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

Florens, Jean-Pierre and Simoni, Anna (2010) Nonparametric Estimation of An Instrumental Regression: A Quasi-Bayesian Approach Based on Regularized Posterior. TSE Working Paper, n. 10-176

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Official URL: http://tse-fr.eu/pub/22895

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: Monograph (Working Paper)
Language: English
Date: March 2010
JEL codes: C11 - Bayesian Analysis
C14 - Semiparametric and Nonparametric Methods
C30 - General
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 18 Jan 2012 06:02
Last Modified: 07 Mar 2018 13:22
OAI ID: oai:tse-fr.eu:22895
URI: http://publications.ut-capitole.fr/id/eprint/3396

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