Difference-in-Differences with Multiple Events

TL;DR

This paper introduces a two-stage Difference-in-Differences method to correct for confounding second events in staggered DiD designs, improving causal effect estimates.

Contribution

It proposes a novel two-stage DiD approach that accounts for multiple confounding events, enhancing the accuracy of treatment effect estimation in complex settings.

Findings

Controlling for Medicaid expansion reduces estimated minimum wage effects by two-thirds.

The method effectively isolates the target treatment effects from confounders.

Application demonstrates significant bias correction in real policy analysis.

Abstract

This paper studies staggered Difference-in-Differences (DiD) design when there is a second event confounding the target event. When the events are correlated, the treatment and the control group are unevenly exposed to the effects of the second event, causing an omitted event bias. To address this bias, I propose a two-stage DiD design. In the first stage, I estimate the combined effects of both treatments using a control group that is neither treated nor confounded. In the second stage, I isolate the effects of the target treatment by leveraging a parallel treatment effect assumption and a control group that is treated but not yet confounded. Finally, I apply this method to revisit the effect of minimum wage increases on teen employment using state-level hikes between 2010 and 2020. I find that the Medicaid expansion under the ACA is a significant confounder: controlling for this bias reduces the short-term estimate of the minimum wage effect by two-thirds.