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

Florens, Jean-Pierre and Simoni, Anna (2012) Nonparametric Estimation of An Instrumental Regression: A Quasi-Bayesian Approach Based on Regularized Posterior. Journal of Econometrics, 170 (2). pp. 458-475.

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Official URL: http://tse-fr.eu/pub/25917

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.

Item Type: Article
Language: English
Date: October 2012
Refereed: Yes
JEL codes: C11 - Bayesian Analysis
C14 - Semiparametric and Nonparametric Methods
C30 - General
Subjects: B- ECONOMIE ET FINANCE
Divisions: Toulouse School of Economics - TSE
Site: UT1
Date Deposited: 09 Jul 2014 17:26
Last Modified: 18 Oct 2017 15:13
OAI ID: oai:tse-fr.eu:25917
URI: http://publications.ut-capitole.fr/id/eprint/15324

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