Shadow Banks and Optimal Regulation

We develop a new framework to study regulatory policy in the presence of unregulated financial institutions ("shadow banks'') when there are pecuniary externalities. Using sufficient statistics, we show that optimal regulation in the presence of shadow banks is scaled by a "regulatory arbitrage multiplier.'' This multiplier only depends on aggregate shadow banking activity. Our framework provides guidance on how to regulate currently unregulated financial institutions and sectors. To first order, the marginal welfare gain of regulating a shadow bank is large when a notion of its intermediary activity substitution effects across its activities is large. We further characterize optimal activity-based regulation whereby the planner regulates a particular activity across all shadow banks, e.g. a tax on debt. To first order, gains from activity regulation are large when average substitution effects across intermediaries are large for the regulated activity. We show how our results extend to broader classes of non-pecuniary externalities.