Difference-in-differences (DID) is commonly used for causal inference in time-series cross-sectional data. It requires the assumption that the average outcomes of treated and control units would have followed parallel paths in the absence of treatment. In this paper, I propose a method that not only relaxes this often-violated assumption, but also unifies the synthetic control method (Abadie, Diamond and Hainmueller 2010) with linear fixed effect models under a simple framework, of which DID is a special case. It imputes counterfactuals for each treated unit in post-treatment periods using control group information based on a linear interactive fixed effect model that incorporates unit-specific intercepts interacted with time-varying coefficients. This method has several advantages. First, it allows the treatment to be correlated with unobserved unit and time heterogeneities under reasonable modelling assumptions. Second, it generalizes the synthetic control method to the case of multiple treated units and variable treatment periods, and improves efficiency and interpretability. Third, with a built-in cross-validation procedure, it avoids specification searches and thus is transparent and easy to implement. An empirical example of Election Day Registration and voter turnout in the United States is provided.
— Awarded the 2014 John T. Williams Dissertation Prize for the best dissertation proposal in political methodology; the 2017 Political Analysis Editors’ Choice; the 2018 Miller Prize for “the best work appearing in Political Analysis in 2017.”