Dynamic covariate balancing: estimating treatment effects over time with potential local projections

TL;DR

This paper introduces a new method for estimating treatment effects over time in panel data, accounting for dynamic treatments, high-dimensional covariates, and treatment heterogeneity, with strong inferential guarantees.

Contribution

It proposes a recursive projection and dynamic balancing approach for treatment effect estimation in complex, high-dimensional, and time-varying settings, extending existing methods.

Findings

Method achieves valid inference even with more covariates than observations.

Numerical simulations demonstrate the estimator's favorable properties.

Empirical application shows practical benefits of the proposed approach.

Abstract

This paper studies the estimation and inference of treatment effects in panel data settings when treatments change dynamically over time. We propose a balancing method that allows for (i) treatments to be assigned dynamically over time based on high-dimensional covariates, past outcomes, and treatments; (ii) outcomes and time-varying covariates to depend on the trajectory of all past treatments; (iii) heterogeneity of treatment effects. Our approach recursively projects potential outcomes' expectations on past histories. It then controls the bias arising from the non-experimental and sequential nature of this setting by balancing dynamically observable characteristics over time. We establish inferential guarantees of the proposed method even when the number of observable characteristics significantly exceeds the sample size. We study numerical properties of the estimator and illustrate the benefits of the procedure in an empirical application.