Practice Job Talk: Yihong Liu, University of California, Santa Barbara

Speaker

Yihong Liu, University of California, Santa Barbara

Biography

Yihong Liu is a fifth-year Ph.D. student in Economics at UCSB. He earned his B.A. in Economics from Shanghai University of Finance and Economics and his M.A. in Economics from Duke University. His research primarily focuses on environmental economics, resource economics, and econometrics. His current research focuses on the estimation of dynamic games in resource economics, and robust inference in two-step estimation procedures, including matching difference-in-differences and matching triple-differences designs. In his spare time, he enjoys watching UCSB Gauchos’ basketball games and Shanghai Shenhua’s soccer matches.

Title

"Matched Triple Differences: A Framework for Covariate Adjustment"

Abstract

Identification in triple-differences (DDD) designs is often justified by a conditional parallel gaps assumption, under which units with similar observed covariates are expected to exhibit similar deviations from parallel trends. In this setting, the common empirical estimation strategy takes one of the two forms: adding the covariates, or their interactions with time indicators, to a three-way fixed effects (3WFE) regression. We formally study both practices and show that, in general, neither consistently estimates the average treatment effect on the treated (ATT). Our diagnosis has two parts. First, the OLS estimands of both 3WFE specifications fail to satisfy the covariate balancing condition that is sufficient for them to equal the ATT. Second, we characterize the additional restrictive assumptions for each OLS estimand to equal the ATT. To address this limitation, we propose a \emph{matched triple-differences} framework that achieves the sufficient covariate balance for consistent estimation. Within this framework, we construct a class of consistent matching estimators, establish their asymptotic normality, and provide a consistent variance estimator accounting for the variability introduced by matching. The framework accommodates a general class of matching procedures, including nearest-neighbor matching and kernel matching. Our empirical application to \cite{Cai_2016_AEJ} shows that our proposed matching estimators can yield estimates and qualitative conclusions that differ from those obtained from the 3WFE regression.

Keywords: Triple-Differences; Difference-in-Differences-Differences; Parallel Gaps; Matching 

JEL Classification: C14, C21, C23