Federal lending and the market for credit

Journal

of Public

Economics

FEDERAL

42 (1990)

1777193.

LENDING

THE William

Universiry of California, Received

November

North-Holland

MARKET

CREDIT

GALE*

Los Angeles, CA YOO24-1477, USA

1988, revised version

received

December

1989

Federal lending is an important, but unrecognized feature of modern credit markets. This paper analyzes the effects of credit interventions on credit allocation and economic efftciency. The underlying model posits asymmetric information between borrowers and lenders, and allows for market clearing, rationed, or redlined equilibria. Principal results include: unsubsidized credit interventions are neutral; the relative effectiveness of alternative lending instruments depends on whether rationing occurs; interactions among programs can have perverse effects; and, even without an informational advantage, the government may enact welfare-improving credit policies under certain conditions.

1. Introduction

The federal government is a major participant on both sides of the capital market. Although federal borrowing has been the subject of heated debate in recent years, relatively little attention has been given to the government’s longstanding and sizeable presence as a lender. The government supplies or reallocates credit through direct lending, loan guarantees, the provision of tax-exempt status, and the activities of Government-Sponsored Enterprises. These federal programs have directly subsidized, guaranteed, or extended approximately one-third of all net credit issued to non-federal sectors since 1980. This paper analyzes the effects of such policies on credit allocation and economic efficiency in a model where borrowers retain private information concerning their ability to repay loans. Although models of asymmetric information in credit markets have proliferated in recent years, only Mankiw (1986) de Meza and Webb (1987, 1988) Smith and Stutzer (1988) and Gale *This paper is based on Chapter 3 of my Ph.D. dissertation. An earlier version circulated under the title ‘Federal Lending Policies and the Market For Credit’ (November 1986). I thank my dissertation committee, Michael Boskin, Doug Bernheim, and John Shoven, for many helpful discussions. I have also benefited from comments from Brad Barham, David Butz, John Duca, Al Harberger, Seonghwan Oh, Russell Roberts, John Karl Scholz, Michael Waldman, and two anonymous referees. Discussions with John Riley have proven particularly helpful. 1 thank the John M. Olin Foundation for financial support, and Lorraine Grams and Kathy Martija for word processing assistance. 0047-2727/90/$03.50

0

199GElsevier

Science Publishers

B.V. (North-Holland)

W.G. Gale, Federal

178

lending

(1989) have studied credit subsidies in this framework.’ These papers show that, in the presence of asymmetric information, credit policy can generate important, non-standard effects on allocation and efficiency. The model presented here differs from the papers above in several ways. Unlike Mankiw or de Meza and Webb, this paper explicitly models the effects of alternative lending instruments. Since the government can choose to intervene through any of a variety of policies, the differing effects of each instrument are important. Unlike Smith and Stutzer, the model examines regimes characterized by market clearing, rationing, or redlining of the target group. Since many recipients of credit assistance are thought to be rationed or redlined without credit subsidies, it is important to examine credit policy in different states of the market. Unlike all other work in this area, interactions among programs that target different groups are examined. Since the government simultaneously assists many groups of borrowers, these interactions are an important policy consideration. Finally, the resource costs of federal credit are explicitly included in the welfare calculations. By modelling these features of federal credit policy, the paper generates several new results, as described below. Section 2 provides an overview of federal lending activity. Section 3 develops the underlying model of the credit market. Section 4 adds credit programs to the model. Section 5 examines the effects of credit subsidies on investment and interest rates. Unsubsidized interventions are shown to be neutral. Guarantees are shown to be relatively more effective than pure subsidies in rationing than in market-clearing equilibria. Subsidies to one group reduce or eliminate investment by other groups. Section 6 analyzes efftciency effects. Because the ordering of projects by expected bank return and expected social return differs, small credit subsidies can improve on the market outcome under certain conditions. The conclusion discusses implications of the principal results and some possible extensions of this research.

