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On the identification of structural linear functionals

  • Juan Carlos Escanciano

    (Institute for Fiscal Studies)

  • Wei Li

    (Institute for Fiscal Studies)

This paper asks which aspects of a structural Nonparametric Instrumental Variables Regression (NPIVR) can be identified well and which ones cannot. It contributes to answering this question by characterising the identified set of linear continuous functionals of the NPIVR under norm constraints. Each element of the identified set of NPIVR can be written as the sum of a common 'identifiable component' and an idiosyncratic 'unidentifiable component'. The identified set for any continuous linear functional is shown to be a closed interval, whose midpoint is the functional applied to the 'identifiable component'. The formula for the length of the identified set extends the popular omitted variables formula of classical linear regression. Some examples illustrate the wide applicability and utility of our identification result, including bounds and a new identification condition for point-evaluation functionals. The main ideas are illustrated with an empirical application of the effect of children on labour market outcomes.

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File URL: http://www.cemmap.ac.uk/wps/cwp481313.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP48/13.

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Date of creation: Oct 2013
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Handle: RePEc:ifs:cemmap:48/13
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  1. 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.
  2. 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.
  3. 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.
  4. Andres Santos, 2012. "Inference in Nonparametric Instrumental Variables With Partial Identification," Econometrica, Econometric Society, vol. 80(1), pages 213-275, 01.
  5. David Card, 1995. "The Wage Curve: A Review," Working Papers 722, Princeton University, Department of Economics, Industrial Relations Section..
  6. Joshua D. Angrist & William N. Evans, 1996. "Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size," NBER Working Papers 5778, National Bureau of Economic Research, Inc.
  7. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, 03.
  8. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
  9. 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.
  10. Joshua Angrist & Alan Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," Working Papers 653, Princeton University, Department of Economics, Industrial Relations Section..
  11. Bronars, Stephen G & Grogger, Jeff, 1994. "The Economic Consequences of Unwed Motherhood: Using Twin Births as a Natural Experiment," American Economic Review, American Economic Association, vol. 84(5), pages 1141-56, December.
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