An optimal transport approach to estimating causal effects via nonlinear difference-in-differences
Name
10.1515_jci-2023-0004.pdf
Description
Published version
Size
4.26 MB
Format
Adobe PDF
Checksum (MD5)
1ab46b8503283e16b2fd517f2eb5e91c
Author(s)
Torous, William
Gunsilius, Florian
Rigollet, Philippe
Date Issued
August 5, 2024
Journal
Journal of Causal Inference
Publisher
Walter de Gruyter GmbH
Citation
Torous, William, Gunsilius, Florian and Rigollet, Philippe. "An optimal transport approach to estimating causal effects via nonlinear difference-in-differences" Journal of Causal Inference, vol. 12, no. 1, 2024, pp. 20230004.
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1515/jci-2023-0004
