Distributed Economics

Here is a thought experiment. Assume that the money supply is completely constant, there are no loan supply induced fluctuations, the government is behaving itself, and there is simply a fixed quantity of money in the banking system. In a period of steadily rising production, due to technological and social change, what happens to prices?

They go down.

Deflation, to use the technical term, occurs because as more and more things, assets, food, granite kitchen tops, hit the market, there is less and less money available per thing, and the price drops. Or to put it another way, in a world with a constant money supply, if you inflate production, you deflate costs. It doesn’t really have anything to do with the social organisation of production, and it’s  highly debatable if it’s a good or a bad thing in terms of the effect on human behaviour. It’s just  math.

Over the last 20 years, there has been a lot more stuff available, at all levels of society. This is the age of the nail gun. The fully automated factory, and the completely unautomated Indian call centre.  There are more people, producing more things than there have ever been on the face of this planet, so the real question of the age should be, why hasn’t there been massive deflation -  rather than mild inflation, and raging asset inflation.

The simple answer, and the one born out by the central bank statistics is the money supply has been increasing. But that just raises the issue of why? And if we accept the idea that it’s not the central banks, and that is something that is also born out by the statistics, then the question is also who?

Equity capital is at the moment, the only real control on the part of the money supply within the commercial banking sector. To clarify, the chart below shows the difference between the ‘reserve’ of deposits that banks may be required to keep against deposits, and the equity capital that acts as a reserve against loan loss.

Under the Basel treaties, individual banks are required to keep equity capital reserves that are at least 10% of their loans.

Reading the Basel treaties, it’s apparent that their main concern is risk. Basel is all about reducing the risk of any individual bank defaulting, and to achieve that, it mandates equity capital reserve requirements, since it’s the equity capital that gets used when a bank suffers losses to ensure that depositors don’t lose their money. So if the only concern is what happens at individual banks, then it makes sense to  regulate that they have adequate equity capital reserves, and that those reserves are held in safe, secure financial instruments, that also provide the bank with some kind of return to compensate it for the ‘cost’ of maintaining a stack of otherwise useless money. (From the individual bank’s selfish point of view.)

Like mortgage backed securities for example.

41. Loans fully secured by mortgage on occupied residential property have a very low record of loss in most countries. The framework will recognise this by assigning a 50% weight to loans fully secured by mortgage on residential property which is rented or is (or is intended to be) occupied by the borrower.

(Clause 41 of the Basel Capital Accord)

Those were the days. Bet they rewrite that for Basel 3.

In fact, there’s a serious problem with allowing any kind of debt based financial instrument into equity capital, however tempting the associated income stream may be, and that is that as soon as you do, it allows the commercial banks to do the one thing that they’re not supposed to be able to do without central bank involvement – create money.

Consider 2 banks:

Bank A creates a $900 Mortgage Backed Security, and sells $800 of it to the depositor at Bank B for $1000. How much would it really be  worth? I’ve yet to be able to track down how much they sold these things for, but it’s a guaranteed (or at least it was before the loan insurers blew up), financial instrument paying anywhere between 5% and 15% a year for 5-25 years. So $1000 seems like a bit of a bargain. It doesn’t actually matter as long as its more than the underlying loans were made for.

Bank A takes the $100 tranche of the MBS it retained, and uses it to increase its equity capital. It counts it as 50% so it only increases its reserves to $150. It takes the $100 and pays that out as bonuses, which get deposited in its employee’s bank accounts, at its branches. One of the perks of being a bank employee is free banking from your employer, and usually reduced rate loans too.

Assuming the strictest case, i.e. that the deposits at Bank A are being held in net transaction accounts, then Bank A can now lend 90% of its deposits ($990), provided that this doesn’t exceed 10 times its equity capital. The new loan then gets deposited at Bank B.

The end result of all this sleight of loan, is that the total money supply has been increased by $90, and the  total loan supply has been increased by $900 MBS and $90 additional loan capacity in the banking system. This makes for a fairly slow leak as these things go, since it can take months or even years to issue the underlying loans. It’s worth noting that the central bank, who supposedly control the money supply, played  no part at all in any of this. It’s the commercial banking system that is out of control here.

