Credit Rationing in Markets with Imperfect Information

Questions & answers

Q1. Why do the authors think credit rationing needs a theoretical explanation, and what does “credit rationing” mean in this paper?

The authors set out to provide “the first theoretical justification of true credit rationing” in equilibrium, defining credit rationing as a situation in which, among observationally identical loan applicants, some receive loans and others do not, even though the rejected applicants would not get a loan at any interest rate, however high, or by offering more collateral than is demanded of recipients (Introduction, p. 393; definition given explicitly on p. 399). They distinguish this from two older, less satisfying explanations: (a) “temporary disequilibrium,” in which rationing reflects sticky wages or prices during a transition, and (b) rationing imposed by non-market constraints such as usury laws. The paper instead shows rationing “may always characterize equilibrium in a loan market” (p. 393) once the interest rate itself affects the riskiness of the pool of borrowers and their behavior.

Q2. How does the interest rate act as a “screening device,” and why can raising it lower the bank’s expected return?

The bank cannot identify which applicants are good risks, so it uses the interest rate itself as an implicit screen: raising the rate it charges tends to drive the safest borrowers out of the applicant pool first (the adverse-selection effect), which can lower the bank’s expected return even as the rate itself rises (Sec. I, pp. 393-395). Formally, each project has a random gross return R drawn from a distribution F(R,θ) parameterized by riskiness θ, with higher θ a mean-preserving spread (p. 395, eq. 1-2); the bank’s return per loan, ρ(R,r̂) = min(R+C, B(1+r̂)), is a concave function of the project’s realized return (Theorem 3, p. 397), while the borrower’s own return, π(R,r̂) = max(R−(1+r̂)B, −C), is convex (Theorem 1, p. 396). Because risk-averse-leaning or low-risk borrowers find a given mean-preserving spread less attractive as the required payment rises, the critical riskiness threshold θ̂ below which firms still apply for loans rises with the interest rate (Theorem 2, p. 396), so “as the interest rate increases, the mix of applicants becomes worse” (p. 397).

Q3. What is the second channel, the “incentive effect,” by which the interest rate affects the bank’s return?

Beyond changing who applies, a higher interest rate changes what borrowers who do take loans choose to do with them: because the borrower’s convex payoff and the bank’s concave payoff diverge more as the promised repayment rises, firms indifferent between a safer and a riskier project at a low rate will prefer the riskier project at a higher rate, which can lower the bank’s expected return on that loan (Sec. II, pp. 401-402, Theorems 7-8). The authors illustrate this with a two-project example (safe project a, risky project b, same mean return) in which there is a critical interest rate r̂* above which all firms switch from the safe to the risky project, after which the bank’s expected return to a loan actually falls as the contract rate keeps rising (Sec. II.B, p. 402, Figure 6).

Q4. What does the “bank-optimal interest rate” imply for market equilibrium, and why doesn’t competition eliminate rationing?

Because the bank’s expected return per dollar loaned, ρ̄(r̂), can be a non-monotonic (even multi-peaked) function of the contract rate, there is generally an interior “bank-optimal” rate r that maximizes the bank’s expected return; if the Walrasian market-clearing rate would be above r, the bank does better charging r* and rationing the resulting excess demand than raising the rate to clear the market, because any additional interest revenue is more than offset by the induced decline in the average quality of the loan pool** (Sec. I, pp. 397-398, Theorem 5; Figure 4). Competition among banks does not compete this away, because every bank faces the identical adverse-selection problem: in equilibrium “each bank may have an excess supply of loanable funds, but no bank will lower its interest rate” since attracting a rival’s customers by undercutting would mean attracting disproportionately the riskiest of those customers (Sec. VI, p. 409).

Q5. Does the model require that borrowers differ in observable type, or that the pool is fully anonymous?

No — the core non-monotonicity result (Theorems 4-6) holds even with a continuum or a discrete number of borrower types that the bank cannot distinguish, and the authors separately analyze the case where the bank CAN distinguish several groups (indexed by expected return to the bank at each group’s own optimal rate), showing that even then the equilibrium return the bank earns must be equalized across all groups actually receiving loans (Theorem 14, p. 406), while any group whose best feasible return to the bank falls below the economy’s cost of funds is entirely excluded — “redlined” — from the credit market regardless of the social or private return its members might offer (Sec. IV, pp. 406-407). The authors stress there is “no presumption that the market equilibrium allocates credit to those for whom the expected return on their investments is highest” (p. 407): a type-1 borrower profitable in aggregate (bank return plus borrower return) can still be excluded if the bank cannot extract enough of that surplus as safely as it can from another group.

Q6. Can banks avoid rationing by raising collateral requirements instead of (or alongside) the interest rate?

Not in general: the authors show collateral has an adverse-selection effect of its own, because wealthier individuals are plausibly less risk-averse, so raising the collateral a bank demands can shift the applicant pool toward wealthier-but-riskier borrowers and lower the bank’s expected return, exactly paralleling the interest-rate result (Sec. III, pp. 403-405, Theorem 12). In a model with decreasing absolute risk aversion, the authors show there is a critical wealth level above which an individual chooses to undertake a risky project itself rather than borrow (Theorem 9-10), and establish that dV_B/dC < 0 is possible — i.e., “it is easy to show that this adverse selection effect may more than offset the positive direct effect” of additional collateral, so increasing collateral requirements can lower, not raise, the bank’s expected return (p. 404; see also the dynamic multiperiod extension, Sec. III.A, pp. 405-406, where increasing the size of a line of credit need not reduce the bank’s exposure for parallel reasons).

Q7. How does the paper connect credit rationing to other “principal-agent” settings, such as landlord-tenant relationships?

The authors note the credit-market analysis “could apply equally well to any one of a number of principal-agent problems,” offering the landlord-tenant rental relationship as a direct analogy: the tenant’s payoff to effort/outcome is convex in the same way the borrower’s is, and the landlord’s recovered rent is capped/concave in the same way the bank’s loan repayment is, so the same screening and incentive logic that generates credit rationing can generate non-market-clearing rental-housing outcomes (Sec. IV, pp. 407-408, Figures 10a-10b). They also discuss why simple fixed-fee contracts, though they avoid distorting the agent’s incentives relative to revenue-sharing arrangements, are not necessarily preferred once the possibility that the agent may fail to pay the fixed fee is taken into account (p. 408).

Q8. What is the paper’s broader conclusion about the “Law of Supply and Demand”?

The authors close by arguing that market-clearing is not in fact a logical necessity of competitive markets but a property specific to models in which prices do not affect the quality of the good being transacted: “The Law of Supply and Demand is not in fact a law, nor should it be viewed as an assumption needed for competitive analysis. It is rather a result generated by the underlying assumptions that prices have neither sorting nor incentive effects” (Conclusions, p. 409). Where prices do have such effects — as with interest rates and loan quality, or (by direct analogy, citing their companion literature) wages and labor quality — “the usual result of economic theorizing, that prices clear markets, is model specific and is not a general property of markets: unemployment and credit rationing are not phantasms” (p. 409).