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Identification in Nonseparable Models

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Andrew Chesher

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Abstract

Weak nonparametric restrictions are developed, sufficient to identify the values of derivatives of structural functions in which latent random variables are nonseparable. These derivatives can exhibit stochastic variation. In a microeconometric context this allows the impact of a policy intervention, as measured by the value of a structural derivative, to vary across people who are identical as measured by covariates. When the restrictions are satisfied quantiles of the distribution of a policy impact across people can be identified. The identification restrictions are local in the sense that they are specific to the values of the covariates and the specific quantiles of latent variables at which identification is sought. The conditions do not include the commonly required independence of latent variables and covariates. They include local versions of the classical rank and order conditions and local quantile insensitivity conditions. Values of structural derivatives are identified by functionals of quantile regression functions and can be estimated using the same functionals applied to estimated quantile regression functions. Copyright The Econometric Society 2003.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 71 (2003)
Issue (Month): 5 (09)
Pages: 1405-1441
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Handle: RePEc:ecm:emetrp:v:71:y:2003:i:5:p:1405-1441

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  1. Lingjie Ma & Roger Koenker, 2004. "Quantile regression methods for recursive structural equation models," CeMMAP working papers CWP01/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  2. Martin Nordin, 2008. "Ability and rates of return to schooling—making use of the Swedish enlistment battery test," Journal of Population Economics, Springer, vol. 21(3), pages 703-717, July. [Downloadable!] (restricted)
  3. Woocheol Kim, 2004. "Identification And Estimation Of Nonparametric Structural," Econometric Society 2004 Far Eastern Meetings 733, Econometric Society. [Downloadable!]
  4. Andrew Chesher, 2007. "Endogeneity and discrete outcomes," CeMMAP working papers CWP05/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  5. Massimo Franchi, 2004. "A Priori Inequality Restrictions and Bound Analysis in VAR Models," Discussion Papers 04-14, University of Copenhagen. Department of Economics. [Downloadable!]
  6. Arthur Lewbel, 2006. "Modeling Heterogeneity," Boston College Working Papers in Economics 650, Boston College Department of Economics. [Downloadable!]
  7. Andrew Chesher, 2003. "Nonparametric identification under discrete variation," CeMMAP working papers CWP19/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  8. Andrew Chesher, 2003. "Nonparametric identification with discrete endogenous variables," CeMMAP working papers CWP06/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  9. Pedro Carneiro & Sokbae 'Simon' Lee, 2005. "Ability, sorting and wage inequality," CeMMAP working papers CWP16/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  10. Sokbae 'Simon' Lee, 2004. "Endogeneity in quantile regression models: a control function approach," CeMMAP working papers CWP08/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  11. Guido W. Imbens & Whitney K. Newey, 2002. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," NBER Technical Working Papers 0285, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  12. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation, Yale University. [Downloadable!]
  13. Vincenzo Atella & Noemi Pace & Daniela Vuri, 2008. "Are employers discriminating with respect to weight? European Evidence using Quantile Regression," CEIS Research Paper 123, Tor Vergata University, CEIS, revised 14 Jul 2008. [Downloadable!]
  14. Susanne Schennach & Halbert White & Karim Chalak, 2007. "Estimating average marginal effects in nonseparable structural systems," Boston College Working Papers in Economics 680, Boston College Department of Economics. [Downloadable!]
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  15. Giorgio Brunello & Margherita Fort & Guglielmo Weber, 2007. ""For One More Year with You": Changes in Compulsory Schooling, Education and the Distribution of Wages in Europe," IZA Discussion Papers 3102, Institute for the Study of Labor (IZA). [Downloadable!]
  16. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments," Cowles Foundation Discussion Papers 1650, Cowles Foundation, Yale University. [Downloadable!]
  17. 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. [Downloadable!]
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  18. Joel Horowitz & Sokbae 'Simon' Lee, 2007. "Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative," CeMMAP working papers CWP02/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  19. Markus Frölich, 2006. "A Note on Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables," University of St. Gallen Department of Economics working paper series 2006 2006-11, Department of Economics, University of St. Gallen. [Downloadable!]
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  20. C. Lanier Benkard & Steven Berry, . "On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: comment on B. Brown (1983) and Roehrig (1988)," Cowles Foundation Discussion Papers 1482, Cowles Foundation, Yale University. [Downloadable!]
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