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NONPARAMETRIC TWO-STEP SIEVE M ESTIMATION AND INFERENCE

Published online by Cambridge University Press:  25 April 2018

Jinyong Hahn ,
Zhipeng Liao  and
Geert Ridder
Jinyong Hahn
Affiliation:
UCLA
Zhipeng Liao*
Affiliation:
UCLA
Geert Ridder
Affiliation:
University of Southern California
*
*Address correspondence to Zhipeng Liao, Department of Economics, UCLA, Los Angeles, CA 90095-1477, USA; e-mail: zhipeng.liao@econ.ucla.edu.
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Abstract

This article studies two-step sieve M estimation of general semi/nonparametric models, where the second step involves sieve estimation of unknown functions that may use the nonparametric estimates from the first step as inputs, and the parameters of interest are functionals of unknown functions estimated in both steps. We establish the asymptotic normality of the plug-in two-step sieve M estimate of a functional that could be root-n estimable. The asymptotic variance may not have a closed form expression, but can be approximated by a sieve variance that characterizes the effect of the first-step estimation on the second-step estimates. We provide a simple consistent estimate of the sieve variance, thereby facilitating Wald type inferences based on the Gaussian approximation. The finite sample performance of the two-step estimator and the proposed inference procedure are investigated in a simulation study.

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 6 , December 2018 , pp. 1281 - 1324
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

We gratefully acknowledge insightful comments from Xiaohong Chen, who was a co-author of the initial version. We appreciate useful suggestions from Liangjun Su, the coeditor and three anonymous referees. The outstanding editorial input by the Editor, Professor Phillips, in our last version of the manuscript is greatly appreciated. All errors are the responsibility of the authors.

References

REFERENCES

Ackerberg, D., Chen, X., & Hahn, J. (2012) A practical asymptotic variance estimator for two-step semiparametric estimators. Review of Economics and Statistics 94, 481–498.CrossRefGoogle Scholar
Altonji, J. & Matzkin, R. (2005) Cross section and panel data estimators for nonseparable models with endogenous regressors. Econometrica 73, 1053–1102.Google Scholar
Blundell, R. & Powell, J.L. (2004) Endogeneity in semiparametric binary response models. Review of Economic Studies 71, 655–679.CrossRefGoogle Scholar
Blundell, R. & Powell, J.L. (2007) Censored regression quantiles with endogenous regressors. Journal of Econometrics 141, 65–83.CrossRefGoogle Scholar
Chen, X. (2007) Large sample sieve estimation of semi-nonparametric models. In Heckman, J.J. & Leamer, E.E. (eds.), Handbook of Econometrics, vol. 6B, pp. 5549–5632. Elsevier.Google Scholar
Chen, X. & Liao, Z. (2014) Sieve M inference of irregular parameters. Journal of Econometrics 182(1), 70–86.CrossRefGoogle Scholar
Chen, X., Liao, Z., & Sun, Y. (2014) Sieve inference on possibly misspecified semi-nonparametric time series models. Journal of Econometrics 178(3), 639–658.CrossRefGoogle Scholar
Chen, X., Linton, O., & van Keilegom, I. (2003) Estimation of semiparametric models when the criterion function is not smooth. Econometrica 71, 1591–1608.CrossRefGoogle Scholar
Chen, X. & Shen, X. (1998) Sieve extremum estimates for weakly dependent data. Econometrica 66, 289–314.CrossRefGoogle Scholar
Chernozhukov, V., Escanciano, J., Ichimura, H., & Newey, W. (2016) Locally Robust Semiparametric Estimation. Working paper, MIT.Google Scholar
Chesher, A. (2003) Identification in nonseparable models. Econometrica 71(5), 1405–1414CrossRefGoogle Scholar
Das, M., Newey, W., & Vella, F. (2003) Nonparametric estimation of sample selection models. Review of Economic Studies 70, 33–58.CrossRefGoogle Scholar
Escanciano, J., Jacho-Chávez, D., & Lewbel, A. (2014) Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing. Journal of Econometrics 178, 426–443.CrossRefGoogle Scholar
Florens, J., Heckman, J., Meghir, C., & Vytlacil, E. (2008) Identification of treatment effects using control functions in models with continuous, endogenous treatment and heterogeneous effects. Econometrica 76, 1191–1206.Google Scholar
Hahn, J. & Ridder, G. (2013) The asymptotic variance of semi-parametric estimators with generated regressors. Econometrica 81, 315–340.Google Scholar
Ichimura, H. & Lee, S. (2010) Characterization of the asymptotic distribution of semiparametric M estimators. Journal of Econometrics 159, 252–266.CrossRefGoogle Scholar
Imbens, G. & Newey, W. (2009) Identification and estimation of triangular simultaneous equations models without additivity. Econometrica 77, 1481–1512.Google Scholar
Lee, S. (2007) Endogeneity in quantile regression models: A control function approach. Journal of Econometrics 141, 1131–1158.CrossRefGoogle Scholar
Lee, Y. (2015) Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models. Working paper, UC-Irvine.Google Scholar
Lewbel, A. & Linton, O. (2002) Nonparametric censored and truncated regression. Econometrica 70, 765–779.CrossRefGoogle Scholar
Li, Q. & Wooldridge, M. (2002) Semiparametric estimation of partially linear models for dependent data with generated regressors. Econometric Theory 18, 625–645.CrossRefGoogle Scholar
Mammen, E., Rothe, C., & Schienle, M. (2012) Nonparametric regression with nonparametrically generated covariates. Annals of Statistics 40, 1132–1170.CrossRefGoogle Scholar
Mammen, E., Rothe, C., & Schienle, M. (2016) Semiparametric estimation with generated covariates. Econometric Theory 32(5), 1140–1177.CrossRefGoogle Scholar
Murphy, K. & Topel, R. (1985) Estimation and inference in two-step econometric models. Journal of Business and Economic Statistics 3, 370–379.Google Scholar
Newey, W. (1984) A method of moments interpretation of sequential estimators. Economics Letters 14, 201–206.CrossRefGoogle Scholar
Newey, W. (1994) The asymptotic variance of semiparametric estimators. Econometrica 62, 1349–1382.CrossRefGoogle Scholar
Newey, W. (2009) Two-step series estimation of sample selection models. Econometrics Journal 12, S217–S229.CrossRefGoogle Scholar
Newey, W., Powell, J., & Vella, F. (1999) Nonparametric estimation of triangular simultaneous equations models. Econometrica 67, 565–603.Google Scholar
Olley, G. & Pakes, A. (1996) The dynamics of productivity in the telecommunications equipment industry. Econometrica 64, 1263–1297.CrossRefGoogle Scholar
Shen, X. (1997) On methods of sieves and penalization. Annals of Statistics 25, 2555–2591.Google Scholar
Wooldridge, J.M. (2002) Econometric Analysis of Cross Section and Panel Data. MIT Press.Google Scholar
Wooldridge, J.M. (2015) Control function methods in applied econometrics. Journal of Human Resources 50, 420–445.CrossRefGoogle Scholar
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