Sunday, November 18, 2007

Income growth and house-price growth: phase portraits

Derek Cheung mentioned last May that his brother observed income as a leading indicator for house prices in Hong Kong. Zhang Da Peng's blog is at http://dpz88.spaces.live.com/.

Now we have data to explore this in the United States.

Standard&Poors/Case-Shiller home-price indices for metropolitan areas are available at http://www2.standardandpoors.com/portal/site/sp/en/us/page.topic/indices_csmahp/0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0.html.

The Internal Revenue Service's Statistics of Income Division http://www.irs.gov/taxstats/index.html has state- and zip-code-level sums of adjusted gross income and exemption sums. One problem with the zip-code-level sums is the cost: $500 per year for the whole United States.

Phase portraits (y = momentum; x = position) can show the behavior of a damped driven harmonic oscillator in different regimes: simple undamped is a circle; underdamped spirals clockwise to the origin; resonance spirals clockwise outward. If we plot inflation-adjusted income growth on the x-axis and inflation-adjusted house-price growth on the y-axis, then counter-clockwise motion would mean income leads housing. I suspect driven or undamped behavior in the first quadrant, and damped behavior in the other three quadrants.

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