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Using quantile regression for optimal risk adjustment

Author

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  • Normann Lorenz

Abstract

This paper analyzes optimal risk adjustment for direct risk selection (DRS). Integrating insurers activities for risk selection into a discrete choice model of individuals’ health insurance choice shows that DRS has the structure of a contest. For the contest success function used in most of the contest literature, optimal transfers for a risk adjustment scheme have to be determined by means of a restricted quantile regression, irrespective of whether insurers primarily engage in positive DRS (attracting low risks) or negative DRS (repelling high risks). This is at odds with the common practice of determining transfers by means of a least squares regression. However, this common practice can be rationalized within a discrete choice model for a new class of contest success functions, but only if positive and negative DRS are equally important; if not, optimal transfers have to be calculated from a restricted asymmetric least squares regression. Using data from a German and a Swiss health insurer, we find considerable differences between the three types of regressions. Optimal transfers therefore critically depend on which contest success function represents insurers’ incentives for DRS and whether positive and negative DRS are equally important or not. Results from the two data sets indicate that if a regulator does not know which case applies, transfers should rather be calculated by means of a quantile than a least squares regression.

Suggested Citation

  • Normann Lorenz, 2014. "Using quantile regression for optimal risk adjustment," Research Papers in Economics 2014-11, University of Trier, Department of Economics.
  • Handle: RePEc:trr:wpaper:201411
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    File URL: http://www.uni-trier.de/fileadmin/fb4/prof/VWL/EWF/Research_Papers/2014-11.pdf
    File Function: First version, 2014
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    References listed on IDEAS

    as
    1. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    2. Schokkaert, Erik & Van de Voorde, Carine, 2004. "Risk selection and the specification of the conventional risk adjustment formula," Journal of Health Economics, Elsevier, vol. 23(6), pages 1237-1259, November.
    3. Yujing Shen & Randall P. Ellis, 2002. "How profitable is risk selection? A comparison of four risk adjustment models," Health Economics, John Wiley & Sons, Ltd., vol. 11(2), pages 165-174.
    4. Thomas G. McGuire & Jacob Glazer, 2000. "Optimal Risk Adjustment in Markets with Adverse Selection: An Application to Managed Care," American Economic Review, American Economic Association, vol. 90(4), pages 1055-1071, September.
    5. Michiel Bijlsma & Jan Boone & Gijsbert Zwart, 2014. "Competition leverage: how the demand side affects optimal risk adjustment," RAND Journal of Economics, RAND Corporation, vol. 45(4), pages 792-815, December.
    6. Ellis, Randall P. & McGuire, Thomas G., 2007. "Predictability and predictiveness in health care spending," Journal of Health Economics, Elsevier, vol. 26(1), pages 25-48, January.
    7. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, April.
    8. Frank, Richard G. & Glazer, Jacob & McGuire, Thomas G., 2000. "Measuring adverse selection in managed health care," Journal of Health Economics, Elsevier, vol. 19(6), pages 829-854, November.
    9. 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.
    10. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387.
    11. Randall P. Ellis, 2012. "risk adjustment," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
    12. Erik van Barneveld & Leida Lamers & René van Vliet & Wynand van de Ven, 2000. "Ignoring small predictable profits and losses: a new approach for measuring incentives for cream skimming," Health Care Management Science, Springer, vol. 3(2), pages 131-140, February.
    13. Jack, William, 2006. "Optimal risk adjustment with adverse selection and spatial competition," Journal of Health Economics, Elsevier, vol. 25(5), pages 908-926, September.
    14. repec:cup:apsrev:v:89:y:1995:i:01:p:49-61_09 is not listed on IDEAS
    15. Stefan Szymanski, 2003. "The Economic Design of Sporting Contests," Journal of Economic Literature, American Economic Association, vol. 41(4), pages 1137-1187, December.
    16. Chernichovsky, Dov & van de Ven, Wynand P. M. M., 2003. "Risk adjustment in Europe," Health Policy, Elsevier, vol. 65(1), pages 1-3, July.
    17. Cao, Zhun & McGuire, Thomas G., 2003. "Service-level selection by HMOs in Medicare," Journal of Health Economics, Elsevier, vol. 22(6), pages 915-931, November.
    18. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    19. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
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    Citations

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    Cited by:

    1. Pilny, Adam & Wübker, Ansgar & Ziebarth, Nicolas R., 2017. "Introducing risk adjustment and free health plan choice in employer-based health insurance: Evidence from Germany," Journal of Health Economics, Elsevier, vol. 56(C), pages 330-351.
    2. repec:spr:eujhec:v:18:y:2017:i:9:d:10.1007_s10198-016-0859-1 is not listed on IDEAS
    3. Richard van Kleef & Thomas McGuire & Rene van Vliet & Wynand van de Ven, 2015. "Improving Risk Equalization with Constrained Regression," NBER Working Papers 21570, National Bureau of Economic Research, Inc.
    4. Timothy J. Layton & Randall P. Ellis & Thomas G. McGuire, 2015. "Assessing Incentives for Adverse Selection in Health Plan Payment Systems," Boston University - Department of Economics - Working Papers Series wp2015-024, Boston University - Department of Economics.
    5. Normann Lorenz, 2014. "A contest success function with a rent-dependent dissipation rate," Economics Bulletin, AccessEcon, vol. 34(2), pages 1091-1102.

    More about this item

    Keywords

    Risk selection; risk adjustment; discrete choice; contest; quantile regression;

    JEL classification:

    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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