Nonlinear Econometric Models with Machine Learning

This chapter introduces machine learning (ML) approaches to estimate nonlinear econometric models, such as discrete choice models, typically estimated by maximum likelihood techniques. Two families of ML methods are considered in this chapter. The first, shrinkage estimators and related derivatives, such as the Partially Penalised Estimator, introduced in Chapter 1. A formal framework of these concepts is presented as well as a brief literature review. Additionally, some Monte Carlo results are provided to examine the finite sample properties of selected shrinkage estimators for nonlinear models. While shrinkage estimators are typically associated with parametric models, tree based methods can be viewed as their non-parametric counterparts. Thus, the second ML approach considered here is the application of treebased methods in model estimation with a focus on solving classification, or discrete outcome, problems. Overall, the chapter attempts to identify the nexus between these ML methods and conventional techniques ubiquitously used in applied econometrics. This includes a discussion of the advantages and disadvantages of each approach. Several benefits, as well as strong connections to mainstream econometric methods are uncovered, which may help in the adoption of ML techniques by mainstream econometrics in the discrete and limited dependent variable spheres.