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  2. ASSA Annual Meeting
  3. 2023
  4. Program
  5. Optimal Transport Meets Econometrics
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Optimal Transport Meets Econometrics

Paper Session

Friday, Jan. 6, 2023 8:00 AM - 10:00 AM (CST)

Hilton Riverside, Chequers
Hosted By: Econometric Society
  • Chair: Timothy Christensen, New York University

Matching for Causal Effects via Multimarginal Optimal Transport

Florian Felix Gunsilius
,
University of Michigan
Yuliang Xu
,
University of Michigan

Abstract

Matching on covariates is a well-established framework for estimating causal effects in observational studies. The principal challenge in these settings stems from the often high-dimensional structure of the problem. Many methods have been introduced to deal with this challenge, with different advantages and drawbacks in computational and statistical performance and interpretability. Moreover, the methodological focus has been on matching two samples in binary treatment scenarios, but a dedicated method that can optimally balance samples across multiple treatments has so far been unavailable. This article introduces a natural optimal matching method based on entropy-regularized multimarginal optimal transport that possesses many useful properties to address these challenges. It provides interpretable weights of matched individuals that converge at the parametric rate to the optimal weights in the population, can be efficiently implemented via the classical iterative proportional fitting procedure, and can even match several treatment arms simultaneously. It also possesses demonstrably excellent finite sample properties.

Optimal Transport as a Regression Tool

Samuel Higbee
,
University of Chicago
Omkar Katta
,
University of Chicago
Guillaume Allaire Pouliot
,
University of Chicago

Abstract

We are concerned with program evaluation when the data is observed, before and after treatment, in the form of empirical distributions. We are interested in treatment impact on features other than the mean. For instance, we are interested in the number of subjects impacted by the treatment. We produce methodology based on optimal transport to estimate such quantities. In one main application of interest, we produce a lower bound on the number of drivers purchasing their license to buy a new car on the black market in Beijing.

Counterfactual Identification and Latent Space Enumeration in Discrete Outcome Models

Jiaying Gu
,
University of Toronto
Thomas Russell
,
Carleton University
Thomas Stringham
,
University of Toronto

Abstract

This paper considers partial identification of counterfactual parameters in a general class of discrete outcome models allowing for endogenous regressors and multi-dimensional latent variables, all without parametric distributional assumptions. Our main theoretical result is that, when the covariates are discrete, the infinite-dimensional latent variable distribution can be replaced with a  finite-dimensional version that is equivalent from an identification perspective. Practically constructing the  finite-dimensional latent variable distribution is done by enumerating regions of the latent variable space with a new and efficient cell enumeration algorithm for hyperplane arrangements. We then show that bounds on a certain class of counterfactual parameters can be computed by solving a sequence of linear programming problems, and show how the researcher can introduce additional assumptions as constraints in the linear programs. Finally, we apply the method to an airline entry game example and a dynamic panel data discrete response model of labor market participation.

Existence of a Competitive Equilibrium with Substitutes, with Applications to Matching and Discrete Choice Models

Liang Chen
,
Wuhan University
Eugene Choo
,
Yale University-NUS College
Alfred Galichon
,
New York University
Simon Weber
,
University of York

Abstract

We propose novel results for the existence of a competitive equilibrium with substitutes. An algorithm is provided. Two applications are given: one to the existence of a stable matching without unassigned agents, and one to the identification of discrete choice models.
JEL Classifications
  • C10 - General
  • C61 - Optimization Techniques; Programming Models; Dynamic Analysis