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An Elusive Relation between Unemployment and GDP Growth: Okun’s Law

The unemployment rate fell from 9.1 percent to 8.3 in 2011, but real GDP grew only 1.6 percent. That is much lower than its average growth of 2.6 percent since 1985. The slow GDP growth has led some observers to question how sustainable the recent improvement in the labor market is. Implicit in this suspicion is the idea that the unemployment rate can improve only so much given the modest growth of economic activity. This idea is based on an empirical relationship sometimes referred to as Okun’s law, which is essentially a simple rule of thumb that associates the growth rate in real GDP to changes in the unemployment rate observed around the same time.

We argue that the pace of improvement in the labor market (as measured by the unemployment rate) is, to a large extent, consistent with the pace of the recovery in GDP.  Looking at the relationship between these two macro variables in slightly different ways shows that, if anything, the recession had a larger impact on unemployment than one might have anticipated, and what we’re seeing during the recovery is not necessarily puzzling.

A simple version of Okun’s law regresses the change in the unemployment rate over a period in time (usually a quarter, or in the picture below, a year) on a constant and the change in real GDP growth over the same period. If we just look at the data from 1990 forward, 2009 and 2011 look somewhat remarkable. In 2009, the unemployment rate jumped up 3.0 percentage points despite just a 0.5 percent decline in real GDP, well above the roughly 1.2 percentage point increase implied by Okun’s law. Skipping over 2010 (which wasn’t too far off the regression line), 2011 was unusual in the opposite direction; output growth increased 1.6 percent while the unemployment rate fell a mere 0.9 percentage point, even though according to Okun’s law, it should have posted a modest increase.

Okun's Law,, 1990-2011

Some analysts suggest that 2011 was a “catch-up” year; they argue that in 2009 firms shed far more workers than necessary (perhaps fearing a further deterioration in the outlook), but once the outlook appeared to be a little brighter, firms started bringing their employment levels back in line with expected growth. While this may be the case, looking at the Okun’s law relationship over a longer period of time makes 2009 and 2011 appear to be less unusual. This leaves open the possibility that these deviations are just noise.

Okun's Law, 1948-2011

However, if we look at another version of Okun’s law, which relates the annual growth rate of GDP over the past year and the associated change in unemployment rate at quarterly frequency since 1970, these years stand out in a different way. There have been many instances over the last five years when the predicted unemployment-rate change was significantly above or below the simple line that represents Okun’s law.  What is more striking is that in six out of ten quarters since the recovery started (through the fourth quarter of 2011), growth rates were below the sample average of 2.6 percent. If anything, the pace of the recovery as measured by output has been very anemic.

Okun's Law, 1970:Q1-2011:Q4

This is not the first time that the behavior of the unemployment rate during the Great Recession and subsequent recovery has puzzled analysts. Over the course of the recession, especially toward the end of 2008 and the first two quarters of 2009, unemployment increased sharply to levels not seen since the 1980s. At the time, we thought the aggregate economy had contracted 3.6 percent over the course of the recession from its pre-recession peak, so the huge jump in the unemployment rate—from 5 percent to 9.5 percent—seemed way out of line. Later, when government agencies revised their estimates of GDP, the true severity of the output loss during the recession was realized. It turns out the the economy contracted 5.1 percent during the downturn, the largest decline in postwar history. In an unfortunate way, this made the recession more consistent with historical patterns. Similarly, part of the puzzle of 2011 (based on the first figure above) might be resolved as we get revised data on GDP in the future, though we think this is not as likely.

After the recession officially ended, the unemployment rate remained high, above 9 percent, for 22 consecutive months. Again, this very small improvement was puzzling to some. However, as we argued elsewhere, unemployment usually lags the economic cycle. Thus we need to look at a longer time span to gauge the cumulative effect of output growth on unemployment. To do this, we compute the overall growth rate of GDP from its recession trough through 10 quarters of the recovery for all postwar recovery episodes and compare it to the unemployment-rate improvement over the same time interval. This exercise produces the following chart, which shows that the fall in the unemployment rate in the current cycle is explained very well by the growth in output. The current recovery lies right along the estimated regression line. So the relatively modest improvement in the unemployment rate can be closely linked to the recovery in output. Relatively weak output growth in fact seems to be a feature of all the recent “jobless” recoveries.

Recovery in Real GDP and Unemployment

It is also important to recognize that Okun’s law is just an empirical relationship. It may not necessarily reflect a structural link between output growth and the unemployment rate.  Moreover, the relationship might change over time as the dynamics of the labor market change.

For instance, one version of Okun’s law suggests that the relationship between unemployment and GDP gets very tight when the growth rate of output is above its potential. However, looking at the data over the last 40 years suggests that there may be some asymmetry in the relationship over the business cycle.  Even though empirically there seems to be a strong correlation between output growth when it is below potential and increases in the unemployment rate, this relationship disappears when output is growing above potential.

Okun's Law—Deviations from Potential

Part of the explanation for this effect has to do with the fact that we will always have some level of unemployment even in good times, due to natural churning in the labor market. As the economy goes through a long expansion, unemployment will stabilize at this lower level, and additional growth may not necessarily generate additional reductions in the unemployment rate. The upshot is that the rate may not go below that level. As a result, further output growth will not necessarily manifest itself as a further decline in the unemployment rate.

To sum up, it seems intuitive to think there is a natural, robust relationship between changes in unemployment and changes in output. However, what exact form it takes is a complicated problem that requires going beyond the simple rule of thumb given by Okun’s law.

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