Global Robust Bayesian Analysis in Large Models

Ho, P.

doi:10.2139/ssrn.3452643

Cited by 3 publications

(3 citation statements)

References 22 publications

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“…First, all priors in our prior class share a single prior for the reduced-form parameters, while this is not necessarily the case in Ho (2019). Allowing for multiple priors for the reduced-form parameters implies that a prior that fits the data poorly, i.e., that is far from the observed likelihood, will yield the worst-case posterior.…”

Section: Related Literaturementioning

confidence: 99%

“…Second, our approaches differ in how to select the radius of the KL neighborhood. Ho (2019) recommends to set the radius so that the set of priors can span the posterior means around the Gaussian-approximated benchmark posterior. This approximation is reasonable only when the model is point-identified.…”

Section: Related Literaturementioning

confidence: 99%

“…Alternatively, one could form the KL neighborhood for the unconditional prior of (θ, φ) around its benchmark, as considered in Ho (2019). However, our approach to constructing priors simplifies the multiple-priors analysis both analytically and numerically.…”

Section: Setting Up the Set Of Priorsmentioning

confidence: 99%

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Estimation Under Ambiguity

Kitagawa¹,

Uhlig²

2019

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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. * We would like to thank Stephane Bonhomme, Lars Hansen, Frank Kleibergen, Matthew Read and several seminar and conference participants for their valuable comments. We gratefully acknowledge financial support from ERC grants (numbers 536284 and 715940) and the ESRC Centre for Microdata Methods and Practice (CeMMAP) (grant number RES-589-28-0001).

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Section: Related Literaturementioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

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Estimation Under Ambiguity

Kitagawa¹,

Uhlig²

2019

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Prior Knowledge Elicitation: The Past, Present, and Future

et al. 2024

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Uncertain identification

Kitagawa

Volpicella

2022

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Uncertainty about the choice of identifying assumptions is common in causal studies, but is often ignored in empirical practice. This paper considers uncertainty over models that impose different identifying assumptions, which can lead to a mix of point‐ and set‐identified models. We propose performing inference in the presence of such uncertainty by generalizing Bayesian model averaging. The method considers multiple posteriors for the set‐identified models and combines them with a single posterior for models that are either point‐identified or that impose nondogmatic assumptions. The output is a set of posteriors ( post‐averaging ambiguous belief), which can be summarized by reporting the set of posterior means and the associated credible region. We clarify when the prior model probabilities are updated and characterize the asymptotic behavior of the posterior model probabilities. The method provides a formal framework for conducting sensitivity analysis of empirical findings to the choice of identifying assumptions. For example, we find that in a standard monetary model one would need to attach a prior probability greater than 0.28 to the validity of the assumption that prices do not react contemporaneously to a monetary policy shock, in order to obtain a negative response of output to the shock.

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Global Robust Bayesian Analysis in Large Models

Cited by 3 publications

References 22 publications

Estimation Under Ambiguity

Estimation Under Ambiguity

Prior Knowledge Elicitation: The Past, Present, and Future

Uncertain identification

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