When Chairman Ben Bernanke of the Council of Economic Advisors made a statement about the U.S. housing market last week, some analysts jumped all over him. It looks to me like Bernanke had his facts exactly right.
In a speech delivered at the American Enterprise Institute last week, Ben Bernanke made the following statement:
The market for residential housing has been remarkably strong recently, in terms of both new construction and home prices. Homeownership has reached an all-time high during this Administration, as now nearly seven of ten American families own their own homes. The increase in house prices has recently received much attention in the media. While speculative behavior appears to be surfacing in some local markets, strong economic fundamentals are contributing
importantly to the housing boom. These fundamentals include low mortgage rates, rising employment and incomes, a growing population, and limited supply of homes or land in some areas. For example, states exhibiting higher rates of job growth also tend to have experienced greater appreciation in house prices.
Several analysts took issue with the last statement that job growth had something to do with house price increases. Angry Bear referred to Bernanke’s claim as an “alleged correlation,” and Calculated Risk stated flatly that “Bernanke misspoke.” Both attributed their views to fact-checking by MSNBC’s Martin Wolk.
So what did Wolk find objectionable in Bernanke’s statement? Wolk wrote,
For one thing, home sales and prices have been rising steadily for five years, breaking records year after year, even throughout the recession of 2001 and the jobless recovery that followed. If home price gains now are explained by rising employment, how do we explain the gains of 2001 to 2003, when the economy lost more than 2 million jobs and the unemployment rate was rising?
There are two facts about house prices that we’re trying to explain. The first is a
statement about the aggregate time series data– overall, house prices in the U.S. increased rapidly between 2000 and 2005. The second is a statement about cross-section data– house prices went up more in some communities than others. Bernanke provided a long list of factors that were making a contribution to house prices, with the first factor he mentioned being the declining mortgage rate. Since the interest rate varies little across different communities, the declining mortgage rate is obviously something that addresses the time-series question rather than the cross-section question. Bernanke’s answer to Wolk’s time-series question is the answer that any reasonable person should give: the drop in mortgage rates, not an aggregate increase in employment, is the primary reason that house prices overall rose so much in the U.S. over the last five years.
On the cross-section question, Wolk says that he
discovered that yes, many of the states that have seen the strongest home price gains over the past year have also seen some of the best job growth, including Nevada, Florida, Arizona and Virginia.
But then Wolk goes on to catalog a number of exceptions to the pattern:
Take a look at California. Over the 12 months ending March 31, California ranked No. 2 in home price growth….But California added only 250,000 jobs last year– about in line with the 1.7 percent job growth rate seen in the nation as a whole. Even more interesting: From 1999 to 2004, California’s work force only grew by 2.9 percent while home prices rose 103 percent. Compare that to the boom years of 1995-2000, when the work force expanded by 17 percent yet home prices rose only 47 percent.
The last point of course again gets back to Wolk’s confusion about the role of low mortgage rates as the dominant factor in the aggregate time-series trend. But after this diversion Wolk returns to his main theme:
The same disconnect can be seen over and over again. In New Jersey, New York and Connecticut, home prices rose an average of 13 to 16 percent over the 12 months ending March 31, a bit better than the national average of 12.5 percent, a near-record rate. Yet job growth in all three states was well below average last year– New York state added only 80,000 jobs, or 1 percent of its work force.
I suppose it is valid and often useful to be reminded that there are always exceptions to any statistical generalization, but this is the kind of argument that can drive a statistician nuts. The question is not whether some states do fit the pattern and some don’t, but rather whether there is any overall statistical tendency that could be used to summarize the combined inference from all 50 states taken together.
One standard way to do this is with statistical regression analysis. I used the data
(represented by hi) for state i’s change in house prices between 2000 and 2005 from
Office of Federal Housing Enterprise Oversight and calculated the logarithmic growth rate of nonfarm employment (represented by ei) for that state between March 2000 and March 2005. The regression estimates are as follows (t-statistics in parentheses):
The raw data along with the fitted regression relation are plotted on the right. One
standard method used to assess whether there is a systematic relation between these two
variables is to ask, if there was really no relation at all between these variables, what is the probability of observing a sample with the degree of correlation found in the data? This probability turns out to be 0.003. Most statisticians would summarize such a relation as highly statistically significant.
Another way such a relation is sometimes summarized is with the regression’s R2,
which is the fraction of the variance of house price increases across states that the regression is able to explain. In this case, the R2 of 17% means that more than 80% of the variance in housing appreciation across states would come from something other than employment differences. Or, another way to describe what this means is the way that Wolk in fact does– you can find lots of examples of states that don’t fit the pattern, and even for states that the pattern does describe (for example, Montana and Nevada), the difference is far from the exact number you’d predict from the relation.
How high an R2 should we have expected from Bernanke’s statement? There are
obviously serious problems with trying to summarize community-by-community differences at a state-wide level, and employment differences are just one of five factors he mentioned that would vary across communities, along with home ownership rates, population growth rates, income growth rates, and housing supply. Perhaps Bernanke’s critics want to insist he report his R2 whenever he makes a statement like, “states exhibiting higher rates of job growth also tend to have experienced greater appreciation in house prices”.
In fact, I would argue that the huge differences across communities in the rate of housing appreciation are much more of an embarrassment for Bernanke’s critics than they are for him. Those challenging Bernanke’s interpretation are forced to suggest that there are hundreds of separate little bubblets, expanding in different communities at curiously different rates. And if you claimed that those differences had nothing at all to do with economic fundamentals, the statistical significance of the regression we just analyzed establishes that your story is pretty conclusively rejected by a statistical analysis of the data.
So, if in fact you do acknowledge that the differences in housing appreciation across
communities are at least in part explained by economic fundamentals, how would you articulate your belief? Maybe with a statement such as
While speculative behavior appears to be surfacing in some local markets, strong economic fundamentals are contributing importantly to the housing boom.