Bayesian Nonparametric Instrumental Variable Regression Approach to Quantile Inference

TL;DR

This paper introduces a Bayesian nonparametric instrumental variable regression model for quantile inference, modeling error distributions with Dirichlet mixtures and incorporating spline functions for flexible mean and variance estimation, demonstrated on historical death rate data.

Contribution

It extends existing models by integrating nonparametric error modeling and spline-based mean and variance functions within a Bayesian IV framework for quantile analysis.

Findings

Flexible quantile function modeling with endogeneity correction

Effective inference via MCMC without Metropolis-Hastings

Successful application to historical Japanese death rate data

Abstract

This study extends the Bayesian nonparametric instrumental variable regression model to determine the structural effects of covariates on the conditional quantile of the response variable. The error distribution is nonparametrically modelled using a Dirichlet mixture of bivariate normal distributions. The mean functions include the smooth effects of the covariates represented using the spline functions in an additive manner. The conditional variance of the second-stage error is also modelled using the spline functions such that it varies smoothly with the covariates. Accordingly, the proposed model allows for considerable flexibility in the shape of the quantile function while correcting for an endogeneity effect. The posterior inference for the proposed model is based on the Markov chain Monte Carlo method that requires no Metropolis-Hastings update. The approach is demonstrated using simulated and real data on the death rate in Japan during the inter-war period.