EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS?

Transcription

1 JOURNAL OF ECONOMIC DEVELOPMENT 4 Volume 32, Number 2, December 2007 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? TOBIAS BROER * European Universiy Insiue This paper shows how growh in financially open developing counries is affeced when relaions wih inernaional lenders suffer from he danger of moral hazard. We find ha if enrepreneurs can gamble wih foreign crediors money, borrowing under sandard deb conracs is consrained by a No-Gambling Condiion similar o ha in Hellmann, Murdock, and Sigliz (2000). However, his incenive consrain is endogenous in he developmen process: growh increases enrepreneurs own capial a risk and hus reduces incenives o gamble. Bu capial accumulaion also decreases he profiabiliy of invesmen, which has he opposie effec. General equilibrium under moral hazard shows a unique and sable seady sae, bu involves a leas emporary raioning of profiable projecs and possibly posiive ne invesmen by developing counries in inernaional financial markes. Keywords: Moral Hazard, Asymmeric Informaion, Open Economy Growh, Inernaional Finance JEL classificaion: F43, O6, D82. INTRODUCTION The lieraure on inernaional finance has frequenly highlighed he incenive problems associaed wih cross-border capial flows. Ofen, implici guaranees o foreign crediors, by domesic governmens or via he prospec of IMF bailous, are seen o cause a moral hazard siuaion, where crediors have no incenives o make sure ha heir money is prudenly invesed. One sandard policy recommendaion is hus o * I would like o hank Prof. Marcus Miller for he very fruiful discussions on his work. Apar from an anonymous referee, I also hank Pascal Coury and seminar paricipans a he Universiy of Warwick, he Bank of England, he European Universiy Insiue and he Royal Economic Sociey s annual conference for useful commens. Thus, Krugman (998) argues ha he main sory behind he 997 Asian crisis is ha of moral hazard

2 42 TOBIAS BROER eliminae guaranees in order o make foreign crediors bear he risk of heir invesmen. However, removing guaranees does of course no eliminae he problem of asymmeric informaion a he origin of moral hazard. As sudies on domesic lender-borrower relaions (such as Holmsröm and Tirole (997), or Hellmann, Murdock and Sigliz (2000)) show, moral hazard-ype conflics of ineres arise under sandard deb conracs whenever limied liabiliy borrowers have insufficien own capial a risk, or insufficien prospecive profis. In he absence of guaranees, inernaional lenders will ake ino accoun hese incenive problems for heir lending policy if informaion asymmeries rule ou conracs coningen on borrower behaviour. Crediors effecively impose a No-Gambling Condiion (Hellmann, Murdock and Sigliz (2000)), which consrains lending by minimum capial requiremens for borrowers, condiional on he profiabiliy of heir projecs. For poor counries ha lack sufficien own capial bu offer numerous invesmen opporuniies, his may well be a severe consrain, wih imporan consequences for he supposedly beneficial impac of inernaional capial mobiliy. This line of argumen shows ha incenive problems can affec he abiliy of poor counries o arac funds, and hus consrain growh. Bu conversely, capial accumulaion and economic growh seem o play an imporan role for incenives. They provide counries more own capial o signal incenives for pruden invesmen, bu presumably also reduce marginal reurns o capial and hus profis. As opposed o parial equilibrium models of moral hazard in financial markes, which usually ake he profi srucure as given, his double role of capial accumulaion for incenives - a beneficial capial a risk effec and a negaive profi effec - requires an analysis ha endogenises boh capial and profis. Thus, only a dynamic general equilibrium model can show he reciprocal relaion beween incenives, which consrain capial accumulaion, and growh, which deermines incenives via capial and profis. This in fac is he endeavour of he presen paper. We analyse he consequences of moral hazard in financial markes for growh in open developing economies when inernaional crediors impose a No-Gambling Condiion à la Hellmann, Murdock and Sigliz (2000). The wo main deerminans of his incenive consrain, enrepreneurs own capial and expeced profis from invesmen, are made endogenous in he growh process using a simple overlapping generaions growh model of he Diamond (965)-ype. Adding our incenive consrain o he oherwise enirely neo-classical model yields resuls quie differen from hose of sandard growh heory: despie inernaional capial mobiliy, poor economies wih low own capial will converge only slowly o a seady sae, where oupu may be lower han i would have been wihou moral hazard. Moreover, no only he degree bu also he exisence of moral hazard is shown o be endogenous in he growh process: decreasing marginal reurns o capial are crucial in ha for high marginal produciviy here is no leading o pangloss overinvesmen: wihou conrol by implicily insured lenders, limied liabiliy borrowers will inves inernaional funds in excessively risky and unprofiable aciviies.

3 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? 43 moral hazard problem, which only arises a some poin in he developmen process. The ne effec of furher capial accumulaion on incenives, combining he impac of rising capial a risk and falling marginal reurns, is shown o be posiive. We hus show a causal link from capial accumulaion o moral hazard, as opposed o he reverse pangloss invesmen mechanism, where moral hazard leads o overaccumulaion of capial. Our paper draws on wo main sources in he lieraure: we ake our incenive srucure from he Hellmann, Murdock and Sigliz (2000) aricle on he danger of banks gambling afer he liberalisaion of domesic financial markes. Bu we endogenise profis as a funcion of aggregae capial in he economy while aking he opporuniy coss of funds as exogenously deermined in inernaional capial markes. This yields a siuaion of capial-consrained borrowing no very differen from ha in Holmsröm and Tirole (997). On he oher hand, our overlapping generaions framework is mos similar o hose in Boyd and Smih (997), or Ma and Smih (996) ha are par of a small bu growing lieraure on growh under asymmeric informaion in financial markes (see also Boyd and Smih (992), Huybens and Smih (998), Gerler and Rogoff (990) or Sakuragawa and Hamada (200)). However, his lieraure usually relies eiher on he assumpion of pure credi consrains prevailing under cosly sae verificaion 2 (noably he work of Smih e al.) or on exogenous profiabiliy of capial. Boh assumpions are in our view quie resricive, which is why we choose a simple moral hazard framework, where however boh profis and moral hazard are endogenous in he growh process. Akeson (99) looks a a similar problem of incenive-consrained inernaional lending, bu in a conex of infiniely-lived agens, and adds he possibiliy of deb repudiaion. The paper proceeds as follows: Afer presening a simple small open economy growh model wih moral hazard in financial relaions (2), we analyse parial equilibrium in financial markes (3), as well as dynamic general equilibrium (4) and give some comparaive saic resuls (5). Our conclusion includes suggesions on policy responses and furher research. 2. A SMALL OPEN ECONOMY MODEL WITH ASYMMETRIC INFORMATION This secion describes an overlapping generaions growh model of a small open economy ha faces moral hazard in an inermediae capial-invesmen secor. Enrepreneurs have he possibiliy o gamble wih borrowed money by invesing in a risky bu inefficien asse. Their incenives o do so are governed by wo facors: expeced profis from successful invesmen projecs increase incenives o avoid failure and hus o inves prudenly. And enrepreneurs own finance in heir projec discourages 2 The seminal paper on pure credi consrains in a domesic cosly sae verificaion framework is Gale and Hellwig (985).

