We introduce a double/debiased machine learning (DML) estimator for the impulse response function (IRF) 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 IRFs. To this end, we extend the theory of DML from an i.i.d. to a time series setting and show that the proposed DML estimator for the IRF 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 IRF 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：本文提出了一种用于脉冲响应函数（IRF）的双重/去偏机器学习（DML）估计器，适用于所关注的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场景。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，为使用灵活的机器学习方法估计IRF提供了可能。为此，我们将DML理论从独立同分布（i.i.d.）设定推广至时间序列设定，并证明所提出的IRF DML估计器具有一致性，且以参数速率渐近正态分布，从而允许在时间序列设定中对动态效应进行半参数推断。通过在存在混淆变量和观测创新过程序列相关性的有限样本中应用该估计器学习IRF，我们数值验证了其性质。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。