Unifying regression-based and design-based causal inference in time-series experiments

TL;DR

This paper demonstrates that regression-based methods, specifically ordinary least squares, can reliably estimate treatment effects in time-series experiments within a design-based framework, even with model misspecification.

Contribution

It establishes the consistency and asymptotic normality of regression estimators for time-series experiments under a design-based approach, allowing for multiple effect estimation and robust variance estimation.

Findings

Regression methods provide consistent treatment effect estimates.

Heteroskedasticity and autocorrelation consistent estimators are conservative.

The approach tolerates regression model misspecification.

Abstract

Time-series experiments, also called switchback experiments or N-of-1 trials, play increasingly important roles in modern applications in medical and industrial areas. Under the potential outcomes framework, recent research has studied time-series experiments from the design-based perspective, relying solely on the randomness in the design to drive the statistical inference. Focusing on simpler statistical methods, we examine the design-based properties of regression-based methods for estimating treatment effects in time-series experiments. We demonstrate that the treatment effects of interest can be consistently estimated using ordinary least squares with an appropriately specified working model and transformed regressors. Our analysis allows for estimating a diverging number of treatment effects simultaneously, and establishes the consistency and asymptotic normality of the regression-based estimators. Additionally, we show that asymptotically, the heteroskedasticity and autocorrelation consistent variance estimators provide conservative estimates of the true, design-based variances. Importantly, although our approach relies on regression, our design-based framework allows for misspecification of the regression model.