This paper shows that it is possible to define an unambiguous notion of the direct effect of a parameter perturbation on the value of an optimization problem’s objective away from an optimum for problems with linearly homogeneous constraints. This notion of the direct effect relies on reformulating the optimization problem using shares as choice variables, and has the interpretation of holding choice variables — when formulated as shares — fixed. This short paper contains one formal “non-envelope” theorem and four applications to i) consumer demand, ii) cost minimization, iii) planning in exchange economies, and iv) planning in production economies.
This paper studies the social value of closing price differentials in financial markets. We show that arbitrage gaps exactly correspond to the marginal social value of executing an arbitrage trade. Moreover, arbitrage gaps and price impact measures are sufficient to compute the total social value from closing an arbitrage gap, which may emerge for different reasons, including nonpecuniary benefits of holding particular assets. Theoretically, we show that, for a given arbitrage gap, the total social value of arbitrage is higher in more liquid markets. We compute the welfare gains from closing arbitrage gaps for covered interest parity violations.
This paper studies the optimal determination of deposit insurance when bank runs are possible. We show that the welfare impact of changes in the level of deposit insurance coverage can be generally expressed in terms of a small number of sufficient statistics, which include the level of losses in specific scenarios and the probability of bank failure. We characterize the wedges that determine the optimal ex ante regulation, which map to asset- and liability-side regulation. We demonstrate how to employ our framework in an application to the most recent change in coverage in the United States, which took place in 2008.
This article studies the optimal design of corporate taxes when firms have private information about future investment opportunities and face financial constraints. A government whose goal is to efficiently raise a given amount of revenue from its corporate sector should attempt to tax unconstrained firms, which value resources inside the firm less than financially constrained firms. We show that a corporate payout tax (a tax on dividends and share repurchases) can both separate constrained and unconstrained firms and raise revenue and is therefore optimal. Our quantitative analysis implies that a revenue-neutral switch from profit taxation to payout taxation would increase the overall value of existing firms and new entrants by 7%. This switch could be implemented in the current US tax system by making retained earnings fully deductible.
This paper studies leverage regulation when equity investors and/or creditors have distorted beliefs relative to a planner. We characterize how the optimal regulation responds to arbitrary changes in investors'/creditors' beliefs, relating our results to practical scenarios. We show that the optimal regulation depends on the type and magnitude of such changes. Optimism by investors calls for looser leverage regulation, while optimism by creditors, or jointly by both investors/creditors, calls for tighter leverage regulation. Our results apply to environments with (i) planners with imperfect knowledge of investors'/creditors' beliefs, (ii) monetary policy, (iii) bailouts and pecuniary externalities, and (iv) endogenous beliefs.
This paper studies the relation between volatility and informativeness in financial markets. We identify two channels (noise-reduction and equilibrium-learning) that determine the volatility-informativeness relation. When informativeness is sufficiently high (low), volatility and informativeness positively (negatively) comove in equilibrium. We identify conditions on primitives that guarantee that volatility and informativeness comove positively or negatively. We introduce the comovement score, a statistic that measures the distance of a given asset to the positive/negative comovement regions. Empirically, comovement scores (i) have trended downwards over the last decades, (ii) are positively related to value and idiosyncratic volatility and negatively to size and institutional ownership.
This paper characterizes the optimal transaction tax in an equilibrium model of financial markets. If investors hold heterogeneous beliefs unrelated to their fundamental trading motives and the planner calculates welfare using any single belief, a positive tax is optimal, regardless of the magnitude of fundamental trading. Under some conditions, the optimal tax is independent of the planner's belief. The optimal tax can be implemented by adjusting its value until total volume equals fundamental volume. Knowledge of (i) the share of nonfundamental trading volume and (ii) the semielasticity of trading volume to tax changes is sufficient to quantify the optimal tax.
This paper studies the social value of closing price differentials in financial markets. We show that arbitrage gaps exactly correspond to the marginal social value of executing an arbitrage trade. Moreover, arbitrage gaps and price impact measures 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 compute the welfare gains from closing arbitrage gaps for covered interest parity violations and several dual-listed companies. The estimated social value of arbitrage varies substantially across applications.
This paper studies optimal second-best corrective regulation, when some agents/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 a subset of policy elasticities, leakage elasticities, determine optimal second-best policy, and characterize the marginal value of relaxing regulatory constraints. We apply our results to scenarios with unregulated agents/activities, uniform regulation across agents/activities, and costly regulation. We illustrate our results in applications to financial regulation with environmental externalities, shadow banking, behavioral distortions, asset substitution, and fire sales.
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.