1. Introduction

Nobody understands money, least of all economists. Too sweeping a statement? Perhaps. But every analysis of the workings of monetary systems that I have ever read has been seriously in error at one or more crucial points. This is true not only of the supposedly impartial opuses of academic economics, but also of the writings of Marxists, socialists, Keynesian dirigists, free-marketeers, anarcho-capitalists, libertarians and utopians of every flavour.

On important issues of monetary policy, then, and whether a free market in money is either workable or desirable, the protestations of the experts must be considered unreliable. In particular, the claims of libertarian-leaning economists, such as Ludwig von Mises, that the operation of "free banking" would be both stable and superior to the system of government monopoly called "central banking" need to be treated with scepticism; they have not proved what they think they have proved.

Here I intend to give a description of certain aspects of the creation and use of money free of major error; it is conceivable that I may not entirely succeed. I shall argue that free banking, as it is usually understood, may be liable to gross instabilities and inefficiencies, especially in a free-market environment, and that a centralised fiat currency has definite advantages. However, I shall then describe an alternative form of free-market banking that appears not to suffer from these deficiencies and into which the current system of state control could be metamorphosed. I shall argue that it is the innate honesty or dishonesty of the banking method that most distinguishes good money from bad; and that it is of the greatest importance to ensure that the laws under which banking takes place are able effectively to restrain all dishonest forms of banking, including those in which the dishonesty is most subtle.

2. What is Money?

So what is money? A deceptively easy question, that. Answers from the past include "gold", "silver and gold", "a medium of exchange", "a promise to pay", "a store of value", "a measure of demand", "just another commodity". Such answers hold a germ of truth, but only lead to controversy, because they miss the essential point. All along we've been asking the wrong question. Instead, let us ask a new one:

What is the function of money?

The function of money is to keep track of who owes what to whom. In a world in which there is division of labour and in which we obtain diverse satisfactions by the voluntary exchange of goods and services we have need of an accounting device to permit this exchange to take place at minimal cost and without undue coercion or confusion. This accounting device we call money. Simple barter is not enough, because the goods I want are seldom held by the person to whom I can render service.

Imagine a central register, detailing every transaction entered into by each and every person, and containing a list of all the favours owed by each and every person to each and every other person. That would do it. It would be hideously complicated, but it would work. Fortunately, though, we needn't go to such lengths, because in a market economy most of that data is redundant. All we really need to know is the current balance to the account of each person — how much the rest of the world owes him or how much he owes the rest of the world — and even that need not be centrally recorded.

In a market economy, then, the function of money is to reduce the transaction costs of honest trade (including gifts and bequests other than those directly in kind) by reliably and efficiently registering the indebtedness resulting from previous transactions. The details of those previous transactions no longer matter; only the present net position counts (except for incomplete transactions, such as when you have bought an item but not yet paid for it).

So, if the function of money is to keep track of honest trade, can we now answer the original question in a more enlightened and constructive way? I think we can.

3. Money is Information

What is money? Money is information. Specifically, it is the information necessary to determine the entitlements of persons and organisations to obtain goods and services on the market. It tells me how much I can consume before I have to go out and produce some more (or beg, or be given, or promise to produce, or otherwise obtain some more). In short, it is a number.

Thus gold, bank notes and other forms of currency are not in themselves money. Rather, they are the embodiments of monetary information, much as a book is the physical embodiment of a story. And just as the same story can be printed in a book or magazine, read out over the radio or television, stored on an audio cassette or CD or transmitted digitally down the telephone lines and displayed on the screen of a computer, yet remain that selfsame story, so can the information that is money be embodied in notes or coin, held as a balance on a bank account, or transmitted electronically from person to person or bank to bank, yet remain that selfsame money.

What we loosely call "money" is not truly a medium of exchange, for the physical exchange could in principle take place without it. This "money" (currency might be a better word) is more correctly described as a storage medium, upon which the information that is money is impressed.

It is unlikely that we could successfully restrict the use of the word "money" to the monetary information itself, nor would there be much to gain by doing so. After all, we are quite happy to use the word "book" to refer either to the paper-and-ink object or to its informational content, and seldom get confused between the two meanings. Yet in continuing to use the word "money" in this conventional way we should always remember that this is merely a verbal shorthand for "monetary information embodied in the form of this currency" and that the true money is the information itself; and we should avoid using the word "money" when we are considering the properties of the form of currency as distinct from its monetary application. Gold miners don't mine money. And money doesn't grow on trees — not even paper money!

Money is not wealth. It feels like wealth, but it isn't wealth. In fact, when money changes hands, the real wealth moves in the opposite direction. Or, better, when real wealth changes hands, we find it convenient for accounting purposes to move monetary counters in the opposite direction, rather like double-entry bookkeeping.

4. Simple Embodiments of Money

There are many embodiments of money, of which one of the most popular and ancient is gold. With good reason. For gold embodies the monetary information with high reliability and convenience. Because gold is gold, every ounce worth the same as every other, the data gold carries are secure and all but incorruptible. As Archimedes famously demonstrated, debased gold coinage can be unmasked simply by weighing the coin itself, then weighing the water it displaces; only gold is that heavy (with the exception of a few noble metals like platinum, osmium and iridium, which cost about as much as gold and are much harder to work). Because gold is a commodity valued for its own sake, its market price is not easily manipulated; distorting the monetary information to any great extent is therefore difficult (though not entirely impossible), even for governments.

Moreover, since gold is so rare and costly it is (perhaps paradoxically) cheap and convenient in use; a considerable amount of money can be carried in a small purse, and huge amounts stored in quite a small vault. Gold can be transferred from bank to bank, or country to country, at minimal cost. In olden days a wagon load of gold was a week's wages for a million men. Indeed, if anything, gold is overqualified for everyday money, and silver and copper have often been pressed into service as small change.

