Economic growth and inequality patterns in the presence of costly technology adoption and uncertainty

Transcription

1 Economic growt and inequay patterns in te presence of costy tecnoogy adoption and uncertainty y Ziv Cinzara Queensand Universy of Tecnoogy and Radika Lairi Queensand Universy of Tecnoogy January 202 bstract e deveop a stocastic endogenous growt mode to expain te diversy in growt and inequay patterns and te non-convergence of incomes in transiona economies were an underdeveoped financia sector imposes an impic, fixed cost on te diversification of idiosyncratic risk. In te mode endogenous growt occurs troug pysica and uman capa deepening, w te atter being te more dominant eement. e interpret te fixed cost as a earning by doing cost for entrepreneurs wo undertake risk in te absence of we deveoped financia markets and instutions tat ep diversify suc risk. s suc, tis cost may be interpreted as te impic returns foregone due to te ack of diversification opportunies tat woud oterwise ave been avaiabe, ad suc instutions been present. Te anaytica and numerica resuts of te mode suggest tree growt outcomes depending on te productivy differences between te projects and te fixed cost associated w te more productive project. e abe tese outcomes as poverty trap, dua economy and baanced growt. Furter anaysis of tese tree outcomes igigts te existence of a diversy win diversy. Specificay, win te poverty trap and dua economy scenarios growt and inequay patterns differ, depending on te inia condions. Tis addiona diversy aows te mode to capture a ricer range of outcomes tat are consistent w te empirica experience of severa transiona economies.

2 . Introduction Since te ate 980s most transiona economies embarked on a series of structura, instutiona and poicy reforms. Tese reforms were mainy meant to remove repressive poicies and started troug te ord ank-sponsored structura adjustment programs (SPs). ie tese reforms focussed on various sectors of te economy, te reforms tat te current study is particuary concerned w are tose w regard to te domestic financia sector. mong tese domestic reforms incude te privatisation and dereguation of te banking sector, te remova of interest rate and cred contros, and te dereguation of financia markets. Tere as been a debate about te impact of tese reforms on te economy. Krugman (995), Edwards (995) and urki and Edwards (995) observe tat tat despe widespread economic reforms, Latin merican economies made te progress in terms of economic growt and poverty eradication. However, atoug De Gregorio and Guidotti (995) aso provide pane regression evidence consistent w te above observations for te Latin merican countries, tey argue tat te negative reation between financia intermediation and economic growt migt be refective of te roe payed by te financia crises experienced by severa countries in te region. Furtermore, a study on East frican deveoping countries by te Uned Nations (2008) documents evidence sowing tat economic deveopment improved w reforms in five countries, wie worsened in two countries. Te debate as not ony been imed to te growt and poverty reduction effects of tese reforms, but aso teir income-redistribution effects. Financia reforms are ikey to improve income distribution if tey improve te access of te poor to finance. However, is possibe tat te benefs of reforms may disproportionatey accrue to te ric and te more skied wo are abe to prompty take te capa-intensive tecnoogica opportunies tat are brougt about by te reforms (Sabaz and Isam, 20). tencourt (2009) documents evidence tat financia deveopment, as measured by increased access to finance, improved income distribution in razi in te 980s and te 990s. Simiary, using a pane of 22 frican countries, atuo, et a. (200) provide evidence tat te financia deveopment was associated w a reduction in te Gini coefficients in te period covering most of te financia reforms. However, Caderon and Serven (2003) estabis tat financia deveopment worsens te income distribution. Simiary, Lopez (2004) documents pane econometric evidence tat ow and stabe infation and education are associated w a 2

3 decrease in inequay, wie financia deveopment and ow government expendure are associated w worsening eves of inequay. Te empirica evidence reviewed above sows tat te growt and inequay experiences of transiona economies during and just after introducing structura and instutiona reforms exib a great dea of diversy. eow we aso present some descriptive and pairwise correation evidence wic seems to be supportive of tis penomenon. Firsty, we anayse te correation between a measure of te financia reforms and growt in GDP for transiona economies in different regions. Secondy, we anayse trends in inequay in a seected group of transiona economies during and after reforms. Measuring te eve of financia reforms is a caenging issue. However, tere is widespread consensus tat financia reforms posivey enance financia deveopment (see Kein and Oivei, 999, De Gregorio, 998). Tus, we use financia deveopment as an indirect proxy for te financia reforms. commony used measure of financia deveopment is te vaue of cred tat banks provide to te private sector as a percentage of GDP. 2 In Figure (a) we pot te correation between te ogarm of tis measure and GDP growt for te period s evident in Figure (a), te correation between FD and GDP growt win tis period ad generay been posive for ow income countries. However, wen we break te ow income countries according to regions, becomes cear tat te correation varies from region to region. For East sian and SS deveoping countries, te correation between financia deveopment and GD growt exibs a posive trend, wie for Europe and Centra sia, Latin merica and Caribbean, and Midde East and Nort frica (MEN) deveoping countries, te correation exibs a negative trend. In Figure (b), we anayse te beaviour of inequay as measured by te Gini coefficient for six transiona economies from te ate 980s to te eary 2000s. Te grapica pots of te Gini coefficient sow tat, on average, inequay as decreased for razi and Taiand, wie as increased for rgentina, Costa Rica, Uruguay and Croatia. Moreover, te pots sow tat some countries suc as Taiand and Costa Rica are caracterised by ig fuctuations in inequay, wie in oter countries suc as rgentina, Croatia and Uruguay te canges in inequay are muc smooter. e do not perform tis anaysis region by region because of data constraints. Moreover, due to data constraints we coud not ook at countries in te Midde East Nort frica (MEN) and sub-saaran frica (SS) regions. 2 toug stock market capaisation as a percentage of GDP is aso used as a measure of financia deveopment, bank cred to te private sector is te most appropriate given tat deveoping stock markets are very sma, iiquid, inactive, and tere is very te participation by te genera pubic. 3