4 44 TOBIAS BROER gambling due o a capial a risk effec. When inernaional crediors are aware of his incenive srucure bu canno observe gambling unless a projec fails, borrowing can be capial - consrained by a simple No-Gambling condiion - a one-period version of ha in Hellmann, Murdock and Sigliz (2000) wih endogenised profis. In fac, boh incenive effecs, he capial a risk and he profi effec, depend on aggregae capial in he economy and are hus endogenous in he developmen process. 2.. Agens The populaion of he economy consiss of overlapping generaions of wo-period lived agens. Each generaion is assumed o be large and of consan size, normalized o one for simpliciy. Given he large populaion, agens neglec he influence of heir individual decisions on he aggregae economy. Agens are endowed wih one uni of labour when young, which hey supply inelasically o earn he going wage rae in he economy, w, and reire a he beginning of period wo. They are risk-neural and care only abou period 2 consumpion. Thus U ( c) =. (A) C old This uiliy funcion is maximised by agens subjec o he limied liabiliy consrain ha agens wealh canno be negaive. Agens have wo saving opporuniies o ransfer heir wage o he consumpion period. They can eiher buy financial asses ha yield he inernaional gross rae of reurn i, or inves in invesmen projecs as described below. Inernaional lenders are numerous, risk-neural and ready o lend any amoun a he expeced rae of reurn i. Since our economy is small, i has no influence on his going rae of ineres Producion of Capial Goods There are wo secors in he economy. Capial for he producion of final goods is produced in an inermediae invesmen secor wih a linear echnology ha requires discree invesmen in projecs. All agens are born wih heir specific projec, say a echnology or invesmen idea, ha hey canno sell bu only carry ou hemselves. These inermediae secor projecs need an indivisible financial invesmen of size q a he end of period in order o yield capial a he beginning of +. This capial is hen used o produce final goods and paid he going renal rae R. The invesmen projecs play a crucial role in he analysis. Their size differs beween some lower bound q, and an upper bound Q. Before hey are born, agens are randomly assigned a projec by independen draws from he probabiliy densiy funcion g(q). Given he law of large numbers g(q) is equal o he densiy of invesmen opporuniies

5 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? 45 in he economy. Furhermore, g(q) is assumed o be differeniable and of mass (i.e., G ( q) = 0 and G( Q) = wih G(q) he associaed cumulaive disribuion funcion). Also we assume Q > w for all. (A2) Thus, here is always a leas one projec ha needs ouside finance o be realised. The oupu of invesmen projecs in erms of capial depends on which of wo invesmen echnologies is employed: agens can op for a pruden invesmen echnology ha yields q unis of capial wih probabiliy one, or for a gambling echnology ha yields β q > q unis of capial wih probabiliy π, and zero oherwise. We make he following assumpions abou β and π, πβ < < β. (A3) (A3) saes ha he gambling echnology is less efficien since is expeced reurn is lower han ha of he safe echnology. However, reurns from gambling are higher if he projec is successful. The reason for his paricular se-up of gambling in an inermediae invesmen secor is o show he effecs of falling marginal produciviy of capial on enrepreneurs incenives o gamble. In fac, one imporan difference beween our No-Gambling Condiion and ha of Hellmann, Murdock and Sigliz (2000) is ha in our model, profis are endogenous and hus affeced by decreasing marginal reurns. Gambling can inuiively be inerpreed in differen ways. One inerpreaion of our model is of projecs o be financial companies ha provide capial services o firms. These financial companies would hen have he possibiliy o gamble by engaging in risk-shifing, as in Hellmann, Murdock and Sigliz (2000) or in Krugman (998), or by borrowing in foreign currency agains domesic asses wihou hedging he involved risk Producion of Consumpion Goods There is a single final consumpion good in he economy ha is produced by he producion echnology F = F( K, N) using labour (N) and capial (K), he oupu from invesmen projecs. The producion echnology saisfies F K ( K) > 0, F KK ( K) < 0 and Inada condiions, where capial-leer subscrips denoe derivaives. Capial is assumed 3 A leas in he case of financial services companies, one would probably wan o limi he possible number of hese companies o some fracion of he populaion, which however only adds one parameer o our model wihou subsanially affecing resuls.

