interpretation, in Section 4, we present the phase shift relative to the relevant
cycle range.
As pointed out by Croux et al. (2001), a measure like the squared coherency
presented above is not suited for analysing the comovement of time series,
because it does not contain information about possible phase shift between
cycles in the series Xt and Yt. In this sense, the correlation coefficient in
time domain is more informative, since it is calculated lag by lag, providing
both information on the lead-lag structure and the degree of linear relationship
between the two series. Croux et al. (2001) propose an alternative measure,
the so-called dynamic correlation p(ω), which measures the correlation between
the “in-phase” components of the two series at a frequency ω:
p(ω) = z Cxy^ -1 ≤ p(ω) ≤ 1. (7)
√Λ(ω)‰(ω)
3 Real hourly earnings decomposition and the
cycle
In the univariate analysis of real earnings within the frequency domain, we can
ascertain the lengths of cycles that are most closely associated with component
parts of the earnings measure. This gives vital pointers to the types of eco-
nomic indicator to work within multivariate applications. The latter involve
exploring the degrees to which each wage component со-varies and is in phase
with selected cyclical indicators. In this section we concentrate on earnings
decomposition itself and suggest the range of economic indicators that might
apply on a priori grounds. We deal first with nominal earnings decomposition
and then we consider the choice of price deflator in the real series.
3.1 Nominal earnings decomposition
A critical feature of earnings decomposition concerns the distinction between
the hourly standard wage rate and overtime payments. Overtime has been
an important recent phenomenon in the United States. During the 1980s
and 1990s, the proportion of overtime workers in manufacturing grew to 40
percent of the workforce. From the early 1990s trough to early 1997, average
weekly overtime in manufacturing increased by 1.6 hours to reach 4.9 hours,
10