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A Simple Ordered Data Estimator For Inverse Density Weighted Functions

Author

Listed:
  • 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.

Suggested Citation

  • Arthur Lewbel & Susanne M. Schennach, 2003. "A Simple Ordered Data Estimator For Inverse Density Weighted Functions," Boston College Working Papers in Economics 557, Boston College Department of Economics, revised 01 May 2005.
    • Handle: RePEc:boc:bocoec:557
    Note: Previously circulated as "A Simple Ordered Data Estimator for Inverse Density Weighted Expectations"
    as

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    References listed on IDEAS

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    1. 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, July.
    2. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
    3. Thierry Magnac & Eric Maurin, 2003. "Identification & Information in Monotone Binary Models," Research Unit Working Papers 0309, Laboratoire d'Economie Appliquee, INRA.
    4. 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.
    5. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    6. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(1), pages 32-51, February.
    7. 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.
    8. Lewbel, Arthur & McFadden, Daniel & Linton, Oliver, 2011. "Estimating features of a distribution from binomial data," Journal of Econometrics, Elsevier, vol. 162(2), pages 170-188, June.
    9. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    10. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    11. Mack, Y. P. & Müller, Hans-Georg, 1988. "Convolution type estimators for nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 7(3), pages 229-239, December.
    12. repec:cup:etheor:v:13:y:1997:i:1:p:32-51 is not listed on IDEAS
    13. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
    14. Denis Cogneau & Eric Maurin, 2001. "Parental Income and School Attendance in a Low-Income Country : A Semi-parametric Analysis," Working Papers 2001-08, Center for Research in Economics and Statistics.
    15. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    16. Newey, Whitney K. & Ruud, Paul A., 1994. "Density Weighted Linear Least Squares," Department of Economics, Working Paper Series qt9fc2n3jc, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    17. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, May.
    18. Daniel McFadden, 1996. "Computing Willingness-to-Pay in Random Utility Models," Working Papers _011, University of California at Berkeley, Econometrics Laboratory Software Archive.
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    Cited by:

    1. Amaresh K. Tiwari & Pierre Mohnen & Franz C. Palm & Sybrand Schim Loeff, 2008. "Financial Constraint and R&D Investment: Evidence from CIS," Palgrave Macmillan Books, in: Cees Beers & Alfred Kleinknecht & Roland Ortt & Robert Verburg (ed.), Determinants of Innovative Behaviour, chapter 10, pages 217-242, Palgrave Macmillan.
    2. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    3. Arthur Lewbel & Yingying Dong & Thomas Tao Yang, 2012. "Comparing features of convenient estimators for binary choice models with endogenous regressors," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 45(3), pages 809-829, August.

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    More about this item

    Keywords

    Semiparametric; Conditional Expectation; Density Estimation; Binary Choice; Binomial Response;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity

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