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.
The paper introduces an estimator for the linear censored quantile regression model when the censoring point is an unknown function of a set of regressors. The objective function minimized is convex and the minimization problem is a linear programming problem, for which there is a global minimum. The suggested procedure applies also to the special case of a fixed known censoring point. Under fairly weak conditions the estimator is shown to have n-convergence rate and is asymptotically normal. In the special case of a fixed censoring point it is asymptotically equivalent to the estimator suggested by Powell (1984, 1986a). A Monte Carlo study performed shows that the suggested estimator has very desirable small sample properties. It precisely corrects for the bias induced by censoring, even when there is a large amount of censoring, and for relatively small sample sizes. The estimator outperforms that suggested by Powell in cases where both apply.