Entrepreneurship, Financiership, and Selection

Transcription

1 ömmföäflsäafaäsflassflassflas ffffffffffffffffffffffffffffffffffff Discussion Paers Entrereneurshi, Financiershi, and Selection Tuomas Takalo ank of Finland and Otto Toivanen ECE Discussion Paer No. 116 Setember 2006 SSN ECE elsinki Center of Economic esearch, P.O. ox 17 (rkadiankatu 7), F University of elsinki, FNND, Tel , Fax , E mail info hecer@helsinki.fi, nternet

2 ECE Discussion Paer No. 116 Entrereneurshi, Financiershi, and Selection bstract We develo an equilibrium model of the market for entrereneurial finance where all agents are endowed with some wealth and a roject whose quality is their rivate information. ll agents are caital constrained and need to choose whether to invest as entrereneurs or financiers, or not to invest. We comare this economy to one where finance comes from the outside. emoving outside investors tends to imrove efficiency by raising the cost of caital and creating advantageous selection where the agents with roductive rojects become entrereneurs and those with unroductive ones become their financiers. f funding is easier to come by, entrereneurshi becomes attractive also for unroductive agents. Financial liberalization may therefore have harmful efficiency effects due to adverse selection. n our model insufficient wealth generally holds back business creation, but the markets for entrereneurial finance can nonetheless exhibit too much activity. JE Classification: D58, G14, G20, G28, G32 Keywords: efficiency of financial markets, unfavorable selection, entrereneurshi, new firm formation, adverse selection Tuomas Takalo Otto Toivanen esearch Deartment ECE ank of Finland University of elsinki P.O. ox 160 P.O. ox 17 F elsinki F University of elsinki FNND FNND e mail: tuomas.takalo@bof.fi e mail:otto.toivanen@helsinki.fi Takalo: ank of Finland, esearch Deartment, P.O. ox 160, F elsinki. tuomas.takalo@bof.fi. Toivanen: ECE (elsinki Center of Economic esearch), University of elsinki, P.O. ox 17, F University of elsinki. otto.toivanen@helsinki.fi. This aer was artly written while Toivanen was visiting the Deartment of Economics at the University of California, erkeley, and Takalo DE, Toulouse, whose hositality they gratefully acknowledge. We hank Guido Friebel, ri yytinen, eo Kaas, Christian Keuschnigg, Klaus Kultti, Toi Miettinen, Juha Pekka Niinimäki, Jean Charles ochet, une Stenbacka, Jean Tirole, Timo Vesala, Jouko Vilmunen, Juuso Välimäki, and articiants in numerous conferences and seminars for constructive comments. Financial suort from the Foundation of Finnish Cooerative anks, Tekes, and the Yrjö Jahnsson Foundation is gratefully acknowledged.

3 . NTODUCTON key choice a would-be entrereneur encounters is how to use her ersonal wealth. Should she really become an entrereneur, invest her wealth in the otential roject of her own and raise the rest from outside? Or is it more rofitable to invest the assets in the financial market to finance the rojects of others? Or is it better yet to ut aside the investment oortunities all together and just to consume the assets? These considerations are inherent in any financial market from microfinance of develoing countries with sarse investment and savings choices to the sohisticated markets of rich countries where access to interest-bearing savings account and mutual funds is widely available and where successful entrereneurs become rivate equity investors and vice versa. Yet, the majority of the economic and finance literature has overlooked this choice and its imlications on financial market efficiency. This choice could matter esecially in the much studied context where the quality of otential entrereneurs' ventures is rivate information, since low quality roject holders might find it more rofitable to give u their entrereneurial asirations and invest in the rojects of others. The defining feature of financial markets might be advantageous rather than adverse selection. The aim of this aer is to exlore entrereneurshi and the functioning of financial markets under asymmetric information when the roles of agents are determined within the model. n a dearture from most of the existing literature, all agents in our model are caital constrained and have an investment roject whose quality is their rivate information. There is an occuational choice in the sense that agents choose whether to articiate in financial markets and, if they articiate, whether to become entrereneurs or financiers. This creates a natural framework to 1

4 study whether entrereneurshi, and by imlication, a market for financial claims emerge in equilibrium and whether the eventual markets are efficient. We find that the financial market without outside financiers works remarkably well desite asymmetric information and the absence of financial institutions mitigating the asymmetric information roblem: Pareto or interim efficient outcomes revail for a large set of arameter values for which artial equilibrium models would redict an inefficient ooling equilibrium or even a collase of the market. The finding has an economic imlication: imorting finance from outside can decrease the efficiency of a financial market. Our model includes both economies where the total wealth is sufficient to imlement all rojects with ositive net resent value, and wealth constrained economies. n turns out that an aggregate shortage of liquidity matters. Pareto efficient and inefficient equilibria exist both in wealth constrained and unconstrained economies, as does autarky. Contrary to what one might exect, the economy-level wealth constraint does not necessarily dilute the erformance of the financial market. When wealth is scarce relative to the economy's roductive otential, agents with low quality rojects refer financing agents with higher entrereneurial otential to investing in the rojects of their own. elaxing the wealth constraint can, however, lower interest rates to the extent that it induces adverse selection since agents with low quality rojects begin to seek funding. This means that increasing wealth may cause a shift from a Pareto efficient equilibrium into a Pareto inefficient one. We build on the large and well-established literature on financial markets with asymmetric information emerging from Stiglitz and Weiss (1981) and de Meza and Webb (1987). n Section we exlore the role of entrereneurs' wealth in a conventional set-u with outside investors and relicate some key results of the 2

