average lengths of these cycles. This helps us to determine the choice of cyclical
economic indicators to be used in the multivariate analysis. We are then in a
position to examine the degree to which the frequency of each component of
wage earnings coheres with each of the selected indicators. We then proceed
to the dynamic correlations discussed in Section 2.2. These allow us not only
to measure if a wage component and a cyclical indicator exhibit pro-, counter-,
or а-cyclical relationships but also the time lengths involved if significant lags
or leads are present.
Before we can analyse the cyclical structure, we need to ensure that the
series are stationary. Since all filtering methods in the literature potentially
distort the cyclical structure dependent on the true data generating process,8
our method of choice is the strategy proposed by Canova (1998): we com-
pare the results for different filtering methods, and judge the robustness of
the outcome. The filters are the Hodrick-Prescott (HP) filter (Hodrick and
Prescott, 1997),9 the Baxter-King filter (Baxter and King, 1999) in a modified
version proposed by Woitek (1998) (BKM),10 and the difference filter (D). In
the following, we report the results for the BKM filter.11
As discussed in relation to Figure 1, we can decompose a series into cyclical
components, defined over multiple frequency bands. The variables included in
the first column of Table 1 are the constituent parts of (8) expressed in real
terms. We show results using both Cp and Pp deflators. The next three
columns show the share of the total variance of each wage series that is ex-
plained by the composite of waves in the respective frequency range. Taking
the premium markup, μ, as an example, 0.01, 0.07 and 0.59 of the total vari-
8Recently it was demonstrated by Cogley and Nason (1995), King and Rebelo (1993) and
Harvey and Jaeger (1993), that the widely used Hodrick-Prescott filter (Hodrick and Prescott
1997) is likely to generate spurious cyclical structure at business cycle frequencies if applied
to difference stationary series. Similar points can be made with respect to the Baxter-King
Filter (Guay and St-Amant 1997), and to moving-average filters in general (Osborn 1995).
Moreover, there is the danger of spurious correlation between Hodrick-Prescott filtered series
(Harvey and Jaeger 1993).
9With the usual smoothing weight of 100 (annual data) and for a series which is I(O), the
HP filter leaves cycles with period length up to about 11 years almost undistorted in the
data.
10The modified Baxter-King Filter uses Lanczos’ σ factors to deal with the problem of
spurious side lobes, which invariably arises with finite length filters. In contrast to the
original filter proposed by Baxter and King (1999), our cut-off period is 15 years, allowing
us to analyse cycles as long as the Juglar cycle.
11The results for all the other filters are comparable and will be made available on request.
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