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Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior

Jean-Pierre Florens and Anna Simoni

Journal of Econometrics, 2012, vol. 170, issue 2, 458-475

Abstract: We propose a quasi-Bayesian nonparametric approach to estimating the structural relationship φ among endogenous variables when instruments are available. We show that the posterior distribution of φ 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 φ. 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.

Keywords: Instrumental regression; Nonparametric estimation; Posterior distribution; Tikhonov regularization; Posterior consistency (search for similar items in EconPapers)
JEL-codes: C11 C14 C30 (search for similar items in EconPapers)
Date: 2012
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Related works:
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
Working Paper: Nonparametric Estimation of An Instrumental Regression: A Quasi-Bayesian Approach Based on Regularized Posterior (2010) Downloads
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:170:y:2012:i:2:p:458-475

DOI: 10.1016/j.jeconom.2012.05.016

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