Combining Difference-in-difference and Matching for Panel Data Analysis

Currently panel data analysis largely relies on parametric models (such as random effects and fixed effects models). These models make strong assumptions in order to draw causal inference while in reality, any of these assumptions may not hold. Compared to parametric models, matching does not make strong parametric assumptions and also helps provide focused inference on the effect of a particular cause. However, matching has been used typically in cross-sectional data analysis. In this paper, we extend matching to panel data analysis. In the spirit of the difference-in-difference method, we first difference the outcomes to remove the fixed effects. Then we apply matching on the differenced outcomes at each wave (except the first one). The results can be used to examine whether treatment effects vary across time. The estimates from the separate waves can also be combined to provide an overall estimate of the treatment effects. In doing so, we present a variance estimator for the overall treatment effects that can account for complicated sequential dependence in the data. We demonstrate the method through empirical examples and show its efficacy in comparison to previous methods. We also outline a Stata add-on "DIDMatch" that we are creating to implement the method.