| This thesis is concerned with theoretical analysis of deposit insurance and Prompt Corrective Action using dynamic models. Chapter 2 addresses the following questions. Is the use of book-value capital a good policy? Is Prompt Corrective Action in US optimal? I build a dynamic model of prudential regulation, analyzing repeated interactions between a banker and the FDIC. The banker enjoys a stochastic profit stream, whose distribution depends on the banker's effort choice. Under hidden choice of risk, private information on returns and limited commitment by the banker and costly liquidation, I first characterize the optimal incentive-feasible allocation which consists of consumption by the banker and the probability of termination by the FDIC, using the banker's continuation utility as the state variable. Then, I set up a corresponding dynamic game between the banker and the FDIC, and demonstrate that the optimal allocation is implementable through the combination of risk-based deposit insurance premium and book-value capital regulation, with book-value capital as the record-keeping device. I show that it is optimal for the FDIC to base bank capital regulation on book-value capital as in PCA, but to use stochastic termination/bailout or rather than deterministic termination with no bailout as in PCA. Moreover, I demonstrate, under some conditions, stochastic termination and partial termination generate the equivalent results. Chapter 3, written jointly with Narayana Kocherlakota, investigates when we need deposit insurance as a socially optimal arrangement and when a regulator should terminate problem banks promptly or exercise forbearance. We construct a dynamic model economy in which entrepreneurs pledge collateral, borrow from banks, and invest in long-term projects. We assume that collateral value has aggregate risk and follows a martingale, that entrepreneurs can choose not to repay, walking away with the project but losing the collateral, and that depositors can choose to withdraw their deposits. We first show, as long as collateral value becomes sufficiently low with positive probability, the optimal contract features deposit insurance. The main result states that the optimal contract exhibits forbearance if the ex-ante probability of collapse in collateral value is sufficiently low, but exhibits prompt corrective action if it is sufficiently high. |