2. Federal lending activity* Prior to agriculture,

19.50, credit and business

subsidies [Saulnier

focused almost et al. (1958)].

exclusively on housing, By 1952, federal credit

‘Smith (1983) discusses optimal government lending with imperfect information, but focuses on monetary policy rather than credit subsidies. Chaney and Thakor (1985) examine emergency loan guarantees. As they point out, these should be distinguished from ongoing guarantee programs, which guarantee many loans, smaller amounts per loan, and do so at the time the loan is made. Bosworth, Carron and Rhyne (1987) present a large amount of information and discussion concerning all aspects of federal credit. Gale (1988a) provides numerical estimates of the effects of current credit policies. ‘Detailed information concerning federal credit programs may be found in ‘Special Analysis F’, SpeciaL Analyses: Budget of the U.S. Government, any year, or Bosworth, Carron and Rhyne (1987). Unless otherwise cited, data in this section are obtained from ‘Special Analysis F’, Specinl Analyses: Budget qf’ the U.S. Gooernment, selected years.

W.G. Gale, Federal lending Table Federal

lending

179

1

and credit market

aggregates,

198&1987. $ (billion)

Net credit advanced in non-financial credit marketsa Net federal and federally assisted lending Direct loans Loan guarantees Government-sponsored enterprises Tax-exempt borrowing Federal borrowing from the public Federal lending as a percentage of: Net credit Federal borrowing Non-federal borrowing

-

4,782 1,208 116 251 442 399 1,253 25 96 34

“Net lending is new lending minus repayments. Sources: Table F-22, ‘Special Analysis F’, Special Analyses: Budget of the United States, 1988; Board of Governors of the Federal Reserve System, Flow of‘ Funds Accounts, Fourth Quarter, 1987, pp. 2-3.

180

3. A model of the credit market 3.1. Description I assume the existence of a large number of risk-neutral entrepreneurs, depositors, and financial intermediaries (‘banks’). Depositors hold initial wealth, but have no investment projects. They supply funds to banks according to a non-decreasing function S(p), where p is the certain gross rate of return on bank deposits. Each entrepreneur has one available project of unit size. Thus, the terms entrepreneur and project are used interchangeably. Entrepreneurs have no initial wealth,3 and must borrow to undertake their project.4 Entrepreneurs are divided into two groups: the target group (T) for federal lending and non-targeted, general (G) borrowers. Each group can be thought of as representing a different type of project, e.g. student loans and general business loans. Thus, the group to which an entrepreneur belongs is public information. I first present a modified version of Stiglitz and Weiss (1981) and model a single group of entrepreneurs. I then aggregate across groups to develop the full model. Each project in group I is characterized by a pair (Pr( j), R,(j)), where P,(j) is the probability that the project succeeds and R,(j) is the gross return if successful. If the project fails, the gross return is zero. Projects can be ordered such that as j rises, pl( j) rises and R,(j) falls. Total expected return, pR, can vary with j.5 Lenders are unable to distinguish project types (PI(j), R,(j)) within a group, but are assumed to know the underlying distribution and density of projects, F,(j) and fl( j), respectively. If banks charge a gross interest rate of rI to borrowers in group I,‘j expected profit to an entrepreneur with project

(PA_& R,(j))

is:

3The results hold as long as projects are larger than entrepreneur’s initial wealth. See Calomiris and Hubbard (1988). 4de Meza and Webb (1987) show that if equity contracts are introduced in the Stiglitz-Weiss model, they are used to the exclusion of debt contracts. However, their model does not capture several costs of issuing equity, including reduced incentives to manage projects efftciently and to report returns honestly. Following de Meza and Webb (1988, p. 17), I assume these costs are prohibitive. This assumption is consistent with the fact that virtually none of the recipients of federal credit issues equity. Problems encountered by students and small businesses in issuing equity are detailed in Nerlove (1975) and Cohen (1981), respectively. ‘Stiglitz and Weiss (1981) and de Meza and Webb (1987, section II) focus on one group and assume that pR is constant across j. The importance of this difference is discussed in section 6. ‘Adding a collateral requirement for each group would change none of the main results, see Wette (1983) or Gale (1988b). For an analysis of credit policy collateral matters, see Gale (1989).

