BANK OF FINLAND DISCUSSION PAPERS

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1 NK O NND DSCUSSON PPES Tuomas Takalo Otto Toivanen esearc Deartment Equilibrium in financial markets wit adverse selection Suomen Pankin keskustelualoitteita inlands anks diskussionsunderlag

2 Suomen Pankki ank of inland P.O.ox 160 N ESNK inland tt://

3 NK O NND DSCUSSON PPES Tuomas Takalo Otto Toivanen esearc Deartment Equilibrium in financial markets wit adverse selection Te views exressed are tose of te autors and do not necessarily reflect te views of te ank of inland. ddresses of te autors: Tuomas Takalo: ank of inland, esearc Deartment, P.O. ox 160, elsinki. tuomas.takalo@bof.fi. Otto Toivanen: Economics Deartment, elsinki Scool of Economics, P.O. ox 1210, elsinki, inland. toivanen@kkk.fi, We tank Viri ndersson for researc assistance. or constructive comments, we would like to tank ri yytinen, Cristian Keuscnigg, Klaus Kultti, Jua- Pekka Niinimäki, Jean Tirole, Jouko Vilmunen, Juuso Välimäki, and seminar articiants at te Norwegian Scool of Economics and usiness dministration, elsinki Scool of Economics, te Workso on Venture Caital, Entrereneursi and te Public Policy at te University of elsinki, and EE 2002 Madrid. inancial suort from te oundation of innis Cooerative anks and Tekes is gratefully acknowledged. Tis researc is art of te researc roject: Te llocation of Government &D Subsidies: Selection, Screening, and Strategic irm eavior. Suomen Pankin keskustelualoitteita inlands anks diskussionsunderlag

4 tt:// SN SSN (rint) SN SSN (online) Suomen Pankin monistuskeskus elsinki 2003

5 Equilibrium in financial markets wit adverse selection ank of inland Discussion Paers 6/2003 Tuomas Takalo Otto Toivanen esearc Deartment bstract We study a financial market adverse selection model were all agents are endowed wit initial wealt and coose to invest as entrereneurs or financiers, or not to invest. We sow tat often a lack of outside finance leads to te emergence of financial markets were availability of outside finance leads to autarky. We find tat i) tere exist Pareto-efficient and inefficient equilibria; ii) adverse selection as more severe consequences for oorer economies; iii) increasing initial wealt may cause a sift from Pareto-efficient to inefficient equilibrium; iv) increasing te roortion of agents wit ositive NPV rojects causes a sift from inefficient to efficient equilibrium; v) equilibrium financial contracts are eiter equity-like or ure debt contracts; vi) agents wit negative (ositive) NPV rojects earn rents only in (non-)wealt-constrained economies; vii) agents earn rents only wen emloying ure debt contracts; and viii) removing storage tecnology destroys te only Pareto-efficient equilibrium in non-wealtconstrained economies. Our model enables analysis of various olicies concerning financial stability, te need for soisticated financial institutions, develoment aid, and te romotion of entrereneursi. Key words: financial market efficiency, adverse selection, financial contracts, creation of firms. JE classification numbers: D58, G14, G20, G28, G32 3

6 aoitusmarkkinoiden teokkuus ja eäsuotuisa valikoituminen Suomen Pankin keskustelualoitteita 6/2003 Tuomas Takalo Otto Toivanen Tutkimusosasto Tiivistelmä Tässä tutkimuksessa tarkastellaan raoitusmarkkinoiden kykyä toimia eäsymmetrisestä informaatiosta uolimatta. isäksi työssä tutkitaan, millaisissa olosuteissa raoitusmarkkinat suosivat osake- tai velkaraoitusta. Karkeasti ottaen osakeraoitusta käytetään, jos taloudessa on aljon tuottavia rojekteja suteessa alkuvarallisuuteen, ja velkaraoitusta käytetään, jos alkuvarallisuutta on runsaasti suteessa tuottaviin rojekteiin. Mallin avulla voidaan lisäksi tutkia mm. likviditeetin tarjontaa, yrittäjyysolitiikkaa, raoitusmarkkinoiden vakautta, ja säännöstelyn tarvetta. vainsanat: raoitusmarkkinoiden teokkuus, eäsuotuisa valikoituminen, raoitussoimukset, uusien yritysten syntyminen JE-luokittelu: D58, G14, G20, G28, G32 4

7 Contents bstract...3 Tiivistelmä ntroduction Te model wit outside investors Te model witout outside investors Examle: e ef Existence of equilibria ents and contracts merfect storage tecnology Policy imlications Conclusions...27 eferences...29 endix

