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

Nicholas Illenberger; Iván Díaz; Audrey Renson

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arXiv · 2406.16234

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

Nicholas Illenberger·Iván Díaz·Audrey Renson

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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.

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Nicholas Illenberger, Iván Díaz, Audrey Renson. 2024-06-23. Efficient estimation of longitudinal treatment effects using difference-in-differences and machine learning. https://arxiv.org/abs/2406.16234

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