Participation, Growth and Social Poverty: Social Capital in a Homogeneous

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1 The Open Economic Journal, 2008,, -3 Open Acce Participation, Growth and Social Poverty: Social Capital in a Homogeneou Society Angelo Antoci *,, Pier Luigi Sacco 2 and Paolo Vanin 3 DEIR, Univerity of Saari, Italy 2 DADI, IUAV, Venice, Italy 3 Department of Economic, Univerity of Padova, Italy Abtract: We introduce ocial capital accumulation into a neoclaical model, howing how it differ from phyical and human capital accumulation. We take the view that ocial capital i crucial to the enjoyment of ocially provided good and that it i mainly accumulated by mean of participation to ocial activitie. Under-invetment in ocial capital may lead a growing economy to fall into a ocial poverty trap. We argue that thi rik i particularly relevant for advanced ocietie. JEL-Claification: D62, I3, J22, O4, Z3. eyword: Social capital, elf-protection choice, ocial poverty trap. INTRODUCTION Growth theory ha been typically concerned with the proce of phyical and human capital accumulation. More recently, much attention ha been devoted to the role played for growth by ocial capital, i.e. by thoe accumulated productive reource that are incorporated in the ocial tructure of a ociety (rather than in phyical good or in ingle individual. By it own nature, the proce of accumulation of ocial capital i quite different from that of other form of capital, becaue a large part of it payoff i not privately appropriable. Thu, individual may not have an adequate incentive to accumulate it. We invetigate the dynamic of ocial capital accumulation within a neoclaical framework and how that under-invetment in ocial capital may lead an economy to a ocial poverty trap. We take the view that ocial capital i crucial to the enjoyment of ocially provided good and that it i mainly accumulated by mean of participation to ocial activitie. Such participation, and the good it provide, may be ubtituted for by ome private activitie, which generate private good. Since mot private good enter in the GNP, wherea many ocially provided good don t, thi ubtitution proce may foter growth exactly a the flip ide of a proce of ocial impoverihment. The choice of how to allocate time between ocial and private activitie ha two external effect: a direct one, on the productivity of other people ocial activitie at a given point in time, and a *Addre correpondence to thi author at the DEIR, Univerity of Saari, Italy; Tel: ; Fax: ; angelo.antoci@virgilio.it We would like to thank Antonio Cabrale, Antonio Ciccone, Benedetto Gui, Giorgio Rampa and Joel Shapiro for helpful dicuion and comment, a well a the audience to eminar in Padova, Pavia and Barcelona, with the uual diclaimer. cumulative one, on ocial capital accumulation over time. If individual are not able to internalize thee externalitie, the overall outcome of their choice may be ub-optimal, notwithtanding the fact that they are generating economic growth. We interpret the poibility that growth and ocial impoverihment move together a relevant in the medium run, i.e. in a time horizon in which the choice of time allocation may change ignificantly, but which till i horter than the very long run, ince in the latter ocial impoverihment render growth unutainable. We conider a ociety with homogeneou population, which empirically turn out to be the mot favorable environment for ocial capital accumulation. Moreover, we diregard any contribution of ocial capital to the production of private good, although uch contribution are empirically relevant. A a conequence, the rik of falling into a ocial poverty trap that we find in our model would hold a fortiori if one take into account a egmented population and the relationhip between ocial capital and private production. The proce we are invetigating i particularly relevant for affluent ocietie, where preure on time and other factor may indeed lead to a ubtitution of time-aving private activitie for timeintenive ocial one. In a companion paper [Antoci, Sacco and Vanin (2007], we tudy the ame proce within the context of an evolutionary model. Both the neoclaical and the evolutionary approach lead to analogou concluion. In another companion paper [Antoci, Sacco and Vanin (2005], we how that the baic reult we find here alo extend to a more complex et-up, with both private and ocial capital accumulation. Therefore, while in the preent context we model growth jut in term of an expanion in private production, explicit conideration of a private accumulable aet would not change the picture. The advantage of / Bentham Open

2 2 The Open Economic Journal, 2008, Volume Antoci et al. focuing on ocial capital alone i that in the preent paper we are able to characterize the dynamic analyi for any poible parameter configuration. In Section 2 we conider the literature on ocial capital and growth and relate our work to it. Section 3 invetigate the link between growth and ocial impoverihment. Section 4 diplay the model and it reult. Section 5 conclude. SOCIAL CAPITAL AND GROWTH In the lat two decade economit have been paying a lot of attention to the role of ocial capital for growth. The term ocial capital wa rendered popular by Coleman and Putnam and the World Bank (2008 ha an entire electronic library on the topic. Coleman (988, 990 mention a example of ocial capital the level of trut and the information potential incorporated in relation, the exitence of civic norm with effective anction, and the preence