Yet gold is not without its disadvantages. If it is easy to carry, it is also easy to steal — which has the effect of falsifying the monetary information and suggesting that the world owes a debt to the thief instead of to his victim. However, this is a problem common to all bearer instruments, with the possible exception of those whose transfers can when necessary be traced back through the chain of legitimate owners.

Sometimes even gold is not as convenient as one might wish; merchants have long been in the habit of depositing their actual gold with the goldsmiths or bankers in exchange for gold certificates or bankers' notes, which represent the gold held for safekeeping in the bankers' vaults. The monetary information is unaffected by these arrangements — so long as the gold really is in the vaults where it's supposed to be.

Sometimes merchants don't even want the bother of carrying around bank notes, especially since notes can be stolen just as easily as gold itself. In this case they deposit their gold with the bank on account; they are then free to withdraw cash on demand (either as gold or in notes) or write cheques against the account in favour of third parties; deposits can also be made in the form of previously issued gold-certificate bank-notes, or by transfer from other deposit accounts. These demand deposits embody money just like the gold they represent, with the added security of being safe from pilferage.

5. The Economic Costs of Commodity Money

All these embodiments of money (coins, notes, deposit accounts) share one failing; they are inefficient. Though inexpensive to circulate or hoard, gold is necessarily expensive in production; a significant fraction of the productive effort of the economy must be diverted to gold-mining and refining. How big a fraction? A little thought shows that the annual cost of producing gold for monetary use can be expected to equal the product of the growth rate and the total value of the gold in circulation as money (deposits plus cash). I assume that the rate of loss of gold in use is negligible, but if not, we should add this rate to the growth rate.

In the latter half of the twentieth century an economic growth rate of 2.5-3.0% pa and an M3 of 30-40% of GDP would be typical of the industrialised nations; if we still used gold as commodity money about 1% of GDP would have to be devoted to its production. This is hardly an excessive price to pay for a secure monetary system, but any savings would surely be welcome.

Now prior to the industrial revolution, economic growth rates were small, so the cost of commodity money was also small; but in a free market, growth rates could be expected to rise far higher, in excess of the 20% pa typical of the less heavily regulated but still far from free "Asian tigers"; gold production would then consume more than 10% of GDP. Furthermore, the demand for a money not subject to inflation and devaluation would probably be much greater than today's M3, perhaps as much as a full year's spending, or even more. If the free market achieved a growth rate of 100% pa (and, astonishingly enough, this might prove a conservative estimate) the cost of gold production would then rise to an impossible 100% of GDP!

Is there a cheaper way? What about reducing the cost of gold mining through improved technology? Useless. That would merely reduce the value of gold so that correspondingly more gold would be needed to embody the same amount of money. The total cost would stay the same. What about using more plentiful metals like silver? Same problem. A correspondingly greater quantity needs to be mined; the total cost stays the same. What about using both silver and gold? No. The total cost is unaltered, and we have the added difficulty of dealing with two currencies at once.

Indeed, the production of any commodity currency whatsoever costs the same amount in total. This is true even for currencies based on sophisticated baskets of industrial and agricultural commodities or retail items. To be used as true commodity money the contents of those baskets must either be circulated as cash or stored by the banks; they cannot be put to other use. In general, the continuing storage and transaction costs for such currencies will be very much higher than for gold. Imagine if the Bank of England had to store £20 billion worth of wheat in its vaults! It would need a building a million times as big.

A small caveat is in order here. I have implicitly assumed that the commodity supply increases in proportion to general production, whichever form of currency is chosen. This is not necessarily true. Growth is not necessarily uniform across the economy. Thus if the costs of mining happen to fall faster than other costs, the price of gold will fall relative to other prices and as a result more gold will be required as currency. The annual cost becomes (the total value of the commodity in circulation) multiplied by (the economic growth rate plus the difference between the rate of increase of productivity for that commodity and that for the whole economy). It is however unlikely that this would differ significantly from the simpler formulation over the long run, unless we attempted to base a currency on human slaves (whose reproductive growth rate of perhaps 5% pa would evidently imply major cost savings for a rapidly growing economy, albeit at the expense of some ethical ambiguities!).

To be really pedantic, we ought also to add to the growth rate term the rate of change in the total value of commodity in circulation as a fraction of GDP. To be even more pedantic, when growth rates are high we should use instantaneous rather than annual figures in order to avoid compound-interest-like nonlinearities.

In principle, the production cost could also be eliminated by employing a currency based on a commodity of fixed supply (original paintings by Constable, say); but the total market value of such pseudo-commodities is far too low to back a general-purpose currency. The bottom line is that when it comes to commodity money, gold is nearly always best.

6. Fiduciary Money and Partial Reserve Banking

What use is gold just sitting in the vaults? It seems such a waste. So why doesn't the banker take the gold from the vault and either lend it out to other customers or spend it himself? The simple answer is that the depositors may want their gold back. Fundamentally, it belongs to them, not the bank. The bank is only taking care of it. Anyone who keeps a deposit account with the bank, or holds a valid cheque against such an account, or holds bank notes issued by that bank, has a right to full and immediate payment on demand in gold. If the bank fails to pay, it cheats both its customers and the general public. Even if it pays, but pays late, it is still cheating them, because it promised to pay on demand. Whether we call this theft, fraud, or oath-breaking, or employ some weaselling legalism or euphemism like bankruptcy or suspension of convertibility, is immaterial; it is not how an honest man behaves; and it is not something the law should permit without punishment.

However, bankers long ago realised that in practice only a small percentage of note and deposit holders will actually demand repayment on any given day. A much smaller reserve of gold will suffice to meet this day to day demand. The rest can safely be reused. Well, fairly safely. There's always a risk. The holders may suddenly take it into their heads to demand all their gold back right now. They have that right. Fortunately for the bankers they seldom exercise it.

Partial reserve banking creates fiduciary money (that is, money embodied in notes and deposits not fully backed by gold), so called because you have to trust the banker not to rip you off, even though he's doing something that on the face of it seems decidedly dodgy. There's no longer enough gold in the bank for all the money, but pray God there'll never need to be!

