerioraion in he free resources. In doing so, hey accelerae boh he long-run growh rae of he economy and he deerioraion of social and environmenal asses, hereby reducing heir long-erm well-being (and he well-being of heir descendans) because he increased availabiliy of produced goods does no compensae for he poorer qualiy of free resources. More inense and uncoordinaed effors by individuals o safeguard heir fuure welfare may reduce he long-erm welfare of all agens as an uninended oucome of heir individual sraegies. This resul reverses he convenional environmenalis explanaion ha he problems of susainabiliy depend on he selfishness of he presen generaion ha is, on is oo high discoun rae (see Pearce, 1993). This explanaion can be inconsisen: one canno argue ha economic growh depends on he accumulaion of producive asses which is boosed by a low rae of ime preference while also claiming ha he problems of social and environmenal susainabiliy which can be exacerbaed by high growh raes are made more serious by a high discoun rae (see Vercelli, 1992). In our approach, he problem is 14 In Norh s growh heory, around 10,000 years of human economic progress have been driven by he esablishmen of righs (firs communal and hen privae) on resources (see Norh and Thomas, 1973; Norh, 1981). 9

11 no inergeneraional conflic, bu coordinaion failure among individuals belonging o he same generaion. Given he public-good characer of environmenal qualiy, his failure requires appropriae policy responses. 15 Growh and is desirabiliy I should be noed ha even in an economy in which growh involves he furher deerioraion of free resources, and mainly concerns heir subsiuion wih produced goods, a higher rae of growh may lead o greaer welfare. Alhough growh is based on a desrucive process, a limied increase in he growh rae may generae Pareo-improvemens. I seems plausible, in fac, ha he social and environmenal coss of indusrializaion are more han offse by, for insance, he decline in child moraliy or by increased life expecancy. However, in he presence of negaive exernaliies, growh ends o exceed he hreshold beyond which is desrucive effecs predominae over is beneficial impac on welfare. As a resul of a coordinaion failure, growh goes oo far, bringing abou an excessive use of labor and he deerioraion of free 15 This call for collecive acion is consisen wih he hypohesis ha even for hose dimensions of environmenal qualiy where growh seems o have been associaed wih improving condiions, here is no reason o believe ha he process is an auomaic one, since he songes link beween income and polluion in fac is via an induced policy response (Grossman and Krueger, 1995, pp ). In is urn, his policy response is driven by ciizen demand. In he recen debae on he so-called environmenal Kuznes curve, i.e., on he hypohesis ha he relaionship beween per capia income and environmenal degradaion akes an invered U-shaped form, also Arrow e al. (1995) claim ha economic growh is no subsiue for environmenal policy. Moreover, hey noe ha reducions in one polluan in one counry may involve increases in oher polluans in he same counry or ransfers of polluans o oher counries (Arrow e al., 1995, p.92). Esimaing a dynamic model, De Bruyn e al. (1998) show ha economic growh has a direc posiive effec on he levels of emissions, hus supporing he radical sandpoin, according o which he idea ha economic growh can be good for he environmen is false and pernicious nonsense (see Ayres, 1995). However, i should be emphasised ha susainabiliy is no simply a funcion of he levels of emissions and resource depleion, since i depends on he capaciy of naural sysems o absorb wases and renew resources (see Kaufmann and Cleveland, 1995). 10

