In a previous article I have presented a working hypothesis–that economic systems are complex and prone to multistability. They are characterized by periods of relative stability punctuated by brief episodes of rapid change when they evolve to a new area of stability. In previous articles on the World Complex, I presented empirical evidence for such behavior in share prices, commodity price ratios, unemployment, and housing prices; as well as in natural systems.
Today we will look at an enhanced record of house prices. The Case-Shiller index is an inflation-adjusted index of home prices across the United States, compiled by Karl Case and Robert Shiller, and available here. The annual index house prices since 1890 are depicted below.
As we see above, there has been no bubble in housing (/sarc). Well, perhaps a blip. We’ll have a contest later to name it.
The idea of multistability is that a system evolves in rapid jumps from one area of stability to another. The classic way to depict such things is through reconstructing a phase space portrait, which is a scatterplot of either the original time series against its time derivatives, or the original time series against a lagged copy of itself. The second type–a lagged plot–is easiest to use, and typically has smaller errors, so is normally the method of choice for empirical data.
Rather than fitting a line to the points, we traditionally draw a smoothed curve through the points in order. The individual plotted observations are called “states” and the line through them is called the “trajectory”, and traces out the time-evolution of the sequential states of the system.
The above graph is the Case-Shiller index plotted against a four-year lagged copy of itself. For instance, the point labelled 2011 represents the index value for 2011 plotted against the index value for 2007.
The system is said to be stable when the trajectory only fills a small region of phase space over a significant time period. In the graph above, there are two areas of stability–one occupied from 1915 to 1945 (the advent of the Fed to the end of the depression/WW2) and one occupied from 1896 to about 1913, and again from 1950 to 1999 (post-war boom). Despite the efforts of recent Fed chairman, no near area of stability has been created at higher prices, although it has been a thrilling ride.
Since 1953, the Case Shiller index is available quarterly. So let’s take a look at a similar plot to the one above using the quarterly data (still with a 4-yr lag).
Prior to the year 2000, the system was confined to the yellow blob. The current excursion through most of phase space has shown no sign of settling down anywhere, and seems most likely to return to the yellow blob.
Very optimistic people might suggest that maybe the area in the above diagram marked by the question mark might be an incipient area of stability–maybe the very place Greenspan and Bernanke were aiming for to keep the “wealth effect” of housing alive. Alas, stable areas must lie along the sloping yellow line in the above figure–which represents points where the housing index of four years ago is the same as the index today. That’s what stability is, no?
What QE1 and QE2 achieved is the bit of hot-doggery around the question mark. They had no ultimate effect in terms of preventing the system from returning to the yellow region. QE3 likely will have even less effect, as the system now has some momentum behind it.
Trying to stop a bubble from deflating is like trying to stop a falling anvil by standing underneath and blowing. Hope the next Fed chairman is a cartoon character!