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Nonparametric Estimation of Nonadditive Random Functions

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  • Rosa L. Matzkin

    (Northwestern University & Universidad de San Andres)

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
File Function: Revised version, 2001
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Bibliographic 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;

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References

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  1. Joseph G. Altonji & Hidehiko Ichimura & Taisuke Otsu, 2008. "Estimating Derivatives in Nonseparable Models with Limited Dependent Variables," NBER Working Papers 14161, National Bureau of Economic Research, Inc.
  2. Horowitz, J. & Gorgens, T., 1995. "Semiparametric Estimation of a Censored Regression Model with an Unknown Transformation of the Dependent Variable," Working Papers 95-15, University of Iowa, Department of Economics.
  3. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
  4. 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.
  5. Bryan W. Brown & Mary Beth Walker, 1992. "Stochastic specification in random production models of cost minimizing firms," Working Paper 92-6, Federal Reserve Bank of Atlanta.
  6. Newey, W.K., 1992. "Kernel Estimation of Partial Means and a General Variance Estimator," Working papers 93-3, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Joseph G. Altonji & Rosa L. Matzkin, 2001. "Panel Data Estimators for Nonseparable Models with Endogenous Regressors," NBER Technical Working Papers 0267, National Bureau of Economic Research, Inc.
  8. James J. Heckman & Robert J. Willis, 1975. "A Beta-Logistic Model for the Analysis of Sequential Labor Force Participation by Married Women," NBER Working Papers 0112, National Bureau of Economic Research, Inc.
  9. 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.
  10. 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 for Research in Economics, Yale University.
  11. 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.
  12. Roehrig, Charles S, 1988. "Conditions for Identification in Nonparametric and Parametic Models," Econometrica, Econometric Society, vol. 56(2), pages 433-47, March.
  13. 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.
  14. Han, Aaron K., 1987. "A non-parametric analysis of transformations," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 191-209, July.
  15. 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.
  16. Ridder, Geert, 1990. "The Non-parametric Identification of Generalized Accelerated Failure-Time Models," Review of Economic Studies, Wiley Blackwell, vol. 57(2), pages 167-81, April.
  17. Elbers, Chris & Ridder, Geert, 1982. "True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model," Review of Economic Studies, Wiley Blackwell, vol. 49(3), pages 403-09, July.
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