Knowledge of arithmetic is a skill in short supply for people involved in economic policy debates. This is especially the case for the Washington Post (Wonkblog excepted).

Neil Irwin gives us an example of the problem when he expresses the hope that increasing house prices will provide a large boost to consumption and thereby spur growth. Irwin cites a recent academic paper on the size of the housing wealth effect:

"In a paper last year, Charles Calomiris, Stanley Longhofer, and William Miles found that the wealth effects from housing vary significantly depending on whether the homeowner is old or young, poor or rich—but their overall estimate is that a dollar of extra housing wealth triggers five to eight cents in additional spending."

He then notes that with house prices rising by roughly $1 trillion this year, this would imply an increase in consumption of between $50 and $80 billion (0.3 to 0.5 percent of GDP).

So far, so good. The Calomiris, Longhofer, and Miles estimate of the wealth effect is certainly within the range of other estimates, although it is worth noting that about 40 percent of the gain in house prices last year could be attributable to inflation. In other words, if house prices had not risen by at least 2.0 percent last year, the real wealth effect on consumption would be lower in 2013 than in 2012. The gains in terms of consumption have to be adjusted accordingly.

But the real problem is when Irwin tells us:

"In the Great Recession, spending fell by even more than could be attributed solely to the wealth effects caused by falling home prices. A vicious cycle set in through which falling home prices contributed to people being underwater on their mortgages, which had an outsized impact on their spending. Research by Atif Mian, Kamalesh Rao, and Amir Sufi last year found that in counties with high degrees of household debt and home price declines, retail sales fell much more than elsewhere."

Hmm, spending fell by even more than could be attributed to the wealth effect. Let's check that one.

If we run over to the Fed's balance sheet tables (Table B100, Line 49), we find that at the end of 2005, near the peak of the bubble, households had $13.2 trillion in housing equity. This was roughly equal to GDP in 2006. Using the Calomiris et al. estimates of the wealth effect, this would imply that housing wealth in 2006 was boosting consumption by an amount equal to 5 to 8 percent of GDP.

If we go to the most recent Fed data, we find that housing equity was equal to $7.7 trillion at the end of the third quarter. We'll call that 50 percent of GDP. We should then expect to see a housing wealth effect on consumption equal to between 2.5 and 4 percent of GDP.

The drop in the size of the housing wealth effect on consumption is between 2.5 and 4.0 percentage points of GDP. If we go back to 2006 we see that consumption was equal to 69.6 percent of GDP ($9.3 trillion out of $13.4 trillion). Turning to the data for the first three quarters of 2012, we find that consumption is equal to 70.6 percent of GDP ($11.0 trillion out of $15.6 trillion). That seems to go the wrong way for Irwin's assertion that "spending fell by even more than could be attributed to the wealth effect."

It's true that disposable income has risen relative to GDP as a result of lower taxes, but even if we look at consumption relative to disposable income we can't find any evidence to support Irwin's assertion. In 2006 the saving rate was 2.6 percent. In the first three quarters of 2012 it averaged 3.7 percent. That's a rise of 1.1 percentage points. The Calomiris et al. estimates of the wealth effect would have predicted a 3.0-5.0 percentage rise in the saving rate, much more than we actually saw.

In short, there is zero evidence that consumption has fallen by more than would be expected given the estimate of the size of the wealth effect that Irwin uses in his piece. Therefore there is no reason to expect the "disproportionate positive effect on spending" that Irwin holds out as a hoped spur to growth as underwater homeowners again come above water.

See what arithmetic can bring to the analysis of economic policy?

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