So the money supply is increasing, but this isn’t effecting inflation nearly as much as it should. In fact its masking what would have been some fairly dramatic deflation over the last 20 years due to productivity improvements. Unfortunately however, the total loan supply is increasing much faster.

Which is where the real problem lies.

© cc

cc Asset Inflation, Credit Crises, Prologue

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?

© cc

cc Credit Crises, Fractional Reserve System, Limits, Prologue

Central banks  are charged with regulating the money supply. Regulating not in the sense of rules, and laws, although they do form part of the framework it operates in. Regulating in the sense of controlling the quantity of. This is from the leaflet,  Modern Money Mechanics, published by the Federal Reserve Bank of Chicago in 1968, and last revised in June 1992:

From the standpoint of money creation, however, the essential point is that the reserves of banks are, for the most part, liabilities of the Federal Reserve Banks, and net changes in them are largely determined by actions of the Federal Reserve System. Thus, the Federal Reserve, through its ability to vary both the total volume of reserves and the required ratio of reserves to deposit liabilities, influences banks’ decisions with respect to their assets and deposits.

Bank’s assets are for the most part their loans.

The  commercial banking fractional reserve system introduces a rather strange money particle/loan anti-particle recursive relationship between some, but not all, of the loans in the monetary system.  This isn’t true for loans made to companies that borrow money through the bond market for example. They borrow money by selling an IOU, as does the Government when it borrows money using treasury certificates.  It’s only within the commercial banking system that money takes on this strange duality, and can expand and contract with the extension and default of loans.

What am i trying to say there. If a loan goes bad in the corporate bond market, then the company goes bankrupt, and my ownership of that bond gets me into the queue of creditors for a claim of assets and not much else. There are no money supply implications. The money i gave the company in return for a bond, is out there somewhere with whoever the company gave it to in return for goods, services, or a passport for tax free exile.  If a bank loan based on my bank deposit defaults however, I still have my deposit. But there is a deposit out there somewhere that should really disappear. That the current implementation doesn’t allow this to occur is one of the stresses on the system.

The bigger problem though, is that since there isn’t a fixed quantity of money within the commercial banking system, it depends after all on how much lending they’re allowed to do, it’s critically important to scrutinise what’s happening within the system quite carefully.  For example, if an expansion of credit is occurring, is it because the system is expanding within it’s allowed limits, or has it found a a way to circumvent them?

The Federal Reserve seems to believe that by controlling the money supply, it also controls the loan or credit supply.  It controls the money supply, by requiring the banks to hold a small portion of their total deposits either in physical bank notes, or on deposit with the federal reserve bank. Let’s look at money supply regulation first.

Leaving aside the banking system’s day to day liquidity issues in terms of satisfying customer’s demands for access to the funds in their deposits, it is arguably the case that it doesn’t matter how much the banks keep in reserve, or how much of that is on deposit at the central bank, as long as it is a fixed portion of the local bank’s reserves.

As long as some known fraction of the money represented in deposits is required to be held at the Federal Reserve (or in bank notes and coins), then the Federal Reserve can calculate what the total money supply is simply by multiplying. It can set what level it thinks is appropriate for that total, and adjust the reserve amount appropriately, or it can inject money to increase it, again by the known percentage that is anchored by the reserve. The only difference from that simplistic perspective, between a 1% and 10% requirement is how much you have to multiply by to get the total money supply. This is the textbook presentation of the reserve based system.

The statistics on commercial bank reserves, and the Monetary Base for the United States of America, are reported in Report H3 by the Federal Reserve. The Monetary Base is the simplest statistic on the quantity of money in the system, and is defined as the total  of commercial bank reserves held at the Federal Reserve, plus the total of printed/coined currency. To wit:

As you can see, things start to get a little funky on the right hand side there when the Federal Reserve starts trying to resolve the 2008 credit crisis. Let’s look at things before that happens though. This graph is showing the totals for all physical currency and the reserves. It is the reserves that are supposed to be regulating the money supply, “through its ability to vary both the total volume of reserves and the required ratio of reserves to deposit liabilities”. So all other quantities of money, within the fractional reserve system, should be derivable as some multiple of the reserve. (This incidentally, is i suspect where the Rothbard fallacy may originate. Individual banks lend a fraction of their deposits, however the federal reserve regulates their deposits, as a multiple of the reserve.)

