Bounds for Treatment Effects in the Presence of Anticipatory Behavior

TL;DR

This paper investigates how anticipatory behavior affects treatment effect estimates in program evaluations, providing bounds and methods to account for such anticipation, with empirical illustration showing potential overestimation of effects.

Contribution

It introduces a framework for bounding treatment effects considering anticipation, along with estimation strategies and empirical applications demonstrating its importance.

Findings

Anticipation can cause overestimation of treatment effects by up to 30%.

The proposed bounds help correct for bias due to anticipation.

Empirical analysis of retirement incentives illustrates the impact of anticipation.

Abstract

In program evaluations, units can often anticipate the implementation of a new policy before it occurs. Such anticipatory behavior can lead to units' outcomes becoming dependent on their future treatment assignments. In this paper, I employ a potential-outcomes framework to analyze the treatment effect with anticipation. I start with a classical difference-in-differences model with two time periods and provide identified sets with easy-to-implement estimation and inference strategies for causal parameters. Empirical applications and generalizations are provided. I illustrate my results by analyzing the effect of an early retirement incentive program for teachers, which the target units were likely to anticipate, on student achievement. The empirical results show the result can be overestimated by up to 30\% in the worst case and demonstrate the potential pitfalls of failing to consider anticipation in policy evaluation.