Locally Robust Semiparametric Estimation

By Hidehiko Ichimura, Whitney K. Newey, Victor Chernozhukov, Juan-Carlos Escanciano, James M. Robins. 2016

243 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Statistics and Probability

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Citations in the corpus

Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands (2018, methodology): “s the recent literature in econometrics showing that the double robustness implies valid inference under weaker conditions 17 on the rst step nonparametric estimates (Belloni et al.,2014;Farrell,2015;Chernozhukov et al., 2018a). Indeed, it is these conditions that we verify using the results of Theo”
Augmented minimax linear estimation (2017, methodology): “Perhaps the most popular existing paradigm for building semiparametrically efficient estimators in this setting is via constructions that first compute stand-alone estimates m̂(·) and γ̂ψ(·) for the regression function and the Riesz representer, and then plug them into (Chernozhukov et al., 2016; Ne”
Policy Learning With Observational Data (2017, methodology): “…to their ability to achieve semiparametric eﬃciency under general conditions, even if nuisance components are estimated via black-box machine learning methods for which we can only guarantee fast enough convergence in mean-squared error (Chernozhukov et al., 2018a; van der Laan and Rose, 2011).”
The influence function of semiparametric estimators (2015, methodology): “Orthogonal moment functions reduce bias in GMM from model selection and regularization of the first step and enable machine learning for high-dimensional first steps, as in Chernozhukov et al. (2018) and Chernozhukov et al. (2020).”
Offline Multi-Action Policy Learning: Generalization and Optimization (2018, methodology): “Cross-fitting is a commonly employed technique in statistical estimation Chernozhukov et al. (2016a) to reduce overfit.”
Estimation of Conditional Average Treatment Effects With High-Dimensional Data (2019, methodology): “In essence, Assumption 3.3 is the local analog of Assumption 5.1(f) used by Chernozhukov et al. (2018) to estimate the unconditional average treatment effect via the cross-fitting (split-sample) approach.”