Staff Reports
On the Validity of Classical and Bayesian DSGE-Based Inference
Number 1084
January 2024

JEL classification: C11, C12, C22

Authors: Katerina Petrova

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.

Full Article
Author Disclosure Statement(s)
Katerina Petrova
The author declares that (s)he has no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at
Suggested Citation:
Petrova, Katerina. 2024. “On the Validity of Classical and Bayesian DSGE-Based Inference.” Federal Reserve Bank of New York Staff Reports, no. 1084, January.

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