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9 1 ntroduction Te aim of tis aer is to exlore te functioning of financial markets wit asymmetric information wen te roles of agents are determined witin te model. n a dearture from most of te existing literature, in our model all agents are endowed wit some initial wealt and an investment roject wose quality is teir rivate information. To initiate a roject, a would-be entrereneur needs outside financing. Tere is an occuational coice in te sense tat agents coose weter to articiate and, if tey articiate, weter to become entrereneurs or financiers. Te set-u creates a natural environment to study weter a market for financial claims emerges in equilibrium, weter te eventual markets are efficient, and wat kind of financial contracts are emloyed. Our model allows us to analyze te effects of different socks to te economy, te need for more soisticated financial institutions, and te usefulness of various olicies suc as develoment aid and te romotion of entrereneursi. We build on a strong foundation: Since kerlof s (1970) seminal article, a large literature on te effects of asymmetric information on te functioning of credit markets as emerged (for surveys, see, eg, Clemenz and ittaler, 1992, and cater 5 in reixas and ocet, 1997). Wile a substantial art of te literature is in a artial equilibrium setting, te suly of funds is exlicitly modeled in a few influential studies suc as ernanke and Gertler (1989, 1990) and olmström and Tirole (1997, 1998). Te literature sares some common elements, and in articular, two key assumtions: irst, tere are otential borrowers wit investment rojects and otential lenders wit funds, but witout rojects. Second, otential borrowers ave rivate information about te ex-ante or ex-ost value of teir rojects, or teir coice of effort. n suc an environment, te well-known roblems of adverse selection, moral azard, credit rationing (Stiglitz and Weiss, 1981, Williamson, 1987) and inefficient investment levels (de Meza and Webb, 1987) may emerge. inancial markets may even collase. t is te first of te above two assumtions tat we relax by allowing te agents to coose between becoming entrereneurs or financiers, or not articiating. 1 t turns out tat te occuational coice of agents mitigates te adverse effects of asymmetric information. s in standard models under adverse selection, te financial market may yield interim or Pareto inefficient outcomes, or te market may collase to autarky. Tese observations rovide a rationale for more soisticated financial institutions tan te one tat we allow for. ut, in stark contrast, we sow tat if te economy is initially sufficiently wealty or as 1 n te recent literature dealing wit belief asymmetry, (eg, de Meza and Soutey, 1996, Manove and Padilla, 1999, and yytinen, 2002) te imact of te second assumtion on te erformance of credit markets as been scrutinized. Surrisingly little as, owever, been said about te first basic assumtion, altoug its imortance is evident from te work of oyd and Prescott (1986). 7

10 sufficiently roductive rojects, a simle form of financial market will emerge endogenously as an equilibrium institution and, for a wide range of arameter values, te financial market yields a Pareto efficient outcome. Paralleling olmström and Tirole (1998), we consider bot economies were te total initial wealt is sufficient to imlement all (ositive NPV) rojects, and wealt-constrained economies were tere is an aggregate sortage of liquidity. We find tat Pareto efficient and inefficient equilibria exist bot in wealtconstrained and unconstrained economies, as does autarky. Contrary to wat one migt exect, wealt constraints do not necessarily dilute te erformance of te financial market: elaxing te economy level wealt constraint may induce te agents wit low quality rojects to seek funding, reducing te efficiency of financial markets (tis is reminiscent of de Meza and Webb s (1987) artial equilibrium results). Wealt constraints, owever, may affect te distribution of economic rents and forms of financial contracts between agent tyes: gents wit good rojects may earn rents and use debt contracts in non-wealt constrained economies, wereas agents wit bad rojects may earn rents and use debt contracts in wealt constrained economies. We also consider ow financial market erformance deends on te efficiency of te storage tecnology. t transires tat te efficiency of storage tecnology as only minor effects, excet tat te scoe of te Pareto-efficient equilibrium in non-wealt constrained economies is increasing in te efficiency of te storage tecnology. t te limit were tere is no storage tecnology, te Pareto-efficient equilibrium disaears. n addition to te aforementioned articles, our study is also insired by gion, accetta, and anerjee (2000) and Caballero and Krisnamurty (2001). Tey oint out tat bot te microeconomic and economy-wide financial constraints matter for te erformance of financial markets, and tat te consequences of traditional financial market frictions suc as moral azard are at teir worst at an intermediate level of financial market develoment or initial wealt. Our model as a link also to te literature on financial market imerfections and te occuational coice between becoming an entrereneur or a worker (eg, Kilström and affont, 1979, anerjee and Newman, 1993, Gatak, Morelli, Sjöström, 2001, and Kanniainen and eämäki, 2002). To te best of our knowledge, owever, oyd and Prescott (1986) is te only study besides ours were tere is a coice between investing as an entrereneur and a financier. n teir model agents i) ave investment rojects wose quality is teir rivate information and ii) can coose weter to invest in teir roject or evaluate te quality of a roject. Our model is simler tan teirs in tat we do not allow information acquisition. We introduce te two deartures from te standard artial equilibrium models of adverse selection sequentially. n te next Section we assume tat otential entrereneurs ave ositive initial wealt but, as in te standard models, tat tere 8

11 are outside investors wo do not ave a otential roject of teir own. Te model of tis Section comes close to te one in de Meza and Webb (1987). n te tird Section, we remove outside investors and caracterize te equilibria and te necessary conditions for teir existence. Most of our discussion rests on a simle graical reresentation of te results: te analytical details are deferred into te endix. n te fourt Section we discuss te effects of different storage tecnologies. Policy imlications are collected into Section five, and conclusions into Section six. 2 Te model wit outside investors Excet for allowing otential entrereneurs wit ositive initial wealt, te model in tis Section contains features tat are generic in te literature. Te economy consists of a unit mass of entrereneurs wo are eac endowed wit a otential roject, and a large number of outside investors witout a roject of teir own. Eac rojects needs financing of to be imlemented. ll agents are risk-neutral and endowed wit assets, 0 < <. We assume tat te number of outside investors is sufficiently large to satisfy te financing needs of all otential entrereneurs. Tis means tat te cost of financing is driven to a level were outside investors are indifferent between investing and not investing. or te moment we assume tat tere is a storage tecnology tat converts te assets to a consumtion good at a zero rate of return. n Section 4 we consider an imerfect storage tecnology under wic dereciates at rate 1, [0,1]. Entrereneurs rojects ave different success robabilities and conditional returns. roject tat fails yields zero to all agents. roortion (0 < < 1) of agents are ig () tyes wo are endowed wit a ositive NPV roject, te rest are ow () tyes wit a negative NPV roject. We assume tat > > and >, were i is te success robability and i te return (conditional on success) of an entrereneur of tye i, i{, }. Project success and wealt () are verifiable, but roject tye is rivate information following, eg, olton and Scarfstein (1990). n wat follows, we resent most of our analysis using a gra in te (, )-sace. Natural arameter boundaries are given by 1, and <. Te financial market works as follows. n te first stage, otential entrereneurs decide weter to aroac outside investors or to resort to te storage tecnology. 2 Contract terms stiulate te amount of financing er roject ( for all), and te conditional ayment from te entrereneur to outside 2 Wen tere are outside investors, agents wo do not become entrereneurs are indifferent between using te storage tecnology and financing entrereneurs rojects. Saying tat all of tem resort to te storage tecnology is an exositional decision witout imlications. 9

