Everything you know about Labor Share is wrong

9:44 AM: Hey, I found this on my Test & Development blog, dated January 2020. But I don't find it on this blog, so I'm posting it now. It's like getting one for free.

Is it too early for a sip of single malt?

Ever since Kaldor (1957, 1961) documented his growth facts, the constancy of the share of income that flows to labor has been taken to be one of the quintessential stylized facts of macroeconomics.

-- Michael Elsby et al

If you want to compare one year's GDP to another to see how the size of the economy has changed, it is necessary to use inflation-adjusted values. If you want to see changes in the size of the economy, it is necessary to distinguish between changes in size and changes in the unit of measurement.

But what if you want consider the change in size of some portion of GDP? For example, labor's share of GDP: Would you still want to use inflation-adjusted values? Just thinking about it, here, as an alternative you could look at a ratio of values that are not adjusted for inflation. Inflation cancels itself out of the ratio, and you end up with the equivalent of an "inflation-adjusted" comparison.

Here is the ratio of Compensation of Employees to Gross Domestic Income -- which should look a lot like a graph of labor share:

Graph #1: Compensation of Employees as a Percent of Gross Domestic Income

Something is fishy, though. Graph #1 doesn't look much like this graph of Labor Share:

Note, 3 October 22: One is labor share of business sector output, and the other is labor share of GDI. This could explain why the graphs look different.

Graph #2: Business Sector: Labor Share  (Source: BLS)

The first graph shows one downtrend from 1953 to 2014. The second displays a gradual downward trend from the mid-1950s to the mid-90s, then rapid downward trend from 2001 to 2012.

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What do experts say about the path of labor share?

• "A detailed description of labor's share of national income in 16 industrialized democracies from 1960 to 2005 uncovers two long-term trends: an increase in labor's share in the aftermath of World War II, followed by a decrease since the early 1980s." -- Tali Kristal
• "Over the past quarter century, labor’s share of income in the United States has trended downward, reaching its lowest level in the postwar period after the Great Recession." -- Michael Elsby et al
• "Figure 1 shows the ... slow and steady decline during the latter half of the 20th century—followed by the sharper decline over the 15 years since then" -- BLS
• "... the BLS measure has a much stronger long-run downward trend than the measure we use." -- EPI [EPI's Figure 2 show uptrend from 1947 to the early 1990s, then downtrend comparable to BLS.]
• "The fall of labor’s share of GDP in the United States and many other countries in recent decades is well documented but its causes remain uncertain." -- David Autor et al

Tabulated comparison:

Kristal:	Increase before 1980	Decrease since the early '80s
Elsby:		Decrease since the late 1980s
BLS:	Slow decrease 1947-2000	Rapid decrease 2001-2016
EPI:	Moderate increase 1947-1990	Rapid decrease 1992-
Autor:		Decrease "in recent decades"

It's difficult to pin 'em down, but there doesn't seem to be a lot of agreement. And none of them agree with Graph #1 above. However, there is a point of similarity: All of these studies find a sharp decline beginning in the 1980s or later, as we see on Graph #2.

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I discovered quite by accident that you can duplicate Labor Share for the business sector by taking the ratio of compensation to current dollar output:

Graph #3: Compensation relative to Nominal Output, (red) and Labor Share (blue)

 

 

It is a ratio of nominals that looks exactly like Labor Share.

Just for the heck of it, let's see what it looks like as a ratio of reals. Actually, I looked at this before. I don't remember why. Maybe it didn't occur to me that the ratio of reals should be the same as the ratio of nominals. Anyway, let's do it again.

FRED has the output number. I can use Business Sector: Real Output in place of Business Sector: Current Dollar Output. But I don't find an inflation-adjusted versions of Business Sector: Compensation. Have to make one.

Conveniently, FRED provides Business Sector: Real Compensation Per Hour and Business Sector: Compensation Per Hour. The one relative to the other makes a price index -- the perfect price index to use for deflating compensation.

Here is Business Sector: Labor Share as a ratio of reals:

Graph #4: Business Sector Labor Share as a Ratio of Reals

It's all downhill from the mid-1950s. No sharp decline starting in the early '80s, or the late '80s or the early '90s or the early 2000s. It's all downhill since Kaldor. Sharp downhill.

It's interesting also that the big, jagged movements have disappeared from Graph #4.

The only thing different about the calculation of graph #4 is that it uses inflation-adjusted values. Nothing else in the calculation has changed. So the graph is different because it is a ratio of reals.

But if the Compensation price index was the same as the Output price index, graph #4 would have come out exactly like the Labor Share graph, graph #2. Graph #4 is different because the price indexes are different.

Is it reasonable to have different price indexes for different things? Probably, yeah.

Okay.

Since we have these different price indexes for a reason, it must be okay to use them when the need arises.

When does the need arise? The need arises when you're looking at a ratio of nominals -- a ratio such as Labor Share -- where each data series has its own price index.

If you don't go with the ratio of reals, your graph will be incorrect. If you just assume that inflation cancels itself out of a ratio of nominals, but there are two different price indexes involved, your graph will be incorrect.

If no one uses the ratio of reals when they figure Labor Share, then everyone is wrong. No, no that's not true. The ratio of nominals is valid for micro or for the individual firm. But it is not valid as a macroeconomic evaluation.

In the world of macro, using the ratio of reals, it turns out that Labor Share has fallen faster and farther than we thought.

Okay, go back to your television now.