181

W.G. Gale, Federal lending

Define j,* as the marginal borrower demand for group I is given by:

in group

I, so that

Erc,(j:)=O.

Loan

.*

LID(r,)=j’f,(j)dj=FO.T). 0 and is downward sloping because aj:l&-, < 0. The expected gross return to banks on loans to group

(2)

I is: (3)

where 4r is the average

repayment

rate and is given by:

Differentiation of (4) yields &p,/&-,
P = &(r,). Banks’ derived

demand

for funds to lend to group

I is therefore:

where P,=B,(r,) is the maximum bank return attainable on loans to group I. Fig. 1 constructs banks’ derived demand for a single borrower group given notional loan demand (in the lower left quadrant) and banks’ expected return (in the upper left quadrant). An upward shift in B,(r,) raises LT vertically. An increase in loan demand shifts LF horizontally to the right. Having solved for the derived demand for loanable funds for a single

W.G. Gale, Federal

182

m

Fig. 1. Banks’ derived

group, I now assumption:

aggregate

lending

‘A

...... E

demand

for loanable

across

groups.

funds to a single borrower

First,

I introduce

group

a further

crucial

Pcb%.7 Banks’ aggregate

derived

(7) demand

for funds is simply:

LB(P) = G(P)+ G4P). By (7) LB(p) has the ‘step’ shape shown

(8) on the right-hand

side of fig. 2.*

3.2. Equilibrium All agents take prices as given. Therefore, competitive equilibrium occurs at the intersection of the supply of funds and banks’ derived demand for funds, i.e. at the level of p that satisfies

S(P)= LB(P). ‘One set of suffxient conditions for (7) is: fT = fo and pT( j) < pG( j). %ee Riley (1987) for a similar derivation of derived demand.

(9)

W.G. Gale, Federal lending

Fig. 2. Alternative

183

equilibria

Since S is non-decreasing in p and LB is decreasing, it follows that for any given S and LB equilibrium exists and is unique. Fig. 2 displays three different supply curves, each of which generates a different type of equilibrium in the market for loans.’ If S(p)=S1, (9) is satisfied at p 0 (I =T, G) so both the target and the general loan markets clear, at ri and r&, respectively. In the marketclearing equilibrium, a small reduction in supply raises all interest rates and reduces quantity demanded by each group. An increase in target group loan demand, as discussed above, induces a horizontal shift in banks’ derived demand for lending to the target group (shown by the dashed line in fig. 2). The effect is to raise all interest rates, reduce quantity demanded by general borrowers, and raise the volume of credit to targeted borrowers. Thus, despite the presence of private information, the market-clearing equilibrium responds in standard ways to supply and demand shocks. If S(p) =S2, (9) is satisfied at P=&-. The general market clears at ri. However, since dB,/dr,=O, the target group is rationed at fr. The allocation of funds to target borrowers in this case is S(&) - Lo, which is less than LF(FT).” Banks do not raise interest rates to targeted borrowers to eliminate

‘Other outcomes are possible as well. If S and D intersect on the horizontal section of D to the left of S,, general borrowers are rationed and the target group is redlined. If S intersects the vertical axis above po, both groups are redlined: there is no market for credit. S and D could also intersect at one of the kinks in D. All of these equilibria are ignored in the text. “If S, were infinitely elastic at &, the target group market would clear at r;. Thus, a necessary condition for rationing (as opposed to redlining) is that S be upward sloping.

