Wealth, Enterprise and Credit Policy

T H E E C O N O M I C J O U R N A LA P R I L 1 9 9 9

d

WEALTH, ENTERPRISE AND CREDIT POLICY

David de Meza and David Webb�

Empirical evidence suggests that capital-market constraints prevent low-wealth individuals fromsetting up in business. This paper shows this ®nding to be consistent with socially excessivelending and an interest-rate tax being welfare-improving. One feature of the model, banks'inability to identify entrepreneurial quality, leads to excessive bank lending and investment inlow-return projects. The reduction in the probability of bankruptcy lowers the cost of borrow-ing and eliminates deadweight costs and hence promotes entry. If the incentive effects aresuf®ciently large, wealth and the volume of entrepreneurial activity move together. A key resultof the paper is to show that a market equilibrium in which there is a positive relationshipbetween entry and the level of wealth is consistent with either subsidies to inactivity or taxes oninterest raising welfare.

A host of empirical studies have found evidence of a positive correlationbetween asset ownership and entrepreneurship.1 The usual interpretation isthat liquidity constraints play a major role in determining who becomes anentrepreneur. A belief that capital-market failure has held back enterprise hasbeen a factor behind policies designed to encourage start-ups and businessexpansion. Examples include the grants and subsidies provided by the FederalSmall Business Administration in the United States and the Loan GuaranteeScheme in the United Kingdom. The purpose of this paper is to show that apositive association between entrepreneurial wealth and business activity doesnot establish a prima facie case for government intervention to encourageentrepreneurship. Even though insuf®cient wealth is all that prevents rationalagents setting up in business, the cost of capital may be too low, so theappropriate government policy is to discourage borrowing.

Theoretical explanations of capital market imperfections have centred uponasymmetric information with Stiglitz and Weiss (1981) being the most notablecontribution. The aim of their paper is to show how credit rationing mayemerge even when agents are optimising. The key to the result is that a bank'sexpected return may eventually start to fall as it increases the interest ratecharged to borrowers. This is because with regular debt contracts the bankbears the downside risk (an adverse-incentive effect), so at high interest rates

The Economic Journal, 109 (April), 153±163. # Royal Economic Society 1999. Published by BlackwellPublishers, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA.

[ 153 ]

� The authors would like to thank Yakov Amihud and two referees for their useful comments andsuggestions.

1 Cross section evidence is provided in Blanch¯ower and Oswald (1995), Evans and Jovanovic(1989), Holtz-Eaken et al. (1994). Evidence that aggregate wealth boosts the total number of start ups ispresented by Black et al. (1996). The latter paper's ®ndings are closest to those examined in this paper.

borrowers switch to riskier projects, For similar reasons, as interest rates rise itis intrinsically safe projects that are hardest hit (full repayment occurs morefrequently) and so are the ®rst to drop out (an adverse-selection effect).Default rates may thus increase by so much that the interest rate rise is counterproductive. This puts a cap on the interest rate charged and is the source ofequilibrium credit rationing whereby, even in the presence of an excessdemand for loans, banks may not choose to raise interest rates. In Stiglitz andWeiss, entrepreneurs differ in terms of their riskiness. An alternative formula-tion is that entrepreneurs can be ranked by ability, so the returns of a high-quality type are in a relationship of ®rst-order stochastic dominance to some-one of lower quality.

In earlier work (de Meza and Webb, 1987), we showed that when entrepre-neurs whose ability differences are private information are ®nanced with debt,the market equilibrium exhibits too much activity.2 The problem arisesbecause in equilibrium more able entrepreneurs cross subsidise the less able,leading to excess entry. However, that model has the feature that, as wealthrises, cross subsidies diminish and so exit occurs. This is at odds with theevidence.

This paper combines the hidden action aspect of Stiglitz-Weiss with thehidden type assumption of de Meza-Webb. Given that project risk is endo-genous, when ®nanced with risky debt, entrepreneurs choose a higher level ofrisk at the expense of expected return compared with self-®nance. As entrepre-neurs become richer and take more equity in their projects, they have areduced incentive to take risk and choose projects of higher expected return.This means that as wealth increases, the deadweight cost of moral hazard islowered which leads to entry.3 The question which concerns us is whethergovernment policy should therefore be directed at encouraging entry.

