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Article overview
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MCMC Confidence Sets for Identified Sets | | Xiaohong Chen
; Timothy Christensen
; Elie Tamer
; | | Date: |
2 May 2016 | | 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. | | Source: | arXiv, 1605.0499 | | Services: | Forum | Review | PDF | Favorites | |
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