We develop a dynamic model in which the probability of failure of an inﬁnitely lived ﬁnancial intermediary (bank) is determined endogenously as a function of observable state and policy variables. The bank takes into account the eﬀect of the optimal policy (the interest on deposits, dividend payouts, risky investments) on the probability of failure, which in turn aﬀects the bank’s ability to extract deposits. With the aid of simulations we study the eﬀect of variables such as bank size, the riskiness of the bank’s investment opportunities, and reserve requirements on the bank’s optimal policy and on its probability of failure. A major ﬁnding is that small banks choose policies that render them more risky than large banks. As the risks are correctly priced by depositors, rates oﬀered by small banks incorporate substantial risk premia. Another interesting ﬁnding is that a tighter reserve requirement induces banks of all sizes to take fewer risks.
Buchinsky, Moshe and Yosha, Oved, "Evaluating the Probability of Failure of a Banking Firm" (1995). Cowles Foundation Discussion Papers. 1351.