Wonjun Choi

A Machine Learning Approach to Affine Conditional Moment Restriction Models

This paper develops a general framework for estimation and inference in a class of affine conditional moment restriction models. Empirical applications of these models often involve a small number of endogenous regressors but a large set of instruments. Exploiting the affine structure, we leverage machine learning methods to develop an estimation procedure that is computationally fast and scales well to high dimensional instrumental variables. Using an orthogonalized minimum distance criterion, we characterize the requirement on the machine learners through their prediction errors, without restricting the analysis to a particular class of learners. Under this requirement, we develop a Wald statistic for hypotheses concerning smooth functionals. We also provide lower-level verification of our requirement for selected machine learning methods, as well as a Gaussian coupling of the estimated sieve coefficients useful for various inference problems. We examine the finite sample performance of our method through simulation studies and illustrate its use in an empirical application to migration in Tanzania.