Nonparametric instrumental regression with errors in variables
This paper considers nonparametric instrumental variable regression when the endogenous variable is contaminated with classical measurement error. Existing methods are inconsistent in the presence of measurement error. We propose a wavelet deconvolution estimator for the structural function that modifies the generalized Fourier coefficients of the orthogonal series estimator to take into account the measurement error. We establish the convergence rates of our estimator for the cases of mildly/severely ill-posed models and ordinary/super smooth measurement errors. We characterize how the presence of measurement error slows down the convergence rates of the estimator. We also study the case where the measurement error density is unknown and needs to be estimated, and show that the estimation error of the measurement error density is negligible under mild conditions as far as the measurement error density is symmetric.
|Date of creation:||Jul 2015|
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References listed on IDEAS
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- Patrick Gagliardini & Olivier Scaillet, 2012. "Nonparametric Instrumental Variable Estimation of Structural Quantile Effects," Econometrica, Econometric Society, vol. 80(4), pages 1533-1562, July.
- Horowitz, Joel L., 2012. "Specification testing in nonparametric instrumental variable estimation," Journal of Econometrics, Elsevier, vol. 167(2), pages 383-396.
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"Nonparametric Instrumental Regression,"
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- Serge Darolles & Jean-Pierre Florens & Eric Renault, 2000. "Nonparametric Instrumental Regression," Working Papers 2000-17, Center for Research in Economics and Statistics.
- Darolles, Serge & Fan, Yanqin & Florens, Jean-Pierre & Renault, Eric, 2003. "Non Parametric Instrumental Regression," IDEI Working Papers 228, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2010.
- DAROLLES, Serge & FLORENS, Jean-Pierre & RENAULT, Éric, 2002. "Nonparametric Instrumental Regression," Cahiers de recherche 2002-05, Universite de Montreal, Departement de sciences economiques.
- Serge Darolles & Jean-Pierre Florens & Yanqin Fan & Eric Renault, 2011. "Nonparametric Instrumental Regression," Post-Print halshs-00677716, HAL.
- Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
- Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
- Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
- Delaigle, Aurore & Hall, Peter, 2008. "Using SIMEX for Smoothing-Parameter Choice in Errors-in-Variables Problems," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 280-287, March.
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