Can an honest banker behave this way? Can he legitimately take that risk — with other people's money? And if he does, how is he different from the man who bets on the horses with money he hasn't got, knowing that if he loses he won't ever be able to make good, but hoping to win and collect his winnings before the other chap finds out he's broke? The insolvent credit gambler is a fraud and a cheat. So too is our banker. The only difference is that the banker is less likely to be caught out, but does far greater harm when he is.

Many people think that's the end of the story. Partial reserve banking is dishonest and shouldn't be allowed. A con trick on a massive scale. Well, yes. But let's look at it from the other side. Partial reserve banking saves a lot of unnecessary expense mining useless metal; it reduces the cost of the monetary function by as much as a factor of ten. The bankers don't keep the extra profits to themselves — in a competitive market they can't. Everyone who uses their fiduciary money benefits, and keeps on benefiting as long as the bubble doesn't burst. Cheaper banking is in everyone's interest. In other words, so long as the public doesn't realise it's being cheated, it isn't! But if it wises up and demands its money back . . . pouf! The banks go bust and the economy takes a nose-dive. Is this crazy, or is this crazy?

What are we saying here? That honesty isn't the best policy? It certainly looks that way. After all, if partial reserve banking can be relied upon to work we'd be fools not to go with it. Wouldn't we? But can it be relied upon?

7. How Banks Fail

If the demand for repayment were statistically independent from day to day and person to person, partial reserve banking could be made, not absolutely safe, yet as safe as we wished. Spread over a million customers, demand would fluctuate from day to day by only one part in a thousand; fluctuations would reach the 10-sigma level of one in a hundred only once in 3x10²¹ years, billions of times longer than the current age of the universe. We could afford to sweep our residual ethical qualms under the carpet.

Unfortunately, that's not how things work. Customers are anything but statistically independent; their behaviour patterns are highly correlated. When Mrs Jones takes her money out, Mrs Smith does the same. The history of banking is replete with "runs" on the banks, when every man and his dog wants his money at the same time. All it takes is a rumour in the pub that Clodhopper's Bank is shaky and the next morning the whole town is camped outside the door, waiting for the bank to open.

There are basically two sorts of "run", the differential mode run and the common mode run. The first sort is not so bad. People lose trust in Clodhopper's Bank and take their money out; but they re-deposit that money in other banks almost at once. In these circumstances the bank in trouble can usually borrow sufficient gold from the other banks to meet its obligations, perhaps even to stop the run.

The common mode run is more worrying. Trouble at one bank leads people to distrust them all. Those depositors and note-holders who get to the banks in time take their gold home and bury it in the garden; they do not re-deposit it in other banks, and so the banking system as a whole suffers a drain on its reserves. Those depositors and note-holders who only get to the banks after the banks have run out of gold get stiffed; and unless they're all wimps, they riot.

In undeveloped rural economies, differential runs are likely to predominate; but to the extent that banks learn to protect themselves from such runs, by means of mutual guarantees and options against each other's reserves, they become ever more interdependent, and the common mode response becomes stronger. In a modern economy, where banking is highly integrated and rumours are instantly broadcast across the entire country, the danger of common mode runs (under a system of partial reserve private banking) would be considerable. A single ill-timed television programme on (say) the international debt crisis could bring the whole banking system crashing down.

8. Dishonest Partial Reserve Banking

Before we consider whether it is possible to ameliorate the effects of banking runs, or to avoid them, we should first distinguish six types of partial reserve banking, in decreasing order of dishonesty.

In the first type, the banker dissipates most of the gold in his care on riotous living or, what comes to much the same thing, the bank's employees embezzle it; this is a flagrant fraud on the public and no halfway decent court would have any hesitation in pronouncing it an offence (though whether such behaviour can always be detected and prosecuted in time to avert catastrophe is another matter).

In the second type, the banker pays for his fun not with his depositors' gold but by issuing additional bank notes or crediting deposit accounts; here the fraud comes from securing more than one IOU on the same lump of gold (like taking out two mortgages on the same house at the same time).

In the third type, the bank uses the gold to purchase real assets, such as shares or property; in such a transaction the net assets of the bank remain unchanged and, so long as market prices remain constant, the bank can always repay its debts by reselling those assets for gold. There may be a slight delay in selling the assets, or borrowing against them, but this is a minor problem. Much more serious is the possibility of a fall in their value, a possibility that becomes near certainty in the event of a run, when the increased demand for gold pushes up its price, and the bank must sell or mortgage more and more of its assets in exchange for less and less gold. To escape default the bank might need assets of several times its liabilities; and even that is likely to prove inadequate in the case of a general recession or a common mode run, when the price of gold relative to other assets may go through the roof. The lower the reserve ratio of the economy as a whole the bigger the problem.

In the fourth type, the bank issues bank notes or credits instead of spending the gold itself. This leads to the interesting possibility of the bank's using its newly issued bank notes to buy gold for its reserves, in itself a blameless transaction, but one which may enable the bank improperly to expand its note issue and market share at the expense of other market participants.

In the fifth type, the bank lends the gold out again to other customers; the bank's assets are then denominated in the same units as its liabilities; so long as the loans don't go bad, the bank will always be able to pay all its debts eventually (though not necessarily when they are due).

In the sixth type, the lending is in the form of bank notes or credits. The bank retains a reserve of gold to cover day to day demand, but still falls short of being sure of meeting all its obligations on demand.

9. Honest Partial Reserve Banking?

As we have seen, partial reserve banking is something of a racket. Is there any way of making it honest?

Suppose the bank tells its depositors that it will always honour cheques drawn on any one of its accounts in favour of any other of its accounts, and will always supply cash on demand in the form of its own bank notes, but that although it hopes to make payments on demand in gold, or in transfer to other banks, it cannot ever guarantee it. If despite this a depositor is still willing to risk being stuck with potentially worthless notes and losing some or all of his money, he accepts the bank's terms with his eyes open.

