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MCMC confidence sets for identified sets

Author

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  • Xiaohong Chen

    (Institute for Fiscal Studies and Yale University)

  • Timothy M. Christensen

    (Institute for Fiscal Studies)

  • Keith O'Hara

    (Institute for Fiscal Studies)

  • Elie Tamer

    (Institute for Fiscal Studies and Harvard University)

Abstract

In complicated/nonlinear parametric models, it is generally hard to determine whether the model parameters are (globally) point identifi ed. We provide computationally attractive procedures to construct con fidence sets (CSs) for identifi ed sets of parameters in econometric models defi ned through a likelihood or a vector of moments. The CSs for the identi fied set or for a function of the identi fied 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 pro file QLR statistics in partially identifi ed models, allowing for singularities. These results imply that the Monte Carlo criterion-based CSs have correct frequentist coverage for the identi fied set as the sample size increases, and that they coincide with Bayesian credible sets based on inverting a LR statistic for point-identi fied 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 pointidentifi ed 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

  • Xiaohong Chen & Timothy M. Christensen & Keith O'Hara & Elie Tamer, 2016. "MCMC confidence sets for identified sets," CeMMAP working papers CWP28/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:28/16
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    3. Chen, Xiaohong & Gao, Fuchang, 2017. "A reverse Gaussian correlation inequality by adding cones," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 84-87.
    4. Francis J. DiTraglia & Camilo Garcia-Jimeno, 2020. "A Framework for Eliciting, Incorporating, and Disciplining Identification Beliefs in Linear Models," Papers 2011.07276, arXiv.org.
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    6. Jiang, Wenxin, 2017. "On limiting distribution of quasi-posteriors under partial identification," Econometrics and Statistics, Elsevier, vol. 3(C), pages 60-72.
    7. JoonHwan Cho & Thomas M. Russell, 2018. "Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments," Papers 1810.03180, arXiv.org, revised May 2023.
    8. Andreas Tryphonides, 2019. "Qualitative Surveys And Margins Of Adjustment In Heterogeneous Agent Economies," 2019 Meeting Papers 1415, Society for Economic Dynamics.

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