This article is motivated by the lack of flexibility in Bayesian quantile regression for ordinal models where the error follows an asymmetric Laplace (AL) distribution. The inflexibility arises because the skewness of the distribution is completely specified when a quantile is chosen. To overcome this shortcoming, we derive the cumulative distribution function (and the moment-generating function) of the generalized asymmetric Laplace (GAL) distribution – a generalization of AL distribution that separates the skewness from the quantile parameter – and construct a working likelihood for the ordinal quantile model. The resulting framework is termed flexible Bayesian quantile regression for ordinal (FBQROR) models. However, its estimation is not straightforward. We address estimation issues and propose an efficient Markov chain Monte Carlo (MCMC) procedure based on Gibbs sampling and joint Metropolis–Hastings algorithm. The advantages of the proposed model are demonstrated in multiple simulation studies and implemented to analyze public opinion on homeownership as the best long-term investment in the United States following the Great Recession.
We thank Professor Ivan Jeliazkov (University of California, Irvine) and the anonymous referee for some valuable comments. Discussion and suggestions from the participants at the Winter School, Delhi School of Economics (2016, New Delhi, India), Asian Meeting of the Econometric Society (2017, Hong Kong), Australasian Meeting of the Econometric Society (2018, Auckland, New Zealand), and Joint Statistical Meeting (2018, Vancouver, Canada) are appreciated.
Shubham Karnawat worked on this chapter while pursuing his MS degree in the Department of Economic Sciences at the Indian Institute of Technology Kanpur, India.
Rahman, M. and Karnawat, S. (2019), "Flexible Bayesian Quantile Regression in Ordinal Models", Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part B (Advances in Econometrics, Vol. 40B), Emerald Publishing Limited, pp. 211-251. https://doi.org/10.1108/S0731-90532019000040B011Download as .RIS
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