Bayesian inference in a class of partially identified models

By Brendan Kline, Elie Tamer. 2016

117 citations recorded by the source corpus.

This paper develops a Bayesian approach to inference in a class of partially identified econometric models. Models in this class are characterized by a known mapping between a point identified reduced‐form parameter μ and the identified set for a partially identified parameter θ. The approach maps posterior inference about μ to various posterior inference statements concerning the identified set for θ, without the specification of a prior for θ. Many posterior inference statements are considered, including the posterior probability that a particular parameter value (or a set of parameter values) is in the identified set. The approach applies also to functions of θ. The paper develops general results on large sample approximations, which illustrate how the posterior probabilities over the identified set are revised by the data, and establishes conditions under which the Bayesian credible sets also are valid frequentist confidence sets. The approach is computationally attractive even in high‐dimensional models, in that the approach avoids an exhaustive search over the parameter space. The performance of the approach is illustrated via Monte Carlo experiments and an empirical application to a binary entry game involving airlines.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a3db393c031214e8cefa7cc0f876653cbd04590b

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Citations in the corpus

Monte Carlo Confidence Sets for Identified Sets (2016, background): “Both Moon and Schorfheide (2012) and Kline and Tamer (2016) would specify a prior on φ and sample from the posterior for φ.”
Counterfactual Sensitivity and Robustness (2019, methodology): “This approach is in the spirit of global sensitivity analysis advocated by Leamer (1985) (see also Tamer (2015)).”