Difference-in-Differences with Latent Variables: A Structural Equation Modeling Framework

Difference-in-differences (DiD) is a widely used research design in the quantitative social sciences. This article demonstrates how the standard econometric DiD model can be implemented within the structural equation modeling (SEM) framework. We show that the traditional DiD estimator can be exactly reproduced in SEM and illustrate extensions that exploit SEM’s ability to model measurement error, latent variables, and model assumptions. Particular attention is given to the identification of DiD models with latent outcomes. Empirical examples examining the effect of COVID-19 vaccination on trust in government institutions are presented using lavaan and Mplus.