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MCMC confidence sets for identified sets

Xiaohong Chen (), Timothy M. Christensen, Keith O'Hara and Elie Tamer ()
Additional contact information
Timothy M. Christensen: Institute for Fiscal Studies
Keith O'Hara: Institute for Fiscal Studies
Elie Tamer: Institute for Fiscal Studies and Harvard University

No CWP28/16, 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 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.

Date: 2016-07-07
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Working Paper: MCMC Confidence sets for Identified Sets (2016) Downloads
Working Paper: MCMC Confidence sets for Identified Sets (2016) Downloads
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