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Nonparametric Estimation of An Instrumental Regression: A Quasi-Bayesian Approach Based on Regularized Posterior

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  • Florens, Jean-Pierre
  • Simoni, Anna
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    Abstract

    We propose a Quasi-Bayesian nonparametric approach to estimating the structural relationship ' among endogenous variables when instruments are available. We show that the posterior distribution of ' is inconsistent in the frequentist sense. We interpret this fact as the ill-posedness of the Bayesian inverse problem defined by the relation that characterizes the structural function '. To solve this problem, we construct a regularized posterior distribution, based on a Tikhonov regularization of the inverse of the marginal variance of the sample, which is justified by a penalized projection argument. This regularized posterior distribution is consistent in the frequentist sense and its mean can be interpreted as the mean of the exact posterior distribution resulting from a gaussian prior distribution with a shrinking covariance operator.

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    Bibliographic Info

    Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 622.

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    Date of creation: Mar 2010
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    Publication status: Published in Journal of Econometrics, vol.�170, n°2, octobre 2012, p.�458-475.
    Handle: RePEc:ide:wpaper:22800

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    Cited by:
    1. Horowitz, Joel L., 2014. "Adaptive nonparametric instrumental variables estimation: Empirical choice of the regularization parameter," Journal of Econometrics, Elsevier, vol. 180(2), pages 158-173.

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