12 investors in case of success. Once financing needs ave been settled, entrereneurs execute teir rojects in te second stage. Project success is verified, successful entrereneurs comensate outside investors according to contract terms, and consumtion takes lace. Te coice of otential entrereneurs can be formalized as an individual e rationality condition. Denoting exected rofits for a tye i entrereneur by i, te constraint is e i i i, i, i (2.1) were suerscrit e denotes entrereneursi and is te (fixed) ayment tat a successful entrereneur ays to er investors. llowing te entrereneurs ositive initial wealt adds one equilibrium tye to te model comared to te standard model. n addition to autarky and a ooling equilibrium were all - and -tye agents become entrereneurs, a Paretoefficient equilibrium exists were only -tye agents become entrereneurs. 3 n igure 1 we ave deicted te (, )-values for wic eac of te tree different equilibria exist. Te standard model were entrereneurs ave no initial wealt lies on te y-axis. igure 1. = 1  Pareto inefficient ooling equilibrium -tye utarky Pareto efficient searating equilibrium -tye Tere are two vertical lines in igure 1: te  ( ) /( ) -line and te  ( ) /( ) ( ) /( ) -line, and two constraints. Using te terminology of olmström and Tirole (1997, 1998), te 3 Tis is unlike de Meza and Webb (1987), because tey assume tat =. 10

13 ledgeable income of te -tye entrereneurs exceeds tat of -tye agents to te left of Â, and vice versa to te rigt of te line. Tis means tat no searating equilibrium is ossible to te left of tis line. ut once te initial wealt becomes large enoug, -tye entrereneurs exected rofit from entrereneursi becomes smaller tan teir initial endowment. Tis aens trivially wen exceeds, but, given te equilibrium, it turns out tat te NPV of -tye rojects is less tan in te wole region to te rigt of. Tus, te - tye constraint can be satisfied only to te left of tis line. s igure 1 sows, te -tye constraint is an uward sloing curve, wereas te -tye constraint sloes downwards. n sum, te ooling equilibrium exists in te uer left-and corner of igure 1, autarky exists below te ooling equilibrium, and te Pareto efficient equilibrium exists to te rigt of. Cometition between outside investors revents te emergence of a searating equilibrium to te left of. Tis suggests tat if finance was rovided by a monooly, te economy would reac Paretoefficiency everywere to te rigt of Â. Note also tat as long as (2.1) is satisfied, bot tyes of agents invest all teir funds to teir own rojects. Tis rules out using as a signaling device to te left of. 3 Te model witout outside investors n te absence of outside investors te amount of funds available for investment is limited. natural consequence is tat all agents face a coice between becoming entrereneurs or financiers. We tink of an economy as being wealt constrained if te total wealt of all agents is not sufficient to finance all -tyes rojects. dentically, an economy is not wealt constrained if te total initial wealt exceeds te financing needs of all -tye rojects. Te diagonal naturally divides economies into wealt constrained (above te = / -line), and te non-wealt constrained ones (below). Te financial market works as before. Since we do not allow for financial institutions tat gater and rocess information, te financial market in our model could be interreted as a frictionless (stock) market. n oter words, after te rojects ave been imlemented, te total ayments from all entrereneurs are divided evenly among all financiers. Tus it is as if a financier buys a stake in te average imlemented roject, instead of imlementing er rivate roject. oosely seaking, it makes no difference weter one envisions a financial market were some otential financiers come togeter to finance one or a few rojects (to equate demand and suly witin te coalition ), or a market were all financiers buy a similar stake in every imlemented roject. ot result in te same exected ayment to financiers. 11

14 n advantage of suc a simle financial market is tat it is easy to evaluate its erformance. Te market collases to autarky wen all agents resort to te storage tecnology and tere are neiter entrereneurs nor financiers. n te Paretoefficient allocation all or as many -tye rojects as ossible are financed wilst no -tye rojects are financed. We define equilibria troug te roortion of tye i agents tat become entrereneurs, denoted by i. s i [o, 1], we ave a 3x3 matrix of equilibria as sown in Table 1. 4 t is immediately clear tat tree out of te nine cannot exist. f no -tye agent becomes an entrereneur, te otential financiers individual rationality constraint is violated. Similarly, due to our assumtion tat <, it is not ossible tat all agents become entrereneurs. Te remaining six configurations cannot be ruled out a riori. Tey consist of autarky and five cases were financial markets may emerge as an equilibrium outcome. We ave named te five otential equilibria wit financial markets according to wat occuations (e = entrereneur, f = financier, s = storage tecnology) agents of tye i coose. or examle, e fs (column one, row one in Table 1) is te equilibrium were all -tye agents become entrereneurs, and -tyes slit between becoming financiers, and using te storage tecnology. Table 1. Tyes of equilibria = 0 0 < < 1 = 1 = 0 UTKY Not ossible Not ossible 0 < < 1 ef f ef ef ef e = 1 e fs e ef, e efs Not ossible Notes: i = te roortion of i tye agents tat become entrereneurs in equilibrium. ot Pareto-efficient equilibria are in te first column of Table 1. Of tese, te one in te last row is strictly better tan te one in te middle row. Similarly, in te middle column, te equilibrium in te last row is more desirable tan te one in te middle row. Te equilibrium in te last column is te worst of te five equilibria wit economic activity. emoving te outside investors canges te adverse selection roblem. n equilibrium is now constrained by four conditions. Te first are te individual rationality () constraints we saw before, wit a sligt modification. Now te agents comare te exected rofits from becoming active, eiter as an entrereneur or as a financier, to resorting to te storage tecnology. n te model wit outside investors, entrereneurs effectively only cose between te storage tecnology and entrereneursi. Second are te incentive comatibility (C) 4 Tese nine categories can be slit furter according to weter all tye i agents articiate or not. 12

