Parallel Trends and Dynamic Choices

Abstract: Difference-in-differences is a common method for estimating treatment effects, and the parallel trends condition is its main identifying assumption: the trend in mean untreated outcomes is independent of the observed treatment status. In observational settings, treatment is often a dynamic choice made or influenced by rational actors, such as policy-makers, firms, or individual agents. This paper relates parallel trends to economic models of dynamic choice. We clarify the implications of parallel trends on agent behavior and study when dynamic selection motives lead to violations of parallel trends. Finally, we consider identification under alternative assumptions that accommodate features of dynamic choice.