Manufacturing Earnings and Cycles: New Evidence

Table 2: Economie indicators: share of total variance

Notes:

(i) GFCF: gross fixed captial formation, Y:
output, N: employment, II: inventory invest-
ment; (ii) share of total variance: share of vari-
ance which can be attributed to the compos-
ite of waves in the respective frequency range;
(iii) (1): 7-10 years (Juglar cycle), (2): 5-
7 years, (3): 3-5 years (Kitchin cycle); (iv)
*∕^rr /***: share of total variance is significant
at the 10/5/1 per cent level.

Analogous to the univariate approach, we require a multivariate method
that allows us to achieve two objectives. First, we want to find out at which
business cycle frequency the ratio of explained to unexplained variance is at
a maximum. Second, we need to determine whether the share of variance
explained by our various indicators of the cycle, in a specific frequency band, is
signihcant.¹⁴ In other words, we would like to test the null hypothesis that the
real wage component(s) and the cyclical indicators are unrelated in a specific
frequency band. As in the univariate case the data may reveal multiple cycles
between any two series. The cells of Table 3 refer to the proportion of total
variance in the respective frequency range for each component of the real wage
explained by the variance of II,N,Y and GFCF respectively. Consider μ in
Table 3 using the GFCF cycle in conjunction with Table 1. This reveals that

¹⁴To determine whether the explained variance, pχγ between two series Y and X, in
the relevant frequency band [ω1,ω2], is Signihcantly different from zero we implement the
following procedure. First, we ht AR models to Y and X and, second, we conduct a
parametric bootstrap to simulate the model under the null hypothesis (i.e. no interaction
between the series). This produces a simulated series (Y_t^sA_t^s) that has the univariate
characteristics of the underlying data, but without interaction. Third, we ht a VAR of hxed
order to (y_t^sA_t^s) and calculate p^,χ_γ ■ Fourth, these steps are then repeated for s = 2000
so that we can obtain an empirical distribution of pχγ under the null conditional on the
series we are examining. Note that Priestley (1981, p705-706) develops a similar test of zero
coherency for the classical spectral estimate, the periodogram.

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