Monte Carlo confidence sets for identified sets

Xiaohong Chen (), Timothy M. Christensen and Elie Tamer ()
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Timothy M. Christensen: Institute for Fiscal Studies
Elie Tamer: Institute for Fiscal Studies and Harvard University

No CWP43/17, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: In complicated/nonlinear parametric models, it is generally hard to know whether the model parameters are point identi?ed. We provide computationally attractive procedures to construct con?dence sets (CSs) for identi?ed sets of full parameters and of subvectors in models de?ned 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 cuto?s 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 pro?le QLR in partially-identi?ed regular models and some non-regular models. These results imply that our MC CSs have exact asymptotic frequentist coverage for identi?ed sets of full parameters and of subvectors in partially-identi?ed regular models, and have valid but potentially conservative coverage in models with reduced-form parameters on the boundary. Our MC CSs for identi?ed 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 identi?ed models. We demonstrate good ?nite-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 ?ows.

Date: 2017-10-03
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Related works:
Journal Article: Monte Carlo Confidence Sets for Identified Sets (2018)
Working Paper: Monte Carlo Confidence Sets for Identified Sets (2017)
Working Paper: Monte Carlo Confidence sets for Identified Sets (2017)
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