Calculus and the Housing Bubble

Jun 24th, 2008 | By | Category: Economics

Bored tonight, I’ve been playing around with the S&P/Case-Shiller Home Price Indices dataset that was just released. With all the hysterical coverage around the housing bubble, it seemed like fun to use some of my high school calculus.

Yeah, yeah, I could just graph the index over time, but why not graph the derivative? Ah yes. When the derivative crosses zero, we’re at a local minima or maxima. Well, let’s look at the graph:

Looking at the chart, we can clearly see right when the bubble burst, right around August of 2007 for most of the country when the derivative dropped sharply below zero. The Northwest States, Oregon and Washington, seemed a bit delayed until December, but had the same dipping below zero in the derivative.

An interesting thing happened in the April, at least in the Northwest. The derivative crossed zero again, this time becoming positive. Hmmm. If the trend holds, the housing “crisis” will be quite a mild one in the Northwest. Even in California, while prices are still declining (as the derivative is still below zero), the trend for the past few months has been an improving one.

Eh. A fun application of some basic calculus.

Now, if I had the data, I’d love to correlate housing prices with access to good mass transit as well as walkability.