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Nonparametric Estimation of Nonadditive Random Functions

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Author Info
Rosa L. Matzkin (Northwestern University & Universidad de San Andrés)
Abstract

We present estimators for nonparametric functions that depend on unobservable random variables in nonadditive ways. The distributions of the unobservable random terms are assumed to be unknown. We show how properties that may be implied by economic theory, such as monotonicity, homogeneity of degree one, and separability can be used to identify the unknown, nonparametric functions and distributions. We also present convenient normalizations, to use when the properties of the functions are unknown. The estimators for the nonparametric distributions and for the nonparametric functions and their derivatives are shown to be consistent and asymptotically normal. The results of a limited simulation study are presented.

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File URL: ftp://webacademicos.udesa.edu.ar/pub/econ/doc38.pdf
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File Function: Revised version, 2001
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Publisher Info
Paper provided by Universidad de San Andres, Departamento de Economia in its series Working Papers with number 38.

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Length: 60 pages
Date of creation: Apr 1999
Date of revision: Sep 2001
Handle: RePEc:sad:wpaper:38

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Related research
Keywords: nonparametric estimation; nonadditive random term; nonseparable models; shape restrictions; conditional distributions; kernel estimators;

References listed on IDEAS
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  1. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 1-21, June. [Downloadable!]
  2. Donald J. Brown & Rosa L. Matzkin, 1998. "Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand," Cowles Foundation Discussion Papers 1175, Cowles Foundation, Yale University. [Downloadable!]
  3. Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-29, July. [Downloadable!] (restricted)
  4. McElroy, Marjorie B, 1987. "Additive General Error Models for Production, Cost, and Derived Demand or Share Systems," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 737-57, August. [Downloadable!] (restricted)
  5. Heckman, James J & Willis, Robert J, 1977. "A Beta-logistic Model for the Analysis of Sequential Labor Force Participation by Married Women," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 27-58, February. [Downloadable!] (restricted)
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  6. Brown, Bryan W. & Walker, Mary Beth, 1995. "Stochastic specification in random production models of cost-minimizing firms," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 175-205. [Downloadable!] (restricted)
  7. Elbers, Chris & Ridder, Geert, 1982. "True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model," Review of Economic Studies, Blackwell Publishing, vol. 49(3), pages 403-09, July. [Downloadable!] (restricted)
  8. Heckman, James J, 1991. "Identifying the Hand of the Past: Distinguishing State Dependence from Heterogeneity," American Economic Review, American Economic Association, vol. 81(2), pages 75-79, May. [Downloadable!] (restricted)
  9. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-37, January. [Downloadable!] (restricted)
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