15 constraints of bot tyes of agents. y C constraints we mean te coice between entrereneursi and being a financier. Te tird relationsi equalizes te suly of funds from financiers wit te demand of funds by entrereneurs. inally, te contracts used in te financial market are determined by equating te ayments by successful entrereneurs to te exected comensation for financiers. Denoting exected rofits for a tye i agent from activity j by constraints are j i, te j i i, j, i,, je,f (3.1) were suerscrit e denotes entrereneursi and f financiersi. Te C constraints are written as j i k i i, j,k, j k, i,, j,k e,f (3.2) Deending on te equilibrium (see Table 1) and agent tye, te C or constraint or bot may bind, and te C constraint may old strictly one way (eg, all -tye agents become entrereneurs) or te oter (eg, all -tye agents become financiers). Te equality of suly (left and side) and demand (rigt and side) of funds is given by (1 ) (1 )(1 ) ( ) (1 ) (3.3) were i and i [0, 1] denote te roortion of tye i agents wo become entrereneurs and wo emloy te storage tecnology. inally, te exected ayment made by entrereneurs must equal te exected return received by financiers: (1 ) (1 )(1 ) (1 ) (3.4) Te term in te square brackets on te left and side is te exected (equilibrium) number of successful entrereneurs wile te term in te square brackets on te rigt and side is te (equilibrium) number of financiers. n (3.4) is te exected ayment received by a financier tat is indeendent of te agent tye. f f Substituting for te C constraints (3.2) sows tat also catures te oortunity cost of entrereneursi. Since solving te range of arameters were conditions (3.1) (3.4) old for all five equilibria wit economic activity (see Table 1) is a straigtforward but tedious exercise, we relegate te details of te calculations to te endix. 13

16 nstead, we next consider te equilibrium e ef graically describe te remaining equilibria. as an examle and ten 3.1 Examle: e ef n e ef, = 1 and 0 < < 1, ie, all -tye agents are entrereneurs and -tye agents become eiter entrereneurs or financiers (ie, nobody cooses te storage tecnology, i = 0, i{,}). Since all agents are active, bot tyes constraints are satisfied in equilibrium. -tye agents C constraint olds wit equality, wereas -tye agents (weakly) refer entrereneursi to being financiers. To guarantee tat all agents articiate, we require tat (3.5) Te -tye agents C constraint is given by ( ) (3.6) Te left and side gives te exected return for an -tye agent from becoming an entrereneur and te rigt and side gives te exected return from becoming a financier. s -tye agents slit between te two coices, tey must be indifferent between tem. Since all -tye agents become entrereneurs, teir exected return from tat coice must (weakly) exceed tat from becoming a financier, ie, ( ) (3.7) Te aggregate suly and demand for finance is balanced wen ( 1 )(1 ) (1 ) ( ) (3.8) olds. inally, our assumtions on financial market transactions yield te following equilibrium relationsi between te ayment by a successful entrereneur, and te exected ayment received by a financier: (1 ) (1 )(1 ) (3.9) Conditions (3.6), (3.8) and (3.9) determine te endogenous variables,, and. Solving first for from (3.8) gives 14

17 (1 ) (3.10) Te roortion of -tyes wo become entrereneurs as to be less tan unity. Tis is guaranteed by our assumtion >. s also as to be nonnegative in e ef, (3.10) immediately reveals tat e ef can only exist if / (, 1). n oter words, e ef cannot exist in a wealt constrained economy (see igure 2). Our next ste is to use (3.10), (3.9) and (3.6) to solve for te equilibrium ayments and. Tey are given by (1 ) ) ( ) (3.11) and 1 ( ) (1 ) ) (3.12) Equations (3.11) and (3.12) suggest for -tyes, te ayments and are indeendent of roject outcome, wereas for -tyes te ayments are functions of roject outcome. One migt temted to tink tat tat te equilibrium financial contract can be interreted as a debt contract for -tye agents, but as an equity contract for -tye agents. Te roblem wit tis interretation is twofold: first, altoug entrereneurs know te tye of te contract tey ave, financiers do not know it at te level of individual entrereneurs. 5 Second, te ayment from a successful -tye entrereneur to er financiers is fixed, altoug it is a function of er roject outcome (conditional on success). owever, we sow in Section 3.1 tat tere is systematic variation of ow eac tye of agents ayments are or are not a function of roject outcome. To clarify discussion, we in te following label witout imlication (and following de Meza and Webb, 1987) contracts tat are a function of roject outcome as equity-like contracts. Te contracts tat are not suc functions we call ure debt contracts. fter solving for te endogenous variables, we still need to find te arameter values satisfying te agents and C constraints (3.5) (3.7). Te -tye C constraint (3.6) binds as tey slit in teir occuational coices. s -tyes strictly refer entrereneursi to becoming financiers, and being a financier is at least as rewarding as resorting to te storage tecnology, teir constraint (3.5) 5 or te same reason, any argument on financial contracting in a ooling equilibrium becomes moot (see, eg, Stigliz and Weiss, 1981, and de Meza and Webb, 1987). 15

