Difference-in-differences and matching on outcomes: a tale of two unobservables

Difference-in-differences combined with matching on pre-treatment outcomes is a popular method for addressing non-parallel trends between a treatment and control group. However, previous simulations suggest that this approach does not always eliminate or reduce bias, and it is not clear when and why. Using Medicaid claims data from Oregon, we systematically vary the distribution of two key unobservables-fixed effects and the random error term-to examine how they affect bias of matching on pre-treatment outcomes levels or trends combined with difference-in-differences. We find that in most scenarios, bias increases with the standard deviation of the error term because a higher standard deviation makes short-term fluctuations in outcomes more likely, and matching cannot easily distinguish between these short-term fluctuations and more structural outcome trends. The fixed effect distribution may also create bias, but only when matching on pre-treatment outcome levels. A parallel-trend test on the matched sample does not reliably distinguish between successful and unsuccessful matching. Researchers using matching on pre-treatment outcomes to adjust for non-parallel trends should report estimates from both unadjusted and propensity-score matching adjusted difference-in-differences, compare results for matching on outcome levels and trends and examine outcome changes around intervention begin to assess remaining bias.