## Sunday, August 16, 2015

### How Changes in GDP, Inflation and Debt Influence the Erosion of Debt

I showed this graph on Saturday:

 Saturday's Graph: Erosion of the Federal Debt Due to Inflation
I said I had a hard time imagining how changes in the data would be related to the changes visible on the graph. I'm back now to look at it.

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.

 TEST #1

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:

 TEST #2
Nope. The line looks just the same. I kept the value 1.04 (an annual growth rate of four percent) for the first 15 years, but changed the number to 1.40 for years 16 to 30. That's forty percent annual GDP growth. That's way more than China was getting. It's a ridiculous number, ridiculously big.

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:

 TEST #3
In TEST #3, some of the numbers below the graph are now so big that I got nothing but cross-hatches. Hash marks I guess they're called now. Or hash tags? Whatever. But the blue line for TEST #3 looks just the same as it did for Test #1 and #2. Even the numbers in the vertical axis are the same. They run from 75 to 105 and that's it.

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:

 TEST #4
For TEST #4 we have 2% inflation for the first 15 years and then 8% inflation for the next 15 years. And you can see that the blue line starts dropping faster as soon as the higher inflation rate enters the calculation.

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?

 TEST #5
Whoa! Now it looks like the Saturday graph! For the first 15 years the blue line goes down as inflation erodes debt. Then debt growth doubles, and now debt is growing so fast that the line goes up despite the 2% inflation!

 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.

Greg said...

"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."

When you say inflation erodes debt that should be a good thing but Im not sure anyone agrees that inflation eroding debt is a positive. Next you show it is a positive only as long as we control the growth of debt so that its not growing fast enough to remove inflations ability to erode it! So are you arguing for more inflation (to erode the debt faster) or are you just arguing for less debt creation? Less debt creation is fine if you specify that its private debt you are talking about. If you mean all debt in general that puts you with all the balanced budget conservatives. I know you dont want debt to grow cuz you called it a "burden" but the burden is different with public vs private. Personally I dont want to be in either the position of calling for more inflation (given how the average American thinks of inflation) or calling for a balanced budget.

This whole notion of inflation adjusting things in order to get some "real" value seems a little misguided at times and I know you too have misgivings about the way its usually done. Its something that the financial types obsess over and it comes off as a way of...... trying to catch someone cheating or something. They will take almost every metric which might get presented as evidence that some policy change had a positive (or negative) affect and do this meta analysis using inflation adjusting which shows the opposite.

I know much of this discussion you are having started as a response to Noah Smiths comment a while back about the spike of federal debt to GDP following the great inflation and to Nathan Tankus' Naked Cap post about inflation NOT helping debtors.I think you have done a great job of showing the flaws in Noahs points, which is really the flaw in all mainstreamers analysis(I know Noah likes to think of himself as something different.....but he's not). Really they were talking about two entirely different things though. Noah, as most of the mainstream is, obsesses over PUBLIC debt as some sort of metric we need to "get under control" while Nathan was talking about individuals and their mortgage or credit card or car loan debts. There isnt one set of analysis which can apply to either situation because in most instances they are opposites from the standpoint of the consumer. Most consumers want get rid of their million dollar mortgage and load up on million dollar T Bonds.

jim said...

The flaw in this entire exercise is the Ceteris paribus nonsense.

Looking at the data it is more than obvious that debt expansion is causally linked to inflation and inflation is causally linked to debt expansion. Ceteris paribus is the same sort of faulty logic that leads to claims that Volker magically put and end to inflation and debt expansion through interest rate when the facts show that debt expansion actually increased to its highest level ever 2 years after Volker's action. Similarly Ceteris Paribus only works if you are willing to not encumber your thought process with facts.

It is pretty obvious to me that had the credit markets not unraveled starting in 1985 (so called "savings and loan crises") there would have been another bout of inflation that followed the early 80's credit expansion. That inflation would have been even greater that the previous spike. But it never happened because the credit market collapsed in 1985.

It is important to remember the credit expansion of the 70's and 80's was even bigger than the credit expansion of the 2000's.

There are 2 assumptions that drove the interaction of credit and inflation in the 70's and 80's. The first is the belief that inflation erodes debt. The second is that inflation (particularly inflation of asset prices) will help pay back debt. People who believe these things are motivated to acquire more debt when confronted by inflation. Of course more borrowing means more spending which in turn will drive prices up. So as long as these beliefs prevail its a very strong feedback loop. This can continue forward for a while until the participants in the credit market suddenly realize the Ponzi nature of what's happening and then that portion of the credit market and the inflation driven by those beliefs all starts to go in reverse. There are two points in time when that realization of truth dawned on the markets. 1985 and 2008. It is interesting that in both cases the amount of excess money available to spend through borrowing had reached a peak of about 30% GDP just prior to collapse.

