Exponential Trends in Real GDP (3): Simulacron

On Thanksgiving day I wrote

Thornton says there was "a marked increase in [Federal] expenditures relative to GDP" beginning in the early 1970s. Fine. But economic performance dropped in the early 1970s. The marked increase in expenditures relative to GDP was a result of the decline in GDP growth.

I'd like to test that hypothesis. And now I know how to do it. This graph is from mine of the 20th:

Graph #1: Early Trend (green), Actual Trends (red), RGDP Values (blue)

In green, the latter years of the graph show a continuation of the early years' real GDP trend. In red is the more laggard latter years' actual trend. In blue you see the RGDP values from which the trends arise.

For the latter years I want to take the RGDP number, divide out the red trend value, and multiply by the green trend value. This will simulate higher values for real GDP in the latter years, based on the performance of the early years.

Then we can look at Federal spending and Federal revenue and such, relative to this simulated improvement of economic performance. We will be able to see what would have happened if -- if the inflation of the 1970s didn't lead to the suppression of economic growth since the 1980s. Would Federal spending still have increased, relative to the bigger GDP? How much would Federal revenue have increased, if we maintained the superior growth of the early period? And then with increased revenue, with less call for social spending because economic performance was better, and with a bigger denominator, what would have happened to Federal debt, relative to GDP?

Interesting questions.


Back in July I looked at the economy's performance in a series of graphs on RGDP growth. Here is Graph #3 along with remarks from that post:

Graph #3: Growth Rate from 1947 to Plotted Year (blue)
and Growth Rate from Plotted Year to 2011 (red)

The higher line here, the blue line, shows compound annual growth rates of Real GDP, the compound rate being figured from 1947 to each year plotted. The first three points on the blue line of Graph #3 show the compound annual growth rates for the periods 1947-48, and 1947-49, and 1947-50. Each subsequent point shows the compound growth rate of a longer period. The general trend shows decline.

At the right, the last blue point shows the rate for the full 1947-2011 period.

The general trend shows decline. The early years are "splashy" because few years are considered. But the blue line shows a peak right around 1967, and all downhill thereafter.

That's where I want to make my trend break, right around 1967. I want to look at the trend up to that point, and compare it to the trend since that point. It would be nice to push the date back a couple years, to 1965 maybe. That would get the whole of the "Great Inflation" out of the early trend and into the late trend.


I have to break this up into a series of posts. I need to go slow and check my work. Tomorrow I'll take a better look at where to put the break in the exponential trend.

Exponential Trends in Real GDP (2): Trend 20, Shift 10, Repeat

This is Graph #4 from mine of the 18th:

Graph #1: Early Trend (green), Actual Trends (red), RGDP Values (blue)

The green line is the RGDP trend for the years 1947-1977, continued out for 60 years.

The red line shows two RGDP trends: the 1947-1977 trend for the first 30 years, and then the 1977-2007 trend for the next 30 years. Real growth was slower in the second half, as the separating lines show.

In order to check the validity of my calculations for the earlier post, I added the blue line -- FRED's values for "GDPC1", which we can call "Real GDP" or "RGDP". I was pleased to see the blue line run close to the red line for the whole 60 years shown on the graph. Oh -- not happy that RGDP growth slowed down, no. But happy that my arithmetic turned up a pretty good match.

But look again at the second half, the right half of the graph where the red and green lines separate. For that whole 30 years, the blue line is almost always below the red. The RGDP numbers are almost always below the trend I show.

My bad. I figured trends as described previously, for the 1947-1977 and 1977-2007 periods. Those are 31-year periods, start to finish. Then when I plotted the exponential trends, I used 30-year periods. Didn't think it through beforehand. I'm doing that now.

What I should have done is to make the first half of my red line 31 years long, not 30. And I should have started the second half at the 31st year, not the 30th. That would have pushed the second half of my red line one year more to the right. It would have moved the red line closer to the "middle" of the blue line. That would have given me a better picture of the second-half trend. Oops.


I am not alone in thinking that the "golden age" after World War Two ended in 1966. That's earlier than is often said, but I see it on lots of graphs.

I am also not alone in thinking that the general uptrend of RGDP growth has been slowing. I think, consistently slowing. I suggested as much before, imagining a graph without the growth suppression of the Great Inflation time, and without the Supply-Side fixes that came after the Great Inflation. "We might have seen the three lines spread more equally apart," I wrote, "suggesting the unrelenting decline of economic growth."

So now I want to look at the RGDP trend up to 1966 -- the best trend, I expect -- and compare it to later trends. Overall, I expect to see the the uptrends showing less "up" as time goes by.

FRED's start-of-data is 1947, so my first trend will be based on the years 1947-1966. Now that's an actual 20-year trend. Count the years, if you like.

In order to make my trend lines comparable, I will use 20-year periods for each trend I figure. And I will let Excel figure the trends for me. Exponential trends, as before: Trends of growth.

I will end each trend ten years after the previous one. So my second trend runs from 1957 to 1976. My third runs from 1967 to 1986. And so on. At the end I'll have a few years left over, so I'll use a 20-year trend that ends with the most recent data. That'll be 2011, as I am using annual (not quarterly) data, to simplify my life.

So that's the plan. Now I have to create the graph.


I created graphs in Excel, one per sheet as before, added exponential trend lines, and put the resulting trend formula in the upper-right corner on each graph. Everything is contained in the ExpoTrends#2.xls file.

After I had all the graphs in place I went back and used the trend formulas to generate trend numbers (in the third column on each worksheet). These numbers are values for points on the exponential trend line. I'll use them to re-create the trend lines all in one graph, and leave out the original source data.

I added a line to each graph, using these trend values. I figured if I could *see* this new line, then it's not in the same place as Excel's trend line, and I have to check my work. I had to fix the first one; after than they all came out good.

I gathered all the exponential trend numbers on Sheet1. I entered the formulas again: more work but less confusion than trying to copy them from six other pages. So the checking I did previously doesn't mean the numbers on Sheet1 are good. But I did compare the first and last expo values on Sheet1 with the first and last "third column" values of each of the six sheets. All good. (But feel free to check my work.)

Graph #2: Variation in Real GDP Trends

The two highest trend lines here are the two oldest 20-year periods plotted. The one lowest trend line is the most recent: the 20-year period ending with the most recent annual data. The other three trend lines (blue, green, and a pink one that just peeks out beneath the green one) fall between the others chronologically as well as vertically.

It's not a perfect, regular decline in economic performance. But it is without question a continuing decline in economic performance. So when somebody shows you one of these straight-line trends cutting through the RGDP numbers...

Graph #3, source: Marcus Nunes

... do not hesitate to point out that the RGDP numbers were going up (relative to that trend) until 1966 or so, and have been declining (relative to that trend) since the '70s.

Kinda puts the recent large decline in perspective, don't you think?

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.

In Failure's Embrace

Bullard, 6 February 2012:

For those who take the “large output gap” view, the expectation is for real GDP to grow rapidly after the recession comes to an end, as the economy catches up to its potential. It is like a rubber band, there is supposed to be a bounce back period of rapid growth.

The wealth shock view puts a different expectation in play. The negative wealth shock lowers consumption and output. But after the recession ends, the economy simply grows from that point at an ordinary rate, neither faster nor slower than in ordinary times. It is more like an earthquake which has left one part of the land higher than another part. There is no expectation of a “bounce back” to a higher level of output after the recession ends.

Sumner, 26 September 2012:

In 2009 I advocated going all the way back to the old trend line. I currently favor going about 1/3 of the way back. If we keep on the same track for a few more years I’ll through in the towel and advocate starting a new 5% trend line from where we are.