Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5096209 | Journal of Econometrics | 2012 | 18 Pages |
Abstract
We propose a quasi-Bayesian nonparametric approach to estimating the structural relationship Ï among endogenous variables when instruments are available. We show that the posterior distribution of Ï 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 Ï. 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
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Jean-Pierre Florens, Anna Simoni,