184

W.G. Gale, Federal

lending

excess demand because doing so would reduce B,.’ ’ In the rationing equilibrium, comparative statics are decidedly different. A small reduction in supply leaves all interest rates and general borrowing unchanged. The entire effect is absorbed by a reduction in targeted lending. In addition, an increase in target group loan demand has no effect at all on the equilibrium. These considerations indicate that credit programs may be expected to have different effects depending on the initial market status. If S(p)=SJ, (9) is satisfied at P>& The general market clears, but the target group is now redlined. Banks will not lend any funds to the target group because the cost of funds exceeds the maximum expected return available on target group loans. The model can be generalized easily to include additional borrower groups. Banks order the groups by maximum rate of return available (p,) and serve them sequentially. Let p* denote the equilibrium value of p. All groups with Pr>p* have clearing credit markets, those with p,
4. Modelling federal credit programs This section defines the parameters of federal credit programs and integrates government into the model described above. Government is assumed to possess the same information as banks. In a loan guarantee, the government guarantees a proportion y of the outstanding principal and interest, and charges a fee for this service. The proportion of default costs not covered by the fee is given by g, where 0 5 c 5 1; (T=0 signifies a fairinsurance loan guarantee, Q= 1 implies no fee is charged.13 In a pure direct lending program, the government lends an amount S, without a subsidy to the target group. In a pure interest subsidy, the government effectively agrees to pay the borrower an amount s (
W.G. Gale, Federal lending

and the probability rather than simply

185

of repayment now depend on what borrowers pay, r-s, Y. Second, the bank return to target lending is now

rather than (3). The first term is the probability of repayment times the amount due. The second term represents expected guarantee payments from the government, (1 - 4)yr, less the guarantee fee, (1 - c)( 1 - q5)yr. Third, equilibrium now occurs at the level of p satisfying

S(P)-x

=LB(P) +&

(11)

rather than (9), where X represents government financing of credit programs. Eq. (11) shows that government funding requirements reduce the available supply of private credit.” Thus, the ensuing results are not driven by shifting resources from an unmodelled sector.

5. Effects of credit subsidies This section examines the effects of credit the allocation and level of investment. Proposition

1.

Unsubsidized

credit

policies

subsidies

have

on interest

no eifects

rates

on credit

and

allo-

cations or interest rates.”

In providing an unsubsidized direct loan, the government simply diverts deposits from the private financial system and lends the funds directly. However, the government borrowing required to fund the program reduces private sector credit supply by the same amount as the size of the lending program. Banks respond by reducing target group loans by the exact amount of the lending programs. The net effect is simply a substitution of publiclyprovided credit for private credit. Unsubsidized guarantees act as break-even

“For simplicity, the lump-sum tax is assumed specifications, in which only a portion of the tax qualitative results. 16For a direct loan, set u = ;I = 0; an unsubsidized and (11) shows that the equilibrium does not unsubsidized guarantee has 0 = 0. By (10) and (A.& or interest.

to be financed wholly is financed by reduced

from savings. Other saving, yield similar

loan has s = 0 and X = 5,. Comparison of (9) change. For a guarantee, set s=S,=O; an there is no change in equilibrium investment

186

W.G. Gale, Federal

lending

insurance contracts and thus do not affect the behavior of risk-neutral Thus, credit programs have real effects only if they lose money.

banks.

