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Bayesian Panel Quantile Regression for Binary Outcomes with Correlated Random Effects An Application on Crime Recidivism in Canada

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Document pages: 36 pages

Abstract: This article develops a Bayesian approach for estimating panel quantileregression with binary outcomes in the presence of correlated random effects.We construct a working likelihood using an asymmetric Laplace (AL) errordistribution and combine it with suitable prior distributions to obtain thecomplete joint posterior distribution. For posterior inference, we propose twoMarkov chain Monte Carlo (MCMC) algorithms but prefer the algorithm thatexploits the blocking procedure to produce lower autocorrelation in the MCMCdraws. We also explain how to use the MCMC draws to calculate the marginaleffects, relative risk and odds ratio. The performance of our preferredalgorithm is demonstrated in multiple simulation studies and shown to performextremely well. Furthermore, we implement the proposed framework to study crimerecidivism in Quebec, a Canadian Province, using a novel data from theadministrative correctional files. Our results suggest that the recentlyimplemented "tough-on-crime " policy of the Canadian government has been largelysuccessful in reducing the probability of repeat offenses in the post-policyperiod. Besides, our results support existing findings on crime recidivism andoffer new insights at various quantiles.

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