Differences

I started out making a version of Fernando Martin's graph from "Why Does Economic Growth Keep Slowing Down?" He shows 10-year averages of annual growth rates.

His data ends in 2016. I can continue it to the third quarter of 2024.

He uses quarterly data, so I went with quarterly also. But he works with annual rates, and that left me with some options, because FRED gives the data in different formats. I could go with "Percent Change from Quarter One Year Ago". Or I could go with "Percent Change from Preceding Period" at an "Annual Rate" as FRED gives it.

So I went with both of them. Might as well see how they differ, right?

Plus I figured the CAGR for the 10-year periods. So, three lines on my graph:

I'm showing the graph bigger than usual this time, because the lines are so close together. It might show up better if you make your browser wider, or just click the graph.

The "Percent Change from Preceding Period" data -- the red line -- shows the growth of a single quarter, multiplied by 4 or perhaps compounded, to create numbers comparable to yearly values. Note that if three quarters of the year are just average and one is really good, the good one will be noticeably above the others, and also noticeably above the "Percent Change from Quarter One Year Ago" line. The red change-from-preceding-period line magnifies three months of growth, as if that really good growth lasted the whole year -- as if there was a whole year at the really good rate of growth. That's why the red line so often runs above the others on my graph.

Of course, if three quarters of the year were just average and one quarter was low, the red line would understate the low quarter, just as it exaggerates the high quarter. On my graph, however, where the red runs low it is fairly well hidden by the green line, the CAGR calc.

The CAGR takes the start and end values of the 10-year periods, and distributes growth at an equal rate over the whole 10-year period. I think this is the most "honest" way to figure growth for periods more than a year in length.

When I figured the CAGR, I used 1/40 as part of the calculation (because there are 40 quarters in 10 years). The result was crazy, and far off from FRED's growth rates. Then I noticed my growth rates were closer to 1 percent than 4 percent, and I figured out my mistake. Using 1/40 in the calculation gave me quarterly growth rates. I changed the calc to use 1/10 (because there are 10 years in each period) and my results suddenly became reasonable. I checked one 10-year period: Using 1/10, the end-value I calculated matched the value at that date in the FRED data. So this confirms what I thought I could do -- use the CAGR to convert annual rates to quarterly or quarterly to annual, for example. But this is the first time I ever did it, so don't take my word for it!

 

When I google "CAGR" I get "Compound Annual Growth Rate". Seems to me, if I'm using it to get quarterly growth rates or 10- or 20-year rates, maybe it is really called "Compound Average Growth Rate" and I just remembered it wrong.

But apparently not. When I google "Compound Average Growth Rate" the search still turns up Compound Annual, almost exclusively. So maybe I didn't remember it wrong.

But I did find something interesting: How to Calculate BOTH Types of Compound Growth Rates in Excel, by Charley Kyd at ExcelUser: the Fitted Average Growth Rate.

Charley Kyd points out that for the CAGR, only the start- and end-values matter. The intermediate values do not affect the result of the calc. (Yeah, I noticed that myself.) So Charley presents the "Fitted" version:

This rate represents the average growth rate returned from an exponential curve fitted to [your data]. With this method, the value for each period DOES matter, because each value affects the average growth rate that the fitted curve displays.

So now I've got something else to look at, if I ever get around to it.