4 6 Low Income Countries: East sia Deveoping: GDP growt Log of Financia Deveopment -2 GDP growt Log of Financia Deveopment GDP growt Europe and Centra sia Deveoping Countries: Log of Financia Deveopment GDP growt Latin merica and Carribian Deveoping Countries: Log of Financia Deveopment GDP growt MEN deveoping countries Log of Financia Deveopment GDP growt Sub-Saaran frican Deveoping Countries Log of Financia Deveopment Figure (a): Correation etween financia deveopment and growt 4

5 rgentina 64.0 razi Year Year Gini Coefficient Costa Rica Year Gini Coefficient 48.0 Uruguay Year Gini Coefficient Gini Coefficient Croatia Year Taiand Year Gini Coefficient Gini Coefficient Figure (b): Trends in Income Inequay Given te foregoing discussion, becomes of interest to anayse wy te growt and inequay experiences of countries and regions sow suc diversy. Furtermore, te differences in period-to-period fuctuations in inequay across countries are of researc interest. Tus far, a number of expanations ave been suggested for te increase of inequay across countries/regions. Studies suc as Gomm and Ravikumar (992), Gomm and Paumbo (993), Ray and Streufert (993), Gaor and Mayer (2004), Cakraborty and 5

6 Das (2005), among oters, empasize te roe of uman capa accumuation as a source of persistence in inequay. Studies by Mokyr (993), Greenwood and Yorukogu (997), Perente and Prescott (994, 2004), Lairi and Ratnasiri (202), among oters, propose on te oter and tat non-convergence can be traced to differences in dates of tecnoogy adoption across nations. However, as discussed above, a monotonic increase in inequay is not te norm as far as te experience of some te countries in Figure (b) is concerned. Te current study, ten, is motivated by te diversy in growt and inequay experiences of countries as we as te differences in period-to-period fuctuations of inequay across countries. e seek to answer te question wy suc differences exist, and wy some countries continue to ave adverse growt and inequay experiences despe empirica evidence of te posive impact of economic reforms (see Godsm, 969, McKinnon, 973, Saw 973, King and Levine, 993, Fiscer et a., 996, Staer, 2005). To tis end we deveop a mode tat expores growt and inequay in an environment were inadequate financia reforms impose a fixed cost on te undertaking of ig-risk, ig-return projects. Put differenty, in te absence of we deveoped financia instutions, entrepreneurs face a earning by doing cost of adopting tecnoogies tat ave a ig return on average, but are associated w risk. Specificay, te mode deveoped is a simpe twoperiod ived overapping generations mode were endogenous growt takes pace troug pysica and uman capa deepening. In te mode, agents can invest in eer one of te two projects avaiabe in te economy; one tat is safe and ess productive and anoter tat is subject to uncertainty but more productive. Te atter project is te one associated w te earning-by-doing cost described above. ased on some of te teoretica outcomes of te mode as we as te resuts of numerica experiments, we are abe to expain a variety of outcomes in a unified framework. Firsty, we sow tat te diversy in growt and inequay outcomes of transiona economies can be traced to te differences in inia productivies of projects and te cost of adoption across countries. To eaborate furter on te nature of tis adoption cost, consists of te cost of earning by doing as we as te cost of returns foregone due te risk diversification opportunies tat woud oterwise ave been avaiabe, ad financia markets and instutions been we deveoped. e empasize tat tis cost is not necessariy imed to monetary vaue paid, but aso a time component representing te time spent earning and acquiring knowedge tat can ony be gained experientiay. Secondy, we sow tat persistence in cross-dynasty inequay can be traced to te deays in pysica and uman capa deepening by te poor dynasties due to teir imed inia resource endowment. feature of te mode is tat bot growt and inequay are subject to fuctuations over time. 6

