Sunday, November 10, 2013

Summing Inflation-Adjusted Deficits

After some exchange of comments on my Inflation-adjusting deficits post, I decided to recreate the Graph #3 from that post, grab the data from FRED, and put it into a Google Drive sheet.

It looked a little plain, so I went back to FRED for USRECM, a recession-date indicator, and added recession bars to the graph. Not perfect, but hey:

Graph #1: Federal Deficits, Corrected for Inflation
The Google Drive Spreadsheet is available
I should say they've added a lot to what you can do easily to customize a graph in Google Drive. I like it.

You know what I want to do with this? I want to add up the numbers and see what the accumulating total looks like. If I add up Federal deficits, I get the Federal debt. So if I add up inflation-adjusted Federal deficits, I get the inflation-adjusted Federal debt.

I want to see what that looks like.

I don't think anybody has a problem with the calculation I used to inflation-adjust the deficits for the above graph. It's the same calculation you'd use to convert "nominal" GDP to "real" GDP. It works fine with flow variables like GDP and deficits. It only doesn't work with stock variables like accumulated debt -- the sum of multiple-year deficits.

Funny thing, though. It seems I'm the only one saying the calculation that works fine to adjust flow variables doesn't work when you use it with stock variables. That's why I want to add up the inflation-adjusted deficits and see what the total looks like. If it looks like everybody else's picture of inflation-adjusted debt, then I guess I'm an idiot.

Everybody else's picture of inflation-adjusted Federal debt shows a big flat spot from World War Two to 1980. This picture makes it look like debt growth was very well contained. But the picture shows a sudden change at 1980, and inflation-adjusted debt suddenly starts rising at a very rapid pace:

From Wikipedia
From Slaying the Dragon of Debt
So when I add up my inflation-adjusted deficits, if the graph looks like these two, if the graph is flat until 1980, then suddenly changes and runs sharply uphill, then I'm an idiot and I'm wrong about the problem with the inflation-adjustment calculation.

But if the graph looks like the yellow line here:

Graph #4: From my Dead Cat post
then... well, then I'm not the idiot. The yellow line is up-curving just about the same before 1980 and after (until the mid-1990s). That's what I expect to see when I add up the inflation-adjusted deficits to construct a version of inflation-adjusted debt.

For the record, the red line on Graph #4 is the "bad" calculation, the same used in the Wikipedia graph and in the Dragon graph shown above. The red line shows the same flat-to-1980-then-sudden-increase pattern those other graphs show. The yellow line shows a continuous increase from the 1960s to the 1990s. So the difference is clear.

Well, it's time to add up some numbers and play Who's the Idiot:

Graph #5: The Sum of Inflation-Adjusted Deficits as a Measure of Inflation-Adjusted Debt
The Google Drive Spreadsheet is available
It's not me. Add up the inflation-adjusted deficits and plot it, and the line curves up. It curves up in the 1960s, you can see, and it continues curving up in the 1970s, thru the 1980s, and into the '90s.

There is no flat line that lasts until 1980. There is no sudden change when Reagan gets elected. There's nothing like that. The sudden change you see in those other graphs, the Wikipedia graph and the Dragon graph, that's just a bad calculation. It survives because people don't want to hear about the error.

I think some people want there to be a sudden change in the Federal debt in 1980, so they can point to it and say Look what Reagan did! or so they can say (like the Dragon site says) "the deficit exploded under Reagan."

You know what that reminds me of? It reminds me of how quickly and how cheerfully a certain segment of the population accepted the pronouncement of Reinhart and Rogoff, that (as BBC News put it): "economic growth slows dramatically when the size of a country's debt rises above 90% of Gross Domestic Product".

Some people wanted that to be true, because it supported their view. Other people revelled in Thomas Herndon's discovery of mistakes in Reinhart and Rogoff's work.

But you know, a lot of those same "other" people are people who want the "sudden change at 1980" debt graph to be true, because it supports their view. But here's the thing. The economy works the way it works without regard to our preferences. The economy doesn't give a damn what we want to be true. No matter which side we're on.

ADDENDUM: Graph #5 on a Log Scale

Graph #6: The Sum of Inflation-Adjusted Deficits on a Log Scale
The Addendum Spreadsheet is available


The Arthurian said...

And debt growth was never well-contained. Not the Federal debt nor any debt.

Jazzbumpa said...

Graph 5 looks to be similar [in the strict geometric sense] to the graph of gross federal debr held by the public with no inflation adjustment.

Can you put it on a log scale? I think there is a bump in the 80's, but quasi-exponential curves are tough to eye-ball.

I'm still baffled by the inflation adjustment.


The Arthurian said...

"Graph 5 looks to be similar [in the strict geometric sense] to the graph of gross federal debt held by the public with no inflation adjustment."

Agreed! Unfortunately, I spent basically ALL of Sunday writing a post to say what you just said, which is for Monday the 11th (today).

I think I see the bump you see. Log scale is a good idea; I was thinking of fitting an exponential curve to the debt curve but that idea went nowhere.

I'm adding an addendum to the post, with the Log Scale graph.

The Arthurian said...

"I'm still baffled by the inflation adjustment."

Try this on for size... Suppose we want to use the normal inflation-adjustment calc, like in the Wikipedia and Dragon graphs above.

Suppose our debt consists of only two borrowings, one in 1960 and one in 1979.

Suppose it is now 1980 and we are making the calculations.

For the 1960 calc we have only one borrowing in our debt; and adjusting 1960 dollars to 1980 dollars is the correct calculation.

But in the years that follow, the existing accumulation of debt (which is only the amount we borrowed in 1960) is "corrected" for 1961-to-1980, then for 1962-to-1980, then 1963-to-1980, etc. By 1978, the Great Inflation has sucked much value out of the original 1960 dollars that we borrowed, and reduced the value on the graph! In truth, the original value borrowed is much greater in 1978, not much less.

The proper correction for inflation would have to consider the 1960 value of the money borrowed in 1960. The commonly used correction for inflation does not.

In 1979 we borrow more, but now the original 1960 borrowing, incorrectly corrected for inflation, is very small relative to the new borrowing. This is how the Wikipedia graph manages to stay flat until the end of the Great Inflation.