It's cheating, but nobody seems to notice.

From yesterday's post, Employee Compensation relative to GDP:

Graph #1: Employee Compensation as a Share of GDP

If Employee Compensation is falling, how can Unit Labor Costs be rising?

Graph #2: Comparing Employee Compensation as a Share of GDP (blue) to Unit Labor Cost (red)

It's because Unit Labor Cost is Employee Comp multiplied by the price level:

Graph #3:  Multiply "Employee Compensation as a Share of GDP" by the GDP Deflator
and it starts to look just like Unit Labor Cost

Oh, they're not so blatant about it, of course.

The calculation for Graph #3 is crude. You can see that the GDP deflator is multiplied in. The deflator is a measure of prices, so you can see that prices are multiplied in. That's crude. But you can rearrange the formula and still get the same graph:

Graph #4: Divide "Compensation of Employees" by "GDP divided by the GDP Deflator"
and we get the same picture as in Graph #3

In this version, we don't multiply prices into the "Employee Compensation/GDP" ratio. Instead we divide prices out of GDP, and divide Employee Compensation by the result.

But the calculations are equivalent, so Graph #4 looks just like Graph #3.

But once we have the formula arranged this way, you might notice that the denominator, the Nominal GDP divided by GDP deflator part, is the calculation that gives what economists call "Real GDP". So you can use that instead:

It's shorter and cleaner, and it has the word "real" in it so everybody likes it. When you make the graph using Real GDP, it still looks just like Graph #3 and Graph #4:

Graph #5: Divide "Compensation of Employees" by "Real GDP" and we get the same picture again
because Real GDP is equal to "nominal" (actual price) GDP divided by the GDP Deflator

It's still the same picture. It's still the same calculation. It still has prices factored in, but now not even an economist can see it.

They'll tell you they are dividing by real GDP you know, but there is no such thing. Oh, the cars are real, and the houses, and the cups of coffee in the morning, those are very real, and the apples, and the oranges. All of it, all the pieces are real. But it's all apples and oranges. You can't add the values of all those things together, na, na, na, you can't figure the values of all those things in prices that never go up without doing complex calculations based on actual GDP, the so-called "nominal" GDP I mean, and the changes in prices.

There is no real GDP. There is only nominal GDP, actual GDP at actual prices. After that, it's all calculation. When they tell you they are dividing by real GDP, they are really dividing by estimates of actual GDP with price changes stripped away. Oh, they may have a series of numbers that's called "Real Gross Domestic Product" all right. And they may have incomprehensible stories about how real GDP is calculated. But if you factor price changes into their numbers you get "nominal" GDP. And if you take actual GDP and factor price changes out of it, you get their so-called "real" numbers.

No matter how you slice it, if you are dividing by "real GDP", you will get exactly the same result if you divide by actual GDP and factor price changes into the result. And the thing is, actual GDP is the actual one. "Real" GDP isn't.

They take numbers like Employee Compensation going down relative to GDP. They times it by prices to make the numbers go up. They say Look, look! Labor costs are going up! And they claim that rising labor costs are pushing prices up.

It's cheating, but nobody seems to notice.

Kaminska and Unit Labor Cost

Another look at the FT post we considered yesterday.

Izzy Kaminska is poking around, trying to explain what the economy is doing. Her discussion starts with a review of several unsatisfying explanations for the excellent productivity of the late 1990s in the U.S. economy. But that excellent productivity long since expired, and Kaminska ends up trying to explain the very bad economic recovery of the present day.

She seems to think Alan Greenspan's original explanation -- technology -- is now working in reverse, undermining jobs instead of creating them.

She shows some graphs to make her case. One of those graphs is the Unit Labor Cost graph. It is the reason we come back to Kaminska for this post. She writes:

unit labour costs — the labour cost attached to the production of one unit — are staying positively muted

She shows a FRED graph:

Graph 1: The Unit Labor Cost scam

The "positively muted" remark refers to recent data at the right end of the plot, where at first glance the blue line seems to be running flat rather than rising. At second glance, however, the line isn't running flat. It went down a bit during the recession, but it has been going up since the recession. And if you look a third time, it appears that the "going up" part is going up at about the same rate as the "going up" that was going on for 20 years before that recession.

So I don't know what Kaminska's talking about. Whatever it is that the Unit Labor Cost graph shows, it is going up now just like it was going up before the Great Recession.


What does it show?

Kaminska seems to think the graph shows labor cost. How does she describe it? "The labour cost attached to the production of one unit". Oh right, right: "One unit".