7 Tese fuctuations are, in part, due to te presence of uncertainty, but intrinsic to te mode is te possibiy of reversas in te growt process, even if uncertainty were to be absent. Te current study is reated to a number of te studies. Firsty, ike Greenwood and Jovanovic (990) and Townsend and Ueda (2006) we expore te reationsip between growt, inequay and finance. However, unike tese studies we do not expicy mode financia intermediation, but rater focus on te growt and inequay outcomes of pysica and uman capa deepening in an environment were inadequate financia reforms pace a wedge on risk diversification. Secondy, ike tkinson and Stigz (980), Townsend (982), ardan et a. (2000) we indirecty expore te idea tat cross-dynasty inequay is exacerbated by te fact tat financia markets and instutions can faciate risk diversification, risk pooing and risk saring for ric dynasties tereby aowing tem to take ig-risk ig-return investment opportunies at te expense of te poor. However, our study does not expicy mode risk diversification. e are ony concerned about te impic cost of diversifying risk (i.e. in te context of time and resources spent in acquiring knowedge of businesses and projects tat are intrinsicay risky but yied a ig return) wen financia markets and instutions are ony partiay reformed. Tirdy, tis study is reated to severa strands of erature tat empasize te roe of uman capa deepening in expaining growt and inequay (see Lairi and Ratnasiri, 202 and references terein). However, wie tey interpret teir cost of uman capa deepening in te form of costs of earning new tecnoogies in te absence of risk, our interpretation is on earning of te type tat occurs in te presence of risk. More specificay, te mode as an K structure and is somewat simiar to te tecnoogy-adoption mode of Lairi and Ratnasiri (202), except tat in our mode te tecnoogy tat is (on average) more productive is subject to uncertainty. Consequenty, using our mode, we are abe to uneart some outcomes in addion to tose of te former mode. Specificay, te presence of uncertainty exacerbates te diversy of outcomes tat emerge from te mode. To eaborate on tis point, te bencmark mode of tis paper is a refinement of Lairi and Ratnasiri (202) and tis refinement adds vaue in te sense tat once aving stripped te mode of inessentias, addiona and sarper insigts emerge. In particuar, te addion of uncertainty in te mode eps interpret te experiences of some economies in a number of addiona and distinct ways to tose suggested in te mode by Lairi and Ratnasiri (202). For instance, our mode suggests tat te ig fuctuations in inequay in some economies discussed above suc as Taiand and Costa Rica may be inked to te existence of a ow cost of diversifying idiosyncratic risk wen te average productivies of projects subject to uncertainty are ig reative to safe projects. Secondy, unike in Lairi and 7

8 Ratnasiri (202) were te poverty traps and dua economy scenarios eac ave a singe type of equiibrium associated w a singe set of productivy parameters and adoption cost, our mode sows tat eac of tese two scenarios as more tan one type of equiibria, eac associated w different sets of productivy parameters and adoption costs. Furtermore eac of tese equiibria sows s own unique growt and inequay patterns, tus suggesting te existence of a diversy win diversy. In summary, te addion of uncertainty in te mode resuts in ricer range of growt and inequay patterns, tus enancing te mode s abiy to account for te diverse patterns tat are observed in te data. Te remainder of te paper is organised as foows. In Section 2, we describe te economic environment, particuary focussing on te teoretica impications of te genera version of te mode. In Section 3, we conduct some numerica experiments to iustrate te insigts derived from te anaysis presented in Section 2. Section 4 concudes te paper. Te appendix presents tecnica detais of te anaysis in Section Te Economic Environment Te economy consists of N two-period ived overapping generations of agents wose weat odings are eterogeneous. Eac agent is born w a un of unskied abour endowment tat can earn tem a subsistence wage,. part from te subsistence wage, an agent born in period t aso iners weat from teir parents in te form of bequests. is discrete, w t = 0,, 2,... Te inia distribution of weat is described by (. ). In eac period t, agents must decide wic among two projects tey soud invest in. e refer to tese projects, Project and Project. Investment in Project is bot cost-free and risk-free. However, tis project ess productive, giving a time-invariant return of. Project as a stocastic return, and is, on average, more productive tan Project. However, te investment in Project is subject to an exogenous investment cost, δ. Furtermore, te return on Project is divided into parts. Te first part of te return is certain. Te second part of te returnε t is subject to uncertainty and depends on te type of sock tat Project is subjected to. If te sock is bad, and tis occurs w te probabiy p, ten ε t = ε < 0, wie if te sock is good ε t = ε > 0. Te magnude of ε is suc tat te return to project in te bad state is ower tan te return from project. Te economy s output (Y) depends on capa (K) invested in eac of te projects. Te production functions F(K) assume a simpe K specification. More specificay we specify te production functions for project and project as F(K t ) = K t and F(K t ) = K t 8