But what of third parties? People who are asked to accept payment in the bank's notes are not in any direct contractual relation with the bank; they have not agreed to the risks. When bank notes were used principally by wealthy merchants and corporations, who knew the ins and outs of the banking world and could reasonably have been expected to have been alive to the dangers, this objection might not have been morally or legally decisive; but when bank notes are intended as a general purpose currency, it is patently unfair to impose such risks upon members of the general public without their consent, and unreasonable to expect them to scrutinise each note in detail or accurately discount its value according to the issuing bank's reputation for trustworthiness.

If a currency is to be accepted for day to day transactions, we have to be able to take it "at face value". Otherwise, third parties (members of the general public) are being conned. At the very least, the issuing bank must print up its notes with a clear and unambiguous disclaimer, in big bold letters, thus:

NOT REDEEMABLE
(except at the discretion of Clodhopper's Bank)

Anything less is dishonest. It is very doubtful whether the public would be willing to accept bank notes on such risky terms, unless they had no alternative; this is a consequence of the underlying dodginess of partial reserve banking.

Even if such potentially irredeemable notes are generally accepted, the arrangement may still not be morally watertight. What about the harm to fourth parties? I mean those persons who refuse to accept the notes, but who will suffer along with the rest if the failure of the fiduciary banking system brings about a failure of the wider economy and the collapse of law and order. They may end up suffering not merely loss of prosperity, but also major violations of their rights, as a result of the reckless behaviour of the banks and their customers.

Perhaps there are other ways of plugging the moral holes in fiduciary banking. For example, we might follow the former practice of certain Scottish banks of granting themselves the option of postponing the redemption of their notes for a period of up to six months, thereby gaining a breathing space in which to realise the bank's assets. Provided that full interest is paid in compensation for the delay, in theory the bank's customers do not suffer, because they can either buy on credit or borrow the gold they need from someone else.

Unfortunately, this won't quite work. Firstly, in a differential mode run it's not necessary, because a solvent bank can borrow, against its assets, all the gold it needs to redeem its notes; for an insolvent bank it merely postpones the crunch. Secondly, in a common mode run there can be no guarantee that the bank will ever be able to redeem its notes, with interest or without, however long the breathing space; its assets may simply fetch too low a price. Furthermore, although the payment of the market rate of interest is normally a just compensation for delay (with an extra dollop for the inconvenience), in a common mode run note holders may need liquid cash immediately; the promise of interest in six month's time is unlikely to repair their loss.

Another approach is for banks to take out insurance against a run on their reserves. This merely shifts the problem to the insurers, who need to hold reserves of their own against the possibility of a common mode run, when they will be called upon to bail out the banks; in their turn they may call upon their reinsurers and underwriters. None of this helps; unless the gold reserves of all the players together add up to 100% they cannot guarantee always to meet their liabilities in full. Since the banks will have to pay for these back-up reserves, through their insurance premiums, there is unlikely to be any net benefit to justify the extra expense and complexity.

As we have seen, it is very difficult, if not impossible, to make the practice of partial reserve banking entirely safe or honest, even under strict regulation. Unless the public can be forced to hold irredeemable notes, common mode runs can destroy any fiduciary system.

9. Instabilities in Partial Reserve Banking

The ethical difficulties described above are not unrelated to the practical problem that has most occupied the minds of both apologists and critics of partial reserve banking; that of the overissue of bank notes.

The basic idea is that a general overissue of bank notes is impossible, because if the banks attempt to issue more notes than the public is willing to hold the excess must inevitably be returned to the banks for redemption. With a few minor caveats, such as the maintenance of full convertibility, this appears to be correct; and if there were only one bank, with a monopoly of note and credit issue, that would be the end of the matter.

However, where several or many banks compete, it is conceivable that an overissue by one bank may take place at the expense of the rest. In other words, differential overissue is not excluded.

The standard free-banking argument states that such differential overissue is effectively prevented by the interbank clearing mechanism. Normally banks will make over-the-counter payments in their own notes only, but accept deposits which include the notes of other banks; these alien notes will be returned to their issuing banks for redemption. Any bank that overissues will suffer a net drain on its reserves, because more notes will be returned to it than it returns to the other banks. Hence overissue will not occur.

There are various formulations of this argument, some more rigorous than others. Without going into unnecessary and confusing detail, I may say that none of them has won universal acceptance; indeed, all are hotly contested. The whole argument is controversial. It is clear that interbank clearing tends to act as a check on overissue; but it is far from clear whether it is an adequate check. If you care to analyse in detail the arguments of von Mises and others you will find an abundance of logical slips and non sequiturs, many of them minor, but others potentially fatal; unfortunately, their opponents' logic is unreliable too.

Throughout this debate it appears to have been accepted without question that overissue takes the form of excessive bank lending. Even here I do not find the argument for stability convincing. But as described in section 8 above, this is not the only way a fiduciary bank can act; it can also spend the new issue on other assets including gold.

Let me give a concrete illustration. Suppose the reserve ratio for all the banks is 10% and that one bank has a 5% market share (5% of the notes in circulation were issued by this bank). The bank decides to double its note issue, spending just 10% of the new issue on buying gold (the rest goes on buying property and on shareholders' dividends). Its reserve ratio stays at 10%. The total circulation of notes has gone up to 105%, more (we assume) than the public wants, so the excess 5% is returned to the banks for redemption. But the general public has no reason to differentiate between the notes of the various banks and will return or deposit notes more or less at random, in proportion to each bank's current share of circulation. Thus only about (5%+5%)/105% or 9½% of the returned notes belong to the issuing bank, leaving most of the new issue still in circulation. The market share of the issuing bank has increased to about 9½%, while its reserve ratio has fallen to 5½% (if it wants to preserve its reserve ratio unchanged at 10% it need only spend an extra ½% of new issue on gold, bringing its total issue up to about 10%). The other banks have each lost about 5% of their circulation and half of their reserves!

