Matching and Regression to the Mean in Difference-in-Differences Analysis

To demonstrate regression to the mean bias introduced by matching on preperiod variables in difference-in-differences studies.

Simulated data.

We performed a Monte Carlo simulation to estimate the effect of a placebo intervention on simulated longitudinal data for units in treatment and control groups using unmatched and matched difference-in-differences analyses. We varied the preperiod level and trend differences between the treatment and control groups, and the serial correlation of the matching variables. We assessed estimator bias as the mean absolute deviation of estimated program effects from the true value of zero.

When preperiod outcome level is correlated with treatment assignment, an unmatched analysis is unbiased, but matching units on preperiod outcome levels produces biased estimates. The bias increases with greater preperiod level differences and weaker serial correlation in the outcome. This problem extends to matching on preperiod level of a time-varying covariate. When treatment assignment is correlated with preperiod trend only, the unmatched analysis is biased, and matching units on preperiod level or trend does not introduce additional bias.

Researchers should be aware of the threat of regression to the mean when constructing matched samples for difference-in-differences. We provide guidance on when to incorporate matching in this study design.