Which unfortunately is not what is being shown in the chart above. Then again, what relationship should the total quantity of physical currency have, to the bank reserves? Physical currency isn’t controlled any more, in terms of a fixed relationship to reserves, rather it’s printed as needed. Even so, it’s reasonable to expect that that need would in some sense reflect a somewhat consistent percentage of the total quantity of money – which is essentially physical currency plus the sum total of all bank accounts. So the chart seems to show that the federal reserve is successfully keeping bank’s reserves constant, but either there has been a consistently growing demand for physical notes over bank accounts in the last four decades, or something else is going on.

The consistently growing demand for physical banknotes theory isn’t entirely discountable as it happens. The US dollar is accepted world wide, and a significant amount of physical cash is held outside the USA. That can be deduced simply from the large amounts that were found during and after the invasion of Iraq.

Digging a little deeper. M1 is the base measure of the actual money supply, and includes physical currency, demand deposits and other checkable deposits. Demand deposits are all bank deposits which allow immediate access, rather than savings accounts and similar, which require deposits to remain for a specified period of time. Looking at the historical data on the components of M1, from the Federal Reserve’s H6. Table 4, and please note the y-axis on this chart is in $ billions, whereas for the other two it is $ millions:

Interestingly, demand and checkable deposits do look like they are holding approximately stable in the last couple of decades at least. In fact they’re holding stable at roughly 10 times the reserves held by the central bank. So, the reserve requirement does appear to be successfully regulating the quantity of money held in demand and chequeing accounts. These in other words appear to be the Net Transaction Accounts, for which the banks are required to keep 10% either on deposit with the federal reserve, or present as physical cash in the bank vaults. So why then, is physical cash going up so much? After all, if the Federal Reserve is actually printing physical cash to increase the Money Supply, then the deposits wouldn’t be staying relatively constant, but would in fact be increasing to match.

Or in other words. Is physical cash being printed in order to increase the money supply, or is physical cash being printed because the money supply is increasing?  One last chart.

This chart shows the Total Reserve, the Monetary Base, M1, and the Total Liabilities of the US Commercial Banks from the H8 data series, table b1152a. Total Liabilities, is the sum of all the money deposited at the Banks by their customers, plus loans from other Banks. That table starts in 1973, and yes those are the right units.

What is the money supply? Is it just the checking accounts most people use for day to day cash, the Net Transaction accounts? Does it include savings as well? Physical cash in Iraq and elsewhere? There are economic arguments for and against counting each of those in fact, that’s why there are the different measures, Monetary base, M1, M2 and before it was discontinued M3.

If the money supply is just the amount held in Net Transaction Accounts, then the Federal Reserve is regulating it successfully. But that’s the only thing that is being regulated. Physical cash is clearly expanding, but that’s nothing besides the total amount of cash represented by deposits with commercial banks. The electronic money supply, the money that is represented as electronic 0’s and 1’s in a computer database somewhere is clearly growing exponentially. And has been for some time.

One definition of the money supply that isn’t explitly reported, but would seem to be fairly important in a fractional reserve system, would be the amount of money that the banks can lend a fraction of. As you might guess from the above chart, it certainly isn’t the amount held in Net Transaction Accounts.

So just as this post attempted to dissect the deposit side of the fractional reserve money/loan dichotomy in the context of the larger system, next time, we’ll look at the loan supply.

©cc

cc Empirical Analysis, 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?

©cc

cc Fractional Reserve System, Prologue

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.

©cc

cc Empirical Analysis, Fractional Reserve System, Prologue

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.

©cc

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.

© cc

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.

© cc

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.

© cc

cc Credit Crises, Fractional Reserve System, Limits, 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.

© cc

cc Credit Crises, Lending, Limits, Prologue