9 respectivey, were and are te respective tota factor productivies associated w te projects, were <. e assume tat te tota factor productivy parameters are time invariant. In te context of tis mode, K represents a compose good embodying bot uman and pysica capa. However, we empasize te dominance of te uman component, wic can be interpreted as investment in iger eve ski needed to invest in te more productive project. In tis case δ can be convenienty interpreted as an impic fixed cost tat resuts due to te experientia earning required wen entrepreneurs undertake risk in te absence of te risk diversification options offered wen markets and instutions are we deveoped. Tis cost as a ski component, acquired troug earning ow to use Tecnoogy and a component tat refects te knowedge gained troug te experience of reading te market condions and making te best use of te tecnoogy in te given circumstances. part from representing te cost of acquiring te iger eve ski, δ can aso be interpreted as resuting from instutiona and structura aspects of te economy. For instance, a country w poor ega instutions, agents may end up paying iger tan necessary costs, in te form of bribes or searc costs to acquire te iger eve ski, resuting in a ig δ for te economy. Simiary an economy wose istorica investment in education is very ow may end up aving a imed suppy of educators reative to te demand for te services resuting in a iger δ. Every period eac generation faces a probem on weter tey soud invest in project or project. Te coice of wic project to invest in is not necessariy dependent on te project tat teir parents invested in. Tat is, offspring of parents wo adopted need not adopt ; ony depends on te magnude of resources tey iner from teir parents. Te agent does not consume in te first period of is ife. 3 Te utiy of te agent, in te event e/se invests in project is described by: U ( c+, b+ ) = n( c+ ) + θ n( b+ ) Te preferences for agents wo invest in Project are described as foows: ( c, c, b, b ) = pn( c ) + ( p)n( c ) + θp n( b ) + θ ( p)n( b U ) () (2) In equation (), c + and b + denote period 2 consumption and bequests for agent i if e invests in Project. In equation (2), c + and b + denote period 2 consumption and bequests 3 Tis type of preference structure is consistent w te idea tat consumption consists of ouseod consumption wic incudes te consumption of te cidren. Te agent terefore consumes part of te consumption of is parents in te first period of is ife and undertakes te consumption decision in te second period w is offspring in mind. 9

10 for agent i if e invests in Project w superscripts and representing te nature of sock tat te economy is subjected to. Subscript represents a bad sock wie subscript denotes a good sock, were te probabiy of te bad sock is represented by p. In bot equation () and equation (2), te parameter describes te extent of imperfect intergenerationa atruism in te mode. gents face different budget constraints depending on te project tat tey invest in. Te budget constraint for agents tat invest in Project is as foows: c + + =φ( w+ ) b (3) were denotes resource endowment of te i t agent in period t and a te oter unknowns are as defined earier. Resource endowments for agents depend on te project tat teir parents invested in. For agents wose parents invested in Project, te endowment is given by given by: = = b. Te endowment of agents wose parents invested in Project is = = b Likewise, agents investing in Project ave te foowing state-contingent budget constraint: c + x x ( η + ε )( w+ ) b δ = t + (4) were te superscript x represents te nature of te sock (i.e. or ) tat project is subjected to. gent i s probem is optimise is utiy subject to is/er budget constraint. gents investing in project maximise equation () subject to constraint (3). Tis yieds te foowing consumption and bequest pans: φ c + = + + θ [ w ] (5) θφ b + = + + θ [ w ] (6) ternativey, te optima state-contingent pans for agents wo invest project depend on te sign of te sock tat teir parent faces. Tese are described by 0

11 c c b b = + θ [( η + ε ) ( w + ) ] (7) + δ = + θ [( η + ε ) ( w + ) ] (8) + δ θ = + θ [( η + ε ) ( w + ) ] (9) + δ θ = + θ [( η + ε ) ( w + ) ] (0) + δ Te i t agent wi invest in project iff. U ( c, b ) U ( c, b ) () were and denote te indirect utiy functions for te agents investing in Project and Project respectivey and te subscript denotes te optima coice of te variabe in question. It can ten be sown tat tis is equivaent to te foowing: p ( p) [( η + ε )( w+ ) δ ] [( η + ε )( w+ ) δ ] φ [ w+ ] (2) In equation (2), te LHS, represents te geometric average of te weat tat is accumuated wen an agent invests in project. Te RHS gives te weat tat is accumuated by an agent wo invests in project. toug we are not abe to anayticay sove equation (2) for te eve of (ereafter to be referred as ) tat woud equate te LHS to te RHS, tere are reasons to beieve tat exists. e provide an informa sketc of te proof ere. Firsty, is obvious from equation (2) tat bot te RHS and te LHS functions are continuous and increasing in. Secondy, since te adoption cost parameter δ as te effect of sifting te LHS function downwards, tere is a reason to beieve te LHS is beow te RHS at east for some ow eves of. Tirdy, because project is on average more productive tan project, must be tat te rate of increase of te LHS w respect to is faster rate tan tat of te RHS and consequenty te LHS wi be above te RHS for some ig eve of. ssuming te above tree points are satisfied, a RHS function. Given tat tere is a proposion can be made: exists were te LHS function intersects w te tat equates te RHS to te LHS, te foowing

