Distributed Economics

Poke around in the entrails of history, and a surprising number of revolutions, and coup’s of one form or the other of etat, can be attributed at least in part to some form of underlying monetary breakdown. Typically the form of breakdown that involves at its heart,too much debt being issued, for the available supply of peasants to support payment of. It would be nice to think that the very least a communist government, formed by and on behalf of the workers and peasants of its country could achieve, would be to avoid that one.

There are two very strange things about the news out of China these days. One, is that there have been clear signs of a loan induced housing bubble for some time now. The other is the succession of increases the People’s Bank of China has made in the required reserve rate for its banks in order to constrain that bubble. The latest increase on May 10th to 17%, follows a raise to 16.5% in February 2010,  and a set of increases over the last couple of years.

According  to the existing Economic theory of how the banking system works, each one of these should have triggered a large contraction in the available money and loan supplies, given that the removal of money from  the system triggered by the reserve increases – is a multiple of the reserve change.

Despite this, there is in China today a rapidly increasing CPI, and a raging housing bubble, alongside  a steadily increasing reserve ratio. The situation gets even worse, if the  underlying non-monetary economy is considered, which in China is one of steadily increasing production. Since production increases cause deflation, as the existing money supply is used to trade and purchase more things, this suggests money and loan supply expansion, rather than the contraction that should have been triggered by the reserve changes.

All of which suggests something has gone very badly wrong indeed, in the Chinese banking system.

Monetary statistics are available on the People’s Bank of China’s web site for the period since 1999.  They are unfortunately not at the same level of detail as the USA, or indeed Iceland.  In particular since there is no break out of the M series components, it’s not possible to know how much debt instrument contamination is present in these series. There is a format change in 2005, and since the number’s don’t quite match up for the different series, the chart below is just for the last 5 years.

Chinese Money Supply

The data for the entire period, assuming that measurement has been reasonably consistent, shows that M1 has increased by approximately 4x in 10 years, about twice the quantitative  increase in the the Dollar and the Euro over the same period. It would also appear from the chart that the process has begun to accelerate.

The data shown is certainly consistent with reports of a credit fueled housing bubble, originating from uncontrolled lending within the banking sector, triggering asset inflation and commercial bank expansion of the money supply. What is perhaps most remarkable about the chart above, is the complete absence of any affects from the reserve increases that the Chinese central bank has been imposing to try and throttle the system back. It has been steadily ratcheting the reserve rate up for the last 3 years, it’s now at 17%, but there has been no corresponding contraction in the money supply. It’s probably the case that the expansion would have been even greater had they not increased the reserve requirements. But still. If economic theory was correct, what the chart should be showing is a massive contraction in the money supply – since changes in the reserve requirements theoretically  have a 10x multiplier effect on the money and loan supplies – and it’s plainly not.

Given the reports of a housing bubble, increasingly lowered lending standards, and CPI, it sounds like this is probably the Equity Capital exploit cutting loose again. Whether this  is because the banks are abusing inter-bank lending mechanisms as occurred in Iceland, or have just figured out they can stuff some form of debt into their equity capital holdings is very hard to say – there simply isn’t the kind of publicly available data to properly analyze the Chinese banking system. Given the repeated increases in the reserve ratio, it seems highly unlikely that any part of this is deliberate government policy though.

Which points to another aspect of this entire problem. Both the exploits discussed here, the Equity Capital exploit, and the Asset backed security loophole, are outlined for a system with full reserve requirements. De facto, the European and American banking systems don’t use reserve requirements for central bank control any more, and rely on market operations. Those don’t in fact work, but as China is currently demonstrating, neither do the textbook, central bank control mechanisms via the reserve requirements either.

The other interesting implication of this, particularly if the expansion continues to accelerate, is that if the Yuan were to be allowed to free float, it would probably depreciate against the Euro and the dollar, rather than appreciate as is being called for by American and European economists.

& won’t that be fun.

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cc Asset Inflation, Empirical Analysis, Exploits, Fractional Reserve System

When debugging complex systems, it can be useful to ask, “What’s missing?”. Especially when looking at  the available monitoring information, which tells you not only what the designers of the system thought it was important to know, but also by omission, what wasn’t. Critical realtime systems, we’re talking Nuclear Power plants and their ilk, are monitored fairly closely, but if the right information isn’t provided to the operator, then that won’t necessarily help all that much.

