Distributed Economics

In the textbook model of Fractional Reserve Banking then, what happens when a loan defaults?

Assume an economy with 3 banks, all of which have maximized their lending, in a 10% fractional reserve regime. In this financial system the total money supply is 3000, the total loan supply is 2700, and the reserves total 300. Bank Bravo’s loan of 100 goes into default, and is completely unrecoverable.

Thinking in detail just about how this should be handled by bank accounting,  suggests possible problems with the simple textbook description in Mankiw, et al. First, how does a Bank distinguish between the lack of loans due to default, and the absence of loans because it hasn’t made any? What stops Bank Bravo in other words, from issuing new loans in this situation, because its new deposit/loan ratio allows it to?

I have a faint suspicion, but unfortunately no access to the necessary library resources to prove this,  that there have been times and places where nothing did. Fractional Reserve Banking is something of an emergent system – it’s the result of custom and practice over several centuries, and there has been a lot of tinkering during that time to fix perceived problems with it. This also makes comparisons between different time periods very tricky – the rules have changed, and its the implementation rules that are quite critical.

It’s also worth noting that the symptoms of different problems under different fractional reserve regimes may well be very similar. There are typically many different ways to destabilize a distributed system of this kind.

Originally, banks or their equivalents issued their own bank notes, or deposit slips, in exchange for gold deposits. If a bank under this regime allowed itself to issue more loans when existing ones defaulted, then it would find that its ratio of loans to deposits/bank notes (leverage) would be steadily increasing. Since each bank then issued separate bank notes (the last remnants of this were the Scottish Banks in Great Britain until this crisis in fact), more and more of that particular bank’s notes would circulate, and presumably would either start to have their face value marked down in trade as people realised this, or just trigger a bank run.

In the modern age, something called the Capital Reserve is supposed to prevent this. When a bank is founded in the USA, it’s founders are required to provide a minimum $5 million dollar capital reserve. This is completely separate to the reserve shown above, which is a portion of the deposits. It is the combination of capital reserve and deposits that appear to control lending, which may also be why the Central Banks have considerably eased  the amount of customer deposits that must be held in reserve.  So the actual picture looks like this:

The loan loss knocks out Bank Bravo’s capital reserve, and leaves it needing to be recapitalized.  Assuming for a moment, no external inputs, &  that the Capital Reserve must be held in monetary units,  what does that do to the rest of the system?

Bank Bravo has to recapitalize by getting money to put into its capital reserve. Lets assume it does this by attracting investments from a depositor at Bank Alpha.

Bank Alpha is now not in conformance on its loan/deposit ratio, and either needs to attract more deposits, or reduce its lending. It can attract a deposit from Bravo to balance up, since Bravo now has a lower loan amount outstanding and has recapitalized. Or, it could not roll over one of its short term loans, and reduce its lending. In the former case, the total money supply is reduced, in the latter case, both the money and loan supplies are reduced. To wit (assuming that the loan was repaid with money on deposit at Bravo):

So what does this all mean?

Well, at the very least, it seems to indicate that one of the more popular American undergraduate Economics textbooks is a tad incomplete, since the system it describes could not in fact be implemented as described. Or to put it another way, if it were implemented as textbook, then as loans defaulted, which statistically speaking some number of loans will do, money and loan capacity would be progressively removed from the system, as the initial deposit expansion caused by the fractional reserve deposit/loan process went into reverse. It would reverse back to the point where the loans at the last remaining bank were in a 90% ratio to the initial deposit, then the next loan default destroys the banking system, until somebody decides to start a new one, kicking off the entire process again.

This also highlights that the theoretical model does not provide a constant money or loan supply. In fact both vary over time as a function of loan defaults.

In other words, the Fractional reserve banking system does not appear to be robust to loan defaults. This was essentially the issue Fisher raised in 1933, in his Debt Deflation Theory of Great Depressions paper. Since this is a system level problem, requiring banks to maintain deposit insurance doesn’t resolve the fundamental issue, which is that although banks are allowed to create money when they make loans, there is no good way for them to destroy that money if the loan that triggered the creation,  defaults.