5 literature. f entrereneurs are very oor so that those with low quality rojects have higher ledgeable incomes than high-quality roject holders, a Stiglitz-Weiss tye financial market emerges where marginal entrereneurs have roductive rojects. f there is sufficient wealth to render the ledgeable incomes of high-quality entrereneurs higher than that of low-quality entrereneurs, the market is of de Meza- Webb tye where marginal entrereneurs have unroductive rojects. There is too much entrereneurial activity and increases in wealth generate efficient exit from entrereneurshi. When entrereneurial wealth is very high, a Pareto efficient searating equilibrium arises. Wealth thus acts akin to entrereneurs' risk-aversion in de Meza and Webb (1990). n Section we close the economy so that rovision of entrereneurial finance becomes endogenous. ll agents now encounter a choice between entrereneurshi, financing others ventures, and remaining outside financial markets. To the best of our knowledge, oyd and Prescott (1986) and Shleifer and Wolfenzon (2002) are the only studies besides ours where there is a genuine choice between investing as an entrereneur and a financier. Whereas the focus in Shleifer and Wolfenzon (2002) has little to do with our analysis, oyd and Prescott's model (1986) is close to ours. There are agents have investment rojects whose quality is their rivate information and who can choose whether to invest their endowment (of time) in their roject or evaluate the quality of a roject. They show that if the agents form intermediary-coalitions that evaluate rojects, they can do better than in decentralized markets. Our model is simler than theirs in that we do not allow for financial institutions that rovide information. owever, oyd and Prescott (1986) focus on an economy where the aggregate liquidity constraint is not binding. ndeed, in Section. we rovide an examle which shows how the market outcome of oyd and 3

6 Prescott (1986) is a secial case of our model. n many other cases in articular when aggregate liquidity constraint binds or agents are rich enough - there is no need for information rovision by financial institutions since the markets are efficient. We also highlight the comarative statics over agents' initial wealth. 1 n Section V we, motivated by olmström and Tirole (1998), consider imacts of imerfect storage technology. lthough the efficiency of storage has trivially major effects on financial market articiation, it has only minor effects on efficiency, excet that the scoe of the Pareto efficient equilibrium in non-wealth constrained economies is increasing in the efficiency of storage. t the limit where there is no storage, the Pareto efficient equilibrium disaears. Policy imlications are collected into Section V. Our model is very stylized and certainly does not corresond exactly to any real-world financial market environment. Nonetheless, we feel that that our finding concerning the detrimental effects of outside financiers and entrereneurial wealth have imortant bearings on two current olicy debates. First, if financial market liberalization amounts to a large inflow of funds from outside investors without a change in the comosition of otential entrereneurs, it may have adverse consequences. That financial liberalization can have a dark side is well known but most of the literature stresses moral hazard as a major roblem. n contrast, our exlanation stems from adverse selection and caital inflows. similar oint is elaborated by Giannetti (2005) and its regulatory imlications by Morrison and White (2004). 1 n oyd and Prescott (1986), agents' (time) endowment is normalized to unity whereas their rojects have variable scale. s also shown by oyd and Prescott, however, variable scale is irrelevant in the absence of financial intermediaries, since all executed rojects have maximum scale regardless of their tye. There are some other differences, e.g., in oyd and Prescott all rojects are rofitable gross of roject evaluation costs whereas in our case low quality rojects have negative net resent values. 4

7 The second olicy imlication we want to raise concerns the romotion of entrereneurshi. n our model wealth and entrereneurial activity are generally ositively correlated, which is in line with existing evidence (e.g., Evans and Jovanovic, 1989, and lack, de Meza and Jeffrey, 1996). Nonetheless, echoing the argument forcefully advanced in the work of de Meza and Webb (1987, 1990, 1999), we find that too low cost of caital attracts too many entrereneurs and, as a result, neither asymmetric information nor insufficient wealth necessarily rovides a reason to subsidize entrereneurs or their finance. 2 ut here the conclusion emerges as art of equilibrium when the agents' have intermediate wealth and the economy-level wealth constraint does not bind. When it binds, increases in wealth cause entry of roductive entrereneurs and a case for subsidizing business creation may arise. esides the aforementioned articles, our study is also insired by olmström and Tirole (1997), Caballero and Krishnamurthy (2001) and ghion, acchetta, and anerjee (2004) who emhasize that both microeconomic and economy-wide financial constraints influence the erformance of financial markets. From this more macroeconomic ersective our study has also a link to the emerging literature on the imact of adverse selection over the business cycle (e.g., Eisfeldt, 2004, and ouse, 2006). Finally, Section V summarizes our findings.. TE MODE WT OUTSDE NVESTOS There is a unit mass of risk-neutral otential entrereneurs who have access to a roject of size, and unlimited entry by risk-neutral outside investors without a roject of their own. roortion h (0<h<1) of otential entrereneurs are high () 2 n our model excessive entrereneurial activity can co-exist with a ositive relationshi between wealth and entrereneurshi. This is the main oint of de Meza and Webb (1999) but here the coexistence arises without a need to introduce moral hazard considerations. 5