In this sense, it’s quite interesting that  Economics doesn’t seem to have  a definition of what money is, in any satisfactory, scientific sense. Rather it seems to have various descriptions of what money does. The “Money is a matter of functions four, a medium, a measure, a standard, a store.” dogeral that is found in some textbooks and on Wikipedia is the perfect illustration of this. This is not a definition of what money is, it’s simply a list of the things money is used for. This confusion can also be found in the various measures used to quantify the total amount of money in the Economy, which are variously M0, M1, M2, and depending on which country you’re in M3 or M4.

Interestingly, and perhaps damningly in the context of the current credit crisis, no single, monitored central bank measure appears to completely capture the information that is of most interest today – which is what is the total quantity of money that commercial banks and reserve based savings institutions are allowed to create loans against.

M0/Monetary Base

This is the “narrowest” definition of the money supply. The British, who technically invented the entire system, used to use M0, but since 2006 it’s the “Notes and coins and reserve balances” figure (YWMB43D), whilst the Federal Reserve simply refers to this as the Monetary Base, and reports it in the H3 Aggregate Series.  It is defined as the reserves from the Banks held on deposit by the Central Bank, and the total amount of physical currency. This measure probably made more sense under the Gold Standard than it does now, when a significant number of bank deposits don’t in fact carry a reserve requirement, and physical currency is simply printed to meet day to day demand.

Reserves held at the central bank used to be a very fixed, and important part of the system’s regulation, since this directly controlled lending. In that implementation of the system, the Commercial Banks had to deposit the reserve on deposits they were required to hold behind for each loan (i.e. the 10% fractional reserve requirement), at the central bank. For two simple reasons. It kept them honest, and it gave the Central Bank complete control, and indeed visibility, on the monetary expansion that was occurring. Assuming for example, that the Banks were correctly depositing their reserve on deposits at the central bank, then if that amount started growing, the central bank immediately knew that the loan supply was increasing and vice versa.

Only net transaction accounts in the US Banking system carry a reserve requirement currently, so that part no longer works very well. Even so – when the Federal Reserve saw the non-borrowed reserves drop by 25% in December 2007, and indeed go negative the following month, it was a clear warning sign of major systemic issues. The Bear Stearns collapse into bankruptcy would occur 3 months later in March 2008. How significant it is that there is also a fall in the British reserve measure, beginning in July 2006 and reaching its nadir in September 2007 before an abrupt recovery, is hard to say.

M1

M1 is technically physical currency and checkable deposits. Quite what it will be when it is no longer possible, as it will be and to a large extent already is in Europe, to write a cheque on a bank account, is an interesting question. It’s reported by the Federal Reserve as part of the H.6 dataset, along with its cohort M2, and they also helpfully break out the different components of M1 if you scroll down a little.

Broadly then, it’s physical currency and demand, or instant access checkable deposit accounts, which appear to be the Net Transaction Accounts for which there is still a reserve requirement. I have an HSBC internet savings account, it has no cheque book, pays a (very) small interest rate, and which i can transfer to and from using the Internet at will. Is it classified under M1 or M2? Does it have a reserve requirement? Does that even matter?

The last question is perhaps the most interesting. The answer appears to be both yes and no as it happens. Since reserve requirements are no longer used to directly regulate loan expansion – equity capital does that – then it doesn’t strictly matter if an account has a reserve requirement or not. Except of course, that the Banks can at the moment get quite a nice interest rate from the Federal Reserve on their reserves, which is why reserves so dramatically increased a year ago. Now there’s no correspondingly dramatic shift in the components of M1, so it looks like the Banks just dumped all their spare money onto the federal reserve – which lends some credence to the claim that this has inhibited lending. Except of course, that they’re still as busy as ever creating and  selling Asset Backed Securities.

M2

Strictly, M2 is all of M1 plus Bank savings accounts and Retail Money Funds. The Federal Reserve helpfully breaks out the non-M1 components of M2 as part of its H6 dataset, which makes life a little easier.

Now this is where it gets quite interesting. Retail Money Funds, which were a non-existent category at the beginning of 1959, and peaked in October 2008  at slightly over $1 trillion are around 15% of the total quantity of M2. Retail money funds are funds that generally provide an extremely safe return, that is expected to track the safest form of investment (government securities), and never not return their capital investment. They’re also expected to be very liquid, i.e. you can get your money back more or less on demand. This essentially means that they invest in short term debt securities, although only ones of very high quality. Like triple A rated, insured, top of the tranche Mortgage Backed Securities for example?