Happy days! Verily, it is a licence to print money, says the issuing bank. And does it all over again. Each new issue leaves the bank healthier and stronger, with a bigger market share. The other banks get weaker, and when their reserves are exhausted, go under.

Obviously, the other banks won't take this lying down; they'll retaliate by expanding their own issue the same way. The result is a mad scramble to hurl new notes into circulation as fast as possible, every bank for itself and devil take the hindmost. What happens in the end is anybody's guess — victory for the strongest or most reckless bank or a common mode run that bankrupts them all.

This is a much more drastic instability than those usually discussed in the literature. In effect, what is happening is that the expansionary bank is purchasing goods and services with the other banks' gold. Since this implies that the rest of the public ends up owning more gold than before, it is likely that some or all of this additional holding will be deposited with the banks; in practice, then, some overall increase in circulation may occur, with fewer notes returned for redemption than we assumed above. However, this would appear a minor complication, actually increasing slightly the incentive to expand.

Can this instability be averted? It is hard to see how. Suppose the government imposes a statutory minimum reserve ratio, thereby ruling out unrestricted note issue or credit expansion. In some circumstances this might instil a beneficial if arbitrary discipline into a competitive banking system; but not in this case, because the issuing bank can easily hold its reserve ratio unchanged throughout the expansionary process.

What if the issuing bank can't buy the extra gold because the other banks won't sell it? This can only work if the banks hold the economy's entire stock of gold. But this is improbable in the extreme. The issuing bank can always buy gold from abroad, or from the general public, or direct from the producers; it could even buy its own gold mines or open new ones. Even if the bank were only able to purchase gold at a premium, the problem would still remain as long as the backing for new currency cost less than the currency itself was worth.

Furthermore, it is entirely possible for a bank to expand its note issue even without buying gold; its reserve ratio falls, but the other banks' reserves fall faster. A bank starting from a sufficiently strong position can drive its competitors into bankruptcy before its own reserves run out.

Perhaps we could try and prevent banks from spending their own notes, by law; but it is hard to see how this could be justified or enforced. We can hardly stop banks from spending money altogether — they have their expenses like any other business. We'd have to make them pay their staff and shareholders in gold; but what prevents the re-deposit of that gold in exchange for notes? We'd have to ban that too — not just for the bank's own people — for everyone. We'd also have to prohibit borrowers from paying off a loan in gold; otherwise the bank could lend its notes to some accommodating merchant on the understanding that he'd buy gold to repay the loan with. Even honest banking would become impossible.

Now I'm not saying that partial reserve banking is necessarily and invariably unstable. It is conceivable that stabilising mechanisms can be found to ameliorate or eliminate these and all other potential or actual instabilities; and it is also conceivable that in a free market such mechanisms would inevitably operate, and operate both effectively and reliably. I do however claim that in the present state of knowledge such stability cannot be guaranteed — indeed, it appears unlikely.

10. Historical Evidence and Partial Reserve Banking

What can history teach us about partial reserve banking? Not as much as either free banking or central banking apologists would have us believe. Certainly, history can teach us how easily things go wrong; beyond that the evidence is unclear.

First we should realise that although authors present a wide variety of examples of so-called free banking (especially 18th & 19th century Scotland), genuine free-market partial reserve banking is notable for its historical non-existence. Banking has always taken place under severe constraints, both legal and religious; and fiduciary note issue has laboured under particularly onerous restrictions, such as the widespread prohibition on issuing bank notes in small denominations (for a long time the smallest note permitted in England was for £10 sterling, more than a working man earned in a year).

Next we should note that circumstances now are quite different than they were then, both qualitatively and quantitatively. Early banking had very little to do with the everyday currencies of ordinary people. Even if we could prove that partial reserve banking worked (or did not work) back then, it would not prove that partial reserve banking would work (or would not work) either now or in a free-market future.

Most authors tend to extrapolate from the historical evidence in a way that mirrors their prior prejudices. Thus one author commends a system of free banking in America because it worked for a whole ten years without disaster (and might have worked longer if it hadn't been changed). Ten years! Even a hundred years is too short, a toss-up whether or not you lose your life savings; but banking systems have seldom survived that long without major upheavals. The lesson of history is that banks do fail — often catastrophically.

The problem with all the evidence is this. Some people say the failures were caused by too much government regulation. Some say they were caused by too little regulation. And some say they were caused by the wrong sort of regulation. Similarly, the comparative successes are put down to less regulation, more regulation, or the right sort of regulation, according to taste. In the absence of an analytically sound and generally accepted theory of money, such explanations are of little value. The truth of the matter is that we simply do not understand the dynamics of banking well enough to give a definitive exposition. One day that may change; but so long as money is such a political football the prospects seem less than bright.

11. Fiat Money and Central Banking

The fundamental problem with partial reserve or fiduciary banking is that it makes promises it may not be able to keep. Fiat money gets around this by promising nothing. Fiat money can be considered as the limiting case of fiduciary money as the reserve ratio tends to zero, with this important distinction, that fiat money cannot be returned for redemption. It is by definition irredeemable, backed only by custom, the good name of the bank, or the power of the state.

Objectively, fiat money seems little more than worthless paper; and for this reason free-marketeers and other theorists have been apt to treat it with contempt. Yet it has proved eminently suited to the modern world; every country on Earth now employs a fiat currency. Whatever else we may say about it, the system works in practice and is not intrinsically dishonest in theory. If the monetary authorities are both competent and honest (a big if ) fiat currencies are stable, reliable and economically efficient. Fiat money costs next to nothing to produce; no gold need be mined or wastefully stored in vaults.

