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Econometrics and Applied Micro Seminar

Monday, May 23, 2016
4:00pm to 5:00pm
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Baxter B125
MCMC Confidence Sets for Identified Sets
Elie Tamer, Professor of Economics, Harvard University,

In complicated/nonlinear parametric models, it is hard to determine whether a parameter of interest is formally point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of parameters in econometric models defined through a likelihood or a vector of moments. The CSs for the identified set or for a function of the identified 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 directly from Markov Chain Monte Carlo (MCMC) simulations of 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 profile QLR statistics in partially identified models, allowing for singularities. These results imply that the MCMC criterion-based CSs have correct frequentist coverage for the identified set as the sample size increases, and that they coincide with Bayesian credible sets based on inverting a LR statistic for point-identified likelihood models. We also show that our MCMC optimal criterion-based CSs are uniformly valid over a class of data generating processes that include both partially- and point- identified 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.

For more information, please contact Sheryl Cobb by phone at 626-395-4220 or by email at sjc@hss.caltech.edu.