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

We develop a new estimator, called Principal Components Difference-in-Differences (PCDID), for treatment effect estimation in scenarios where the parallel trend assumption may be violated. Our estimator, which is applicable to both aggregate and micro-level data, integrates a data-driven method to proxy unobserved trends, and it can be easily implemented in two steps. We develop various estimation and inference procedures for the average treatment effect of the treated (ATET) and individual treatment effect of the treated (ITET). We also develop and compare two statistical tests — the Hausman and Alpha tests — for the parallel trend assumption. In empirical illustrations, we examine variations of placebo designs by Bertrand, Duflo, and Mullainathan (2004), and the effects of welfare waiver programs on welfare caseloads in the US. Overall, our approach delivers more reasonable and robust results than conventional difference-in-differences approaches.

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