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Improving risk equalization with constrained regression

Author

Listed:
  • Richard C. Kleef

    () (Erasmus University Rotterdam)

  • Thomas G. McGuire

    () (Harvard Medical School
    National Bureau of Economic Research)

  • René C. J. A. Vliet

    () (Erasmus University Rotterdam)

  • Wynand P. P. M. de Ven

    () (Erasmus University Rotterdam)

Abstract

State-of-the-art risk equalization models undercompensate some risk groups and overcompensate others, leaving systematic incentives for risk selection. A natural approach to reducing the under- or overcompensation for a particular group is enriching the risk equalization model with risk adjustor variables that indicate membership in that group. For some groups, however, appropriate risk adjustor variables may not (yet) be available. For these situations, this paper proposes an alternative approach to reducing under- or overcompensation: constraining the estimated coefficients of the risk equalization model such that the under- or overcompensation for a group of interest equals a fixed amount. We show that, compared to ordinary least-squares, constrained regressions can reduce under/overcompensation for some groups but increase under/overcompensation for others. In order to quantify this trade-off two fundamental questions need to be answered: “Which groups are relevant in terms of risk selection actions?” and “What is the relative importance of under- and overcompensation for these groups?” By making assumptions on these aspects we empirically evaluate a particular set of constraints using individual-level data from the Netherlands (N = 16.5 million). We find that the benefits of introducing constraints in terms of reduced under/overcompensations for some groups can be worth the costs in terms of increased under/overcompensations for others. Constrained regressions add a tool for developing risk equalization models that can improve the overall economic performance of health plan payment schemes.

Suggested Citation

  • Richard C. Kleef & Thomas G. McGuire & René C. J. A. Vliet & Wynand P. P. M. de Ven, 2017. "Improving risk equalization with constrained regression," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 18(9), pages 1137-1156, December.
  • Handle: RePEc:spr:eujhec:v:18:y:2017:i:9:d:10.1007_s10198-016-0859-1
    DOI: 10.1007/s10198-016-0859-1
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    References listed on IDEAS

    as
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    14. Timothy J. Layton & Randall P. Ellis & Thomas G. McGuire, 2015. "Assessing Incentives for Adverse Selection in Health Plan Payment Systems," NBER Working Papers 21531, National Bureau of Economic Research, Inc.
    15. 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.
    16. McGuire, Thomas G. & Glazer, Jacob & Newhouse, Joseph P. & Normand, Sharon-Lise & Shi, Julie & Sinaiko, Anna D. & Zuvekas, Samuel H., 2013. "Integrating risk adjustment and enrollee premiums in health plan payment," Journal of Health Economics, Elsevier, vol. 32(6), pages 1263-1277.
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    Citations

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    Cited by:

    1. Keith M. Marzilli Ericson & Kimberley H. Geissler & Benjamin Lubin, 2018. "The Impact of Partial-Year Enrollment on the Accuracy of Risk-Adjustment Systems: A Framework and Evidence," American Journal of Health Economics, University of Chicago Press, vol. 4(4), pages 454-478, Fall.
    2. Thomas G. McGuire & Anna L. Zink & Sherri Rose, 2020. "Simplifying and Improving the Performance of Risk Adjustment Systems," NBER Working Papers 26736, National Bureau of Economic Research, Inc.
    3. Patel, Leila & Graham, Lauren & Chowa, Gina, 2020. "Evidence of non-economic indicators as markers of success for youth in youth employability programs: Insights from a South African study," Children and Youth Services Review, Elsevier, vol. 118(C).
    4. Layton, Timothy J. & McGuire, Thomas G. & van Kleef, Richard C., 2018. "Deriving risk adjustment payment weights to maximize efficiency of health insurance markets," Journal of Health Economics, Elsevier, vol. 61(C), pages 93-110.
    5. Savannah L. Bergquist & Timothy J. Layton & Thomas G. McGuire & Sherri Rose, 2018. "Intervening on the Data to Improve the Performance of Health Plan Payment Methods," NBER Working Papers 24491, National Bureau of Economic Research, Inc.
    6. Anna Zink & Sherri Rose, 2020. "Fair regression for health care spending," Biometrics, The International Biometric Society, vol. 76(3), pages 973-982, September.
    7. Bergquist, Savannah L. & Layton, Timothy J. & McGuire, Thomas G. & Rose, Sherri, 2019. "Data transformations to improve the performance of health plan payment methods," Journal of Health Economics, Elsevier, vol. 66(C), pages 195-207.
    8. Thomas G. McGuire & Sonja Schillo & Richard C. van Kleef, 2018. "Reinsurance, Repayments, and Risk Adjustment in Individual Health Insurance: Germany, The Netherlands and the U.S. Marketplaces," NBER Working Papers 25374, National Bureau of Economic Research, Inc.
    9. Beck, Konstantin & Kauer, Lukas & McGuire, Thomas G. & Schmid, Christian P.R., 2020. "Improving risk-equalization in Switzerland: Effects of alternative reform proposals on reallocating public subsidies for hospitals," Health Policy, Elsevier, vol. 124(12), pages 1363-1367.

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    More about this item

    Keywords

    Health insurance; Risk equalization; Capitation; Risk selection; Constrained regression;
    All these keywords.

    JEL classification:

    • I11 - Health, Education, and Welfare - - Health - - - Analysis of Health Care Markets
    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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