Semiparametric Difference-in-Differences Estimators

TLDR

The difference‑in‑differences estimator is widely used in economics but relies on the parallel‑trend assumption, which can be violated when pre‑treatment characteristics differ between treated and control groups. This paper addresses the situation where observed characteristic differences induce non‑parallel outcome dynamics between treated and controls. The authors develop a semiparametric two‑step DID framework that incorporates covariates to model how the average treatment effect varies with observed characteristics. They demonstrate that this two‑step strategy can recover the average treatment effect for the treated even when the parallel‑trend assumption is violated.

Abstract

The difference-in-differences (DID) estimator is one of the most popular tools for applied research in economics to evaluate the effects of public interventions and other treatments of interest on some relevant outcome variables. However, it is well known that the DID estimator is based on strong identifying assumptions. In particular, the conventional DID estimator requires that, in the absence of the treatment, the average outcomes for the treated and control groups would have followed parallel paths over time. This assumption may be implausible if pre-treatment characteristics that are thought to be associated with the dynamics of the outcome variable are unbalanced between the treated and the untreated. That would be the case, for example, if selection for treatment is influenced by individual-transitory shocks on past outcomes (Ashenfelter's dip). This article considers the case in which differences in observed characteristics create non-parallel outcome dynamics between treated and controls. It is shown that, in such a case, a simple two-step strategy can be used to estimate the average effect of the treatment for the treated. In addition, the estimation framework proposed in this article allows the use of covariates to describe how the average effect of the treatment varies with changes in observed characteristics.