Econometrica · 2022 · Victor Chernozhukov、Juan Carlos Escanciano、Hidehiko Ichimura、Whitney K. Newey、James M. Robins
中文摘要
许多经济与因果参数依赖于非参数或高维第一步估计。我们给出了广义矩估计（GMM）局部稳健/正交矩函数的一般构造，其中第一步估计对平均矩函数没有局部影响。使用这些正交矩可以减少模型选择与正则化偏误，这在许多应用中十分重要，尤其是对于机器学习第一步估计。此外，当矩函数数量与感兴趣的参数数量相同时，相关的标准误对误设具有稳健性。我们使用这些正交矩与交叉拟合，构造了高维条件分位数函数及具有高维状态变量的动态离散选择参数的去偏机器学习估计量。我们证明了正交矩函数所需的额外第一步估计对平均正交矩函数没有全局影响。我们给出了估计这些额外第一步估计的一般方法。我们刻画了双重稳健性，并给出了多种新的双重稳健矩函数。我们给出了渐近理论的一般且简单的正则性条件。
Abstract
Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification when there is the same number of moment functions as parameters of interest. We use these orthogonal moments and cross‐fitting to construct debiased machine learning estimators of functions of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that additional first steps needed for the orthogonal moment functions have no effect, globally, on average orthogonal moment functions. We give a general approach to estimating those additional first steps. We characterize double robustness and give a variety of new doubly robust moment functions. We give general and simple regularity conditions for asymptotic theory.