The Arthurian said...

Greg: "When you say inflation erodes debt that should be a good thing but Im not sure anyone agrees that inflation eroding debt is a positive."

I'm pretty sure Krugman thinks inflation eroding debt is a positive. And there are others. There was a whole flurry of activity in favor of it a couple years back.

"Next you show it is a positive only as long as we control the growth of debt so that its not growing fast enough to remove inflations ability to erode it! So are you arguing for more inflation (to erode the debt faster) or are you just arguing for less debt creation?"

I often try in my writing to present the facts as I understand them, rather than saying what I think about the situation. (Sometimes I think that's why so few people ever agree with me. People seem to think that if they agree, they might get caught on the wrong side of an argument.) (Those people are not doing science.)

I think you know I see excessive private sector debt as the source of our economic troubles and that I argue in favor of policy that accelerates the repayment of debt. But in the post, I am trying to understand the forces the move the line on the graph up or down. If it is true that inflation can erode debt only if we limit the growth of debt, that would probably be a good thing to know.

//

Jim, ceteris paribus does not mean that nothing else has any effect. It means we are trying to understand the relation between (in this case) inflation and debt: What effect does inflation have on debt... as opposed to what effect does financialization and the level of interest rates and a million other things have on inflation and debt. People have such trouble to simplify things!

...the man who is wont to attend to many things at the same time by means of a single act of thought is confused in mind...

Greg said...

"I think you know I see excessive private sector debt as the source of our economic troubles and that I argue in favor of policy that accelerates the repayment of debt. But in the post, I am trying to understand the forces the move the line on the graph up or down. If it is true that inflation can erode debt only if we limit the growth of debt, that would probably be a good thing to know."

I do know that, you have sounded off about that for a long time but I think you might be making a mistake. You might be thinking that the forces that affect public debt, like inflation, also affect private debt the same way. Am I right? If so I think that is false. You are just using a generic term "debt" in pretty much all your posts the last few weeks and I think that it is a mistake to not differentiate.

What if its only true that inflation can erode public debt and that its affect on private debt is unreliable?
---------

"I often try in my writing to present the facts as I understand them, rather than saying what I think about the situation. (Sometimes I think that's why so few people ever agree with me. People seem to think that if they agree, they might get caught on the wrong side of an argument.) (Those people are not doing science.)"

Fair enough but Ill just add that its not enough to do science if that science isnt informing some decision. Its not just an academic exercise. Additionally to be counted as a fact it must be true in all instances. Im not sure its "a fact" that inflation erodes all debts in all circumstances, even if the debt isnt growing. I dont see how inflation erodes my mortgage payment or my car payment regardless of whether or not mortgages or car loans are growing or shrinking.

jim said...

Of course ceteris paribus means nothing else has
an effect. You know what you are doing becomes meaningless without the underlying assumption that we can pretend nothing else changes.

What you are doing is constructing a model of what debt levels might look like if inflation was removed (assuming everything else remains the same). Looking at the past we can see that debt growth tends to be low when inflation is low and debt growth is high when inflation is high. That suggests that a model of what debt growth would look like without inflation should show debt growth lower than it was with inflation.

The Arthurian said...

"What you are doing is constructing a model of what debt levels might look like if inflation was removed ..."

Nosir. I am calculating the difference in the value of debt (loss to the lender, gain to the borrower) due to inflation.

"... (assuming everything else remains the same). Looking at the past we can see that debt growth tends to be low when inflation is low and debt growth is high when inflation is high. That suggests that a model of what debt growth would look like without inflation should show debt growth lower than it was with inflation."

Yes, okay, probably a model of debt growth without inflation would have debt lower than the model with inflation. I have often suggested a policy of accelerated debt repayment as a way to fight inflation. My policy and your model are in agreement.

But I am not trying to show what the economy would look like without inflation. I am calculating the difference in the value of debt that is due to the changing value of the dollar.

The Arthurian said...

Greg: "What if its only true that inflation can erode public debt and that its affect on private debt is unreliable?"

Let me repeat what I just said to Jim. I am calculating the difference in the value of debt that is due to the changing value of the dollar.

