Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals
AbstractThis paper studies nonparametric estimation of conditional moment models in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space. Some of the PSMD procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty; some use large dimensional sieves with lower semicompact and/or convex penalties. We establish their consistency and the convergence rates in Banach space norms (such as a sup-norm or a root mean squared norm), allowing for possibly non-compact infinite dimensional parameter spaces. For both mildly and severely ill-posed nonlinear inverse problems, our convergence rates in Hilbert space norms (such as a root mean squared norm) achieve the known minimax optimal rate for the nonparametric mean IV regression. We illustrate the theory with a nonparametric additive quantile IV regression. We present a simulation study and an empirical application of estimating nonparametric quantile IV Engel curves.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1650R.
Length: 50 pages
Date of creation: Apr 2008
Date of revision: Jul 2009
Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Arellano, Cristina, 2008.
"Default risk and income fluctuations in emerging economies,"
7867, University Library of Munich, Germany.
- Cristina Arellano, 2008. "Default Risk and Income Fluctuations in Emerging Economies," American Economic Review, American Economic Association, vol. 98(3), pages 690-712, June.
- Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2009.
"Identification and Estimation by Penalization in Nonparametric Instrumental Regression,"
TSE Working Papers
09-076, Toulouse School of Economics (TSE).
- Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2011. "Identification And Estimation By Penalization In Nonparametric Instrumental Regression," Econometric Theory, Cambridge University Press, vol. 27(03), pages 472-496, June.
- FLORENS, Jean-Pierre & JOHANNES, Jan & VAN BELLEGEM, Sébastien, 2007. "Identification and estimation by penalization in nonparametric instrumental regression," CORE Discussion Papers 2007085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Bissantz, Nicolai & Hohage, T. & Munk, Axel & Ruymgaart, F., 2007. "Convergence rates of general regularization methods for statistical inverse problems and applications," Technical Reports 2007,04, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
- Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
- Joel Horowitz & Sokbae 'Simon' Lee, 2006.
"Nonparametric instrumental variables estimation of a quantile regression model,"
CeMMAP working papers
CWP09/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, vol. 75(4), pages 1191-1208, 07.
- Thomas A. Severini & Gautam Tripathi, 2005.
"Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors,"
2005-12, University of Connecticut, Department of Economics.
- Severini, Thomas A. & Tripathi, Gautam, 2006. "Some Identification Issues In Nonparametric Linear Models With Endogenous Regressors," Econometric Theory, Cambridge University Press, vol. 22(02), pages 258-278, April.
- Xiaohong Chen & Markus Reiss, 2007.
"On Rate Optimality for Ill-posed Inverse Problems in Econometrics,"
Cowles Foundation Discussion Papers
1626, Cowles Foundation for Research in Economics, Yale University.
- Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(03), pages 497-521, June.
- Xiaohong Chen & Markus Reiss, 2007. "On rate optimality for ill-posed inverse problems in econometrics," CeMMAP working papers CWP20/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
- Matzkin, Rosa L., 2007. "Nonparametric identification," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 73 Elsevier.
- Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
- Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July.
- Horowitz, Joel L. & Lee, Sokbae, 2012.
"Uniform confidence bands for functions estimated nonparametrically with instrumental variables,"
Journal of Econometrics,
Elsevier, vol. 168(2), pages 175-188.
- Joel Horowitz & Sokbae 'Simon' Lee, 2009. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," CeMMAP working papers CWP18/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Joel Horowitz & Sokbae 'Simon' Lee, 2010. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," CeMMAP working papers CWP19/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Panle Jia Barwick & Parag A. Pathak, 2011. "The Costs of Free Entry: An Empirical Study of Real Estate Agents in Greater Boston," NBER Working Papers 17227, National Bureau of Economic Research, Inc.
- Khan, Shakeeb, 2013. "Distribution free estimation of heteroskedastic binary response models using Probit/Logit criterion functions," Journal of Econometrics, Elsevier, vol. 172(1), pages 168-182.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.