Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Friday, February 10, 2012

Greek unemployment in phase space

Today's chart is a reconstructed phase space plot in two dimensions of the reported Greek unemployment numbers. The methodology is the same as that used to reconstruct the recent plots of US unemployment, with data available here and here.

First up is the time series of unemployment rate since 1998. The data is quarterly except for the last eight months, which is monthly.

And here is the two-dimensional phase space of Greek unemployment plotted with a six-month lag. Recall that we create these plots by making a scatterplot of the data against a lagged copy of itself. In this case, the lag is six months.

The points are quarterly, with the exception of the last two, which are monthly. Note how rapidly the system has evolved into the region of phase space characterized by high unemployment. This rapid excursion was preceded by a steady drop in the unemployment rate from 2004 until about mid-2008. The effect is reminiscent of a tightening spring which is suddenly released.

Ordinarily, after such a large excursion, we would expect to see these numbers stabilize. Stability in this region of phase space would suggest we have reached a long-term state of very high unemployment in Greece.

We see the same thing in the US unemployment rate phase space reconstruction below, with data from BLS.

Unemployment was relatively high in December of '03, and fell until early in 2008, before a sudden move to a much higher rate. Was the earlier decline in unemployment a precondition of the later increase? I think it was a reflection of the gaming of the economy due to low interest rate and the ensuing mortgage-market free-for-all. A lot of jobs were created in real estate sales and renovations--jobs which did not turn out to be based on a sustainable model.

The recent reported decline in unemployment rate appears to be forming some sort of excursion from the more recent area of Lyapunov stability, near the top right of the plot. If this were a natural system, we would look to see if it evolves towards the LSA at the bottom left of the plot. Systems which cycle slowly through two (or more) metastable equilibria are not uncommon in nature. Unfortunately, I still have some residual doubt that the decline in unemployment is not real, but a statistical fabrication.

Systems with more than one equilibrium state are very difficult to control, because their reaction to forcing (think policy) is dependent not only on the mathematical "laws" of the system, but also its past history. Arguably, each moment in history is unique--so the response of the system to the same policy will be different at each point in history. A Keynesian fixation on creating credit in response to all problems cannot be a viable solution at all times. Sometimes it will work. Sometimes new and unexpected behaviours will result, causing central bankers to apologize for their failures.

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