6 46 TOBIAS BROER o depreciae fully in producion. We hus have wo producion echnologies: a binary invesmen echnology ha yields capial, and a well-behaved neo-classical echnology ha combines his capial wih labour o produce consumpion goods, a framework similar o hose of Boyd and Smih (997), or Ma and Smih (996). Noe ha we do no include echnological progress. Since also our populaion is assumed o be consan, here will be no seady sae growh in he model. We choose his simplifying framework since we are primarily ineresed in he convergence process o he seady sae, and he seady sae level of capial and oupu per capia under asymmeric informaion wih respec o he full informaion case Informaion Srucure Lenders are assumed o have ex ane informaion abou agens preferences, he proporion of heir wealh (or, which is equivalen in his framework, he proporion of las period s wage) ha enrepreneurs inves in heir own projecs and heir invesmen echnology opions. However, ex pos hey have no informaion abou de faco payoffs or he chosen producion echnology unless hey see he projec fail. Failure reveals he zero payoff and hus he invesmen echnology employed (since he pruden echnology never fails). Bu limied liabiliy means ha here canno be any financial penalies in he failure case, since borrower wealh is zero (assuming full equiy paricipaion, an inssue which we will look a below). So lenders canno ex pos punish enrepreneurs for choosing he wrong echnology: if gambling is successful hey canno observe he choice of echnology, if i fails here is no possibiliy of punishmen as enrepreneurs have no funds lef. One srong assumpion is ha lenders know he gambling echnology. I is no immediae ha lenders have a chance o observe his, as in equilibrium gambling will ofen be avoided. So one may wan o inerpre he gambling echnology as a wors case guess by lenders, agains which hey ry o be robus. Noe ha his seup does no allow for monioring of projecs. Monioring could be inroduced by assuming ha lenders can observe he chosen echnology a a cerain cos. Broer (200) shows he effecs his has in he curren framework. 3. EQUILIBRIUM IN FINANCIAL MARKETS We sar by analysing he parial equilibrium in financial markes. The analysis is parial in he sense ha i akes he expeced reurn o capial and enrepreneurs wages as given, o derive equilibrium invesmen as a funcion of he inernaional ineres rae and incenive consrains. In a general equilibrium analysis we will aferwards endogenise profis and wages o derive he impac of economic developmen on incenive consrains and vice versa.

7 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? Conracs, Incenive Consrains and Definiion of Equilibrium A conrac in our seup is an agreemen ha specifies he size of a loan b ha an inernaional lender gives an enrepreneur in period, and he repaymens T made in period +. Paymens are poenially a funcion of all observable characerisics of enrepreneurs (i.e., he size of heir idiosyncraic projec and heir equiy sake in he projec) and hose saes of naure in period + ha are disinguishable ex pos. Since boh enrepreneurs and lenders are assumed o be risk-neural, individual raionaliy consrains simply require ha boh ge, for every conrac, a leas expeced reurns equal o he opporuniy coss of funds i, where expecaions are aken condiional on informaion ha may differ beween lenders and enrepreneurs. The individual raionaliy consrain for lenders is hus E [ Γ] = pt + ( p)* 0 > ib, (IR) where Γ are reurns o he lender in differen saes of naure, b is he size of he loan, and p denoes he probabiliy ha he projec is successful. (Noe ha for he remainder of his secion we drop ime subscrips for period variables for convenience.) The individual raionaliy consrain for enrepreneurs is equivalenly E Π ] = p[ τ R + ( w + b) T ( b)] wi, (IR2) [ where Π indicaes profis in differen saes of naure, R + is he renal rae on capial in he nex period, w is he amoun of period borrower wealh invesed in he projec and τ equals payoff in unis of capial when he projec goes hrough (and so equals for pruden invesors and β > for gamblers). To define equilibrium in financial markes, noe ha projecs canno be sold by enrepreneurs who are he only ones ha have he knowledge o run hem. I is hus he number of projecs ha adjuss o yield equilibrium in financial markes and no heir prices. 4 Equilibrium is hus characerised by a se of opimal conracs, a se of projecs ha ges carried ou and a echnology chosen for each of hese, such ha individual raionaliy consrains and he limied liabiliy consrain of borrowers hold. To derive he srucure of he opimal conrac, noe ha agens have complee monopoly power over heir invesmen projec, and ha inernaional capial markes are compeiive. So wihou loss of generaliy we can assume ha enrepreneurs propose a conrac as a ake-i-or-leave-i offer o crediors, hus maximising heir profis subjec o he consrains. 4 Allen and Gale (2000) presen a model where moral hazard and risk shifing under sandard deb conracs lead o a bubble in asse prices. Krugman (998) also presens a simple model in he same spiri.

8 48 TOBIAS BROER 3.2. Opimal Conracs and Equilibrium under Full Informaion Noe ha in he described lending relaion here are 3 possible saes of he world ha deermine payoffs. The firs corresponds o he pruden invesmen being chosen, he second o a risky invesmen ha is successful, he hird o a risky invesmen ha has failed. In he benchmark case of full and free informaion, conracs can be coningen on all saes of he world, plus borrower characerisics. If we assume full equiy paricipaion, i.e., enrepreneurs inves heir enire wealh and only borrow wha hey need o carry ou heir projec, he paymen when he projec fails is necessarily zero. The design of he opimal conrac is equivalen o choosing paymens in saes one and wo, such ha (IR) holds wih equaliy for boh echnologies individually, and for all b. So ransfers are simply T = i * b and T = i /π * B for he pruden and risky echnologies respecively. In oher words, he opimal conrac is a sandard deb conrac. Enrepreneurs pay a consan ineres rae r, wih r = i or r = i / π for safe and risky projecs respecively, unless hey go bankrup. Noe ha ineres raes are independen of enrepreneur characerisics, i.e., do no depend on heir wealh or he size of heir projec. Given sandard deb conracs, he resuling equilibrium is very simple and emerges from he wo individual raionaliy consrains: Enrepreneurs will inves as long as expeced reurns o heir projecs ne of ineres paymens are greaer han heir opporuniy coss. However, expeced profis Π from gambling are wih r = i / π. E[ Π gambling ] = p[ τe[ R = π[ βe[ R Π pruden ]( w + b) rb] ]( w + b) i / πb] = πβe[ R = E[ R ]( w + b) ib, ]( w + b) ib () where he inequaliy follows from assumpion (A3) ha he gambling echnology has lower expeced oupu. () shows wo hings: firs, under full informaion i is never opimal for agens o gamble. And second, in equilibrium all projecs ge realised as long as R is greaer han i Opimal Conracs and Equilibrium under Asymmeric Informaion We firs show ha even under asymmeric informaion, he opimal conrac is simply a sandard deb conrac. In a second sep, we derive he condiions for he projecs ha ge finance in equilibrium. Sandard Deb Conracs Under asymmeric informaion, paymens from enrepreneurs o lenders can only be

