IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v72y2004i3p947-962.html
   My bibliography  Save this article

Twicing Kernels and a Small Bias Property of Semiparametric Estimators

Author

Listed:
  • Whitney K. Newey
  • Fushing Hsieh
  • James M. Robins

Abstract

The purpose of this note is to show how semiparametric estimators with a small bias property can be constructed. The small bias property (SBP) of a semiparametric estimator is that its bias converges to zero faster than the pointwise and integrated bias of the nonparametric estimator on which it is based. We show that semiparametric estimators based on twicing kernels have the SBP. We also show that semiparametric estimators where nonparametric kernel estimation does not affect the asymptotic variance have the SBP. In addition we discuss an interpretation of series and sieve estimators as idempotent transformations of the empirical distribution that helps explain the known result that they lead to the SBP. In Monte Carlo experiments we find that estimators with the SBP have mean-square error that is smaller and less sensitive to bandwidth than those that do not have the SBP. Copyright The Econometric Society 2004.

Suggested Citation

  • Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, May.
  • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:3:p:947-962
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00518.x
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. S. Boragan Aruoba & Randall Wright, 2003. "Search, money, and capital: a neoclassical dichotomy," Proceedings, Federal Reserve Bank of Cleveland, pages 1085-1117.
    2. Levine, David K., 1991. "Asset trading mechanisms and expansionary policy," Journal of Economic Theory, Elsevier, pages 148-164.
    3. Daron Acemoglu & Joshua D. Angrist, 2001. "Consequences of Employment Protection? The Case of the Americans with Disabilities Act," Journal of Political Economy, University of Chicago Press, vol. 109(5), pages 915-957, October.
    4. Shouyong Shi, 1997. "A Divisible Search Model of Fiat Money," Econometrica, Econometric Society, pages 75-102.
    5. Nobuhiro Kiyotaki & John Moore, 2002. "Evil Is the Root of All Money," American Economic Review, American Economic Association, pages 62-66.
    6. Wallace, Neil, 2001. "Whither Monetary Economics?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 847-869, November.
    7. Shouyong Shi, 1995. "Money and Prices: A Model of Search and Bargaining," Working Papers 916, Queen's University, Department of Economics.
    8. Peter Howitt, 2005. "Beyond Search: Fiat Money In Organized Exchange," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(2), pages 405-429, May.
    9. Christopher A. Pissarides & Barbara Petrongolo, 2001. "Looking into the Black Box: A Survey of the Matching Function," Journal of Economic Literature, American Economic Association, pages 390-431.
    10. Kocherlakota, Narayana R., 1998. "Money Is Memory," Journal of Economic Theory, Elsevier, pages 232-251.
    11. P. A. Diamond, 1982. "Money in Search Equilibrium," Working papers 297, Massachusetts Institute of Technology (MIT), Department of Economics.
    12. Aleksander Berentsen & Guillaume Rocheteau & Shouyong Shi, 2007. "Friedman Meets Hosios: Efficiency in Search Models of Money," Economic Journal, Royal Economic Society, vol. 117(516), pages 174-195, January.
    13. Miguel Molico, 2006. "The Distribution Of Money And Prices In Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(3), pages 701-722, August.
    14. Johri, Alok, 1999. "Search, Money, and Prices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 439-454, May.
    15. Ricardo Lagos & Randall Wright, 2005. "A Unified Framework for Monetary Theory and Policy Analysis," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 463-484, June.
    16. Kenneth Burdett & Shouyong Shi & Randall Wright, 2001. "Pricing and Matching with Frictions," Journal of Political Economy, University of Chicago Press, vol. 109(5), pages 1060-1085, October.
    17. Dale T. Mortensen & Randall Wright, 2002. "Competitive Pricing and Efficiency in Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(1), pages 1-20, February.
    18. Green, Edward J. & Zhou, Ruilin, 1998. "A Rudimentary Random-Matching Model with Divisible Money and Prices," Journal of Economic Theory, Elsevier, pages 252-271.
    19. Andreas Blume & Douglas V. DeJong & George R. Neumann & Nathan E. Savin, 1998. "Learning in Sender-Receiver Games," CIG Working Papers FS IV 98-13, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG).
    20. Trejos, Alberto & Wright, Randall, 1995. "Search, Bargaining, Money, and Prices," Journal of Political Economy, University of Chicago Press, vol. 103(1), pages 118-141, February.
