Distributed Economics

In the textbook presentation of the Fractional Reserve Banking System, the example of the reserve redeposit process typically shows the expansion from the starting condition of an initial deposit. This is more than slightly misleading. The banking system that we have has been running more or less continuously, depending on which country you’re in, for several hundred years. The expansion from initial conditions can be presumed to be long past.

Theoretically then, we should be in a state where the money and loan supplies are fairly constant, or varying between known limits, and where the total commercial bank debt is 90% of the total money supply, assuming a 10% reserve requirement.

Clearly not in the world we’re living in. Especially the known limit part.

The explanation this blog is exploring, is that the primary reason for this is an interaction between the effects of  allowing loans to be sold in the form of Asset Backed Securities, and using equity capital rather than reserves to control total bank lending.

At the macro-economic level Asset Backed Securities have effectively increased the total amount of loans outstanding in the economy, and have done that within the part of the loan supply that comes from fractional reserve operations, rather than say somebody going out and buying a Corporate bond or government security. The end effect of this is that the ratio of commercial bank originated loans to deposits is no longer a fraction of total deposits, but rather a multiple. For example, in addition to the approximately $10 trillion commercial bank assets (loans to the rest of us)  held by the United State’s commercial banks, must be added the outstanding amount of Asset Backed Securities that have been sold on by the commercial banks. The net outstanding total for Asset Backed Securities for the USA as of June 2009, was $6,5 trillion. Back of the envelope, and assuming that most ABS is held as part of equity capital, then probably at least $5 trillion is being held outside of the commercial banking system, by pension funds, insurance companies, and other entities that need a store of money.

The immediate question this raises then, is how many of these things are there out there, and which currencies or countries are worst effected?

I’m personally convinced you can get a rough idea just by counting building cranes and uncompleted luxury condo blocks in any major city at the moment. Tracking down actual figures is a little tricky. Most Central Banks don’t seem to publish separate statistics on ABS sales, or if they do they’re not readily identifiable. However, the Bank of International Settlements does put out some high level aggregated data. Quite what their source for it is, I have no idea, but it seems to be the best there is at the moment.

The chart above shows the quarterly totals of newly issued debt securities from table 12a, which includes Asset Backed Securities and Pfandbriefe (covered bonds). The data is quite interesting. For one thing, it indicates that the 2008 credit crunch was primarily a failure in issuance of Asset Backed Securities. The drop, early in the year, suggests that at $1 trillion in capacity was removed from the system, which is a lot of loans. Even though the visible symptoms of the credit crunch were in areas like letters of credit, and revolving credit, it was very probably a knock on effect from the removal of Asset Backed security credit. The other takeaway from the chart is the subsequent, central bank and government financed recovery to 2006 levels. Somewhat akin to treating gangrene with a band aid, really.

Working out which are the worst afflicted countries is problematic. Whilst $6.5 trillion is a lot of debt, the USA is a lot of country, and a very powerful economy. Ireland on the other hand, is a rather soggy island on the left hand side of Europe, and they’re currently sitting on $546 billion of the things. With a population of 5 million, that’s just over $100,000 each.

An alternative to normalizing by population is to normalize by GDP. The problem there is that loan financed activity, building luxury condominiums for example, is counted as part of GDP. It’s the Exon Valdez disaster problem again – measured purely by its contribution to GDP, cleaning up an ecologically catastrophic oil spill was economically beneficial because of the extra work and spending it caused. Normalised by population Ireland comes out 4 times worse than the USA, normalised by GDP the USA is twice as bad as Ireland. On either measure, Greece, Iceland, Ireland, the Netherlands, Spain and the United Kingdom, and of course the USA, all stand out. No surprises there.

So where does this all end up? Asset backed securities have proliferated throughout the western developed economies, so almost all countries are involved to a greater or lesser degree. Norway for example, which is sitting on the proceeds from their share of North Sea Oil, has still managed to accumulate an outstanding, per head of population amount of around $35,000. The closest the banking system has ever come to generating this kind of situation before, was probably in 19th century America, a period known for rampant bank failure. There were assorted reasons for this, but a fair amount of it was caused by deliberate fraud, in the form of banks making loans that exceeded their deposits, typically to colluding cronies, sorry, ‘business associates’ of the men controlling the banks. It seems possible that the total loan supply might at some points have exceeded the total money supply in the US during this period, even with the gold standard, but who knows. The American financial system at that period was regarded as a thieves charter by British economists, and even by some Americans.