of hierarchical and horizontal relation and organization. Putnam (993 make the point that a richer network of civic engagement and of horizontal organization (thi way he define ocial capital explain much of the economic advantage of Northern Italy over Southern Italy. Putnam (995 and 2000 argue that ocial capital ha been declining in the U.S. in the lat thirty year, mainly due to the impact of televiion and to the aging of a generation with a trong civic commitment. Different author emphaize different apect of ocial capital and the literature may be divided into two main branche, according to whether ocial capital i defined at the individual level or at the group level 2. To the firt branch, pioneered by Coleman, belong, for intance, Glaeer, Laibon and Sacerdote (2002 and DiPaquale and Glaeer (999, who invetigate individual ocial capital and focu on individual invetment in ocial kill and in connection to other, repectively. Both ocial kill and ocial connection yield a private return: for intance, Becker (98 offer a claical example of the return to ocial kill in the marriage market and Granovetter (973 how the relevance of weak connection to find a job. Group level definition of ocial capital focu on the economic impact either of trut and civic norm or of voluntary aociation and horizontal organization 3. Paldam and Svenden (2000 ummarize a line of thought that goe from Arrow (97 to Fukuyama (995 and emphaize that the denity of trut in a group or in a ociety influence Cota and ahn (2003 how that the decline in the ocial capital produced outide home i mainly due to riing community heterogeneity (epecially income inequality, wherea the decline of the ocial capital produced at home i mainly explained by women increaed labor force participation rate. 2 At the highet level of generality, Narayan (999 define ocial capital a the norm and ocial relation embedded in the ocial tructure of ocietie that enable people to coordinate action to achieve deired goal. 3 Collier (998 ditinguihe among ocial capital created in different group, i.e., at different intitutional level: family, firm, government and civil ociety. Narayan (999 point out that the relation between governmental ervice and ocial capital i not univocally of ubtitution or of complementarity. Bowle and Ginti (2002 make imilar conideration, but they criticize the term ocial capital. economic outcome becaue it determine how eaily people work together. The empirical relevance of ocial capital for growth ha been highlighted, among other, by nack and eefer (997, Temple and Johnon (998, Zak and nack (200 and nack (2003. The broad meage of thi literature i that generalized trut ha a trong and robut poitive impact on growth 4. On the other ide, although ocial participation foter trut, it growth impact doe not appear to be relevant. In other word, mot effect of ocial participation remain confined to the ocial phere 5, wherea trut directly affect growth. Different form of ocial capital may have different effect. Social capital tend to exert poitive aggregate effect when trut, norm and network that foter cooperation extend beyond primary, ethnic, linguitic or even income group and form bridge among different group. Thi lat point i made with particular trength by Narayan (999, who oberve that the ame link that keep together the member of a group may alo exclude the non-member, and who diplay an analytical framework to tudy bonding (intra-group and bridging (inter-group link. On a imilar line, Annen (200 adapt Spagnolo (999 model to tudy the different impact of incluive and excluive ocial capital (defined in term of entry cot into ocial network. He argue that incluive ocial capital can combine high gain from trade with low enforcement cot, thereby raiing economic performance, wherea excluive ocial capital may impede growth by limiting gain from trade and diffuion of new idea, a well a by generating rent-eeking. The different impact of different ocial network on private activitie with poitive external effect i alo emphaized by Nepal, Bohara and Berren (2007. Yet they focu on private contribution to environmental capital, wherea our focu i on ocial capital accumulation. A number of contribution tackle the iue of how ocial capital, in it variou form, i accumulated. Glaeer, Laibon and Sacerdote (2002 how theoretically and empirically that individual invet in ocial kill in the ame way a they do in human capital 6. DiPaquale and Glaeer (999 diplay a model predicting that homeowner invet more than renter both in ocial connection and in local amenitie. The data confirm thi prediction and how that the main reaon i that homeownerhip decreae mobility. Aleina and La Ferrara (2002, Zak and nack (200, nack and eefer (997 and Glaeer, Laibon, Scheinkman and Soutter (2000 all find empirically that ocial heterogeneity and ocial ditance, in term of income, race 4 The empirical problem of meauring trut ha been deeply addreed by Glaeer et al. (2000, who find that tandard urvey quetion about trut provide a better meaure of trutworthine than of truting behavior. However, Berg, Dickhaut and McCabe (995 preent experimental evidence that higher trut increae trutworthine. Indeed, thee two apect are highly correlated. 5 Jut to give two example, Leung (2002 find that everal form of ocial participation reduce the probability of becoming a delinquent and Buonanno, Montolio and Vanin (2008 find that ocial capital reduce property crime. 6 Since they call ocial capital the ocial component of human capital, their reult i not urpriing.