Leaving aside the interesting co-incidence that the growth of retail money funds begins in the same period as MBS were introduced (late 1973, sales don’t really kick off until the S&L crisis in the early eighties); just the total quantity of retail money funds indicates that some of them must be in MBS securities. There simply aren’t enough other suitably ’safe’ instruments paying a suitable rate of return otherwise. Which means that some proportion of the M2 money supply measure, is actually debt.

This helps to explain the divergence in the growth between M1 and M2, in the USA and other countries, since thanks to the Asset Backed Security loophole, debt is currently growing faster than money within the banking system. It also i think, provides a measure of proof, that the Central Banks really don’t understand what’s going on in the system these days. Because if they did, they would not publish statistics that obviously confuse money with debt, especially in a system where money is regulating the total quantity of debt, and vice versa. Of course, if they did understand that, then Banks wouldn’t be allowed to hold debt instruments in their equity capital holdings either.

M3

And then there’s M3. Which was somewhat notoriously, and to the great delight of the FRLF, discontinued by the Federal Reserve in 2006. If you want proof that many of the critics of the current banking system also have no idea how it actually works, threads on the Federal Reserves  discontinuance of M3 can be quite enlightening, if for no other reason than their blind assurance that it was a valid measure of the money supply.

But no, if you look at the largest, and towards its end, most rapidly growing components of M3, it’s Institutional Money Funds, followed by something called “RPS”. Institutional money funds are retail money funds writ large, and stuffed with those wonderful top tranche Asset Backed Securities. RPS are,  i believe i’m correct in saying, Repurchase agreements owned by the banks. Repo’s as they’re otherwise called are one of those interesting pieces of financial alchemy, whereby you sell a financial instrument to somebody, for cash, along with a guarantee that you will buy it back at a specified amount sometime in the future. It’s essentially a loan in return for an agreement to buy a loan.

Quite how you can get away with calling that part of any money supply measure, I have no idea.

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cc Credit Crises, Empirical Analysis, Fractional Reserve System

There is a lot of discussion on the net, good and very accurate discussion, about the reserve requirements, and the current almost absence of same. The Eric deCarbonnel post (hat tip Andre. G. and Mickanomics) has a nice summary of the situation in the US. There is one unfortunate problem though with these discussions -  fractional reserve requirements no longer have anything to do with controlling how much money a bank can lend.

What has replaced it, is the regulatory capital requirement. Regulatory or equity capital is a completely separate pile of money that the owners of the bank are required to provide when a bank is started, and maintain at a minimum ratio to their loan book, as the bank is run. The FDIC requires that this be at least $2 million when a bank is founded, plus the anticipated startup costs.  The Basel treaties then specify what percentage or leverage ratio the Bank is allowed to maintain between its equity capital and its loan book, and also what kind of financial instruments the Bank can hold the equity capital in.

There are two things then that control the immediate size of the loan book, of any bank in a Basel treaty conforming country. The amount of money it has on deposit (including savings accounts, and term deposits), and the size of its equity or regulatory capital. The fractional reserve requirement, i.e. the difference between the total amount of money it has on deposit, and the total money it has lent out, is relevant only insomuch as it is not allowed to lend out more money than it has on deposit. Just to ensure that complete confusion reigns, the recommended maximum total capital ratio, ie. the leverage ratio of equity capital to amount being loaned, is 10%. The same as the textbook fractional reserve requirement.

This is the 21st century. Weren’t we supposed to have moon bases by now?

It makes some sense, if you only think about the situation at the individual banks. If a bank makes a loan that doesn’t get paid back, and the loan loss can’t be covered out of profits, then equity capital is there, to in theory, prevent the depositors losing the money in their accounts. This is what is being referred to when there is talk about ‘recapitalizing’ the banks. Obviously too, given that this is all that stands between the depositors, national deposit insurance funds, and significant losses in the case of loan defaults, it’s critical that the equity capital be held in extremely safe forms of financial instruments.  This is why so much of the discussion and rules around equity capital are framed by the risk of default represented by the underlying securities, and the desirability of keeping that as low as possible. Solutions to the current crisis that involve increasing the equity capital are also being floated.