Finally what the last table also indicates is that the system has multiple states. In other words, there is no single total value for the money and loan supply that the fractional reserve banking process ends up producing. It can naturally vary without any intervention in the system at all.

Anybody reading this, please comment if you think there’s anything at all wrong with the argument above.  With the preceding essays as some sort of basis for understanding the theoretical basis of the system, the next essay will take a look at the empirical evidence on how the system is implemented, before we take a look at where the central banks appear in all this.

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cc Fractional Reserve System, Lending, Prologue

At the core of the banking system, is an interesting, and oft misunderstood recursive function. The next couple of essays will attempt to explain this recursive process, and analyze how it might in fact behave within the economy.

Banks are allowed to create loans from a fraction of their deposits, whilst the owners of the deposits retain a right to withdraw those funds. As the loans are re-deposited at other banks within the banking system, money is created “out of thin air”, as many like to put it with a certain degree of apoplexy. It’s quite true that money is created initially by this process, but at least in theory, the money creation is limited, or bounded.

Consider two banks, and an initial deposit of $1000 at Bank Alpha. For now, we will ignore the role of the central banks, and concentrate on the theoretical model, described in undergraduate textbooks such as Mankiw.

Bank Alpha is founded with an initial deposit of 1000 monetary units. If the fractional reserve requirement is 10%, then it is required to keep10% of all deposits in reserve, and can make loans totalling no more than 90% of deposits. Assume that Bank Alpha creates a loan of 900.

In making that loan, Bank Alpha effectively creates money, as soon as the recipient of the loan deposits that money back into the banking system, say at Bank Beta.

Understanding the loan/deposit duality that fractional reserve banking creates within the commercial bank’s part of the monetary system is very important, but the concentration on the process of money expansion in most textbooks can be misleading. Deposits cost banks money, interest may have to be paid, checking and ATM facilities have to be maintained, etc. Loans on the other hand, bring income. So a bank in bank Beta’s position, with deposit liability, and no assets (loans) to bring in income, isn’t going to be very happy.

We would expect each individual bank then, to attempt to maximise its lending, and as we will see later, this does appear to be what happens in practice. So Bank Beta in turn, lends the maximum that its reserve ratio permits, and more money is created as this loan is redeposited.

This sets up the recursive process, of lending and redepositing, that can be expressed as a geometric series:

where x is the original deposit. In general the series converges to .

So that for example F = 20 yields the limit
[Credit: Mathias, Talk:Fractional Reserve Banking 2/11/2008]

This is however just the initial starting conditions for the banking system. Once the deposit and loan process has run for a few iterations, the money and loan supply expansion, as described in the theoretical model, should stabilize. If it is assumed that banks will tend to maximise their lending, in order to maximise their profitability, then the money and loan supplies, the sum of the deposits and loans at all the banks, would be expected to increase to the maximum allowed and stay there.

Once at the maximum allowed by the reserve requirement, and assuming no loan defaults, then the banks can only create new loans as old loans are repaid. Since loans are repaid from money from the deposit side, money is removed from thin air when that occurs. So in continuous, day to day operation, there should be no money or loan creation per se, assuming no additional money is introduced into the system, and assuming there are no loan defaults.

So why then is there a widespread belief across the Net, that the fractional reserve banking system is creating money?

Because it is. Any examination of the macro-economic statistics for the USA and other major industrial economies today shows that quite clearly. This is why the Wikipedia Fractional Reserve Banking page has some quite gratuitous graphs of several different currency’s money supplies, helpfully showing an exponential curve.

Or at least, something about the way fractional reserve banking system has been implemented is causing money creation, because the textbook description described above doesn’t do this. But the textbook description leaves out a lot of details, that are from a distributed systems perspective, extremely important.

For example, the textbook description shows a clear and presumably distinguishable difference between loans and money. In practice, this is not necessarily the case, some financial instruments are treated as money, but are in fact loans. Basel 2, the banking regulatory framework, allows some of those loan based instruments to be used for reserves. The textbook says very little about what happens when loans default, that will be examined next time, and nothing about the effect of sale of loans outside of the commercial banking system.

