MCMC Confidence sets for Identified Sets

Xiaohong Chen (), Timothy Christensen (), Keith O’Hara and Elie Tamer ()
Additional contact information
Timothy Christensen: New York University
Keith O’Hara: New York University
Elie Tamer: Harvard University

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

Abstract: In complicated/nonlinear parametric models, it is generally hard to determine whether the model parameters are (globally) 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 via Monte Carlo simulations directly from 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 Monte Carlo 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 Monte Carlo 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. Finally, our proposed procedures are applied in two empirical examples.

Pages: 106 pages
Date: 2016-05, Revised 2016-07
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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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