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

Author

Listed:
  • Georges Bresson
  • Guy Lacroix
  • Mohammad Arshad Rahman

Abstract

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.

Suggested Citation

  • Georges Bresson & Guy Lacroix & Mohammad Arshad Rahman, 2020. "Bayesian Panel Quantile Regression for Binary Outcomes with Correlated Random Effects: An Application on Crime Recidivism in Canada," Papers 2001.09295, arXiv.org.
    • Handle: RePEc:arx:papers:2001.09295
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    Cited by:

    1. Arjun Gupta & Soudeh Mirghasemi & Mohammad Arshad Rahman, 2021. "Heterogeneity in food expenditure among US families: evidence from longitudinal quantile regression," Indian Economic Review, Springer, vol. 56(1), pages 25-48, June.
    2. Yu-Zhu Tian & Man-Lai Tang & Wai-Sum Chan & Mao-Zai Tian, 2021. "Bayesian bridge-randomized penalized quantile regression for ordinal longitudinal data, with application to firm’s bond ratings," Computational Statistics, Springer, vol. 36(2), pages 1289-1319, June.
    3. Hossain, Mohammed Sawkat, 2021. "A revisit of capital structure puzzle: Global evidence and analysis," International Review of Economics & Finance, Elsevier, vol. 75(C), pages 657-678.
    4. Mohit Batham & Soudeh Mirghasemi & Mohammad Arshad Rahman & Manini Ojha, 2021. "Modeling and Analysis of Discrete Response Data: Applications to Public Opinion on Marijuana Legalization in the United States," Papers 2109.10122, arXiv.org, revised May 2023.
    5. Qi Li & Vasilis Sarafidis & Joakim Westerlund, 2021. "Essays in honor of Professor Badi H Baltagi," Empirical Economics, Springer, vol. 60(1), pages 1-11, January.
    6. Ivan Jeliazkov & Shubham Karnawat & Mohammad Arshad Rahman & Angela Vossmeyer, 2023. "Flexible Bayesian Quantile Analysis of Residential Rental Rates," Papers 2305.13687, arXiv.org, revised Sep 2023.
    7. Li, Qi & Sarafidis, Vasilis & Westerlund, Joakim, 2020. "Essays in Honor of Professor Badi H Baltagi: Editorial," MPRA Paper 104751, University Library of Munich, Germany.
    8. Manini Ojha & Mohammad Arshad Rahman, 2020. "Do Online Courses Provide an Equal Educational Value Compared to In-Person Classroom Teaching? Evidence from US Survey Data using Quantile Regression," Papers 2007.06994, arXiv.org.

    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • K14 - Law and Economics - - Basic Areas of Law - - - Criminal Law
    • K42 - Law and Economics - - Legal Procedure, the Legal System, and Illegal Behavior - - - Illegal Behavior and the Enforcement of Law

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