12 resources. This coordinaion failure is obviously due o marke incompleeness: missing markes for scarce resources generae undesirable growh. 16 Hence, he exisence of subsiue consumpion may worsen welfare, compared wih he case in which here is no opporuniy for subsiuion. 17 In oher words, he reacion of agens o a worsening in heir living condiions may cause heir furher deerioraion. This is a coordinaion failure: he model describes a world of individuals whose uncoordinaed effors o improve heir posiion may give rise o a general worsening of individual posiions. This migh be a facor in explanaion of he broken promises of growh : dissaisfacion wih he world creaed by he advanced economies, which people perceive as sressful, fraugh wih economic difficulies, and characerized by he deerioraion of he social and naural environmen. Analyses of subjecive daa, like he percepions by individuals of heir own welfare, conclude ha he correlaion beween growh and well-being seems, in he mos opimisic of evaluaions, very sligh 18 : growh does no make people feel significanly beer. 16 This amouns o claiming ha a marke sysem may generae excessive growh on accoun of he fac ha i is incomplee. We would emphasise he difference here wih respec o he endogenous growh lieraure, where markes are incomplee (given ha here are posiive exernaliies) and growh is sub-opimal (if markes for posiive exernaliies exised, seady sae growh raes would be higher). This implies ha he compleeness of markes generaes growh. In our model, by conras, he compleeness of markes lowers he seady-sae rae of growh raher han enhancing i. 17 In he lieraure on susainable developmen, he degree of susiabiliy beween 'man-made' capial and naural capial is considered crucial for susainabiliy. If hey are perfec subsiues, he condiion for susainabiliy is ha he aggregae sock of capial ( 'man-made' plus naural) should no decline ('weak' susainabiliy) (see, for insance, Harwick, 1986). If hey are no perfec subsiues, susainable developmen requires ha here be no ne damage o environmenal asses ('srong' susainabiliy) ( see, for insance, Pearce e al., 1990, Daley, 1991). Boh conceps of susainabiliy impliciely assumes ha a high degree of susiuabiliy can be welfare improving for fuure generaions. In conras, our model shows ha he possibiliy of subsiuing man-made goods for environmenal asses can give rise o a self-reinforcing process ha leads o a long-erm worsening of individual well-being. 18 The expression is Oswald s (1997), who makes he mos opimisic evaluaion of he daa on individuals percepions of heir own happiness. More pessimisic is Easerlin (1974, 1995), for whom happiness is he same in rich and poor counries, and growh does no increase well-being. 11

13 The mos general policy implicaion of he exisence of Pareo-worsening growh dynamics is ha here may be socially undesirable growh mechanisms whereby growh is he oucome (and he cause) of social and environmenal deerioraion. When growh is of his ype ha is, based on high social coss i is unlikely o give rise o an improvemen in welfare (and neiher, probably, o social sabiliy). This paper counsels grea cauion wih regard o growh policies able o achieve heir goals bu a high social and environmenal coss. Welfare-generaing processes and social insiuions ha do no work hrough he marke may be complex and fragile. Fuelled by heir degeneraion, and a he same ime provoking heir someimes irreversible crisis, a growh dynamic may deermine a non-ransiory deerioraion in he welfare of he populaions concerned. 2. The model and he opimizing behavior of agens We consider an economy in discree ime wih an infinie ime horizon. There is a large number I of idenical households wih finie lifeimes: hey have a sricly posiive and consan probabiliy ω, 0 < ω < 1, of dying in each period. Thus, he probabiliy of dying in each period is assumed o be independen of he age of he individual; and i is also assumed ha he moraliy rae of a large group of individuals does no flucuae sochasically even hough each individual s lifespan is uncerain. This implies ha a he end of each period a consan number (1 - ω )I of households dies and is replaced by an equal number of newly born individuals. Households uiliy The period uiliy funcion of he represenaive household, U, is addiively separable beween consumpion and leisure: U = β f ( x ) + (1- β ) g( l ), 0 < β < 1, f ' > 0, f ' ' < 0, g' > 0, g' ' 0, (1) < where x is he amoun of services generaed by a consumer aciviy in period, and l is leisure. Households generae x by combining a resource o which all individuals have free access in every period and a consumer good ha can be privaely appropriaed: x = R C, (2) where R is he endowmen (or an index of he qualiy) in of he free resource, and C is he amoun of a produced good consumed in. Noe ha here is non-rivalry in he consumers use of R, from which no 12

