IDEAS home Printed from https://ideas.repec.org/a/wly/hlthec/v26y2017i6p724-742.html
   My bibliography  Save this article

Using Quantile and Asymmetric Least Squares Regression for Optimal Risk Adjustment

Author

Listed:
  • Normann Lorenz

Abstract

In this paper, we analyze 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 (csf) used in most of the contest literature (the Tullock‐csf), optimal transfers for a risk adjustment scheme have to be determined by means of a restricted quantile regression, irrespective of whether insurers are primarily engaged 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 for a new csf, but only if positive and negative DRSs are equally important; if they are not, optimal transfers have to be calculated by means of a restricted asymmetric least squares regression. Using data from German and Swiss health insurers, we find considerable differences between the three types of regressions. Optimal transfers therefore critically depend on which csf represents insurers' incentives for DRS and, if it is not the Tullock‐csf, whether insurers are primarily engaged in positive or negative DRS. Copyright © 2016 John Wiley & Sons, Ltd.

Suggested Citation

  • Normann Lorenz, 2017. "Using Quantile and Asymmetric Least Squares Regression for Optimal Risk Adjustment," Health Economics, John Wiley & Sons, Ltd., vol. 26(6), pages 724-742, June.
    • Handle: RePEc:wly:hlthec:v:26:y:2017:i:6:p:724-742
    DOI: 10.1002/hec.3352
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/hec.3352
    Download Restriction: no
    File URL: https://libkey.io/10.1002/hec.3352?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Breyer, Friedrich & Bundorf, M. Kate & Pauly, Mark V., 2011. "Health Care Spending Risk, Health Insurance, and Payment to Health Plans," Handbook of Health Economics, in: Mark V. Pauly & Thomas G. Mcguire & Pedro P. Barros (ed.), Handbook of Health Economics, volume 2, chapter 0, pages 691-762, Elsevier.
    3. Stam, Pieter J.A. & van Vliet, René C.J.A. & van de Ven, Wynand P.M.M., 2010. "A limited-sample benchmark approach to assess and improve the performance of risk equalization models," Journal of Health Economics, Elsevier, vol. 29(3), pages 426-437, May.
    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. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    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. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, January.
    8. Lorenz, Normann, 2015. "The interaction of direct and indirect risk selection," Journal of Health Economics, Elsevier, vol. 42(C), pages 81-89.
    9. Skaperdas, Stergios & Grofman, Bernard, 1995. "Modeling Negative Campaigning," American Political Science Review, Cambridge University Press, vol. 89(1), pages 49-61, March.
    10. Stefan Szymanski, 2010. "The Economic Design of Sporting Contests," Palgrave Macmillan Books, in: The Comparative Economics of Sport, chapter 1, pages 1-78, Palgrave Macmillan.
    11. Mark V. Pauly & Thomas G. Mcguire & Pedro P. Barros (ed.), 2011. "Handbook of Health Economics," Handbook of Health Economics, Elsevier, volume 2, number 2.
    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. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    14. 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.
    15. Normann Lorenz, 2014. "A contest success function with a rent-dependent dissipation rate," Economics Bulletin, AccessEcon, vol. 34(2), pages 1091-1102.
    16. Glazer, Jacob & McGuire, Thomas G., 2002. "Setting health plan premiums to ensure efficient quality in health care: minimum variance optimal risk adjustment," Journal of Public Economics, Elsevier, vol. 84(2), pages 153-173, May.
    17. Van de ven, Wynand P.M.M. & Ellis, Randall P., 2000. "Risk adjustment in competitive health plan markets," Handbook of Health Economics, in: A. J. Culyer & J. P. Newhouse (ed.), Handbook of Health Economics, edition 1, volume 1, chapter 14, pages 755-845, Elsevier.
    18. 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.
    19. Jack, William, 2006. "Optimal risk adjustment with adverse selection and spatial competition," Journal of Health Economics, Elsevier, vol. 25(5), pages 908-926, September.
    20. 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.
    21. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Normann Lorenz, 2014. "Using quantile regression for optimal risk adjustment," Research Papers in Economics 2014-11, University of Trier, Department of Economics.
    2. Lorenz, Normann, 2015. "The interaction of direct and indirect risk selection," Journal of Health Economics, Elsevier, vol. 42(C), pages 81-89.
    3. Normann Lorenz, 2014. "The interaction of direct and indirect risk selection," Research Papers in Economics 2014-12, University of Trier, Department of Economics.
    4. 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.
    5. Normann Lorenz, 2013. "Adverse selection and risk adjustment under imperfect competition," Research Papers in Economics 2013-05, University of Trier, Department of Economics.
    6. 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.
    7. Jia, Hao & Skaperdas, Stergios & Vaidya, Samarth, 2013. "Contest functions: Theoretical foundations and issues in estimation," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 211-222.
    8. 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.
    9. 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.
    10. Colleen Carey, 2017. "Technological Change and Risk Adjustment: Benefit Design Incentives in Medicare Part D," American Economic Journal: Economic Policy, American Economic Association, vol. 9(1), pages 38-73, February.
    11. Mathias Kifmann & Normann Lorenz, 2011. "Optimal cost reimbursement of health insurers to reduce risk selection," Health Economics, John Wiley & Sons, Ltd., vol. 20(5), pages 532-552, May.
    12. Hao Jia & Stergios Skaperdas, 2011. "Technologies of Conflict," Working Papers 101111, University of California-Irvine, Department of Economics.
    13. 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.
    14. Dosis, Anastasios, 2019. "Optimal ex post risk adjustment in markets with adverse selection," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 52-59.
    15. Bijlsma, Michiel & Boone, Jan & Zwart, Gijsbert, 2017. "The complementarity between risk adjustment and community rating: Distorting market outcomes to facilitate redistribution," Journal of Public Economics, Elsevier, vol. 155(C), pages 21-37.
    16. Cedric Duvinage & Peter-J. Jost, 2019. "The Role of Referees in Professional Sports Contests," Journal of Sports Economics, , vol. 20(8), pages 1014-1050, December.
    17. Normann Lorenz, 2014. "A contest success function with a rent-dependent dissipation rate," Economics Bulletin, AccessEcon, vol. 34(2), pages 1091-1102.
    18. Schmid, Christian P.R. & Beck, Konstantin, 2016. "Re-insurance in the Swiss health insurance market: Fit, power, and balance," Health Policy, Elsevier, vol. 120(7), pages 848-855.
    19. Michele Fioretti & Hongming Wang, 2023. "Performance Pay in Insurance Markets: Evidence from Medicare," The Review of Economics and Statistics, MIT Press, vol. 105(5), pages 1128-1144, September.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:hlthec:v:26:y:2017:i:6:p:724-742. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www3.interscience.wiley.com/cgi-bin/jhome/5749 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.