Critical commentary on the fractional reserve system is fixated upon money, on the deposits, on the pulling of money out of thin air, and the lack of a solid gold basis for that money. But at least in the opinion of this author, that’s not where the actual problems are. It’s the loan supply, loan regulation, and the masquerading of loans for money, that have caused systemic instability problems, quite possibly for several centuries.

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cc Fractional Reserve System, Prologue

There was a time when it was possible to go slumming on the Net and only risk being mildly perturbed, rather than long term psychological counseling and subsequent arrest for the contents of your browser’s cache. Back before the binary newsgroups got completely out of control, when an occasional foray over to alt.tasteless was just harmless fun.

Its been years since that was a good idea, but an acceptable substitute for those lost innocent pleasures in these online days of rage and diatribe, is a Google search for “Fractional Reserve Banking”.

So before  attempting to explain how Economists appear to think Fractional Reserve Banking works, and then examining how it in fact seems to be working in the presence of at least two bugs in the official description which apparently doesn’t in fact exist, let’s take a look at how it demonstrably does not.

There seems to be a  fairly common misconception that fractional reserve banking allows a Bank to lend 10 times its customer’s deposits. Oh, I wish. Let’s assume for a moment that that is true, and see what happens  if a couple of computer scientists, Alice and Bob, were allowed to set up banks.

Bank of Alice takes its $1000, and lends out $10,000 to a trusted intermediary, Eve; who deposits it in Bank Bob. Bank Bob then lends $100,000 (10 times the deposit), back to Eve. Eve then uses $10,000 to repay her debt to Bank Alice, and ponders what to do with the remaining $90,000. Since $90,000 isn’t really enough to buy 3 people tropical retirement these days, Eve deposits the $90,000 back at  Bank of Alice. Bank of Alice now has $101,000 in deposits,  and so can lend Eve $1 million, and well, you see where this is going.

Since it only takes $5 million to establish a bank in the USA,  I think the world would have noticed the mass retirement of American computer scientists by now.

This particular misunderstanding appears to be traceable to an article by Murray N. Rothbard,, where he writes:

I set up a Rothbard Bank, and invest $1,000 of cash (whether gold or government paper does not matter here). Then I “lend out” $10,000 to someone, either for consumer spending or to invest in his business.

There is a reason why it’s called  fractional reserve banking, Banks are allowed to lend a fraction of their deposits, where  a fraction is defined as a number that can represent part of a whole,  i.e. no more than 1, no matter what dark thoughts may be harboured about 5/4. In the classical textbook explanation, banks are allowed to lend up to 9/10 of their deposits, and required to keep 1/10 in reserve. That situation today is a tad more complicated, but we’ll look into that some other time.

Rothbard was an educated economist and mathematician, so it seems a  strange mistake for him to have made, particularly given the detail he uses in other places in the book.  He  was a member of the Austrian school, but this isn’t as far as I know part of von Mises analysis, who stands out as an economist who was trying to understand the economy as a distributed system – long before computer science started formalizing an understanding of them. Rothbard wrote this particular piece in the 1980’s, which is when the macro-economic statistics started looking distinctly odd. It’s possible that he noticed from the macro economic statistics that there was clearly something wrong, but then leapt to completely the wrong idea about what that was.Which is a pity, because some of the other points he makes later on about deposit insurance are actually quite prescient.

Unfortunately, the book and paper that contain this error, are hosted fairly prominently by the Austrian Economists on the von Mises website, amongst other places, and the abstract from it containing the error is currently the third hit on Google for “Fractional Reserve Banking”.

It bears repeating. Individual banks cannot do what Rothbard claimed, they can individually only lend a fraction of their deposits. They are required to file quarterly call reports demonstrating that. The recursive nature of the deposit, and redeposit of the money that they lend back into the system results in the banking system, which is to say all the banks, multiplying the original deposit into the system 10 times. But the implications of the system multiplying by 10 are completely different to any individual bank being able to do that.