14 consumer can be excluded, since i has he naure ypical of a public good. The inuiion underlying (2) is ha individuals are unable o gain any uiliy from he consumpion of privae goods if hey have no access o some free resource (air, environmen ec.). However, households may respond o a deerioraion in he free resource by using increasing quaniies of privae goods in subsiuion for i, hus resricing he worsening of heir welfare. Producion There is only one good Y produced in his economy. Each household produces his single good according o he echnology Y = AK h, A > 0, (3) The sock of capial evolves according o where A is a parameer measuring he sae of echnology, K is he sock of capial exising in, and h =1- l are he unis of ime spen working in by he household (he oal amoun of ime available o each household in period is normalized o be one). Capial can be inerpreed in a broad sense, inclusive of all reproducible asses, and h can be defined as he capial operaing ime. Capial K + 1 = Y + (1-σ )K - C, 0 < σ < 1, K 0, K 0 given, (4) where σ is a capial depreciaion parameer. For he sake of simpliciy, we assume ha he individuals born in inheri K from he households ha have jus died. 19 Free resource The moion of he free resource is governed by R + 1 = ρr + γ, 0 < ρ < 1, γ > 0, R 0 given, (5a) or, alernaively, by γ R + 1 = ρr +, α > 0, R0 αiy given. (5b) In (5a) he evoluion over ime of he common resource R is no affeced by he volume of producive aciviy, while (5b) capures in simple manner he idea ha he abiliy of he free resource o regenerae declines wih he level of aggregae producion, whose impac on R +1 depends on he echnological 19 All he resuls of his model also hold if one assumes ha households ake accumulaion decisions wih a view o he welfare of heir descendans, hereby linking individuals in infinie lived dynasies. 13

15 parameer α. Given ha he economy is populaed by a large number of households, he negaive effec of a single household s oupu on he fuure endowmen of he resource is negligible. Households objecive In each period, he represenaive household mus decide on h and C in order o maximize he discouned sequence of uiliies ha i expecs during is lifeime: i θ U + i, θ ζ (1 - ω), 0 < ζ 1, (6) i= 0 where ζ is a ime preference parameer. Expecaions are raional, in he sense ha hey are consisen wih he rue processes followed by he relevan variables. Opimizing behavior Maximizing he Hamilonian i θ { +i λ +i[ +i+1 +i +i σ +i C i ]} wih respec o C, h and K +1, where H = U - K - AK h - (1- )K + + i=0 λ+i is he muliplier, we obain he following condiions ha an opimal pah mus saisfy: df (.) βr = λ, dx dg(.) (1- β ) = AK λ dl and (7a) (7b) λ = λ + 1 θ ( Ah σ ). (8) lim θ An opimal pah mus also saisfy he laws of moion (4) and (5), and he ransversaliy condiion λ K = 0. (9) According o condiions (7), he marginal uiliy of leisure mus be equal for opimaliy o he incremen in uiliy obainable by devoing one addiional uni of ime o work. The laer depends on boh he endowmen of free resource available in, which influences he uiliy ha he household can obain by consuming he privae good, and he sock of capial available in, which affecs he marginal produciviy of labor. The ineremporal rade-off faced by he household along an opimal pah is capured beer if (7) and (9) are used o rewrie (8) as R df (.) i i-1 df (.) = θ (1- σ ) Ah + ir + i. (10) dx dx i= 1 + i 14

16 Equaion (10) saes ha along an opimal pah he marginal uiliy of consuming an addiional uni of a privae good mus be equal o he incremen in he discouned sequence of fuure uiliies ha he household can expec o obain during is lifeime by accumulaing an addiional uni of capial. Obviously, he fuure produciviy of capial depends on he ime ha he household decides o devoe o work, and on he sae of he echnology. 3. Equilibrium pahs In his secion we give an example 20 which shows ha his economy can achieve a sricly posiive long-run growh rae only if here are negaive exernaliies, i.e. if he moion of he free resource is governed by (5b). f Le us specify he following funcional forms for he uiliy funcion in (1): ( x ) = ln( x - m), m > 0, (11) and g( l ) = ln( l ). (12) In (11), C and R are subsiues, in he sense ha f (.) is decreasing in R holding C consan, 21 and m C represens a subsisence level of consumpion: f x ) - as x m. ( Equilibrium as he evoluion of he resource is no affeced by producive aciviies Using (4), (7), (8), (11) and (12), one can obain he sysem of equaions ha ogeher wih (5a) ( ) + 1 (13) and govern his economy in he absence of negaive exernaliies: K + 1(1- h + 1) = K (1- h ) θ Ah + 1-σ Aβ (1- h )K K AK h K (1- ) = + σ (1- β ) m -. R (14) Z 1 (1 + µ By wriing he sysem (5a), (13) and (14) as K 1 - K = ρz + γk, Z R K, µ ) K + +, (15) 20 See he appendix for anoher example. 21 The oher example oulined in he appendix shows ha unbounded growh is possible in he presence of negaive exernaliies even if C and R are complemens, i.e. even if f (.) C is increasing in R holding C consan. 15

