Saturday, October 6, 2012

"Unit Labor Cost" definitions on the BEA website (1)

Response to a comment on the 4AM post.

Under Composition of GPO in the article "Gross Product by Industry, 1995–97" at BEA we read:

For the total economy, the share of GDP accounted for by compensation of employees decreased slightly, from 58.4 percent in 1992 to 57.8 percent in 1997

At FRED, the "Nonfarm Business Sector: Unit Labor Cost" graph shows an increase during that period (from 83.5% of the 2005 value, to about 89.9% of the 2005 value).

As defined by yourdictionary.com, Unit Labor Cost is "calculated by dividing total labor compensation (including benefits) by real output."

The YourDictionary phrase "total labor compensation (including benefits)" is equivalent to the BEA article's phrase "compensation of employees". Substituting the BEA phrase into the YourDictionary definition, we have this:

Unit Labor Cost is calculated by dividing compensation of employees by real output.

That looks like this:

However, RGDP is not something that occurs naturally in nature. What occurs naturally is NGDP, Nominal GDP, which is output valued at actual prices, the prices we paid to buy the stuff we bought. To get NGDP, all you have to do is add up the relevant spending. No calculation beyond that is required.

RGDP, by contrast, is a calculated value. One may attempt to count the number of homes built this year, and the number of automobiles, and the number of egg sandwiches sold, and cups of coffee, and everything else we produce in our multi-trillion-dollar economy. And one may attempt to count the number of everything produced the previous year. And one may then compare quantities, item by item, to determine how many more homes this year than last, how many more cars this year than last, how many more egg sandwiches this year than last, how many more cups of coffee...

And when you are done making these comparisons, you still have somehow to integrate all of these many and various growth comparisons into one number that rigorously indicates how much larger the economy is this year, as compared to last year.

RGDP is not a naturally occurring number. It is calculated.

The Cautionary Box article from BEA states: "As a convenience for data users, BEA also prepares dollar-denominated real output series". These numbers are also calculated. This is the relation between real and nominal GDP:

We can substitute this definition of RGDP into the ULC formula above, thus:

Or we can express it this way:

Then, to divide by a fraction, invert and multiply:

We can re-arrange that formula to show that Unit Labor Cost is the ratio "Compensation of Employees relative to Nominal GDP" multiplied by prices:

Unit Labor Cost takes labor cost in current dollars as a share of GDP in current dollars, and multiplies this ratio by prices. This is the only reason that the Unit Labor Cost numbers so closely follow the price numbers.

Current dollars are actual dollars, the ones in our pockets. The ones we spend.

Unit Labor Cost takes labor cost in actual dollars as a share of GDP in actual dollars, and multiplies this ratio by prices. This is the only reason that the Unit Labor Cost numbers so closely follow the price numbers.