334 Economic Cycles
−0.55, and the average amplitude of upswings is 0.55 with a coefficient of vari-
ation of 0.33. Since falls in unemployment appear about evenly matched with
rises in unemployment, this lends some credence to the idea of a natural rate.
The overall sample average unemployment rate is about 5.61%, although at times
there were large deviations from the average. For example, in November 1982 the
unemployment rate reached a high of 10.8%.
There are, however, significant differences between upswings and downswings.
For downswings, the average cumulative movement isFc=−18.43, the average
excess isC=−0.046 and the coefficient of variation in the excess is−1.32. For
upswings, the average cumulative movement isFe=6.40, the average excess is
E=0.009 and the coefficient of variation in the excess is 5.70. The average cumu-
lative movement in downswings is well over twice the magnitude of the cumulative
movement in upswings; this is consistent with the longer average duration of
downswings. From the average excessC, employment tends to fall at a decreas-
ing rate during contractions, or downswings, and fromE, employment tends to
rise at a decreasing rate during expansions, or upswings. The steep initial decline
in unemployment during downswings is more prominent than the steep initial
ascent in unemployment during upswings. In fact, from the coefficient of varia-
tion, there is much more relative variability in the excess for upswings than for
downswings. Long durations in downswings, large cumulative movements, and
stable excess across downswings all reflect favorably on current economic policy.
7.8.2 Synchronization with business cycles
From Figure 7.3, cycles in output and unemployment appear highly synchronized.
However, even though there are about as many turning points in the unemploy-
ment cycle as there are in the business cycle (see the summary statistics in Table
7.1), the two binary series representing unemployment and output are not per-
fectly correlated. LetS 1 t=1 if output is rising andS 2 t=1 if unemployment is
rising; also letS 1 t=0 if output is falling andS 2 t=0 if unemployment is falling.
The coincidence indicator for the binary series iŝI =0.17 and the correlation
between them isrs=−0.61. In other words, about 83% of the time rising output
is associated with falling unemployment.
We can test the null hypothesisH 0 :ρs=0 by using Harding and Pagan’s (2006)
method of moment test. With a bandwidth of eitherm=8orm=9wefind
thattSNSis about−5.5, and thus we reject the null hypothesis that unemploy-
ment and output are statistically independent. Regression-based tests yield the
same conclusion. Unemployment and output appear to be statistically dependent.
Separating upswings from downswings in unemployment provides an important
insight. When measured at monthly intervals with our censoring rules, falling
unemployment is coincident with rising output, though rising unemployment
is not necessarily coincident with falling output. In fact, conditional on rising
unemployment, output is falling only about half the time. In other words, unem-
ployment is perfectly synchronized with output when unemployment is falling,
but it is a coin toss when unemployment is rising.