Estimation Under Ambiguity

Raffaella Giacomini (), Toru Kitagawa () and Harald Uhlig ()
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Toru Kitagawa: Institute for Fiscal Studies and University College London

No CWP24/19, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: To perform Bayesian analysis of a partially identified structural model, two distinct approaches exist: standard Bayesian inference, which assumes a single prior for the structural parameters, including the non-identified ones; and multiple-prior Bayesian inference, which assumes full ambiguity for the non-identified parameters. The prior inputs considered by these two extreme approaches can often be a poor representation of the researcher’s prior knowledge in practice. This paper fills the large gap between the two approaches by proposing a multiple-prior Bayesian analysis that can simultaneously incorporate a probabilistic belief for the non-identified parameters and a concern about misspecification of this belief. Our proposal introduces a benchmark prior representing the researcher’s partially credible probabilistic belief for non-identified parameters, and a set of priors formed in its Kullback-Leibler (KL) neighborhood, whose radius controls the “degree of ambiguity.” We obtain point estimators and optimal decisions involving non-identified parameters by solving a conditional gamma-minimax problem, which we show is analytically tractable and easy to solve numerically. We derive the remarkably simple analytical properties of the proposed procedure in the limiting situations where the radius of the KL neighborhood and/or the sample size are large. Our procedure can also be used to perform global sensitivity analysis.

Date: 2019-05-28
New Economics Papers: this item is included in nep-ecm and nep-ore
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Citations: View citations in EconPapers (7)

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