The PCDID Approach: Difference-in-Differences when Trends are Potentially Unparallel and Stochastic

Marc Chan and Simon Sai Man Kwok

No 2020-03, Working Papers from University of Sydney, School of Economics

Abstract: We develop a class of regression-based estimators, called Principal Components Difference-in-Differences estimators (PCDID), for treatment effect estimation. Analogous to a control function approach, PCDID uses factor proxies constructed from control units to control for unobserved trends, assuming that the unobservables follow an interactive effects structure. We clarify the conditions under which the estimands in this regression-based approach represent useful causal parameters of interest. We establish consistency and asymptotic normality results of PCDID estimators under minimal assumptions on the specification of time trends. We show how PCDID can be extended to micro/group-level data and be used for testing parallel trends under the interactive effects structure. The PCDID approach is illustrated in an empirical exercise that examines the effects of welfare waiver programs on welfare caseloads in the US.

Keywords: principal components difference-in-differences; interactive fixed effects; factor- augmented regressions; treatment effects; parallel trends (search for similar items in EconPapers)
Date: 2020-03
New Economics Papers: this item is included in nep-ecm and nep-gen
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Citations: View citations in EconPapers (5)

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Journal Article: The PCDID Approach: Difference-in-Differences When Trends Are Potentially Unparallel and Stochastic (2022)
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