Monte Carlo Confidence sets for Identified Sets

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

No 2037R2, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Pages: 104 pages
Date: 2016-05, Revised 2017-09
New Economics Papers: this item is included in nep-cmp and nep-ecm
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Citations: View citations in EconPapers (1)

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Related works:
Working Paper: Monte Carlo Confidence Sets for Identified Sets (2017)
Working Paper: Monte Carlo confidence sets for identified sets (2017)
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