You can see the mental process path that’s being followed here. If banks take a hit to their equity capital, it reduces their loan capacity. If they take a hit that’s bigger than 10%, they have no equity capital left, and then their depositor’s money is endangered. Do everything possible to prevent that happening, the depositor’s money is now safe, and banking can go back to being boring again.

Unfortunately, system design doesn’t work well, when only the individual entities are considered, and not the interactions between them. Concentrating on the risk of individual bank losses, ignores the larger issues being created by a system whose core set of rules, embodies a relationship and an interdependence between loans and the money supply. Especially, if owing to “financial innovation”, some loan instruments are being allowed to masquerade as money.

The simple answer then, to the question  – what is the limit on commercial bank lending? -  is that for any given Bank, it is the  lesser of the total of their deposits (minus a very small fractional reserve requirement that applies only to Net Transaction accounts), or ten times their equity capital. It follows then, that the instantaneous limit for all the Banks, is simply the sum of their deposits, or equity capital allowance.

But that’s merely the instantaneous limit. It tells us  nothing about the way that the system will evolve over time, as loans are made, money is created, loans are repaid and money is destroyed, within the commercial banking sector. Especially within a larger system, that allows debt to be turned into financial instruments, and those instruments to be used as part of the bank’s equity capital.

Or to put it another way, what controls the total amount of equity capital in the system? The old reserve requirement, and its associated commitment to deposit a part of that reserve with the Central Bank, provided the central bank with direct control over the money and loan supplies.  What is the equivalent control over the total quantity of equity capital in the system, since it now effectively regulates the money supply? The quick answer, which will be explored in considerably more detail in the next post, is that there isn’t one.

The regulators were concentrating on local risk at the banks. They appear to have overlooked the systemic risks associated with removing control over the money supply.

The hardest problems to correctly diagnose in distributed systems almost invariably involve two or more concurrent bugs interfering with each other. In the banking system at the moment, we have the Asset Backed Security bug, allowing banks to create an arbitrary quantities of loans; and the Equity Capital snafu, which has essentially introduced a slow leak into the money supply. Next post, i’ll run through a detailed example of how they interwork with each other.

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cc Credit Crises, Fractional Reserve System, Limits

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

What is the limit on the amount the Commercial Banks are allowed to lend?

The story of credit crises is usually told from the demand side. The irrational exuberance of speculators down the ages drives inflated prices for over priced assets.  Inevitably the bubble bursts. Inevitably everybody pays the price. But the supply side of this formula always seems to get overlooked.  Why are the commercial banks able to supply a seemingly  limitless quantity of  loans to fuel the credit bubble? Why does a speculative bubble in Beanie Baby’s merely cause general embarrassment, while one in real estate cause massive economic dislocation?

This is a deceptively simple question, in the context of the larger fractional reserve banking system, since it is not just the quantity of the  loans that is potentially problematic. Through the fractional reserve process, commercial bank lending also has potential money supply implications. If there is no limit on the total quantity of commercial bank loans, then there is effectively no limit on the commercial banks’ ability to create money through the fractional reserve re-deposit process.

It is also notable that discussion of the problem of credit supply last year, concentrated on the supposed fear that the banks have of the risk in lending to each other in the inter-bank markets, rather than the possibility that they might simply not have had any money to lend.

Hypothetically then, the question can be framed in at least three ways. Either there is a limit on bank lending, in which case it might be reasonable to suppose that it is that limit that is preventing inter-bank lending, and not a sudden outbreak of pathological loan aversion in bankers; or there isn’t, in which case the money supply is being controlled by the commercial bank’s individual lending policies  rather than the central banks, which would be contrary to every foundational Economics textbook.  The third possibility  is that there is supposed to be a limit on lending, but some elements of the financial industry have found a way around it. However, given the entanglement that fractional reserve lending creates between the money and loan supplies, how exactly could this even be detected?

Going back to the previous post, a side effect of the fractional reserve banking system is that it creates two different kinds of debt within the economy. One is straightforward transfers in exchange for IOU’s of various kinds, either between individuals, businesses primarily in the form of bonds, and the government (treasuries). The other are the loans from the commercial banks, which represent a deposit somewhere in the banking system. For want of any better ideas, I’m going to channel physic’s particle/anti-particle structure and call them anti-deposits.  Commercial bank originated loans for long. Debt that results from a direct transfer of monetary tokens will be referred to as transfer debt.

