1 Quantile Stochastic Frontier Models with Endogeneity Mike G. Tsionas, ** A. George Assaf , * Athanasios Andrikopoulos † Abstract In this paper, we extend Jradi et al. (2019). First, we use the asymmetric Laplace distribution, which is a more reasonable assumption in quantile models. Second, we address the issue of statistical inference for the optimal quantile. Finally, we allow for endogeneity in quantile stochastic frontier models. The new formulation is implemented in a Bayesian framework using Markov Chain Monte Carlo. We employ the celebrated Philippine rice data as in Jradi et al. (2019). Jradi et al. (2019) did not provide efficiency measures, which, in our framework, is straightforward to do. Keywords: Quantile estimation; Stochastic frontier models; Efficiency, Bayesian analysis; Markov Chain Monte Carlo. JEL codes: C11, C13. Corresponding Author: *Albert. George Assaf. Isenberg School of Management, University of Massachusetts-Amherst, 90 Campus Center Way, 204A Flint Lab, Amherst, MA, 01003, United States, assaf@isenberg.umass.edu.** Mike G. Tsionas. Lancaster University Management School, LA1 4YX, UK., m.tsionas@lancaster.ac.uk. † Athanasios Andrikopoulos. Hull University Business School, University of Hull, Hull HU6 7RX, UK., A.Andrikopoulos@hull.ac.uk. Acknowledgments: We are grateful to an anonymous reviewer for several useful remarks on an earlier version. ©2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/