VOL. 71 NO. 3 STIGLITZ AND WEISS: CREDIT RATIONING the self-selection effect, and the more like is an interior bank optimal interest rate I. Interest Rate as an Incentive Mechanism (14) B(1-F(1+P)B-C) A. Sufficient Conditions Thus, if at some A. / the increase in F lowers the expected return to the borrower The second way in which the interest rate from the project with the higher probability affects the bank's expected return from a of paying back the loan by more than it loan is by changing the behavior of the bor- lowers the expected return from the project ower. The interests of the lender and the with the lower probability of the loan being borrower do not coincide. The borrower is repaid only concerned with returns on the invest- On the other hand, if the firm is indiffer ment when the firm does not go bankrupt; ent between two projects with the same mean, the lender is concerned with the actions of we know from Theorem 2 that the bank the firm only to the extent that they affect prefers to lend to the safer project. Hence the probability of bankruptcy, and the re- raising the interest rate above p could so turns in those states of nature in which the increase the riskiness of loans as to lower the firm does go bankrupt. Because of this, and expected return to the bank ecause the behavior of a borrower cannot be perfectly and costlessly monitored by the THEOREM 8: The expected return to the lender, banks will take into account the ef- bank is lowered by an increase in the interest fect of the interest rate on the behavior of rate at F if, at A, the firm is indifferent between two projects and k with distributions F(R) his section, we show that increasing the he and FK(R),j having a higher probability of rate of interest increases the relative at- bankruptcy than k, and there exists a distribu tractiveness of riskier projects, for which the tion F/(R) such that return to the bank be lower. Hence (a)F(r)represents a mean preserving raising the rate of interest may lead bor- spread of the distribution F/(R), and owers to take actions which are contrary to K(R) satisfies a first-order dominance the interests of the lender, providing another relation with F(R); i.e., F(R)>F(R) for all r than raise the interest rate when there is an excess demand for loanable funds PROOF We return to the general model presented Since has a higher probability of bank- jects, denoted by superscripts j and k. We and k, an increase in the interest rate r leads first establish and Theorem 3, the return to the bank on a THEOREM 7: If, at a given nominal interest project whose return is distributed as Fr(R) rater, a risk-neutral firm is indifferent be- is higher than on project j, and because of tween two projects, an increase in the interest ( b) the return to the bank on project k is rate results in the firm preferring the project higher than the return on a project distrib- with the higher probability of bankruptcy. uted as F(R) PROOF: B. An Example The expected return to the ith project is given by To illustrate the implications of Theorem 8. assume all firms are identical and have a (13)丌= R +P)B -O hoice of two projects, yielding, if successful returns R and R, respectively(and nothingVOL. 71 NO. 3 STIGLITZ AND WEISS: CREDIT RATIONING 401 the self-selection effect, and the more likely is an interior bank optimal interest rate. II. Interest Rate as an Incentive Mechanism A. Sufficient Conditions The second way in which the interest rate affects the bank's expected return from a loan is by changing the behavior of the bor￾rower. The interests of the lender and the borrower do not coincide. The borrower is only concerned with returns on the invest￾ment when the firm does not go bankrupt; the lender is concerned with the actions of the firm only to the extent that they affect the probability of bankruptcy, and the re￾turns in those states of nature in which the firm does go bankrupt. Because of this, and because the behavior of a borrower cannot be perfectly and costlessly monitored by the lender, banks will take into account the ef￾fect of the interest rate on the behavior of borrowers. In this section, we show that increasing the rate of interest increases the relative at￾tractiveness of riskier projects, for which the return to the bank may be lower. Hence, raising the rate of interest may lead bor￾rowers to take actions which are contrary to the interests of the lender, providing another incentive for banks to ration credit rather than raise the interest rate when there is an excess demand for loanable funds. We return to the general model presented above, but now we assume that each firm has a choice of projects. Consider any two pro￾jects, denoted by superscripts jand k. We first establish: THEOREM 7: If, at a given nominal interest rate r, a risk-neutral firm is indifferent be￾tween two projects, an increase in the interest rate results in the firm preferring the project with the higher probability of bankruptcy. PROOF: The expected return to the ith project is given by (13 w-E axR'(I+-),_ so (14) d =-B(1-Fi((l+r')B-C)) Thus, if at some r, X} =7 k, the increase in r lowers the expected return to the borrower from the project with the higher probability of paying back the loan by more than it lowers the expected return from the project with the lower probability of the loan being repaid. On the other hand, if the firm is indiffer￾ent between two projects with the same mean, we know from Theorem 2 that the bank prefers to lend to the safer project. Hence raising the interest rate above r could so increase the riskiness of loans as to lower the expected return to the bank. THEOREM 8: The expected return to the bank is lowered by an increase in the interest rate at r if, at r, the firm is indifferent between two projects j and k with distributions Fj(R) and Fk(R), j having a higher probability of bankruptcy than k, and there exists a distribu￾tion F,(R) such that (a) Fj(R) represents a mean preserving spread of the distribution F,(R), and (b) Fk(R) satisfies a first-order dominance relation with F,(R); i.e., FI(R)>Fk(R) for all R. PROOF: Since j has a higher probability of bank￾ruptcy than does k, from Theorem 7 and the initial indifference of borrowers between j and k, an increase in the interest rate r leads firms to prefer project j to k. Because of (a) and Theorem 3, the return to the bank on a project whose return is distributed as F,(R) is higher than on project j, and because of (b) the return to the bank on project k is higher than the return on a project distrib￾uted as F,(R). B. An Example To illustrate the implications of Theorem 8, assume all firms are identical, and have a choice of two projects, yielding, if successful, returns Ra and Rb, respectively (and nothing