MCMC Confidence sets for Identified Sets

Xiaohong Chen (xiaohong.chen@yale.edu), Timothy Christensen (timothy.christensen@nyu.edu) and Elie Tamer (elietamer@fas.harvard.edu)
Additional contact information
Timothy Christensen: New York University
Elie Tamer: Harvard University

No 2037, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: In complicated/nonlinear parametric models, it is hard to determine whether a parameter of interest is formally point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of parameters in econometric models defined through a likelihood or a vector of moments. The CSs for the identified set or for a function of the identified set (such as a subvector) are based on inverting an optimal sample criterion (such as likelihood or continuously updated GMM), where the cutoff values are computed directly from Markov Chain Monte Carlo (MCMC) simulations of a quasi posterior distribution of the criterion. We establish new Bernstein-von Mises type theorems for the posterior distributions of the quasi-likelihood ratio (QLR) and profile QLR statistics in partially identified models, allowing for singularities. These results imply that the MCMC criterion-based CSs have correct frequentist coverage for the identified set as the sample size increases, and that they coincide with Bayesian credible sets based on inverting a LR statistic for point-identified likelihood models. We also show that our MCMC optimal criterion-based CSs are uniformly valid over a class of data generating processes that include both partially- and point- identified models. We demonstrate good finite sample coverage properties of our proposed methods in four non-trivial simulation experiments: missing data, entry game with correlated payoff shocks, Euler equation and finite mixture models.

Pages: 68 pages
Date: 2016-05
New Economics Papers: this item is included in nep-ecm and nep-pke
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Citations: View citations in EconPapers (8)

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Related works:
Working Paper: MCMC Confidence sets for Identified Sets (2016)
Working Paper: MCMC confidence sets for identified sets (2016)
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