We introduce a double/debiased machine learning estimator for the impulse response function in settings where a time series of interest is subjected to multiple discrete treatments, assigned over time, which can have a causal effect on future outcomes. The proposed estimator can rely on fully nonparametric relations between treatment and outcome variables, opening up the possibility to use flexible machine learning approaches to estimate impulse response functions. To this end, we extend the theory of double machine learning from an i.i.d. to a time series setting and show that the proposed estimator is consistent and asymptotically normally distributed at the parametric rate, allowing for semiparametric inference for dynamic effects in a time series setting. The properties of the estimator are validated numerically in finite samples by applying it to learn the impulse response function in the presence of serial dependence in both the confounder and observation innovation processes. We also illustrate the methodology empirically by applying it to the estimation of the effects of macroeconomic shocks.

翻译：本文提出了一种双重/去偏机器学习估计器，用于估计在时间序列受到多个离散处理（随时间分配）且这些处理可能对未来结果产生因果效应的情况下的脉冲响应函数。该估计器能够基于处理变量与结果变量之间的完全非参数关系，从而为利用灵活的机器学习方法估计脉冲响应函数提供了可能。为此，我们将双重机器学习理论从独立同分布设置扩展至时间序列设置，并证明所提出的估计器具有一致性，且以参数速率渐近正态分布，从而实现了时间序列动态效应的半参数推断。通过在有限样本中应用该估计器来学习存在混淆变量与观测创新过程序列依赖时的脉冲响应函数，我们数值验证了估计器的性质。此外，我们通过将该方法应用于宏观经济冲击效应的估计，进行了实证说明。