18 does not bind. Tis means tat te relevant constraints are te -tye constraint (3.5) and te -tye C constraint (3.7). Substituting (3.12) into (3.5) sows tat te -tye constraint is satisfied (guaranteeing tat no -tye agent stores er initial wealt) if ( ) ( ) (3.13) Te -tye C constraint (guaranteeing tat no -tye agent refers becoming a financier over entrereneursi) is satisfied if ( ) (1 )) ( ) (3.14) n igure 2 we use te (, )-sace to reresent te set of arameter values for wic e ef exists. igure 2. ( e ef ) = 1 > 0 (11) -tye (14) -tye C (15) e ef does not exist in wealt constrained economies as suggested by (3.10). Te -tye C constraint (3.14) is a downward sloing line in te (, )-sace: it cuts out te vertical and orizontal axes close to te origin, ie, oor economies wit a small number of good rojects do not satisfy tis constraint. -tyes constraint (3.13) is a monotonically uward sloing curve tat starts at te origin and cuts te = / diagonal once. elow te curve, some -tyes would refer not to articiate. -tyes C constraint binds in non-wealt constrained 16

19 economies (as it sould), and -tyes constraint does not bind (as it sould not). 3.2 Existence of equilibria ollowing a similar rocedure as for te case of e ef in Section 3.1, we derive te values of te endogenous variables and determine te necessary and sufficient conditions for te existence of te six candidate equilibria (see te endix). We first resent graically te equilibria and discuss tem. t te end of te Section, we summarize our main results. n igure 3, we emloy te labeling of Table 1 to indicate te areas in wic articular equilibria exist in te (, )-sace. 6 Tere are two key lines: te = / diagonal and te vertical  ( ) /( ) -line. Te diagonal not only divides te economies into wealt and non-wealt constrained ones, but also is a border of various equilibria in many cases. To te rigt of te vertical Â-line te equilibria are unique. igure 3. = 1  P  ef f ef ef ef e e fs e ef e efs UTKY et us first examine wealt-constrained economies, ie, te area above te diagonal, starting from te rigt and side of te igure. n wealt constrained economies all available wealt is not enoug to finance all available -tye rojects. n te uer rigt and corner we find economies aving a ig roortion of -tyes, and relatively ig initial wealt. Tere, an equilibrium exists were all -tyes become financiers, and -tyes mix in teir occuations 6 n te endix, we resent a searate figure for eac equilibrium. 17

20 between entrereneursi and finance ( ef f ). ll funds are directed into -tye rojects, and terefore te equilibrium is Pareto-efficient. Moving to te left, entrereneursi becomes an otion to -tyes wen we reac te vertical Â-line. etween it and anoter vertical line, Â(/ ), we ave two or tree equilibria in te uer art of te igure. One is te same ef f as on te rigt and side of tat line. noter is ef ef were bot tyes mix teir occuational coices, ie, bot - and -tyes become entrereneurs and financiers. Te tird equilibrium is ef e were all -tyes are entrereneurs and -tyes mix teir occuations between entrereneursi and finance. Since tere are -tye agents among entrereneurs in ef ef and ef e, tey are Paretoinferior to ef f. To exlain multile equilibria recall from Section 2 te necessary and sufficient conditions for te existence of a searating equilibrium. Te necessary condition is tat te oortunity cost of entrereneursi ( ) exceeds Â, because ten te ledgeable income of -tye agents exceeds tat of te -tye agents. Te sufficient condition is tat te oortunity cost of entrereneursi exceeds te -tye agents exected rofit from entrereneursi, ie, tat bot te equilibrium ayments and are sufficiently ig. n Section cometition between outside financiers drove down te equilibrium ayments and te searating equilibrium emerges only to te rigt of te vertical ( ) /( ) -line. Comared wit outside financing, wealtconstraints generate iger equilibrium ayments. n articular, in ef f te equilibrium ayments and are so ig tat te oortunity cost exceeds bot  and te -tyes exected rofits from entrereneursi to te rigt of Â(/ )-line and terefore a searating equilibrium also exists between it and Â. To te left of  it is also ossible to construct te ooling equilibria ef ef and ef e were te oortunity cost of entrereneursi remains below  and, accordingly, te -tye agents ledgeable income below te -tye agents. etween te vertical lines, Â(/ ) and Â, a triangle exists close to te = 1 border, were only te Pareto-efficient ef f exists. n tis region tere are sufficiently many -tyes to raise te returns on financing ig enoug to revent -tyes from becoming entrereneurs. Proceeding to left, once we cross Â(/ ) financial markets cease to oerate excet for a small area close to te = 1 border. Quite naturally, wen is sufficiently ig, te financial market emerges as an equilibrium institution. Te lower is te agents initial wealt, te iger te needed roortion of -tye agents tat revents te collase of te financial market. We ten turn to te non-wealt constrained economies tose below te diagonal, and again start from te rigt. Te first equilibrium, e fs, is Paretoefficient. ll -tye rojects are financed, and -tyes are indifferent between financing te -tyes and using te storage tecnology. On te rigt and side of 18

21 te vertical -line, te storage tecnology is by assumtion more lucrative tan entrereneursi for all -tye agents. ecause of costly financing ( > 0), te storage tecnology initially remains suerior to entrereneursi for -tye agents on te left of te -line. Going furter to left, once we it te vertical -line, te equilibrium canges. Te area to te left of te line suorts e ef wic is Pareto-inefficient. ltoug all -tye agents become entrereneurs, so do some -tye agents, too. elow te -tye -curve (equation (3.13)), te -tye articiation constraint is satisfied wit equality troug some -tyes oting for te storage tecnology. Tis means tat below te curve, te equilibrium is e efs were all financiers (tyes) earn only in exectation, and ence all -tye entrereneurs also earn only in exectation. -tye entrereneurs C (and ) constraint is given by (3.14). bove te -tye -curve, all -tye agents articiate and tus nobody uses te storage tecnology even toug available assets exceed te financing needs of -tye agents. Demand and suly of funds is equated troug some -tye agents becoming entrereneurs. -tyes C constraint (3.14) and Â(/ ) cross te diagonal at te same oint. To te left tese lines, autarky is te only equilibrium in te lower triangle. major observation of te above analysis comes from a comarison of te results to te standard model wit outside investors (contrast igure 3 to igure 1). To te rigt of te only difference between outside finance and endogenous finance is in financially constrained economies; tere, outside finance allows te execution of all ositive NPV rojects. To te left of te difference is stark: aart from te uer left and corner (close to te y-axis), not aving outside investors yields a better outcome tan aving tem. Wit outside finance, autarky is te equilibrium for a large range of arameter values for wic in our model, a financial market emerges in equilibrium. n financially constrained economies, outside finance may lead to autarky were endogenous finance yields Paretoefficiency. To conclude te discussion we investigate weter te Pareto-inefficient equilibria are interim efficient in te sense of olmström and Myerson (1983). n te wealt-constrained economies te ooling equilibria ef ef and ef e cannot be interim efficient to te rigt of Â(/ ) because te Pareto-efficient ef f exists tere. To te left of Â(/ ), a social lanner cannot induce searation as te ledgeable income of -tye agents exceeds tat of -tye agents. Similarly, in te non-wealt constrained economies te ooling equilibria e ef and e efs are not interim efficient, because te social lanner could acieve Pareto efficiency by imosing a ig enoug (= ( )/ ). Tis would work 19

