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Causality in the Long Run

Published online by Cambridge University Press:  11 February 2009

W.J. Clive  and
Jin-Lung Lin
W.J. Clive
Affiliation:
University of California, San Diego, Institute of Economics, Academia Sinica
Jin-Lung Lin
Affiliation:
University of California, San Diego, Institute of Economics, Academia Sinica
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Extract

The definition of causation, discussed in Granger (1980) and elsewhere, has been widely applied in economics and in other disciplines. For this definition, a series yt is said to cause xt+l if it contains information about the forecastability for xt+l contained nowhere else in some large information set, which includes xt−j, j ≥ 0. However, it would be convenient to think of causality being different in extent or direction at seasonal or low frequencies, say, than at other frequencies. The fact that a stationary series is effectively the (uncountably infinite) sum of uncorrelated components, each of which is associated with a single frequency, or a narrow frequency band, introduces the possibility that the full causal relationship can be decomposed by frequency. This is known as the Wiener decomposition or the spectral decomposition of the series, as discussed by Hannan (1970). For any series generated by , where xt, and are both stationary, with finite variances and a(B) is a backward filter

with B the backward operator, there is a simple, well-known relationship between the spectral decompositions of the two series.

Information

Type
Articles
Information
Econometric Theory , Volume 11 , Issue 3 , June 1995 , pp. 530 - 536
Copyright
Copyright © Cambridge University Press 1995

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References

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