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OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 80, 2 (2018) 0305–9049
Data-Driven Identiﬁcation Constraints for DSGE
Markku Lanne† and Jani Luoto†
†Department of Political and Economic Studies, and HECER, University of Helsinki,
Helsinki, Finland (e-mail: markku.lanne@helsinki.ﬁ; jani.luoto@helsinki.ﬁ)
We propose imposing data-driven identiﬁcation constraints to alleviate the multimodality
problem arising in the estimation of poorly identiﬁed dynamic stochastic general equilib-
rium models under non-informative prior distributions. We also devise an iterative pro-
cedure based on the posterior density of the parameters for ﬁnding these constraints. An
empirical application to the Smets and Wouters (2007) model demonstrates the properties
of the estimation method, and shows how the problem of multimodal posterior distributions
caused by parameter redundancy is eliminated by identiﬁcation constraints. Out-of-sample
forecast comparisons as well as Bayes factors lend support to the constrained model.
Advances in Bayesian simulation methods have recently facilitated the estimation of rela-
tively large-scale dynamic stochastic general equilibrium (DSGE) models. However, when
using the commonly employed random walk Metropolis–Hastings (RWMH) algorithm,
typically relatively tight prior distributions have to be assumed to tackle ﬂat and multi-
modal posterior distributions arising from weak identiﬁcation in these models (see e.g.
Koop, Pesaran and Smith, 2013 and the references therein). This has the unfortunate con-
sequence that the resulting posterior distributions may not have much to say about how
well the structural model ﬁts the data, but the priors are likely to be driving the results,
which precludes us from learning about the parameters of the model from the data.
Under less informative priors, one potential solution to the problem of weak identi-
ﬁcation is offered by the so-called data-driven identiﬁability constraints put forth in the
statistics literature (see Fr¨uhwirth-Schnatter, 2001) but, to the best of our knowledge, not
applied to DSGE models. Such constraints can be found by inspection of the output of
JEL Classiﬁcation numbers: C11, C32, C52, D58.
*We would like to thank Francesco Zanetti (the Editor), and an anonymous referee for useful comments. Financial
support from the Academy of Finland (grants 268454 and 308628) is gratefully acknowledged. The ﬁrst author also
acknowledges ﬁnancial support from CREATES (DNRF78) funded by the Danish National Research Foundation,
while the second author is grateful for ﬁnancial support from the Research Funds of the University of Helsinki. Part
of this research was done while the second author was visiting the Bank of Finland, whose hospitality is gratefully