The Promise and Pitfalls of Differences-in-Differences: Reflections on 16 and Pregnant and Other Applications

Abstract

We use the exchange between Kearney/Levine and Jaeger/Joyce/Kaestner on 16 and Pregnant to reexamine the use of DiD as a response to the failure of nature to properly design an experiment for us. We argue that (1) any DiD paper should address why the original levels of the experimental and control groups differed, and why this would not impact trends, (2) the parallel trends argument requires a justification of the chosen functional form and that the use of the interaction coefficients in probit and logit may be justified in some cases, and (3) parallel trends in the period prior to treatment is suggestive of counterfactual parallel trends, but parallel pre-trends is neither necessary nor sufficient for the parallel counterfactual trends condition to hold. Importantly, the purely statistical approach uses pretesting and thus, generates the wrong standard errors. Moreover, we underline the dangers of implicitly or explicitly accepting the null hypothesis when failing to reject the absence of a differential pre-trend.

Key Words:

• Experimental design
• Natural experiments
• Preexisting trends

ACKNOWLEDGMENTS

We are grateful to the five authors of the original papers on 16 and Pregnant and to Ivan Fernandez-Val, Shulamit Kahn, Adrienne Sabety, and Jonathan Roth for helpful comments and suggestions. The usual caveat applies with particular force in this case.