Manufacturing Earnings and Cycles: New Evidence

should expect this latter finding on a priori grounds. For instance, the level
of the standard hourly wage rate typically reflects an agreement between (at
least) two bargaining parties. The bargaining agenda is comprised of a va-
riety of economic issues of concern to each side. The uppermost interest of
workers in a given firm might be for wage changes to cover cost of living in-
creases while management might place greatest weight on product demand. As
a result, wage outcomes may be conditioned, to a greater or lesser extent, by
the cyclical characteristics of representative proxies for each of these economic
influences.

2 Econometric Method

2.1 Univariate Measure

In empirical research on economic cycles, the predominant paradigm has been
to examine auto- or cross-covariances in the time domain.³ The information on
the cyclical structure contained in the autocovariance function can be trans-
formed into frequency domain, revealing a more detailed picture. The spectrum
of a process is defined as the Fourier transform of the autocovariance function
₇√τ), τ = 0, ±1, ±2,...:

₁ ∞

= — J2 7√^)e^^wτ; ω ∈ [-π,π].             (1)

Z7Γ ^z—^z

T = -CO

Figure 1 illustrates the plot of a spectrum.⁴ The interpretation is like that of a
probability density function; f_x(ω)dω is the part of the overall variance of X_t
which is due to the component with frequencies over the interval [ω,ω ⅛ dω].
The total area under the spectrum equals the process variance:

Z7Γ
f_x(ω)dω.                          (2)

■7Г

³Widely cited examples are Kydland and Prescott (1990) and Backus and Kehoe (1992).
For a recent exception, working in the frequency domain, see A’Hearn and Woitek (2001).

⁴We estimate parametric spectra, i.e. we start in the time domain by fitting autoregressive
models to the data. A detailed explanation of the estimation procedure can be found in the
Appendix, Section A. 1.1.

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