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Nonparametric Identification Using Instrumental Variables: Sufficient Conditions For Completeness

  • Yingyao Hu
  • Ji-Liang Shiu

This paper provides sufficient conditions for the nonparametric identification of the regression function m(.) in a regression model with an endogenous regressor x and an instrumental variable z. It has been shown that the identification of the regression function from the conditional expectation of the dependent variable on the instrument relies on the completeness of the distribution of the endogenous regressor conditional on the instrument, i.e., f(x|z). We provide sufficient conditions for the completeness of f(x|z) without imposing a specific functional form, such as the exponential family. We show that if the conditional density f(x|z) coincides with an existing complete density at a limit point in the support of z, then f(x|z) itself is complete, and therefore, the regression function m(.) is nonparametrically identified. We use this general result provide specific sufficient conditions for completeness in three different specifications of the relationship between the endogenous regressor x and the instrumental variable z.

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Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 581.

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Date of creation: Jun 2011
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Handle: RePEc:jhu:papers:581
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  1. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, 01.
  3. Xavier d'Haultfoeuille, 2006. "On the Completeness Condition in Nonparametric Instrumental Problems," Working Papers 2006-32, Centre de Recherche en Economie et Statistique.
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