The switchback is an experimental design that measures treatment effects by repeatedly turning an intervention on and off for a whole system. Switchback experiments are a robust way to overcome cross-unit spillover effects; however, they are vulnerable to bias from temporal carryovers. In this paper, we consider properties of switchback experiments in Markovian systems that mix at a geometric rate. We find that, in this setting, standard switchback designs suffer considerably from carryover bias: Their estimation error decays as $T^{-1/3}$ in terms of the experiment horizon $T$, whereas in the absence of carryovers a faster rate of $T^{-1/2}$ would have been possible. We also show, however, that judicious use of burn-in periods can considerably improve the situation, and enables errors that decay as $\log(T)^{1/2}T^{-1/2}$. Our formal results are mirrored in an empirical evaluation.

翻译：开关实验是一种通过重复对整个系统开启和关闭干预措施来衡量处理效应的实验设计。开关实验是克服跨单元溢出效应的一种稳健方法，但其易受时间遗留效应导致的偏差影响。本文研究了在几何速率混合的马尔可夫系统中开关实验的性质。我们发现，在此设定下，标准开关实验设计因遗留效应而遭受显著偏差：其估计误差随实验时间跨度 $T$ 以 $T^{-1/3}$ 的速率衰减，而在无遗留效应时本可实现更快的 $T^{-1/2}$ 衰减速率。然而，我们也表明，合理使用预热期可显著改善此情况，使误差以 $\log(T)^{1/2}T^{-1/2}$ 的速率衰减。我们的理论结果得到了实证评估的印证。