## Sunday, December 17, 2017

### Labor share: Where do they get those numbers?

So I can answer a question that's been in the back of my mind for a long time now.

Why is labor share more than 100%?

It's not percent, Art. It's an index.

Yeah I know. But how did it get so high? It's useless. It tells me labor share is going down, but it doesn't tell me what the share is, the share that labor gets. It should be a percentage. It's not, I know, but it should be.

So where do they get those numbers?

Labor share, as I learned a couple days ago, is calculated by taking compensation as a percent of current-dollar output.

It is a percentage -- see? I was right. It has to be a percentage.

But the thing is, it takes one set of indexed values as a percent of another set of indexed values. Indexed values are not the actual values. Indexed values are like a price index (duh, Art). They pick one year to be the base year, and they figure all the values as a percent of the base year value. So right away when they do that, the actual values are gone. You get a line on a graph that is the exact same shape you get from the original values, but the whole shape has been moved up or down until the base year value is equal to 100.

Seems harmless, right? Except of course the original numbers are gone. So you cannot look at labor share and find compensation as a percent of current dollar output, because you don't have those numbers anymore.

The name "labor share" sounds like it would give you compensation as a percent of current dollar output. But it doesn't work that way. When they pick a year to be the base year, something they do again every few years, they pick a date from the recent past. An arbitrary choice, let's say. Then they re-figure the data for all the years so that the new base year gets the value 100. All the numbers get changed.

One thing that's for sure is that the base year value is 100. If you have two data sets like compensation and current-dollar output, you can be sure that when you plot them on a graph, the two lines will cross in the base year. Because both data sets have the value 100 for the base year.

I don't know what compensation is, as a percent of current-dollar output. Maybe it's 80%. Maybe it's six. But I know for sure that compensation is going to be 100% of current-dollar output in the base year of a graph, because the numbers are indexed and the base year values are equal.

It's ridiculous to think that compensation and output are equal. That would mean labor share is 100% and capital share is zero, and I'm sure that's not the case. But that's all we can get from the indexed series called "labor share". That's all we can get even if we go back to the data that is used to calculate labor share, because that data is indexed, too.

So anyway, we know that labor share is compensation as a percent of current-dollar output, except the two lines cross at the 100 level in the base year. We also know that labor share has been going downhill for a long time.

Labor share goes downhill for a long time, and then the lines cross at the 100 level. So that means labor share has to be higher than the 100 level in the years before the base year. And sure enough, it is.

The Arthurian said...

From BLS:

Footnote 8: 'See “LPC databases,” Labor productivity and costs (U.S. Bureau of Labor Statistics), https://www.bls.gov/lpc/data.htm. Click the link that says, “Download the complete Major Sector Productivity and Costs dataset.” A zip file that contains the annual and quarterly datasets will open. This is the sole location on the BLS website where data on labor share levels can be found: the other data search tools on the Productivity and Costs homepage supply only percent-change and index data.' (my bold)

This BLS article is a gold mine!