Fiat money has one major drawback; it must have a monopoly. Suppose there are two competing general-purpose fiat currencies within the same economy; for the sake of argument let's give them equal market shares and an exchange rate at par. Now, allow random fluctuation to boost demand for one of the currencies over the other; in accordance with the law of supply and demand its price goes up, it's worth more, and, by symmetry, the other is worth less. The public will then naturally prefer to hold on to the currency that has risen in price rather than the one that has fallen. Positive feedback drives price and demand spiralling upwards for the former and downwards for the latter, which quickly becomes a "hot potato" everyone is desperately trying to unload. Soon only the one currency remains in active circulation; the other is wallpaper. This is the phenomenon of hypertransfer.

Fiat money, because it has no intrinsic value, is highly vulnerable to hypertransfer. Its use therefore effectively mandates a central bank, a de facto if not de jure branch of government. It is true that other banks may be permitted to issue their own notes, but in a fiat system they will be required to denominate them in the national currency and back them 100% with the notes of the central bank (or other claims upon it). Thus, in the UK, Scottish bank notes are secondary issue backed by the Bank of England's primary issue of fiat notes, themselves designated legal tender by statute law; the "promise to pay" on Bank of England notes is a leftover from the days of commodity and fiduciary currency and no longer has any real significance.

The system of fiat central banking is largely immune from catastrophic runs, precisely because the note issue is not redeemable. If too many account holders withdraw their savings at the same time, a "note run" can still occur; however, unless the central bank deliberately abrogates its responsibilities as the "lender of last resort", solvent banks can always borrow sufficient note issue to meet their current obligations. Normally, banks will borrow what they need on the market; however, the central bank guarantees to meet any liquidity shortfall, usually at a premium above the market rate, a premium intended to discourage private banks from over-reliance on the central bank. The security of this system is absolute, because the liabilities and responsibilities of the central bank are denominated in a currency it has the unconditional right to create in unlimited quantities by fiat. It can never run out of money, because it can always print more.

A caveat must be added here. Central banks acting under political motives may not always fulfil their financial responsibilities. The American Federal Reserve is an example; it exacerbated the crisis of the early 1930s by monetary tightening at the very time the banks were most in need of increased liquidity; yet on other occasions it has not hesitated to approve damaging and inflationary expansion at the politicians' behest.

Inflation is the bugbear of fiat money, because the state-protected monopoly of the central bank gives it the ability to expand note issue at will, while its role as a branch of government subjects it to all the temptations of politics. Acting as lender of last resort is not of itself inflationary, so long as the lending is not made permanent; all that happens is that money on current account is changed into the form of notes. However, few if any central banks can be trusted so to limit themselves, even those that are nominally independent.

By printing fiat money governments can increase their spending power without the unpopularity of explicit taxation; the gain to the monetary authorities through inflation, known as seigniorage, is equivalent to the revenue of gold producers under a system of commodity money, except that here it is almost pure profit, limited only by the danger of hyperinflation. Ordinary inflation is proportional to the increase in currency supply (usually, but somewhat misleadingly, called the money supply) over and above the increase in national product; double the quantity of notes in circulation and, other things being equal, the price of goods will also double. Hyperinflation is different. It is the single-currency equivalent of hypertransfer. It occurs when inflation is eroding the value of a currency sufficiently rapidly to make people unwilling to hold more of it than they need for their immediate spending; the quantity of notes in circulation cannot fall (remember, fiat notes cannot be redeemed), but in trying to get rid of them the public spends them faster and faster, in a grand game of pass-the-parcel. The value of the currency plummets, or, to put the same thing another way, prices soar. Hyperinflation is prone to set in above an inflation rate of around 2% a month or 25% pa. The opposite effect, hyperappreciation, is a speculative ramp we might expect to set in at a negative inflation rate of similar magnitude — by no means impossible in a rapidly growing free-market economy.

We should not exaggerate the economic costs of inflation. Although there were teething problems during the changeover from fiduciary to fiat currencies, by now most governments are quite capable of keeping inflation within reasonable bounds. Contrary to many predictions a moderate and predictable rate of inflation does not lead inescapably to runaway prices or boom-and-bust, and in practice causes little economic harm (indeed, within a "mixed" economy, in which trade-union power and government regulation makes wages and prices "sticky", it may even be modestly beneficial). Moreover, it is doubtful whether government expenditure would be significantly reduced in its absence; the deficit would simply be financed by borrowing instead (which because it draws on savings that might otherwise have been invested is actually more damaging than the inflation it replaces).

Where governments have lost control and hyperinflation has set in, it has not been the fault of fiat central banking per se; their economies have already been in dire straits on account of war, revolution, corruption or gross economic mismanagement across the board. For example, Hungary after the communist take-over, Germany after World War II, Russia after the fall of the USSR. Even then, stability has usually been restored to the currency within about five years.

Nevertheless, state control over the monetary function is at best a necessary evil. Politicians just can't stop meddling. So central banks distort the market rates of interest and the rates of foreign exchange, intervene in the money and commodity markets, fiddle with the stock market, and conspire with other central banks abroad; they facilitate excessive government borrowing, impose stultifying regulations, block free competition yet obstruct co-operation. In countless ways they interfere in the economy for political ends. They can't be relied upon even to stick to their own ever-changing rules, and despite all their sound and fury frequently fail adequately to perform even their most basic monetary functions.

12. Fiat Money in an Ultraminimal State

The problems of fiat money and central banking are political rather than economic in nature; they are not intrinsic to the monetary function. Let us consider then how and whether a fiat currency could operate in a just ultraminimal state (technical note: a minimal state defends a monopoly of law and order; an ultraminimal state allows any person to opt out of state protection). We shall assume that the monetary authorities are honest in themselves, or kept honest by subjection to an honest court of law.

