An optimal transport approach to estimating causal effects via nonlinear difference-in-differences

Torous William (), Gunsilius Florian and Rigollet Philippe
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Torous William: Department of Statistics, University of California, Berkeley, CA 94720, United States of America
Gunsilius Florian: Department of Economics, University of Michigan, Ann Arbor, MI 48109, United States of America
Rigollet Philippe: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America

Journal of Causal Inference, 2024, vol. 12, issue 1, 26

Abstract: We propose a nonlinear difference-in-differences (DiD) method to estimate multivariate counterfactual distributions in classical treatment and control study designs with observational data. Our approach sheds a new light on existing approaches like the changes-in-changes estimator and the classical semiparametric DiD estimator, and it also generalizes them to settings with multivariate heterogeneity in the outcomes. The main benefit of this extension is that it allows for arbitrary dependence between the coordinates of vector potential outcomes and includes higher-dimensional unobservables, something that existing methods cannot provide in general. We demonstrate its utility on both synthetic and real data. In particular, we revisit the classical Card & Krueger dataset, which reports fast food restaurant employment before and after a minimum wage increase. A reanalysis with our methodology suggests that these restaurants substitute full-time labor with part-time labor on aggregate in response to a minimum wage increase. This treatment effect requires estimation of the multivariate counterfactual distribution, an object beyond the scope of classical causal estimators previously applied to this data.

Keywords: changes-in-changes; difference-in-differences; heterogeneous treatment effects; minimum wage; optimal transportation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:12:y:2024:i:1:p:26:n:1001

DOI: 10.1515/jci-2023-0004

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