On the Validity of Classical and Bayesian DSGE-Based Inference

Katerina Petrova

No 1084, Staff Reports from Federal Reserve Bank of New York

Abstract: This paper studies large sample classical and Bayesian inference in a prototypical linear DSGE model and demonstrates that inference on the structural parameters based on a Gaussian likelihood is unaffected by departures from Gaussianity of the structural shocks. This surprising result is due to a cancellation in the asymptotic variance resulting into a generalized information equality for the block corresponding to the structural parameters. The underlying reason for the cancellation is the certainty equivalence property of the linear rational expectation model. The main implication of this result is that classical and Bayesian Gaussian inference achieve a semi-parametric efficiency bound and there is no need for a “sandwich-form” correction of the asymptotic variance of the structural parameters. Consequently, MLE-based confidence intervals and Bayesian credible sets of the deep parameters based on a Gaussian likelihood have correct asymptotic coverage even when the structural shocks are non-Gaussian. On the other hand, inference on the reduced-form parameters characterizing the volatility of the shocks is invalid whenever the structural shocks have a non-Gaussian density and the paper proposes a simple Metropolis-within-Gibbs algorithm that achieves correct large sample inference for the volatility parameters.

Keywords: DSGE models; generalized information equality; sandwich form covariance (search for similar items in EconPapers)
JEL-codes: C11 C12 C22 (search for similar items in EconPapers)
Pages: 33
Date: 2024-01-01
New Economics Papers: this item is included in nep-dge, nep-ecm and nep-ets
Note: Revised August 2024.
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Persistent link: https://EconPapers.repec.org/RePEc:fip:fednsr:97624

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DOI: 10.59576/sr.1084

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