17 (1 + µ θ ) + 1 = ( Ah + 1-σ ) + 1 ) (16) i is eviden ha (15)-(17) has no fixed poin such ha µ = µ = 0 : in he absence of negaive + 1 µ > (1- h )(1- h and Aβ (1- h ) m 1+ µ Ah (1- ) - = + σ -, 17) (1- β ) Z exernaliies, his economy canno grow forever a a consan rae. The unique seady sae of he economy when R evolves according o (5a) is characerized by µ = 0, (18a) γ R =, 1- ρ (18b) 1-θ (1- σ ) h = θa (18c) and m K R. Aβ (1- h) Ah -σ - (1- β ) I is worh noing in (18c) ha he elasiciy of h wih respec o he sae of echnology, A, is uniary: in he long run, a once and for all echnological improvemen causes a fall in he unis of ime devoed o work of he same proporion. One can also check for reasonable parameer values ha he sysem which is obained by linearizing (5a), and (13)-(14) around (18) exhibis saddle-pah sabiliy. 22 Moreover, he sable arm converging o (18) is he unique opimal pah of his economy. 23 Even if he producion funcion is such ha for given levels of echnology and labor effor he marginal produciviy of capial does no decline as K is raised, i is never opimal o allow capial o grow 22 Linearizing (13)-(14) around (18) yields he following characerisic equaion: 2 θa(1- h) [(1- β )(Ah + 1-σ ) - Aβ (1- h) ] + (1- β )(2 -σ + A) A + (1-σ ) ξ ξ + = 0, where ξ 1 and ξ 2 (1- β )[1+ θa(1- h)] 1+ θa(1- h) are γ and ρ =. 75 he characerisic roos. Leing A =.5625, = 1, θ =.8, m = σ =.2, β =. 5 h =.8, ξ =.962 and ξ2 1 = , one obains 23 Explosive pahs of K and h can be ruled ou because hey violae he ransversaliy condiion, while implosive pahs can be ruled ou because--as K approaches zero--consumpion mus fall o a level ha is inconsisen wih he opimaliy condiions. 16

