Liao, Yuan and Simoni, Anna (2012): Semiparametric Bayesian Partially Identified Models based on Support Function.

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Abstract
Bayesian partially identified models have received a growing attention in recent years in the econometric literature, due to their broad applications in empirical studies. Classical Bayesian approach in this literature has been assuming a parametric model, by specifying an adhoc parametric likelihood function. However, econometric models usually only identify a set of moment inequalities, and therefore assuming a known likelihood function suffers from the risk of misspecification, and may result in inconsistent estimations of the identified set. On the other hand, momentcondition based likelihoods such as the limited information and exponential tilted empirical likelihood, though guarantee the consistency, lack of probabilistic interpretations. We propose a semiparametric Bayesian partially identified model, by placing a nonparametric prior on the unknown likelihood function. Our approach thus only requires a set of moment conditions but still possesses a pure Bayesian interpretation. We study the posterior of the support function, which is essential when the object of interest is the identified set. The support function also enables us to construct twosided Bayesian credible sets (BCS) for the identified set. It is found that, while the BCS of the partially identified parameter is too narrow from the frequentist point of view, that of the identified set has asymptotically correct coverage probability in the frequentist sense. Moreover, we establish the posterior consistency for both the structural parameter and its identified set. We also develop the posterior concentration theory for the support function, and prove the semiparametric Bernstein von Mises theorem. Finally, the proposed method is applied to analyze a financial asset pricing problem.
Item Type:  MPRA Paper 

Original Title:  Semiparametric Bayesian Partially Identified Models based on Support Function 
Language:  English 
Keywords:  partial identification; posterior consistency; concentration rate; support function; twosided Bayesian credible sets; identified set; coverage probability; moment inequality models 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General 
Item ID:  43262 
Depositing User:  Yuan Liao 
Date Deposited:  14 Dec 2012 05:30 
Last Modified:  26 Sep 2019 13:50 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/43262 