TY - JOUR
AU - Chernozhukov, Victor
AU - Chetverikov, Denis
AU - Demirer, Mert
AU - Duflo, Esther
AU - Hansen, Christian
AU - Newey, Whitney
AU - Robins, James
TI - Double/Debiased Machine Learning for Treatment and Structural Parameters
JF - National Bureau of Economic Research Working Paper Series
VL - No. 23564
PY - 2017
Y2 - June 2017
DO - 10.3386/w23564
UR - http://www.nber.org/papers/w23564
L1 - http://www.nber.org/papers/w23564.pdf
N1 - Author contact info:
Victor Chernozhukov
Department of Economics
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, Mass. 02139
E-Mail: vchern@mit.edu
Denis Chetverikov
UCLA, Department of Economics
315 Portola Plaza
Bunche Hall, Room 8283
Los Angeles, CA 90095-1477
E-Mail: chetverikov@econ.ucla.edu
Mert Demirer
Department of Economics
Massachusetts Institute of Technology
77 Massachusetts Avenue E52-300
Cambridge, MA 02139
E-Mail: mdemirer@mit.edu
Esther Duflo
Department of Economics, E52-544
MIT
50 Memorial Drive
Cambridge, MA 02142
Tel: 617/258-7013
Fax: 617/253-6915
E-Mail: eduflo@mit.edu
Christian Hansen
University of Chicago Booth School of Business
5807 South Woodlawn Avenue
Chicago, IL 60637
E-Mail: chansen1@chicagobooth.edu
Whitney Newey
Department of Economics, E52-424
MIT
50 Memorial Drive
Cambridge, MA 02142
Tel: 617/253-6420
Fax: 617/253-1330
E-Mail: wnewey@mit.edu
James Robins
677 Huntington Avenue
Kresge Building Room 823
Boston, MA 02115
E-Mail: robins@hsph.harvard.edu
AB - We revisit the classic semiparametric problem of inference on a low dimensional parameter θ_0 in the presence of high-dimensional nuisance parameters η_0. We depart from the classical setting by allowing for η_0 to be so high-dimensional that the traditional assumptions, such as Donsker properties, that limit complexity of the parameter space for this object break down. To estimate η_0, we consider the use of statistical or machine learning (ML) methods which are particularly well-suited to estimation in modern, very high-dimensional cases. ML methods perform well by employing regularization to reduce variance and trading off regularization bias with overfitting in practice. However, both regularization bias and overfitting in estimating η_0 cause a heavy bias in estimators of θ_0 that are obtained by naively plugging ML estimators of η_0 into estimating equations for θ_0. This bias results in the naive estimator failing to be N^(-1/2) consistent, where N is the sample size. We show that the impact of regularization bias and overfitting on estimation of the parameter of interest θ_0 can be removed by using two simple, yet critical, ingredients: (1) using Neyman-orthogonal moments/scores that have reduced sensitivity with respect to nuisance parameters to estimate θ_0, and (2) making use of cross-fitting which provides an efficient form of data-splitting. We call the resulting set of methods double or debiased ML (DML). We verify that DML delivers point estimators that concentrate in a N^(-1/2)-neighborhood of the true parameter values and are approximately unbiased and normally distributed, which allows construction of valid confidence statements. The generic statistical theory of DML is elementary and simultaneously relies on only weak theoretical requirements which will admit the use of a broad array of modern ML methods for estimating the nuisance parameters such as random forests, lasso, ridge, deep neural nets, boosted trees, and various hybrids and ensembles of these methods. We illustrate the general theory by applying it to provide theoretical properties of DML applied to learn the main regression parameter in a partially linear regression model, DML applied to learn the coefficient on an endogenous variable in a partially linear instrumental variables model, DML applied to learn the average treatment effect and the average treatment effect on the treated under unconfoundedness, and DML applied to learn the local average treatment effect in an instrumental variables setting. In addition to these theoretical applications, we also illustrate the use of DML in three empirical examples.
ER -