2 Model
Consider a simple one-period economy, with N banks and M firms. There are three parties:
firms (borrowers), an arm’s length credit market, and banks. We describe each of these
below.
Borrowers: Each firm can invest in a risky project with gross payoff of R when successful
and 0 when not, and will choose to do so as long as the expected return from the project
is greater than what it can earn in its next best alternative, rB ≥ 0. The manager of the
firm can choose how much effort E to spend in running the project and increase its success
probability at a cost of E2, and how much time to spend on other activities, 1 — E, for
which he enjoys a private benefit B . For simplicity, we also let E represent the probability of
success of the investment project, so that effort increases the expected return of the project
and reduces the probability of failure. The firm’s shareholders can choose between financing
the project with an arm’s length loan or with a bank loan.
Credit market financing: A competitive arm’s length market provides financing at a gross
interest rate of rU . This loan is unmonitored, giving the firm’s manager full discretion in
choosing how much effort to exert.
Banks: Banks finance themselves with an amount of capital k at a cost rE per unit, and
an amount of deposits 1 — k at a cost rD , with rE ≥ rD . Deposits are fully insured so that
the deposit rate rD does not depend on the risk of bank portfolios. (We analyze the case
where there is no deposit insurance in Section 6.1.) This assumption captures the idea that
bank capital is a particularly expensive form of financing, and that depositors don’t have
the specialized skills necessary to become bankers, therefore having a lower opportunity cost
(see Berger et al., 1995, for a discussion of this issue. Hellmann et al., 2000, and Repullo,
2004, make a similar assumption).4
4 The assumption that rE ≥ rD is fairly standard in the literature, and is generally used to argue why
capital requirements should be binding, in that banks wish to minimize the use of the more costly input.
Eliminating this assumption only strengthens our results, as banks may then want to use capital as a cheaper
source of financing relative to deposits.