## Friday, February 4, 2011

### Doubting the Numbers

Then I got email from my son Jerry:

Hey,
I'm trying to figure out your post numbers problem... Could you try using
(gross federal debt from "hist07z1") / (nominal GDP from measuringworth)
(gross federal debt as a percentage of GDP from "hist07z1")
and see what happens?

Jerry thinks the discrepancies in the numbers may arise because the "federal debt relative to GDP" table has embedded GDP numbers that differ from the Measuringworth numbers I'm using. It was a good idea, I thought.

So I made another copy of the first spreadsheet, deleted everything but the original source table, and started over.

Took the Gross Federal Debt numbers from the "hist07z1.xls" source the Supporting Evidence site provides. Deleted the "TQ" row right away.

Took the Nominal GDP numbers from Measuringworth, as Jerry suggested. And calculated my own "Federal Debt Relative to GDP" numbers from the two sources.

Then to satisfy curiosity, I compared my calculated numbers to those given in the "hist07z1" table, for the 1955-1973 period:

 GRAPH #1

The one is consistently lower than the other; this is exactly the problem that kept recurring in the previous analyses. I think Jerry has identified the problem. The discrepancy is in the GDP numbers. Not in my arithmetic. Well, that's a relief.

Next step was to generate a "best-fit" exponential trend based on the 1955-1973 years of the improved "Federal Debt Relative to GDP" numbers. I also have to grab the exponential formula from Excel:

y = 0.6854e-0.0381x

The R-squared value came out at 0.9891, even higher than I had before. So that's good.

 GRAPH #2

Using this formula in my Google Docs sheet, the base-period comparison looked good:

 GRAPH #3

And the full-period trend will look familiar by now:

 GRAPH #4

The next step is to calculate the hypothetical output for which growth is fast enough that the gross federal debt declines along the exponential curve. To do this I'm using federal debt numbers from the "hist07z1" divided by the exponential curve number, again following Jerry's suggestion.

I generated the GHP numbers and made graphs comparing hypothetical output to actual ("nominal") output. First, the base period 1955-1973:

 GRAPH #5

I was relieved to see that the two lines cross repeatedly in these years, just as they do in Graph #3 above. Finally, the little things were taken care of, and I could move on. Only the big thing remains:

 GRAPH #6

But before I go, here again is a close-up of the start of the Federal Debt problem:

 GRAPH #7