Friday, January 28, 2011

Dunno where this is goin' yet...


The mind goes where it will. So I Googled federal debt relative to GDP. Supporting Evidence had a nice graph. I clicked the link below their graph,

Budget of the U.S. Government, FY2011 Historical Tables, Table 7.1-Federal Debt At The End Of Year: 1940-2015
and found myself looking at numbers. So, I did what comes natural: I made a graph and started looking for trends.

The curve from the high point around 1946 to the bottom around 1981 looked like a trend to me. Before 1946 was World War II, which is an outlier, certainly. And since the early 1980s we had Reaganomics, which was an attempt to fix the economic problems of the 1970s. So I wanted to focus on the trend of the 1946-1981 period. Also, I wanted to use an exponential curve for the trend, because exponential curves are associated with growth and decay of societies and such.

I let Excel figure the trend line for me. I don't know any other way, any easier way to get the y=cebx formula noted in the Excel Help.

I cropped the data to 1946-1981 and had Excel overlay an exponential curve on it. Pretty close, but the actual numbers are all higher at the beginning and higher at the end, and all lower in the middle.
So I chopped off the last few years. I decided to end the graph at 1973 because that's the end of the "golden age" of economic growth. So anything after 1973 would probably be a different trend anyway. Now the exponential is a good match except in the early years. You can see that the R-squared value increased to 0.9743 in this graph, from 0.9412 in the previous one. The closer this value is to 1.0, the better the "fit" between the exponential trend and the actual numbers.

So I shortened the graph some more, to remove the mismatch of the early years. Now the graph starts in 1955, after the Korean War. And the exponential is a good match to the actual numbers. The two lines cross each other repeatedly, as though the exponential is centered on the actuals. Also, the R-squared value increased to 0.9854.

Now I was happy. Now I had a formula that fit the numbers.

y = 70.108e-0.0369x

I took this formula from Excel and put it into my Google Docs spreadsheet, extending the exponential curve for the full 1940-2009 period:


One glitch, one break in the exponential curve: The red line is interrupted between 1976 and 1977 where there was a change in the way the numbers are figured. I don't recall what the change was, but I've run across it before. (In the source data, in the YEAR column there is "TQ" which stands for "Third Quarter." The interruption in the graph occurs at that point.)

The red and blue lines of graph #1 shows a definite similarity in the 1955-1973 period, and a definite difference beginning in 1974. One could say there is a second trend that runs from 1974 to 1981, where a third trend seems to begin...

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