Pseudo-Panel Event Studies: Econometric Foundations for Credible Applications

Event studies with panel data are widely used to estimate treatment effects. With repeated cross-sections, future treatment dates are unobserved for untreated individuals. Pseudo-panel event studies impute pre-treatment outcomes of the treated using matched untreated individuals. This paper establishes identification in such designs and characterizes bias when identification conditions fail. I show that the pseudo-panel regression is equivalent to weighted least squares with group means. This representation simplifies computation and yields analytical inference. In simulations, analytical confidence intervals attain near-nominal coverage, whereas conventional intervals substantially undercover. I also develop a doubly robust estimator using richer covariates, a symmetric matching design with synthetic type fixed effects, and a fully nonparametric estimator that accommodates heterogeneous treatment effects. In a Korean panel survey, the pseudo-panel regression yields an employment child penalty of 42.1%, close to 46.9% in the actual panel. Applications to repeated cross-sections yield employment penalties of about one-third.