The wild stock market run of the 90’s and the more recent boom in the housing market share a similar property: irrational exuberance. In his book “Irrational Exuberance”, Yale Economics Professor Robert Shiller describes the phenomenon “as a situation in which news of price increases spurs investor enthusiasm, which spreads by psychological contagion from person to person, in the process of amplifying stories that might justify the price increases and bringing in a larger and larger class of investors, who, despite doubts about the real value of an investment are drawn to it partly through envy of others’ successes and partly through a gambler’s excitement.”

In the statistics world, irrational exuberance manifests itself in the numbers as something called serial autocorrelation. Simply put, that just means that the prices we see today were largely determined by what we saw yesterday. But, what about the role of space, particularly in real estate markets where location is such a prominent force in dictating the price of assets. In a speculative housing bubble, is there is a spatial dimension to the psychological contagion that Shiller says is a defining characteristic of irrational exuberance?

To begin to explore this, we look at an index of housing prices that the Office of Federal Housing Enterprise Oversight (OFHEO) publishes quarterly for a large number of MSAs across the United States. The index, called the HPI, reflects the average price changes in repeat sales or refinancing of single-family homes whose mortgages were financed by Fannie Mae or Freddie Mac. While the HPI has been criticized for providing a dampened perspective of market prices, owing to the 400k cap on Fannie and Freddie loans, it does offer the best spatio-temporal coverage out of all publicly available sources of information on housing prices.

The maps in the slideshow below, which show percent changes in the 3d quarter HPI by MSA going back to 1988-89, do provide some evidence of spatial contagion. (Note: on each map, warmer hues indicate price appreciation while on the other end of the continuum the darker colors are areas of depreciation. All maps are on the same scale – i.e., in reference to the minimum and maximum change in HPI over the 19 time periods.) Towards the beginning of this decade, areas of northern California and the northeast begin to heat up, quickly spilling over into more locations along the east and west coast and Florida, and then to cities inward. The once hot markets eventually take a sharp downturn in 2006-2007.

How can we measure the spatial contagion? One way is through the Global Moran’s I statistic, which is a measure of the spatial counterpart to serial autocorrelation. It is a number that ranges from -1 to 1, where values in the negative territory would indicate a checkerboard pattern in the phenomenon being analyzed and those on the positive side just the opposite: spatial clustering of similarly, high valued units.

Shown in the figure below is the Moran’s I statistic computed for each time period on the lags of the changes in HPI. While it is important to keep in mind that the values of the statistic during the bubble may be lower than what they should be due to limitations of the HPI in terms of the cap on loans, there is a sharp and rapid incline during that period suggesting that irrational exuberance in real estate markets may in fact involve a spatial dimension.

More data can be found here:

OFHEO Housing Price Index (HPI) by MSA/CBSA - 3d Quarter (1988-2007)

Housing Variables (Prices/Supply/Demand) by MSA (2000-2007)

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