3 Participation, Growth and Social Poverty The Open Economic Journal, 2008, Volume 3 and ethnic origin, reduce trut. Aleina and La Ferrara (2000 focu on the effect of heterogeneity on participation in aociational activitie like religiou group, port group, hobby club, union, and o on. Uing data for metropolitan area in the U.S. from 974 to 994 and controlling for individual and community characteritic, they how that ocial participation i higher where income inequality, racial egmentation and ethnic egmentation are lower 7. Summing up, heterogeneity ha a negative effect on both ocial participation and trut, but while trut ha a poitive effect on economic outcome, participation ha mainly ocial effect. We retrict our attention to a homogeneou ociety and to the time allocation choice between private and ocial activitie. We argue that aggregate ocial participation today increae the productivity of the time pent in ocial activitie both today and tomorrow, ince it contribute to the formation of a better, ocially more rewarding environment. In other word, it contribute to ocial capital accumulation. Invetment in ocial capital take here the primary form of time invetment in ocial activitie and it cot can be meaured in term of forgone private conumption. A mentioned above, Glaeer, Laibon and Sacerdote (2002 diplay a neoclaical model of invetment in ocial capital. The main difference between their model and our arie from the fact that what they call ocial capital i the ocial component of individual human capital, wherea we look at ocial capital from an aggregate point of view. In our framework, individual forgo private conumption and undertake ocial activitie primarily becaue they eek ocially provided good. Social capital accumulation emerge a a by-product, a an external effect 8. Such apect make the proce of ocial capital accumulation quite different from phyical and human capital accumulation. We emphaize thi point and how how it tranlate into an otherwie tandard neoclaical model. Routledge and von Amberg (2003 preent a model which i very cloe in pirit to our to tudy the effect of technological change on labor mobility and, a a by-product, on ocial capital, but they do not preent an explicit dynamic model of ocial capital accumulation, which i preciely one of the main contribution of our paper. GROWTH AND SOCIAL IMPOVERISHMENT We tart with the conideration that individual have material and relational need. Mot of the firt one may be 7 Thi happen in the North/Northwet of the U.S., the oppoite feature appearing in the South/Southeat. Moreover, looking at participation in different kind of group, they find that heterogeneity matter le for participation in group with a relatively high degree of excludability or a low degree of cloe interaction among member. Finally, they find that racial egmentation matter more for individual more avere to racial mixing. 8 Indeed, it i a common feature of non-material form of capital that invetment and conumption come cloe to one another: think e.g. of knowledge. In the cae of ocial capital omething imilar happen: to ome extent individual participate to ocial activitie with an intentional purpoe to invet in relation, but to ome extent participation i more a conumption than an invetment activity, where the good conumed are relational rather than private. atified by private conumption activitie, wherea the econd one are motly atified by ocially provided good. Thee good are referred to by Uhlaner (989 a relational good ; other author, e.g. Corneo and Jeanne (999, prefer to peak of ocially provided private good 9. We make ue of either terminology. Example of relational good include friendhip and enjoyment of hared leiure 0. Two peculiar apect of relational good are that they cannot be enjoyed alone and that it i motly very difficult to eparate their production form their conumption, ince they eaily coincide. Indeed, not only conumer and producer are the ame agent, but ocial participation produce relational good at the ame time that it let participant conume them, i.e. enjoy them: relational good are a pecial cae of Corne and Sandler (984 joint production model. Relational good are carce good becaue their enjoyment i ubject to a time budget contraint (poibly alo to a monetary budget contraint, but we focu on the firt one. They are brought about by participation to ocial activitie, which are time-intenive. At leat ince Becker (965 pioneering contribution, we know that time i a carce reource and that an increaed preure on it (an increae in the value of time lead to a ubtitution of time-aving activitie for time-intenive one. Growth itelf bring about an increae in the opportunity cot of time, which i clearly more expenive today in advanced ocietie than it ued to be in the pat 2. An early account of thi proce i provided by Hirch (976: A the ubjective cot of time rie, preure for pecific balancing of peronal advantage in ocial relationhip will increae. Perception of the time pent in ocial relationhip a a cot i itelf a product of privatized affluence. The effect i to whittle down the amount of friendhip and ocial contact. The huge increae in peronal mobility in modern economie add to the problem by making ociability more of a public and le of a private good. The more people move, the lower are the chance of ocial contact being reciprocated directly on a bilateral bai (Hirch 976, p. 80. The relevance of the lat point, i.e., of peronal mobility, for the ubtitution of private for ocial activitie, i alo invetigated by Schiff (992 and 999 and by the above mentioned contribution by Routledge and von Amberg (2003 and by DiPaquale and Glaeer (999. When thi ubtitution take place, we may oberve at the ame time ocial impoverihment and private growth, a, according to Putnam (2000, we have indeed oberved in the U.S. in the lat three decade of the XX century. The overall effect in term of well-being may be either negative (o that we can 9 They argue that the deire of uch good may lead individual to invet more in their own human capital and may thu have a poitive impact on growth. 0 Survey data on time ue, on the frequency of friend meeting and on participation to variou aociation, eaily available in everal countrie, may be ued to contruct empirical proxie of relational good. Fat-food are ucceful becaue they are fat, not becaue they offer good food! 2 It may be argued that ocially provided good become carce in affluent ocietie, when growth, increaing the value of time, render the time budget contraint binding.

