This paper studies the social value of closing price differentials in financial markets. We show that arbitrage gaps (price differentials between markets) exactly correspond to the marginal social value of executing an arbitrage trade. We further show that arbitrage gaps and measures of price impact are sufficient to compute the total social value from closing an arbitrage gap. Theoretically, we show that, for a given arbitrage gap, the total social value of arbitrage is higher in more liquid markets. We apply our framework to compute the welfare gains from closing arbitrage gaps in the context of covered interest parity violations and several duallisted companies. The estimates of the value of closing arbitrage gaps vary substantially across applications.
This paper studies the optimal design of second-best corrective regulation, when some agents or activities cannot be perfectly regulated. We show that policy elasticities and Pigouvian wedges are sufficient statistics to characterize the marginal welfare impact of regulatory policies in a large class of environments. We show that the optimal second-best policy is determined by a subset of policy elasticities: leakage elasticities, and characterize the marginal value of relaxing regulatory constraints. We apply our results to scenarios with unregulated agents/activities and with uniform regulation across agents/activities. We illustrate our results in applications to shadow banking, scale-invariant regulation, asset substitution, and fire sales.