Ed Lambert's "UT" Graph

I hope it's okay I call him Ed.

Graph #1: Edward Lambert's UT Graph
Click Graph for FRED Source Page

Steve Roth says UT stands for “Unused Total”. Roth shows the graph of UT and says: "The regularity of its coincidence with recessions (especially the ends of recessions), at least, seems like it should raise eyebrows."

Mine is raised.

Replication of results is useful for many reasons. I like it today because replicating a graph helps me understand the graph. Even when FRED makes replication easy. Across the top of Graph #1 we read

PRS84006173/100*0.78 - TCU/100 * (1-UNRATE/100)

The value 100 occurs three times in that calculation. Those hundreds are in there to convert percentage numbers to decimal numbers. For some reason, maybe because they're not good at simple math, economists seem unable to deal with a number like 0.09 and need to have FRED multiply it by 100 to produce a number like 9 to help them think about 9% unemployment or whatever. But then to do a calculation you have to divide the 100 out again, as Ed Lambert does.

To simplify the thought process, I want to eliminate the hundreds. This, then, is the calculation for the graph:

PRS*0.78 - TCU * (100-UNRATE)

I've also shortened the PRS ID number. The PRS is "Labor Share". TCU is Total Capacity Utilization. And UNRATE is the Civilian Unemployment Rate.

But Lambert isn't really using the unemployment rate. He's using 100 minus the unemployment rate (or 1 minus the decimal equivalent). So Lambert is using the employment rate.

He also takes 78% of the Labor Share value. That gives him a number he calls the effective labor share. I don't know how he came up with the 0.78 number. But it reduces the PRS number by 22%.

From the Effective Labor Share he subtracts TCU-times-the-Employment-Rate. The employment rate is a number up near 100%, but somewhat less, that goes down when the unemployment rate goes up. It varies inversely with unemployment, and is always less than 100%.

(Maybe I should point out that the "order of operations" plays a role here. The form of the calculation is: value minus value times value. When you read it, the minus comes before the times. But when you do arithmetic, you do the multiplication first and the subtraction later. So Lambert isn't subtracting TCU from the PRS. He's subtracting TCU times the Employment Rate from the PRS.)

Multiplying TCU by the Employment Rate reduces the TCU values and exaggerates the TCU changes. (In a recession, both employment and capacity utilization fall. In a recovery, both rise. The trends complement each other, so the multiplication makes the trend more obvious.)

What Lambert gives us, then, is 78% of the Labor Share, from which is subtracted a measure of economic activity. In times of recession, when capacity utilization and employment both fall, a smaller number is being subtracted and what remains shoots up to a sharp peak. And that is just what Lambert's graph shows.


Maybe Labor Share is itself a measure of economic activity? That would help me make sense of what Ed Lambert is doing.

Graph #2: Labor Share (Index Values, not Percent of GDP or anything like that)

Peaks seem to be associated with recessions. So yes, Labor Share is in part an indicator of economic activity. But there is obviously something else going on, for the overall trend shows an increasingly rapid downhill run.

From Labor Share Lambert subtracts Total Capacity Utilization times the Employment Rate, which looks like this:

Graph #3: Total Capacity Utilization times the Employment Rate

Also goes downhill. And also seems to have peaks associated with recessions -- but these are down-pointing peaks. If we were to minus the whole calculation (for example, by subtracting it from Labor Share as Lambert does) those peaks would be thrusting up. And the overall trend would also be in the upward direction.

So when Lambert subtracts the Graph #3 values from the Graph #2 values, the recession-related peaks are again emphasized, while the overall uphill and downhill trends tend to cancel each other out. What he ends up with is a relatively flat overall trend punctuated by the highly exaggerated recession-related, eyebrow-raising peaks that you see in Graph #1.

So that's the arithmetic in Lambert's UT graph. I've not considered the significance of the relation among the particular datasets he has chosen to combine, but hopefully something will pop into my head about that.

Meanwhile, look at the numbers on the vertical scale of Graph #3. They run from 6000 to 8800! That's because FRED expresses percent values in the "multiplied by 100" form rather than as decimal numbers; again, as 9 rather than 0.09. If we took TCU and divided it by 100 (as Lambert does) the vertical scale numbers would run from 60 to 88. Then if we replaced (100-UNRATE) with Lambert's (1-UNRATE/100), our vertical scale numbers would run from 0.6 to 0.88 -- in other words, from 60% to 88%, a much more reasonable range of values.

Also, notice that the TCU values start in 1967, so that my Graph #3 and also Lambert's graph (Graph #1) both show the plot starting in 1967.


Okay. I went weed wacking for an hour, trying to keep "Labor Share" and "Capacity Utilization" and "Employment Rate" in my head all at the same time. But the only brilliant insight I had was that I really don't like weed wacking.