ance earnings is explained by the composite waves in the (1) 7-10, (2) 5-7 and
(3) 3-5 year frequency ranges, respectively. Only the third band is found to
yield a significant share of the total variance. The final column of Table 1
gives the cycle length at which the explained variance is maximised across the
entire spectrum for each series, e.g. μ has a cycle length of 4.18 years.
|
Table 1: |
Earnings: |
: share of total |
variance | |
|
(ɪ) |
(2) |
(3) |
Cycle | |
|
P |
0.01 |
0.07 |
0.59*** |
4.18 |
|
λ |
0.08 |
0.64*** |
0.22 |
5.94 |
|
W/Cp |
0.14 |
0.43*** |
0.33 |
5.82 |
|
W/ Pp |
0.24** |
0.41*** |
0.25 |
6.74 |
Notes:
(i) W: standard hourly wage; μ: premium
markup; λ: proportion of workers working
overtime; Pp: producer price index; Cp: con-
sumer price index; (ii) share of total variance:
share of variance which can be attributed to
the composite of waves in the respective fre-
quency range; (iii) (1): 7-10 years (Juglar cy-
cle), (2): 5-7 years, (3): 3-5 years (Kitchin
cycle); (iv) */**/***; share of total variance is
signihcant at the 10/5/1 per cent level.
As alluded to above, statistically determining the cyclical length of under-
lying cycles in a series amounts to testing the null hypothesis of no cyclical
structure or in other words that the series is white noise.12 Accordingly, if the
explained variances reported in columns 1-3 are signihcant then the series can
12To establish significance we follow Reiter and Woitek (1999) and simulate white-noise
processes to assess whether the share of total variance in the frequency intervals of interest
is Signihcantly different from the result we would obtain if the data generating process was
white noise. For example, we ht an AR model of order 5 to a white noise process, which has
the same variance as the series under analysis, and repeat this 2000 times. We then use the
univariate spectral measures from this experiment to derive the empirical distribution under
the null hypothesis (i.e. no cyclical structure). Note that we employ empirical distributions
since asymptotic distributions are extremely difficult to derive in this context. In any event,
since we employ relatively short time series, the asymptotic properties would most certainly
not be correct. In addition to the white-noise processes, we also used hltered random walks
as null models, to ensure that the cyclical structure is not created by an inappropriately
chosen hlter. This procedure basically produced the same results.
16