Tuesday, November 20, 2012

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?


Luke Smith said...

A lot of inflation in the 1970s: higher oil prices and a housing bubble which I believe was fueled by depressed wages and bad petrodollar recycling.

In nominal terms, the average price of oil multiplied by the US's annual oil consumption in the same year was 8.3% of GDP in 1979, 1% of GDP in 1998 (pre-embargo level) and 5% of GDP in 2011.

I am energy centric. I sometimes wonder if the 1970s was just the inevitable to the great post-WWII housing bubble - just like there was an end to the great railroad land grab. After WWII, many people decided that the suburbs were a great place to live, so they bought a car, got a spouse, had a kid and headed to the suburbs. Cheap oil made that dream an easy possibility.

The Arthurian said...

...and cost got built in to our way of life, and it all came to a head in the Great Inflation of the 1970s. It's a good argument. I like your "price of oil multiplied by oil consumption" numbers.

I am credit centric. My comparable numbers are "the interest rate multiplied by the use of credit".

Either way, cost is at the core.

Anyhow... Happy Thanksgiving.