12 Proposion : Tere is an tresod eve of inia endowment, tat is required for an agent to invest in project. Tis eve of endowment is impicy defined as te soves equation (3): p ( p) [( η + ε )( w+ ) δ ] [( η + ε )( w+ ) δ ] = φ [ w ] (3) + tat n agent wi invest in Project iff. To gain more intuion about we carry out some comparative static anaysis to examine ow tis tresod eve of endowment canges w te parameters of te mode. Tis is done by impicy differentiating of w respect to eac of te parameters in equation (3). Our resuts are intuivey pausibe; we find tat is decreasing in parameters: w, η, ε and increasing in parameters φ δ, p, ε,. 4 s in Lairi and Ratnasiri (202) and Kan and Ravikumar (2002), te outcomes of our mode are independent to incusion of borrowing to finance investment in project. Firsty, tis is because access to borrowing may not directy ep te agents since te investment needed to undertake project is a uman-capa intensive activy. Secondy, even if te agents can access consumption oans, borrowing to invest in project may not be economicay tenabe. Tis is because our mode is suc tat agents wo want to borrow access te oans from tose wo are wiing to end, wo in tis case are tose wo ave invested in project. For te enders to be wiing to end, tey soud at east earn an ( p) interest equa to te expected net return on project i.e. ( η + ε ) ( η + ε ). However, tis is not possibe given tat agents wo adopt must aso incur te adoption cost δ. s suc is not possibe to te ender and te borrower to reac a dea. p 4 More specificay te foowing are te partia derivatives: d = < 0, dw d px Y + ( p) X Z d px Y = < 0, = dη p( η + ε ) XZ + ( p)( η + ) XY YZ dε p( η + ε ) XZ + ( p)( η + ε ) XY YZ d d ε ( p) X Z = p( η + ε ) XZ + ( p)( η + ε ) XY YZ 2 > 0, ε dφ φ [ p( η + ε ) XZ + ( p)( η + ) XY YZ] d dδ = X ( Z + Y ) p( η + ε ) XZ + ( p)( η + ε ) XY YZ > 0, d = d dp XYZ ε XYZ n ( Z / Y ) = p( η + ε ) XZ + ( p)( η + ε ) XY YZ < 0, > 0, > 0, were X = w +, Y = ( n + ε )( w + ) δ, Z = ( n + ε )( w + ) δ. Since w + > w + δ, is easy to see tat p( η + ε ) XZ + ( p)( η + ε ) XY YZ > 0. 2

13 Te dynamics of te mode are described by te evoution of bequests overtime. Tis is given by te foowing truncated system of first order difference equations: [ w + ] + = γ for < (2) and + + = γ = γ [ w + ] θδ /( + θ ), w probabiy p [ w + ] θδ /( + θ ), w probabiy ( p) for > (3) were b + in equiibrium, γ = + θφ =, γ + θ = θ ( η + ε ), γ + θ = θ ( η + ε ), and + θ is defined in Proposion. Equations (2) and (3) igigt te importance of te sopes, γ, γ, γ of te bequests function in determining te dynamics of te mode. Tese sopes are proportionay reated to te productivies of te respective projects. 5 Of particuar importance are te sizes of tese sopes reative to te 45 0 ine, wic as a sope equa to. To deveop some intuion regarding ow te economy evoves over time, we anayse a deterministic version of te mode in wic project is associated w a deterministic return equa to a weigted average of te ow and ig sock cases. Tat is, in te case of project we do not anayse te sopes of te two bequest functions individuay, but we focus on te weigted sope i.e. γ w = p. γ + ( p). γ. 6 Consequenty, for project equation (3) can be wrten in as a singe weigted weat function as foows: w w + = γ [ w + ] θδ /( + θ ). Combined w equation (2), ten, tis function describes wat appens on average in te stocastic version of te economy. Depending on te parameter representing te cost associated w project δ and te productivy parameters, γ, γ w, tree possibe outcomes are possibe. Tese predictions can be abeed poverty trap, dua economy, and baanced growt, respectivey. in te poverty trap case tere are two possibiies, caracterized by Figures (a) and (b) respectivey. In Figure (a) we ave a suation in wic agents above adopt 5 Note tat te productivy of project depends on te sock tat te economy is subjected to. 6 Te anaysis ere is somewat simiar to tat of Lairi and Ratnasiri (202). Te deterministic version of our mode may in fact be regarded as a specia case of te mode of tat paper. 3