In our modern age, though it is strictly illegal for individual Banks to lend more than their deposits; Asset Backed Securities have unfortunately managed to allow the entire banking system to do it.

No collusion required.

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cc Empirical Analysis, Lending

Viewed from a computer scientist’s perhaps somewhat jaundiced perspective, the history of Fractional Reserve Banking and the many changes that have been made to it over the centuries is one of neither careful design, nor careless conspiracy  - careful conspirators typically don’t publish their meeting’s minutes online. Rather it is a history of kludges.

Every time the banking system has blown up, either in the form of some kind of speculative credit bubble, or through a collapse in the value of money through general inflation, the proximate cause has been identified and “fixed”.  Almost inexorably, or so it seems, thereby setting the larger economic system on track for the next problem.

One of the classic problems acknowledged in the textbook implementation of the Fractional Reserve Banking System is the inherent problem in relying on statistical multiplexing of a small reserve to satisfy deposit demands. What happens if a Bank hits a statistical outlier, and more than 10% of the bank’s depositors turn up on the same day asking for funds?  The other 90% of the bank’s deposits is represented by loans, and not immediately available. The probability of this happening depends on a number of factors, but two obvious, and historically relevant ones,  are the size of the bank, and its geographic coverage. The smaller the bank in terms of the number of its depositors and loan recipients, and the more locally based its depositor base, the more vulnerable it is to external events. For example, a bank that takes all its depositors money and makes five large  loans with it, is much more exposed if one of them defaults, than one that makes one hundred.

As a side note, this also means that the stability of a fractional reserve based banking system itself, depends in part on the distribution of monetary tokens within the community. A society where all the monetary tokens are controlled by a small number of people, is potentially far more vulnerable to banking crises than one where ownership of monetary tokens is more evenly distributed.

The pattern of a large number of small, locally based banks, was especially the case in the 18th and 19th centuries, when there a much higher incidence of bank runs than even today. Customer demand for money that exceeded the available reserves could just happen  randomly, because at the end of the quarter money had to be transferred from depositors to lenders at different banks. Ludwig von Mises also mentions this problem occurring in the Austrian Banking system in The Theory of Money and Credit.  It could happen because some event acted to co-ordinate borrower’s demand for funds – say a local crop failure requiring food to be purchased with savings, which might also put pressure on the bank from both directions, if the crop failures also caused local  farmers to default on their bank loans. It could even happen because the owners of the town’s other bank started a rumour, in order to get customers to switch their deposits.

From the perspective of the people running the banks though, this is regarded more as an annoyance than a real issue with the system itself. After all the depositor’s money is out there somewhere  in the form of a loan which will eventually be paid back. If the depositors would only wait, then they could receive their funds. Silly people for not understanding modern banking concepts and panicking. This is what comes of letting the common people have bank accounts. Etc.

The solution that was found in Great Britain in the 19th century was to introduce the concept of a central bank, in their case the Bank of England, as the lender of last resort. If a bank didn’t have enough funds to satisfy instantaneous demand, the Bank of England would provide funds to do so, and the Bank could then repay the Bank of England when its loans came due. Problem solved.

From 1866 onwards there were no financial crises in Britain at least for the rest of the 19th century. The banking system in the United States of America on the other hand, which at that time consisted of a large numbers  of very small banks,  saw repeated local bank panics, and occasionally some non-local ones with their associated major financial crises. It wasn’t until the early 20th century, that the United States copied the British system and setup the Federal Reserve Banks to act in a similar role as lenders of last resort in 1913. Following the wide spread bank failures during the Great Depression there,  a further support in the form of deposit insurance was introduced to the American system (and subsequently copied in Europe), and since then, there have been remarkably few bank failures, at least until the Savings and Loan crisis in the 1980’s.

From a distributed systems perspective, these are both good and valid solutions to the problem created by excessive demand for instantaneous funds.  Essentially what both these changes did was to distribute the problem represented by instantaneous demand for funds that exceeded the available local reserves of a small bank across the entire banking system.  While the available funds/loan balance of  single  bank could be badly de-stabilised by a single customer with a large deposit moving their account to another bank say, within the context of the entire banking system, this is a non-event.

Unfortunately, either lulled into a sense of complacency by the absence of bank panics, or perhaps because it was something that was never explicitly acknowledged,  the Central Banks appear to have forgotten the other purpose the individual bank’s reserve requirement played in the monetary system.

Providing a limit on the total quantity of loans made available by all the commercial banks.

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cc Credit Crises, Fractional Reserve System, Lending

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

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