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Series Estimation of Regression Functionals

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  • Newey, Whitney K.

Abstract

Two-step estimators, where the first step is the predicted value from a nonparametric regression, are useful in many contexts. Examples include a non-parametric residual variance, probit with nonparametric generated regressors, efficient GMM estimation with randomly missing data, heteroskedasticity corrected least squares, semiparametric regression, and efficient nonlinear instrumental variables estimators. The purpose of this paper is the development of consistency and asymptotic normality results when the first step is a series estimator. The paper presents the form of a correction term for the first step on the second-step asymptotic variance and gives a consistent variance estimator. Data-dependent numbers of terms are allowed for, and the regressor distribution can be discrete, continuous, or a mixture of the two. Results for several new estimators are given.

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  • Newey, Whitney K., 1994. "Series Estimation of Regression Functionals," Econometric Theory, Cambridge University Press, vol. 10(1), pages 1-28, March.
    • Handle: RePEc:cup:etheor:v:10:y:1994:i:01:p:1-28_00
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    1. Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2014. "Testing for additivity in partially linear regression with possibly missing responses," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 51-61.
    2. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    3. Rajeev Dehejia & Cristian Pop-Eleches & Cyrus Samii, 2021. "From Local to Global: External Validity in a Fertility Natural Experiment," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 217-243, January.
    4. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-1297, November.
    5. Chatelain, Jean-Bernard & Teurlai, Jean-Christophe, 2001. "Pitfalls in investment Euler equations," Economic Modelling, Elsevier, vol. 18(2), pages 159-179, April.
    6. Yukitoshi Matsushita & Taisuke Otsu, 2017. "Likelihood inference on semiparametric models: Average derivative and treatment effect," STICERD - Econometrics Paper Series 592, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    8. Chen, Linkun & Clarke, Philip M. & Petrie, Dennis J. & Staub, Kevin E., 2021. "The effects of self-assessed health: Dealing with and understanding misclassification bias," Journal of Health Economics, Elsevier, vol. 78(C).
    9. Jaumandreu, Jordi & Moral, Maria Jose, 2006. "Identifying behaviour in a multiproduct oligopoly: Incumbents reaction to tariffs dismantling," MPRA Paper 1248, University Library of Munich, Germany.
    10. Su, Liangjun & Jin, Sainan, 2012. "Sieve estimation of panel data models with cross section dependence," Journal of Econometrics, Elsevier, vol. 169(1), pages 34-47.
    11. Cui, Li-E & Zhao, Puying & Tang, Niansheng, 2022. "Generalized empirical likelihood for nonsmooth estimating equations with missing data," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    12. Muhammad Nazmul Khan, 2022. "Estimating empirical marginal adjustment cost function: a power series approach," Empirical Economics, Springer, vol. 63(6), pages 3185-3210, December.
    13. Robinson, Peter M., 2002. "Denis Sargan: some perspectives," LSE Research Online Documents on Economics 2263, London School of Economics and Political Science, LSE Library.
    14. Alberto Abadie, 2000. "Semiparametric Estimation of Instrumental Variable Models for Causal Effects," NBER Technical Working Papers 0260, National Bureau of Economic Research, Inc.
    15. Miller, Steve & Startz, Richard, 2019. "Feasible generalized least squares using support vector regression," Economics Letters, Elsevier, vol. 175(C), pages 28-31.
    16. Parente, Paulo M.D.C. & Smith, Richard J., 2017. "Tests of additional conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 200(1), pages 1-16.
    17. Gayle, George-Levi & Viauroux, Christelle, 2007. "Root-N consistent semiparametric estimators of a dynamic panel-sample-selection model," Journal of Econometrics, Elsevier, vol. 141(1), pages 179-212, November.
    18. Robinson, Peter M., 2003. "Denis Sargan: some perspectives," LSE Research Online Documents on Economics 292, London School of Economics and Political Science, LSE Library.
    19. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    20. Gutierrez, Roberto G. & Carroll, Raymond J., 1995. "Plug-in semiparametric estimating equations," SFB 373 Discussion Papers 1997,13, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    21. Donald, Stephen G., 1995. "Two-step estimation of heteroskedastic sample selection models," Journal of Econometrics, Elsevier, vol. 65(2), pages 347-380, February.
    22. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    23. Tetsuya Kaji, 2021. "Theory of Weak Identification in Semiparametric Models," Econometrica, Econometric Society, vol. 89(2), pages 733-763, March.
    24. Peter M Robinson, 2002. "Denis Sargan: Some Perspectives," STICERD - Econometrics Paper Series 437, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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