Bayesian Endogenous Tobit Quantile Regression

TL;DR

This paper introduces a Bayesian endogenous Tobit quantile regression model that accounts for endogenous variables and unknown quantile levels, using parametric and semiparametric methods, demonstrated on simulated and real labor data.

Contribution

It develops a novel Bayesian Tobit quantile regression framework that handles endogenous variables and unknown quantiles, extending existing models.

Findings

Model effectively estimates quantiles with endogenous regressors.

Demonstrates applicability on simulated and real labor supply data.

Provides a flexible approach for quantile regression with endogenous variables.

Abstract

This study proposes $p$-th Tobit quantile regression models with endogenous variables. In the first stage regression of the endogenous variable on the exogenous variables, the assumption that the $\alpha$-th quantile of the error term is zero is introduced. Then, the residual of this regression model is included in the $p$-th quantile regression model in such a way that the $p$-th conditional quantile of the new error term is zero. The error distribution of the first stage regression is modelled around the zero $\alpha$-th quantile assumption by using parametric and semiparametric approaches. Since the value of $\alpha$ is a priori unknown, it is treated as an additional parameter and is estimated from the data. The proposed models are then demonstrated by using simulated data and real data on the labour supply of married women.