Monte Carlo Confidence Sets for Identified Sets

104 Pages Posted: 29 Sep 2017

See all articles by Xiaohong Chen

Xiaohong Chen

Yale University - Cowles Foundation

Timothy Christensen

New York University (NYU) - Department of Economics

Elie T. Tamer

Harvard University

Date Written: September 25, 2017

Abstract

In complicated/nonlinear parametric models, it is generally hard to know whether the model parameters are point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of full parameters and of subvectors in models defined through a likelihood or a vector of moment equalities or inequalities. These CSs are based on level sets of optimal sample criterion functions (such as likelihood or optimally-weighted or continuously-updated GMM criterions). The level sets are constructed using cutoffs that are computed via Monte Carlo (MC) simulations directly from the quasi-posterior distributions of the criterions. We establish new Bernstein-von Mises (or Bayesian Wilks) type theorems for the quasi-posterior distributions of the quasi-likelihood ratio (QLR) and profile QLR in partially-identified regular models and some non-regular models. These results imply that our MC CSs have exact asymptotic frequentist coverage for identified sets of full parameters and of subvectors in partially-identified regular models, and have valid but potentially conservative coverage in models with reduced-form parameters on the boundary. Our MC CSs for identified sets of subvectors are shown to have exact asymptotic coverage in models with singularities. We also provide results on uniform validity of our CSs over classes of DGPs that include point and partially identified models. We demonstrate good finite-sample coverage properties of our procedures in two simulation experiments. Finally, our procedures are applied to two non-trivial empirical examples: an airline entry game and a model of trade flows.

Suggested Citation

Chen, Xiaohong and Christensen, Timothy and Tamer, Elie T., Monte Carlo Confidence Sets for Identified Sets (September 25, 2017). Cowles Foundation Discussion Paper No. 2037R2, Available at SSRN: https://ssrn.com/abstract=3043470 or http://dx.doi.org/10.2139/ssrn.3043470

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

Elie T. Tamer

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

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