18 forever. This is because leisure can be subsiued for consumpion. Indeed, an economy ha has he prospec of becoming richer by accumulaing capial ends o reduce he saving rae because he reurn on capial invesmen is lowered by he shorer ime ha individuals will devoe o work as he capial sock grows larger and he economy becomes more producive. Equilibrium as he evoluion of he resource is affeced by producive aciviies In he presence of exernaliies, he economy moves along he pah governed by (5b), (13) and (14). Again, his sysem can be rewrien as (16), (17) and Z + 1 γ = ρz +. (19) (1+ µ ) αiah By seing 1 = µ =, Z+ 1 = Z = Z and h + 1 = h = µ + µ h in (16), (17) and (19), one can solve and ~ h = h(a, γ, α, m, β, σ, ρ, θ, I). 24 (20d) In general, we have µ ~ 0 : 25 he long-run per capia growh rae of his economy can be sricly posiive. Moreover, i is possible o check for reasonable parameer values ha he sysem which is obained by linearizing (16), (17) and (19) around (20) exhibis saddle-pah sabiliy: 26 he sable arm converging o he long-erm equilibrium is he only pah consisen wih (7)-(9). 2 for he seady sae of his economy in he presence of negaive exernaliies: ~ µ ~ = θ (Ah + 1- σ ) -1, (20a) (1 ~ ) Z ~ γ + µ = ~ ~, (20b) αiah[1- ρ(1 + µ )] ~ ~ βa(1- h)z ~ x = + m (20c) (1- β ) 24 h (.) = b/2a + (b/2a) - c/a, where a = γθ A [(1- β )(1-θ ) + β ] + mαi(1- β ) ρθa, b = γθ A[ βa - 2(1- β )(1-θ )(1- σ )] + mαi(1- β )A[1- ρθ (1- σ )] - γθβ (1- σ )A, 2 26 The economy governed by (16), (17) and (19) evolves according o he following sysem of difference equaions in h 2 c = γθ (1- σ )[(1- β )(1-θ )(1-σ ) - βa] (i is reasonable o assume ha c<0). 25 I is apparen in (20a) ha ~ ~ 1-θ (1- σ ) µ = 0 if and only if he parameers values are such ha h =. θa and Z : IAα hz+ 1 θ ( Ah σ )(1- h ) =, IAαhρZ + γ (1- h+ 1) IAαhZ + 1 βa(1- h ) m = Ah + 1-σ -. IAαh ρz + γ (1- β ) Z 17

19 An economy ha has he prospec of increasing is privae wealh by accumulaing capial ends o keep he saving rae consan as households anicipae ha he fuure endowmen of he free resource will be negaively affeced by he growh process, which induces hem o increasingly subsiue he privae good for R in heir consumer aciviy. As he capial sock grows, and as he free resource deerioraes, he value of C for households increases relaively o he value of ime, and he reurn on capial invesmen is no depressed by he willingness of households o work less. The increasing labor produciviy brough abou by he rising capial sock is no used o reduce he ime devoed o work, because he deerioraion of R makes i more urgen o increase privae consumpion. In oher words, growh is a self-fuelling process caused by a coordinaion failure. Acing enirely independenly of each oher, households seek o defend heir fuure welfare agains he deerioraion of he free resource by increasing heir abiliy o consume privae goods in subsiuion for R. They can do so by keeping boh heir saving raes and heir labor supplies relaively high. Accordingly, hey cause a furher deerioraion of R, hereby fuelling he process. Perpeual growh is he oucome of his self-fuelling process. 4. Implicaions of he model and possible exensions Some implicaions There are various implicaions of he mechanism described above. 1) In he absence of negaive exernaliies, opimizing households reac o echnological progress by reducing heir working ime: in he long run, a echnological improvemen leads o a fall in he unis of ime dedicaed o work of he same proporion. This is no he case in he presence of negaive exernaliies even if preferences are exacly he same. The increased oupu obainable wih given quaniy of K and L hanks o a permanen improvemen in he level of echnology (higher A) ends o The characerisic equaion of he sysem obained by linearizing his sysem around (20) is he following: ~ ~ ~ + α ρ θ ( ha + 1- σ ) + (1- h)a[1 + β/(1- β )] ζ + + α ρz ~ Z ~ 2 IA h ~ IA h + γ θ (A + 1- σ ) ζ ~ ~ ~ θ ( ha + 1- σ ) + (1 - h)a[1 + β/(1- β )] IAαh ~ 0, where and are he [IA h Z ~ ρz ~ = ζ 1 ζ 2 θ (A + 1- σ ) α ρ + γ ] ~ γ = α, θ =.8, m = σ =.2, β =.5 and ρ = yields: h = , Z ~ = , + characerisic roos. Leing 1=A=I=.6 µ ~ =.2212, ζ 1 = and ζ 2 =

