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

Music City Center 

Time series experiments, sometimes called switchback experiments in modern digital platforms, are a fundamental experimental design in practice. In this paper, we examine the design-based properties of regression-based methods for estimating treatment effects in such settings. We demonstrate that the treatment effect of interest can be consistently estimated using ordinary least squares (OLS) with an appropriately specified working model. Our analysis extends to estimating a diverging number of treatment effects simultaneously, and we establish the asymptotic properties of the resulting estimators. Additionally, we show that the heteroskedasticity and autocorrelation consistent (HAC) estimator provides a conservative estimate of the variance. Importantly, while our approach relies on OLS regression, our theoretical framework accommodates misspecification of the regression model.

time series experiments

potential outcome

randomization inference

robust standard error 

IMS