Proposition 2. Interest subsidies are relatively less effective than guarantees in reallocating credit when the target group is rationed than when the target market clears.” In both the market-clearing and rationing equilibria, subsidized loan guarantees operate through two channels. First, at any rT, guarantees raise ,o~ by raising bank payments in the event of default.” This effect shifts effective demand vertically. Second, funding requirements reduce the supply of funds available for private lending at any level of p. In the market-clearing equilibrium, interest subsidies operate through three channels. First, they raise pT by raising the probability of repayment, thus shifting effective demand vertically. Second, subsidies require funding which reduces the available supply of funds. The third effect is that subsidies drive a wedge between borrower payments and bank receipts and thereby raise target group loan demand. This shifts effective demand horizontally to the right, crowds out general borrowers, and increases targeted investment. However, in the rationing equilibrium, the third channel has no effect, because the horizontal shift in effective demand does not raise & (see the dashed line in fig. 2). The intuition is that an interest subsidy does little to relieve the original cause of rationing, namely insufficient return on lending to the target group. The direct effect of reducing borrower payments is to shift effective demand horizontally, but such shifts have no effect in the rationing equilibrium. To raise targeted lending, the government needs instead to raise the bank return to such activity; that is, it must shift the effective demand curve vertically. Loan guarantees accomplish this task equally effectively in market-clearing or rationing regimes. If the target group is redlined without credit subsidies, this reasoning follows a fortiori. Specifically, a group shifts from redlined to clearing status because of changes in banks’ return to lending to that group, not because of the effect of a subsidy on borrowers’ demand. These results stand in sharp contrast to traditional analyses of subsidies, where zero allocation would be taken as lack of willingness to pay. In imperfect credit markets, a zero allocation of credit represents an unwillingness on banks’ part to lend. Therefore, subsidies, which primarily reduce borrower costs, are less effective in reallocating credit than guarantees, which “The formal proof involves straightforward but tedious comparative static calculations, see Gale (1988b, appendix). IsA full (100 percent) guarantee creates a horizontal pT curve. Any partial guarantee raises the pT curve but retains the original shape.

W.G. Gale, Federal lending

187

Fig. 3. The effects of interactions.

directly raise the bank’s the credit constraint.

return

to lending,

and thereby

address

the source

of

Proposition 3. When it subsidizes one target group, the government either partially or wholly crowds out other target groups from the market, or must raise the subsidy provided to those groups.” By subsidizing one group, the government (potentially) changes the ordering of groups by PI. The reordering can have severe effects on other groups’ credit allocation. Suppose there are two target groups, A and B. With loan guarantees for group A only, effective demand is given by D, in fig. 3. If S = S,, equilibrium occurs at E,. and all markets clear. Now suppose the government guarantees B’s debt, raising & to PA from p”,. The key point is that the guarantee changes the relative ordering of borrower groups by P,. At the new equilibrium, E,, all markets continue to clear, but some borrowing by general applicants and group A is crowded out. Thus, by subsidizing more than one group, the government at least partially offsets the effects of its own policies. To maintain A’s previous level of investment, the government must increase pA. Therefore, credit subsidies to one group may well induce additional subsidies to other groups. “Again,

the formal

proof is tedious

but straightforward.

188

W.G. Gale, Federal

lending

A more extreme case occurs if the initial equilibrium is E,, representing redlining of group B. Now the guarantee to B moves the market to E, and crowds A completely out of the market, despite the willingness of the government to guarantee some portion of A’s debt. Thus, in providing subsidies for one target group, the government can inadvertently eliminate credit for other groups it is trying to assist. Again, in order to induce private lending to A, the government must raise pA.20

6. Welfare For simplicity, the analysis focuses on the market-clearing case with infinitely elastic supply, unless otherwise stated. The welfare criterion employed is aggregate net wealth.2’ Accordingly, project (I, j) is socially efficient if pr(j) R,( j) 2 p. Proposition 4. (Small) welfare-improving.

credit

subsidies

financed

by

lump-sum

taxes

are

A formal proof is provided in the appendix. Consider an interest subsidy. The costs are the lump-sum taxes imposed on depositors. Benefits accrue to inframarginal borrowers (who would have invested without public assistance) and marginal borrowers. For each type of borrower, the benefits are larger than the costs. The marginal borrower is characterized by R,(j,*) = rI. Since the marginal borrower has a safer project than average, it follows that

(14 where the equality is just eq. (3). If pR is continuous in j, then projects by at least some 3> j* will yield p,(T)R,(T) > p, but will not be undertaken. Therefore, with asymmetric information, the market will not fund all socially efficient projects. As long as the subsidy is sufficiently small, the difference between p,(i)R,(j^) and p will exceed the lump-sum taxes. The lump-sum transfers from depositors to inframarginal borrowers may appear to be a straight transfer, with no welfare consequences. In fact, inframarginal borrowers benefit by more than depositors are made worse off.