9 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? 49 made coningen on he echnology if he projec fails, as lenders canno disinguish success saes one and wo. Again, paymens if he projec fails are necessarily zero, so he design of he opimal conrac reduces o choosing an amoun T ha borrowers ransfer o lenders when he projec is successful. To see ha he opimal conrac is simply a sandard deb conrac, noe firs ha he paymen T can be condiioned on he amoun of heir own wealh ha enrepreneurs inves. Furhermore, for a given T expeced profis o enrepreneurs from pruden and risky invesmen projecs are respecively. E( Π E( Π pruden gambling ) = R ) = π[ βr ( w + b) T, ( w + b) T ]. (2) The imporan hing o noe is ha for given T profis increase linearly wih w, bu a differen raes: profis from pruden invesmen increase faser han profis from risky invesmen as πβ <. Thus, for a given level of borrowing and ransfers, here is a level w* (no necessarily posiive) ha makes profis from gambling equal o hose from pruden invesmen. Enrepreneurs ha inves less own capial will prefer o gamble, enrepreneurs ha inves more will inves prudenly. This means enrepreneurs wih enough equiy can obain he same conracs as hose for he pruden echnology under full informaion, as lenders know hey will never gamble. Bu he bes conrac ha enrepreneurs wih lile equiy can obain is ha for he risky echnology and involves a hefy exernal finance premium. Thus, under asymmeric informaion we ge he same sandard deb conracs as under full informaion. Bu ineres raes are condiional on he funds ha enrepreneurs inves in heir projecs, no on he chosen echnology which is unobservable. No-Gambling Condiion and Maximum Projec Size Condiional on a sandard deb conrac wih ineres rae i, we can express he condiion ha agens (pure) profis from invesing prudenly mus be higher han expeced profis from gambling as follows 5 Π pruden ( R > E( Π gambling ) i)( w + b) > π[( βr + i)( w + b)] + ( )( iw). π (3) Taken w and R as given, and again imposing maximum equiy paricipaion, we can solve his for b, which yields an upper bound on borrowing, he No-Gambling Condiion 5 In he following, i urns ou o be convenien o phrase he discussion in erms of pure profis, i.e., here is always an opporuniy cos of wi o own funds invesed in projecs.

10 50 TOBIAS BROER ( πβ) R + b < w for ( πβ ) R + + i( π ) > 0. (NGC ) ( πβ ) R + i( π ) From NGC we ge he maximum projec size q* as he sum of period wage income and he maximum loan size i( π ) q* = w + bmax = w for ( πβ ) R + + i( π ) > 0. ( NG C ) ( πβ ) R + + i( ) π NGC makes borrowing of enrepreneurs consrained by w, heir own capial in projecs, he expeced reurn and inernaional ineres raes. Inuiively, own R capial miigaes he moral hazard problem because he enrepreneur faces he whole down-side risk on his invesed capial: His opporuniy cos in he bad sae is wi, he gains from he alernaive invesmen in he safe asse yielding safe reurn i. Tha means ha his ne expeced loss from gambling wih his own capial equals he difference in expeced payoffs beween he wo echnologies, wr ( πβ) < 0. These losses are opposed o expeced gains from gambling wih borrowed money of b[ π ( βr i) ( R i)]. NGC hen says ha for pruden invesmen o be opimal, he expeced gains from gambling wih borrowed capial have o be smaller han he expeced losses from gambling wih he amoun of own capial employed in he projec. Thus, enrepreneurs wih lile own capial will pay a poenially large exernal finance premium of ( π ) / π, as hey are assumed o gamble wih crediors funds. If we inerpre he gambling echnology as a wors case scenario for crediors, implying a small probabiliy of payoff π, hen his exernal finance premium migh be oo large for he projec o go hrough. Enrepreneurs wih grea ideas bu no capial will hen never be able o borrow and realise heir projec. The condiion for his o be he case is E( Π ) = π [ βr + ( w + b) i / π * b] iw < 0 + gambling R < Rrisky = i /( πβ). In our model, informaion asymmeries can hus cause some enrepreneurs wih profiable invesmen opporuniies o ge raioned in equilibrium. However, i is ineresing o noe ha for hose projecs ha do ge financing, here is no exernal finance premium - hey can borrow a he inernaional riskless rae i. This is differen for example o models such as Bernanke, Gerler and Gilchris (999), where a variable exernal finance premium drives mos of he resuls. This is because in our model projecs do no fail in equilibrium, as enrepreneurs ha mee NGC always inves prudenly and he reurn o pruden invesmen is non-sochasic. This differs from a cosly sae verificaion seup such as ha in Bernanke, Gerler and Gilchris, where he probabiliy of failure of invesmen projecs, and hus he expeced audiing coss ha

11 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? 5 need o be covered by an exernal finance premium, is a funcion of economic condiions. П Profis from Gambling from Pruden Invesmen πβr-βi R-i πβr-i w q* q Figure. Profis from Gambling and Pruden Invesmen for Given Wealh Above q* gambling yields higher profis for enrepreneurs П Δq Δw w q* w q * q Figure 2. Increasing Wealh by Δ w Increases he Maximum Projec Size by Δq > Δw

12 52 TOBIAS BROER A Graphical Represenaion of he Equilibrium Figure shows how for fixed w and R enrepreneurs expeced profis are higher from gambling han from invesing prudenly above he hreshold size q* given by NG C. Figure 2 shows how higher wages, or wealh a he end of period, increase q* by more han he change in w. This is he capial a risk effec of rising enrepreneur own capial on borrowing limis. This can also be shown by differeniaing NG C wih respec o w q * i( π ) = w ( πβ ) R + i( + π assuming for now ha ( πβ ) + + i( π ) > 0. >, (4) ) R q* NGC binding NGC no binding w 0 R* = i(-π)/( πβ) R Figure 3. Maximum Projec Size q* as a Funcion of he Renal Rae R NGC is no binding for high raes of profi Figure 3 shows how he maximum projec size for deb finance q* rises wih profiabiliy, i.e., he renal rae of capial R. This is because he effec of a marginal rise in R on profis from pruden invesmen, equal o, is bigger han is impac on profis from gambling, πβ <, hus reducing incenives o gamble as R rises. Inuiively, as enrepreneurs only make profis in good saes, hey like high probabiliies of success he more, he higher he possible gains in success saes. Crediors who know his will hus be willing o lend more money when profis are high, leading o a posiive relaion

