Sunday, November 18, 2012

Exponential Trends in Real GDP

Not just for ha-ha's, I took FRED's annual data for "GDPC1" and put it into Excel. Ended up with three separate Excel files with graphs, data, and calcs. Click on the link at the top of each section to preview or download the file.

20-Year Exponential RGDP Trends.xls

I took 60 years of RGDP since 1947 and split it up into three 20-year periods, 21 years, whatever: 1947-67, 1967-87, and 1987-2007. Pretty well corresponds to the golden age, the great inflation, and the great moderation.

I graphed each 20-year period separately. I used Excel to put an exponential trend line on each graph, along with the formula for the trend line.

Then on a new sheet I used Excel's exponential trend formulas to generate the three 20-year trends. I scaled each set of values so each series starts at 100. Then I plotted the three exponential trends together in one graph:

Graph #1: Comparison of Real GDP Trends for Three 20-Year Periods
The green line shows the substantially higher growth of the 1947-67 period. The orange and red lines show the slower uptrends of the middle and late periods. There is barely any difference between these latter two. In other words, despite all of the suppression of growth to fight the great inflation of the middle period, and despite all of the supply-side enhancements of the latter period, real growth was very nearly the same in both the middle and the late years.

In other words: Without the inflation-fighting of the middle period, the inflation would not have been quashed; but growth would have been better than it was. And then, without the supply-side policy inventions of the latter period, growth would have been much worse than it was. Instead of one-line-high-and-two-lines-low, we might have seen the three lines spread more equally apart, suggesting the unrelenting decline of economic growth.

30-Year Exponential RGDP Trends.xls

I took the 20-Year Trends workbook and copied it over for 30-Year Trends. Deleted one of the 20-year worksheets, and stretched the other two to make 30-year graphs: 1947-77 and 1977-2007. This breakdown fairly well corresponds to the shift from Keynesian economics to Reaganomics in the U.S. economy.

Graph #2: Comparison of Real GDP Trends for Two 30-Year Periods
Again, the green line shows that there was substantially higher real growth in the early period. The red shows growth substantially lower in the late period.

60-Year Exponential RGDP Trends.xls

Next, I copied the 30-Year Trends file over to a 60-Year Trends file. I stretched out the exponential trend calcs to 60 years. The one for the early years I kept unchanged. So it shows, the green line shows the exponential trend of Real GDP for 1947-1977, extended for the whole of the 1947-2007 period (as if growth never slowed).

For the red line, I changed it all up. The red line is based on the early-years trend for the 1947-1977 period, and on the late-years trend for the 1977-2007 period. I had to revise the indexing of this series, to get a smooth transition in the values. This much is done on Sheet1 of the 60-Year file.

Graph #3: The Early-Years Trend for the full 60 (green) and
the Two Trends Joined at the 30-Year mark (as really happened) (red)
The change in trend of the red line is barely visible. If you didn't know the green line shows just one trend from start to finish, you might think the red line has no change in trend. But the red one changes at the mid-point.

Looking at Graph #3, it seemed to me that the red line was a good match to the Real GDP graphs I've seen, and the green line was not a good match. That's as it should be; that's what the numbers present. Still, I wanted a better look.

I copied over Sheet1 from the 60-Year file, and named it Sheet2. Then I added the original FRED numbers for Real GDP (in blue) to the graph, so I could see how they match up with the exponential trend values. Good match, I think:

Graph #4: Early Trend (green), Actual Trends (red), RGDP Values (blue)

This last graph, if you click on it you get a bigger one.

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