‘“The results in Proposition 3 have been recognized independently by Bosworth et al. (1987). Penner and Silber (1973) focus on interactions among programs that target the same group. “The same criterion is employed by Mankiw (1986) and de Meza and Webb (1987, 1988). For examples of Pareto-improving credit policies in different models, see Smith and Stutzer (1988) and Gale (1989).

WC.

Gale,

Federrl

189

lending

This occurs because the subsidy raises the overall probability of repayment. With p constant, the rate charged by banks, rr, falls when the subsidy is introduced, which implies that the rate paid by inframarginal borrowers, rT-s, falls by more than s. Since the cost to depositors of providing the subsidy is s, there is a welfare gain here as well. The intuition behind this result is explained by Greenwald and Stiglitz (1986). They show that in markets with adverse selection, any intervention that raises the average quality of the commodity is beneficial. Here, the concern is loan quality. By crowding in safer projects, subsidies reduce the probability of default and raise average loan quality. de Meza and Webb (1987) show that investment in the Stiglitz-Weiss model is below the socially optimal level and that a subsidy to interest income (p) can achieve the socially efficient allocation. Although Proposition 4 deals with similar issues, it differs from their result in several ways. First, they assume (following Stiglitz and Weiss) that total expected return, pR, is constant for all borrowers. This implies that all projects are socially efficient, so that investment is ‘too low’ unless all projects are undertaken. In contrast, I allow the total expected return to vary continuously with j and vary across groups. Thus, even if the projects crowded in by subsidies have lower pR than already existing ones, and even if target projects have lower expected social return than general ones, small credit subsidies are still welfareimproving. Second, de Meza and Webb analyze subsidies to the overall supply of funds, while Proposition 4 analyzes subsidies to individual investment sectors. Since their model has only one borrower group, the distinction is unimportant. However, with multiple borrower groups, the distinction is critical. For example, if there were several borrower groups already undertaking the efficient level of investment and one that invested too little, a general capital subsidy would crowd in investment by all groups and thus provide funding for many inefficient projects (as well as some efftcient ones). Proposition 4 shows that targeted, rather than general, subsidies can be welfare-improving.22 Proposition 5. It may also otherwise redlined group.

be efficient

for

the government

to subsidize

an

A numerical example is given in the appendix. The result holds because banks are unable to identify or share in projects with abnormally high returns, but are forced to absorb the costs of default. Since bank payoffs are a concave function of R, while borrower payoffs are convex in R, it is possible for the expected total return (pR) on a group’s loans to exceed p, “Proposition Webb do not.

4 also explicitly

includes

the costs of Iinancing

the subsidy,

while de Meza and

190

W.G. Gale, Federal lending

while the expected bank return (@) is less than p. In that case, the group will be redlined, but its projects would nevertheless be socially efficient.

