State-contingent bank regulation with unobserved actions and unobserved characteristics

Optimal bank regulation is studied in a model where bank quality is private information and bank portfolio choice is subject to moral hazard. Regulators wish to control bank risk solely because high risk adversely affects a bank incentives to improve its mean return. Numerical methods are developed to study the model. Capital regulation alone has a limited ability to separate types. Including ex post fines achieve separation at lower cost, resulting in improved welfare. Low-quality banks are fined on high returns in order to control risk-taking. High-quality banks face fines on lower returns mainly to ensure truth-telling by low-quality banks. High-quality banks bear the full cost of regulation.