What's Logs Got to do With it: On the Perils of log Dependent Variables and Difference-in-Differences

Brendon McConnell

Papers from arXiv.org

Abstract: The log transformation of the dependent variable is not innocuous when using a difference-in-differences (DD) model. With a dependent variable in logs, the DD term captures an approximation of the proportional difference in growth rates across groups. As I show with both simulations and two empirical examples, if the baseline outcome distributions are sufficiently different across groups, the DD parameter for a log-specification can be different in sign to that of a levels-specification. I provide a condition, based on (i) the aggregate time effect, and (ii) the difference in relative baseline outcome means, for when the sign-switch will occur.

Date: 2023-07, Revised 2023-08
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