Optimal time-consistent macroprudential policy

Collateral constraints widely used in models of financial crises feature a pecuniary externality: Agents do not internalize how borrowing decisions taken in "good times" affect collateral prices during a crisis. We show that agents in a competitive equilibrium borrow more than a financial regulator who internalizes this externality. We also find, however, that under commitment the regulator's plans are time-inconsistent, and hence focus on studying optimal, time-consistent policy without commitment. This policy features a state-contingent macroprudential debt tax that is strictly positive at date t if a crisis has positive probability at t + 1. Quantitatively, this policy reduces sharply the frequency and magnitude of crises, removes fat tails from the distribution of returns, and increases social welfare. In contrast, constant debt taxes are ineffective and can be welfare-reducing, while an optimized "macroprudential Taylor rule" is e effective but less so than the optimal policy.