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On the identification of structural linear functionals

  • Juan Carlos Escanciano
  • Wei Li

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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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. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, 03.
  2. FLORENS, Jean-Pierre & JOHANNES, Jan & VAN BELLEGEM, Sébastien, 2007. "Identification and estimation by penalization in nonparametric instrumental regression," CORE Discussion Papers 2007085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Thomas A. Severini & Gautam Tripathi, 2007. "Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors," CeMMAP working papers CWP13/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. 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.
  5. David Card, 1995. "The Wage Curve: A Review," Journal of Economic Literature, American Economic Association, vol. 33(2), pages 285-299, June.
  6. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
  7. Andres Santos, 2012. "Inference in Nonparametric Instrumental Variables With Partial Identification," Econometrica, Econometric Society, vol. 80(1), pages 213-275, 01.
  8. 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.
  9. Thomas A. Severini & Gautam Tripathi, 2005. "Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors," Working papers 2005-12, University of Connecticut, Department of Economics.
  10. Joshua D. Angrist & Alan B. Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," NBER Working Papers 3572, National Bureau of Economic Research, Inc.
  11. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(03), pages 497-521, June.
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