14 However, given te dynamics of te system, tey converge to te steady state associated w tecnoogy. In Figure (b), even toug te productivy of tecnoogy is ig enoug so tat te bequest functions of agents w weat above ave a sope greater s tan uny, te inia distribution is suc tat a agents ave a weat eve beow, te unstabe steady state associated w te tecnoogy. s suc, a dynasties in te s economy converge to, te stabe steady state associated w Tecnoogy. ecause project is te ony one tat exists in te ong run, inequay aways converges to zero irrespective of te condions under wic te poverty trap arises. However, ong run growt rate is ikey to differ depending on te productivy parameter of project. Tere are two cases in wic a dua economy arises, and tese are caracterized by Figures 2(a) and 2(b) respectivey. Figure 2(a), as evident, is identica to Figure (b), but te inia distribution of te economy is suc tat tere are some agents w a weat eve above tat of te unstabe steady state s. Te dynasties of tese agents experience s continuous growt, wie a dynasties w weat eve beow converge to te stabe steady state associated w tecnoogy. Tis dua economy is associated w a growt rate tat is above tat of te poverty trap as we as ig and persistent inequay. In Figure 2(b) we ave a different type of dua economy. Here te productivy associated w bot tecnoogies is reativey ow, so tat te sopes associated w tem are beow, and oter parameters of te mode are suc tat some agents in te inia distribution fa above. Te dynasties w inia weat above ten converge to te stabe steady state associated w Tecnoogy wie te remaining dynasties converge to te stabe steady state associated w Tecnoogy. Since a agents wo invest in project ave a unique and stabe steady state, inequay in te dua economy sown by Figure 2(b) is not as ig as te inequay tat resuts in te dua economy sown in Figure 2(a). Finay, in Figure 3 we present te baanced growt case. Here, te productivy associated w bot tecnoogies is ig, eading to sopes of bequest functions associated w tem tat are above uny. It is straigtforward to see tat te dynamics of te mode impy compete adoption of te Tecnoogy by a dynasties in te economy, regardess of te inia distribution caracterizing te economy. Te inequay win te baanced growt economy increases sarpy in te transion towards te ong run and is persistent. Tis is because of two reasons. Firsty te fact tat some agents invest in project and some in project means tat te atter group wi become ric and catcing up wi be take time. Secondy, in te stocastic version of tis 4

15 economy, catcing up is made more difficut due to te fact tat project is subject to uncertainty. For instance, agents of a particuar dynasty may face a bad sock soon after teir parents swc from project to project resuting in tese agents faing back to project. Since a agents eventuay invest in project growt rate of te economy is driven by te productivy of tis project and is iger tan te growt rate under te poverty trap and te dua economy s Figure (a): Poverty trap case s s Figure (b): Poverty trap case 2. 5

16 s s Figure 2(a): Dua economy case s s Figure 2(b): Dua economy case Figure 3: aanced growt case 6

17 3. Numerica Experiments and Discussion In tis section we use numerica experiments to iustrate te intuion underying te teoretica predictions tat were reported in te preceding section. Te inia distribution of weat for te reported resuts is assumed to be ognorma w a mean of 2. 5 and standard error of 0.4 and tere are 50 agents. 7 Te parameter vaues used in tis anaysis for te tree cases discussed above are reported in Tabe. so reported are te sope/productivy parameters tat resut from tese parameter coices. Tabe : Parameter Vaues φ η θ ε ε p δ w γ γ γ w γ Poverty Trap: Case Poverty Trap: Case Dua Economy: Case Dua Economy: Case aanced growt Figure 4(a) iustrates te impications for project coice, inequay and economic growt for te poverty trap case. Pane (a) of Figure 4(a) sows te number of agents tat invest in project or in different time periods. s evident in pane (a), atoug bot project and project co-exist in te inia stages, a agents in te economy eventuay adopt te former project. Pane (b) iustrates te evoution of inequay win tis poverty trap economy over time. Te inequay win tis economy iniay fuctuates at ig eves and ten decreases sarpy in te transion process and eventuay converges to zero. Te inia, reativey ig eve of inequay is due to te fact tat some agents adopt project wie oters adopt project. However, because project is costy yet not very productive, agents wo invest in tis project find temseves unabe to pass sufficient resources to teir offspring to enabe tem to adopt project and consequenty te offspring swc to project. Tis expains te rapid fa in inequay and te convergence of inequay to zero. Te inia fuctuations in inequay refect te uncertain nature of te weat of te agents wo iniay adopt project. Once project is fuy adopted, inequay stabiises. In pane (c) of Figure 4(a) we sow te beaviour of growt. For te same reason as in te case of inequay, average growt is subject to fuctuations in te inia stages. However, growt sarpy increases in te transion from beow 0.7% and converges to a steady state of %. 7 e coose parameters in suc a manner tat optima consumption coice under te bad state is restricted to posive vaues i.e. η + ε ) ( + ) ( δ w. 7

