Article dans une série de papiers de travail :

Jean-Pierre Florens et Anna Simoni, « Nonparametric Estimation of An Instrumental Regression: A Quasi-Bayesian Approach Based on Regularized Posterior », TSE Working Paper, n°10-176, mars 2010.
[ Texte complet ]


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.

Thème de recherche TSE

Méthodologie: économétrie, statistique et théorie économique

Codes JEL

C11 : Bayesian Analysis
C14 : Semiparametric and Nonparametric Methods
C30 : General