John Cochrane weighs in on the discussion of unit roots:
Unit roots, redux: Arnold Kling's askblog and Roger Farmer have a little exchange on GDP and unit roots. My two cents here.
I did a lot of work on this topic a long time ago, in How Big is the Random Walk in GNP? (the first one) Permanent and Transitory Components of GNP and Stock Prices” (The last, and I think best one) "Multivariate estimates" with Argia Sbordone, and "A critique of the application of unit root tests", particularly appropriate to Roger's battery of tests.
The conclusions, which I still think hold up today:
Log GDP has both random walk and stationary components. Consumption is a pretty good indicator of the random walk component. This is also what the standard stochastic growth model predicts: a random walk technology shock induces a random walk component in output but there are transitory dynamics around that value.
A linear trend in GDP is only visible ex-post, like a "bull" or "bear" market. It's not "wrong" to detrend GDP, but it is wrong to forecast that GDP will return to the linear trend or to take too seriously correlations of linearly detrended series, as Arnold mentions. Treating macro series as cointegrated with one common trend is a better idea.
Log stock prices have random walk and stationary components. Dividends are a pretty good indicator of the random walk component. (Most recently, here.) ...
Both Arnold and Roger claim that unemployment has a unit root. Guys, you must be kidding. ...
He goes on to explain.