22 because in tis region te ledgeable income of -tye agents is iger tan tat of -tye agents. 7 We summarize te above discussion in te following roosition: POPOSTON 1: a. ll logically ossible six equilibria exist for some set of arameters. b. utarky is te unique equilibrium in bot wealt constrained and non-wealt constrained economies 1) To te left of Â(/ ) and below (4.18) (see te endix for (4.18)) and 2) elow (3.14) and to te left of Â. c. Pareto-efficient and inefficient equilibria exist bot in wealt constrained and non-constrained economies. d. Excet for autarky te Pareto-inefficient equilibria to te rigt of Â(/ ) are not interim efficient. e. Multile equilibria may only exist between Â(/ ) and Â, and above (3.14). 3.3 ents and contracts We define economic rents as rofits in excess of tose tat an agent would ave earned in er next best occuation; we call informational rents rofits to agents of tye i tat are in excess of te rofits tat agents of tye j earn from te same occuation. 8 moment of reflection and a look at igure 3 reveal tat -tye agents may only earn economic rents as entrereneurs in non-wealt constrained economies. Tere, excet in equilibrium ef ef, tey strictly refer entrereneursi to oter occuations, wilst -tye agents are indifferent between at least two occuations. Te rents are also informational, as -tye agents earn more from entrereneursi tan -tyes. 7 f te social lanner were allowed to dictate te occuational coices of agents, efficiency could in some cases be furter imroved. n te region to te left of Â(/ ), te lanner could raise efficiency by randomly allocating agents into entrereneursi. Tis would be feasible wen ( )/( ). mrovements on autarky would also be ossible between Â(/ ) and  and below (3.14), if te social lanner were allowed to randomly select agents to use te storage tecnology. Wit ositive robability, a ig-enoug roortion of -tye agents would be forced to use te storage tecnology, using te roortion of -tye agents in te remaining oulation above te tresold (/) needed to obtain economic activity. 8 Tese are close, but not necessarily te same as te standard definitions, because in our model, agents can coose teir occuation, ie, cange from te suly side of a resource to te demand side. 20

23 nalogously, it turns out tat only -tyes may earn rents in wealtconstrained economies. n ef f, -tye agents earn economic rents as teir rofits from becoming financiers strictly exceed rofits from becoming entrereneurs, or of not articiating. n ef e, -tyes earn bot economic and informational rents since tey strictly refer entrereneursi to financier-si wereas -tyes are indifferent between tem. Concerning contracts forms, different redictions ave been obtained in environments reminiscent of ours: in de Meza and Webb (1987), only (ure) debt is an equilibrium contract form, wile in Stiglitz and Weiss (1981), equilibrium contracts are equity(-like) (see de Meza and Webb (1987),. 291). s already ointed out, our model generates bot ure debt and equity-like contracts. s Table 2 sows, tere is a clear attern in ow contract form is determined. f neiter Cs nor s for agents of tye i bind, ie, te agents are on a single occuation, tey ave ure debt contracts. f agents C constraints are binding, teir outside otion deends on te roject return and, consequently, tey must ave equity-like contracts. f agents constraints are binding, teir outside otion deends on teir initial wealt and, consequently, tey must ave ure debt contracts. n equilibrium e efs, were -tyes C and constraints bind, tey use equity-like contracts as entrereneurs and ure debt contracts as financiers. Entrereneurs and financiers of te same agent tye also ave different contract forms in equilibrium ef ef were bot tyes Cs are binding. -tye entrereneurs and -tye financiers ave equity-like contracts wereas -tye financiers and -tye entrereneurs use inverse equity-like contracts. Table 2. Exected equilibrium ayments Equilibrium e fs ef f ( ) ( ) (1 ) e ef e efs ef ef ef e ( ) ( ( )) ( ) 1 (1 ) ( )(1 ) ( ( )) 21

24 Tere is also a link between contractual form and rents: agents only earn rents wen tey use ure debt contracts. -tye entrereneurs are financed by equitylike contracts in wealt-constrained economies were tey do not earn rents but wit ure debt contracts in non-wealt constrained economies wen tey do earn rents. -tyes earn rents as financiers in ef f and as entrereneurs in ef e were tey emloy ure debt contracts, but -tyes ave equity-like contracts. We can, owever, draw no inference about causality relationsi between rents and contract form, since tey are simultaneously determined as a art of equilibrium. Since wealt constraints are relative to te amount of ositive NPV rojects, one can tink tat in non-wealt constrained economies te ig roductivity rojects are scarce in comarison to initial wealt. Our model redicts tat in suc economies, financial contracts are ure debt contracts. n contrast, even if absolute initial wealt is ig, economies resort to equity-like contracts wen te roortion of roductive rojects becomes large enoug. f te roortion of ig NPV rojects is exogenous as assumed in our model our model would redict tat bot over time and over a cross section of economies, tose eriods or countries tat can be caracterized by a relatively ig roortion of ig NPV rojects sould also be caracterized by wide-sread use of equity-like contracts. We summarize our findings regarding rents and contracts in te following roosition: POPOSTON 2: a. -tye agents may earn rents only in non-wealt constrained economies; - tye agents may earn rents only in wealt-constrained economies. b. -tye agents earn rents only as entrereneurs; -tye agents may earn rents as entrereneurs and as financiers. c. Wen agents earn rents as entrereneurs, economic and informational rents coincide. d. gents only earn rents wen tey use ure debt contracts. e. Wen agents of tye i slit in teir occuational coices in equilibrium, tey use equity-like contracts. f. contract can be an equity-like contract for tye i entrereneurs wile simultaneously being a ure debt contract for tye i financiers. 22