In the first place the monetary authorities might issue a fixed quantity of fiat currency and leave it at that. Whether that currency takes the form of fiat notes, electronic cash or bookkeeping entries is secondary, and the central bank should allow the balance of the various components to change in accordance with changing demand. As lender of last resort, the central bank will also make available to the banks whatever extra liquidity they require, or are willing to pay for, at a standard premium above the market rate. If the central bank charges on loans and pays on deposits an interest rate equal to the nominal market rate multiplied by the ratio of the current issue to the authorised issue, this will permit temporary expansions and contractions as the banks require, but will stabilise the supply of currency in the long-term. If the central bank doesn't know what the market rate should be, no matter; all it has to do is guess; the market rate and circulation will automatically adjust themselves to the correct value.

In a stationary economy there will then be no inflation, whilst in a growing economy prices will fall and the fiat currency will appreciate in value (negative inflation). There is no necessity to increase the currency supply in line with economic growth, though notes and coins of smaller denominations may have to be issued as time goes on.

Here we have a secure, honest and efficient fiat currency well-suited to a minimal state. But there's a snag. In a free market economic growth is likely to exceed the 25% pa above which hyperappreciation might be apt to set in. If so, the resulting speculative ramp, sending the value of the currency through the roof, may be followed by a crash, overshooting into hyperinflation, then bouncing up again from the floor; the system may be driven into wild oscillations or full-blown chaos. Once such instability is manifest, the central bank may be powerless to stop it.

On the upward ramp, the interest rate at which the central bank will lend is far below the rate at which the currency is gaining value, so speculative borrowing from the central bank will greatly increase the currency supply, tending to slow and then reverse the rise in value. Conversely, on the downwards slide, previously-issued currency comes rushing back to the bank, where the positive interest rate at least offsets some of the losses; again this tends to slow and then reverse the fall in value. Will this damp out the oscillations and restore stability? It is hard to be certain, but it seems not, because the borrowing is out of phase with the value; the restoring force is not linearly proportional to the displacement; instead there are lags and nonlinearities and enormous amplification factors, conditions known to be conducive to chaos.

The central bank might also attempt to offset any tendency to hyperappreciation by expansionary purchases of assets on the open market (followed by contractionary sales). However, central banks have proved notoriously bad at stabilising currencies in the past; more often than not they make matters worse. Unless the behaviour of the central bank can be controlled by a mathematically rigorous and unquestionably stabilising formula, the almost inevitable lags, nonlinearities and amplifications will themselves tend to induce chaotic fluctuations in the value of the fiat currency.

A possible solution is for the central bank to expand its fiat issue at a rate that holds prices steady or at least one that keeps currency appreciation safely below 20% pa. This averts instability, but creates several new problems instead.

The first problem is a moral one. Expanding the currency supply transfers wealth to the central bank; if the fiat national currency is the only sort of legal tender permitted this is a form of coercion or taxation, and thus morally unacceptable in a just ultraminimal state. The solution to this is fairly simple; lift the prohibition on competing currencies. The national currency will still retain its effective monopoly, because of the economic efficiency of fiat currency and the overwhelming advantages of standardisation. Any individual who wishes not to use the national currency is at liberty to use any other currency available, or to create his own; and no doubt gold or silver will be employed in some transactions; but most people will in practice be happy to continue using the fiat national currency. There is then no longer any valid moral objection to the government's receiving revenue from its issue of fiat currency (though we should note that if it takes too much the competitive advantage will revert to the private currencies).

The second problem is a practical one. In a rapidly growing free-market economy the amount of currency that needs to be issued to keep prices constant may correspond to a large fraction of GDP; the analysis parallels that of section 5 and will not be repeated here. However, whereas the production of commodity money imposes real economic costs, with fiat money the wealth is transferred to the government as pure profit. But a minimal or ultraminimal government has by its very nature few expenditures, and is therefore likely to be swamped by excess money it doesn't know how to spend!

If the central bank restricts its issue, so that the currency appreciates by say 20% pa it will make the currency even more attractive than a stable one; consequently the public will choose to hold an even larger fraction of GDP in this currency, its value will be that much greater, and the net revenue to the government may end up even higher — and even harder to get rid of. And people worry where an ultraminimal state is going to get its money from!

It will also be important to ensure that industrial investment provides a markedly higher return than simply holding cash; otherwise real investment will fall and the economy will fail. However, so long as the central bank issues enough to avoid hyperappreciation this problem should not arise.

13. Ownership of Fiat Currency Issuing Rights and the Central Bank

Anyone can print "notes" to his own design; and as the copyright holder he is entitled to print as much of this "money" as he wishes, and to prohibit others from "counterfeiting" it. The intrinsic value of these notes may be next to nothing, but once the public starts accepting them as fiat currency, this copyright becomes a valuable asset; considerable wealth may be transferred to its owner. In the case of a single national currency the copyright holder is of course the central bank.

Now in essence the central bank may already belong to the citizenry through the underlying common ownership of state and country. Is there any way we can make this ownership more explicit? If every citizen held a single share in the bank, every citizen would receive the same dividend; indeed currency issue would take place through the distribution of that dividend. This would seem to impose an egalitarian pattern upon the whole economy, guaranteeing everyone a income not very far below the average income, for so long as the economy continued to grow. Would this constitute an unjust redistribution of wealth? In some circumstances, perhaps so; but not if the citizen's share were an asset initially purchased from the central bank at the capital value of this income.

There are a few points to note here. If citizenship entails ownership of certain rights and assets it ought not to be conferred as an automatic privilege of birth; both immigrants and infants (or their parents or guardians) should (one way or another) pay the market price for those entitlements; and upon death or emigration their residual value should revert to the estate or emigrant. The difficulty with applying this principle to ownership of the fiat currency is that the capital value of the dividend income increases in proportion to the net revenue the bank obtains from the sale of citizen's shares (positive if the number of citizens is increasing, negative if it falls); in the absence of any secondary market in those shares, their exact capital value may be hard to define.

