We consider the estimation of treatment effects in settings when multiple treatments are assigned over time and treatments can have a causal effect on future outcomes. We formulate the problem as a linear state space Markov process with a high dimensional state and propose an extension of the double/debiased machine learning framework to estimate the dynamic effects of treatments. Our method allows the use of arbitrary machine learning methods to control for the high dimensional state, subject to a mean square error guarantee, while still allowing parametric estimation and construction of confidence intervals for the dynamic treatment effect parameters of interest. Our method is based on a sequential regression peeling process, which we show can be equivalently interpreted as a Neyman orthogonal moment estimator. This allows us to show root-n asymptotic normality of the estimated causal effects.
翻译:我们考虑在多种治疗随着时间推移被分配,而且治疗可能会对未来结果产生因果关系的情况下对环境中的治疗效果的估计。我们把这一问题发展成具有高维状态的线性空间Markov进程,并提议扩大双偏差机器学习框架以估计治疗的动态效应。我们的方法允许使用任意的机器学习方法来控制高维状态,但以平均平方错误保证为条件,同时仍然允许对动态治疗效果参数进行参数估计和构建信任间隔。我们的方法基于一个连续的回归剥离过程,我们显示这个过程可以被等同于Neyman 或thogomental瞬间测算仪。这使我们能够显示估计的因果关系的根值和零值的正常性。