## Monday, December 18, 2017

### Exploring labor share

To figure labor share they take compensation, divide it by current dollar output, and multiply by 100.

This is what labor share looks like:

 Graph #1: Labor Share (red) and the Calculation that produces it (blue)
Pretty, huh. Except it's going downhill. But hey, you ain't seen nothin yet.

I got onto this topic a few days ago after looking at productivity and compensation. Productivity is output per hour worked. It is a way to evaluate economic growth. Because it is a way to look at growth, the "output" number has to have the inflation component removed. Otherwise, if prices are changing, you get a false reading of how much the output component actually changed.

Hours are hours. Inflation doesn't make the "hours worked" number different. But compensation is money. If we are using real output to figure productivity, and we are comparing it to compensation, then the compensation number also has to have the inflation component removed. Otherwise, inflation distorts the result.

But you don't always have to remove the inflation component. Labor share, for example, is not a measure of economic growth. So it is okay to leave inflation in the numbers used to calculate labor share, as long as you leave it in both compensation and output.

FRED uses the words "current dollar output" in Graph #1, to make it explicit that the data is a "nominal" series and the inflation component has not been removed. Compensation, the other series used in the calculation, is also nominal. The version of that series that has the inflation component removed would be called "real compensation" if FRED had that series. (They do have "real compensation per hour" data sets.)

Anyway, I started out looking at productivity and compensation, where inflation-adjusted data is used. Then I changed to nominal (inflating) data and discovered that compensation relative to output gives me labor share.

So now I'm looking at labor share, and I want to see how it looks if I use inflation-adjusted data for the calculation. I still can't find a "Business Sector: Real Compensation" series at FRED, but I can make one. I can take their "Real Compensation per Hour" series and divide it by "Compensation per Hour" to get a price index for the compensation data, then multiply by Compensation to get Real Compensation.

Hours cancels hours, comp cancels comp, and what remains is real compensation.

Then divide that by Real Output to get the inflation-adjusted version of Labor Share:

 Graph #2: "Real" (Inflation-Adjusted) Labor Share, calculated as ((Business Sector: Real Compensation Per Hour / Business Sector: Compensation Per Hour) * Business Sector: Compensation) / Business Sector: Real Output
You were looking for downhill? There's downhill for ya.

You can eyeball it and see that I got a value of 1.0 for the base year 2009. That's because I didn't multiply by 100 because, you know, you multiply by 100 to get percent, and labor share is definitely not percent. As we discussed the other day.

But I can multiply it by 100 to make my number compatible with FRED's labor share. Then I'll add FRED's series to the graph in red so we can compare the two:

 Graph #3: Labor Share (red) and "Real" Labor Share (blue)
Nice, huh? Now you can see what downhill really looks like.

The ratio of reals is not the same as the ratio of nominals because, in the business sector numbers, the inflation measures for compensation and for output are not the same.

Note that the two lines cross in the base year (2009) at the level 100. Or in that neighborhood; it's hard to see exactly.

But you know, this is why I hate those updates they do every few years, where they change the base year to a more recent date. Everything after the base year on Graph #3 is all bunched together. The blue is not any lower than the red, really, at the end, the years after 2009.

But it has to be lower, because it falls more. The graph is deceiving.

Yeah, now I sound like those guys that whine about how much value the dollar has lost since 1913. But you just don't get a good picture, when the base year is repeatedly changed to a more recent date. Maybe that's why those updates are done: to blur the picture and keep us confused. Oh Art, that's not a nice thing to say.

Maybe they do the updates because they are confused.

Sorry, that's as nice as it gets.

I'm going to index these two data sets using the data-start date as the base year. So they will start out, the two lines, together at the 100 level. And what happens after that, well, we'll see.

The start date for these data sets is January 1947. Back then, my dad was a young guy getting his start in the world, and I was still a couple years away from being born. The graph will show things from my dad's perspective, how things changed since that early point in his life.

The graph shows how "the greatest generation" got screwed. It shows a 50-year decline of labor share that could and should have been stopped somewhere along the way:

 Graph #4: Labor Share, nominal (red) and real (blue), Indexed to 1947 Q1
It's interesting, I think, that the "real" line (the blue line) suggests that the decline in labor share definitely started in 1961. Some people say the red line shows no decline until 1970.

Some say labor share was flat until around 2001. Those guys are 40 years off.

I spent a lot of time on this "real labor share" thing. I don't mean to suggest that labor share should be figured using inflation-adjusted quantities. I haven't yet had so much as a thought about that. I'm just looking, to see how things look.

The blue line shows a decline with a remarkably straight trend. That's gotta mean something. But again, I haven't yet had so much as a thought.