7. Conclusion Federal credit interventions are marked by three notable features: (1) programs employ different instruments; (2) programs target many groups simultaneously; and (3) the target groups are often thought to be rationed or redlined in the absence of credit assistance. In the model presented above, these features generate several important results. First, unsubsidized credit policies have no effects on the credit market. This result may help explain why virtually all federal credit programs lose money. Second, in the presence of rationing, pure interest subsidies do little to assist targeted borrowers. The interest subsidy operates primarily by reducing borrower payments; however, rationing exists because of insufficient creditworthiness of borrowers, not their unwillingness to pay. In contrast, loan guarantees operate equally effectively in either clearing or rationed regimes, because they operate primarily by raising the bank’s return. These results indicate that guarantees are relatively more effective than subsidies in reallocating credit if the target group is rationed or redlined than when the target market clears. The results may also provide a possible basis for empirical tests for the existence of rationing. Third, subsidies to one group will partially crowd out or eliminate other target groups. Thus, to at least some extent, the government is simply rearranging credit among target groups and incurring program costs. These observations can help explain the rapid rise in both the volume and applications of federal lending over the past twenty years. As each group obtained credit assistance, marginal groups were increasingly crowded out and increased their subsidy requests in order to maintain their original credit level. Credit subsidies create demand for more credit subsidies. Fourth, because of the divergence between public and private returns, there is a potential efficiency role for government. Small credit subsidies can sometimes improve on the market outcome. It should be stressed that the welfare results derived are generic to adverse selection models, and apply only to small subsidies. There is no basis for a conclusion that current credit policies are welfare-improving [see Gale (1988a)]. The model may be extended to include collateral [Gale (1988b)]. Allowing for risk-aversion by lenders dampens some of the effects, but leaves the main results unchanged [see Penner and Silber (1973) and Friedman (1978)]. The most challenging extension would separate financing and investment choices. For example, borrowers might want to substitute subsidized debt for equity, or subsidized capital for labor. In such cases, the change in credit will not be fully reflected in a change in real activity. On the other hand, if government

W.G. Gule. Federal

Icnding

191

provides the marginal source of funding, the change in federal credit will understate the change in real activity. The one-to-one assumption employed in this paper is a useful benchmark and is frequently employed. Future research should examine this issue in more depth, from both theoretical and empirical perspectives.

Appendix

A. I. Government ,jnancing

requirements

To issue a $1 direct loan, the government X(S,)=S,.

must first raise $1, so that

(A.1)

For a loan guarantee, the expected default cost is (1 - cjj)yr, the probability of default times the guarantee rate times the contingent liability. The government subsidizes a portion CJof this amount, so

X(0, y) = G(1 - c$)j,r

(A.2)

per dollar of principal guaranteed. In a pure subsidy program, the government pays s if the project succeeds. Therefore funding requirements per dollar subsidized are given by: X(s) = SC).

A.2. Proqf of Proposition

(A.3)

4

Consider an interest subsidy. (Similar calculations for guarantees are available upon request.) Let j,( j,) be the marginal borrower before (after) the subsidy is imposed, and h, (hi) be borrower payments before (after) the subsidy is imposed. That is, b, =r& where rt is the rate determined in a private equilibrium; 6, =r!,-s, and where ri is determined in an equilibrium with government. Since p is fixed, rt>r+.

(A.4)

The benefit to inframarginal borrowers is p$’ pj(bO-_,)f( j)dj. They benefit by b,, -b, only if their project succeeds. The benefit to marginal borrowers is S{Apj(Rj_6,)f(j)dj. They are better off by (Rj-6,) if their project succeeds. The direct cost to depositors is ijdpjf(j)sdj, which can be obtained from (A.l), (2) and (4). The bank’s net earnings on marginal

W.G. Gale, Federal lending

192

investments depositors.

is jjj; [p,(b, +s) -p] dj. These earnings are distributed Subtracting costs from benefits yields a welfare change of

to

dw=ypj(bo-b,-s)f.(j)dj 0

+j!bjC(Rj-b,)+(bt +S)--I-P)f(j)dj. h

The first term on the right is positive due to (A.4). The second term reduces to J$, (pjRj--)f(j)dj. If j, is sufficiently close to jo, this term is also unambiguously positive due to (12), and the assumed continuity of pR. Therefore, for small s, dw > 0.

A.3. Proof of Proposition

5

Let p(j) = j and f(j) be uniform. Then $(r( j*)) = j*/2. Let R(j) = 3-j. Then p( j)R( j) = 3j- j2. The total return to the groups’ projects is given by

!(3j-j2)dj=7/6. 0

(A.3

The bank return to lending to this group at rate T is given by B,= 4(r). r. Any interest rate r* can be expressed as r* =3- j*. Banks offering r* earn (3-j”) j*/2. As j increases, this return increases, but at j* = l,B,= 1. Thus, the gross bank return to targeted lending is never greater than 1. If 1