In our model, even with a positive association between wealth and activity, inthe laissez-faire equilibrium marginal entrepreneurs have negative expectedvalue and should be excluded from the market. Policies which do this withoutnegative incentive effects on active entrepreneurs are clearly desirable. Oneway of accomplishing this is by subsidising inactivity, though there are pro-blems implementing this policy. An alternative means of in¯uencing the levelof activity is by changing the cost of capital and this is the form of intervention,along with various forms of direct grants, that policy discussions generally focuson. Our main ®nding here is that even though incentive effects create apositive association between wealth and activity, a tax on borrowing may raisesocial surplus, despite increasing the deadweight cost of moral hazard. Finally,we ®nd conditions under which a balanced budget tax/subsidy scheme yields astrict Pareto improvement.

2 The model of Bernanke and Gertler (1990) also generates a negative relationship between wealthand entry due to advantageous selection argument analogous to that in de Meza and Webb. (1987)

3 Similar conclusions follow if, instead of facing a risk-return trade off, entrepreneurs can increasethe probability of success by expending costly effort.

154 [ A P R I LT H E E C O N O M I C J O U R N A L

# Royal Economic Society 1999

1. The Model

1.1. Entrepreneurs

There is a population of risk-neutral agents. Each has the option of becomingan entrepreneur. Individuals differ in their entrepreneurial ability indexed bya 2 [a, a] but all have the same initial wealth W . 0. However, entrepreneurshave discretion over the type of project, in the form of a risk-return trade-off.All projects require an outlay of K . As K . W , an entrepreneur must raiseoutside ®nance. The entrepreneur's ability and the project's risk are assumedto be private information.

More speci®cally, projects are described as follows: an investment of K by anentrepreneur of ability a in a project with risk characteristic è yields a randomreturn stream of aX (è) with probability p(è) and zero with probability1ÿ p(è), where X (è) . 0. Then the expected gross value of the project is

E � p(è)aX (è), (1)

which is increasing in a. The project's expected return varies with the chosenrisk-return characteristics. As è increases the return in the event of success ishigher (X 9(è) . 0), but the probability of success decreases ( p9(è) , 0) even-tually by so much that the expected return decreases. In other words, for highè, the risk of the project only increases at the expense of a lower expectedreturn. So, assuming all functions are continuously differentiable, under self®nance, è � ~è, which we assume is the unique turning point of E , satis®es

dE

dè� a[ p9(~è)X (~è)� p(~è)X 9(~è)] � 0: (2)

The equilibrium form of ®nance in this setting is sensitive to the informationstructure. When project returns are costlessly veri®able the conjunction ofmoral hazard arising from hidden action, and adverse selection arising fromhidden ability makes the equilibrium contract a complex instrument. Statedependent repayment will be designed to elicit appropriate self-selection andalso create incentives for ef®cient risk taking. What emerges has limitedresemblance to the standard debt contract typically observed in practice. Herewe will assume that project returns cannot be veri®ed by outsiders. All that canbe observed is whether a payment is made. As a result, the only incentive-compatible form of ®nance is a ®xed repayment, with the provision that if thepayment is missed, the investor is entitled to seize the value of the project. Theentrepreneur is then always better-off making the ®xed payment if he can.4

4 The classic papers of Gale and Hellwig (1992) and Townsend (1979) derive debt ®nance as aresponse to costly state veri®cation. Debt economises on these costs since veri®cation is only required indefault states. It is implicitly assumed that the borrower can hide income so unless the bank commits toverify in default states it would never be repaid. In contrast, we assume that if the bank takes controlfollowing a (costlessly observed) default there is nothing an entrepreneur can do to prevent the banktaking whatever has been earned. Thus, the debt contract is incentive compatible without veri®cationcosts being incurred. This case is a very much simpli®ed version of the incomplete contracting modelsas in, for example, Aghion and Bolton (1992) and Hart (1995) and Hart and Moore (1994). Notice thatif veri®cation costs were involved in default the fundamental properties of our model would not beaffected but the analysis becomes very messy.

