Analisis Estadistico

economics letters Economics

Letters

46 (1994) 243-249

The nature of credit-market Jane Black” 1* , David

failure

de Mezaalb

“University of Exeter, Exeter, EX4 4RJ, UK bUniversity of Guelph, Guelph, Ontario, Nl G 2W1, Canada Received

27 December

1993; accepted

21 March

1994

Abstract Hidden borrowers sufficiently JEL

preferred knowledge gives rise to over-lending if, as evidence suggests, the returns distributions are also favoured by lenders. Even the Stiglitz-Weiss model yields over-lending when entrepreneurs risk averse.

classification:

by are

D82

1. Introduction Following the discussion in Akerlof (1970) a presumption has arisen that hidden knowledge distorts credit market equilibrium towards under-lending. This paper demonstrates that if in each state of the world returns are an increasing function of entrepreneurial ability or, even less restrictively, if the distributions of entrepreneurs’ returns can be ranked by first-order stochastic dominance, then the volume of lending exceeds that under full information. Over-lending arises in these circumstances whatever the risk preferences of entrepreneurs. This generalises the example of de Meza and Webb (1987) which involves risk-neutrality and two-point return distributions with entrepreneurs differing only in their success probabilities. Using the approach developed here it is easy to show that the under-lending result, implicit in Stiglitz and Weiss (1981), arises when return distributions differ by mean-preserving spreads but that if risk aversion is sufficiently great, then even their equilibrium involves overlending. The concluding section identifies the general principle determining whether under-lending or over-lending emerges and shows that the evidence favours the latter. * Corresponding

author.

0165-1765/94/$07.00 0 1994 Elsevier SSDI 0165-1765(94)00473-F

Science

B.V. All rights reserved

244

J. Black,

D. de Meza

i Economics

Letters 46 (1994) 243-249

2. The basic model As in Stiglitz and Weiss (1981) all potential entrepreneurs own liquid wealth W and have the opportunity to undertake a project of fixed size requiring capital input k > W and yielding random end-of-period return gross of capital cost, y”. There are at least two risk-neutral banks able to attract deposits at the safe interest rate Y, which is set on the world market. Banks move first and make simultaneous and irrevocable offers of finance. In this setting such Bertrand-style competition drives expected bank profit to zero. Borrowers/entrepreneurs have private ex-ante information about the probability distribution of their ex-post returns. The nature of entrepreneur heterogeneity has implications for equilibrium financial contracts (de Meza and Webb, 1987; Innes, 1993). Debt generally emerges under first-order stochastic dominance and equity with second order. The Stiglitz-Weiss model must therefore invoke some further factor such as costly state verification (Townsend, 1979; Gale and Hellwig, 1985; Williamson, 1987) to explain the use of debt. To relate to much of the literature and for brevity, standard debt contracts will henceforth be exogenously imposed. That is, the entrepreneur repays in full if project realisation, y, exceeds the loan plus interest charged, with the bank receiving y in the event of default.’

3. Analysis We start by assuming risk neutrality and that projects can be ranked by first-order stochastic dominance. In de Meza and Webb (1987) it is shown that maximum self-finance is a feature of equilibrium. The reason is that reluctance to invest in your own project would be a strong signal of poor quality. Innes (1993) extends this property to more general distributions and proofs will not be repeated here. If projects can be ranked by first-order stochastic dominance the properties of equilibrium are easily established graphically. Let F(y) be the cumulative distribution function for the gross return from a project with y the lower bound of y. Integrating by parts,

WI =

ix Y

For distribution

Y./-(Y)dY = Y + i Y

aCl-

F(Y))

dY.

A in Fig. 1 this is the shaded

area above

the cdf enclosed

by the lines y = 0,

F=l

Fig. 1. ’ It is easily seen that equilibrium. The problem

whatever the form of finance, ability may be more severe in equity markets

differences lead to over-lending than in debt markets.

