  This article develops a Bayesian approach for estimating panel quantile
regression with binary outcomes in the presence of correlated random effects.
We construct a working likelihood using an asymmetric Laplace (AL) error
distribution and combine it with suitable prior distributions to obtain the
complete joint posterior distribution. For posterior inference, we propose two
Markov chain Monte Carlo (MCMC) algorithms but prefer the algorithm that
exploits the blocking procedure to produce lower autocorrelation in the MCMC
draws. We also explain how to use the MCMC draws to calculate the marginal
effects, relative risk and odds ratio. The performance of our preferred
algorithm is demonstrated in multiple simulation studies and shown to perform
extremely well. Furthermore, we implement the proposed framework to study crime
recidivism in Quebec, a Canadian Province, using a novel data from the
administrative correctional files. Our results suggest that the recently
implemented "tough-on-crime" policy of the Canadian government has been largely
successful in reducing the probability of repeat offenses in the post-policy
period. Besides, our results support existing findings on crime recidivism and
offer new insights at various quantiles.
