## Monday, June 20, 2011

### The Ratio of Debt to Money

13 June 2011.

Next-Blog brings me to Jake's EconomPic, where the second post -- Federal Debt per Employee -- links to "Steve Keen's epic piece that changed my understanding of the economic collapse," Jake says. I'm reviewing the epic piece.

"This month’s Debtwatch," Keen writes,

is dedicated to analysing how these Cavaliers actually “make” money and debt—something they think they understand, but in reality, they don’t.

I don't know how he gets from that to 'the myth of the money multiplier', but he does. Let me quote a chunk of it, just because it is so irritating:

The conventional model: the “Money Multiplier”

Every macroeconomics textbook has an explanation of how credit money is created by the system of fractional banking that goes something like this:

Banks are required to retain a certain percentage of any deposit as a reserve, known as the “reserve requirement”; for simplicity, let’s say this fraction is 10%.
When customer Sue deposits say 100 newly printed government \$10 notes at her bank, it is then obliged to hang on to ten of them—or \$100—but it is allowed to lend out the rest.

The bank then lends \$900 to its customer Fred, who then deposits it in his bank—which is now required to hang on to 9 of the bills—or \$90—and can lend out the rest. It then lends \$810 to its customer Kim.

Kim then deposits this \$810 in her bank. It keeps \$81 of the deposit, and lends the remaining \$729 to its customer Kevin.

And on this iterative process goes.

Over time, a total of \$10,000 in money is created—consisting of the original \$1,000 injection of government money plus \$9,000 in credit money—as well as \$9,000 in total debts...

Keen follows that explanation with a spreadsheet where the sequence of lendings runs for 20 weeks (one new loan per week), generating a total of more than \$8900 from an original deposit of \$1000.

He then shows that the final total would come to \$10000. But he neglects to say that it would take eternity for that to happen. Here's the picture after the first 20 relendings of that original thousand-dollar deposit:

 Graph #1

It came out orange.

The first vertical bar is the original \$1000 deposit. Each subsequent vertical bar is 90% of the previous bar, because 10% of the previous deposit is kept in reserve and 90% is lent to another customer and becomes a new deposit, of which 10% is kept in reserve and 90% is loaned out...

This reminds me of a bad joke my chemistry teacher told, many years ago. I don't understand why there is hunger in the world, he said. Give 'em a pound of butter and tell 'em to eat half of what's left every day. They'll always have butter.

My teacher wasn't making a joke, really. He was explaining the concept of always approaching a number yet never getting there. If you have something and you take 10% of it away, or 50% of it, you always have something left no matter how many times you take a bit away.

 Graph #2

After 100 weeks the amount available for lending is three cents. After 116 weeks the amount available is so small that at two decimal places, it rounds off to zero. After 250 weeks, however, if we run the numbers out that far, the amount available for additional lending is still greater than zero. These are the fractions of fractions of pennies that gave Richard Prior the big paycheck in that old Superman movie.

As the new-loan amounts approach zero, the total amount of money created by this fractional-reserve lending process approaches (but never reaches) a maximum.

Suppose you draw a square on a piece of paper. Then you draw a line down the middle of it, and shade in one half. Then you draw a line down the middle of the unshaded portion, and shade in one half. Then you draw a line down the middle of the unshaded portion, and shade in one half...

Eventually, the square will be almost all shaded-in. But you could keep going forever, shading-in half of what's left undone, and never get done. However, the total amount of the shaded-in area would before long be almost equal to the total area of the square you started with.

What this means is the approximate total shaded-in area is known or can be determined. By exactly the same logic, the approximate total amount of money created by the fractional-reserve process is also a known amount. That total depends on the amount that must be kept in reserve. And there is a simple way to figure it out.

The textbooks always use a ten-percent reserve requirement. Ten percent can be written as a decimal, as 0.10, okay? Take one dollar, or just the number one, and divide it by 0.10 and it tells you the total amount of money that can be created by the fractional-reserve process, from one dollar deposited.

If the reserve requirement is 10%, \$10 can be created. If the reserve requirement is 20%, \$5 can be created. If the reserve requirement is 50%, \$2 can be created.

If the reserve requirement is zero, there is no limit to how much money can be created from one dollar deposited. (But expect to get an error if you try to work that out with a calculator!)

