Nonparametric Estimation of An Instrumental Regression: A Quasi-Bayesian Approach Based on Regularized Posterior
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.
|Date of creation:||Mar 2010|
|Date of revision:|
|Publication status:||Published in Journal of Econometrics, vol.�170, n°2, octobre 2012, p.�458-475.|
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- Xiaohong Chen & Markus Reiss, 2007.
"On rate optimality for ill-posed inverse problems in econometrics,"
CeMMAP working papers
CWP20/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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- Chen, Xiaohong & White, Halbert, 1998. "Central Limit And Functional Central Limit Theorems For Hilbert-Valued Dependent Heterogeneous Arrays With Applications," Econometric Theory, Cambridge University Press, vol. 14(02), pages 260-284, April.
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