Conditional Triple Difference-in-Differences

TL;DR

This paper addresses biases in triple difference-in-differences methods caused by covariate distribution differences, proposing a new estimator that fixes covariate distributions for more accurate causal inference.

Contribution

It introduces a novel causal estimand fixing covariate distributions and develops a double-robust estimator to improve triple difference-in-differences analysis.

Findings

Standard controls induce bias when covariate distributions differ.

The proposed estimator reduces bias by fixing covariate distributions.

Application demonstrates improved causal effect estimation.

Abstract

Triple difference-in-differences designs are widely used to estimate causal effects in empirical work. Surveying the literature, we find that most applications include controls. We show that this standard practice is generally biased for the target causal estimand when covariate distributions differ across groups. To address this, we propose identifying a causal estimand by fixing the covariate distribution to that of one group. We then develop a double-robust estimator and illustrate its application in a canonical policy setting.