So there was a drastic change in the speculation volume ratio to all sales of homes (a threshold) in the course of US housing bubble of the 2000s (see post “Critical Mass of Speculation Triggers Asset bubbles”). I have hypothesized that crossing this threshold triggered the bubble, the positive feedback loop of booming prices of the period.
Let us see if the adequate threshold could be detected in the Case-Shiller index of home prices of the time. Threshold is a twist, may be a kink, a drastic change in price dynamics.
Can we see something like that in the dynamics of Case-Shiller index for the period 2000- 2006? I added two tangent lines to the picture of the index to catch the approximate region of the supposed price threshold (see below).
The graph shows two distinctive periods, with different slopes of the curve. The approximate slope (the first derivative of the price function) in the beginning of the period until, perhaps, the year 2003 is much flatter than afterwards. The change is obvious and significant (I am skipping numbers). It looks like the price threshold was reached in the year 2003.
Mathematical modeling ( see post “Modeling the US Housing Bubble of the 2000s”) reveals this drastic change too. Let us see it again with some simplifications.
In Model 1 the price grows with constant rate (in the traditional economic interpretation). It is a typical exponential growth. The first derivative of the price function is changing, of course, yet the change is gradual, nothing suggests a twist or some drastic change of speed.
In Model 2 the price grows with accelerating rate. As we can see, it is much closer to the dynamics of the Case-Shiller index of the period. Moreover, it reflects better the essence of a bubble with its explosive character. The price in Model 2 at first grows slowly, and after some point explodes. Still, the price threshold is not very much pronounced, so this model may be regarded as a rough approximation of bubble dynamics. It smooths out the threshold-type change, yet it is there, in about 2003, which is also the year of drastic change in the ratio of flipping activities to all sales in the housing market ( http://libertystreeteconomics.newyorkfed.org/2011/12/flip-this-house-investor-speculation-and-the-housing-bubble.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+LibertyStreetEconomics+%28Liberty+Street+Economics%29).
In fact, there was no housing bubble in the US before 2003. It is the year when the price threshold of speculation in the US housing market was crossed, creating the explosive market frenzy of 2003-2006.
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