PREMISE: If somebody borrows \$100 when a dollar is worth a dollar, and pays back \$100 when a dollar is worth fifty cents, the borrower has saved himself \$50 of value, which the lender has lost.

You want me to agree than my premise is true for public debt but not true for private debt. I don't see it. You could be right and I could be wrong, but you would have to convince me.

And because I am making a pretty well-developed argument at this point -- I've been developing the idea since 2011 -- in order to convince me, you would have to understand the arithmetic in my argument well enough to find flaws in it and then point out those flaws when I was having a good day....

Claiming that sovereign and private debts differ in other ways is not evidence that they differ in the amount that inflation reduces the value of those debts.

jim said...

"I am calculating the difference in the value of debt (loss to the lender, gain to the borrower) due to inflation."

To get a "difference" wouldn't you need to be subtracting something from something else?

You are calculating what debt would be without inflation. If that calculation were valid and if you actually subtracted the nominal debt from your result then yes, that would be the loss to lenders and gain to borrowers. But if you haven't arrived at an accurate figure for what debt would be without inflation then no, it cannot really represent a method to find the cost to lenders and benefit to borrowers.

The calculation of the loss to the lender and gain to the borrower due to inflation is already made by lender and borrower. The gain to the borrower and loss to the lender is covered in the debt contract in the form of interest charged.

In the case of the federal debt which is perpetually rolled over, the net interest outlays are part of the annual deficit. Each years deficit is already increased by the cost of interest paid. In the case of inflation adjusted securities (TIPS) they even wait to find out what inflation is to make that cost adjustment. So it seems to me what you are doing is double counting the effect of inflation.

The Arthurian said...

Jim: "The gain to the borrower and loss to the lender is covered in the debt contract in the form of interest charged."

1. Except in the case of negative interest rates, interest on a loan is loss to borrower and gain to lender.

2. Interest is not the same as inflation, not by definition and not by amount.

3. "Risk" -- loss due to inflation, I suppose -- is one of the things interest is supposed to compensate for. One of the things.

//

"To get a "difference" wouldn't you need to be subtracting something from something else?"

Intentional misunderstanding? I don't have time for that.

Greg said...

"PREMISE: If somebody borrows \$100 when a dollar is worth a dollar, and pays back \$100 when a dollar is worth fifty cents, the borrower has saved himself \$50 of value, which the lender has lost."

But thats not how it works. The borrower pays back 150\$ over time, sometimes as much as 300\$ in the case of mortgages. The interest is calculated considering inflation. I agree with Jim here.

Now there are merchants who finance same as cash ( for smaller purchases) for up to 3 years sometimes but I think they just work that in to the up front cost. IOW I think that same as cash deals drive up base prices. Merchants are going to cover their costs and get a profit somehow.

It would take pretty high inflation rates, rates that we've never seen here, to have the types of affects you are talking about...... but those types of inflation rates would also affect the person paying back the loans making it more difficult. I think its far from obvious that those types of inflation rates would be good for people who are paying back money to banks.

Now in the case of govt debt, a high inflation rate does affect the price of the debt and since these types of investment vehicles are traded I think its much more consistent to measure the affects of inflation on the debt. There are very deep and liquid markets for govt debt instruments and its much simpler to figure in the affects of inflation.

The Arthurian said...

Greg: "But thats not how it works."

That's how the part of it works that I am looking at.

With GDP, you take the nominal value, divide it by the price level, and multiply by the base year price level. That gives you an inflation-adjusted value.

That calculation works for any "flow" variable. It does not work for "stock" variables. For a stock variable like accumulated debt, a different calculation is needed. I'm trying to point that out. Do you see how everything you are saying is not relevant?

Oilfield Trash said...

Art

“PREMISE: If somebody borrows \$100 when a dollar is worth a dollar, and pays back \$100 when a dollar is worth fifty cents, the borrower has saved himself \$50 of value, which the lender has lost.”

You are using increases in the price level as a proxy for increasing nominal income, but you have not connected your arguments about inflation to income levels.

A household is not helped in paying its mortgage if the price it pays for groceries rises. But it will be easier to make mortgage payments if the household's wage increases.

Also this idea about savings and losing is not quite right. Interest rates always mitigate the effects of inflation.

The Arthurian said...

"You are using increases in the price level as a proxy for increasing nominal income"

Nope. Not at all. I didn't say anything about income in the premise. I said if a dollar is worth half as much when you pay it back, half what it was when you borrowed it, then you get to keep half the value that you borrowed.