As I showed the other day, the Unit Labor Cost plot is almost identical to the price level plot:

Graph #2: Unit Labor Cost (blue) and the price level (red)

The similarity between ULC and the price level is so remarkable as to inspire disbelief. And well it should, for the red line is used to calculate the blue line. To calculate Unit Labor Cost, labor costs are multiplied by prices.

And then the graph is used to claim that Labor cost makes prices go up.

To use the Unit Labor Cost graph is to say

INFLATION times X looks like INFLATION, so X is the cause of INFLATION
The price number series is used to calculate Unit Labor Cost. But if you take the price number out of the labor number, you see that the labor number is just going down, relative to GDP:

Graph #3: Total Labor Compensation (including benefits) relative to GDP
(Index 2005=100)
Click graph for FRED source page

Again: The labor number is going down. The labor number multiplied by prices is going up. And the labor number, multiplied by prices, is used to support the claim that the labor number is what makes prices go up.

The graph is worse than worthless. It's fraudulent.


Related posts:
Unit Labor Cost
The Uses of Fake GDP (2): Unit Labor Cost
No Matter What the Red Line Does
The Fraudulent Use of Arithmetic

The Fraudulent Use of Arithmetic

Just about a year ago I considered a post by Steve Randy Waldman:

I need another look at Steve Waldman's interesting layout of our economic problem:

"Prior to the 1980s, the marginal unit of CPI was purchased from wages... Prior to the 1980s, central bankers routinely had to choose between inflation or recession."

Then came the “Great Moderation”. The signal fact of the Great Moderation was that the marginal unit of CPI was purchased from asset-related wealth and consumer credit rather than from wages.

So in this view, the policy-change was a change from intermittent wage-suppression to continuous wage-suppression. It's a tidy thought, but that doesn't make it right.

I do not accept Waldman's tidy analysis. The Federal Reserve does not manage wages.

What Waldman was saying just didn't make sense to me, despite several attempts by himself and myself to make it make sense to me.

Time goes by.

My recent "Symmetry in Deception" series drawing to a close the other day, I Googled unit labor costs and turned up interfluidity » Restraining unit labor costs is a right-wing conspiracy, from half a year back.

Waldman opens thus:

In an otherwise excellent post, Matt Yglesias commits one of the deadly sins of monetary policy:

[M]y favorite indicator of inflation is “unit labor costs”… Unit labor costs are basically wages divided [by] productivity. It’s not the price of labor, in other words, but the price of labor output. If productivity is rising faster than wages, then even if wages themselves are rising unit labor costs are falling. Conversely, if wages rise faster than productivity than unit labor costs are going up...

That all sounds reasonable. But Yglesias has fallen into a trap. Unit labor costs are not “basically wages divided [by] productivity”. That’s not the right definition at all. Unit labor costs are nominal wages per unit of output. With a little bit of math, it’s easy to show that

UNIT_LABOR_COSTS = PRICE_LEVEL × LABOR_SHARE_OF_OUTPUT

An increase in unit labor costs can mean one of two things. It can reflect an increase in the price level — inflation — or it can reflect an increase in labor’s share of output.

I've omitted Waldman's "update", where he acknowledges that something like Yglesias's definition of Unit Labor Cost -- a one hour's wage version, I think -- may be correct.

Update omitted, Waldman's definition of ULC agrees with the YourDictionary definition, and with the OECD's definition. And with my definition, as created by YourDictionary and confirmed by OECD.

(Waldman refers to "nominal wages" as labor share. My accepted sources refer to total labor cost, or wages plus benefits, let us say. The confusion here is the same confusion described in Wikipedia: Compensation of employees, which I noted here. But Waldman is close enough, for now. That discrepancy is not my topic.)

Waldman writes: Unit labor costs are nominal wages per unit of output. "Nominal" means "at the prices actually paid, inflating though they be". "Output" is GDP with caveats: Often, the word "output" is used to mean "real output" or "real GDP" or "figured at prices that have been reduced to remove the effects of inflation". All too often, with the effects of inflation surreptitiously removed. Waldman points it out.

By Waldman's definition (and mine) Unit Labor Cost divides an inflating quantity by an inflation-adjusted quantity. Division by an inflation-adjusted quantity is a back-door, sneaky, deceptive way to bring inflation *INTO* the result of the calculation. Waldman points this out, too:

UNIT_LABOR_COSTS = PRICE_LEVEL × LABOR_SHARE_OF_OUTPUT

It is a very big deal.

