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Using quantile regression for optimal risk adjustment

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  • Normann Lorenz
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    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.

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    File URL: http://www.uni-trier.de/fileadmin/fb4/prof/VWL/EWF/Research_Papers/2014-11.pdf
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    Bibliographic Info

    Paper provided by University of Trier, Department of Economics in its series Research Papers in Economics with number 2014-11.

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    Length: 28 pages
    Date of creation: 2014
    Date of revision:
    Handle: RePEc:trr:wpaper:201411

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    Related research

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

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    References

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    1. 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.
    2. Kenneth Train, 2003. "Discrete Choice Methods with Simulation," Online economics textbooks, SUNY-Oswego, Department of Economics, number emetr2, Spring.
    3. 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.
    4. Bijlsma, M. & Boone, J. & Zwart, G., 2011. "Competition Leverage: How the Demand Side Affects Optimal Risk Adjustment," Discussion Paper 2011-071, Tilburg University, Center for Economic Research.
    5. 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.
    6. 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.
    7. Erik SCHOKKAERT & Carine VAN DE VOORDE, 2000. "Risk Selection and the Specification of the Conventional Risk Adjustment Formula," Center for Economic Studies - Discussion papers ces0011, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
    8. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
    9. Stefan Szymanski, 2003. "The Economic Design of Sporting Contests," Journal of Economic Literature, American Economic Association, vol. 41(4), pages 1137-1187, December.
    10. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603, September.
    11. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275.
    12. Chernichovsky, Dov & van de Ven, Wynand P. M. M., 2003. "Risk adjustment in Europe," Health Policy, Elsevier, vol. 65(1), pages 1-3, July.
    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. 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.
    15. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
    16. 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.
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    Cited by:
    1. Normann Lorenz, 2014. "A contest success function with a rent-dependent dissipation rate," Economics Bulletin, AccessEcon, vol. 34(2), pages 1091-1102.

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