State-contingent bank regulation with unobserved action and unobserved characteristics

This paper studies bank capital regulation under deposit insurance when bank attributes and actions are private information. Banks are heterogeneous in quality and choose both the mean and variance of their investment strategy. Regulatory tools include capital regulation and state-contingent fines. We use numerical methods to study the properties of the model with two different bank types. Without fines, capital requirements only have limited ability to separate bank types. When fines are added, separation is much easier. Fine schedules and capital requirements are tailored to bank type. Generally, low quality banks face a higher capital requirement and pay lower fines than high quality banks. Utility of low quality banks increases and utility of high quality banks decreases relative to the case where bank type is public information. Often, randomization is incorporated in the optimal policy. In addition, truth-telling constraints may bind in both directions