Spectral Analysis and Distributed Lags in Geographical Studies of Local Unemployment: 2. Distributed Lags

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Abstract
This is the second part of a two-part paper in which the related topics of spectral analysis and the identification and estimation of distributed-lag models between time series are discussed. This paper is mainly concerned with distributed-lag models, in particular the use of spectral estimators developed by Hannan. A number of previous studies have used the phase statistics from the cross-spectrum as an indication of lead/lag relations between unemployment series, but it is shown here that this is likely to lead to incorrect conclusions. As an empirical example, lead/lag relations between local unemployment in Severnside and the national series are investigated. The correspondence between time-domain (regression) and frequency-domain (spectral) methods of estimating relations between time series is also discussed, using empirical material from both parts of the paper.