18 Figure 4(b) iustrates te impications for project coice, inequay and economic growt for te poverty trap case 2. Here te productivy of project is above average wie tat of project is beow average. However, because project is too costy reative to te endowment of most agents very few agents iniay invest in project. Moreover, because te few agents tat invest in project may face a bad sock, te entire economy ends up adopting project in te steady state. Tis is evident in pane (a) of Figure 4(b). Te transiona beaviour of growt and inequay for case 2 are que simiar to tat of case. However, in case 2, te inia fuctuations in bot growt and inequay are more pronounced tat in case. Moreover, because te productivy of project is above average, takes more time for bot growt and inequay to converge to teir steady state equiibrium. (a) 600 (b) 0.8 Number of gents Project Project Gini Coefficient (c) verage Growt Figure 4(a) Project coice, inequay and economic growt in te Poverty Trap case 8

19 (a) 600 (b) 0.8 Number of gents Project Project Gini Coefficient (c) verage Growt Figure 4(b): Project coice, inequay and economic growt in te Poverty trap case 2 Figure 5(a) presents te numerica resuts for te dua economy case. In tis economy project and project co-exist in te steady state. gents wo adopt project wi be poorer wie tose tat invest in project wi be ricer. Tus, as sown in pane (b) of Figure 5(a), tis economy is caracterised by very ig eves of inequay. ecause of te stocastic nature of project project coice as we as te growt and inequay patterns of tis economy are subject to fuctuations. Te average growt rate for tis economy is sigty above tat of te poverty trap. Tis is due to te component of growt tat is emanates from agents wo invest in te more productive project. Figure 5(b) presents te numerica resuts for te dua economy case 2. Tere are tree notabe differences between tese resuts and tose of case. Firsty, comparing pane (a) for te two cases is cear tat in case, more agents invest in project tan in case 2. Te main reason for tis is tat in case 2 te productivy of project is beow average. However, in case 2 agents invest in tis project because te cost of investing in te project is ow reative to teir inia endowment. Secondy, te fuctuations in growt in case are muc more tan tose in case 2. Case 2 is anaogous to te deterministic version of te mode presented in Figure 2(b) were bot tecnoogies are associated w a stabe steady state wie case is anaogous to te case presented in Figure 2(a) were tecnoogy is associated w an unstabe steady state. Terefore in case 2, tere is a tendency for agents wose weat is above to sette around an average wic is represented by te non- 9

20 stocastic steady state in Figure 2 (b). Simiary, in case agents w weat sufficienty iger tan te non-stocastic unstabe steady state presented in Figure 2(a) experience continuous growt, abe one tat is subject to fuctuations. Tirdy, wie in case transiona inequay sarpy increases before becoming very ig and persistent, in case 2, inequay never reaces steady state as keeps fuctuating between 0.9 and 0.8. Tis is because in case 2 no agent wi experience continuous growt as a agents wo invest in project converge around te non-stocastic, stabe steady state under tat project (see Figure 2(b) in te anaytica anaysis, wic represents te deterministic version of tis economy). Te fuctuations in equay as sown in Figure 5 are an empirica feature of severa transiona economies (see for instance te inequay experiences of Costa Rica and Taiand in Figure (b)). (a) 600 (b) Number of gents Project Project Gini Coefficient (c) verage Growt Figure 5(a): Project coice, inequay and economic growt dua economy' case 20

21 (a) 600 (b) Number of gents (c) Project Project Gini Coefficient verage Growt Figure 5(b): Project coice, inequay and economic growt in te dua economy' case 2 Figure 6 presents te numerica resuts for te baanced growt case. In tis case, te productivies of bot projects are ig enoug to aow agents weat to grow at a reativey ig rate. Consequenty, a agents in te economy eventuay invest project. Inequay in tis economy increases in te transion process and remains persistenty ig. Te ig eve and persistence of inequay is due to te fact tat agents swc from project to project at different times. Furtermore, some of tose tat ave swced to project may be subjected to a negative sock resuting in teir offspring reverting back to project. gents wo swc to project earier and aso receive a good sock wi accumuate more weat tan tose tat remain in project and tose tat invest in project and face a bad sock. Te steady state average growt rate for te baanced growt economy is muc iger tan tat of te dua economy since bot project are very productive. Furtermore, since ony te stocastic project exists in te steady state, fuctuations in growt in te baanced growt economy are muc more pronounced tan in te dua economy case. Te steady state project coice, growt and inequay outcomes of te baanced growt are independent of cost of associated w adopting project. However, te cost tends to affect transiona beaviour of te baance growt economy. More specificay, te time taken for te economy to fuy adopt project and for growt and inequay to converge to teir steady state pats is increasing in te adoption cost. 2

