Stiglitz–Weiss Credit Rationing Model

The Stiglitz–Weiss credit rationing model is a foundational result in business and economics theory demonstrating that a competitive loan market with imperfect information can have an equilibrium in which some borrowers are denied credit even though they would accept the going interest rate. Published by Joseph Stiglitz and Andrew Weiss in the 1981 American Economic Review article "Credit Rationing in Markets with Imperfect Information", it overturns the textbook claim that excess demand for loans must bid up the price until the market clears. Because the interest rate itself affects the riskiness of the loan pool, the lender's expected profit is not monotonic in the rate, and the profit-maximizing rate may lie below the market-clearing one.

Banks lend to entrepreneurs who each need a fixed amount B to finance a project. Projects differ in risk but, by assumption, share the same mean return. Each project yields a gross return R drawn from a distribution F(R, θ), where a higher θ denotes a mean-preserving spread, so that riskier projects have higher variance with the same expected value. Loans are made under limited liability with a debt contract that requires repayment of principal and interest, B(1 + r). If project revenue falls short, the borrower defaults and the bank collects only the revenue, while the borrower's loss is limited to zero.

The critical informational assumption is that the bank cannot observe θ and cannot distinguish safe from risky applicants, an instance of information asymmetry. The bank can observe the interest rate it charges, and it cannot condition the contract on other terms in the baseline model, so collateral and loan size are not available as sorting devices.

The borrower's expected payoff is a call option on project revenue with strike B(1 + r). A borrower undertakes the project if

π(R, r) = max(R − B(1 + r), 0)

has positive expected value net of the opportunity cost of effort. Because option values rise with variance, riskier projects offer greater expected payoffs to the borrower at any given interest rate. A mean-preserving spread raises the borrower's gain from the upside while the downside is truncated at zero, so risky borrowers value loans more than safe borrowers do.

As the interest rate rises, the strike price increases and the option becomes less valuable. The decline is steeper for safe projects, whose payoffs cluster nearer the mean. Consequently, safe borrowers drop out of the market first. For each rate r, there is a critical riskiness threshold θ̂(r) above which projects remain in the applicant pool, and this threshold rises with r.

Stiglitz and Weiss identify two channels through which higher rates reduce the bank's expected return per loan.

1. Adverse selection effect: as r rises, the average riskiness of the applicant pool rises because safe borrowers exit. The lender's proceeds per dollar lent fall since riskier borrowers default more often. This is a direct application of the adverse selection mechanism that Akerlof (1970) described for markets with hidden quality.
2. Incentive effect: when borrowers can choose between projects after receiving the loan, higher interest rates make riskier projects relatively more attractive, so borrowers shift toward them. This is a form of moral hazard, operating through the hidden action of project choice.

The bank's expected return per loan, ρ(r), equals the contractual rate multiplied by the repayment probability, plus the recovery in default states. Initially ρ(r) increases with r because the mechanical gain of a higher rate dominates. Past a threshold, the two negative effects dominate and ρ(r) falls. The return function is therefore hump-shaped (backward-bending) in the interest rate, with a maximum at an interest rate r* that is the bank's optimal lending rate.

Suppose that at r* the demand for loans exceeds the supply of funds. A competitive market would suggest that banks raise rates to clear the market. However, raising the rate above r* lowers expected bank profit, so no bank has an incentive to do so. Similarly, a bank will not lower the rate below r* for loans because profit would also fall. Hence r* is a stable equilibrium rate, with excess demand persisting. The equilibrium is a Nash equilibrium in which each bank's rate is a best response to the others, and the allocation is credit rationing: some applicants who are observationally identical to those who receive loans are denied them.

Two forms of rationing arise. In Type I rationing, among identical borrowers, some obtain loans and others do not. In Type II rationing, or redlining, certain groups cannot obtain credit at any rate, because at any rate the bank's expected return is lower for them than for another group. The model shows that the supply of credit may be unresponsive to monetary expansions at the margin, and that credit availability can shift independently of the price of credit, implications for the credit view of monetary transmission.

Rationing is also not necessarily Pareto efficient in the sense of Pareto efficiency. If the planner could observe risk types, the market could allocate funds toward higher-surplus projects. Under the information constraint, however, the equilibrium may be constrained efficient, a distinction central to the Grossman–Stiglitz paradox and related analyses of information-constrained markets.

David de Meza and David Webb (1987) argued that credit rationing is not the only possible outcome when borrowers differ in the probability of success rather than in risk. If entrepreneurs have different probabilities of success and the bank cannot observe them, the pool at any interest rate contains the more optimistic or higher-return borrowers, and overinvestment results. In the de Meza–Webb setup, the borrowers who accept loans are those with the most to gain, who are also the better credit risks, so adverse selection is favorable and higher interest rates raise the average quality of the pool. The contrast indicates that the Stiglitz–Weiss conclusion depends on the specific form of heterogeneity, namely mean-preserving spreads versus first-order stochastic dominance shifts. The debate showed that the welfare consequences of asymmetric information in credit markets depend on the information structure.

Several remedies are known. Banks may use collateral as a screening device, since high-risk borrowers are less willing to pledge assets, though Bester (1985) shows how contracts that menu collateral and rates can sort types and eliminate rationing. The result mirrors the separating contracts in the Rothschild–Stiglitz insurance screening model. Relationship lending, credit scoring, and monitoring also reduce the information gap. The model has been applied in analyses of small-business finance, microfinance, sovereign lending, and credit crunches.

The framework also established the field of information economics recognized by the 2001 Nobel Prize awarded to George Akerlof, Michael Spence, and Joseph Stiglitz. It remains central to the study of financial accelerators, bank capital channels, and the observation that quantity restrictions in credit markets may persist even in competitive environments.

1. Stiglitz, J. E., & Weiss, A. (1981). Credit Rationing in Markets with Imperfect Information. The American Economic Review, 71(3), 393–410. https://doi.org/10.2307/1802787
2. Akerlof, G. A. (1970). The Market for "Lemons": Quality Uncertainty and the Market Mechanism. The Quarterly Journal of Economics, 84(3), 488–500. https://doi.org/10.2307/1879431
3. Rothschild, M., & Stiglitz, J. (1976). Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information. The Quarterly Journal of Economics, 90(4), 629–649. https://doi.org/10.2307/1885326
4. Stiglitz, J. E. (2000). The Contributions of the Economics of Information to Twentieth Century Economics. The Quarterly Journal of Economics, 115(4), 1441–1478. https://doi.org/10.1162/003355300554827