8 tyes who are endowed with a ositive NPV roject, the rest are low () tyes with a negative NPV roject. The rojects have two-oint return distribution: we assume that >> and >, where i is the success robability and i the return (conditional on success) of an entrereneur of tye i, i {, }. Failed rojects yield zero regardless of their tye. Project success and wealth are verifiable, but roject tye is rivate information following, e.g., olton and Scharfstein (1990). 3 Potential entrereneurs have some liquid funds, 0<<, which they entirely invest either in their own roject or in the storage technology. 4 For the moment we assume that storage is erfect, converting initial wealth to consumtion at a zero rate of return. We resent most of our analysis using a grah in the (, h)-sace where natural arameter boundaries are given by h<1, and <. The financial market works as follows. First, otential entrereneurs decide whether to invest their initial funds in their roject or in storage. f they initiate the roject, the rest of required funds (-) needs to be raised from outside investors. Contract terms stiulate the conditional ayment from the entrereneur to outside investors in case of success. 5 Once financing needs have been settled, entrereneurs execute their rojects. Successful entrereneurs comensate outside investors according to contract terms, and consumtion takes lace. The otential entrereneurs' individual rationality condition is given by e (1) π ( ) i i i i, i {, }, 3 n alternative assumtion used, e.g., in de Meza and Webb (1999) is that only ayments from entrereneurs to financiers are verifiable and that entrereneurs cannot hide income in case they default. 4 t is cheaer for -tye entrereneurs to use their own rather than outside funds. s a result, -tye entrereneurs have no other otion but to follow and invest all their wealth in their own rojects. See de Meza and Webb (1987). 5 s there is no outside collateral in our model, introducing collateral into the contract does not change the final wealth of an entrereneur (of either tye) in case of default: This is zero for any level of collateral. Collateral requirements cannot thus be used as a screening device in our model. s is well 6

9 e where suerscrit e denotes entrereneurshi so that π i is the exected rofits of a tye i entrereneur and is the (fixed) ayment that a successful entrereneur ays to her investors. Equation (1) shows how the otential entrereneurs' wealth determines the oortunity cost of entrereneurshi. The richer she is, the larger should her exected ayoff be to make entrereneurshi lucrative. ecause of cometitive suly of finance, the cost of financing is determined by outside investors zero-rofit condition, i.e., (1) =, where is the average success robability of those who become entrereneurs. From (1) and (2) we observe four otential equilibrium outcomes. First, a Pareto efficient searating equilibrium where only -tyes become entrereneurs ( = ), occurs if e π > π e. Second, a Pareto inefficient ooling equilibrium where all otential entrereneurs also actually become entrereneurs ( = h +(1-h) ), occurs if both e π and e π are larger than. Third, there may be a semi-searating equilibrium where all -tyes are entrereneurs, but -tyes slit with some becoming entrereneurs and others oting out of the financial market. 6 n this case = [h +µ (1-h) ]/[h+µ (1-h)] where µ denotes the roortion of -tyes that become entrereneurs. 7 Now -tyes' indifference condition (1) and outside investors' zero rofit condition (2) give µ =h[ ( -)-( - )]/ (1-h) and =( -)/. known, if collateral consisted of non-liquid (outside) wealth, such collateral would facilitate the emergence of a searating equilibrium (see, e.g., ester, 1987). 6 t is easy to show that a semi-searating equilibrium where -tyes are indifferent between entrereneurshi and using storage does not exist when outside finance is available. 7 Since there is a continuum of otential entrereneurs, we model mixed strategies by a distributional aroach where the roortion µ of -tyes use the ure strategy of becoming an entrereneur and the roortion 1-µ use the ure strategy of investing in storage. 7

10 Finally, if both e e π and π are smaller than, the financial market does not oen and all agents invest in storage. We term this outcome autarky. n Figure 1 we have deicted the (, h)-values for which each of the four different equilibria exist. The downward sloing line is -tyes' constraint in the ooling equilibrium and the uward sloing line is the corresonding constraint of - tyes. The -tyes' constraint also divides the ooling and the semi-searating equilibria so that µ =1 holds above the line and µ <1 below it. n the semi-searating equilibrium, -tyes' constraint is given by the vertical ˆ ( ) /( ) -line, and the vertical ˆ + ( ) /( ) = ( ) /( ) -line is -tyes' - constraint. s a result, Figure 1 shows that the ooling equilibrium exists in the uer art to the left of and above the constraints. elow the ooling case, autarky revails to the left of  and the semi-searating equilibrium between  and. The Pareto efficient equilibrium exists to the right of. FGUE 1 EE The two vertical lines and the three regions they define will also be crucial in the subsequent sections. On the one hand, the Pareto efficient equilibrium emerges for >, since the oortunity cost of entrereneurshi rises with wealth. The oortunity cost matters more for -tyes, because the exected return on their roject is lower. The oortunity cost trivially exceeds -tye entrereneurs' exected rofit when but, given the equilibrium >0, the -tye entrereneurs' exected rofit is less than in the whole region to the right of <. When, the level of wealth becomes low enough to temt -tyes to bet it in their rojects. igher interest rates cannot be charged to revent -tyes from becoming 8

11 entrereneurs in cometitive financial market. This suggests that if the suly of finance was restricted, e.g., by a monooly sulier, the economy could reach Pareto efficiency also to the left of. The suggestion will be confirmed in the next section. On the other hand, financial markets have difficulties in oening u to the left of Â. This observation has attracted much attention in the literature: s articulated by Stiglitz and Weiss (1981), the markets can collase because of adverse selection. The observation that financial markets and entrereneurshi generally emerge when  but not when < can be exlained by adoting the concet of ledgeable income (olmström and Tirole 1997, 1998), defined as the maximum amount of an entrereneur can romise to ay back to a financier. From (1) we see that the ledgeable income of tye i agent is given by i -/ i. When otential entrereneurs are oor (<Â), limited liability makes -tye entrereneurs' ledgeable income higher than that of -tyes. ecause -tyes can always match the maximum reayment that -tyes are able to offer, adverse selection may lead to the collase of the financial market. ut since increases in wealth raise -tyes' liability more, the ledgeable incomes of - and -tye entrereneurs are equal when = and, when >Â, -tyes' ledgeable income exceeds that of -tyes. There bad rojects cannot drive out good ones and financial markets can oerate. n contrast, the inefficiency in the middle area ( [ ˆ,,] ) is that there is too much entrereneurshi, as in de Meza and Webb (1987). To further relate our findings to Stiglitz and Weiss (1981) and de Meza and Webb (1987), note that Stiglitz and Weiss (1981) consider a mean-reserving sread between rojects. ere it would mean that = and, consequently, -tye entrereneurs ledgeable income would always be higher than -tye entrereneurs, like in the area to the left of  in Figure 1. Similarly to Stiglitz and Weiss (1981), 9

