August 25 2022, 5pm Paris time / 11am NY time
Susanne M. Schennach
Optimally-Transported Generalized Method of Moments (joint with Vincent Starck)
Abstract: We propose a novel optimal transport-based version of the Generalized Method of Moment (GMM). Instead of handling overidentified models by reweighting the data until all moment conditions are satisfied (as in Generalized Empirical Likelihood methods), this method proceeds by introducing measurement error of the least mean square magnitude necessary to simultaneously satisfy all moment conditions. This approach, based on the notion of optimal transport, aims to address the problem of assigning a logical interpretation to GMM results even when overidentification tests reject the null, a relatively common situation in empirical applications. We discuss the implementation of the method as well as its asymptotic properties and illustrate its usefulness through examples.
September 29 2022, 5pm Paris time / 11am NY time
(Massachusetts Institute of Technology)
Persuasion as Matching (joint with Anton Kolotilin and Roberto Corrao)
Abstract: In persuasion problems where the receiver’s action is one-dimensional and his utility is single-peaked, optimal signals are characterized by duality, based on a first-order approach to the receiver’s problem. A signal is optimal if and only if the induced joint distribution over states and actions is supported on a compact set (the contact set) where the dual constraint binds. A signal that pools at most two states in each realization is always optimal, and such pairwise signals are the only solutions under a non-singularity condition on utilities (the twist condition). We provide conditions under which higher actions are induced at more or less extreme pairs of states. Finally, we provide conditions for the optimality of either full disclosure or negative assortative disclosure, where signal realizations can be ordered from least to most extreme. Optimal negative assortative disclosure is characterized as thesolution to a pair of ordinary differential equations.
October 20 2022, 5pm Paris time / 11am NY time
(New York University)
Counterfactual Sensitivity and Robustness (joint with Benjamin Connault)
Abstract: We propose a framework for analyzing the sensitivity of counterfactuals to parametric assumptions about the distribution of latent variables in structural models. In particular, we derive bounds on counterfactuals as the distribution of latent variables spans nonparametric neighborhoods of a given parametric specification while other “structural” features of the model are maintained. Our approach recasts the infinite-dimensional problem of optimizing the counterfactual with respect to the distribution of latent variables (subject to model constraints) as a finite-dimensional convex program. We develop an MPEC version of our method to further simplify computation in models with endogenous parameters (e.g., value functions) defined by equilibrium constraints. We propose plug-in estimators of the bounds and two methods for inference. We also show that our bounds converge to the sharp nonparametric bounds on counterfactuals as the neighborhood size becomes large. To illustrate the broad applicability of our procedure, we present empirical applications to welfare analysis in matching models with transferable utility and dynamic discrete choice models.
November 17 2022, 5pm Paris time / 11am NY time