IDEAS home Printed from
   My bibliography  Save this paper

Regression Discontinuity Designs with an Endogenous Forcing Variable and an Application to Contracting in Health Care


  • Patrick Bajari
  • Han Hong
  • Minjung Park
  • Robert Town


Regression discontinuity designs (RDDs) are a popular method to estimate treatment effects. However, RDDs may fail to yield consistent estimates if the forcing variable can be manipulated by the agent. In this paper, we examine one interesting set of economic models with such a feature. Specifically, we examine the case where there is a structural relationship between the forcing variable and the outcome variable because they are determined simultaneously. We propose a modi...ed RDD estimator for such models and derive the conditions under which it is consistent. As an application of our method, we study contracts between a large managed care organization and leading hospitals for the provision of organ and tissue transplants. Exploiting "donut holes" in the reimbursement contracts we estimate how the total claims filed by the hospitals depend on the generosity of the reimbursement structure. Our results show that hospitals submit significantly larger bills when the reimbursement rate is higher, indicating informational asymmetries between the payer and hospitals in this market.

Suggested Citation

  • Patrick Bajari & Han Hong & Minjung Park & Robert Town, 2011. "Regression Discontinuity Designs with an Endogenous Forcing Variable and an Application to Contracting in Health Care," NBER Working Papers 17643, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:17643
    Note: HC IO

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Miguel Urquiola & Eric Verhoogen, 2009. "Class-Size Caps, Sorting, and the Regression-Discontinuity Design," American Economic Review, American Economic Association, vol. 99(1), pages 179-215, March.
    2. Martin Gaynor & James B. Rebitzer & Lowell J. Taylor, 2004. "Physician Incentives in Health Maintenance Organizations," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 915-931, August.
    3. Donald, Stephen G. & Paarsch, Harry J., 1996. "Identification, Estimation, and Testing in Parametric Empirical Models of Auctions within the Independent Private Values Paradigm," Econometric Theory, Cambridge University Press, vol. 12(03), pages 517-567, August.
    4. Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639,
    5. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    6. David C. Wyld, 2010. "ASecond Life for organizations?: managing in the new, virtual world," Management Research Review, Emerald Group Publishing, vol. 33(6), pages 529-562, May.
    7. McCrary, Justin, 2008. "Manipulation of the running variable in the regression discontinuity design: A density test," Journal of Econometrics, Elsevier, vol. 142(2), pages 698-714, February.
    8. Jonathan Gruber & Maria Owings, 1996. "Physician Financial Incentives and Cesarean Section Delivery," RAND Journal of Economics, The RAND Corporation, vol. 27(1), pages 99-123, Spring.
    9. Hodgkin, Dominic & McGuire, Thomas G., 1994. "Payment levels and hospital response to prospective payment," Journal of Health Economics, Elsevier, vol. 13(1), pages 1-29, March.
    10. Martin Gaynor & Paul Gertler, 1995. "Moral Hazard and Risk Spreading in Partnerships," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 591-613, Winter.
    11. Dranove, David & Wehner, Paul, 1994. "Physician-induced demand for childbirths," Journal of Health Economics, Elsevier, vol. 13(1), pages 61-73, March.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Murat G. Kýrdar & Meltem Dayýoglu Tayfur & Ýsmet Koç, 2010. "The Effect of Compulsory Schooling Laws on Teenage Marriage and Births in Turkey," Koç University-TUSIAD Economic Research Forum Working Papers 1035, Koc University-TUSIAD Economic Research Forum.
    2. Martin Gaynor & Kate Ho & Robert J. Town, 2015. "The Industrial Organization of Health-Care Markets," Journal of Economic Literature, American Economic Association, vol. 53(2), pages 235-284, June.
    3. Jales, Hugo & Ma, Jun & Yu, Zhengfei, 2017. "Optimal bandwidth selection for local linear estimation of discontinuity in density," Economics Letters, Elsevier, vol. 153(C), pages 23-27.
    4. Gerard, Francois & Rokkanen, Miikka & Rothe, Christoph, 2015. "Identification and Inference in Regression Discontinuity Designs with a Manipulated Running Variable," IZA Discussion Papers 9604, Institute for the Study of Labor (IZA).
    5. Gaynor, Martin & Town, Robert J., 2011. "Competition in Health Care Markets," Handbook of Health Economics, Elsevier.
    6. Kowalski, Amanda E., 2015. "Estimating the tradeoff between risk protection and moral hazard with a nonlinear budget set model of health insurance," International Journal of Industrial Organization, Elsevier, vol. 43(C), pages 122-135.
    7. Kate Ho & Ariel Pakes, 2014. "Hospital Choices, Hospital Prices, and Financial Incentives to Physicians," American Economic Review, American Economic Association, vol. 104(12), pages 3841-3884, December.
    8. François Gerard & Miikka Rokkanen & Christoph Rothe, 2016. "Bounds on Treatment Effects in Regression Discontinuity Designs under Manipulation of the Running Variable, with an Application to Unemployment Insurance in Brazil," NBER Working Papers 22892, National Bureau of Economic Research, Inc.
    9. Rudy Douven & Minke Remmerswaal & Ilaria Mosca (Ecorys), 2014. "Unintended effects of reimbursement schedules in mental health care," CPB Discussion Paper 292, CPB Netherlands Bureau for Economic Policy Analysis.
    10. Douven, Rudy & Remmerswaal, Minke & Mosca, Ilaria, 2015. "Unintended effects of reimbursement schedules in mental health care," Journal of Health Economics, Elsevier, vol. 42(C), pages 139-150.
    11. Sojourner, Aaron J. & Frandsen, Brigham R. & Town, Robert J. & Grabowski, David C. & Chen, Michelle M., 2014. "Impacts of Unionization on Quality and Productivity: Regression Discontinuity Evidence from Nursing Homes," IZA Discussion Papers 8240, Institute for the Study of Labor (IZA).

    More about this item

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • I10 - Health, Education, and Welfare - - Health - - - General
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:nbr:nberwo:17643. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.