12 there could be underinvestment since insufficient wealth holds back -tye entrereneurs more easily. n this case the Pareto efficient equilibrium cannot exist. De Meza and Webb (1987) in turn assume that the roject returns conditional on success are the same. ere it would mean that = and, consequently, Â=0. The ledgeable income of -tye entrereneurs would exceed that of -tye entrereneurs, as in the area to the right of  in Figure 1. That area is characterized by overinvestment. ncreases in wealth cause efficient exit from entrereneurshi, since marginal entrereneurs (in the semi-searating equilibrium) are those of low quality. We summarize the results of the model with outside investors in the following roosition: POPOSTON 1: With outside investors, a. When, the Pareto efficient searating equilibrium exists. b. When <, the Pareto inefficient ooling equilibrium exists above the -tye entrereneurs constraint. c. When Â<<, the Pareto inefficient semi-searating equilibrium exists below the -tye entrereneurs constraint. d. When <Â, the financial markets collases to autarky below the -tye entrereneurs constraint. e. When <Â, an increase in entrereneurial wealth (eventually) hels the market out of autarky but when >Â, it (eventually) leads to exit.. TE MODE WTOUT OUTSDE NVESTOS The absence of outside investors limits the amount of funds available for investment. natural consequence is that all agents face a choice between becoming entrereneurs or financiers. We regard an economy as wealth constrained if the total initial wealth of all agents is insufficient to finance all -tyes rojects. 10

13 Corresondingly, an economy is not wealth constrained if the total wealth exceeds the financing needs of all -tye rojects. The financial market works as in the revious section. Since we allow no financial institutions that gather and rocess information, the financial market in our model could be interreted as a frictionless (stock) market, a mutual fund, or a microfinance institution. fter the rojects have been imlemented, the total ayments from all entrereneurs are divided evenly among all financiers. Thus it is as if a financier buys a stake in the average imlemented roject, instead of imlementing her own roject. oosely seaking, it makes no difference whether one envisions a financial market where some otential financiers come together to finance one roject (or a few rojects), or a market where all financiers buy a similar stake in every imlemented roject. oth result in the same exected ayment to financiers. The market collases to autarky when all agents resort to the storage technology and there are neither entrereneurs nor financiers. n a Pareto efficient allocation all or as many -tye rojects as ossible are financed whereas no -tye rojects receive finance. Corresondingly, in a Pareto inefficient equilibrium at least some -tye rojects are carried out. et us denote the roortion of tye i agents that become entrereneurs by µ i. With [ 0,1] µ, we have a 3x3 matrix of otential equilibria as shown in Table 1. 8 t i is immediately clear that three out of the nine cannot exist. f no -tye agent becomes an entrereneur, the otential financiers individual rationality constraint is violated. Similarly, due to our assumtion that <, it is imossible that all agents become entrereneurs. The remaining six configurations cannot be excluded a riori. They consist of autarky and five cases where financial markets emerge as an 8 These nine categories can be slit further according to whether all tye i agents articiate or not. 11

14 equilibrium outcome. We name the five otential equilibria with financial markets according to what occuations (e = entrereneur, f = financier, s = user of storage technology) agents of tye i choose. For examle, e fs (column one, row one in Table 1) is the equilibrium where all -tye agents become entrereneurs, and - tyes slit between becoming financiers and using storage. TE 1 EE oth Pareto efficient equilibria are in the first column of Table 1. Of these, the one in the last row is strictly better than the one in the middle row. Similarly, in the middle column, the equilibrium in the last row is more desirable than the one in the middle row. The equilibrium in the last column is the worst of the five equilibria with economic activity. n equilibrium is now constrained by four conditions. The first arises from the individual rationality () constraints we saw in the revious section, with a slight but crucial modification. Now all agents comare the exected rofits from becoming active, either as an entrereneur or as a financier, investing in storage. The second set of conditions comes from the incentive comatibility (C) constraints of both agent tyes, which guide the choice between entrereneurshi and being a financier. The third relationshi equalizes the suly of funds from financiers with the demand of funds by entrereneurs. Finally, contract terms are determined by equating the exected ayments by successful entrereneurs to the exected comensation for financiers. constraints are Denoting exected rofits of a tye i agent from activity j by j π i, the j (2) π i i, j, i {, }, j { e, f }. The C constraints can be written as 12

