Bank Leverage Restrictions in General Equilibrium: Solving for Sectoral Value Functions

This paper develops a tractable method to solve a general equilibrium model with bank runs and exogenous leverage ratio restrictions, enabling welfare analysis of macroprudential policy across the business cycle. By computing bankers’ value functions via backward induction from steady state, the framework quantifies how leverage caps affect capital allocation, asset prices, and run probabilities during recovery from crises. Calibrated simulations show that welfare-enhancing policy is time-varying—lenient when households’ marginal utility of consumption is high, and restrictive in low-marginal-utility states. The results highlight a trade-off: tighter leverage restrictions improve stability but risk persistent efficiency losses if imposed too harshly after crises.