Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors
In applied work economists often seek to relate a given response variable y to some causal parameter mu* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a conditional expectation is central to its identification and estimation. However, the interpretation of mu* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when mu* is modelled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate mu*. In contrast, handling endogenous regressors in nonparametric models, where mu* is regarded as fully unknown, presents difficult theoretical and practical challenges. In this paper we consider an endogenous nonparametric model based on a conditional moment restriction. We investigate identification related properties of this model when the unknown function mu* belongs to a linear space. We also investigate underidentification of mu* along with the identification of its linear functionals. Several examples are provided in order to develop intuition about identification and estimation for endogenous nonparametric regression and related models.
|Date of creation:||Apr 2005|
|Date of revision:|
|Note:||We thank Jeff Wooldridge and two anonymous referees for comments that greatly improved this paper.|
|Contact details of provider:|| Postal: |
Phone: (860) 486-4889
Fax: (860) 486-4463
Web page: http://www.econ.uconn.edu/
More information through EDIRC
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.:
- 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.
- Serge Darolles & Jean-Pierre Florens & Eric Renault, 2000. "Nonparametric Instrumental Regression," Working Papers 2000-17, Centre de Recherche en Economie et Statistique.
- DAROLLES, Serge & FLORENS, Jean-Pierre & RENAULT, Éric, 2002. "Nonparametric Instrumental Regression," Cahiers de recherche 2002-05, Universite de Montreal, Departement de sciences economiques.
- Jeffrey M Wooldridge, 2010.
"Econometric Analysis of Cross Section and Panel Data,"
MIT Press Books,
The MIT Press,
edition 2, volume 1, number 0262232588, June.
- Jeffrey M. Wooldridge, 2001. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262232197, June.
- Whitney K. Newey & James L. Powell & Francis Vella, 1999.
"Nonparametric Estimation of Triangular Simultaneous Equations Models,"
Econometric Society, vol. 67(3), pages 565-604, May.
- Whitney K. Newey & James L. Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-6, Massachusetts Institute of Technology (MIT), Department of Economics.
- Whitney Newey & James Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-16, Massachusetts Institute of Technology (MIT), Department of Economics.
- Jean-Pierre Florens & James Heckman & Costas Meghir & Edward Vytlacil, 2002.
"Instrumental variables, local instrumental variables and control functions,"
CeMMAP working papers
CWP15/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Florens, Jean-Pierre & Heckman, James & Meghir, Costas & Vytlacil, Edward, 2003. "Instrumental Variables, Local Instrumental Variables and Control Functions," IDEI Working Papers 249, Institut d'Économie Industrielle (IDEI), Toulouse.
- Oliver Linton & Enno Mammen & Jens Perch Nielsen & C Tanggaard, 2000.
"Yield Curve Estimation by Kernel Smoothing Methods,"
STICERD - Econometrics Paper Series
385, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Linton, Oliver & Mammen, Enno & Nielsen, Jans Perch & Tanggaard, Carsten, 2001. "Yield curve estimation by kernel smoothing methods," Journal of Econometrics, Elsevier, vol. 105(1), pages 185-223, November.
- Oliver Linton & Enno Mammen & Jens Perch Nielsen & C Tanggaard, 2000. "Yield curve estimation by kernel smoothing methods," LSE Research Online Documents on Economics 2270, London School of Economics and Political Science, LSE Library.
- Oliver B. Linton & Enno Mammen & J. Nielsen & Carsten Tanggaard, 2000. "Yield Curve Estimation by Kernel Smoothing Methods," Econometric Society World Congress 2000 Contributed Papers 0235, Econometric Society.
- Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
- Peter Hall & Joel Horowitz, 2003. "Nonparametric methods for inference in the presence of instrumental variables," CeMMAP working papers CWP02/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
- 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.
When requesting a correction, please mention this item's handle: RePEc:uct:uconnp:2005-12. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mark McConnel)
If references are entirely missing, you can add them using this form.