15 (4) π π i, j, k, k j i k i j, i {, }, j k { e, f },. Deending on the equilibrium (see Table 1) and agent tye, the C or constraint or both may bind, and the C constraint may hold strictly one way (e.g., all -tye agents become entrereneurs) or the other (e.g., all -tye agents become financiers). The equality of demand and suly of funds is given by (5) ( ) [ h + µ (1 h) ] = [ (1 µ χ ) h + (1 µ χ )(1 h) ] µ, where µ and [ 0,1] i χ denote the roortion of tye i agents who become i entrereneurs and who emloy the storage technology. The left hand side of (5) catures the demand. Each entrereneur lacks - of funds to be able to carry out her roject and the term in the square brackets is the equilibrium mass of entrereneurs. n the right hand side of (5) we have the suly of funds from financiers, whose equilibrium mass can be seen from the term in the square brackets. Finally, the exected ayments by entrereneurs must equal the exected ayments received by financiers (6) [ µ h + µ ( 1 h) ] = [(1 µ χ ) h + (1 µ χ )(1 h) ] F The term in the square brackets on the right-hand side of (6) is the equilibrium mass of financiers as in (5), whereas the term on the left now equals the exected equilibrium mass of successful entrereneurs. n (6) is, as before, the fixed ayment an entrereneur has romised to ay back in case of success, and F is the exected ayment received by a financier. Solving the range of arameters where conditions (3)-(6) hold for all five equilibria with economic activity (see Table 1) is a straightforward but tedious. exercise. We consider the equilibrium e ef as an examle and then grahically describe the remaining equilibria, relegating calculations to the endix. 13

16 . Examle: e ef n e ef, = 1 µ and 0 µ < 1, i.e., all -tye agents are entrereneurs and -tye < agents become either entrereneurs or financiers (i.e., nobody chooses the storage technology, = 0 χ, i {, } i ). This equilibrium corresonds to the decentralized market equilibrium in oyd and Prescott (1986) and is comarable to the semisearating equilibrium with outside financiers (Section ). 9 s it turns out, this equilibrium also dislays lausible emirical imlications and the de Meza-Webb tye results and olicy recommendations. The examle also illustrates one of our main results of how a decrease in initial wealth can imrove the efficiency of a financial market. Since financial market articiation is comlete in this equilibrium, we require that both tyes' constraints are satisfied, i.e., (7) F. -tye agents C constraint must hold with equality, which means that (8) ( ) = F. The left hand side gives the exected return for an -tye agent from becoming an entrereneur and the right hand side gives the exected return from becoming a financier. s -tye agents slit between the two occuations, they must be indifferent between them. ecause all -tye agents refer entrereneurshi to being financiers, their exected return from entrereneurshi must be at least as large as that of becoming a financier, i.e., e efs 9 The equilibrium (see Section in the endix) erhas corresonds even more accurately to the semi-searating equilibrium of Section. owever, it is immaterial whether e efs or e ef is chosen as a benchmark because, as we will show, they together san a smaller roortion of the arameter sace than the semi-searating equilibrium in the model with outside financiers. 14

17 (9) ( ) F. The aggregate demand and suly for finance is balanced when (10) ( ) [ h + (1 h) ] = (1 )(1 h) holds. µ µ Finally, the (exected) reayments from successful entrereneurs must equal the ayments received by their financiers: (11) [ h + ( 1 h) ] = (1 µ )(1 h) µ. F Conditions (8), (10) and (11) determine the endogenous variables µ,, and F. Solving first for µ from (10) gives (12) h µ =. (1 h) The roortion of -tyes who become entrereneurs has to be less than unity. This is guaranteed by our assumtion >. s µ also has to be nonnegative in e ef, (12) immediately reveals that e ef can only exist if / h. n other words, e ef cannot exist in a wealth constrained economy where the total wealth is insufficient to finance all -tyes rojects. Using (11), (10) and (7) we can solve for the equilibrium ayments and F. They are given by (13) ( ) = ) and [ h + (1 h) ] (14) F = 1 ( ) [ h + (1 h) )]. Equations (13) and (14) suggest that for -tyes, the ayments and F are indeendent of roject outcome, whereas for -tyes the ayments are functions of 15

18 roject outcome. The ayment from a successful -tye entrereneur to her financier is fixed, although in equilibrium, it is a function of her roject return. fter solving for the endogenous variables, we still need to find the arameter values satisfying the agents' and C constraints (7)-(9). The -tye C constraint (8) binds as they slit in their occuational choices. Since -tyes refer entrereneurshi to becoming financiers, and being a financier is at least as rewarding as investing in storage, their constraint (7) does not bind. This means that the relevant constraints are the constraint (7) for -tyes and the -tye C constraint (9). Substituting (14) into (7) shows that the -tye constraint is satisfied (guaranteeing that no -tye agent stores her wealth) if (15) h( h( ) + ) ( ). The -tye C constraint (guaranteeing that no -tye agent refers becoming a financier to entrereneurshi) is satisfied if (16) ( ) ( [ h + (1 h) )]. ) which n Figure 2 we use the (, h)-sace to reresent the set of arameter values for e ef exists. FGUE 2 EE The h=/ diagonal divides economies into wealth constrained (above), and nonwealth constrained ones (below). e ef only exists in non-wealth constrained economies as suggested by (12). There -tyes C constraint binds, whereas -tyes constraint does not. -tyes C constraint (16) is a decreasing line in the (, h)- sace so that oor economies with a small roortion of good rojects fail to satisfy this constraint. -tyes constraint (15) is a monotonically increasing curve that 16