13 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? 53 beween q* and R. This is he profi effec, equivalen o he franchise value effec in a muli-period seing, such as Hellmann, Murdock and Sigliz (2000). I can be obained algebraically by differeniaing NGC wih respec o R : q * i( π ) = w ( πβ) > 0 for ( πβ ) R ( ) 0. (5) i π > R [( πβ ) R + i( π )] Profis hus relax gambling incenives. In fac, hey can even eliminae hem alogeher as we show now. High profis eliminae incenive problems: The Moral Hazard Condiion Noe ha all our resuls so far have been condiional on ( πβ ) R R < R + i( π ) > 0 NGC = i( π ) /( πβ). (MHC) Figure 3 shows why his is he case: NGC is no binding for values higher han R NGC, since in his case he denominaor in NGC becomes negaive and he inequaliy is reversed, such ha NGC holds for all posiive values of borrowing. In oher words, agens borrowing is no incenive-consrained for high values of R. The inuiion for his is ha enrepreneurs gain from gambling since under limied liabiliy hey need no (and canno) pay he conracual ineres in he bad sae. This leads o an expeced gain from lower ineres paymens of bi ( π ) > 0. However, he borrower loses from he lower expeced payoffs on he borrowed capial, equal o br ( βπ ) < 0. NGC only applies when he sum of he wo is posiive, i.e., when here are gains from gambling wih borrowed money. This yields he Moral-Hazard-Condiion (MHC) ha NGC only binds for a renal rae of capial below R NGC. In our general equilibrium analysis his is he reason why incenives o gamble arise endogenously in he developmen process as he renal rae and hus profis fall. The denominaor in NGC, i ( π ) R( πβ), can hus be inerpreed as he degree of moral hazard : he higher i, he higher incenives o gamble (since gambling reduces ineres paymens in bad saes), he higher R, he lower hese are since enrepreneurs expeced gains from high profiabiliy are less under gambling. Noe in passing ha he impac of he inernaional ineres rae on he maximal projec size under deb finance is given by q * = w i ( π )( πβ) R + < 0. (6) [( πβ ) R + i( π )] 2

14 54 TOBIAS BROER This also shows ha he effec of rising ineres raes on q* is smaller he higher he ineres rae. Maximum Equiy Paricipaion So far we have assumed ha enrepreneurs inves all of heir wealh in heir projec, and only borrow he difference beween own funds and he required invesmen. To see ha his is opimal for risk-neural enrepreneurs noe ha by invesing an addiional uni of heir wealh in heir own projec, enrepreneurs never ge less (bu someimes more) han he opporuniy cos i. So hey always weakly prefer o inves in heir own enerprise han in he safe inernaional financial asse. In he following we will hus assume maximum equiy paricipaion for all projecs DYNAMIC GENERAL EQUILIBRIUM The previous secion showed how a moral hazard problem can lead o a No-Gambling consrain ha limis borrowing by a funcion of enrepreneurs own capial and expeced profis of heir projecs. However, boh hese variables depend crucially on he per capia capial sock in he economy, which makes i naural o proceed o a dynamic general equilibrium analysis. More specifically, he number of realised projecs is affeced in wo ways in he developmen process: firs of all labour s surplus and wages rise when capial is accumulaed, hus leading o more own finance and a less consraining No-Gambling Condiion (he capial a risk effec). On he oher hand, capial accumulaion leads o a falling marginal produciviy of capial, hus a falling renal rae and less profis o enrepreneurs. The danger of moral hazard arises when profiabiliy falls below he level where gambling wih borrowed money suddenly becomes opimal, indicaed by MHC above. Tha is, moral hazard arises as a by-produc of developmen. Furher capial accumulaion alleviaes he No-Gambling Condiion by higher capial a risk, bu aggravaes i by falling marginal reurns. In his secion, we look a he resuling ne effec of capial accumulaion in general equilibrium, and analyse he exisence, sabiliy and uniqueness of a seady sae in he economy, as well as he process of convergence. I urns ou o be sraighforward o derive general equilibrium properies for our model, characerised by he compeiive marke clearing raes for wages and he renal rae on capial, he individual raionaliy condiions (IR) and (IR2), as well as he 6 In a more general cosly sae verificaion framework, Gale and Hellwig (985) show more formally ha sandard deb conracs wih maximum equiy paricipaion (i.e., where a risk-neural borrower pus up all his own wealh o co-finance a loan) are indeed opimal. Bu noe ha he assumpion of risk-neural agens is key for his resul.

15 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? 55 No-Gambling Condiion. 4.. Equilibrium in Markes for Labour and Capial We firs derive he equilibrium in he markes for labour and capial o ge expressions for he wage w, equal o he equiy sake of enrepreneurs, and he marginal produciviy of capial R ha deermines profis. As boh markes are compeiive, in equilibrium capial and labour are simply paid heir marginal produc. Therefore F = [ F( K ) K R ] = w, N and F = K, R. where We also assume F K ( Kmax ) < i, (A4) K MAX is he capial oupu when all invesmen projecs ge realised. According o (A4), i is no efficien o run all projecs in he economy, since in ha case he marginal produciviy of capial would be lower han he inernaional rae of reurn i Benchmark General Equilibrium wih Full Informaion We have seen above ha under full informaion, i is never opimal for agens o gamble. Agens borrow funds and inves hese in he pruden echnology such ha he marginal produciviy of capial in period, which is he expeced reurn o period invesmen projecs, equals reurns from financial asses. Thus Π pruden R = E[ R = i = F K, ]( w + b) ib = w i ( K ). (7) (7) implicily defines a unique level of full informaion capial K, since F K is a monoonically decreasing funcion by assumpion. So wih full informaion here is no convergence process: in line wih oher simple neoclassical growh models, under full informaion he economy jumps o is seady sae capial level K beween period and. Also, under full informaion enrepreneurs do no earn rens in equilibrium, as he profiabiliy of heir projecs is equal o he inernaional ineres rae.

