Expertise:
Intermediate
What have we seen?
Phase-plane plotting is revealing because it focuses our attention on the
dynamics of the seasonal component of variation in the goods index. We plot
velocity on the horizontal axis, representing the rate of change of the process;
and plot acceleration on the vertical axis, indicating the input or withdrawal of
whatever resources or forces produce this change. Because seasonal components
tend to exhibit oscillatory or harmonic behavior, we can interpret what we see
as a transition between two types of energy: kinetic associated with velocity,
and potential associated with acceleration. Harmonic behavior, in which the
system moves between these two states, shows up as a loop surrounding the
origin. The bigger the radius of the loop, the more energy the system has, and
the smaller or closer it is to zero, the less the energy.
We saw that the typical year shows three such loops, associated with the
spring, summer, and fall. The summer loop typically has the largest associated
energy. But the fall loop seems to be most affected by shocks such as the stock
market crash of 1929, the shutting down of the money supply in 1937, and the
end of the Vietnam War in 1974. This is probably due to the fact that the
fall production loop is associated with buying for the Christmas holidays, and
therefore is something consumers can turn on and off according to whether times
are good or tough, respectively.
We also saw the seasonal dynamics reflecting longer-term changes. There
is much less energy in the system now than in the 1960s, as reflected in the
smallness of loops in recent times.
The dynamics of a process typically show more variation than the statics or
position of the process, and we could see things happening in the phase-plane
plots that would be hard to spot in the plot of the process itself.
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