1999] 155W E A L T H , E N T E R P R I S E A N D C R E D I T P O L I C Y


The terms of the standard debt contract are that the entrepreneur borrowsan amount B, and promises to repay the bank D, and in the event of defaulthe forfeits the project. The net return to an entrepreneur of ability a ®nancedwith a standard debt contract is

ð(D; a, è) � max[aX (è)ÿ D, O]: (3)

It turns out that all active entrepreneurs provide maximum self ®nance,5 sothat B � K ÿ W . The entrepreneur's expected pro®t on the project is thus

ð(D; a, è) � p(è)[aX (è)ÿ D]: (4)

The entrepreneur will want to undertake a project ®nanced with a debtcontract if and only if

ð(D; a; è) > (1� r)W (5)

where r is the rate of interest if W is invested in a safe asset which is assumedto be in perfectly elastic supply. As the supply of funds to the economy is notincreasing in the rate of interest, r , a credit rationing equilibrium is ruled out.

For an entrepreneur of type `a' facing a given D . 0, his choice of èmaximises (4) and so satis®es

dð

dè� p9(è)[aX (è)ÿ D]� p(è)aX 9(è) � 0: (6)

Denote the optimal value of è by è�(D, a). Note, by inspection of (2) and (6),è�. ~è. When ®nanced with risky debt, all entrepreneurs are driven toexcessive risk taking relative to the value which maximises total expectedreturn. The reason is that with debt the entrepreneur does not bear all thedownside risk of an increase in è. We can now prove:

Proposition 1. Given debt repayment, D, the more able the entrepreneur thesafer the project chosen.

Proof. From condition (6) and using the implicit function theorem

@è�@a� ÿ [ p9(è�)X (è�)� p(è�)X 9(è�)]

Ä, 0, (7)

where the signing follows from Ä, 0, the second-order condition for a maxi-mum, and by (6) the term in square brackets in the numerator is negative.This implies that

@f p[è�(D, a)]g@a

� p9(è�) @è�

@a. 0: (8)

h

5 There are two reasons for this. More self ®nance lowers D and thereby reduces the deadweight costof excessive risk taking. There is also a signalling argument. In a pooling equilibrium, entrepreneurscan always ®nance themselves on better terms than they obtain in the market for risky debt in whichthey subsidise less able entrepreneurs. Failure to invest their own wealth would reveal an entrepreneuras low-quality (see de Meza and Webb (1987) and Innes (1992)). An alternative but equivalentequilibrium is that entrepreneurs post all their wealth as collateral or that the debt contract is unlimitedliability.



According to this result, more able entrepreneurs adopt safer projects and areless likely to default. Since with given D the more able type capture a highershare of project returns, their choice of è is more closely aligned to the sociallyef®cient value.

Next, we need to show the effect of a change in the debt payment D on thechoice of project for an entrepreneur of type a. This is a simple corollary ofProposition 1.

Proposition 2. An entrepreneur of type a ®nanced with risky debt will switch toriskier projects as D increases.

Proof. Differentiating (6) we obtain

@è�@D� p9(è�)

Ä. 0, (9)

which implies that

@ p[è�(D, a)]

@D� p9(è�) @è

�@D

, 0: (10)

h

The intuition here is well known (see for example, Jensen and Meckling(1976)). As the debt payment increases entrepreneurs care increasingly aboutthe upper tail of the project return distribution, leading to greater risk taking.The next result follows from a simple application of the envelope theorem.From (4) the effect of an increase in D on entrepreneur pro®t is

@ð[D; a, è�(D, a)]

@D� ÿ p[è�(D, a)]: (11)

1.2. Banks

Banks do not know the characteristics of individual entrepreneurs but areinformed of the population distribution of entrepreneurs' abilities and of theinvestment opportunities with which they are faced. Let G(a) be the distribu-tion function of abilities and g(a) the corresponding density function. De®nethe expected gross return to a bank on a loan to an entrepreneur of type `a'with promised repayment D as

r(D, a) � p[è�(D, a)]D: (12)

We assume that (uniformed) banks move ®rst and offer ®nancial contracts.(Informed) entrepreneurs move second and apply for the most attractivecontract offer. With banks offering debt contracts, entrepreneurs apply for thecontract with the lowest repayment. Then the only possible equilibriuminvolves pooled-debt contracts yielding banks zero expected pro®t. A bankwhich offers a contract with principle K ÿ W and repayment D attracts asample of applicants with abilities a > a, where a is the ability of the worstentrepreneur who applies.