    21. Jafarey, Saqib & Masters, Adrian, 2003. " Output, Prices, and the Velocity of Money in Search Equilibrium," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(6), pages 871-888, December.
    22. P. Diamond, 1980. "Aggregate Demand Management in Search Equilibrium," Working papers 268, Massachusetts Institute of Technology (MIT), Department of Economics.
    23. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, pages 1179-1232.
    24. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-954, August.
    25. Moen, E.R., 1995. "Competitive Search Equilibrium," Memorandum 37/1995, Oslo University, Department of Economics.
    26. Julien, B. & Kennes, J. & King, I., 1998. "Bidding for Labour," Discussion Papers dp98-03, Department of Economics, Simon Fraser University.
    27. Camera, Gabriele & Winkler, Johannes, 2003. "International monetary trade and the law of one price," Journal of Monetary Economics, Elsevier, pages 1531-1553.
    28. Lagos, Ricardo & Wright, Randall, 2003. "Dynamics, cycles, and sunspot equilibria in 'genuinely dynamic, fundamentally disaggregative' models of money," Journal of Economic Theory, Elsevier, pages 156-171.
    29. Dean Corbae & Ted Temzelides & Randall Wright, 2003. "Directed Matching and Monetary Exchange," Econometrica, Econometric Society, pages 731-756.
    30. Diamond, Peter A, 1982. "Aggregate Demand Management in Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 90(5), pages 881-894, October.
    31. Kiyotaki, Nobuhiro & Wright, Randall, 1993. "A Search-Theoretic Approach to Monetary Economics," American Economic Review, American Economic Association, pages 63-77.
    32. S. Boragan Aruoba & Randall Wright, 2003. "Search, money, and capital: a neoclassical dichotomy," Proceedings, Federal Reserve Bank of Cleveland, pages 1085-1117.
    33. Ruilin Zhou, 1996. "Individual and aggregate real balances in a random matching model," Staff Report 222, Federal Reserve Bank of Minneapolis.
    34. Lakshmi Raut, 2006. "Two-sided altruism, Lindahl equilibrium, and Pareto optimality in overlapping generations models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(3), pages 729-736, April.
    35. Camera, Gabriele & Corbae, Dean, 1999. "Money and Price Dispersion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 985-1008, November.
    36. Chris Shannon., 1996. "Determinacy of Competitive Equilibria in Economies with Many Commodities," Economics Working Papers 96-249, University of California at Berkeley.
    37. Lagos, Ricardo & Wright, Randall, 2003. "Dynamics, cycles, and sunspot equilibria in 'genuinely dynamic, fundamentally disaggregative' models of money," Journal of Economic Theory, Elsevier, pages 156-171.
    38. Guillaume Rocheteau & Ricardo Lagos, 2004. "Superneutrality and the welfare effects of inflation," 2004 Meeting Papers 93, Society for Economic Dynamics.
    39. Arthur J. Hosios, 1990. "On The Efficiency of Matching and Related Models of Search and Unemployment," Review of Economic Studies, Oxford University Press, vol. 57(2), pages 279-298.
    40. Diamond, Peter A, 1984. "Money in Search Equilibrium," Econometrica, Econometric Society, vol. 52(1), pages 1-20, January.
    41. Shi Shougong, 1995. "Money and Prices: A Model of Search and Bargaining," Journal of Economic Theory, Elsevier, pages 467-496.
    42. Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 385-411, April.
    43. Lucas, Robert Jr. & Prescott, Edward C., 1974. "Equilibrium search and unemployment," Journal of Economic Theory, Elsevier, pages 188-209.
    44. Benoit Julien & John Kennes & Ian King, 2000. "Bidding for Labor," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(4), pages 619-649, October.
    45. Kiyotaki, Nobuhiro & Wright, Randall, 1991. "A contribution to the pure theory of money," Journal of Economic Theory, Elsevier, pages 215-235.
    46. Zhou, Ruilin, 1999. "Individual and Aggregate Real Balances in a Random-Matching Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 1009-1038, November.
    47. Acemoglu, Daron & Shimer, Robert, 1999. "Holdups and Efficiency with Search Frictions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 827-849, November.
    48. Shouyong Shi, 1996. "A Divisible Search Model of Fiat Money," Working Papers 930, Queen's University, Department of Economics.
    Full references (including those not matched with items on IDEAS)

    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:ecm:emetrp:v:72:y:2004:i:3:p:947-962. 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: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/essssea.html .

    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 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.