Flexible Bayesian Quantile Regression in Ordinal Models

• Activity Number: 330 - Bayesian Analysis of Latent Variable Models in Economics
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Mohammad Arshad Rahman* and Shubham Karnawat
• Companies: Indian Institute of Technology Kanpur and Credit Suisse
• Keywords: Generalized asymmetric Laplace distribution; Gibbs Sampling; Great Recession; homeownership; Markov chain Monte Carlo; Metropolis-Hastings

Abstract

The paper introduces an estimation method for flexible Bayesian quantile regression in ordinal (FBQROR) models i.e., an ordinal quantile regression where the error follows a generalized asymmetric Laplace (GAL) distribution. The GAL distribution, unlike the asymmetric Laplace (AL) distribution, allows to fix specific quantiles while simultaneously letting the mode, skewness and tails to vary. We also introduce the cumulative distribution function (necessary for constructing the likelihood) and the moment generating function of the GAL distribution. The algorithm is illustrated in multiple simulation studies and implemented to analyze public opinion on homeownership as the best long-term investment in the United States.