"Nonlinear Bank Capital Regulation"
with Maximilian Jager

Abstract :
Prudential authorities mandate that banks hold equity capital exceeding a share of their risk-weighted assets. How should policymakers design this central tool of financial regulation ? We propose a unifying framework for bank capital regulation. Adopting a perturbation approach, we characterize the positive and normative effects of reforming risk weights through sufficient statistics, including credit-supply elasticities and welfare externalities from financial intermediation. We estimate these statistics and apply the framework to evaluate the Federal Reserve’s recent proposal to flatten the risk-weight schedule. Our analysis reveals nonlinear effects on credit allocation, resulting in a reduction of total credit supply but a rise in bank equity, enhancing bank stability. Finally, we derive novel sufficient statistics formulas for the optimal risk-weight schedule, balancing allocative efficiency with risk externalities of credit supply while accommodating market failures and regulatory constraints. Numerical simulations suggest that the Fed’s proposed weights are close to optimal, generating significant welfare gains for households at the expense of bankers and entrepreneurs.