16 56 TOBIAS BROER 4.3. General Equilibrium under Asymmeric Informaion The equilibrium condiions under asymmeric informaion are more complicaed, as here are hree consrains which may be binding in some sages of he convergence process, bu no in ohers. Firs, we saw ha he No-Gambling Condiion consrains borrowing only below a hreshold level of produciviy given by he Moral Hazard Condiion (i.e., for laer sages of convergence where capial is more abundan). Second, depending on he parameers of he gambling echnology, inefficien gambling projecs may sill ge financing if hey are able o pay he necessary premium (which is more likely o be he case in earlier sages where capial is scarce). And finally, he individual raionaliy consrains of crediors and enrepreneurs pu a binding upper limi on capial inensiy, corresponding o a lower limi on he marginal produciviy of capial equal o he inernaional rae of reurn. Assume for now ha he economy is in he region where NGC binds, and where he exernal finance premium is oo large for gambling projecs o be profiable (i.e., R = FK ( K) < min{ i( π ) /( πβ, i / πβ) ) and ha K is less han he full informaion capial sock. Under hese assumpions he period + capial sock under asymmeric informaion is simply he oupu of invesmen projecs ha ge financing according o he No-Gambling Condiion. Capial oupu per invesed uni of finance is one, since when NGC holds no agens gamble. The assignmen of projecs o agens is done by independen draws from he disribuion g(q) which is normalised o one as well as he number of agens in he economy. So he amoun of capial in period + is simply he expecaion of he projec size condiional on he projec being realised, i.e., being smaller han q * given by NG C. This yields q * K + = qg( q) dq, (8) q where q * is a funcion of K, via period wages, and of K, via expeced reurns on capial E[ R ]. (8) implicily defines + capial as a funcion of capial in period implicily since he righ hand side depends on expeced + profiabiliy. Since K is he only sae variable in he model, (8) is he law of moion for he economy. If we assume raional expecaions of nex period s renal rae, we can derive he slope of he law of moion by differeniaing (8) implicily 7 7 This is admissible since (8) is an ideniy.

17 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? 57 i( π ) q * g( q * ) KFKK, K ( πβ ) F, ( ) + + i π + K = > 0 for K i( π )( πβ) F > 0. (9) K KK, + q * g( q * )[ F KFK, ] 2 [( πβ ) F + i( π )] K, + Thus, assuming Inada condiions and ha NG C is binding, (8) is always upward-sloping. This is equivalen o saying ha under asymmeric informaion he posiive capial a risk effec on borrowing consrains from rising wages is always larger han he negaive profi effec from falling profiabiliy of invesmen as he economy accumulaes capial. However, for a general disribuion of projecs g(q) and a general producion funcion, we canno say very much abou he curvaure of he law of moion, required o draw conclusions abou uniqueness and sabiliy of a seady-sae of he economy. Inuiively, he imporance of he disribuion g(q) is eviden: he more concenraed projecs are in he lower region of possible qs, he less severe is he raioning of invesmen due o borrowing limis. On he oher hand he more large poenial projecs here are in he economy, he higher he benefis from measures ha relax he raioning. I seems plausible ha he number of projecs in an economy decreases wih size, i.e., ha here are less large-scale projecs han small-scale projecs, which is equivalen o g(q) being a decreasing funcion. However, he disribuion of capial as a funcion of projec size, qg(q), may sill be increasing or decreasing. For analyical racabiliy, we choose here he inermediae case, a uniform disribuion of capial wih respec o projec size, which requires g ( q) = / q. (A5) (A5) yields a simplified law of moion q * q i K = * ( π ) + q dq = q = q * q = w q q q ( πβ ) E( R ) + i( π ), (0) q wih

18 58 TOBIAS BROER i( π ) KFKK, K ( πβ ) F, ( ) + + i π + K = > 0 for K > 0. (9 ) K i( π )( πβ) F KK, + [ F KFK, ] 2 [( πβ ) F + i( π )] K, + Sill, he curvaure of he law of moion depends on he hird derivaive of he producion funcion, which is no pinned down by our assumpions. Galor and Ryder (989) show ha Inada condiions do no suffice o ensure exisence of a unique and sable non-rivial equilibrium in he Diamond (965) model, and develop a se of srenghened Inada condiions ha are sufficien. The condiions in our model are likely o be very differen, given he addiional link beween periods due o he role of expeced produciviy for incenive consrains and hus curren oupu. Therefore, we ake a shor-cu and assume a Cobb-Douglas producion echnology for our economy 8 α α F = F( K, N) = K N. (A6) Remembering ha labour supply is inelasic and normalised o one, and seing 9 q = 0 for simpliciy, we ge he seady sae capial sock, where K + = K = K *, as 8 Noe, however, ha he resul abou he slope of (0) and (8) depends on he way expecaions are made abou fuure produciviy. If expecaions are raional, i.e., K is derived by agens using he rue model of he economy (0), he above resul holds. If however, expecaions are compleely naive, a simplifying assumpion wih respec o he more general case of adapive expecaions, i.e., E ( R + ) = F K,, hen we ge K + KFKK, i( π )[( πβ ) FK, + i( π )] + [ F KFK, ] i( π )( πβ) FKK, = K [( πβ ) FK, + i( π )] 2, (F) which can be negaive or posiive. The inuiion for his is ha wih raional expecaions an increase in period capial affecs period capial direcly only by he wealh effec i.e., via period wages ha miigaes borrowing consrains, whereas he effec of diminishing reurns in due o increased capial is second order and only shows up in he denominaor. However, wih naive expecaions he diminishing reurn effec shows up direcly as a downward effec on gains from higher capial as of period, which is firs order. Is magniude depends on he bowedness of he producion funcion ( F KK being large or small) and of he sage of developmen (he amoun of capial and herefore he magniude of F K ). 9 Noe ha g(q) is no defined for q = 0. However, since he probabiliy of any paricular value of q occurring is 0 for any coninuous probabiliy densiy funcion we implicily exclude q = 0 wihou affecing he resuls. For general q, he expression ha defines K* in erms of he raio beween minimum projec size and

