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

Jean-Pierre Florens and Anna Simoni

No 622, IDEI Working Papers from Institut d'Économie Industrielle (IDEI), Toulouse

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.

JEL-codes: C11 C14 C30 (search for similar items in EconPapers)
Date: 2010-03
New Economics Papers: this item is included in nep-ecm and nep-ore
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Related works:
Journal Article: Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior (2012) Downloads
Working Paper: Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior (2012)
Working Paper: Nonparametric Estimation of An Instrumental Regression: A Quasi-Bayesian Approach Based on Regularized Posterior (2010) Downloads
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