Publication: Testing for fundamental vector moving average representations
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2017-03-29
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Wiley
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Abstract
We propose a test for invertibility or fundamentalness of structural vector autoregressive
moving average models generated by non-Gaussian independent and
identically distributed structural shocks. We prove that in these models and under
some regularity conditions the Wold innovations are a martingale difference
sequence (mds) if and only if the structural shocks are fundamental. This simple
but powerful characterization suggests an empirical strategy to assess invertibility.
We propose a test based on a generalized spectral density to check for the
mds property of the Wold innovations. This approach does not require the specification
and estimation of the economic agent’s information flows or the identification
and estimation of the structural parameters and the noninvertible roots.
Moreover, the proposed test statistic uses all lags in the sample and it has a convenient
asymptotic N(0 1) distribution under the null hypothesis of invertibility,
and hence, it is straightforward to implement. In case of rejection, the test can be
further used to check if a given set of additional variables provides sufficient informational
content to restore invertibility. A Monte Carlo study is conducted to
examine the finite-sample performance of our test. Finally, the proposed test is
applied to two widely cited works on the effects of fiscal shocks by Blanchard and
Perotti (2002) and Ramey (2011).
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Keywords
Fundamental representations, Generalized spectrum, Identification, Invertible moving average
Bibliographic citation
Chen, B., Choi, J., & Escanciano, J. C. (2017). Testing for fundamental vector moving average representations. Quantitative Economics, 8 (1), pp. 149-180.