Hostname: page-component-6766d58669-h8lrw Total loading time: 0 Render date: 2026-05-24T03:44:37.454Z Has data issue: false hasContentIssue false
  • English
  • Français

SEMIPARAMETRIC ESTIMATION WITH GENERATED COVARIATES

Published online by Cambridge University Press:  04 June 2015

Enno Mammen ,
Christoph Rothe  and
Melanie Schienle
Enno Mammen
Affiliation:
Heidelberg University and National Research University Higher School of Economics
Christoph Rothe*
Affiliation:
Columbia University
Melanie Schienle
Affiliation:
Karlsruhe Institute of Technology
*
*Address correspondence to Christoph Rothe, Department of Economics, Columbia University, 420 W 118th Street, New York, NY 10027, USA; e-mail: cr2690@columbia.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

We study a general class of semiparametric estimators when the infinite-dimensional nuisance parameters include a conditional expectation function that has been estimated nonparametrically using generated covariates. Such estimators are used frequently to e.g., estimate nonlinear models with endogenous covariates when identification is achieved using control variable techniques. We study the asymptotic properties of estimators in this class, which is a nonstandard problem due to the presence of generated covariates. We give conditions under which estimators are root-n consistent and asymptotically normal, derive a general formula for the asymptotic variance, and show how to establish validity of the bootstrap.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 5 , October 2016 , pp. 1140 - 1177
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Ai, C. & Chen, X. (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica 71(6), 1795–1843.CrossRefGoogle Scholar
Ai, C. & Chen, X. (2007) Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables. Journal of Econometrics 141(1), 5–43.Google Scholar
Andrews, D. (1994) Asymptotics for semiparametric econometric models via stochastic equicontinuity. Econometrica 62(1), 43–72.Google Scholar
Andrews, D. (1995) Nonparametric kernel estimation for semiparametric models. Econometric Theory 11(03), 560–586.Google Scholar
Blundell, R. & Powell, J. (2004) Endogeneity in semiparametric binary response models. The Review of Economic Studies 71(3), 655–679.Google Scholar
Caetano, C., Rothe, C., & Yildiz, N. (2014) A Discontinuity Test for Identification in Triangular Nonseparable Models. Working paper.Google Scholar
Chen, X., Linton, O., & Van Keilegom, I. (2003) Estimation of semiparametric models when the criterion function is not smooth. Econometrica 71(5), 1591–1608.Google Scholar
Chen, X. & Pouzo, D. (2009) Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals. Journal of Econometrics 152(1), 46–60.CrossRefGoogle Scholar
Chen, X. & Shen, X. (1998) Sieve extremum estimates for weakly dependent data. Econometrica 66(2), 289–314.CrossRefGoogle Scholar
Einmahl, U. & Mason, D. (2005) Uniform in bandwidth consistency of kernel-type function estimators. Annals of Statistics 33(3), 1380–1403.Google Scholar
Escanciano, J., Jacho-Chávez, D., & Lewbel, A. (2015) Identification and estimation of semiparametric two step models. Quantitative Economics.Google Scholar
Escanciano, J., Jacho-Chávez, D., & Lewbel, A. (2014) Uniform convergence of weighted sums of non- and semi-parametric residuals for estimation and testing. Journal of Econometrics 178, 426–443.CrossRefGoogle Scholar
Giné, E. & Zinn, J. (1990) Bootstrapping general empirical measures. The Annals of Probability, 18, 851–869.CrossRefGoogle Scholar
Hahn, J. (1998) On the role of the propensity score in efficient semiparametric estimation of average treatment effects. Econometrica 66(2), 315–331.CrossRefGoogle Scholar
Hahn, J. & Ridder, G. (2013) Asymptotic variance of semiparametric estimators with generated regressors. Econometrica 81(1), 315–340.Google Scholar
Heckman, J., Ichimura, H., & Todd, P. (1998) Matching as an econometric evaluation estimator. Review of Economic Studies 65(2), 261–294.Google Scholar
Hirano, K., Imbens, G., & Ridder, G. (2003) Efficient estimation of average treatment effects using the estimated propensity score. Econometrica 71(4), 1161–1189.Google Scholar
Ichimura, H. & Lee, S. (2010) Characterization of the asymptotic distribution of semiparametric M-estimators. Journal of Econometrics 159(2), 252–266.Google Scholar
Imbens, G. (2004) Nonparametric estimation of average treatment effects under exogeneity: A review. Review of Economics and Statistics 86(1), 4–29.Google Scholar
Kong, E., Linton, O., & Xia, Y. (2010) Uniform Bahadur representation for local polynomial estimates of M-regression and its application to the additive model. Econometric Theory 26(05), 1529–1564.Google Scholar
Levinsohn, J. & Petrin, A. (2003) Estimating production functions using inputs to control for unobservables. Review of Economic Studies 70(2), 317–341.Google Scholar
Li, Q. & Wooldridge, J. (2002) Semiparametric estimation of partially linear models for dependent data with generated regressors. Econometric Theory 18(03), 625–645.Google Scholar
Linton, O., Sperlich, S., & Van Keilegom, I. (2008) Estimation of a semiparametric transformation model. Annals of Statistics 36(2), 686–718.Google Scholar
Mammen, E., Rothe, C., & Schienle, M. (2012) Nonparametric regression with nonparametrically generated covariates. Annals of Statistics 40, 1132–1170.CrossRefGoogle Scholar
Masry, E. (1996) Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis 17(6), 571–599.CrossRefGoogle Scholar
Murphy, K.M. & Topel, R.H. (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(2–3), 201–206.Google Scholar
Newey, W. (1994) The asymptotic variance of semiparametric estimators. Econometrica 62, 1349–1382.Google Scholar
Newey, W. (1997) Convergence rates and asymptotic normality for series estimators. Journal of Econometrics 79(1), 147–168.Google Scholar
Olley, G. & Pakes, A. (1996) The dynamics of productivity in the telecommunications equipment industry. Econometrica 64(6), 1263–1297.CrossRefGoogle Scholar
Oxley, L. & McAleer, M. (1993) Econometric issues in macroeconomic models with generated regressors. Journal of Economic Surveys 7(1), 1–40.Google Scholar
Pagan, A. (1984) Econometric issues in the analysis of regressions with generated regressors. International Economic Review 25(1), 221–247.Google Scholar
Powell, J., Stock, J., & Stoker, T. (1989) Semiparametric estimation of index coefficients. Econometrica 57(6), 1403–1430.Google Scholar
Rosenbaum, P. & Rubin, D. (1983) The central role of the propensity score in observational studies for causal effects. Biometrika 70(1), 41–55.Google Scholar
Rothe, C. (2009) Semiparametric estimation of binary response models with endogenous regressors. Journal of Econometrics 153(1), 51–64.Google Scholar
Song, K. (2008) Uniform convergence of series estimators over function spaces. Econometric Theory 24(6), 1463–1499.Google Scholar
Song, K. (2012) On the smoothness of conditional expectation functionals. Statistics & Probability Letters 82(5), 1028–1034.CrossRefGoogle Scholar
Song, K. (2013) Semiparametric Models with Single-index Nuisance Parameters. Working paper.Google Scholar
Sperlich, S. (2009) A note on non-parametric estimation with predicted variables. Econometrics Journal 12(2), 382–395.Google Scholar
van de Geer, S. (2009) Empirical Processes in M-Estimation. Cambridge University Press.Google Scholar
Van der Vaart, A. & Wellner, J. (1996) Weak Convergence and Empirical Processes: With Applications to Statistics. Springer Verlag.Google Scholar