Applications of Machine Learning on Econometrics for Two-stage Regression, Bias-adjusted Inference with Unobserved Confounding, and Test for High Dimensionality

Abstract

Nonparametric approaches have been extensively studied and applied when no assumption is made regarding the model specification. More generally, a sieve can be constructed as a collection of subsets of finite-dimensional approximating parameter spaces, over which the target function is estimated by an optimization of fitting without demanding a parametric specification. Although the concept of sieves is devised in such a general way, classic sieve estimation in literature has been mostly focusing on single-layer approximations. When the target functions are of intricate patterns, however, these single-layer estimators show limited capability despite allowance for data-generated sieve bases, whereas characterizing different attributes of the target functions progressively through multiple layers is often more sensible. Deep neural networks (DNNs) offer a multi-layer extension of the traditional sieves by modelling the connections among variables through data transformations from one layer to another. DNNs have a larger freedom than the single-layer ones in increasing the sieve complexity to ensure consistent estimation while maintaining a relatively simple structure in each layer for feasible estimation. This thesis contains three chapters developing methodologies and motivating applications of DNNs on Econometrics for two-stage regression, bias-adjusted inference with unobserved confounding, and test for high dimension.