Type 2 Tobit Sample Selection Models with Bayesian Additive Regression Trees

TL;DR

This paper develops a Bayesian Additive Regression Trees approach for Type 2 Tobit sample selection models, addressing nonlinearities, model uncertainty, and non-normal errors to improve treatment effect estimation.

Contribution

It extends TOBART-2 by incorporating sums of trees in both equations and using a Dirichlet Process Mixture for flexible error modeling, advancing nonparametric treatment effect estimation.

Findings

Enhanced modeling of nonlinearities and uncertainties.

Improved treatment effect estimates in simulations.

Application to health insurance data demonstrates practical utility.

Abstract

This paper introduces Type 2 Tobit Bayesian Additive Regression Trees (TOBART-2). BART can produce accurate individual-specific treatment effect estimates. However, in practice estimates are often biased by sample selection. We extend the Type 2 Tobit sample selection model to account for nonlinearities and model uncertainty by including sums of trees in both the selection and outcome equations. A Dirichlet Process Mixture distribution for the error terms allows for departure from the assumption of bivariate normally distributed errors. Soft trees and a Dirichlet prior on splitting probabilities improve modeling of smooth and sparse data generating processes. We include a simulation study and an application to the RAND Health Insurance Experiment dataset.