20 accelerae he deerioraion of he free resource, hereby eliminaing he incenive o use he higher labor produciviy o obain more leisure. 27 2) As capial and labor grow more producive as a resul of echnological progress, he economy ends o be characerized by a higher long-run growh rae of capial and oupu, which compensaes for he faser degradaion of R. Therefore, a permanen improvemen in echnology ends o be associaed wih a higher seady-sae rae of saving. 28 Noe ha a seady sae he saving rae does no decrease even if privae wealh (capial) grows larger. This is because social wealh also comprises R, which declines a seady sae as K is accumulaed. 3) Seady-sae growh consiss in he progressive subsiuion of goods ha can be privaely appropriaed for commonly owned goods whose endowmen is declining. 29 4) Boh a larger populaion size (larger I) and a greaer impac of a given level of producion on he free resource (larger α ) end o boos long-run per capia growh, bu a he cos of a declining seady-sae level of household welfare. 30 In fac, everyhing ha exers greaer pressure on he free resource and acceleraes is decline induces individuals o reac by working and saving more. Thus, according o he model, policies which reduce populaion growh and he environmenal impac of producive aciviies resrain he long-erm per capia growh rae of he economy. 5) I is worh noing ha an insiuional shock causing a collapse of he free resource (a once and for all fall in R ) acceleraes growh. This acceleraion is only ransiory and in he long run he economy will resume he seady-sae per capia rae of growh deermined by is srucural feaures. As a permanen effec of his acceleraion, he economy ends o be endowed wih a higher capial sock a any fuure poin in ime. However, he ne expeced impac of such a shock on households lifeime well-being is 27 Leing 1=A=I= γ = α, θ =.8, m = σ =.2, β =.5 and ρ =.6, a 10% increase in A yields a 1.01% increase in ~ h, o a 23% increase in µ ~ and o a 6% increase in he seady-sae (gross) rae of saving. 28 See he previous noe. 29 In a seady sae wih µ ~ > 0, we have boh Y and R 0 as = A =, θ =.8, m = σ =.2, β =.5 and ρ =.6 γ, we have µ ~ =.2212 and U ~ = wih I = α = 1, while µ ~ =.2216 and U ~ = wih α = and I = 1 or wih I = and α = 1. 19

21 negaive, since as he economy moves back o seady sae individuals suffer from he welfare decline due o he fall in R. 31 6) As individuals discoun he fuure less heavily (higher θ ), seady-sae welfare ends o decline. 32 Households more anxious abou he fuure are inclined o save more in order o safeguard heir welfare (or he welfare of heir descendans in a dynasic framework) in anicipaion of deerioraion in he free resource. In so doing, hey accelerae boh he long-run growh rae of he economy and he deerioraion of R, hereby lowering heir seady-sae uiliy (and he uiliy of heir descendans). 7) In his economy, indeed, a higher long-run rae of growh of per capia oupu may be associaed wih a lower seady-sae level of uiliy 33. A benevolen planner would enjoin households o save less and o enjoy more leisure han hey would be inclined o do if hey aced in full auonomy, hus lowering he seady-sae rae of growh (see he Appendix). Possible exensions A huge amoun of empirical and heoreical research is required o find sysemaic evidence consisen wih he growh paradigm oulined in he paper and o enrich is formal foundaions. On he heoreical agenda, we give prioriy o exension of he model in wo direcions. Technological progress boh in he form of advances which boos he produciviy of labor and capial, and in he form of improvemens which reduce he impac of producion on free resources should be reaed as he oucome of agens behavior condiioned by insiuional consrains and public policies. Furhermore, a highly 31 Le he parameers values be 1=A=I= γ = α, m = σ =.2, θ =.8, β =.5 and ρ =.6, and suppose ha he economy is a is seady sae. In he absence of shock, he economy will grow a a consan rae µ ~ = Linearizing he sysem ha governs he moion of he economy around he seady sae, one can compue ha a 1.59% fall in Z will cause an immediae acceleraion of growh ( µ =.258 ) as he economy sars moving back o is seady sae (afer 4 periods, he capial sock is higher han i would be wihou he shock: 3 (1 ) (1 ~ ) 4 + µ + i = > + µ = ). This acceleraion is accompanied by a 5.26% fall in he sequence of i= 0 discouned uiliies of he firs 4 periods afer he shock. 32 Leing 1=A=I= γ = α, m = σ =.2, β =.5 and ρ =.6, we have µ ~ =.2212 and U ~ = wih θ =.8, while µ ~ =.27 and U ~ = -.4 wih θ = See he preceding noe. 20