4 4 The Open Economic Journal, 2008, Volume Antoci et al. peak of ocial poverty trap, becaue efficiency gain may be outweighted by the lo in ocial capital, or poitive, when the revere happen 3. For the ake of concretene, in the model we identify private activitie with the time pent working or conuming and ocial activitie with the time pent in ocial participation outide the job. Of coure, we are aware of the ocializing value of working, a well a of the fact that working i almot never a truly private activity, ince it require cooperation with other people, but, a hown empirically by Aleina and La Ferrara (2000, among employed people there i a negative relation between the time pent in ocial participation and in private production. Moreover, our interpretation correpond to the tandard view that labor time i a bad and not a good and, ince in our model there i no unemployment, we feel that thi i a good firt approximation. THE MODEL Preference and Technology We conider an economy contituted by a continuou population of identical individual (indicated a [0,], who every day (we model day in continuou time, indicate them with t and normalize their length to chooe how to allocate their time between private and ocial activitie. In day t, the fraction of time pent by individual in ocial activitie, (t, provide him or her utility in the form of a ocially provided good B (t, whoe amount depend, beide on (t, on average ocial participation, (t= (td, and on the quality of the ocial 0 environment inherited from the pat, i.e., on ocial capital (t. We aume that there i a private good C (t which i a perfect ubtitute of the relational good B (t and we denote l (t the fraction of time pent by to produce and conume C (t. Finally, individual atify their ubitence need by devoting time l (t to produce and conume a ubitence good C (t. We think of the activitie of production and conumption of C (t and of C (t a of private activitie. We aume that C (t and C (t are not accumulable and let the intantaneou individual utility function be: u (t=ln[c (t] + b ln[b (t + ac (t], ( where a >0 i the marginal rate of ubtitution between B (t and C (t, and b >0 capture the relative weight attributed to non-ubitence v ubitence need. 3 We acknowledge that mobility might improve orting and the potential quality of ocial matche, but we emphaize that it may reduce the time available to build relationhip-pecific ocial capital and it may ubtantially faten it depreciation. Thi correpond to the common experience of migrant and of cholar tudying or working abroad. We aume linear technologie in the production of private good and a Cobb-Dougla technology in the production of the relational good: C (t=l (t, >0, (2 C (t=l (t, >0, (3 B (t= (t (t (t,,,, >0. (4 Social capital in thi economy i accumulated a individual pend time in ocial activitie and generate durable relation, which become the bai for the development of trut, civic norm and voluntary aociation. It eem therefore natural to model aggregate invetment in ocial capital I (t a an increaing function of the quantity of relational good produced (and conumed at a certain time in the economy, according to a ort of learning-bydoing mechanim. Perhap the eaiet way to model uch invetment i the following: I (t= B (td. (5 0 Notice that we ue the term invetment in analogy with what drive the accumulation of other form of capital. Neverthele, it ha to be treed that here individual do not invet time in ocial activitie with the purpoe of accumulating ocial capital, but rather to enjoy the relational good they get through participation to ocial activitie. Indeed, they conider ocial capital a a public good and they do not internalize the effect of their choice on it accumulation. Such accumulation appear therefore jut a a byproduct of