Bootstrapping DSGE models

By Giovanni Angelini, Giuseppe Cavaliere and Luca Fanelli

This paper explores the potential of bootstrap methods in the empirical evaluation of dynamic stochastic general equilibrium (DSGE) models and, more generally, in linear rational expectations models featuring unobservable (latent) components. We consider two dimensions. First, we provide mild regularity conditions that suffice for the bootstrap Quasi-Maximum Likelihood (QML) estimator of the structural parameters to mimic the asymptotic distribution of the QML estimator. Consistency of the bootstrap allows to keep the probability of false rejections of the cross-equation restrictions under control. Second, we show that the realizations of the bootstrap estimator of the structural parameters can be constructively used to build novel, computationally straightforward tests for model misspecification, including the case of weak identification. In particular, we show that under strong identification and bootstrap consistency, a test statistic based on a set of realizations of the bootstrap QML estimator approximates the Gaussian distribution. Instead, when the regularity conditions for inference do not hold as e.g. it happens when (part of) the structural parameters are weakly identified, the above result is no longer valid. Therefore, we can evaluate how close or distant is the estimated model from the case of strong identification. Our Monte Carlo experimentations suggest that the bootstrap plays an important role along both dimensions and represents a promising evaluation tool of the cross-equation restrictions and, under certain conditions, of the strength of identification. An empirical illustration based on a small-scale DSGE model estimated on U.S. quarterly observations shows the practical usefulness of our approach.

Nice discussions on ways to improve the assessment of estimated DSGE models. However, this applies only to linear models, which are a subset of DSGE models, not the other way around like the abstract seems to imply.


One Response to Bootstrapping DSGE models

  1. Luca Fanelli says:

    Thank you for the comment.

    The focus of the paper is on linearized DSGE models and, more generally, on linear(ized) Rational Expectations models which feature unobserved components.
    The paper does not claim that the suggested bootstrap approach can be extended to nonlinear representations of dynamic equilibrium models. At first glance, the generalization to the class of nonlinear DSGE models seems puzzling (yet not impossible at all under certain conditions). But that is surely the topic of another paper.

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