Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T13:38:05.943Z Has data issue: false hasContentIssue false
  • English
  • Français

QUANTILE REGRESSION WITH MISMEASURED COVARIATES

Published online by Cambridge University Press:  04 April 2008

Susanne M. Schennach
Susanne M. Schennach*
Affiliation:
University of Chicago
*
Address correspondence to Susanne M. Schennach, Department of Economics, University of Chicago, 1126 East 59th Street, Chicago, IL 60637, U.S.A.; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper establishes that the availability of instrumental variables enables the identification and the consistent estimation of nonparametric quantile regression models in the presence of measurement error in the regressors. The proposed estimator takes the form of a nonlinear functional of derivatives of conditional expectations and is shown to provide estimated quantile functions that are uniformly consistent over a compact set.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 4 , August 2008 , pp. 1010 - 1043
Copyright
Copyright © Cambridge University Press 2008

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.)

References

REFERENCES

Abadie, A., Angrist, J.D., ’ Imbens, G.W. (1998) Instrumental Variables Estimation of Quantile Treatment Effects. Working paper 229, National Bureau of Economic Research.CrossRefGoogle Scholar
Abadie, A., Angrist, J.D., ’ Imbens, G.W. (2002) Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings. Econometrica 70, 91–117.CrossRefGoogle Scholar
Andrews, D.W.K. (1995) Nonparametric kernel estimation for semiparametric models. Econometric Theory 11, 560–596.CrossRefGoogle Scholar
Angrist, J.D., Chernozhukov, V., ’ Fernandez-Val, I. (2006) Quantile regression under misspecification, with an application to the U.S. wage structure. Econometrica 74, 539–563.CrossRefGoogle Scholar
Bollinger, C.R. (1998) Measurement error in the current population survey: A nonparametric look. Journal of Labor Economics 16, 576–594.CrossRefGoogle ScholarPubMed
Chalak, K. ’ White, H. (2006) An Extended Class of Instrumental Variables for the Estimation of Causal Effects. Working paper, University of California, San Diego.Google Scholar
Chernozhukov, V. ’ Hansen, C. (2005) An IV model of quantile treatment effects. Econometrica 73, 245–261.CrossRefGoogle Scholar
Chernozhukov, V., Imbens, G.W., ’ Newey, W.K. (2007) Instrumental variable estimation of nonseparable models. Journal of Econometrics 139, 4–14.CrossRefGoogle Scholar
Chesher, A. (2001) Parameter Approximations for Quantile Regressions with Measurement Error. Working paper CWP02/01, Department of Economics, University College London.CrossRefGoogle Scholar
Chesher, A. (2003) Identification in nonseparable models. Econometrica 71, 1405–1441.CrossRefGoogle Scholar
Fan, J. (1991) On the optimal rates of convergence for nonparametric deconvolution problems. Annals of Statistics 19, 1257–1272.CrossRefGoogle Scholar
Fan, J. ’ Truong, Y.K. (1993) Nonparametric regression with errors in variables. Annals of Statistics 21, 1900–1925.CrossRefGoogle Scholar
Grenander, U. (1981) Abstract Inference. Wiley Series in Probability and Mathematical Statistics. Wiley.Google Scholar
Härdle, W. ’ Stoker, T. (1989) Investigating smooth multiple regression by the method of average derivatives. Journal of the American Statistical Association 84, 986–995.Google Scholar
Hausman, J., Newey, W., Ichimura, H., ’ Powell, J. (1991) Measurement errors in polynomial regression models. Journal of Econometrics 50, 273–295.CrossRefGoogle Scholar
Hausman, J., Newey, W., ’ Powell, J. (1995) Nonlinear errors in variables. Estimation of some Engel curves. Journal of Econometrics 65, 205–233.CrossRefGoogle Scholar
Heckman, J. (1990) Varieties of selection bias. American Economic Review 80, 313–318.Google Scholar
Imbens, G.W. ’ Newey, W.K. (2003) Identification and Estimation of Triangular Simultaneous Equations Models without Additivity. Working paper, Department of Economics, MIT.CrossRefGoogle Scholar
Lewbel, A. (1998) Semiparametric latent variable model estimation with endogenous or mismeasured regressors. Econometrica 66, 105–121.CrossRefGoogle Scholar
Li, T. ’ Vuong, Q. (1998) Nonparametric estimation of the measurement error model using multiple indicators. Journal of Multivariate Analysis 65, 139–165.CrossRefGoogle Scholar
Lighthill, M.J. (1962) Introduction to Fourier Analysis and Generalized Function. Cambridge University Press.Google Scholar
Liu, M. ’ Taylor, R. (1989) A consistent nonparametric density estimator for the deconvolution problem. Canadian Journal of Statistics 17, 427–438.CrossRefGoogle Scholar
Matzkin, R.L. (2003) Nonparametric estimation of nonparametric nonadditive random functions. Econometrica 71, 1339–1375.CrossRefGoogle Scholar
Newey, W. (2001) Flexible simulated moment estimation of nonlinear errors-in-variables models. Review of Economics and Statistics 83, 616–627.CrossRefGoogle Scholar
Newey, W. ’ McFadden, D. (1994) Large sample estimation and hypothesis testing. In Engel, R.F. ’ McFadden, D.L. (eds.), Handbook of Econometrics, vol. IV, pp. 2112–2245. Elsevier Science.Google Scholar
Newey, W.K. ’ Powell, J.L. (2003) Instrumental variable estimation of nonparametric models. Econometrica 71, 1565–1578.CrossRefGoogle Scholar
Schennach, S.M. (2004a) Estimation of nonlinear models with measurement error. Econometrica 72, 33–75.CrossRefGoogle Scholar
Schennach, S.M. (2004b) Nonparametric estimation in the presence of measurement error. Econometric Theory 20, 1046–1093.CrossRefGoogle Scholar
Schennach, S.M. (2007) Instrumental variable estimation of nonlinear errors-in-variables models. Econometrica 75, 201–239.CrossRefGoogle Scholar
Schwartz, L. (1966) Théorie des distributions. Hermann.Google Scholar
Wang, L. ’ Hsiao, C. (1995) Simulation-Based Semiparametric Estimation of Nonlinear Errors-in-Variables Models. Working paper, University of Southern California.Google Scholar
White, H. ’ Chalak, K. (2006) A Unified Framework for Defining and Identifying Causal Effects. Working paper, University of California, San Diego.Google Scholar