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Some Identification Issues In Nonparametric Linear Models With Endogenous Regressors

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  • Severini, Thomas A.
  • Tripathi, Gautam

Abstract

In applied work economists often seek to relate a given response variable y to some causal parameter * 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 * as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when * is modeled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate *. In contrast, handling endogenous regressors in nonparametric models, where * 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 * belongs to a linear space. We also investigate underidentification of * along with the identification of its linear functionals. Several examples are provided to develop intuition about identification and estimation for endogenous nonparametric regression and related models.We thank Jeff Wooldridge and two anonymous referees for comments that greatly improved this paper.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 02 (April)
Pages: 258-278

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Handle: RePEc:cup:etheor:v:22:y:2006:i:02:p:258-278_06

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  1. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
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  3. 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.
  4. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, 09.
  5. Peter Hall & Joel L. 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.
  6. 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.
  7. 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.
  8. Jeffrey M. Wooldridge, 2001. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262232197, January.
  9. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
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Cited by:
  1. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Cowles Foundation Discussion Papers 1650RR, Cowles Foundation for Research in Economics, Yale University, revised Jan 2011.
  2. Komunjer, Ivana, 2007. "Global Identification In Nonlinear Semiparametric Models," University of California at San Diego, Economics Working Paper Series qt8dk0n386, Department of Economics, UC San Diego.
  3. Chen, Xiaohong & Pouzo, Demian, 2008. "Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments," Working Papers 47, Yale University, Department of Economics.
  4. Cohen, Michael & Shaw, Philip & Chen, Tao, 2008. "Nonparametric Instrumental Variable Estimation in Practice," Research Reports 149936, University of Connecticut, Food Marketing Policy Center.
  5. Steven T. Berry & Philip Haile, 2010. "Identification in Differentiated Products Markets Using Market Level Data," Cowles Foundation Discussion Papers 1744, Cowles Foundation for Research in Economics, Yale University, revised Mar 2010.
  6. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
  7. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
  8. Thomas A. Severini & Gautam Tripathi, 2007. "Efficiency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors," Working papers 2007-18, University of Connecticut, Department of Economics.
  9. Pierre-Andre Chiappori & Ivana Komunjer, 2008. "Correct Specification and Identification of Nonparametric Transformation Models," Working Papers 2009-003, Becker Friedman Institute for Research In Economics.
  10. Juan Carlos Escanciano & Wei Li, 2013. "On the identification of structural linear functionals," CeMMAP working papers CWP48/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Cowles Foundation Discussion Papers 1650R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2009.
  12. Xavier d'Haultfoeuille & Philippe Février, 2011. "Identification of Nonseparable Modes with Endogeneity and Discrete Instruments," Working Papers 2011-28, Centre de Recherche en Economie et Statistique.
  13. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments," Cowles Foundation Discussion Papers 1650, Cowles Foundation for Research in Economics, Yale University, revised Oct 2008.
  14. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of nonparametric conditional moment models with possibly nonsmooth moments," CeMMAP working papers CWP12/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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