19 starts at the origin and cuts the diagonal once. elow the curve, some -tyes refer not to articiate. et us consider how a decrease in wealth affects the equilibrium in Figure 2. Decreasing reduces the funds available to entrereneurs. ecause of the tightened financial market, increases, meaning that entrereneurs are worse off. Since in this equilibrium -tyes refer entrereneurshi to becoming a financier and -tyes are indifferent, any marginal change in has a first-order imact on -tyes occuational choice, but -tyes continue to be entrereneurs. Therefore, exit from entrereneurshi occurs ( µ declines). From a financier's oint of view, the imrovement in the quality of entrereneurial ool and the increase in the lending rate increase her ayoff. owever, a decline in µ also means that the ratio of entrereneurs to financiers diminishes, driving financiers' returns downwards to the extent that the net result is a lower ayoff er financier ( F ). ence, decreasing dilutes the ayoff from both entrereneurshi and finance. y definition, -tyes remain indifferent, but -tyes' returns to entrereneurshi wane relatively faster. f continues to decrease, it will inevitably also affect -tyes actions. Thus the outcome deends on the roortion of -tyes in the economy. f the roortion is sufficiently high, the financial market will eventually run out of funds. When this haens, all -tyes are financiers. n terms of Figure 2, we hit the µ 0 constraint, and some -tyes must also become financiers. The new equilibrium is Pareto efficient. f the roortion of -tyes in the market is sufficiently low, however, there is less risk of running out of funds. Therefore -tyes' C constraint (the downward sloing line in Figure 2) is breached before the µ 0 constraint. This will cause an 17

20 abrut dro in the average quality of entrereneurs, leading to a collase of the market. The examle suggests a role of financial intermediaries that would mitigate the asymmetric information roblem. ased on oyd and Prescott (1986), we conjecture that such intermediaries would emerge if agents had access to a roject evaluation technology. Our focus is however on the effects of wealth. The examle illustrates how a decrease in wealth tightens the financial market, which is beneficial from the efficiency oint of view. The underlying reason is the same as in de Meza and Webb (1987): marginal entrereneurs are of low quality and can be driven out by higher interest rates. major difference to de Meza and Webb (1987) is that here the roblem of overinvestment emerges as art of equilibrium: the economy's total initial wealth relative to the roortion of high quality rojects is too large. Moreover, there is a ositive relationshi between wealth and entrereneurshi. This is at odds with the rediction of de Meza and Webb (1987) but has emirical aeal. 10 n the next Section we describe the all equilibria of the economy and show that interest rates can sometimes be endogenously high enough to discourage -tyes from becoming entrereneurs.. Existence and Efficiency of Equilibria Following a similar rocedure as for the case of e ef in Section.., we derive in the endix the values of the endogenous variables and determine the conditions for the existence of the six candidate equilibria. ere we resent grahically the equilibria 10 De Meza and Webb (1999) add moral hazard to their basic framework to generate a ositive relationshi between wealth and entrereneurshi. Our examle shows that one does not need moral hazard considerations to obtain the de Meza-Webb tye results and olicy recommendations while maintaining the emirically lausible relationshi between wealth and business creation. 18

21 and describe their efficiency roerties. t the end of the Section, we summarize our main results and exlain them. n Figure 3, we emloy the labeling of Table 1 to indicate the areas in which each equilibrium exists in the (, h)-sace. 11 There are two key lines: the h=/ diagonal and the vertical ˆ ( ) /( ) -line, familiar from Section. The diagonal not only divides the economies into wealth and non-wealth constrained ones, but is also a border of various equilibria in many cases. To the right of the vertical Â-line the equilibria are unique. FGUE 3 EE et us first examine non-wealth constrained economies, i.e., those below the diagonal in Figure 3. ecause there is no aggregate shortage of liquidity, this region has similarities to the case of outside finance of Section. Corresonding to the Pareto efficient searating equilibrium with outside finance (see Figure 1), we find a Pareto efficient equilibrium, e fs, in the right art of Figure 3. ll -tye rojects are financed, and -tyes are indifferent between financing the -tyes and using the storage technology. On the right hand side of the vertical -line, -tyes refer investing in storage to entrereneurshi by assumtion. ecause of costly financing ( >0), -tyes continue to find storage suerior some distance to the left of the -line. Going further to the left, once we hit the vertical -line, a Pareto inefficient semi-searating equilibrium, e efs, emerges much as in the case of outside finance. ll -tye agents are entrereneurs, but so are some -tye agents. elow the -tye -curve (equation (15)), the -tye articiation constraint is satisfied with equality through some -tyes oting for storage. bove the -tye -curve, we have the 11 n the endix, we resent a searate figure for each equilibrium. 19

22 Pareto inefficient equilibrium e ef that was characterized in Section.. ll - tye agents articiate and thus nobody uses storage even though available assets exceed the financing needs of -tye entrereneurs. Demand and suly of funds is equated through some -tye agents becoming entrereneurs. -tye entrereneurs C (and ) constraint is given by (16). utarky revails to the left of it. We then turn to wealth-constrained economies, i.e., the area above the diagonal in Figure 3. ere the contrast with the case of outside finance is stark. n the middle and right art we find relatively rich economies with a high roortion of - tyes. There, an equilibrium exists where all -tyes become financiers, and -tyes mix in their occuations between entrereneurshi and finance ( ef f ). ll funds are directed into -tye rojects, and therefore the equilibrium is Pareto efficient. Moving to the left, entrereneurshi becomes an otion to -tyes when we reach the vertical Â-line. etween it and another vertical line, Â(/ ), we have one to three equilibria in the uer art of Figure 3. One is the same ef f as on the right hand side of that line. nother is ef ef where both - and -tyes can be found among entrereneurs and financiers. The third equilibrium is ef e where all -tyes are entrereneurs and -tyes mix their occuations between entrereneurshi and being a financier. Since there are -tye agents among entrereneurs in ef e, they are Pareto inferior to ef f. ef ef and Once we cross Â(/ ) financial markets cease to oerate excet for a small area close to the h=1 border. There we find ef e where all -tyes are entrereneurs. lthough the equilibrium is inefficient, it survives thanks to a very high roortion of -tye entrereneurs. The lower is the agents wealth, the higher the needed roortion of -tye agents to avoid the collase of the financial market. 20

