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

    1. Yevgeniy Kovchegov & Nese Yildiz, 2014. "Orthogonal Polynomials for Seminonparametric Instrumental Variables Model," Papers 1409.1620, arXiv.org.
    2. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey, 2016. "Locally robust semiparametric estimation," CeMMAP working papers CWP31/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. 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.
    4. Timothy M. Christensen, 2014. "Nonparametric identification of positive eigenfunctions," CeMMAP working papers CWP37/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. repec:eee:econom:v:199:y:2017:i:2:p:213-220 is not listed on IDEAS
    6. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
    7. Carolina Caetano & Juan Carlos Escaniano, 2015. "Identifying Multiple Marginal Effects with a Single Binary Instrument or by Regression Discontinuity," Caepr Working Papers 2015-009 Classification-C, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    8. Severini, Thomas A. & Tripathi, Gautam, 2012. "Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 491-498.
    9. Pierre-André 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. Xavier d'Haultfoeuille & Philippe Février, 2011. "Identification of Nonseparable Modes with Endogeneity and Discrete Instruments," Working Papers 2011-28, Center for Research in Economics and Statistics.
    12. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    13. Shaw Philip & Cohen Michael Andrew & Chen Tao, 2016. "Nonparametric Instrumental Variable Estimation in Practice," Journal of Econometric Methods, De Gruyter, vol. 5(1), pages 153-177, January.
    14. Laurent Davezies & Xavier d'Haultfoeuille, 2013. "Endogenous Attrition in Panels," Working Papers 2013-17, Center for Research in Economics and Statistics.
    15. 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.
    16. 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.
    17. 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.
    18. repec:eee:econom:v:201:y:2017:i:1:p:95-107 is not listed on IDEAS
    19. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    20. Chen, Xiaohong & Pouzo, Demian, 2008. "Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments," Working Papers 47, Yale University, Department of Economics.
    21. 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.
    22. 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.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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