Historical Patterns, Okun's Law, and the Great Recession

Arin Dube shows that estimates of Okun's law are inconsistent with the assertion that most of the unemployment problem is structural rather than cyclical:

Historical Patterns, Okun's Law, and the Great Recession, by Arin Dube: After reading Paul Krugman's post today, I decided to follow up by actually estimating out-of-sample unemployment rate change forecasts during the Great Recession based on a pre-2007 Okun's law relationship (i.e., a regression of change in the unemployment rate on percentage change in real GDP).

As a starting point, let's estimate the pre-2007 Okun's Law relationship using data from 1948 to 2006. (I use 2007 instead of 2008 just because the unemployment rate started rising in 2007 - but as you will see, this makes no real difference for any of the conclusions below.)

As expected, it shows that you need GDP growth above 2 percent or so to bring down the unemployment rate.

So what happens if we use this historical Okun's law to predict unemployment rate changes in the 2007-2011 period? In the next graph I plot the actual unemployment change by quarter with the predicted amount. The red line is just the 45 degree line to help us see what the actual change in unemployment would be if it behaved exactly according to the historical Okun's Law relationship. (The labels are a little bit off here: "01jan2010" really means "2010q1," "01apr2010" means "2010q2," etc.) I think this chart shows quite clearly what's going on:

Several things jump out:

1. First of all, note that over this period, during 9 quarters the historical forecast underpredicted the change in the unemployment rate, while during 8 quarters it overpredicted it. The forecast error ranged from -0.85 to 0.73, with a mean of 0.03. So there is absolutely no evidence that the unemployment rate stands at a much higher level than would be predicted by movements in GDP.

2. In fact, during the past 6 quarters, the actual reduction in unemployment rate has been greater than what would be predicted by real GDP growth--i.e., the forecast errors have been negative.

3. However, it is also the case that during the initial downturn (especially 2008-2009), the unemployment change was greater than would have been predicted by GDP reduction - i.e., positive forecast errors. (You can also see that the inclusion of 2007 makes very little difference here - as those data points are quite close to the predictions.)

4. Overall, the main conclusion is that based on a historical Okun's Law and actual GDP growth, at least as of 2011q1, both the initial rise in unemployment and the subsequent reduction had been more amplified. This not the signature of structural unemployment. A structural unemployment scenario would show an asymmetry: a growth in unemployment that is near or even above the norm based on GDP slowdown, but a reduction in unemployment that is muted in comparison to the GDP growth. This is not what we see. The point is made even more sharply in the next graph which simply plots the same red 45 degree line along with the in-sample linear fit (with data from 2007 forward).

The blue in-sample linear regression line has a slope of around 1.96 - in other words, the sensitivity of the unemployment rate to GDP growth during the Great Recession seems to have been twice as large as compared to historical norms - and this is true both in the downturn and the "expansion." (Split sample regressions confirm this point, which is also clearly shown in the earlier scatterplot.)

Now what is behind the "excess sensitivity" of unemployment rate to GDP growth? This is indeed an interesting question - and deserves to be studied further. It's possible that financial accelerators played a role early on, and as the financial markets stabilized, this effect unwound - leaving (normal) aggregate demand as the main constraint. This of course is just speculation, and I myself have some doubts about this story. However, what is not in question is that growth has been anemic, and that this anemic growth can more than explain the unemployment trajectory during the "expansion." Structural unemployment? Not so much. Reality-sensitive economists (and dare we say politicians?) should digest this simple fact.

Data Source: http://www.stlouisfed.org/
The two data series are UNRATE and GDPC1