The bank's expected pro®t per loan is given by

Ð(D) � pa D ÿ (1� r)(K ÿ W ), (13)

where

pa ��

a

p(è�)g(a)da

1ÿ G(a)

is the average probability of success.A straightforward but important result follows from the fact that competition

forces Ð to zero.

Proposition 3. In equilibrium, marginal projects have negative expected value.

Proof. By de®nition, the marginal entrepreneur expects to earn the normalreturn on his self investment, W . So the overall performance of the projectequals the net return of the bank. De®ning p as the success probability of themarginal project, the expected pro®t of a bank on an entrepreneur of ability ais pD ÿ (1� r)B � ( p ÿ pa)D , 0. The equality follows from Ð � 0 and theinequality holds by Proposition 1. h

The intuition here is that in a pooling equilibrium the bank must makepositive expected pro®t on loans to entrepreneurs with positive expected netreturn projects. This pro®t is dissipated in equilibrium through cross-subsidiesto low quality entrepreneurs with low expected net return projects and somewith negative expected net return projects who are drawn into the market. Theset up therefore involves advantageous rather than adverse selection.

2. Wealth Dependency

We now examine the effects of changes in the level of wealth on theequilibrium. In the de Meza and Webb (1987) model increased wealth reducesentrepreneurial activity. The lower amount of borrowing must reduce theequilibrium cross-subsidies to poorer projects including those of negativeexpected net return, leading to exit. However, in the model presented herethe lower level of borrowing has a countervailing incentive effect. We will showthat the counterfactual feature of the de Meza and Webb (1987) model canthen be overturned without affecting the welfare properties.

Proposition 4. In the presence of incentive effects, an increase in entrepreneur-ial wealth can lead to the entry of lower ability entrepreneurs.

Proof. Suppose that the rise in wealth is accompanied by a fall in D justsuf®cient to induce the marginal entrepreneur to remain active. With nochange in a, from (13), the impact on bank pro®t is

dÐ

dW� pa � D

�a

p9(è�) @è�

@D

g(a)da

1ÿ G(a)

" #dD

dW� (1� r): (14)



Using (5) set to equality and the envelope theorem, we ®nd that as the wealthof the marginal entrepreneur increases participation is just preserved if

dD=dW � ÿ(1� r)= p, (15)

which upon substitution into (14) yields

dÐ

dW� (1� r)

p( p ÿ pa)ÿ D

�a

p9(è�) @è@D

g(a)da

1ÿ G(a)

� �, (16)

where p , pa , so that the ®rst term in the bracket is negative, but the secondterm (the incentive effect) is positive. Hence, if the incentive effect is strongenough, competition will force the banks to cut D by even more, thusattracting additional entrepreneurs. h

The intuition behind this result is as follows: in the neighbourhood of zerowealth effects, wealth rises and the amount of borrowing declines, if D falls tothe level which makes the marginal entrepreneur, a, indifferent to entry and,holding project risk ®xed, the bank expects a loss. However, as D falls there isan offsetting increase in bank pro®tability due to the reduced riskiness ofloans. If this latter effect dominates, entry will occur. Clearly, in the absence ofincentive effects (16) will be negative and increased wealth will be associatedwith exit.

3. Policy

In a competitive equilibrium, inef®ciencies arise from two sources. On the onehand there is the problem of hidden type and on the other hand there is anexcessive amount of risk taking because of the moral hazard induced by thedebt contract. Government policy should be directed at ensuring the rightoverall volume of investment and the appropriate degree of risk-taking.

For the moment, ®scal policy is appraised in terms of the total social surpluscontributed by the pool of active entrepreneurs:

S ��

a[ap(è�)X (è�)ÿ (1� r)K ]g(a)da

��

afð[D, a, è�(D, a)]� p[è�(D, a)]D ÿ (1� r)(K ÿ W )gg(a)da: (17)

This criterion assumes a utilitarian social welfare function. Proposition 3provides the key to designing policy. A welfare improvement is certainlyachieved if the loss making marginal entrepreneurs drop out and there are noadverse incentive effects on active entrepreneurs. In our model there exists asimple policy which achieves this.