25 4 merfect storage tecnology So far we ave maintained te standard assumtion of an exogenous storage tecnology tat fully converts te initial assets to consumtion goods. Te existence of suc a storage tecnology is vital in te literature tat studies te stability of te banking system. or instance, it is known tat removing te storage tecnology eliminates bank runs in Diamond and Dybvig s (1983) model and its variations. To verify weter our findings are sensitive to te efficiency of te storage tecnology, we now assume tat tere is an imerfect storage tecnology under wic dereciates at rate 1, [0,1]. Te only difference to te general model is tat te agents constraints (3.1) sould be rewritten as j i i, j, i,, je,f (4.1) Wen is close to unity, our revious analysis is robust to te introduction of imerfect storage tecnology by continuity. s one migt exect, owever, te equilibria will cange if becomes small, because all agents are willing to invest eiter as financiers or as entrereneurs even if teir returns are small. To get an idea of te canges, let us reconsider te examle of Section 3.1 ( e ef ) under an imerfect storage tecnology. To guarantee tat all agents articiate, we require tat (4.2) ll oter equations remain uncanged excet tat te -tye constraint (3.13) now takes te form ( ( ) ) (4.3) Wen is close to unity, (4.3) remains a monotonically uward sloing curve in te (, )-sace. Decreasing sifts te curve to te rigt, increasing te range of arameters were e ef exists. t can be sown tat wen aroaces zero, e ef exists for all arameter values in te non-wealt constrained region in so far as -tyes C constraint (3.14) olds. Tis is quite natural, since witout a storage tecnology, te -tye constraint is trivially satisfied. We now reort te canges for te oter equilibria wen = 0. esides sortening te discussion, letting = 0 furter generalizes our model. Tere is no longer an exogenous storage tecnology, but te only way to transfer wealt over time, and to transform it from initial wealt to a consumtion good, is to invest 23

26 eiter as an entrereneur or as a financier. ltoug our model lacks te second investment eriod, tis is similar in sirit to olmström and Tirole (1998) wo evaluate weter financial markets alone are able to suly enoug liquidity. igure 4. = 1 Â P Â P ef f ef ef ef e e ef UTKY Te results of tis exercise are summarized in igure 4 (te calculations are available from te autors uon request). Obviously, e fs and e efs, te equilibria were te storage tecnology was a viable otion, cease to exist. nstead, ef f, ef ef and ef e exist for larger arameter value ranges. ef f remains uncanged. Tus, removing te storage tecnology causes only modest canges to financial market erformance, suggesting tat financial markets alone can take care of transformation of wealt over time. Te largest effect is an efficiency effect: te inefficient e ef exists were te efficient e fs used to exist. s a result, only Pareto-inefficient equilibria exist in non-wealt constrained economies. 24

27 5 Policy imlications Toug tere are several limitations 9 to our simle model, we boldly offer some olicy recommendations. Te first deals wit widely adoted olicies tat seek to romote entrereneursi (see, eg, Euroean Commission, 2001). straigtforward olicy exeriment is to move te vertical ( ) /( ) -line to left. Tis increases te set of arameter values for wic a Pareto-efficient equilibrium exists in non-wealt constrained economies. Te worse is eiter te return on te successful rojects of -tye agents or te smaller teir robability of success, or te iger is te success robability of -tye agents rojects, te smaller are te roblems created by adverse selection. n te limit, te exected value of te -tye agents rojects is zero; tis is ractically equivalent to assuming tat agent tye is observable ex ante. Our exeriment tus suggest tat if te olicies romoting entrereneursi raise te returns on te successful -tye rojects witout succeeding in making tem ositive NPV rojects, tey may be misguided. Tis also means tat a rogressive tax on firm rofits above may el restore efficiency (for a similar finding, see de Meza and Webb, 1987). Socks to model arameters cange te values of te endogenous variables even if te equilibrium tye remains te same as before te sock. Wen te arameters initially are close to a border, even small socks may cange te tye of equilibrium. t is clear tat in our model, decreases in initial wealt may sift te economy from a Pareto-efficient equilibrium to an inefficient one (eg, from e fs to e efs ), or even to autarky (eg, from ef f to autarky). ut it is also ossible tat an increase in initial wealt may ave te same effect. Tink of an economy tat is in a Pareto-efficient ef f equilibrium (oint 1 in igure 5). ncreasing initial wealt may move suc an economy to te Pareto-inefficient e ef (oint 2), if te increase is sufficient to turn a wealt constrained economy into an unconstrained one. Even substantial increases in initial wealt may result in suc an adverse sift. One could interret suc olicies as develoment aid, as te increase in initial wealt comes from outside te economy in question. Suc olicies will result in an increase of aggregate roduction, but ossibly at te cost of inefficiency. owever, increasing initial wealt is an effective tool in raising an economy out of autarky. 9 or instance, future work sould consider more tan two tyes of agents, allow variation in agents initial wealt, and render te model more dynamic. 25