If there is something going wrong uniquely within the fractional reserve banking system, then one expected outcome might be a change in the proportion of anti-deposits  to transfer loans within the general economy. If the amount of outstanding commercial bank loans is increasing faster than the quantity of transfer loans for example. Conversely, if the actual cause of the systemic problems that we’re currently living through is in fact government transfer debt, or increases in “fiat money” as I was confidently told by an Austrian economist back a few months, then we would also see a change, but it would be an increase in the amount of government originated transfer debt relative to commercial bank originated anti-deposits.

The quantity of outstanding debt within the United States economy is reported on a sector basis in the Z1 Flow of Funds report, Table D.3 The chart below shows the per sector information on Debt Outstanding.

From the explanatory notes in the current report. Foreign debt represents amounts borrowed by foreign financial and non-financial entitities in U.S markets only. Domestic financial sectors consist of government-sponsored enterprises, agency and GSE backed mortgage pools and private financial institutions.

The sectors aren’t totally clean with respect to being able to divide into transfer versus anti-deposit (bank originated debt). The domestic financial sector debt is for the most part being derived from bank loans in the forms of mortgages, since it includes Fannie Mae and Freddie Mac, who buy mortgages from U.S. banks and repackage them as bonds. Presumably also student loans, under the guise of Ginnie Mae.

Even so, it’s noticeable  from the chart above that bank originated debt is growing faster than other sources. Comparing proportionately the amounts owed by each sector in 1975 versus 2008, shows this quite clearly:

Proportionally, the last 30 years have seen a shift away from government debt towards commercial bank debt, primarily in the form of mortgages, since that is the main component of the Domestic Financial Sectors sector. They have also seen an extraordinary rise in the total amount of debt, as was shown in the original flow of funds chart, and it also appears that this new debt has predominantly originated from the commercial banks, chiefly in the form of mortgages.

In theory, the fractional reserve mechanisms don’t allow banks to issue arbitrary amounts of debt.  Originally they were  limited to a fraction of their deposits, now they are limited to a multiple of their equity capital. So what exactly has gone wrong that is allowing the commercial banks both to create so many loans, and to increase the money supply?

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cc Credit Crises, Fractional Reserve System, Limits, Prologue

The Reserve Requirement and the Equity Capital requirements are two very different things, which often, and not at all surprisingly, get confused.    The best explanation I’ve found so far for the reserve requirement for the US banks is provided by Federal Reserve Board’s Reserve requirements page. It is fairly clear from that description there that the reserve requirement is the difference between the amount that the bank has on deposit and the amount it can lend, and is required so that the Banks can handle day to day demands for cash and transfers.

The reserve requirement today is 10% for Net Transaction Accounts above $44 million in deposits, 3% below that. A net transaction account is broadly a current account. There is no longer a reserve requirement for time deposits, which are presumably savings accounts with access restrictions.This amount of money either has to be present in the Bank’s vaults, as physical cash, or on deposit at the Federal Reserve, as a reserve.

Requiring the Banks to have some amount of physical cash, and/or a fixed percentage deposit of their total deposits at the Federal Reserve, is a way of synchronising the entire system. From a distributed systems perspective, this can be very important, if you want agreement between independent agents on say, a fixed ceiling on the amount of money or credit that the entire system can supply. There’s a nice distributed systems proof called the Fisher consensus problem, which shows that it is impossible to guarantee agreement without some element of synchronisation (which generally means a central point of some kind) between the distributed members of a system. However, it’s not entirely clear that the Federal Reserve understands it this way.

There is a very interesting paper from the Federal Reserve by Joshua N. Feinman, called Reserve Requirements: History, Current Practice, and Potential Reform. The paper reviews current and past reserve requirements and the reasons for them, at least according to the Federal Reserve.

Perhaps the most interesting thing about the paper is what it doesn’t say. At no point does Feinman discuss reserves as an integral part of systemic regulation of the loan and money supplies. In the main, the paper is about avoiding undue quantity of reserves – because of the cost to the banks of maintaining them (cost of deposits, with no loan income to match), and providing the necessary liquidity to meet day to day requirements. Which it seems, the Federal Reserve believes it has solved by being the lender of last resort, and providing shortfall funds to the banks whenever they need them.