References Board of Governors of the Federal Reserve System, 1987, Flow of Funds Accounts, Fourth Quarter. Bosworth, Barry P., Andrew S. Carron, and Elizabeth Rhyne, 1987, The economics of government credit (Brookings Institution, Washington, DC). Calomiris, Charles W. and R. Glenn Hubbard, 1988. Firm heteroaeneitv, internal linance, and credit rationing, NBER Working paper no. 2497. Chanev. Paul K. and Anian V. Thakor. 1985. Incentive effects of benevolent intervention: The cask of loan guarantees, Journal of Public Economics 26, no. 2, 1699189. Cohen, David L., 1981, Small business capital formation, Public Policy and Capital Formation (Board of Governors of the Federal Reserve System). de Meza, David and David C. Webb, 1987, Too much investment: A problem of asymmetric information, Quarterly Journal of Economics, CII, no. 2, 281-292. de Meza, David and David C. Webb, 1988, Credit market efficiency and tax policy in the presence of screening costs, Journal of Public Economics 36, t-22.

W.G. Gale, Federal lending

I93

Friedman, Benjamin, 1978, Crowding out or crowding in? Economic consequences of financing Government deficits, Brookings Papers on Econon& Activity 3, 593%641.Gale. William G.. 1987. The allocational and welfare effects of federal credit nrograms, Ph. D. dissertation (Stanford University, Stanford, CA). Gale, William G., 1988a, Economic effects of Federal credit programs, UCLA Working paper no. 483, Aug., forthcoming in American Economic Review. Gale, William G., 1988b, Federal lending and the market for credit, UCLA Working paper no. 504, Nov. Gale, William G.. 1989, Collateral, rationing, and Government intervention in credit markets, NBER Working paper no. 3024, in: R.G. Hubbard, ed., Asymmetric information, corporate Jinance and investment (University of Chicago Press, Chicago, forthcoming). Greenwald, Bruce C. and Joseph E. Stiglitz, 1986, Externalities in economies with imperfect information and incomplete markets, Quarterly Journal of Economics Cl, no. 2, 229-264. Mankiw, N. Gregory, 1986, The allocation of credit and financial collapse, Quarterly Journal of Economics CI 3, Aug., 455-470. Nerlove, Marc, 1975, Some problems in the use of income-contingent loans for the linance of higher education, Journal of Political Economy 83, no. I, 1% 183. Office of management and budget, Special analysis F, Special Analyses: Budget of the United States Government, selected years. Ordover, Janusz and Andrew Weiss, 1981, Information and the law: Evaluating legal restrictions on competitive contracts, American Economic Review Papers and Proceedings, LXXI, 399404. Penner, Rudolph G. and William L. Silber, 1973, The interaction between federal credit programs and the impact on the allocation of credit, American Economic Review 63, no. 5, 858-872. Riley, John G., 1987, Credit rationing: A further remark, American Economic Review 77, no. I. 244227. Rosen, Kenneth T., 1981, A comparison of European housing finance systems, in: The future of the thrift industry, Sponsored by the Federal Reserve Bank of Boston, 144-160. Saulnier, R.J., Harold G. Halcrow and Neil H. Jacoby, 1958, Federal lending and loan insurance (Princeton University Press). Smith, Bruce, 1983, Limited information, credit rationing, and optima1 Government lending policy, American Economic Review 73, no. 3, 305-318. Smith, Bruce and Michael Stutzer, 1988, Credit rationing and Government loan programs: A welfare analysis, Working paper 395, Federal Reserve Bank of Minneapolis. in markets with imperfect Stiglitz, Joseph E. and Andrew Weiss, 1981, Credit rationing information, American Economic Review 71, no. 3, 393-410. Wette, Hildegard, 1983, Collateral and credit rationing in markets with imperfect information, American Economic Review 73, no. 3, 442-445. Woodhall, Maureen, 1978, Review of student support schemes in selected OECD countries, Organization for Economic Cooperation and Development.