Proposition 5. A small subsidy to not being an entrepreneur raises aggregateincome.

Proof. As a result of the subsidy marginal entrepreneurs will no longerparticipate. By Proposition 3 this will increase S . However, these entrepreneurs



involved the banks in an expected loss, so their disappearance will result in afall in D and an associated reduction in the risk of remaining entrepreneurs,which further raises S . h

The effects of the subsidy to not being an entrepreneur provides a clearillustration of the working of the model and serves as a warning that theopposite policy, often used in practice, of subsidising entrepreneurs may haveperverse welfare effects. Still, there are quali®cations. Implicit in Proposition 5,is the assumption that the revenue to pay for the subsidy can be raised bymeans of a tax elsewhere in the economy with zero deadweight cost. A land taxmight perhaps ®t the bill. Still, it is unlikely that the subsidy outlay is easilyfound. There is also the question of identifying inactive potential entrepre-neurs to receive the payment. There will also be a distortionary incentive effecton savings in banks. There is therefore interest in examining a policy of taxingentrepreneurs rather than subsidising non-entrepreneurs. Although expellingloss-making entrepreneurs, this policy has the drawback of encouraging risktaking and so adding to the deadweight cost of those remaining. The issue weaddress is whether a welfare improving tax is consistent with a positive wealtheffect.

Consider a tax ô, payable by the banks on loans. In effect, the banks mustnow pay an interest rate of r � ô on deposits. However, if an agent does notparticipate he continues to earn the world interest rate, r , on his wealth.De®ne ç � jDN 9(D)=N j as the absolute elasticity of entry N � 1ÿ G(a) withrespect to D. Then

Proposition 6. At zero wealth effect, a tax on lending raises income if the(absolute) elasticity of entry with respect to repayment, D is greater than unity.

Proof. Differentiating (17) with respect to the interest rate tax, ô and usingthe entrepreneur's ®rst-order condition (6) we obtain

dS

dô�ÿ g(a)

da

dD

dD

dôfð[D, a; è�(D, a)]� pD ÿ (1� r)Kg

� dD

dôD

�a

p9(è�) @è�

@Dg(a)da: (18)

For zero wealth effect, in the sense that the number of active entrepreneurs isinvariant to aggregate wealth, it is required that (16) equals zero,

D

�a

p9(è�) @è�

@D

g(a)da

1ÿ G(a)� p ÿ pa : (19)

Using (19) and the fact that ð[D, a; è�(D, a)] � (1� r)W and pa D �(1� r)(K ÿ W ) we obtain from (18)

dS

dô� [1ÿ G(a)]( pa ÿ p)

g(a)

1ÿ G(a)

da

dDD ÿ 1

� �dD

dô: (20)

Hence, a tax is appropriate if



ç � g(a)

1ÿ G(a)

da

dDD . 1: (21)

h

By continuity, it follows from Proposition 6 that if ç. 1, there will be a positiveupper bound on the wealth effect for which a tax is welfare improving. Thuswe see that the tax eliminates losses on negative expected net return projects,but increases the deadweight cost of moral hazard on those projects under-taken. For every magnitude of wealth effect, there exists a threshold exitelasticity for which welfare is unchanged by the tax. When incentive effects arerelatively large, wealth effects are higher and possibly positive. Then thedeadweight cost of moral hazard is higher and so the threshold elasticity rises.Black and de Meza (1996) found the elasticity of exit with respect to theinterest rate to be 1.3. But note that since a higher interest rate also increasesthe return to non-participation this is an underestimate of ç.6 Finally weconsider a balanced budget policy. Since the returns to entrepreneurs arestochastic, our criteria for a strict Pareto gain is that the expected utility of noagent is lower and that of some is higher.

Proposition 7. If ç.[ p=( pa ÿ p)]G(a)=[1ÿ G(a)] introducing a smalltax on borrowing with the proceeds used to subsidise inactive entrepreneurs yields astrict Pareto gain.

