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Free, publiclyaccessible full text available December 10, 2024

Many causal and policy effects of interest are defined by linear functionals of highdimensional or nonparametric regression functions. Rootn consistent and asymptotically normal estimation of the object of interest requires debiasing to reduce the effects of regularization and/or model selection on the object of interest. Debiasing is typically achieved by adding a correction term to the plugin estimator of the functional, which leads to properties such as semiparametric efficiency, double robustness, and Neyman orthogonality. We implement an automatic debiasing procedure based on automatically learning the Riesz representation of the linear functional using Neural Nets and Random Forests. Our method only relies on blackbox evaluation oracle access to the linear functional and does not require knowledge of its analytic form. We propose a multitasking Neural Net debiasing method with stochastic gradient descent minimization of a combined Riesz representer and regression loss, while sharing representation layers for the two functions. We also propose a Random Forest method which learns a locally linear representation of the Riesz function. Even though our method applies to arbitrary functionals, we experimentally find that it performs well compared to the state of art neural net based algorithm of Shi et al. (2019) for the case of the average treatment effect functional. We also evaluate our method on the problem of estimating average marginal effects with continuous treatments, using semisynthetic data of gasoline price changes on gasoline demand. Code available at github.com/victor5as/RieszLearning.more » « less

Debiased machine learning is a metaalgorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e., scalar summaries, of machine learning algorithms. For example, an analyst may seek the confidence interval for a treatment effect estimated with a neural network. We present a nonasymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies a few simple, interpretable conditions. Formally, we prove consistency, Gaussian approximation and semiparametric efficiency by finitesample arguments. The rate of convergence is $n^{1/2}$ for global functionals, and it degrades gracefully for local functionals. Our results culminate in a simple set of conditions that an analyst can use to translate modern learning theory rates into traditional statistical inference. The conditions reveal a general double robustness property for illposed inverse problems.more » « less

Imbens, G. (Ed.)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 crossfitting 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.more » « less