MCMC Con dence Sets for Identi ed Sets

107 Pages Posted: 8 Jul 2016

See all articles by Xiaohong Chen

Xiaohong Chen

Yale University - Cowles Foundation

Timothy Christensen

New York University (NYU) - Department of Economics

Keith O'Hara

New York University (NYU)

Elie T. Tamer

Harvard University

Date Written: July 6, 2016


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.

Suggested Citation

Chen, Xiaohong and Christensen, Timothy and O'Hara, Keith and Tamer, Elie T., MCMC Con dence Sets for Identi ed Sets (July 6, 2016). Cowles Foundation Discussion Paper No. 2037R. Available at SSRN: or

Xiaohong Chen (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Timothy Christensen

New York University (NYU) - Department of Economics ( email )

269 Mercer Street, 7th Floor
New York, NY 10011
United States

Keith O'Hara

New York University (NYU) ( email )

Bobst Library, E-resource Acquisitions
20 Cooper Square 3rd Floor
New York, NY 10003-711
United States

Elie T. Tamer

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

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