Parallel Trends and Dynamic Choices

TL;DR

This paper explores the relationship between the parallel trends assumption in difference-in-differences and models of dynamic decision-making, clarifying when dynamic choices violate this assumption and proposing alternative identification strategies.

Contribution

It connects economic models of dynamic choice with the parallel trends assumption, analyzing conditions under which dynamic selection affects causal inference and suggesting new identification approaches.

Findings

Parallel trends can be violated by dynamic selection motives.

Dynamic decision-making influences the validity of difference-in-differences.

Alternative assumptions can help identify treatment effects under 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.