Efficient estimation of longitudinal treatment effects using difference-in-differences and machine learning

TL;DR

This paper introduces robust, efficient methods for estimating intervention-specific means in longitudinal studies using difference-in-differences and machine learning, accommodating complex covariate histories and relaxing parametric assumptions.

Contribution

It develops multiply-robust, efficient estimators based on influence functions that leverage machine learning for flexible modeling of time-varying covariates and treatment effects.

Findings

Simulation studies show good performance at modest sample sizes.

Application to US minimum wage data illustrates practical utility.

Proposed methods improve robustness over traditional parametric approaches.

Abstract

Difference-in-differences is based on a parallel trends assumption, which states that changes over time in average potential outcomes are independent of treatment assignment, possibly conditional on covariates. With time-varying treatments, parallel trends assumptions can identify many types of parameters, but most work has focused on group-time average treatment effects and similar parameters conditional on the treatment trajectory. This paper focuses instead on identification and estimation of the intervention-specific mean - the mean potential outcome had everyone been exposed to a proposed intervention - which may be directly policy-relevant in some settings. Previous estimators for this parameter under parallel trends have relied on correctly-specified parametric models, which may be difficult to guarantee in applications. We develop multiply-robust and efficient estimators of the intervention-specific mean based on the efficient influence function, and derive conditions under which data-adaptive machine learning methods can be used to relax modeling assumptions. Our approach allows the parallel trends assumption to be conditional on the history of time-varying covariates, thus allowing for adjustment for time-varying covariates possibly impacted by prior treatments. Simulation results support the use of the proposed methods at modest sample sizes. As an example, we estimate the effect of a hypothetical federal minimum wage increase on self-rated health in the US.