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RECURSIVE DIFFERENCING FOR ESTIMATING SEMIPARAMETRIC MODELS

Published online by Cambridge University Press:  18 August 2022

Chan Shen Open the ORCID record for Chan Shen [Opens in a new window]  and
Roger Klein Open the ORCID record for Roger Klein [Opens in a new window]
Chan Shen*
Affiliation:
Penn State University
Roger Klein
Affiliation:
Rutgers University
*
Address correspondence to Chan Shen, Departments of Surgery and Public Health Sciences, Penn State University, College of Medicine, Hershey, PA, USA; e-mail: chanshen@gmail.com.
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Abstract

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Controlling the bias is central to estimating semiparametric models. Many methods have been developed to control bias in estimating conditional expectations while maintaining a desirable variance order. However, these methods typically do not perform well at moderate sample sizes. Moreover, and perhaps related to their performance, nonoptimal windows are selected with undersmoothing needed to ensure the appropriate bias order. In this paper, we propose a recursive differencing estimator for conditional expectations. When this method is combined with a bias control targeting the derivative of the semiparametric expectation, we are able to obtain asymptotic normality under optimal windows. As suggested by the structure of the recursion, in a wide variety of triple index designs, the proposed bias control performs much better at moderate sample sizes than regular or higher-order kernels and local polynomials.

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 1 , February 2024 , pp. 37 - 59
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

We thank the seminar participants at Columbia University and New York University for helpful comments and suggestions. We also thank the Editor and referees for their insightful comments and suggestions. The authors are solely responsible for any errors.

References

REFERENCES

Blundell, R.W. and Powell, J.L. (2003) Endogeneity in nonparametric and semiparametric regression models. Econometric Society Monographs 36, 312–357.Google Scholar
Blundell, R.W. and Powell, J.L. (2004) Endogeneity in semiparametric binary response models. The Review of Economic Studies 71(3), 655–679.CrossRefGoogle Scholar
Fan, J. and Gijbels, I. (1995) Adaptive order polynomial fitting: Bandwidth Robustification and bias reduction. Journal of Computational and Graphical Statistics 4(3), 213–227.Google Scholar
Fan, J. and Gijbels, I. (1996) Local Polynomial Modeling and Its Applications . Chapman & Hall.Google Scholar
Gu, J., Li, Q., and Yang, J.C. (2015) Multivariate local polynomial kernel estimators: Leading bias and asymptotic distributions. Econometric Reviews 34, 979–1010.CrossRefGoogle Scholar
Honoré, B.E. and Powell, J.L. (2005) Chapter 22: Pairwise difference estimation of nonlinear models. In Andrews, D.W.K. and Stock, J.H. (eds.), Identification and Inference in Econometric Models. Essays in Honor of Thomas Rothenberg , pp. 520–553. Cambridge University Press.Google Scholar
Horowitz, J. (1996) Semiparametric estimation of a regression model with an unknown transformation of the dependent variable. Econometrica 64, 103–137.CrossRefGoogle Scholar
Ichimura, H. (1993) Semiparametric least squares (SLS) and weighted SLS estimation of single index models. Journal of Econometrics 58, 71–120.CrossRefGoogle Scholar
Ichimura, H. and Lee, L.F. (1991) Semiparametric least squares (SLS) and weighted SLS estimation of multiple index models: Single equation estimation. In Barnett, W., Powell, J., and Tauchen, G. (eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics . Cambridge University Press.Google Scholar
Klein, R. and Shen, C. (2010) Bias corrections in testing and estimating semiparametric, single index models. Econometric Theory 26, 1683–1718.CrossRefGoogle Scholar
Klein, R., Shen, C., and Vella, F. (2015) Estimation of marginal effects in semiparametric selection models with binary outcomes. Journal of Econometrics 185(1), 82–94.CrossRefGoogle Scholar
Klein, R. and Spady, R. (1993) An efficient semiparametric estimator for the binary response model. Econometrica 61, 387–421.CrossRefGoogle Scholar
Li, Q. and Sun, Y. (2014) Nonparametric and semiparametric estimation and hypothesis testing with nonstationary time series. In Racine, J., Su, L., and Ullah, A. (eds.), The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics , pp. 444–482. Oxford University Press, New York, NY.Google Scholar
Lu, Z.Q. (1996) Multivariate locally weighted polynomial fitting and partial derivative estimation. Journal of Multivariate Analysis 59, 187–205.CrossRefGoogle Scholar
Masry, E. (1996) Multivariate regression estimation local polynomial fitting for time series. Stochastic Processes and Their Applications 65, 81–101.CrossRefGoogle Scholar
Maurer, J., Klein, R., and Vella, F. (2011) Subjective health assessments and active labor market participation of older men: Evidence from a semiparametric binary choice model with nonadditive correlated individual-specific effects. The Review of Economics and Statistics 93(3), 764–774.CrossRefGoogle Scholar
Müller, H.G. (1984) Smooth optimum kernel estimators of densities, regression curves and modes. Annals of Statistics 12, 766–774.CrossRefGoogle Scholar
Newey, W.K., Hsieh, F., and Robins, J. (2004) Twicing kernels and a small bias property of semiparametric estimators. Econometrica 72, 947–962.CrossRefGoogle Scholar
Newey, W.K. and McFadden, D. (1994) Large sample estimation and hypothesis testing. In: Handbook of Econometrics , vol. 4, pp. 2111–2245. North-Holland.Google Scholar
Powell, J., Stock, J., and Stoker, T. (1989) Semiparametric estimation of index coefficients. Econometrica 51, 1403–1430.CrossRefGoogle Scholar
Robinson, P.M. (1988) Root N-consistent semiparametric regression. Econometrica 56, 931–954.CrossRefGoogle Scholar
Ruppert, D. and Wand, M.P. (1994) Multivariate locally weighted least-squares regression. Annals of Statistics 52(3), 1346–1370.Google Scholar
Shen, C. (2013) Determinants of health care decisions: Insurance, utilization, and expenditures. The Review of Economics and Statistics 95(1), 142–153.CrossRefGoogle Scholar
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