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Monte Carlo Confidence Sets for Identified Sets

Xiaohong Chen, Timothy Christensen, Elie Tamer

arXiv 2 May 2016 · Statistics — Methodology · publishedEconometrica (2018) · 81 citations (OpenAlex)

arXiv:1605.00499 · PDF · DOI · OpenAlex · Extracted main text

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.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Chernozhukov, V. and H. Hong (2003) An MCMC approach to classical estimation1.00054100%
2Moon, H. R. and F. Schorfheide (2012) Bayesian and frequentist inference in partially identified models1.00053100%
3Andrews, D. and G. Soares (2010) Inference for parameters defined by moment inequalities using generalized moment selection0.81142100%
4Romano, J. P. and A. M. Shaikh (2010) Inference for the identified set in partially identified econometric models0.73732100%
5Helpman, E., M. Melitz, and Y. Rubinstein (2008) Estimating trade flows: Trading partners and trading volumes0.69361100%
6Robert, C. P. and G. Casella (2004) Monte Carlo Statistical Methods0.64422100%
7Kline, B. and E. Tamer (2016) Bayesian inference in a class of partially identified models0.64422100%
8Rosen, A. M (2008) Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities0.64422100%
9van der Vaart, A. W (2000) Asymptotic statistics0.5853333%
10Herbst, E. and F. Schorfheide (2014) Sequential monte carlo sampling for DSGE models0.5113233%

Showing the top 10 of 53 scored citations.

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