Fun with trendlines

In the comments from a few days ago, JAC asks:

One question for you. You mention that Shiller's "own graph" suggest home prices are still overvalued. When I look at the graph and then "add a trend line" to "home prices", then home prices are indeed below the trend line now, which suggests they are undervalued, no?

My response to JAC was:

Are you including the bubble period in your trend? If you've got a 110-year period of relatively flat prices (adjusted for inflation), followed by a huge and temporary bubble, of course the trendline will be upward sloping. The bubble distorts the trendline's slope.

With my graphs I measure the pre-bubble trend only, to avoid any distortion. And surprise, surprise! It gives me a slope that closely matches the change in rental prices.

Here is Professor Robert Shiller's graph of housing prices (adjusted for inflation) since 1890. On it, I have drawn two trendlines. Eyeballing the two trendlines, which looks to you like a better measure of normal housing prices, the black trendline or the red trendline?

The black trendline measures housing prices for the entire 1890-2010 period, with 1950 being the midpoint. Notice it has two periods that add significant slope to the line. To the left of the midpoint, there is a roughly 25-year dip in prices from the end of World War I to the end of World War II. To the far right of the midpoint, there is a 10-year housing bubble.

The red trendline only measures housing prices for the post-World War II part of the 20th century, i.e. 1945-1999. I'm guessing that most people will see what they want to see, but to my eyes the red trendline is a better measure of normal. It goes straight through the the graph of the 1890-1917 period, even though that's not data used to draw the red trendline.

Now look at this graph, below. The dark blue line graphs housing prices since 1983. The magenta line graphs owner-equivalent rents since 1983. The two straight black lines are trendlines for housing prices and rents, respectively. It should be obvious which trendline is measuring which data set.

Theoretically, housing prices and rents should rise at roughly the same rate. After all, rent is the revenue that housing generates. Yet, in the graph, the house price trendline is significantly steeper than the rent trendline, because the housing bubble distorts the house price trend.


Now look at this graph below. In this graph, the rent trendline has been removed (although the graph of owner-equivalent rent remains). As a replacement for the rent trendline, I have added a trendline for pre-bubble (1983-1999) house prices. Notice that although the pre-bubble trendline is slightly flatter than the graph of rents, its slope is still much closer to the rent line than the original house price trendline. To me, this verifies that a trendline of pre-bubble housing prices is a better measure of normal than a trendline of all housing prices.


Ultimately, however, the change in rents is a better measure of the long-term house price trend than any trendline you can draw.