IDEAS home Printed from
   My bibliography  Save this paper

Asymptotic Bias and Optimal Convergence Rates for Semiparametric Kernel Estimators in the Regression Discontinuity Model


  • Jack Porter


The regression discontinuity model has recently become a commonly applied framework for empirical work in economics. Hahn, Todd, and Van der Klaauw (2001) provide a formal development of the identification of a treatment effect in this framework and also note the potential bias problems in its estimation. This bias difficulty is the result of a particular feature of the regression discontinuity treatment effect estimation problem that distinguishes it from typical semiparametric estimation problems where smoothness is lacking. Here, the discontinuity is not simply an obstacle to overcome in estimation; instead, the size of discontinuity is itself the object of estimation interest. In this paper, I derive the optimal rate of convergence for estimation of the regression discontinuity treatment effect. The optimal rate suggests that the appropriate choice of estimator the bias difficulties are no worse than would be found in the usual nonparametric conditional mean estimation problem (at an interior point of the covariate support). Two estimators are proposed that attain the optimal rate under varying conditions. One estimator is based on Robinson's (1988) partially linear estimator. The other estimator uses local polynomial estimation and is optimal under a broader set of conditions.

Suggested Citation

  • Jack Porter, 2002. "Asymptotic Bias and Optimal Convergence Rates for Semiparametric Kernel Estimators in the Regression Discontinuity Model," Harvard Institute of Economic Research Working Papers 1989, Harvard - Institute of Economic Research.
  • Handle: RePEc:fth:harver:1989

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Jose Manuel Campa & Linda S. Goldberg, 1997. "The evolving external orientation of manufacturing: a profile of four countries," Economic Policy Review, Federal Reserve Bank of New York, issue Jul, pages 53-81.
    2. Chu-Chia S. Lin & Ivan Png, 2003. "Monitoring costs and the mode of international investment," Journal of Economic Geography, Oxford University Press, vol. 3(3), pages 261-274, July.
    3. Ethier, Wilfred J. & Markusen, James R., 1996. "Multinational firms, technology diffusion and trade," Journal of International Economics, Elsevier, vol. 41(1-2), pages 1-28, August.
    4. Grossman, Gene M. & Helpman, Elhanan, 2004. "Managerial incentives and the international organization of production," Journal of International Economics, Elsevier, vol. 63(2), pages 237-262, July.
    5. Horn, Henrik & Lang, Harald & Lundgren, Stefan, 1995. "Managerial effort incentives, X-inefficiency and international trade," European Economic Review, Elsevier, vol. 39(1), pages 117-138, January.
    6. Gene M. Grossman & Elhanan Helpman, 2005. "Outsourcing in a Global Economy," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 135-159.
    7. Holmstrom, Bengt & Milgrom, Paul, 1991. "Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design," Journal of Law, Economics, and Organization, Oxford University Press, vol. 7(0), pages 24-52, Special I.
    8. Markusen, James R., 2001. "Contracts, intellectual property rights, and multinational investment in developing countries," Journal of International Economics, Elsevier, vol. 53(1), pages 189-204, February.
    9. David L. Hummels & Dana Rapoport & Kei-Mu Yi, 1998. "Vertical specialization and the changing nature of world trade," Economic Policy Review, Federal Reserve Bank of New York, issue Jun, pages 79-99.
    10. Robert C. Feenstra, 1998. "Integration of Trade and Disintegration of Production in the Global Economy," Journal of Economic Perspectives, American Economic Association, vol. 12(4), pages 31-50, Fall.
    11. Lawrence F. Katz, 1986. "Efficiency Wage Theories: A Partial Evaluation," NBER Chapters,in: NBER Macroeconomics Annual 1986, Volume 1, pages 235-290 National Bureau of Economic Research, Inc.
    12. Gordon H. Hanson & Raymond J. Mataloni & Matthew J. Slaughter, 2001. "Expansion Strategies of U.S. Multinational Firms," BEA Papers 0012, Bureau of Economic Analysis.
    13. Gordon H. Hanson & Raymond J. Mataloni & Matthew J. Slaughter, 2005. "Vertical Production Networks in Multinational Firms," The Review of Economics and Statistics, MIT Press, vol. 87(4), pages 664-678, November.
    14. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
    15. Ignatius Horstmann & James R. Markusen, 1987. "Licensing versus Direct Investment: A Model of Internalization by the Multinational Enterprise," Canadian Journal of Economics, Canadian Economics Association, vol. 20(3), pages 464-481, August.
    16. Hummels, David & Ishii, Jun & Yi, Kei-Mu, 2001. "The nature and growth of vertical specialization in world trade," Journal of International Economics, Elsevier, vol. 54(1), pages 75-96, June.
    17. Robert Feenstra & Gordon Hanson, 2001. "Global Production Sharing and Rising Inequality: A Survey of Trade and Wages," NBER Working Papers 8372, National Bureau of Economic Research, Inc.
    18. repec:pri:wwseco:dp218 is not listed on IDEAS
    19. Wilfred J. Ethier, 1986. "The Multinational Firm," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 805-833.
    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. Karen M. Pence, 2003. "Foreclosing on opportunity: state laws and mortgage credit," Finance and Economics Discussion Series 2003-16, Board of Governors of the Federal Reserve System (U.S.).
    2. Battistin, Erich & Rettore, Enrico, 2008. "Ineligibles and eligible non-participants as a double comparison group in regression-discontinuity designs," Journal of Econometrics, Elsevier, vol. 142(2), pages 715-730, February.

    More about this item


    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:fth:harver:1989. 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: (Thomas Krichel). 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.

    We have no references for this item. You can help adding them by using 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.