by Calculated Risk on 9/26/2007 01:07:00 PM

## Wednesday, September 26, 2007

### Graphing Housing Prices

My apologies to Tanta, this is my version of an UberNerd post: How to graph housing prices.

The NY Times included a graph of real house prices based on the Case-Shiller index in the following article: They Cried Wolf. They Were Right.

**Click on graph for larger image in new window.**The graph has several interesting events annotated, including when economist Dean Baker sold his condo in May 2004, and Fed Chairman Ben Bernanke's comment in Feb 2006 that Fed policy makers "expect the market to cool but not to change very sharply".

Unfortunately I think this graph is somewhat misleading and technically incorrect. So I'd like to use this graph to illustrate how to graph housing prices.

This graph is based on the quarterly S&P/Case-Shiller® U.S. National Home Price Values. The S&P/Case-Shiller® index is for nominal house price (not adjusted for inflation).

To adjust for inflation, the NY Times used the CPI from the BLS. This is a slight technical error; an economist would adjust the Case-Shiller index using "CPI less shelter". Admittedly the differences are minor.

Setting Q1 1987 to 100, the NY Times calculated prices fell to 92 in Q4 1996. Using CPI less Shelter, prices would have only fallen to 93 (minor difference).

However, the NY Times calculated prices peaked at 171 in Q1 2006. Using CPI less Shelter, the peak was actually 176, about a 3% difference.

The other problem with the NY Times graph is the choice of scale without warning the reader. IMO the starting value for the y-axis should be clear. This graph is fine if the reader understands that the graph shows the changes in real values, but not the relative absolute values.

**Click on graph for larger image.**The second graph shows the same data with the scale starting at zero (the blue line is the NY Times calculation of real values, the shaded area is the technically correct calculation).

But even this graph could mislead the reader. Will prices return to 100 (the Q1 1987 price)? Unlikely. First, 1987 was chosen because that is one the Case-Shiller index starts. We do not know from this chart if prices in 1987 were too high, too low, or just about right.

Second, real prices for houses do increase over time - perhaps on the order of 1% to 2% per year. Using 1987 as a starting point, a 2% real return would have put current real prices at 150; a 1% annual return would put the current value at 122.

What people really want to know is what will happen to nominal prices in the future. But the focus on real prices helps predict changes in future nominal prices. I'll have more on this later.