Optimal dynamic capital requirements and implementable capital buffer rules

We build a quantitatively relevant macroeconomic model with endogenous risk-taking. In our model, deposit insurance and limited liability can lead banks to make risky loans that are socially inefficient. This excessive risk-taking can be triggered by aggregate or sectoral shocks that reduce the return on safer loans. Excessive risk-taking can be avoided by raising bank capital requirements, but unnecessarily tight requirements lower welfare by limiting liquidity producing bank deposits. Consequently, optimal capital requirements are dynamic (or state contingent). We provide examples in which a Ramsey planner would raise capital requirements: (1) during a downturn caused by a TFP shock; (2) during an expansion caused by an investment-specific shock; and (3) during an increase in market volatility that has little effect on the business cycle. In practice, the economy is driven by a constellation of shocks, and the Ramsey policy is probably beyond the policymaker's ken; so, we also consider implementable policy rules. Some rules can mimic the optimal policy rather well but are not robust to all the calibrations we consider. Basel III guidance calls for increasing capital requirements when the credit to GDP ratio rises, and relaxing them when it falls; this rule does not perform well. In fact, slightly elevated static capital requirements generally do about as well as any implementable rule.