//

I don't really know how much the effects of inflation are mitigated by interest on borrowed money. But I do know that even if it balances to the penny, it is a separate sum. It is interest, not principal. You create a massive complication when you add interest to the mix. Even if it is a fixed rate, the rate varies from one loan to the next. Payment schedules vary, too. And then, they front-load it so they get their interest up front. Do you want to calculate all that out and make a graph and write it up? I'll put it on the blog if you like...

Oilfield Trash said...

Art

"I said if a dollar is worth half as much when you pay it back, half what it was when you borrowed it, then you get to keep half the value that you borrowed."

One dollar is always worth a dollar, you want to give it some intrinsic value when it has none. The price level is the only thing that changes. So if you borrow 100 dollars to spend at the current price level and by the time you pay the dollars back the price level doubles you simply avoid the change in the price level less your interest payments.

The only way you can inflate the debt away is if nominal incomes increase such that a debtor has additional income to increase the amount of principle payment he makes each month to accelerate repayment and reduce interest cost.

Like I said "A household is not helped in paying its mortgage if the price it pays for groceries rises. But it will be easier to make mortgage payments if the household's wage increases."

The Arthurian said...

"One dollar is always worth a dollar"

Mmm, and I said

"there is just as much money in circulation as there ever was"

Things said in ignorance.

You can't step in the same river twice, OT. The value of a dollar now is not the same as the value of a dollar now. The value of a dollar today is certainly not the same as the value of a dollar in 1947.

The price level changes but the value of the dollar doesn't, you say. Bullshit, I say.

//

"The only way you can inflate the debt away is if nominal incomes increase such that a debtor has additional income to increase the amount of principle payment he makes each month to accelerate repayment and reduce interest cost."

Of course. Did you think I disagree?

But whether our incomes are going up as much as other things is a separate question that has more to do with income inequality and sectoral shifts than with inflation.

Oilfield Trash said...

Art

"The price level changes but the value of the dollar doesn't, you say. Bullshit, I say."

If you want to run graphs and weave camp fire stories that the dollar is a store of value, OK, if you do a good job I will listen to them for amusement and call bullshit myself when I see it.

"The only way you can inflate the debt away is if nominal incomes increase such that a debtor has additional income to increase the amount of principle payment he makes each month to accelerate repayment and reduce interest cost."

Of course. Did you think I disagree?"

I guess I am confused, which is not uncommon for me, but I thought that your graphs were making the argument that inflation reduces the burden of debt on the borrower. "Inflating the debt away" so to speak. I thought to myself that if Art is making this argument then the only way it works is if "You are using increases in the price level as a proxy for increasing nominal income". I guess I am misreading your argument.

"But whether our incomes are going up as much as other things is a separate question that has more to do with income inequality and sectoral shifts than with inflation."

Yes differential between consumer price and wage inflation just tells us about the distribution of incomes within the economy.

But we need to also be looking at output per worker. If the amount of output per worker rises over time, wages would need to rise by that amount in order to keep the profit share of income stable. Since it has not, the private sector has turned to debt as a replacement for the loss.

The Arthurian said...

Okay, Oilfield Trash, I apologize for using the one-word argument. Let me try something more verbose.

OT: "One dollar is always worth a dollar ..."

That's why a cashier will make change for a dollar if you ask. But what you said means only that a dollar at this moment is worth a dollar at that moment. It does not mean a dollar today is worth the same as a dollar last year, or the same as a dollar when Thomas Jefferson invented it. The worth, or value, of a dollar changes over time. I know that, and I think you know it, too.

Now, the rest of that sentence.

OT: "... you want to give it some intrinsic value when it has none."

I'm saying the value of a dollar changes. That is not the same as saying a dollar has intrinsic value. The value we put on the dollar changes: The value of the dollar changes.

If I can go to the store and buy something -- if I can exchange a dollar for something of value -- then the dollar also must have value, at least to the person who receives it as payment.

OT: "The price level is the only thing that changes."

So you are saying that [the general level of] prices going up is not the same as the value of the dollar going down? How can you say that????? Look at the economy as widgets and money. If the price of widgets goes up, it takes more money to buy one, so the value of the money has gone down, relative to widgets. If the whole economy is widgets, the value of money has gone down, period.

OT: "So if you borrow 100 dollars to spend at the current price level and by the time you pay the dollars back the price level doubles you simply avoid the change in the price level less your interest payments."

So you are saying, then, that calculating the inflation adjustment of debt is ... bullshit.

Do you hold the same view regarding the inflation adjustment of GDP?