A Bank’s equity capital is something quite different. This is the capital that was used to found the bank – it is a completely separate pile of funds to the deposits that are held by the bank. Nominally, this is the money the founders had to provide in order to be allowed to setup a bank in the first place. It is also referred to as Tier 1, 2 or 3 capital following the Basel accords. Equity capital is also generally what is meant when the problem of recapitalizing the banks is referred to.

When Banks take a loss on their loans, they first cover the loss from profits. In the absence of profits, they use their equity capital. That in and of itself can create problems, given that money then has to be brought in to replace the equity capital, which nominally at least reduces the amount on deposit, and hence the amount that can be lent.

Which returns to the problem of controlling the loan or credit supply for the whole banking system – i.e. how much in total are the Banks allowed to lend – and what in fact controls it? The reserve requirement – as implied by Feinman, or the amount of equity capital held by the banks, as implied by the Tier 1 and 2 capital ratio’s reported in every bank’s call report?

Who really controls the loan supply? The federal reserve? Or the commercial banks?

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All Banks licensed to operate within the United States of America have to file detailed quarterly reports on their lending and deposit status with the Federal Financial Institutions Examinations Council (FFIEC). These are known as banking Call Reports, and since 2001, are available for download, and public examination.

If there’s any kind of guide to reading and understanding them, I’ve yet to find it. Still, it’s amazing what can be done with python scripts, and a little patience.

There are two ways to get call reports – either as a consolidated set of files for all the banks per quarter, or individually per bank. It’s easier to understand call reports by looking at the individual consolidated ones, but for systemic analysis, the consolidated files can’t be beaten. It’s also useful to know that in the consolidated files, the Bulk POR report has the names, addresses and FDIC/IDRSSD numbers for all the Banks, which can otherwise be quite hard to find.

So, taking the Citibank FDIC #27606 call report for December 2001, we can  find the ratio of deposits, reserve and loans – at least, we can with a little decoding.

Deposits are known as liabilities in the alternative universe of Bank accounting. Total liabilities, are RCON2948; Total Equity Capital is RCON3210, and Total loans and leases are RCON2170. The forms aren’t completely consistent. For Wachovia, the RCON3210 field is missing, but RIAD3210 is listed as Total Equity Capital, Total Liabilities come under RCFD3300, Total loans are still under RCON2170 though. So in tabular form:

Then there is the question, which Citibank? For the big banks, there often seem to be several separate listings. There is also Citibank Delaware, Citibank New York State, Citibank Nevada, Citibank (South Dakota), and a couple of others.27606 is Citibank USA, using the form for a Bank with domestic offices only.

Another interesting question, in which field are the reserves? Equity capital is normally used to refer to the capital invested in a firm by its owners. So this would presumably be the capital reserve, which is the money used to found the Bank. It also matches the Tier 1 Capital entry, RCON8274.  Presumably then, the reserve of deposits referred to in textbooks, is not listed separately, but is simply the excess of deposits over loans. For which, for Citibank at least in December 2001, would appear to be  -$109,040,000. Interesting.

Actually, it gets worse further down the form. In RC-R the Regulatory Capital section, where Total Risk Weighted Assets are $2,470,549,000 (RCONA223).

Wachovia’s numbers also seems a little strange, since and at least in 2001, they were somewhat over capitalised. However, they seem to be reporting some kind of change to Equity Capital of $6,819,394,000 and it looks like they spent 2001 merging with First Union, which might explain it.Their Total Assets (loans) really are exactly equal to their Total Liabilities(deposits). I’m afraid most engineers, almost innately, tend to find exact matches like that suspicious as hell.

So from the empirical evidence, it seems that Banks can lend out as much as they have on deposit, and the Equity Capital reserve is in fact, the shareholders capital investment into the Bank, and is completely separate to the money deposited by the customers. Banks are required by the Basel treaties to maintain a minimum leverage ratio between theri Equity Capital and their Loans, which Citibank is within the limits of. (RCON7204-6). Presumably this explains why Citibank can get away with lending more money than it has on deposit, it’s still within its ratio with respect to its equity capital.

All the same, it seems a little strange. So, pausing only to drop this lot into a nice little sqlite database, next time I think we’ll look at the figures for some of the banks that have failed this year, versus some hopefully healthy ones, and also look at the situation across the eight years of data available.

One thing can be said though. The Murray Rothbard claim, that Banks can lend ten times their deposits, is shall we say, not supported by the available data.

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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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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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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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