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cc FRLF, Fractional Reserve System, Prologue

One of the many excuses that computer scientists occasionally proffer in order to justify the, well let’s be polite about this, totally appalling standards of documentation in our profession, is that systems are more secure if nobody knows how they work. Seriously.

Regrettably, all of the available empirical evidence suggests that poorly documented systems are in fact wide open to any evil cracker with spare time on their hands, whilst their legitimate users waste considerable amounts of time struggling to figure them out.

Fortunately, at least for the purposes of a quick exchange of fire in a greenhouse, compared to the financial system, the average badly documented computer system looks like it was written up by Shakespeare.

Which means that the biggest challenge in writing a paper describing possible systemic problems in the fractional reserve banking system, is actually trying to determine how that system is implemented and run in the first place.

For example. Go to the Bank of England’s web site, or the Federal Reserve Bank of America, or the European Central Bank, and do a search for “Fractional Reserve Banking”. Since it’s really the central bank’s sole purpose to regulate the FRB system, it doesn’t seem unreasonable to expect some kind of description of what they think they’re regulating. As of writing, in early May 2009, there is nothing.

Of course, an explanation of fractional reserve banking can be found in most economics textbooks. Usually though, that’s just a brief explanation of the reserve function of the central bank, and an explanation of the re-deposit process. I’ve yet to find anything that completely covers in detail what accounts are covered by reserve requirements and what aren’t, the limits the process places on loans, the financial instruments that can be used to hold reserves,  how increases and decreases in reserves are managed, and the effects of changes of some of these factors over time. There are minor but significant differences between countries which also need to be included.  Some attempt to relate the theory to actual macro-economic data would also be useful, if only for the sheer entertainment value.

There are regrettable consequences to this oversight. Currently the third hit for a Google search for Fractional Reserve Banking is a  1995 diatribe by Murray Rothbard which has very fundamental errors in it. In fact, the Net is currently swamped with plausible but demonstrably incorrect explanations of how the reserve banking system works, and enables <insert conspiracy theory of your choice here>. This all presents a fairly sizable barrier to anybody attempting to either understand the system, or even have a rational discussion about it.

Indeed, the best way to see this playing itself out, is to  take a look at the discussion page for the top hit, the Wikipedia entry on Fractional Reserve Banking. This must set a record for Wikipedia discussion pages,both for length, and general confusion..

This is the system of entities, rules, and regulations that control the total quantity of money and loans currently being supplied to the entire world’s economy.

Nothing important then.

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cc Credit Crises, Fractional Reserve System, Limits, Prologue

Paul Krugman had an interesting article in the NYT at the weekend, that inadvertently highlights several problems with current economic analysis. He is essentially discussing the presumed evils of deflation.

“Whatever the specifics, however, falling wages are a symptom of a sick economy.”

Really? Why?

Here’s how the paradox works. Suppose that workers at the XYZ Corporation accept a pay cut. That lets XYZ management cut prices, making its products more competitive. Sales rise, and more workers can keep their jobs. So you might think that wage cuts raise employment — which they do at the level of the individual employer.

But if everyone takes a pay cut, nobody gains a competitive advantage. So there’s no benefit to the economy from lower wages.

However, as stated, “XYZ management cut prices” – this is a benefit to the economy. Individual access to goods is controlled by price. Let’s say, all the food manufactuers engaged in a competitive wage cut process, triggering a 10% pay cut, and this resulted in a 1% cut in everybody’s food bill. Krugman goes on to suggest that if wage cuts trigger an arms race across all manufacturers, then everybody is poorer. But this assumes that consumption is performed solely by wage earners. It ignores people on fixed incomes (pensioners), recipients of wages from tax (civil servants).

It seems impossible to predict the actual consequences of what Krugman is describing, outside of the distributed system context that he is implicitly ignoring. For example, tax payments on the reduced wages would fall, presumably triggering a drop in wages derived from tax. But this wouldn’t happen until the following year, since government budgets are typically calculated on the previous years receipts. This introduces a latency component to the problem as well.

