Sunday, January 9, 2011

Revisiting Greg Mankiw and the Unit Root Hypothesis

I saw the graph above at American Thinker and realized that it was time to revisit a hypothesis of my favorite Keynesian economist: Greg Mankiw. First, here's what I see in the graph above. You've got the economy, pre-2008 adding about a million jobs a year. Then the economy sheds jobs from about 2008 to 2010. Finally, it looks like 2010 saw the addition of about a million employees with a little bump tapering out that represents hiring temporary workers for the census.

On March 3rd, 2009, Greg Mankiw blogged Team Obama and the Unit Root Hypothesis. Mankiw's post was inspired by the following in the CEA's forecast analysis:
a key fact is that recessions are followed by rebounds. Indeed, if periods of lower-than-normal growth were not followed by periods of higher-than-normal growth, the unemployment rate would never return to normal.
Mankiw's summary follows:
That is, according to the CEA, because we are now experiencing below-average growth, we should raise our growth forecast in the future to put the economy back on trend in the long run. In the language of time-series econometrics, the CEA is premising its forecast on the economy being trend stationary.
In other words, the assumptions of the Obama administration as it took office were that after the economic downturn the economy would return to pre-recession levels. I should note that the original debate focused on GDP, while the graph above is one of employment. Mankiw cites a paper that he co-authored that disputes this view and introduces the unit root hypothesis:
According to the conventional view of the business cycle, fluctuations in output represent temporary deviations from trend. The purpose of this paper is to question this conventional view. If fluctuations in output are dominated by temporary deviations from the natural rate of output, then an unexpected change in output today should not substantially change one's forecast of output in, say, five or ten years. Our examination of quarterly postwar United States data leads us to be skeptical about this implication. The data suggest that an unexpected change in real GNP of 1 percent should change one's forecast by over 1 percent over a long horizon.
Wikipedia notes the debate and provides a wonderful graph to illustrate it with the following explanation:
The diagram above depicts an example of a potential unit root. The red line represents an observed drop in output. Green shows the path of recovery if the series has a unit root. Blue shows the recovery if there is no unit root and the series is trend stationary. The blue line returns to meet and follow the dashed trend line while the green line remains permanently below the trend. The unit root hypothesis also holds that a spike in output will lead to levels of output higher than the past trend.
In other words, Delong and Krugman argue for the blue line while Mankiw is suggesting the green. Another caveat: to the extent that there's any recovery, it's only a year old and everyone in the debate at the time (including Paul Krugman and Brad Delong) was looking at longer time horizons. It's too early to say whether there's been a permanent net loss of 10 million jobs—if the 2006 to 2008 trend had continued to 2010, then there would've been about 140 million workers instead of 130 million.

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