Sunday, January 23, 2011

Debt Accumulation

Let's say we have a \$100 economy. GDP is \$100 in "year one."

Or GDP could be 100 percent, or 100 conceptual units of output or 100 "apples and oranges" or 100 "atoms and sweat." Whatever's the easiest way for you to think about it. For me, it's dollars.

So we have GDP at 100. And let's say we have no debt at all, to start with. Zero debt.

That's probably not realistic, for a developed economy. Call it a simplification.

I want to look at the effect of credit-use in this little economy. Let's say we borrow an amount equal to 6% of GDP each year. I don't know how that compares to the real world, but just say.

And say we pay back, on average, 4% of our outstanding debt each year.

And one more thing. Say our credit efficiency is 80%. In other words, every dollar of new credit-use boosts GDP by 80 cents. That's pretty high, I think.

I'm not saying any of these numbers are realistic. But they do produce interesting results in a spreadsheet:

1. Even though debt starts at zero, it rises rapidly and soon is greater than GDP.

2. As the accumulation of debt grows in size, the increase in GDP gradually falls off. GDP reaches a peak and starts to decline as the drag from debt repayment grows relative to the boost from credit use.

3. This outcome is purely mathematical. The decline of GDP is the consequence of simple arithmetic. There is no politics in it. There is no China in it. There is no peak oil in it. There is no regulation in it. The only operative factor is the accumulation of debt.

You can fiddle with the spreadsheet. I saved it as a Google Docs template, so if your fiddling messes it up, you can open a fresh copy. Click this link to bring up the Google Docs template preview. Click the "Use this template" button to open the spreadsheet.

If you can't access the spreadsheet: The Google Docs help says You need to be signed in to your Google Account in order to use a template. ...Or maybe the template got deleted again, and I'll have to find a different way to make it available.

I involved my son Jerry in testing the spreadsheet. He wrote back,

This is a neat idea. I'm trying to think if i could make a little web
app to do it...

That was at 10:30 in the morning. By 1:00 in the afternoon, he had it working and was into revisions already:

hmmm... there is something missing from the model, here: interest and
minimum payments. As it is, i think the best solution is to set debt
repayment to 0 - then GDP just grows for ever !

And making my spreadsheet into a template -- that was my daughter-in-law's idea. All in all, a big family day for me.

Here's the link to Jerry's version of our Debt Accumulation economic model.

Notes on the calculations:

I set the sheet up so you only have to change numbers in the top row.

In the top row of my spreadsheet are three numbers. In Column D, above the words "New Credit Use" is the value 6.00%. You can change this number. The number in cell D1 is used to figure the "credit-use" values in column D. For any row, the "new credit use" value is 6% of the GDP value in that row: 6%, or whatever percent is in cell D1.

Above the words "Debt Repayment", in cell E1 is the number 4.00%. You can change this number. The number in cell E1 is used to figure the "debt repayment" values in column E. For any row, the "debt repayment" number is 4% of the Accumulated Debt number in column C on that row: 4%, or whatever percent is in cell E1.

Don't get mixed up between the "Year" numbers in column A, and the row numbers of the spreadsheet which are to the left of the "Year" numbers.

The third number in row 1 of the spreadsheet is 80.00%, in cell F1. This is the credit efficiency number, used to figure the "GDP Boost" values. Each GDP Boost number is figured as 80% of the "new credit use" value, less the "debt repayment" value from that row. Again, 80% or whatever percent is in cell F1.

It takes a lot of words to put calculations into English. But the arithmetic is simple. And the arithmetic tells me that the accumulation of debt puts downward pressure on GDP. The graph shows it.