Two-way fixed effects, the two-way mundlak regression, and difference-in-differences estimators

Abstract I derive a result on the equivalence between the two-way fixed effects (TWFE) estimator and an estimator obtained from a pooled ordinary least squares regression that includes unit-specific time averages and time-period-specific cross-sectional averages—the two-way Mundlak (TWM) regression. The equivalence between TWFE and TWM implies that various estimators used for intervention analysis can be computed using pooled OLS that controls for time-constant treatment cohort indicators, time-period indicators, covariates, and interactions among them—allowing for considerable treatment effect heterogeneity. An extended version of TWFE (ETWFE) is equivalent to the POLS approach. I show that an imputation…

• AA
  Agricultural and Applied Economics Association
• UC
  University College London
• CO
  College of Engineering, Michigan State University