Difference-in-Differences with Sample Selection

TL;DR

This paper examines the challenges of identifying treatment effects in difference-in-differences studies with endogenous sample selection and proposes methods to partially identify and bound these effects under various assumptions.

Contribution

It reveals limitations of conventional DiD estimands under sample selection and develops new identification strategies with bounds and assumptions for more accurate causal inference.

Findings

Conventional DiD estimand may fail to identify causal effects with endogenous sample selection.

Partial identification and bounds can be derived for the ATT under different assumptions.

Empirical applications demonstrate the practical usefulness of the proposed methods.

Abstract

We consider the identification of average treatment effects on the treated (ATT) in difference-in-differences (DiD) settings in the presence of endogenous sample selection. We first establish that the conventional DiD estimand generally fails to recover causally meaningful treatment effects, even if selection and treatment assignment are independent. We then partially identify the ATT for individuals whose outcomes would be observed post-treatment under either counterfactual treatment state, and derive sharp bounds on this parameter under different sets of assumptions on the relationship between sample selection and treatment assignment. These identification results are extended to allow for covariates, repeated cross-section data, and two-by-two comparisons in staggered adoption designs. Furthermore, we present identification results for the ATT of three additional empirically relevant latent groups by imposing outcome mean dominance assumptions that have intuitive appeal in applications. Finally, two empirical illustrations demonstrate the approach's usefulness by revisiting (i) the effect of a job training program on earnings and (ii) the effect of a working-from-home policy on employee performance.