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Regression by clustering using metropolis-hastings


  • Simón Ramírez Amaya


  • Adolfo J. Quiroz


  • Álvaro José Riascos Villegas



High quality risk adjustment in health insurance markets weakens insurer incentives to engage in inefficient behavior to attract lower-cost enrollees. We propose a novel methodology based on Markov Chain Monte Carlo methods to improve risk adjustment by clustering diagnostic codes into risk groups optimal for health expenditure prediction. We test the performance of our methodology against common alternatives using panel data from 500 thousand enrollees of the Colombian Healthcare System. Results show that our methodology outperforms common alternatives and suggest that it has potential to improve access to quality healthcare for the chronically ill.

Suggested Citation

  • Simón Ramírez Amaya & Adolfo J. Quiroz & Álvaro José Riascos Villegas, 2019. "Regression by clustering using metropolis-hastings," Documentos de Trabajo Quantil 018180, Quantil.
  • Handle: RePEc:col:000508:018180

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    References listed on IDEAS

    1. Jason Brown & Mark Duggan & Ilyana Kuziemko & William Woolston, 2014. "How Does Risk Selection Respond to Risk Adjustment? New Evidence from the Medicare Advantage Program," American Economic Review, American Economic Association, vol. 104(10), pages 3335-3364, October.
    2. Castano, Ramon & Zambrano, Andres, 2006. "Biased selection within the social health insurance market in Colombia," Health Policy, Elsevier, vol. 79(2-3), pages 313-324, December.
    3. van de Ven, Wynand P. M. M. & van Vliet, Rene C. J. A. & Schut, Frederik T. & van Barneveld, Erik M., 2000. "Access to coverage for high-risks in a competitive individual health insurance market: via premium rate restrictions or risk-adjusted premium subsidies?," Journal of Health Economics, Elsevier, vol. 19(3), pages 311-339, May.
    4. Jonathan Gruber, 2017. "Delivering Public Health Insurance through Private Plan Choice in the United States," Journal of Economic Perspectives, American Economic Association, vol. 31(4), pages 3-22, Fall.
    5. Ã lvaro Riascos & Eduardo Alfonso & Mauricio Romero, 2014. "The Performance of Risk Adjustment Models in Colombian Competitive Health Insurance Market," Documentos CEDE 012062, Universidad de los Andes - CEDE.
    6. Shmueli, Amir & Nissan-Engelcin, Esti, 2013. "Local availability of physicians' services as a tool for implicit risk selection," Social Science & Medicine, Elsevier, vol. 84(C), pages 53-60.
    7. Alvaro J. Riascos & Mauricio Romero & Natalia Serna, 2017. "Risk Adjustment Revisited using Machine Learning Techniques," Documentos CEDE 015601, Universidad de los Andes - CEDE.
    8. Michael Geruso & Timothy Layton, 2020. "Upcoding: Evidence from Medicare on Squishy Risk Adjustment," Journal of Political Economy, University of Chicago Press, vol. 128(3), pages 984-1026.
    9. Joseph P. Newhouse, 1996. "Reimbursing Health Plans and Health Providers: Efficiency in Production versus Selection," Journal of Economic Literature, American Economic Association, vol. 34(3), pages 1236-1263, September.
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    More about this item


    Risk adjustmenthealth insurance clusteringMarkov chain Monte Carlohealth expenditure;

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health

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