19 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? 59 α α( πβ) K * = + ( α), () i( π ) and 2 K 2 K < 0. (2) So wih Cobb-Douglas echnology, he law of moion is concave in and hus has a sable and unique seady sae given by (). However, o characerise he law of moion for capial compleely we have o bear in mind he assumpions made a he beginning of his secion. Firs, we assumed NGC o bind and risky projecs no o ge finance, i.e., R = FK, < min{ i( π ) /( πβ), i / πβ} for all. Due o Inada condiions, his is cerainly no he case for low values of K, where marginal produciviy is high. Thus boh of hese condiions pu a lower bound on capial in he economy even wih financial fricions. Inuiively, even when K = w = 0, enrepreneurs obain ouside finance unil boh he non-gambling condiion and he individual raionaliy consrain for enrepreneurs wih risky projecs are binding. The corresponding lower bound on he capial sock of our open economy is hus K min ( α ) ( α ) i( π ) i( π ) = max{ K NGC, Krisky} = max,. (3) α( πβ) α( πβ) So here is a jump in he law of moion a K = 0 o K or K, he level corresponding o a reurn of R. For all > 0 he borrowing consrain NGC will be risky binding (his is since from he second period, K will always be greaer han Krisky, as he law of moion is increasing in K for all > 0 ). The hird assumpion we made when deriving he law of moion was K NGC K risky K NGC and K < K, i.e., ha capial was lower han he full informaion level. This was necessary since he full informaion capial sock is a binding upper limi for K : oherwise he capial oupu of invesmen projecs would no be sufficien o mee (IR) and (IR2), i.e., enrepreneurs and ouside invesors would no ge heir required rae of reurn. The period + q α( πβ)( ) + ( α)( π ) i seady sae capial per capia is K* = K * q. ( )( π ) i K *

20 60 TOBIAS BROER capial sock hus says a K for all periods when he law of moion (8) aains his upper limi. Under Cobb-Douglas echnology he full informaion capial sock is simply α i K =. (4) α This yields proposiion. Proposiion : Seady Sae Convergence Wih asymmeric informaion, he economy never jumps o is full informaion capial sock. Raher, here is always some process of convergence if he iniial capial of he economy is low. Proof From (3) and (4) i is eviden ha max{ K, Krisky} < K, i.e., he lower bound of he capial sock is smaller han he full informaion capial sock for all parameer values and ineres raes, since ( π ) max ( πβ) ( α ) ( α ) ( π ), ( πβ) NGC <. (QED) Incorporaing incenive consrains under inernaional deb finance hus eliminaes he usual insananeous convergence of sandard neoclassical growh models under inernaional mobiliy of capial. However, his resul migh no be oo relevan as long as we are sure ha he economy evenually converges o he same long-run equilibrium. This is no necessarily he case, however, as long as he minimum projec size is large enough. To show his, we express he minimum projec size in erms of he seady sae level of capial per capia, o ge a leas some idea of is magniude. Proposiion 2: Non-Convergence o he Full Informaion Seady Sae There is non-convergence in our economy if he minimum projec size is sufficienly large. In oher words, under asymmeric informaion capial sock and oupu are lower han hose under full informaion even when he economy has converged o a seady sae if

21 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? 6 ( π )( α) i q K * ( ) >. (5) απ β Proof The proposiion is easily derived from seing K * < K and solving for q from () and (4). Noe ha since (0) is an increasing funcion for all parameer values, i never crosses K as long as he seady sae capial sock K * is lower han K. (QED) From proposiion 2 i is immediae ha agens ha obain funding for heir projec can earn rens in equilibrium, since whenever (4) holds marginal produciiviy is sricly higher han i and (IR) holds wih equaliy. For specific parameer values he minimum q o ge non-convergence may be greaer han zero, bu will ofen be significanly smaller han seady sae capial per head. However, his resul of course depends crucially on he simplifying assumpion abou he disribuion of capial. Finally, since oal (pruden) invesmen in he economy in period is equal o period + capial, and savings are equal o wage paymens, we ge he possibiliy of Souh-Norh ne invesmen, whenever savings are greaer han domesic invesmen, a resul known from Gerler and Rogoff (990), or Boyd and Smih (997). This is saed in proposiion 3. Proposiion 3: Souh-Norh Capial Fligh The economy will experience ne capial ouflows, whenever w E[ R + ]( πβ) q >. (6) ( πβ ) E[ R ] + i( π ) Proof The proposiion follows from seing w K by solving for q. (QED) > I is sraighforward o subsiue he seady sae values for wages and capial in (6) o derive a condiion for ne ouward invesmen in seady sae. There is hus he possibiliy of ransiory capial fligh in he economy, if (6) holds in he iniial sages of developmen, where wages are low, bu no in seady sae. Figure 4 summarises our resuls for he law of moion graphically for a Cobb-Douglas producion echnology, for a case where K min = K NGC. Noe ha K is bounded below by K NGC and above by K. The doed curves indicae laws of moion for differen

22 62 TOBIAS BROER values of minimum projec size q in (8) when (5) holds only for large q 0. K + K (Full informaion seady sae) q = 0 q >0 q > q K min 0 45 K * ( q ) K * ( q) = K * ( q ) = K K Figure 4. The Law of Moion for Differen Values of q This secion hus yields he main resuls of he paper: as long as we accep he assumpions on echnology and he disribuion of invesmen opporuniies, here exiss a single and unique seady sae for our financially open model economy, despie 0 Noe ha even for q very large, he capial sock a K = 0 says K NGC. Inuiively his is because a K = K NGC he maximum projec size is in fac infinie according o NGC (since he denominaor is zero). The behaviour of K for rising q wih K held consan can be seen by differeniaing (8) wih respec o q, which yields K + = < 0 for F K, + < i( π ) /( πβ ). (F2) q i( π )( πβ) FKK, [ F KFK, ] 2 [( πβ ) FK, + i( π )] This derivaive is always negaive when NGC is binding, bu i goes o zero as K approaches K NGC (since he denominaor goes o plus infiniy). Thus rising q moves he law of moion downwards bu he effec dampens ou near K NGC, i.e., he laws of moion sar a he same poin (0, K NGC ) bu are flaer han ha for q = 0, as drawn.