activitie with different aim. Thi i indeed one of the firt intuition about ocial capital, already pointed out by Coleman. Since relation deteriorate if they are not taken care of, the full dynamic of ocial capital ha to incorporate a depreciation rate 0 : (t=i (t (t. (6 Individual Maximization Problem Let r be the rate at which individual dicount future utility. The individual maximization problem in our economy i then: max, l, l 0 u (te rt dt,.t. (7 (t, l (t, l (t 0, (t + l (t + l (t=, (t=i (t (t. The aociated Hamiltonian function i: H[ (t,l (t,l (t, (t,]=u (t + [I (t (t]. Since the population i continuou, the choice of (t by a ingle individual ha no impact on I (t, o that each

5 Participation, Growth and Social Poverty The Open Economic Journal, 2008, Volume 5 individual conider I (t a exogenou (notice that the ame i true for (t. Hence,, the hadow-price of, doe not appear in the condition for the maximization of the Hamiltonian function with repect to the control variable. A a conequence, thee condition coincide with thoe obtained for the maximization of u (t in each intant of time with repect to the ame control variable. We therefore omit the time index and, ince individual are identical, alo the index, and olve the repreentative individual pointwie problem: max u =ln(l + b ln( + al.t. (8, l, l, l, l 0, + l + l =. (9 Remark Since contraint (9 determine a compact et and the objective function u i continuou, for any level of problem (8 - (9 ha a olution. The Lagrangean function i: L(, l, l, =ln(l + b ln( + al ( + l + l and the olution mut atify the following firt order condition (where we exploit the fact that ex pot = : L l L = l 0; L l =0, l 0; (0 l = L l = b al 0; ab + + al 0; L =0, 0; ( L l l =0, l 0; (2 + l + l =. (3 From the expreion of u in problem (8 it i immediate to conclude that the repreentative agent allocate hi or her time in uch a way that [l >0 ( >0 l >0] alway hold (o that we have 0<l <. Now, condition (0 implie l =. A traightforward ubtitution in the firt order condition then how that a neceary condition to have both >0 and l >0 i: + =0. (0 It i eay to how that condition (4 may define the repreentative agent optimal choice only if + <, wherea for + the repreentative agent chooe either or l equal to zero 4. We can thu eparate thee two cae. Cae (a: + If the repreentative agent chooe =0,l = l, it mut hold that L = b l l =0, o that: l l = + b, l = b + b. ( If the choice i intead uch that l =0, = l, it mut hold that L = b l =0, o that: l l = + b, = b + b. (2 Straightforward ubtitution of thee value in the utility function yield that choice (6 i trictly better than choice (5, if and only if: > ˆ ab( + b + + b. (3 (b + ( + b + b For < ˆ the repreentative agent chooe =0 and l >0, wherea for > ˆ he or he chooe >0 and l =0 5. Cae (b: + < When + <, lim B 0 =, o that the repreentative individual alway chooe >0, whatever the value of. Equation (4 then implie that for ufficiently high l =0 i choen, for ufficiently low intead l >0. The critical threhold may be determined by plugging l =0 and = into equation ( and (2 l and by equalizing L = L =0, o to obtain the value of l for which l =0 and = l, but the non-negativity contraint on i not yet binding. Thi yield: L L l = = b + + l = b =0, (8 ab + l = ab + =0. (9 Equation (8 implie = b, which, ubtituted in + b equation (9, yield: 5 For = ˆ the repreentative agent i indifferent between the two 4 If + >, condition (4 determine a local minimum intead of a local maximum, wherea, if + =, L i independent of and again we have either =0 or l =0. choice; whatever the choice, in = ˆ dynamic (22 below i dicontinuou from right. Notice that one could peculate on the effect of the parameter on ˆ, but at the preent tage they do not contitute our main focu. The ame will be valid with below.

