Feldstein’s Deceptive Statistics

According to Martin Feldstein, writing in today’s (Monday) Wall Street Journal (in an op-ed piece cited variously by Greg Mankiw, Brad DeLong, Mark Thoma, and William Polley, among undoubtedly many others):

The result of the slower productivity growth and rising compensation per hour (from a 4% rate in 2003 to 5.1% in 2005) caused the increase in unit labor costs to accelerate from 1.3% in 2003 to 2.1% in 2004 and 2.8% in 2005.

These numbers don’t quite agree with what I just downloaded from the BLS, but they tell roughly the same story if you take them at face value. Unfortunately, the face value is deceptive. As best I can tell, these numbers compare annual aggregates from one year to the next. If you look more closely and examine the quarterly data, the story they tell is very different.

In the third quarter of 2003, there was a dramatic and unexpected increase in productivity. Unit labor costs fell by about 4% in one quarter, which depressed their growth rate for both 2003 and 2004, if you compare each annual aggregate to the previous year. In the third and fourth quarters of 2004, there were dramatic increases in hourly compensation, which appear to be the result of a combination of rising benefit costs and a shift in employment toward higher paying jobs. These increases in hourly compensation exaggerated the growth rate of unit labor costs for 2005, as compared to 2004.

If you look at unit labor costs on a fourth-quarter-to-fourth-quarter basis, rather than a year-to-year basis, the pattern of acceleration is revealed as a statistical illusion. The growth rate was about 0.3% in 2003, about 3.5% in 2004, and about 0.3% in 2005.

Of course, the right way to analyze these data is neither by comparing years to years nor by comparing fourth quarters to fourth quarters, but by smoothing the quarterly data over time to extract an estimate of the general trend. Any reasonable smoothing procedure (such as the one I used in the previous post) will show that there is no clear pattern of acceleration. (Possibly that will change with tomorrow’s revisions, but I doubt the change will be dramatic.) There are plenty of reasons to worry about inflation in the prices of goods and services, but as of this afternoon, there is still no reason to worry about inflation in labor costs.