23 To conclude the discussion on the efficiency of equilibria, we investigate whether the Pareto inefficient equilibria are interim (incentive) efficient in the sense of olmström and Myerson (1983). 12 n the non-wealth constrained economies the equilibria e ef and e efs are not interim efficient. The social lanner could achieve efficiency, albeit not a Pareto imrovement, by imosing a high enough ( / = ( ) ) or otherwise taxing entrereneurial rofits or subsidizing inactivity. This would work because in this region the ledgeable income of -tye agents is higher than that of -tye agents. n wealth-constrained economies the equilibria ef ef and ef e cannot be interim efficient to the right of Â(/ ) because the Pareto efficient ef f exists there. To the left of Â(/ ), a social lanner cannot simultaneously discourage -tye entrereneurshi and encourage - tye entrereneurshi as the ledgeable income of -tyes is much larger than that of -tye agents. 13 We summarize the above discussion in the following roosition: POPOSTON 2: Without outside investors, a. equilibria are tyically unique: multile equilibria can only exist in an area shaed by Â(/ ), Â, (16) and (D.20) (see the endix for (D.20), b. the unique equilibrium is autarky if the level of initial wealth is sufficiently low and Pareto efficient if the level of initial wealth is sufficiently high, 12 oosely, in an interim incentive efficient equilibrium a benevolent social lanner encountering the same informational imerfections as the individual agents cannot imrove uon the market outcome without violating the agents individual rationality and incentive comatibility constraints. 13 f the social lanner were allowed to dictate the agents' occuations, efficiency could also be imroved in some other cases. n the region to the left of Â(/ ), the lanner could raise efficiency by randomly allocating agents into entrereneurshi. This would be feasible when h ( )/( ). mrovement on autarky would be ossible between Â(/ ) and  and below (15), if the social lanner could force some agents to use storage. With ositive robability, a high-enough roortion of -tye agents would using storage, ushing the roortion of -tye agents in the active oulation above the threshold (/) needed to obtain economic activity. 21

24 c. in the intermediate range of initial wealth, both Pareto efficient and inefficient equilibria exist, d. the Pareto inefficient equilibria with active financial markets are not interim efficient in the intermediate range of initial wealth, and e. the threshold levels of wealth that revent the market from collasing to autarky and yield a Pareto efficient equilibrium are higher in a non-wealth constrained economy than in a wealth constrained one. lthough arts a-d) of Proosition 2 aly both to wealth and non-wealth constrained economies, we emhasize that the aggregate wealth constraint matters. Most clearly this can be seen from art e) of Proosition 2: in wealth constrained economies  is a sufficient condition for a Pareto efficient equilibrium whereas in non-wealth constrained economies it is only a sufficient condition to avoid a collase of the market to autarky. That the equilibria are tyically more efficient when the aggregate wealth constraint binds suggests that oening u the financial market to outside investors might have adverse efficiency effects. ndeed, a comarison of Figures 1 and 3 reveals striking findings: Only to the right of outside finance dominates over endogenous finance, because in wealth constrained economies, outside finance allows the execution of all ositive NPV rojects. n non-wealth constrained economies, the equilibria coincide. To the left of, outside finance reduces the efficiency aart from the uer left hand corner where the equilibrium ef e revails. We obtain the following result: POPOSTON 3: a. When < Â(/ ) and > the outcome with outside investors weakly Pareto dominates the outcome without outside investors. 22

25 b. When [Â(/ ), Â], the outcomes without outside investors Pareto dominate the outcomes with outside investors if equilibrium ef f revails. c. When [Â, ], the outcomes without outside investors Pareto dominate the outcomes with outside investors. n other words, only if the economy is very oor ( < Â(/ ) or very rich ( > ), oening u the financial markets to outside investors may yield efficiency gains. n the intermediate range of wealth, allowing outside finance can reduce the efficiency of the financial markets: With outside finance, the equilibrium is an inefficient ooling or semi-searating equilibrium while without, the equilibrium may even be Pareto efficient. The difference in the two cases lies in the oortunity cost of entrereneurshi. Without outside financiers, all agents cannot be entrereneurs. The relative scarcity of funds raises the interest rates and the oortunity cost of entrereneurshi. This makes entrereneurshi less attractive, articularly in wealth constrained economies. When >Â, the -tye entrereneurs ledgeable income exceeds the one of the -tye entrereneurs. n such an environment the higher oortunity costs discourages foremost -tye entrereneurs, imroving the quality of the entrereneurial ool. The same logic does not aly when Â, because there the ledgeable income of -tye entrereneurs is higher. The higher oortunity cost first affects -tyes choice, causing an adverse effect on the average quality of entrereneurs. n wealth constrained economies the efficient ef f equilibrium can nonetheless be suorted for some arameter values, since the high quality of the entrereneurial ool raises the returns on finance sufficiently to kee -tyes as financiers. 23

