I showed this graph on Saturday:
|Saturday's Graph: Erosion of the Federal Debt Due to Inflation|
I made up a spreadsheet with some made-up numbers for debt, GDP, and a price index in columns on the left. I made up 30 years of data.
The yellow cells are numbers I might want to change. The other cells are calculated from the yellow cells or from calculations that depend on them.
The graph is generated by the numbers in the rightmost column, the NN / RR column.
As the third row of yellow cells shows, I started with a "price index" value of 100, an initial GDP of 100, and an initial debt of 50 (half the size of GDP). The latter two numbers are somewhat arbitrary; I had to pick numbers to get started.
The initial price index value of 100 is not arbitrary. By convention or on principle or for reasons unknown, the "base year" of a price index is always given the value 100. It's probably to simplify matters. Whatever. Since I'm using 100 as my first year's price index value, you should be able to guess that I am using the first year as the base year for my calculations. Didn't have to be. But it is.
Economists tend not to do that. But I'm not an economist and I'm free to put the base year any where I want. Besides, it just makes sense. When I think about the economy, I like to set things up, start the action, and see what happens. It's just natural that where I start is the beginning.
So, the graph. Test #1, above, figures 2% inflation each year, 4% annual GDP growth -- that's nominal GDP, by the way -- and an 8% annual increase of outstanding debt.
(How that works: For inflation, I take each year's value and multiply it by 1.02 to get the next year's value. The new value turns out to be 2% bigger than the value I started with. For GDP, multiplying by 1.04 makes each new value 4% bigger than the one before. For debt, multiplying by 1.08 makes each new number 8% bigger.)
The numbers I use to set my growth rates -- 1.02, 1.04, and 1.08 -- appear in the yellow cells on the first two lines of the TEST #1 spreadsheet image. I use the numbers on the top row in the calcs for the first 15 years -- for the left half of the blue line on the graph. I use the numbers from the second row for the next 15 years, the right half of the blue line.
In TEST #1, the blue line is a nice smooth curve because the numbers on row one and the numbers on row two are the same. Now I can change one of the growth rates on the second row and maybe we'll see a kink show up right in the middle of the blue line:
Still, there is no change in the blue line. No kink there in the middle. Making a huge change in the growth rate of GDP (and leaving the inflation rate and the debt growth rate unchanged) made absolutely no difference in this graph.
I thought that was pretty weird. And hey, maybe I have something wrong. It wouldn't be the first time. But I can't find it if there is. So anyway I figured let me get even more extreme with the change in GDP growth rates. So I used 0.01 for the first 15 years and then 100.0 for the next fifteen.
Still no change in the blue line:
What this is telling me is the growth rate of GDP has no bearing on the rate of erosion of debt. I still think that's odd. And like I said, I could have mistakes in the spreadsheet. But that's what it's telling me.
So I set the GDP growth numbers back to 1.04 so the second period matches the first, so we are starting from the TEST #1 picture again. And then I increased inflation, the annual rate of inflation, from 2% to 8% on the second line. That gave me a kink in the graph:
So TEST #4 tells me that the blue line is falling because of inflation.
Remember now, the blue line is a "model" of Saturday's graph, which showed the value remaining after inflation as a percent of the total value borrowed: the value after inflation as a percent of the value at the time the money was borrowed.
So TEST #4 says 2% inflation makes debt erode slowly, and 8% inflation makes debt erode rapidly. Pretty interesting to see that on a graph, I think.
Okay. So changing the GDP growth rate has no effect, but changing the inflation rate does have an effect. What about debt? What happens if we start at TEST #1 again and then double the rate of debt growth from 8% to 16% annual?
|The Saturday Graph Again (for comparison to TEST #5)|
TEST #5 shows a much smoother line than the Saturday graph, because growth rates on the spreadsheet change once in 30 years, not every year like the real world. But you can see from these tests that inflation erodes debt, that more inflation erodes debt more, and that if debt is growing fast enough, the burden of debt increases regardless of inflation.
Here's a link to the Google Drive template. And the Excel XLSX file.