22 promising line of inquiry would be examinaion of how wealh and income disribuion ineracs wih he growh mechanism described here. Appendix 1) Anoher example of an economy exhibiing endogenous growh only in he presence of negaive exernaliies Le g(l ) sill be given by (12) and specify f(x ) as f =. (A1) ( x ) x (4), (7), (8), (12) and (A1) can be used o obain he equaion ha ogeher wih (15) and (16) governs his economy in he absence of negaive exernaliies: 2 Again, i is eviden ha he sysem consising of (15)-(16) and (A2) has no fixed poin such ha µ = µ = 0 : in he absence of negaive exernaliies, neiher can his economy grow forever a a + 1 µ > consan rae. The unique seady sae of he economy wih a sricly posiive capial sock and wih R evolving according o (5a) is characerized by (18a), (18b), (18c) and 2 ~ 2 h = b/a - (b/a) - c/a, (A4b) 2 βa(1- h ) 1 Ah (1- ) - Z + µ = + σ. (A2) 2(1- ) β (Ah - σ )(1- β ) 2(1- β ) K =. (A3) R A(1- h) β One can check for reasonable parameer values ha he sysem obained by linearizing (15)-(16) and (A2) around his seady sae is saddle-pah sable, which suggess ha his economy has a unique opimal pah. In he presence of exernaliies, his economy moves along he pah governed by (16), (19) and (A2). Solving for he seady sae of his economy in he presence of negaive exernaliies, one obains (20a), (20b), ~ 2 ~ βa(1- h)z ~ x = (A4a) 2(1- β ) and Aβ θγ where c =, b = c + 2(1-θ )[1- ρθ (1- σ )] and a = c + 4(1-θ ) ρθa. Leing A = I = γ = α = 1, 2 αi(1- β ) m = σ =.2, θ =.8, β =.5 and ρ =.6 yields ~ h = and µ ~ = One can check ha he seady sae characerized by (20a), (20b), (A4a) and (A4b) is he unique seady sae of his economy, and ha he 21

23 wih respec o C, h, K +1 and R +1, where [ ], λ + i and ζ + i are he mulipliers, we obain he following condiions ha he opimal pah mus saisfy: (.) βr = λ, dx (A5a) sysem obained by linearizing he sysem of wo difference equaions governing he moion of he economy in a neighborhood of his seady sae is saddle-pah sable. Also in his case, he model has he implicaions discussed in he ex. 2) The opimal pah seleced by a benevolen planner in he presence of negaive exernaliies A benevolen planner would inernalize he negaive exernaliies caused by producive aciviies. For simpliciy and wihou loss of generaliy, we normalize he large number of households o be one. Therefore, maximizing he Hamilonian i γ H = θ U + i λ+ i K + i+ 1 - AK + i h + i - (1-σ )K + i + C+ i + ζ + i R + i+ 1 - ρr + i - i 0 AK ih = α + + i (.) γζ (1- β ) dg = AK λ -, (A5b) dl αak h λ = λ ( Ah 1-σ ). + 1θ θγζ - αak h + 1 (A6a) and df (.) ζ = ζ + 1θρ + θβc+ 1. dx (A6b) lim θ + 1 The opimal pah mus also saisfy he laws of moion (4) and (5b), and he ransversaliy condiions λ K = 0 (A7a) and lim θ ζ R = 0. (A7b) Noe ha ζ capures he incremen in he discouned sequence of fuure uiliies ha he represenaive household can expec o obain during is lifeime hanks o a marginal increase in he curren endowmen of he free resource. Comparing (A5b) wih (7b) shows ha he benevolen planner also akes accoun of he negaive effec of a marginal incremen in working ime on he fuure endowmen of he free resource, and herefore ends o choose more leisure han each household would choose were i acing in full auonomy. Similarly, (A6a) can be compared wih (8): in evaluaing he expeced effec on households lifeime welfare 22