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Implementing Nonparametric and Semiparametric Estimators

In: Handbook of Econometrics

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  • Ichimura, Hidehiko
  • Todd, Petra E.

Abstract

This chapter reviews recent advances in nonparametric and semiparametric estimation, with an emphasis on applicability to empirical research and on resolving issues that arise in implementation. It considers techniques for estimating densities, conditional mean functions, derivatives of functions and conditional quantiles in a flexible way that imposes minimal functional form assumptions. The chapter begins by illustrating how flexible modeling methods have been applied in empirical research, drawing on recent examples of applications from labor economics, consumer demand estimation and treatment effects models. Then, key concepts in semiparametric and nonparametric modeling are introduced that do not have counterparts in parametric modeling, such as the so-called curse of dimensionality, the notion of models with an infinite number of parameters, the criteria used to define optimal convergence rates, and "dimension-free" estimators. After defining these new concepts, a large literature on nonparametric estimation is reviewed and a unifying framework presented for thinking about how different approaches relate to one another. Local polynomial estimators are discussed in detail and their distribution theory is developed. The chapter then shows how nonparametric estimators form the building blocks for many semiparametric estimators, such as estimators for average derivatives, index models, partially linear models, and additively separable models. Semiparametric methods offer a middle ground between fully nonparametric and parametric approaches. Their main advantage is that they typically achieve faster rates of convergence than fully nonparametric approaches. In many cases, they converge at the parametric rate. The second part of the chapter considers in detail two issues that are central with regard to implementing flexible modeling methods: how to select the values of smoothing parameters in an optimal way and how to implement "trimming" procedures. It also reviews newly developed techniques for deriving the distribution theory of semiparametric estimators. The chapter concludes with an overview of approximation methods that speed up the computation of nonparametric estimates and make flexible estimation feasible even in very large size samples.

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This chapter was published in:

  • J.J. Heckman & E.E. Leamer (ed.), 2007. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 6, number 6b, January.
    This item is provided by Elsevier in its series Handbook of Econometrics with number 6b-74.

    Handle: RePEc:eee:ecochp:6b-74

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    Cited by:
    1. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.
    2. repec:idb:brikps:8378 is not listed on IDEAS
    3. Heckman, James J. & Schmierer, Daniel, 2010. "Tests of Hypotheses Arising in the Correlated Random Coefficient Model," IZA Discussion Papers 5205, Institute for the Study of Labor (IZA).
    4. Kristensen, Dennis, 2010. "Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models," Journal of Econometrics, Elsevier, vol. 156(2), pages 239-259, June.
    5. Cattaneo, Matias D. & Farrell, Max H., 2013. "Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators," Journal of Econometrics, Elsevier, vol. 174(2), pages 127-143.
    6. Heckman, James J. & Schmierer, Daniel & Urzua, Sergio, 2009. "Testing the Correlated Random Coefficient Model," IZA Discussion Papers 4525, Institute for the Study of Labor (IZA).
    7. Pedro Cerqueira, 2013. "A closer look at the world business cycle synchronization," International Economics and Economic Policy, Springer, vol. 10(3), pages 349-363, September.
    8. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, School of Economics and Management, University of Aarhus.
    9. Rothe, Christoph, 2009. "Semiparametric estimation of binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 153(1), pages 51-64, November.
    10. Mogstad, Magne & Wiswall, Matthew, 2010. "Instrumental Variables Estimation with Partially Missing Instruments," IZA Discussion Papers 4689, Institute for the Study of Labor (IZA).
    11. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2010. "Robust Data-Driven Inference for Density-Weighted Average Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1070-1083.
    12. Hill, Jonathan B. & Shneyerov, Artyom, 2013. "Are there common values in first-price auctions? A tail-index nonparametric test," Journal of Econometrics, Elsevier, vol. 174(2), pages 144-164.
    13. Carlos A. Flores & Alfonso Flores-Lagunes & Arturo Gonzalez & Todd C. Neumann, 2009. "Estimating the Effects of Lenght of Exposure to Traning Program: The Case of Job Corps," Working Papers 2010-3, University of Miami, Department of Economics.

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