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-The Energy in the Nondurable Goods Index
-The Phase-plane Plot of Acceleration Versus Velocity
-Plotting the Depression and World War II
-The Mid 70's: A time of Structural Change
-What have we seen?



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Phase-Plane Plotting of the Goods Index
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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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