23 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? 63 incenive consrains. Equivalenly, he posiive capial a risk effec sricly dominaes he negaive profi effec, of falling profiabiliy of capial ha ighens borrowing consrains. However, conrary o he full informaion case, incenive compaibiliy consrains always lead o a ime-consuming process of convergence and possibly o ne ouward invesmen from developing counries. Seady sae oupu and capial are for sufficien minimum projec size sricly lower han he full-informaion level. Tha is, some enrepreneurs can be raioned in equilibrium: hey have projecs ha could generae he required rae of reurn, bu hey do no obain funds o finance he invesmen due o incenive consrains Monioring Conracs Secion 4.3 is based on he assumpion ha lenders canno observe he echnology chosen by enrepreneurs a any cos. So i seems worhwhile o ask wheher he resuls are robus o he inroducion of cosly monioring of enrepreneurs by lenders. The answer o his quesion depends on he cos srucure of monioring. This secion briefly discusses wo polar cases: proporional and fixed monioring coss. In he simples case, monioring coss are proporional o he size of he loan. This inroduces an exernal finance premium for projecs ha canno mee NGC equal o he per uni monioring cos. If he laer are high enough, enrepreneurs ha fail o mee NGC will prefer o inves in safe inernaional financial asses and he resuls are unchanged. Wih inermediae monioring coss, some risky projecs will ge realised (and moniored) in he iniial sages of developmen when expeced reurns are high, bu no when he marginal produciviy of capial decreases owards he inernaional ineres rae during he developmen process. Broer (200) considers he opposie case of fixed monioring coss. In his case here are reurns o scale from monioring large projecs, so he exernal finance premium of projecs ha canno mee NGC declines wih heir size. The companion paper shows ha his can lead o a gap in he credi supply, where small projecs ge sandard deb, very large projecs ge monioring conracs (inerpreed as foreign direc invesmen in Broer (200)), bu medium-sized projecs are raioned in equilibrium. 5. RESPONSE TO PRODUCTIVITY SHOCKS In order o ge he response of he economy o produciviy shocks, we add a sochasic shock erm o he producion funcion θ G K ) = θ F( K ). (7) ( We hus ge he responses of + capial o produciviy shocks by implicily differeniaing (8):

24 64 TOBIAS BROER K θ i( π ) [ F KFK, ] ( πβ ) E( R + ) + i( π ) = i( π )( πβ) FKK, θ [ F K F ] K, [( πβ ) E( R ) + i( π )] + 2 > 0. (8) A negaive shock o period produciviy and hus o he wage rae a ime ineviably reduces period + capial and wealh by ighening he NGC and hus he borrowing limi. This gives rise o he following proposiion: Proposiion 4 If an economy is borrowing consrained due o limied wealh, one-ime negaive shocks o produciviy are propagaed o fuure periods by a credi crunch. Proof From (9) and (8) we ge K θ n + n K + i+ K + = > 0 K = + i i θ. (20) The effec hus dampens ou in fuure periods whenever K K + i+ + i < for all i > 0. (QED) Thus, our model predics financial condiions (here enrepreneur wealh) o have real effecs by causing lasing consequences of one-ime shocks, as in he financial acceleraor models of for example Bernanke and Gerler (989). Concerning he response o he expeced profis of projecs we can sae he following. Proposiion 5 An expeced negaive shock o he economy is anicipaed by a credi crunch. Proof

25 EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS? 65 To prove proposiion 5 i is sufficien o show ha capial inpus ( ) depend posiively on expeced shocks o oupu, or produciviy ( E[ θ ] ), i.e., ha here is a credi crunch a he end of period as a resul of lower expeced profis in. i( π )( πβ) F K, + w 2 K [( ) [ ], ( )] πβ E θ + F + + i π + K = > 0. (2) E[ θ ] i( π )( πβ) F + KK, + θ[ F KFK, ] 2 [( πβ ) E[ θ ] F + i( π )] + K, + K (QED) 6. CONCLUSION This sudy has shown ha moral hazard, resuling from informaion asymmeries in financial markes, may have imporan consequences for growh in financially open developing counries. We showed ha if domesic enrepreneurs can gamble wih crediors money, sandard deb finance is consrained by heir own capial a risk in heir projec, as indicaed by a No-Gambling Condiion similar o ha of Hellmann, Murdock, and Sigliz (2000). This can be an imporan consrain for capial-poor developing economies. The consrain was shown o be endogenous in he developmen process via he effec of growh on capial a risk and profis o capial invesmen: firs of all, here is a hreshold for reurns o capial above which enrepreneurs never have incenives o gamble. Capial accumulaion, by reducing marginal reurns o capial and invesmen, was hus shown o give rise o moral hazard a some poin of he developmen process. However, we also showed ha once one akes ino accoun he posiive effec of capial accumulaion on wealh and hus enrepreneurs capial a risk, furher developmen alleviaes he No-Gambling consrain. The seady sae was shown o be unique and sable under Cobb-Douglas producion echnology, and may involve raioning of poenially profiable projecs. Depending on he minimum scale of invesmen projecs, here can be posiive ne invesmen from developing counries in inernaional financial markes. Also, one period shocks o our economy have lasing effecs in he fuure, and expeced fuure shocks are anicipaed by lenders behaviour oday. In summary, our sudy suggess ha while here migh be oher benefis of inernaional financial liberalisaion, he effec of inernaional capial mobiliy on capial accumulaion in poor counries is no unambiguously beneficial as simple models would sugges. Even our limied amendmen of an oherwise very neo-classical framework, o include limied informaion abou invesmen choices, has led o a much more pragmaic picure of he effecs of inernaional financial liberalisaion on developmen. Wha could be he appropriae policy responses o he described consequences of