The Billy Blog here has an explanation similar to Keen's:

The formula for the determination of the money supply is: M = m x MB. So if a \$1 is newly deposited in a bank, the money supply will rise (be multiplied) by \$10 (if the RRR = 0.10). The way this multiplier is alleged to work is explained as follows (assuming the bank is required to hold 10 per cent of all deposits as reserves):

• A person deposits say \$100 in a bank.
• To make money, the bank then loans the remaining \$90 to a customer.
• They spend the money and the recipient of the funds deposits it with their bank.
• That bank then lends 0.9 times \$90 = \$81 (keeping 0.10 in reserve as required).
• And so on until the loans become so small that they dissolve to zero …

Like Keen, Bill Mitchell shows a spreadsheet which runs through the first 20 steps of the process. Mitchell observes:

In this particular case, I have shown only 20 sequences. In fact, this example would resolve at around 94 iterations as you can see on the graphs where the succesive loans, then fractional deposits get smaller and smaller and eventually become zero.

Keen says the money multiplier is "completely inadequate as an explanation."

Wordy Bill says the money multiplier is "not even a slightly accurate depiction of the way banks operate in a modern monetary economy characterised by a fiat currency and a flexible exchange rate."

I say: So why then do these guys spend so much time going step by step by step by step through the process? Look, it's simple. Clear your calculator, hit the number 1, hit the 'divided-by' key, type in the reserve requirement, and hit the 'equal' key. That's it. That's how much money can be created from a dollar.

The question as to whether the money-multiplier process actually works (or not) has nothing to do with determining how much money can be created by fractional reserve lending. I think the "how much" question is raised as a smoke-screen. Something to distract and confuse the reader, so that when Keen and Mitchell tell you it doesn't work, you're glad to hear it, and glad to toss the concept aside.

Keen presents two "hypotheses" about money, that arise from the money multiplier model. One is that government money is created first, and credit money is created from it, but after the government money is created. Keen references a study showing that the opposite is true.

The other is that each new loan in the fractional-reserve process creates new money and new debt in equal amounts, so that at the end there should be exactly the same amount of money and debt... Except when we add in the money we started with, we end up with more money than debt:

The amount of money in the economy should exceed the amount of debt, with the difference representing the government’s initial creation of money.

"Therefore, Keen says, "the ratio of Debt to Money should be less than one..."

This is the first time I have seen anybody other than me talk about the ratio of debt to money, which I call "debt per dollar". So I'm kinda thrilled by this. More than 'kinda', because it's Keen.

But I've been looking at it for 30 years, and it never occurred to me that if the money-multiplier idea is correct, there should be more money than debt. Maybe Keen's right. I don't know. But let me show you why I've been looking at the thing for 30 years.

Back when I first looked at it, using numbers from the Historical Statistics, the history of the ratio of debt to money looked like this:

 Graph #3

Starting with five and one-half dollars of debt for every circulating dollar of money, debt rose to over \$7. A Depression ensued, but debt kept rising, reaching eight and one-half dollars for every circulating dollar of money. Then, from 1933 to 1947, debt fell, reaching a low of less than \$4. Then it started rising again. By 1970 it was higher than it had been at any time during the Great Depression.

I didn't have to know why this happened to know that it was significant. I've been watching Debt-per-Dollar ever since. I figured policymakers would stop the increase of debt before it gave us another Great Depression. I was wrong.

 Graph #4

But my graph only goes up to 2007, which is before the crisis. So it doesn't show what happened since. But FRED shows it:

 Graph #5
The peak is far higher this time than it was in the 1930s.

The bigger they are, the harder they fall.

Oh. But to tie up a loose end, both Steve Keen and Bill Mitchell deny that the money multiplier is an accurate picture of what happens in the economy.

Could be they're right. When I look into it a little, it seems like they're right: Loans create deposits. If the bank doesn't have enough reserves to lend what it wants to lend, it lends anyway, and gets the reserves later.

But what happens if the bank *does* have enough reserves to lend what it wants to lend? Then the money multiplier works normally, right? The bank's not going to borrow reserves if it has the reserves it needs. Do Keen and Mitchell deny that? So I think their rejection of the money multiplier is a bit stronger than it should be.

Or again: If the banks always borrow the reserves they need in order to lend, then the ratio of debt to reserves should be more or less constant, it seems to me. Taking a guess what measure of reserves is relevant, I'll look at total credit market debt relative to "Required Reserves, not adjusted for changes in reserve requirements."
How required reserves can possibly be *not* adjusted for changes in requirements, I cannot fathom. But hey, I didn't make it up.

 Graph #6

Not constant at all. Not even close. So maybe I picked the wrong data. But while we're looking at this graph, look at the 1980s when the ratio is about 200 dollars of debt for every dollar of required reserves. That figures to be an effective reserve requirement of one-half of one percent. And at the peak there, when there was \$1200 of debt per dollar of required reserves... that's less than one-tenth of one percent in reserve.

Hopefully, I'm looking at the wrong data.