Estimating treatment effects with a unified semi-parametric difference-in-differences approach

TL;DR

This paper introduces a unified semi-parametric difference-in-differences method that estimates multiple treatment effects under a single assumption, avoiding the need for outcome transformations and multiple assumptions.

Contribution

It proposes a novel DID approach using a semi-parametric model that unifies estimation of various treatment effects with one parallel trends assumption.

Findings

Method accurately estimates diverse treatment effects.

Simulation studies demonstrate robust performance.

Application shows impact of Medicaid expansion on health outcomes.

Abstract

Difference-in-differences (DID) approaches are widely used for estimating causal effects with observational data before and after an intervention. DID traditionally estimates the average treatment effect among the treated after making a parallel trends assumption on the means of the outcome. With skewed outcomes, a transformation is often needed; however, the transformation may be difficult to choose, results may be sensitive to the choice, and parallel trends assumptions are made on the transformed scale. Recent DID methods estimate alternative treatment effects that may be preferable with skewed outcomes. However, each alternative DID estimator requires a different parallel trends assumption. We introduce a new DID method capable of estimating average, quantile, probability, and novel Mann-Whitney treatment effects among the treated with a single unifying parallel trends assumption. The proposed method uses a semi-parametric cumulative probability model (CPM). The CPM is a linear model for a latent variable on covariates, where the latent variable results from an unspecified transformation of the outcome. Our DID approach makes a universal parallel trends assumption on the expectation of the latent variable conditional on covariates. Hence, our method avoids specifying outcome transformations and does not require separate assumptions for each estimand. We introduce the method; describe identification, estimation, and inference; conduct simulations evaluating its performance; and apply it to assess the impact of Medicaid expansion on CD4 count among people with HIV.