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A Simple Ordered Data Estimator For Inverse Density Weighted Functions

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Author Info

  • Arthur Lewbel

    ()
    (Boston College)

  • Susanne M. Schennach

    (University of Chicago)

Abstract

We consider estimation of means of functions that are scaled by an unknown density, or equivalently, integrals of conditional expectations. The "ordered data" estimator we provide is root n consistent, asymptotically normal, and is numerically extremely simple, involving little more than ordering the data and summing the results. No sample size dependent smoothing is required. A similarly simple estimator is provided for the limiting variance. The proofs include new limiting distribution results for functions of nearest neighbor spacings. Potential applications include endogeneous binary choice, willingness to pay, selection, and treatment models.

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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 557.

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Length: 27 pages
Date of creation: 04 Apr 2003
Date of revision: 01 May 2005
Publication status: forthcoming, Journal of Econometrics
Handle: RePEc:boc:bocoec:557

Note: Previously circulated as "A Simple Ordered Data Estimator for Inverse Density Weighted Expectations"
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Related research

Keywords: Semiparametric; Conditional Expectation; Density Estimation; Binary Choice; Binomial Response;

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References

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  1. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics 454, Boston College Department of Economics.
  2. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, 07.
  3. Klein, R.W. & Spady, R.H., 1991. "An Efficient Semiparametric Estimator for Binary Response Models," Papers 70, Bell Communications - Economic Research Group.
  4. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
  5. Arthur Lewbel & Oliver Linton & D. L. McFadden, 2006. "Estimating features of a distribution from binomial data," LSE Research Online Documents on Economics 4418, London School of Economics and Political Science, LSE Library.
  6. Daniel McFadden, 1996. "Computing Willingness-to-Pay in Random Utility Models," Working Papers _011, University of California at Berkeley, Econometrics Laboratory Software Archive.
  7. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, 05.
  8. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November.
  9. Denis Cogneau & Eric Maurin, 2001. "Parental Income and School Attendance in a Low-Income Country : A semi-parametric analysis," Working Papers DT/2001/16, DIAL (Développement, Institutions et Mondialisation).
  10. Barbe, Philippe, 1994. "Joint approximation of processes based on spacings and order statistics," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 339-349, October.
  11. repec:cup:etheor:v:13:y:1997:i:1:p:32-51 is not listed on IDEAS
  12. Mack, Y. P. & Müller, Hans-Georg, 1988. "Convolution type estimators for nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 7(3), pages 229-239, December.
  13. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
  14. Alberto Abadie & Guido W. Imbens, 2002. "Simple and Bias-Corrected Matching Estimators for Average Treatment Effects," NBER Technical Working Papers 0283, National Bureau of Economic Research, Inc.
  15. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(01), pages 32-51, February.
  16. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
  17. Whitney K. Newey and Paul A. Ruud., 1994. "Density Weighted Linear Least Squares," Economics Working Papers 94-228, University of California at Berkeley.
  18. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
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Citations

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Cited by:
  1. Mohnen, Pierre & Tiwari, Amaresh & Palm, Franz & Schim van der Loeff, Sybrand, 2007. "Financial Constraint and R&D Investment: Evidence from CIS," MERIT Working Papers 011, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
  2. Yingying Dong & Arthur Lewbel, 2012. "Simple Estimators for Binary Choice Models with Endogenous Regressors," Working Papers 111204, University of California-Irvine, Department of Economics.
  3. Yingying Dong & Arthur Lewbel & Thomas Tao Yang, 2012. "Comparing Features of Convenient Estimators for Binary Choice Models With Endogenous Regressors," Boston College Working Papers in Economics 789, Boston College Department of Economics, revised 15 May 2012.

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