The actual problem Krugman is worried about is further down:

In particular, falling wages, and hence falling incomes, worsen the problem of excessive debt: your monthly mortgage payments don’t go down with your paycheck.

Well the problem for most of the american indebted is a little worse than that since their house prices are dropping steadily as well. One might speculate that this problem is particularly acute for NYT journalists, given their location at one of the ground zero’s for the flow of funds out from the financial industry, but that would perhaps be a little discourteous. Quantitatively it seems this is because the artificially boosted loan supply from the securitization pipeline has dropped from approximately $3 trillion in 2007, to $1,300 trillion in 2008. I’ve yet to see any evidence of a Fisher debt cascade in the Federal Reserve statistics, but it could be being masked by the reserve’s rescue activities. It is interesting, to put it mildly, that there are still buyers out there for that amount, but perhaps not so surprising given the Federal Reserves willingness to swap them out for treasuries in the various TALF schemes.

I really need to build a computer model to understand this more thoroughly, but my feeling at the moment is that the tax payer is essentially pumping money through a leveraged loop, to try and sustain some degree of securitized lending, in order to prevent a complete Fisher debt cascade collapse. This puts the tax payer on the wrong side of the money multiplier, and consequently at a distinct disadvantage to Wall Street. But I think we already knew that.

It seems that there might be a need within economic analysis to separate out deflation caused by increased productivity – which is what the computer/datacommunications industries have been experiencing – from deflation caused by fluctuations in the reserve lending system’s loan and money supplies. The latter is really more of a mathematical abstraction, albeit one with very real consequences. Possibly the cause of the business cycle?

The other issue that this highlights is that this is very much an example of loans behaving exactly like money in the general economy. An increase in supply caused (Asset) inflation, a decrease in supply caused (Asset) deflation, with all sorts of side effects triggered by differential latency problems, as the different factors affect the real time economy over different periods of time. Which is support for the idea that stability of the loan supply, is just as critical as that of the money supply.

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An exploit, laut Wikipedia, is “a sequence of commands that take advantage of a bug, glitch or vulnerability in order to cause unanticipated behavior.” One of the many things that makes designing distributed systems such a challenge is trying to avoid creating such vulnerabilities. It can be a complete nightmare trying to fix any that make it into a live system, especially if they’re the sleeper kind that only get uncovered after years of successful operation.

The Fractional Reserve Banking System, is a distributed system. It has a set of rather poorly documented rules that are implemented by banks worldwide, which have emerged for the most part from empirical experience. So is this the bug that caused the credit crisis?

Consider two banks:

Bank A has $1000 in deposits, has lent out $900 and has kept a reserve of $100 as it is required to. To be very specific , since it matters more than might be imagined: Bank A is an American bank, and the $1000 is being kept in daily checking accounts, so there is a reserve requirement. To make the example as simple as possible, Bank B just has deposits, and no loans. Bank A creates a Mortgage Backed Security of $900, and sells it to the deposit holder at Bank B.

So far so good. Bank A lends out $900 again. It is allowed to do this, this in some sense is what being a bank is all about. The $100 it keeps as a reserve, is a contingency fund to cover any daily demand for funds. The $900 borrowed is then used to purchase something, and eventually is deposited at bank B. This gives the following:

Notice that the third table is identical to the first, with respect to the money, loans and reserves at each bank. The only difference is the $900 mortgage backed security, representing the $900 in loans that were sold by bank A. Bank A in other words, can go through this loop as many times as it wants, as long as it can find people to lend to, and people to buy the resulting securitised loans.

I haven’t yet found much in Economics about what limits there should be on commercial bank lending. The fractional reserve banking system itself, if it were working as described in textbooks, would impose an implicit limit on the amount, but even this doesn’t appear to be directly acknowledged. The other problem, is that loans are made for many years. So any failure in their systemic regulation, wouldn’t necessarily be noticeable for quite a long time. By the time it was noticed, it might even be thought to be the normal behaviour of the system.

Which does indeed appear to be what’s happening now.

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cc Credit Crises, Lending, Limits, Prologue