Manufacturing Earnings and Cycles: New Evidence

perspective. The common procedure is to test whether or not a limited num-
ber of mainline cyclical indicators can explain significant degrees of the wage
variation. One such indicator may be output deviations from trend, selected
to capture business cycle activity. If output deviations are strongly correlated,
say, with a 5-7 year wage cycle, and if that frequency range represents a dom-
inant explanation of wage movements, we would be inclined to lean towards a
business cycle explanation of wage cyclicality. Of course, we have a choice of
proxies for the business cycle and each would be expected to offer greater or
lesser со-variations with different wage cycles. Finding statistical support for
business cycle effects may not complete the story, however. Shorter and longer
frequency ranges, exhibiting strong correlation with other economic phenom-
ena, may also add significantly to explained wage variation.

Suppose that the peaks and troughs of an influential constituent cycle of
the wage time series coincide with the respective turning points of the selected
business cycle measure. Then we would conclude that the wage is both pro-
cyclical and in phase with the cycle. But the two series may be highly pro-
cyclical and out of phase. For example, in common with time series analyses,
adjustment impediments associated with bargaining may lead to consistent
phase lags of the wage to the cycle. Or the two series may be partly in phase
and partly out of phase.

We apply and develop frequency domain techniques to offer detailed in-
sights into these aspects of wage cyclicality. We Frst consider ‘explained vari-
ance’ from a frequency domain perspective. This is achieved via the squared
coherency measure (sc) which assesses the degree of linear relationship between
cyclical components of two series X_t and Tj, frequency by frequency. The sc
is dehned as

^s÷> = 7⅜⅛τw ⁰≤^s÷) ≤ ι,          (3)

jx∖^ω)jy∖^ω)

where f_x(ω^) is the spectrum of the series X_t, and f_yx(ω) is the cross-spectrum
for Y_t and X_t.⁶ Using this expression, we can decompose f_y(ω) into and ex-

⁶The spectrum is the Fourier transform of the autocovariance function, and the cross-

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