6 6 The Open Economic Journal, 2008, Volume Antoci et al. ab = (b + ( + b. (4 For < the choice of and l i determined by equation (4 a: = a. (5 For it i determined by equation (6. Social Participation, Growth and Social Poverty Trap Taking into account the repreentative individual equilibrium choice, dynamic (6 become: (t=( +. (6 where ( i the following function 6 : Cae (a: + : ( = Cae (b: + <: ( = 0 < ˆ b ˆ + b a b + b < (23 (24 Remark 2 =0 i alway a fixed point of dynamic (22 and in uch tate the repreentative agent chooe = 0. Thi mean that both ocial capital and ocial participation are null, wherea production and conumption of private good reach their maximum. If relational good played no role in determining well-being, thi would be the bet poible outcome, but if we introduce relational concern in the utility function, uch a reult may be completely revered, a the next remark make clear. Remark 3 The fixed point with =0 i Paretodominated by any other point in which >0 and the repreentative agent chooe > 0. Moreover, if * ** and are two fixed point uch that ** > *, then * i Paretodominated by **. The firt part of Remark 3 follow from a traightforward ubtitution in the utility function. The intuition behind the econd tatement i a well traightforward, ince an increae in the level of amount to an expanion of the production and conumption poibility et. In fact, any choice of 6 Notice that in equation (23, when = ˆ, the repreentative individual i indifferent between =0 and = b, but the pecific value of + b choen in a ingle point i not relevant for dynamic (22; in equation (24 thi problem doe not even arie, ince it define in that cae ( i a continuou function., l, l that i poible under * i till poible under ** ; moreover, it provide at leat the ame utility and, if >0, a trictly higher utility. We can therefore introduce the following definition. * Definition 4 Let be the highet value of in a locally attracting fixed point of dynamic (22. We call ocial poverty trap any other fixed point uch that < *, if exiting. It i perhap ueful to tre again at thi point that we are ignoring the poible double link between ocial capital and private production activitie: empirical reearch how that ocial capital increae private production and growth; on the other hand, the-job interaction might generate ocial capital, in the ame way a ocial interaction. The firt link, if conidered, would reinforce our definition of ocial poverty trap, wherea the econd one would make it le compelling. Recall from our dicuion in the previou ection that, if we neglect unemployment, a negative relation emerge between working time and ocial participation, o that the firt link eem to prevail. An additional argument may come from the obervation that voluntary ocial participation uually involve a higher degree of internal pro-ocial motivation than working activitie, which play a key role in the development of trut. The empirical and the motivational argument, taken together, make u confident that the omitted link i more likely to reinforce our definition of ocial poverty trap than to weaken it. Dynamic of Social Capital Accumulation In the Appendix we claify dynamic (22 under (23 (24, taking into account all the poible combination of parameter value. Here we focu on jut one cae of particular interet. Aumption 5 Aume + <, <, + + > and let be mall 7. In thi cae, a hown in Fig. (4 of the Appendix, that we reproduce here for eae of reading, there exit two locally attracting fixed point, one with no ocial capital, which contitute a ocial poverty trap, and a Pareto-uperior one with poitive ocial capital 8. Their attraction bain are eparated by a repulive fixed point. If initial ocial capital i above thi threhold, the economy converge to the fixed point with a poitive tock of ocial capital. Now oberve that along decreaing path of private production and conumption increae, wherea ocial participation decreae. 7 + < mean that we are in cae (b: intuitively, we can think of thi aumption in term of decreaing return to cale of ocial participation, even though thi i not literally correct, ince ocial participation i a fraction [0,]. < mean that ocial capital ha decreaing return to cale in the production of B. + + > reemble the idea of aggregate increaing return to cale in the production of B. A mall mean that ocial capital doe not depreciate too fat. 8 In the figure we call f ( [( ] +, where ( i given by equation (23 and (24, o that = f (.

7 Participation, Growth and Social Poverty The Open Economic Journal, 2008, Volume 7 Therefore, if convergence take place from below, we have ocial development at the expene of private activitie; if it take place from above, along the convergence path we oberve an expanion of private activitie. If initial ocial capital i below the threhold, the economy experience an expanion of private activitie along the convergence path, but converge to the Pareto-inferior fixed point, i.e., to the ocial poverty trap. The role of ocial capital depreciation rate i to move the threhold: the fater ocial capital depreciate, the larger the attraction bain of the ocial poverty trap. Indeed, if i too high, the attractor with poitive ocial capital diappear. f( η f( participation, i.e. take into account the effect of their own participation on average ocial participation today, and thereby on the amount of ocially provided good they enjoy themelve today, and on ocial capital accumulation, and thereby on the amount of relational good they will be able to enjoy tomorrow. Such aim can probably be achieved to ome extent through educational policy. Notice that reward cheme of a Pigouvian kind could in principle olve the direct externality problem, ince thi would only require information about technology, but to olve the cumulative externality problem the public authority need to know the individual intertemporal dicount rate. Moreover, beide all the traditional problem aociated to thee policy intrument, a further problem i generated by the role of intrinic motivation in determining ocial participation. A pointed out by Gneezy and Rutichini (2000, incentive may have the effect of changing the way people frame a ituation (for intance they can let individual re-interpret a nonmarket good in market term, o that they can crowd out intrinic (or ocial motivation. Since voluntary ocial participation doe not belong to the cla of market activitie, one hould be careful in applying incentive cheme that have been deigned to operate within the cope of the market. CONCLUSION * The poibility of two attractor, one of which i a ocial poverty trap. Policy Speculation Even though the preent framework doe not allow to formulate olid policy concluion, it doe allow to make ome policy peculation. It eem plauible to think that the peed of ocial capital depreciation i trictly related to the degree in individual mobility of a ociety. From thi point of view, our framework lead, through a different way, to the ame point of Schiff (992 analyi of the impact of labor mobility on ocial capital and welfare. Our reult i alo in accordance to Schiff (999 and 2002 dicuion of the difference between the two main form of factor mobility: migration and trade. While the former one ha relevant and often overlooked ocial conequence, the ame i not true for the latter one. The bottom line of thi dicuion i not to argue againt individual mobility, ince it poitive apect have not been taken into account here. Rather, it i to tre that the evaluation of it well-being conequence hould take into account it effect on ocial capital and enjoyment of relational good. A we have een, beide the problem generated by a high ocial capital depreciation rate, there i the problem determined by the preence of externalitie. If policy ha any cope from thi point of view, it hould be to let individual internalize the direct and the indirect externality of ocial The baic argument driving the preent model tart with the recognition that individual well-being depend on atifaction of both material and relational need. The firt one may be atified to a great extent through private activitie, wherea the econd one may only be atified by participating to ocial activitie. The outcome of private activitie typically enter in the GDP, but much of the outcome of ocial activitie, namely what we call relational good, doe not. Moreover, ocial participation generate a direct externality, in that it raie the productivity of the time other individual pend in ocial activitie, and a cumulative externality, in that it contribute to the formation of ocial capital. Social capital poitively increae the return to both private and ocial activitie, but we jut concentrate on the latter effect, arguing that our baic reult would till hold if we conidered the former one a well. Our baic reult can be tated a follow: even with a homogeneou population of optimizing agent, an economy may get tuck in a ocial poverty trap, i.e., in a Paretodominated equilibrium, if it initial tock of ocial capital i too low or if the depreciation rate of ocial capital i too high. Along the tranition path toward a ocial poverty trap an economy may experience at the ame time private growth, regitered in national accounting, and ocial impoverihment. The reaon why optimizing agent may fail to reach the optimum i traightforward: they are not able to internalize the direct and cumulative external effect of their action. In particular, we focu on the poibility of ubtituting ome kind of private good for relational good. When individual operate uch ubtitution they do not calculate that ome poitive externalitie go lot. We argue that thi ubtitution proce may be of empirical relevance epecially for advanced economie: ince ocial activitie are typically

8 8 The Open Economic Journal, 2008, Volume Antoci et al. time-intenive, the increaing preure on time experienced by advanced ocietie provide a trong incentive to ubtitute time-aving private activity for ocial participation. Moreover, the proce may be elf-feeding, becaue when an economy i experiencing at the ame time private growth and a decline in ocial participation and ocial capital, the time pent in ocial activitie become both more expenive (in term of opportunity cot and le productive (in term of relational good. Thi framework allow policy peculation on the impact of labor mobility on well-being through it effect on ocial capital depreciation rate and on the poibility and the difficulty to provide adequate incentive to ocial participation. In two companion paper [Antoci, Sacco and Vanin (2007 and 2005] we invetigate thi proce within the framework of an evolutionary growth model and introducing private capital accumulation beide ocial capital accumulation, repectively. Both extenion confirm the validity of the baic reult that under-invetment in ocial capital may lead a growing economy to fall into a ocial poverty trap. Empirical tet of the theory and theoretical tudy of a heterogeneou population are in our future reearch agenda. APPENDIX Cae (a: + In thi cae equation (22 and (23 imply: = b + b + < ˆ ˆ (7 Notice firt that if =0, i.e. if we neglect the role of depreciation of ocial capital, we have that every value [0, ˆ i a fixed point, wherea tarting from higher initial value of ocial capital (0 ˆ we have. The extenion of the locu of ocial poverty trap i then determined by the parameter that affect ˆ, identified in equation (7. Let u now aume that ocial capital depreciate, i.e. 9. We can then ditinguih the following ubcae. > 0 (a.: >. With increaing marginal productivity of, we have the three cae illutrated in Fig. (2-4, there are alway two attractor, =0 and =. For low value of (Fig.,2 the repective attraction bain are eparated by ˆ (in Fig. (2 ˆ i a repulive fixed point, in Fig. ( it i not a fixed point; for high value of (Fig. 3 they are eparated by a repulive fixed point > ˆ, which mean that a higher depreciation rate expand the bain of attraction of ocial poverty. f( Fig. (. f( Fig. (2. f( f( η f( f( η η 9 The aumption of linear depreciation, proportional to the exiting tock of, i the eaiet and mot immediate one, but other form of depreciation, poibly more realitic, could be conceived a well. Fig. (3.