in a pooling

.I. Black, D. de Meza I Economics

Letters 46 (1994) 243-249

245

F = 1 and the function F(y). In like fashion, if the bank sets a repayment of D, the expected receipts of the bank are given by the cross-hatched area which lies to the left of the line y = D, and the entrepreneur’s expected return is correspondingly given by the single hatched area lying to the right of this line.’ Fig. 1 shows the cdfs of three different entrepreneurs with A the least able and C the most able. The equilibrium repayment required of borrowers is D. If the safe interest rate is Y and the cross-hatched area equals (1 + r)W, it follows that the owner of project A is indifferent between investing his wealth and applying for funds to undertake the project. For the banks to break even the areas enclosed by y = D and the cdfs, averaged across all projects seeking finance, must equal (1 + r)(K - W). Since A’s expected repayments are less than the average, it follows that for project A the expected gross return, E(y2, is less than (1 + r)K. That is to say, project A yields an expected social loss. Since at D the bank’s expected return is lowest on project A, under full information it would face a higher interest rate and so would not be undertaken. This line of reasoning makes it easy to extend the results to entrepreneurial risk aversion. If all agents have the same preferences, the marginal entrepreneur would be of higher quality than is A and the pooling interest rate correspondingly lower than under risk neutrality. Nevertheless, the entrepreneur on the margin of wishing to invest remains the least profitable to the bank of all those in the pooling equilibrium. Under full information this project would be charged a higher rate of interest and so this and other low yielding projects would be eliminated. Under risk aversion the fact that there is more investment than under full information does not guarantee that policies which eliminate projects are beneficial because they may entail adverse insurance consequences. The welfare link is forged later, but for now the positive economics is summarised.3 Proposition 1. If projects can be ranked by first-order stochastic dominance, then even under risk aversion investment is higher under asymmetric information than under full information. In seeming contrast to this result, Stiglitz and Weiss (1981) explore rationing using examples where projects differ by mean-preserving *The

total expected

WI = j-O yf(y) P and the expected

receipts 2

dy + D I, receipts

E[Gl =

I,,(Y - DMY)

of the bank are f(r)

dy = Y + I ” (1 -F(y)) L

of the borrower,

r

the possibility of credit spreads. The welfare

less repayment

dy > of the bank,

are

m

dy =

I, Cl-

F(Y))

dy

3 De Meza and Webb (1990) assume equity and debt are both feasible. For a two-point distribution with stochastic dominance and risk-aversion they show that a pooling equilibrium must involve some projects being funded with an expected gross return below the cost of the capital. Here we assume debt is the only possible form of finance and it is then possible that with risk aversion the marginal project has expected return in excess of the cost of capital. Even so, it is subsequently shown that there is excess investment.

246

J. Black,

D. de Meza

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Letters 46 (1994) 243-249

implications are examined in de Meza and Webb (1987). For a class of two-point distributions it is shown that whether or not credit rationing emerges, under risk-neutrality and assuming debt contracts, the pooling equilibrium involves under-investment. To see how far this result generalises, consider Fig. 2 where E(fi is the same for project A (relatively safe) and project B (risky). The expected return to an entrepreneur undertaking project A is the shaded area, which must be less than that of project B. Project A, which as far as the entrepreneur is concerned has the lowest expected return of all those in the pooling equilibrium, is thus the one which contributes most to the bank’s expected return. Under full information it would be charged a lower interest rate than represented by D and so be strictly profitable to the entrepreneur, as would all those even safer projects excluded from the pooling equilibrium but yielding the same E(y> as those which are funded. When projects differ by mean-preserving spreads and entrepreneurs are risk neutral, investment is below the full information level. The basic reasoning here is that, Introducing risk aversion may upset this conclusion. though at given D riskier projects offer a higher expected return to the entrepreneur, if at the equilibrium D riskier projects have higher default probabilities, then they may be less attractive to risk-averse entrepreneursP If so, since risk projects would carry higher interest rates in the pooling equilibrium than under full information, hidden knowledge would expand investment. Proposition 2. When entrepreneurs are risk neutral and project returns differ by rneanpreserving spreads investment is lower than under full information, but if entrepreneurs are risk averse, investment may be higher than under full information.

r

1

Fig. 2.

’ Let F, and Fz be two cdfs where Fz is a mean preserving spread both entrepreneurs the difference in expected utilities is r * A= D U(Y-DV,(y)dyD u(y-Dlfi(y)dy= i 0= WY - DU, I I Normalising U(0) = 0 and integrating I A= u’(Fz-F,)dy. I I) A is positive

provided

of F,. Assuming

-.b)

the same utility function

for

dy

by parts:

F, > F, at D and U’ is sufficiently

decreasing.

Obviously

D = y would guarantee

that A > 0.

.I. Black, D. de Meza I Economics

247

Letters 46 (1994) 243-249

Under risk aversion the policy implications of Propositions 1 and 2 are not immediate. Nevertheless, a simple and strong result is available. Consider a policy of levying on banks at tax t per loan with the proceeds given to non-entrepreneurs. Provisionally suppose that this does not affect the number of entrepreneurs, ~1. Let F, be the cdf for the ith entrepreneur. Since the banks must break even, dDldt=n

Assume all entrepreneurs entrepreneur: dEW d dD

1

(1)

i (l-F,(D)). I i=l have the same utility

function.

Let U, be the utility

of the ith

0 = WW

- W4) - I,

U”(Y

- WU

- F,(Y))

dy >

giving dE(u,)/dt

i

= i:

[-v’(O)

- c

(I nF(o))

I

i

but n/C (1 -E;)(D))>1 -i

dE(U,)/dr i

i,: u”(Y - D)(l

- K(y))

dy] ’

(2)

I

and U”