Rule #1: Always be wary of the word "output". It is often found in bad arithmetic.


Waldman looks at his formula, notices that two things (the price level thing, and the labor share thing) go into Unit Labor Cost, and translates the math into English:

An increase in unit labor costs can mean one of two things. It can reflect an increase in the price level — inflation — or it can reflect an increase in labor’s share of output.

Yes.

But. Let me ask you this: What is Unit Labor Cost used for? Easy answer, just recall what Yglesias said, as quoted by Waldman:

[M]y favorite indicator of inflation is “unit labor costs”
Unit Labor Cost is used as an indicator of inflation.

Right.

Multiply inflation into Labor Share of Output, use the resulting numbers as an indicator of inflation, and when you see inflation in the numbers, blame Labor Share.

Again: Multiply inflation into the Labor number, feign to discover a similarity between inflation and the resulting number, and blame the Labor number for inflation!

Used in the denominator, the calculated value called "real output" -- often simply called "output" -- surreptitiously creates the appearance of similarity between inflation and the labor number. Refer to Rule #1.


Waldman's Unit Labor Cost post isn't really about ULC. Really, it is about the Fed's "direct suppression of labor’s share" -- same as his post that I reviewed a year ago. Funny thing is, in this post that made sense to me. This part sums it up:

For labor’s share to expand, either the price level must fall, or unit labor costs must rise faster than the price level. But the Fed responds aggressively to rising unit labor costs, and is committed to preventing any decrease in the price level. Under this policy regime, expansions in labor’s share are pretty difficult to come by!

Agreed.

Okay. But now that I've belatedly agreed with Steve Randy Waldman about the suppression of labor's share, now I feel free to disagree with him over ULC.

Waldman finds a bad definition of Unit Labor Cost, corrects the definition, and then evaluates it. Given that there are two factors (prices and labor's share) that go into ULC, Waldman expresses the relation clearly: "An increase in unit labor costs can mean one of two things..."

Yes, and I don't deny it. Given the formula for Unit Labor Cost, Waldman reaches the only conclusion that can reasonably be reached.

This is where I disagree with Waldman: Given the Unit Labor Cost formula, Waldman accepts that formula. I do not.

Waldman thinks of the ULC as economics to be evaluated. I see it as bad arithmetic, to be dismissed.

If the formula// no, wait.

We don't accept or reject formulas because we think they produce results we like or don't like. Rather, formulas are either valid or not, on their own merits.

If the formula is valid, we must accept it.

If the formula is not valid, we must not accept it.

The Unit Labor Cost formula is not valid -- not when ULC is used as an indicator of inflation. It is not valid because inflation is factored into the ULC numbers. On a graph, ULC appears similar to inflation because inflation is factored into the numbers. Any comparison of ULC to inflation is a fraudulent use of arithmetic.



The Unit Labor Cost formula factors the price trend into its results and allows us to discover that the results show similarity to the price trend. The logic is circular. The logic is not valid. The formula must be rejected.

Rule #2: If "real output" is in the denominator, reject first and ask questions later.

Symmetry in Deception: Similarities between "Unit Labor Cost" and "Money Relative to Output"

Consider the mathematical deception entangled in the "Unit Labor Cost" (ULC) calculation, and in the comparison of "money relative to output" (MRTO) to inflation. Both follow the same pattern:

1. Divide GDP by a price index to get a fraction called "real" GDP.
2. Use this fraction as the denominator of another fraction.
3. Compare the result to inflation, and find similarity.

The MRTO uses this formula: (M2) / (GDP/Prices)
The ULC uses this formula: (Total Labor Cost) / (GDP/Prices)

In both cases we divide by the fraction (GDP/Prices). The schoolboy's rule "To divide by a fraction, invert and multiply" tells us that:

The MRTO calculation in fact is (M2 / GDP) * Prices
The ULC calculation in fact is (Total Labor Cost / GDP) * Prices

In both cases a ratio is multiplied by prices, and the resulting numbers climb upward on a path comparable to the path of prices. (For "Prices", both use the GDP Deflator.) Without multiplying by Prices, neither ratio is similar to the trend of prices.

Milton Friedman's "Money relative to output" graphs compare the quantity of money to the "real GDP" ratio, show similarity to inflation, and are used as evidence that printing money causes inflation.

The "Unit Labor Cost" calculation compares Total Labor Cost to the "real GDP" ratio, shows similarity to inflation, and is used as evidence that rising labor costs are the cause of inflation.

These are fraudulent uses of arithmetic, and are not acceptable.

Unit Labor Cost