Okun's Law

Brad DeLong (The Life and Strange Death of Okun's Law) writes (quoting from a piece of his from 2003):

We used to have considerable confidence in Okun's law: that an extra one percentage point rise (or fall) in the unemployment rate over a year would reduce (or boost) that real GDP growth by an extra 2.5 percent over that year because a rising (or falling) unemployment rate would also be accompanied by a falling (rising) share of the population in the labor force and by falling (rapidly rising) productivity. Productivity would fall when the unemployment rate rose for two reasons: first, even when factories are not running at full capacity they still incur substantial setup and maintenance costs; second, even when there isn't enough work for them to do firms would rather hold onto skilled workers than watch them drift away and have to pay to train their replacements the next time the wheel of the business cycle turns.

Things have been different, however, in this [2001] recession (and to a lesser extent in the preceding early-1990s recession...

Yes, as many commentators have noted, employment losses in this recession, as well as those of 2001 and 1990-91, have been out of proportion to the drop in output. DeLong points us to Groshen and Potter (2003) for an explanation pointing to structural change in labor markets (hey, Potter was my TA in graduate macro - he once took points off one of my homework assignments for "not having the courage of your convictions" - a propos of nothing).

Anyway, what DeLong and others seem not to have accounted for is the fact that since the 1970s at least unemployment always rises disproportionately to output losses at the end of recessions. Then fairly quickly during the recovery Okun's Law restores itself as the unemployment rate falls faster than would otherwise be predicted. In other words, Okun's Law's "strange death" always seems to be followed by a miraculous resurrection.

I demonstrate this using a slightly different formulation than that used by the CEA and DeLong. Take the Congressional Budget Office's measures of the natural rate of unemployment and potential output. Account for the fact that movements in unemployment tend to lag those of output by a quarter or so. Use an Okun's coefficient of 2 instead of 2.5 (turns out 2.5 applied to the 1970s, but the coefficient is closer to 2 for the 1980s-present). Let's predict the unemployment rate using

U = .5*(output gap) + natural rate

Then compute the difference between actual unemployment and the rate predicted as above. We get the following graph:


Note the regularity: at the end of the last 6 recessions, the unemployment rate was usually 0.5-1.0 percentage points higher than would be predicted by Okun's Law. Then during the recovery period, unemployment goes back to the level Okun would have predicted. For example, in 1982Q4, the trough of the 1981-82 recession, the unemployment rate stood at 10.7 percent whereas Okun's Law would have predicted a rate of 9.7 percent. There followed a period of extraordinary growth: the output gap fell by 5 percent from 1982Q3 to 1984Q1, which according to the rule should have reduced the unemployment rate by 2.5% to 8.1% by 1984Q2. It actually fell to 7.4%. So if history repeats itself today, we should see the unemployment rate falling by more than 1/2 percentage point for every 1 percentage point of excess output growth until eventually the unemployment rate is in line with the output gap. Specifically, we've got 1.4 percentage points of unemployment that should melt away even without excess output growth - whether that happens in one year or more is anyone's guess, but I believe in Okun's Law so I believe it will happen eventually.

That's not to say that there has been no structural change since the 1980s. Growth in employment and decline in unemployment now follows recovery of output by a quarter or two, whereas in the 70s and 80s employment rose and unemployment fell immediately once output started growing. But the main reason the unemployment rate was stubbornly high after the 1990-91 and 2001 recessions was not because of structural change, but because of slow output growth.