Treatment-Effect Estimation in Complex Designs under a Parallel-trends Assumption

TL;DR

This paper develops methods for identifying and estimating dynamic treatment effects in complex panel data settings under parallel-trends assumptions, highlighting the limitations of traditional models and proposing a simpler estimation approach.

Contribution

It introduces a novel identification strategy for dynamic effects under complex treatment designs and proposes a straightforward estimation method within a random coefficients model.

Findings

Event-study effects can be identified under no-anticipation and parallel-trends assumptions.

Traditional distributed-lag fixed effects models may be misleading in this context.

A simple estimation approach is proposed for the random coefficients model.

Abstract

This paper considers the identification of dynamic treatment effects with panel data, in complex designs where the treatment may not be binary and may not be absorbing. We first show that under no-anticipation and parallel-trends assumptions, we can identify event-study effects comparing outcomes under the actual treatment path and under the status-quo path where all units would have kept their period-one treatment throughout the panel. Those effects can be helpful to evaluate ex-post the policies that effectively took place, and once properly normalized they estimate weighted averages of marginal effects of the current and lagged treatments on the outcome. Yet, they may still be hard to interpret, and they cannot be used to evaluate the effects of other policies than the ones that were conducted. To make progress, we impose another restriction, namely a random coefficients distributed-lag linear model, where effects remain constant over time. Under this model, the usual distributed-lag two-way-fixed-effects regression may be misleading. Instead, we show that this random coefficients model can be estimated simply. We illustrate our findings by revisiting Gentzkow, Shapiro and Sinkinson (2011).