Locally- but not Globally-identified SVARs

Bacchiocchi, Emanuele ; Kitagawa, Toru (2022) Locally- but not Globally-identified SVARs. Bologna: Dipartimento di Scienze economiche, p. 63. DOI 10.6092/unibo/amsacta/6925. In: Quaderni - Working Paper DSE (1171). ISSN 2282-6483.
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This paper analyzes Structural Vector Autoregressions (SVARs) where identification of structural parameters holds locally but not globally. In this case there exists a set of isolated structural parameter points that are observationally equivalent under the imposed restrictions. Although the data do not inform us which observationally equivalent point should be selected, the common frequentist practice is to obtain one as a maximum likelihood estimate and perform impulse response analysis accordingly. For Bayesians, the lack of global identification translates to non-vanishing sensitivity of the posterior to the prior, and the multi-modal likelihood gives rise to computational challenges as posterior sampling algorithms can fail to explore all the modes. This paper overcomes these challenges by proposing novel estimation and inference procedures. We characterize a class of identifying restrictions that deliver local but non-global identification, and the resulting number of observationally equivalent parameter values. We propose algorithms to exhaustively compute all admissible structural parameters given reduced-form parameters and utilize them to sample from the multi-modal posterior. In addition, viewing the set of observationally equivalent parameter points as the identified set, we develop Bayesian and frequentist procedures for inference on the corresponding set of impulse responses. An empirical example illustrates our proposal.

Document type
Monograph (Working Paper)
Bacchiocchi, EmanueleUniversity of Bologna, Department of Economics0000-0002-7365-3630
Kitagawa, ToruBrown University, Department of Economics0000-0001-5550-1281
Local identification, Bayesian inference, Markov Chain Monte Carlo, robust Bayesian inference, frequentist inference, multi-modal posterior
Deposit date
08 Jun 2022 10:53
Last modified
09 Jun 2022 07:23

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