Nonparametric Estimation of An Instrumental Regression: A Quasi-Bayesian Approach Based on Regularized Posterior
AbstractWe 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.
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Bibliographic InfoPaper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 622.
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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Find related papers by JEL classification:
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-08-21 (All new papers)
- NEP-ECM-2010-08-21 (Econometrics)
- NEP-ORE-2010-08-21 (Operations Research)
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- Horowitz, Joel L., 2014. "Adaptive nonparametric instrumental variables estimation: Empirical choice of the regularization parameter," Journal of Econometrics, Elsevier, vol. 180(2), pages 158-173.
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