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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Identification Number : 10.1016/j.jeconom.2012.05.016


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 Classification: C11 - Bayesian Analysis
C14 - Semiparametric and Nonparametric Methods
C30 - General
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 09 Jul 2014 17:26
Last Modified: 02 Apr 2021 15:47
OAI Identifier: oai:tse-fr.eu:25917
URI: https://publications.ut-capitole.fr/id/eprint/15324
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