5. Comparison of different comovement measures
This paper shows that using a rich set of statistics that captures the dynamic
features of the data makes it possible to bring to light characteristics of the data that
simpler procedures cannot. In particular, in contrast to the established procedures both the
VAR methodology of Section 3 and the frequency-domain filters of Section 4 directly,
and in an intuitive manner, reveal that in several samples the relationship between prices
and output is characterized by a positive as well as a negative comovement.
The idea of descriptive statistics is that they summarize key features of the data in
an efficient manner. Different (comovement) statistics obviously capture different aspects
of a set of time series. In this paper this occurred when we compare the two different
sample periods. In particular, with the VAR method we find that correlation coefficients
are substantially more negative for the sample consisting of only the last two decades for
five of the nine cases considered in Figures 1 and 2. In contrast, with the frequency filters
we do not observe such a decrease in any of the nine cases.
The question arises what can explain these differences. Productivity increases
because of technological inventions clearly have been important during the last two
decades. Arguably, a decrease in regulations and other market distortions may have
increased productivity as well. The productivity increases have been credited for
increasing output and keeping inflation low. If these changes in productivity are
persistent it may very well be that the price and output movements associated with these
productivity changes are captured by the VAR forecast errors but correspond to low
frequency movements that are not captured by the high-pass filters considered.