Wednesday, December 12, 2012

Simulacron: Make that three trends

Graph #2 from mine of 28 November, renumbered:

Graph #1: RGDP Fitted to the Trend Lines

The blue line shows Real GDP. The red line is an exponential trend fitted to the RGDP data for the period 1947-1979. The green line is an exponential trend fitted to the 1980-2007 period. You can see that RGDP growth appears to have slowed around 1980, so that the green trend line falls away from the red trend line.

You can see RGDP growth slow again around 2008, as the blue line falls away from the green trend line. That little blue tail over on the right seems an awful lot like the start of a third trend, lower yet than the one that dies out in 2007.

I took another look at the numbers, quarterlies this time. I made close-up graphs of the trend transition periods and selected "best case" dates for the trend start- and end-points.

As in the earlier post I let Excel generate exponential trend lines and formulas for the three periods. I gathered up the numbers needed to duplicate the trend lines and put them into a table along with compound annual growth rate (CAGR) values for the three periods:

And I plotted the RGDP numbers along with the three trend lines, extending the latter out to the fourth quarter of 2020:

Graph #2: Stages of the slowdown in real growth
By the fourth quarter of 2007 when real GDP reached 13.3 trillion, blue trend GDP was 17 trillion, more than 25% greater.

By the third quarter of 2012, with the most recent real GDP number at 13.6 trillion, the yellow (1982-2007) trend shows 15.8 trillion, and the blue trend shows 20.3 trillion real GDP. For every dollar of income you earn today, the blue trend would have got you a dollar and a half.

By the fourth quarter 2020, the present trend suggests 16.25 trillion RGDP. The 1982-2007 trend would have brought us to 20.5 trillion. And the 1947-1980 trend shows 27.6 trillion real GDP.

So the next time somebody shows you a graph of RGDP with a constant-rate-of-growth trend line through it like this one,

Marcus's graph

and when they tell you

It´s more or less recognized that US RGDP is trend stationary (maybe that´s changed now!), with real growth averaging about 3.3% from the early 50s to 2007

well, do not hesitate to respond Yeah, maybe that´s changed now!

Preview or download the SIMULA 7 Q&A.XLS file containing these graphs. (Q&A stands for Quarterly and Annual.)


Anonymous said...

There's a great short eBook on this topic called "The Great Stagnation: How America Ate All the Low-Hanging Fruit of Modern History, Got Sick, and Will(Eventually) Feel Better"

João Marcus said...

Art I´ll give you the same comment I did when you first broached this topic 5 months ago:
Art – It´s more or less recognized that US RGDP is trend stationary (maybe that´s changed now!), with real growth averaging about 3.3% from the early 50s to 2007. Given that empirical ‘fact’, what I did was regress the log of RGDP on a constant and trend up to 1997 and project to 2012.
I start the period in 1952 to avoid the post war adjustment which distorts the data. For example, in 1950 real growth was 13.4%! For the rest of the 1950s, real growth averaged 3.1% with a very high s.d. (3.3) which compares to an average growth of 3.2% and s.d. of 1.5.from 1984 to 2007.
And the "maybe that´s changed now"! was clearly sarcastic (you apparently took it literally as if I had any doubt.
And there are many studies which conclude that US RGDP from the mid-fifties on (for quite reasonable reasons) and up to 2007 does not have a unit root, i.e. it´s "trend stationary". And if you revisit the economic policy history, especially the one played out in the 1960s (The Kennedy CEA) you will see that the chart conforms to that history.

The Arthurian said...

I would love to be able to say economic growth is not in decline. But when I look at my graphs I see decline. And when I look at your graphs I see decline.

If you could fool me into thinking growth is good -- if you could fool *everyone* into thinking growth is good -- you would not by changing expectations actually make growth good. Not for long.

Anonymous said...

Yes, there's a similar economic theory at the website below. Do you agree with the conclusion? Curious if you have any comments.

The Arthurian said...

The liberty-love-and-justice post offers an excellent analysis, thorough and well-documented.

Not sure about the conclusion. I like to think we can still fix the problem if we try. I'm not into "the end of the world as we know it" unless that means things get better from here on out.

That Telegraph excerpt threw me off. I like your last paragraph, about exploring the options.

Jerry said...

On Marcus's graph, it looks to me like the blue line is below the red line for the first half of pre-1980, above the red line for the second half of pre-1980... starts out on the red line for post-1980, and goes down from there. It's never above the red line in post-1980.

So it says to me, "the blue line has two trends: faster growth than the red line pre-1980, and slower growth than the red line post-1980."

Of course, if you ASSUME that the form of the graph is a straight line, you can use a complicated computer program to make the fit. And the fit will be a straight line. But it doesn't mean anything about the data.

How about this: get your r-squared (or whatever) for the one line ... then fit two independent lines (pre-1980 and post-1980) and see if they have a lower r-squared. And read off their growth rates, and tell me which one is higher.