Gordon's Way

Graph #1: The Unemployment Rate (blue) and RGDP Growth

According to the NBER blurb that we saw yesterday for Robert J. Gordon's paper,

Measured between quarters with identical unemployment rates, U. S. economic growth slowed by more than half from 3.2 percent per year during 1970-2006 to only 1.4 percent during 2006-16...

Measured between quarters with identical unemployment rates: I thought that might be an interesting way to look at growth.

I used UNRATE, with the frequency changed to quarterly (the average of monthly values), and A191RL1Q225SBEA, a measure of Real GDP growth that shows the percent change from preceding quarter at a seasonally adjusted annual rate.

That sentence from NBER finishes up with these words:

... and only half of this GDP growth slowdown is accounted for diminished productivity growth.

An important afterthought. But I want to leave productivity out of it, at least until I see if I can duplicate Robert Gordon's 3.2% and 1.4% numbers.

Close. I'll be happy if I just come close to his numbers.

The RGDP growth numbers come from FRED with one decimal place. But the unemployment numbers have more decimal places than I can count. I'll be comparing growth numbers for dates that have "identical unemployment rates" but damn few of them will be identical if all those decimal places have to match. I started a new column of data with =TEXT(B13,"0.0") and copied it down to create numbers with one decimal place.

How'm I going to compare 1970-2006 to 2006-2016? I can sort 'em by one-digit UnRate. I can sort 'em, but first I have to make two separate batches of numbers. Then I can sort 1970-2006 by unemployment rate, and separately sort 2006-2016 by the unemployment rate. I'm thinking I can plot the two separate batches as two lines on a scatter graph, with unemployment on the horizontal and growth on the vertical. I should get two jiggy lines and, I expect to see the 2006-2016 line reliably lower than the 1970-2006 line.

So I made two copies of the data and eliminated items from before 2006 from the one, and items from after 2006 from the other. Then I sorted them on my =TEXT values. Excel challenged me on the sort, saying that it "may not sort as expected because it contains some numbers formatted as text". (Yeah, I know.) But Excel offered to "sort anything that looks like a number, as a number", and that's what I wanted.

Graph #2: First Try

Well that graph didn't come out right. For one thing, all of the 2006-2016 values are clustered on the left side, as if the unemployment rates were all low. They should be scattered across the full width of the graph, more or less.

For another thing, what the hell are those numbers on the X axis? They're supposed to be my unemployment rate numbers to one decimal place. Four percent, maybe, or 8% or 10%. But definitely not zero, and definitely not 160%. Wow.

Maybe my one-decimal-place conversion is the problem. Excel thinks my numbers are not numbers. I'll try rounding instead.

Graph #3

Oh yeah, that makes a difference already. The unemployment values run from about 4% to about 10%. And the later years are scattered about as widely as the early years on the graph. This is promising.

I cleaned the graph up some to make it easier to look at:

Graph #4

And now (hopefully) it gets interesting. Now I put a trend line on the early years, and a trend line on the late years:

Graph #5

I just used linear (straight line) trend lines, Excel's default, because they are close to flat and they obviously run at different levels. The heavy blue trend line for the early years is definitely higher than the heavy red trend line for the later years. As expected.

The blue trend line runs very slightly uphill (it is higher on the right than on the left) and the red one runs very slightly downhill (it is lower on the right than the left). I know, because the red trendline equation begins with a minus sign, and the blue one doesn't.

I know the slopes are very slight because I can see it, and because 0.0261 and -0.0347 are very small numbers, compared to the numbers on the Y axis.

The values 3.0212 and 1.7214 in the trendline equations are the Y-intercept values. Extend the trend lines leftward, off the graph, to the point where the X-axis value is zero, I think that will be the spot where the trend lines have the values shown in the equations. On the graph, where we actually see the lines, the blue will be more than 3.0212 (because the line slopes up) and the red will be something less than 1.7214 (because the line slopes down).

What were Robert Gordon's numbers again? 3.2 percent and 1.4 percent. More than 3.0212, the one, and less than 1.7214, the other. So I'm definitely in the ballpark.


I increased the number of decimal places in the trendline equations to 8 (whether I need to do that or not for linear trends, I don't know) and used those equations to figure values for those lines.

The blue (1970-2006) values run from 3.12 to 3.30, with an average of 3.18.

The red (2006-2016) values run from 1.57 to 1.38, with an average of 1.49.

If I round my averages to one decimal place, I get 3.2 for the early years, the same as Robert Gordon. And I get 1.5 for the later years, compared to Gordon's 1.4. Close enough.

I'm happy now.