Proof. Consider a small per capita subsidy of ds to inactive entrepreneurs, thetotal value of the subsidy being G(a)ds. This subsidy is ®nanced by a tax onactive entrepreneurs. The subsidy lowers D and the tax raises D so there existsa tax/subsidy scheme which leaves D unchanged. Keeping D ®xed, therevenue from the tax equals the loss the banks made on the entrepreneurswhich leave, so the tax revenue is ( pa ÿ p)Dg(a)da, where g(a)da entrepre-neurs leave because of the tax/subsidy scheme. Then, in the case of a balancedbudget, we have

G(a)ds � ( pa ÿ p)Dg(a)da: (22)

Now for the marginal entrepreneur, it follows from (11) that a per capitasubsidy of ds to inactivity has the same impact on activity as a change in Dequal to ds= p. Substituting into (22) and multiplying and dividing by1ÿ G(a), we obtain

çpa ÿ p

p

!1ÿ G(a)

G(a)� 1: (23)

where ç given in (21), is the exit elasticity consistent with the budget being

6 A referee has pointed out that the threshold value of ç for zero wealth effect is alo unity in a ratherdifferent formulation. Suppose each entrepreneur can increase the success probability by increasingeffort. The marginal and average cost of effort is lower for more able entrepreneurs and this is the onlyheterogeneity present. All our results are mirrored in this model and, with success payoffs the same forall types, and zero in the event of failure, even with costless veri®cation, ®nance is the form of debt.



balanced and D ®xed. If activity is even more responsive to D than the valuesatisfying (23), then were D to remain at its initial level, the same tax/subsidypolicy will generate more tax revenue than is needed to pay the given subsidyso the tax can be cut. This implies that D will fall, thereby raising the welfare ofactive entrepreneurs. Inactive entrepreneurs are also better-off due to thesubsidy. Hence there is a strict Pareto improvement. h

The conditions for a Pareto gain are more likely to be ful®lled if theproportion of active entrepreneurs is relatively large, for then the tax ®nancesa large per capita subsidy to non-participation. The marginal project being ofconsiderably lower quality than the average also helps, since then any transi-tion to inactivity raises more tax revenue. Finally, it is clear that the moreresponsive entry to return differentials, the better the prospects for a Paretogain.

4. Conclusion

This paper has shown that even though more people become entrepreneurs aswealth increases, welfare improving intervention may actually reduce the num-ber of entrepreneurs.7 These results emerge in a model in which hidden typesand hidden action are present. Not only can suitable policies raise aggregatewelfare, it is shown that a balanced budget policy which subsidies non-participation and taxes participation may yield a strict Pareto improvement.

These ®ndings have an element of paradox. It is consistent with the modelthat entry is monotonically increasing in wealth. When wealth is suf®cient toallow full self ®nance, the number of projects and their execution is such as tomaximise aggregate income. It therefore seems that if wealth is below thislevel, there must be too few projects and policy should be designed to increaseentry rather than decrease it. The reconciliation involves the fact that theallocation achieved when everyone in the economy is very wealthy cannot bereplicated by intervention. If wealth could be created out of thin air, then theeconomic problem would indeed be solved. In the absence of such powers,what the policy maker can achieve is limited. Giving a grant to those becomingentrepreneurs to enable them to self ®nance eliminates the deadweight cost ofexcessive risk taking but, since the grant is dependant on participation, itevidently leads to excessive entry. Taxing non-participation, even if feasible,fails because the projects induced to enter must face high debt repayments soare designed by their owners to be excessively risky from the social viewpoint.These are the projects that would be worth undertaking if self-®nanced,because then they would be better run, but are of unambiguously negativevalue when debt ®nanced. This is why it is right to exclude such entrepreneurs,even though they would contribute to social surplus if their net worth werehigher.

7 In de Meza and Southey (1996) the same conclusion follows for a very different reason.Entrepreneurs are self selected as those with the most extreme excess optimism.



University of Exeter and London School of Economics

London School of Economics

Date of receipt of ®rst submission: March 1997Date of receipt of ®nal typescript: October 1998

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Wealth, Enterprise and Credit Policy

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