Difference-in-Differences with Time-varying Continuous Treatments using Double/Debiased Machine Learning

TL;DR

This paper introduces a novel difference-in-differences framework for analyzing time-varying continuous treatments using double/debiased machine learning, enabling flexible causal inference with high-dimensional data.

Contribution

It develops kernel-based ATET estimators within a DiD framework that accounts for high-dimensional covariates and treatment histories, with theoretical guarantees and empirical validation.

Findings

Higher COVID-19 vaccination rates reduce mortality after several weeks

Estimator performs well in finite samples with high-dimensional data

Method accommodates lagged effects and compositional changes in covariates

Abstract

We propose a difference-in-differences (DiD) framework designed for time-varying continuous treatments across multiple periods. Specifically, we estimate the average treatment effect on the treated (ATET) by comparing distinct non-zero treatment intensities. Identification rests on a conditional parallel trends assumption that accounts for observed covariates and past treatment histories. Our approach allows for lagged treatment effects and, in repeated cross-sectional settings, accommodates compositional changes in covariates. We develop kernel-based ATET estimators for both repeated cross-sections and panel data, leveraging the double/debiased machine learning framework to handle potentially high-dimensional covariates and histories. We establish the asymptotic properties of our estimators under mild regularity conditions and demonstrate via simulations that their undersmoothed versions perform well in finite samples. As an empirical illustration, we apply our estimator to assess the effect of the second-dose COVID-19 vaccination rate in Brazil and find that higher vaccination rates reduce COVID-19-related mortality after a lag of several weeks.