9 Participation, Growth and Social Poverty The Open Economic Journal, 2008, Volume 9 (a.2: =. With contant return to cale of ocial capital in the production of relational good, low value of (Fig. 4 are again aociated with the preence of the attractor =0 and =, eparated by ˆ (which i b not a fixed point. The intermediate value = + b (Fig. 5 render all [ ˆ, fixed point; [0, ˆ i the attraction bain of the ocial poverty trap =0. Finally, for higher value of (Fig. 6, =0 become globally attracting. Notice that in thi lat cae we do not peak any more of a ocial poverty trap, ince there i no way the economy can avoid it, unle the primitive, i.e. preference and technology, change. On the contrary, when ocial poverty trap are preent, i.e. when there are two or more locally attracting fixed point, in which one of them the economy end up depend crucially on it initial endowment of ocial capital: different previou hitorie, reflected in different initial endowment, explain why otherwie identical economie may end up with completely different ocial and cultural tructure, in term of allocation of time between the ocial and the private phere. f( + Fig. (6. f( (a.3: <. With decreaing return to cale to ocial capital, = i never an attractor. For low value of (Fig. 7 there are two locally attracting fixed point, =0 and > ˆ, whoe attraction bain are repectively [0, ˆ and [ ˆ, ; a increae, firt converge to ˆ, until it reache thi value (Fig. 8, then, for even higher value of (Fig. 9, =0 become the only, globally attracting fixed point. f( η f( f( η η f( Fig. (4. f( Fig. (7. f( η, f( η f( Fig. (5. Fig. (8.

10 0 The Open Economic Journal, 2008, Volume Antoci et al. f( η (0, i the attraction bain of the ocial poverty trap =0. For even higher value of (Fig. 3, =0 become the only, globally attracting fixed point. f( f( f( η Fig. (9. Cae (b: + < In thi cae equation (22 and (24 imply: a = b + b + + < (8 Fig. (0. f( It i eay to how that equation (26 define a a continuou function of (in particular, it i continuou at, even if it i not derivable at thi point. Let u now conider the exponent of for < ; ince >, then if, it hold >; if <, it hold + +, i.e. when the function G(,, = ha either contant return to cale (cae + + = or increaing return to cale (cae + + >. In the following claification we conider all thee cae and omit for implicity thoe one which are not robut, meaning that a light change in the parameter modifie qualitatively dynamic (26. Fig. (. f( f( η (b.: >. There alway exit a repulive fixed point which eparate the attraction bain of the ocial poverty trap =0 from the tate of the economy tarting from which (Fig. 0; may be greater, equal or le than. An increae of the depreciation rate ha the effect of expanding the attraction bain of =0. η f(, (b.2: =. In thi cae, for low value of (Fig. a repulive fixed point < eparate the attraction bain of the ocial poverty trap =0 from that of =. A ; when it reache thi increae, converge to value (Fig. 2, all (, are fixed point, wherea Fig. (2.

11 Participation, Growth and Social Poverty The Open Economic Journal, 2008, Volume f( reache it (Fig. 8 we have a egment [0, of fixed point which correpond to ocial poverty trap and the fixed point whoe bain of attraction i [,. Higher value of (Fig. 9 render =0 globally attracting. f( η f( η f( Fig. (3. (b.3: <. We have now to ditinguih among the following ubcae. (b.3.: + + >. In thi cae, a in cae (a.3, = i never an attractor. For low value of (Fig. 4 there are two locally attracting fixed point, =0 and * >, whoe attraction bain are eparated by a Fig. (5. f( repulive fixed point < and are repectively [0, and (,. A increae, and * converge to each other, until the ituation decribed in Fig. (5 i reached. For even higher value of (Fig. 6, = 0 become the only globally attracting fixed point. η f( f( η f( Fig. (6. f( Fig. (4. (b.3.2: + + =. In thi cae, once again, = i never an attractor. For low (Fig. 7, there exit a fixed * η f( point > whoe attraction bain i (0, : any economy with a poitive initial ocial capital end up there; of coure, =0 i till a fixed point, but it i now repulive. A grow, converge to and when it Fig. (7.

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