26 C. Wealth and Entrereneurshi Proosition 3 shows some efficiency effects of wealth, but removing outside financiers also affects the way wealth and entrereneurshi is linked. s exected, the link in non-wealth constrained economies has similarities with the case of outside finance: when <Â, insufficient wealth suresses entrereneurial activity because it leads to autarky, and when Â, increases in wealth cause efficient exit of -tye entrereneurs in equilibrium e efs. owever, as the examle of Section. shows, increases in wealth stimulates inefficient entry of -tye entrereneurs in equilibrium e ef. n wealth constrained economies the relationshi between wealth and entrereneurshi is quite different: in all equilibria excet ef ef, wealth is ositively associated with efficient entry of -tye entrereneurs. n ef ef -tye entrereneurs are relaced by -tyes as wealth rises. The aggregate amount of entrereneurshi in ef ef is nonetheless increasing in wealth. The relationshi between wealth and entrereneurshi can succinctly be written as follows: POPOSTON 4: Wealth and entrereneurshi are (weakly) negatively correlated only if storage is used. Otherwise, they are (weakly) ositively correlated. The negative relationshi between wealth and entrereneurshi arises only if some agents invest in storage also in the case of outside finance. ut there storage is used for a much wider range of arameter values. Moreover, with outside financiers, increases in wealth cannot lead to entry of -tye entrereneurs once the financial markets oen u The wealth constraint also affects the distribution of economic rents: n a wealth constrained economy, -tyes earn rents, whereas -tyes earn rents if the aggregate wealth constraint does not 24

27 V. MPEFECT STOGE TECNOOGY So far we have assumed an exogenous storage technology that fully converts the initial liquid assets to consumtion goods. This assumtion, while standard, is not realistic. For examle, oor eole in develoing countries have no safe storing lace and they need invest whatever extra liquid funds they have in livestock that may die, in jewellery that may be stolen, etc. n the richer world, available storage technologies such as cash are generally better but their efficiency hinges on the stability of monetary olicy. Moreover, the assumtion is not necessarily harmless. For instance, removing the storage technology eliminates bank runs in Diamond and Dybvig's (1983) model and its variations. To verify whether our findings are sensitive to the efficiency of the storage technology, we now assume that storage is imerfect so that dereciates at rate 1-δ, δ [0,1]. The only difference to the revious model is that the agents' constraints (3) should be rewritten as j (17) π δ i, j i, i {, }, j { e, f }. When δ is close to unity, our revious analysis is robust to the introduction of imerfect storage by continuity. s one might exect, however, the equilibria will change if δ becomes small, because all agents are willing to invest either as financiers or as entrereneurs even if their returns are small. To get an idea of the changes, let us reconsider the examle of Section. ( e ef ). To guarantee that all agents articiate, we require that bind. -tyes only earn rents as entrereneurs, but -tyes may earn them also as financiers. The rents are studied in more detail in the discussion aer version (ECE DP, 2006). 25

28 (18) δ. F ll other equations remain unchanged excet that the -tye constraint (15) now takes the form (19) h( h( ) + ) ( δ ). When δ is close to unity, (19) remains a monotonically increasing curve in the (, h)- sace. Decreasing δ shifts the curve to the right, increasing the range of arameters where e ef exists. t can be shown that when δ aroaches zero, e ef exists for all arameter values in the non-wealth constrained region in so far as -tyes' C constraint (16) holds. This is quite natural, since without storage, the -tyes' constraint is trivially satisfied. For the rest of the section we focus on the case when δ=0. esides shortening the discussion, letting δ=0 generalizes our model. When the agents no longer have an access to an exogenous storage technology, investing either as an entrereneur or as a financier becomes the only way to transfer initial wealth to a consumtion good. lthough our model lacks a second investment eriod, the exercise is similar in sirit to olmström and Tirole (1998) who evaluate whether financial markets alone are able to suly enough liquidity and transform wealth over time. FGUE 4 EE The results of this exercise are summarized in Figure 4 (the calculations are available uon request). The equilibria e fs and e efs, where storage is a viable otion in the basic model with δ=1, cease to exist. nstead, e ef, ef ef and ef e exist for larger arameter value ranges. ef f remains unchanged. The largest change in efficiency occurs in non-wealth constrained economies for >, where the inefficient e ef exists instead of the efficient e fs. s a result, only Pareto 26

29 inefficient equilibria exist in non-wealth constrained economies. Without storage, - tyes are certain to invest either as entrereneurs or as financiers. Once the needs of all -tye entrereneurs are satisfied, it is imossible to revent the remaining - tyes from slitting between entrereneurshi and financiershi. For, removing storage causes only modest changes to financial market erformance, suggesting that financial markets alone can take care of transformation of wealth. V. POCY MPCTONS Though there are several limitations 15 to our simle model, we boldly offer some olicy recommendations. The first deals with financial market liberalization. f financial market liberalization means the introduction of outside investors without rojects of their own, the redictions are rather clear. iberalization can hel a very oor country from autarky and generate a Pareto efficient searating equilibrium in a rich country. ut liberalization is likely to result in a deterioration of entrereneurial quality and the erformance of financial markets in countries with medium initial wealth (comare the middle sections of Figures 1 and 3). 16 Our findings also have imlications on widely adoted olicies that seek to romote entrereneurshi (see, e.g., Euroean Commission, 2001). These olicies are often motivated by the observation that ersonal wealth facilitates entrereneurshi. lthough designing an otimal budget-balancing tax-subsidy olicy is beyond the scoe of our study, our findings can be read to suort the findings of de Meza and Webb (1987 and 1999) who argue that neither asymmetric information nor 15 For instance, future work should consider more than two tyes of agents, heterogeneity in agents wealth, non-walrasian market clearing, and more dynamic environment. n articular, we think that aying closer attention to coalition formation and the effect of creditor concentration on financial market efficiency in an equilibrium model of entrereneurshi and financial markets is a romising avenue for further research. dvances in this direction are made by ris and Welch (2005). 16 This is reminiscent of ghion et al. (2004) where financial market liberalization destabilizes an economy at an intermediate level of financial develoment which, in their model, is directly related to the initial wealth of the economy. 27