22 (a) 600 (b) Number of gents (c) verage Growt Project Project Gini Coefficient Figure 6: Project coice, inequay and economic growt in te baanced growt case e carried addiona experiments to anayse ow te inia eve of inequay, te parameters representing te probabiy of a bad sock, p and te degree of atruism, θ affect te predictions of te stocastic version of te mode. 8 ie te basic predictions of te mode remain quaativey te same, one addiona observation is wort noting. Te canges in te inia inequay and te degree of atruism θ tend to affect te period tat takes for growt and inequay to reac steady state eves. More specificay, te iger te eve of inia inequay, te onger time period taken for growt and inequay to reac teir steady states. Tis resut aso appies for te degree of atruism, θ. 4. Concuding Remarks Te purpose of tis paper was to examine te ink between growt and inequay in transiona economies wen risk diversification is constrained by insufficient financia reforms. Te underying motivation for tis study stems party from tree empirica observations. Firsty, is motivated by empirica evidence suggesting te existence of intracountry and cross-country non-convergence of incomes overtime. Secondy, is motivated by te evidence presented in Section tat suggests tat tere is diversy in growt 8 Note tat teoreticay, p and θ affect te sope of te bequest function tus do not cange te main predictions of te mode. 22

23 experiences of countries during and after impementation structura and instutiona reforms, for instance financia reforms. Tirdy, is motivated by te empirica observation tat some countries are caracterised by ig fuctuations in inequay wie oters are caracterised by muc smooter canges in inequay. e deveop a simpe endogenous growt mode in wic growt takes pace troug pysica and uman capa deepening, and agents are eterogeneous in teir inia resource endowments. In te mode, an agent faces te coice of investing in two projects, one tat is safe but as ow return and anoter tat as ig return but is subject to uncertainty. Furtermore, tere is a cost associated w investment in te ig return project. e interpret tis cost as an impic fixed cost tat resuts due to experientia earning required by entrepreneurs wen tey take risk in te absence of we deveoped financia instutions and markets. Depending on te inia productivy differences between te projects and te impic fixed cost of investing in project tree outcomes are possibe. e caracterize tese as poverty trap, dua economy and baanced growt. Furter anaysis of tese tree outcomes reveas tat tere exists a diversy win diversy in te poverty trap and dua economy outcomes. More specificay, eac of tese two outcomes as more tan one type of equiibria eac associated w different sets of productivy parameters and adoption costs. Moreover, eac of tese equiibria sows s own unique growt and inequay patterns. Consequenty, our mode is abe to account for te diverse growt and inequay patterns observed in te data. Furter numerica resuts revea tat deays in convergence of growt and inequay to teir steady state pats are reated to inia inequay in resource endowment of agents as we as te degree of atruism. 23

24 ppendix : Proof of Proposion gents invest in project iff indirect utiy of project is greater tat indirect utiy of project. Tis impies tat agents invest in project iff U ( c +, c +, b +, b + ) U ( c +, b + ) Substuting for te functiona forms of te utiy function we get, p + n( c + ) + ( p)n( c + ) + θp n( b + ) + θ ( p)n( b + ) n( c + ) + n( b ) Recognising tat b + = θc + we can substute for b + and simpify te resuting inequay to obtain te foowing: p + n( c + ) + ( p)n( c + ) + θp n( θc + ) + θ ( p)n( θc + ) n( c + ) + n( θc ) Using aws of ogarms and ten simpifying te above inequay we can obtain: n( c ) + ( p)n( c ) n( c ) p Rewring c +, c +, c + we obtain te foowing: in terms of teir definions in steady state equations (5), (7), (8) ( η + ε )( w + p n ( + θ) ) δ ( η + ε ) ( w + ) + ( p) n ( + θ ) δ φ ( w + n ( + θ ) ) Using aws of ogarms, we can simpify te above inequay to get te foowing: [( η + ε )( w + ) δ ] + ( p) n [( η + ε )( w + ) δ ] n[ φ ( w )] p n + Since og is a monotonic transformation, must be tat: p ( p) [( η + ε )( w+ ) δ ] [( η + ε )( w+ ) δ ] φ [ w+ ] Since tere is a eve of endowment tat equates te RHS to te LHS, we can wre: p ( p) [( η + ε )( w+ ) δ ] [( η + ε )( w+ ) δ ] = φ [ w ] + 24

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