28 igure 5. = 1 Â P Â ef f ef ef ef e 1 2 e fs e ef e efs UTKY n contrast, increases in te roortion of good entrereneurs always ave a beneficial effect on te economy. Keeing initial wealt constant, an increase in eiter kees te economy in te initial equilibrium category, or moves it from te existing equilibrium into a better one. n oter words, it is not necessarily disadvantageous for an economy to be wealt constrained. n our model it is a relative measure, indicating tat te economy as a large number of ositive NPV rojects in relation to its initial wealt. Policies tat el raising te roortion of ositive NPV rojects in te economy are always beneficial, even if tey lead to aggregate wealt constraints. inally, let us consider te role for financial intermediaries tat collect and analyze information. n ernanke and Gertler (1989, 1990) and olmström and Tirole (1997, 1998) te financial intermediaries mitigate te moral azard roblem. n our model were te source of asymmetry is adverse selection instead of moral azard, tere is no need for comlicated financial institutions in te Pareto efficient equilibria. n tis resect our findings contrast wit te common view tat moral azard and adverse selection are qualitatively similar roblems. owever, financial intermediaries could imrove te functioning of te economy wen we ave low initial wealt (autarky), moderate initial wealt ( ef ef ), or moderate to ig initial wealt and a non-wealt constrained economy ( e ef ). Tis is in line wit te work in financial develoment suggesting tat banks are imortant in less develoed economies, wile financial markets become imortant in develoed economics (see evine, 1997, and llen and Gale, 2001, for surveys). Te welfare-imroving rosects of financial intermediaries also increase wen financial markets alone ave to erform transformation of wealt over time (ie, wen = 0). 26

29 Peras te most surrising rationale for financial intermediaries comes from te observation tat cometitive financial markets can drive interest rates too low from an efficiency oint of view. s in de Meza and Webb (1987), we sow in Section 2 ow cometition between outside financiers results in te oversuly of funds for a wide range of arameter values. Suc oversuly of funds also occurs wit endogenous finance in non-wealt constrained economies were cometition between agents wo become financiers generates te ooling equilibria e ef and e efs. 6 Conclusions n tis aer we study weter financial markets can endogenously emerge in equilibrium, weter te eventual markets are efficient, and wat te equilibrium forms of financial contracts are. We take te basic building blocks of our model from te literature and sulement tem by endowing all agents wit initial wealt and allowing tem to coose teir occuations. n te usual artial equilibrium setting, te only equilibria are autarky and a Pareto-inefficient equilibrium were all agents wit a roject become entrereneurs. We first sow tat merely allowing otential entrereneurs to ave initial wealt may lead to a Pareto-efficient equilibrium if te initial wealt is ig enoug. We ten exclude outside investors and find tat Pareto-efficient equilibria exist bot in wealt constrained and non-wealt constrained economies, as do Pareto-inefficient equilibria. utarky is also an equilibrium, but only for te oorest economies were agents initial wealt is low. n tis resect, it makes only a modest difference weter tere are many or few good rojects in te oulation. We sow tat excluding outside investors (mostly) imroves te erformance of financial markets, sometimes to te extent tat were existence of outside finance leads to autarky, excluding it yields Pareto-efficiency. Tere also turns out to be a link between rents and contracts, and contract tye and te roortion of ig-tye agents in te economy. gents only earn rents wen tey use ure debt contracts (ie, contracts were te ayment is not a function of te roject outcome, conditional on success). Wen agents slit in teir occuational coices in equilibrium, tey use equity-like contracts were te sum tat a successful entrereneur ays to er financiers is a function of er roject s roject outcome. ig-tye agents may earn economic and informational rents and use ure debt contracts only in non-wealt constrained economies. n wealt-constrained economies tat ave a ig roortion of ig-tye agents, tey do not earn rents and are financed by equity-like contracts, wereas low-tye agents may earn rents and ave ure debt contracts only tere. 27

30 Our model sows tat, in te face of asymmetric information, te simlest tye of financial markets may erform teir role in resource allocation and asset transformation surrisingly well, and tat wile increasing te roortion of igquality entrereneurs is a remedy for removing inefficiency, increasing te initial wealt of an economy may not be. 28

31 eferences gion, P. accetta, P. anerjee,. (2000) Caital Markets and te nstability of Oen Economies. Mimeo, arvard University, University of ausanne, and Massacusetts nstitute of Tecnology. kerlof, G. (1970) Te Market for emons : Quality, Uncertainty, and te Market Mecanism. Quarterly Journal of Economics, Vol. 85, llen,. Gale, D. (2001) Comarative inancial Systems: Survey. Mimeo, Warton Scool and NYU. anerjee,.v. Newman,. (1993) Occuational Coice and te Process of Develoment. Journal of Political Economy, Vol. 101, ernanke,. Gertler, M. (1989) gency Costs, Net Wort, and usiness luctuations. merican Economic eview, Vol. 79, ernanke,. Gertler, M. (1990) inancial ragility and Economic Performance. Quarterly Journal of Economics, Vol. 105, olton, P. Scarfstein, D. (1990) Teory of Predation ased on gency Problems in inancial Contracting. merican Economic eview, Vol. 80, oyd, J. Prescott, E. (1986) inancial ntermediary-coalitions. Journal of Economic Teory, Vol. 38, Caballero,. Krisnamurty,. (2001) nternational and Domestic Collateral Constraints in a Model of Emerging Market Crises. ortcoming in te Journal of Monetary Economics. Clemenz, G. ittaler, M. (1992) Credit Markets wit symmetric nformation: Survey. innis Economic Paers, Vol. 5, De Meza, D. Soutey, C. (1996) Te orrower s Curse: Otimism, inance and Entrereneursi. Economic Journal, Vol. 106, De Meza, D. Webb, D. (1987) Too Muc nvestment: Problem of symmetric nformation. Quarterly Journal of Economics, Vol. 102,