Furthermore, since central bank ownership covers only part of the entitlements of citizens we may question whether an ultraminimal state can justify bundling it all together. Why cannot persons chose to purchase citizenship without membership of the central bank and the income this entails? Yet in de-bundling this membership we revert to private ownership of a national fiat currency, without real assets, whose profitability depends upon growth in the rest of the economy; the stability implications are unclear but worrying. The same applies a fortiori if we allow unrestricted share ownership, as in an ordinary joint stock company, instead of the co-operative device of one member one share. Once ownership is concentrated in the hands of only some of the citizenry, opportunities arise for manipulating the value of the fiat currency to the benefit of the owners at the expense of everyone else (this is why government control over the central bank is also undesirable, since the interests of the government are seldom identical with the interests of the general public).

I have my doubts as to the long-term viability of such arrangements, which in the end come up against the fact that fiat money has only a customary not an intrinsic value. With this in mind, I now proceed to the consideration of an approach to the issue of currency that focuses more realistically upon the underlying wealth of the economy.

14. Share Money

Share money is a proposed form of currency consisting of bearer shares in the issuing bank. A bearer share is simply a share in a company — one that can be passed from hand to hand without notifying the company of the change in ownership. In this respect it is like a bearer bond, but where a bearer bond recognises a specific monetary debt, a bearer share grants an equity stake in the issuing company itself. If all the shares in a company are bearer shares, the holders of those shares own the company and all its assets.

Bearer shares may carry similar entitlements to ordinary shares, such as the right to vote in General Meetings and elections; but the payment of dividends is a little tricky, since the current holder has to collect them in person from a branch or agent of the company. This is less of a problem than it might at first appear, since there is no necessity for a firm ever to pay any dividends at all; retained profits merely increase the capital value of the shares. If the holders of bearer shares wish to spend some of their profits they need only exchange some of their shares for cash.

I must make the point that although bearer shares are an entirely honest and viable form of ownership, government regulations may make them illegal or impracticable in most countries at present. I here assume a more liberal regime.

Bearer shares can clearly be used as the basis of a currency. An existing bank seeking to issue share money ("money embodied in the form of bearer shares") need only replace its existing shares with bearer shares. These will be issued in the form of certificates like bank notes, denominated not by monetary value but as a certain number of shares. Demand deposits, credits and loans will also be denominated in share units. The bank promises nothing it cannot deliver.

The value of a bearer share is proportional to the value of the assets owned by the bank. These assets can take any form. They could include land, property, commodities, market positions, other currencies, bonds and securities, loans and liens, stocks and shares, industrial plant and machinery, firms and corporations — anything at all. The bank is not limited to assets like gold that must be stored unused; indeed, it will presumably wish to keep most of its assets actively invested as capital yielding profits or interest at the market rates.

It does not matter if the value of these assets rises or falls, since all the liabilities of the bank are denominated the same way, as a specified proportion of the assets of the bank. Even the debts owed to the bank by borrowers are included in the assets, so if those debts go bad it only means that the shares of the bank will be worth less than previously thought. Nobody guarantees how much the bearer shares will be worth at any time, only that they will be a specified fraction of whatever the bank then happens to be worth. It all comes out in the wash.

The value of the shares will be set at all times by the market. There can be no run on the bank against the share holders because the note holders and depositors are the share holders. It is true that depositors may wish to take charge of their shares themselves, instead of leaving them on account in the bank, by withdrawal from their accounts; but this changes only the way the shares are held, not their number or value. The very same bearer shares may be held indifferently as notes or electronic cash or on account, and converted from one form to another at will.

The bank should be prepared at any time to state the total number of shares currently extant, but there is no overriding reason either to expand the issue at any particular rate or to keep it fixed, though following a consistent and publicly declared policy may be desirable. The bank may be happy relying upon the organic growth of its existing capital to increase the value of its shares in line with the general performance of the economy, altering neither its total share issue nor its relative size. Its bearer shares will then appreciate at approximately the normal rate of return on capital, typically a few percent above the economic growth rate (given a reasonably balanced portfolio of assets).

But suppose the bank wishes to expand its operations further. It may, at its discretion, purchase assets on the open market by means of new bearer shares issued for that purpose. The new shares are indistinguishable from the old. Assuming stable market prices, the value of each share is unchanged, because the bank's assets have increased by the same proportion as the total number of shares in circulation. The bank may also expand by making additional loans, crediting new shares to the borrowers' accounts. Good loans are assets too. In neither situation is the bank expanding illegitimately at anyone else's expense (in sharp distinction to the case of partial reserve banking).

How big can we expect the bank to grow? Basically, the market decides. People would like to hold a certain proportion of their assets in the form of bearer shares. If the bank has issued too few to meet the demand, each share will be valued at a positive premium or, to put the same thing another way, the public will value their other assets at a slight discount relative to bearer shares. Thus the bank will benefit by purchasing additional assets in exchange for new issue. Conversely, if the bank is too big, it will benefit by selling off some of its excess assets and contracting its issue.

How would share banking work in the hypothetical equilibrium economy, in which the growth rate is zero? Would the rate of return drop to zero too? In fact, share money would still appreciate in value, so long as the bank's invested assets continued to yield a profit, which, returning to the bank, would permit the bank continually to contract its issue, thus generating a steady negative inflation rate and positive real interest rate. From time to time, bearer shares would then have to be subdivided or lower denominations issued.

In a real economy, we would expect the total demand for share money to be much greater than is usual for other types of currency, ultimately subsuming a large fraction of the entire capital stock. Why? Because share money is not only liquid currency; it is also a highly convenient yet secure and profitable form of investment. No savings scheme can match it for simplicity; to save, and to receive the full market rate of return on your savings, you need only leave your money unspent in your pocket or in an ordinary bank account. For most people, simply putting some share money into a separate savings account for their old age would be far better than subscribing to today's complicated pension schemes. But if pension or trust funds are required, share money is the ideal depository for them, since returns are good, whilst management costs are negligible.

One curious feature of share money is that nominal interest rates are zero. No interest or dividend is paid on either loans or deposits — perhaps the old religious prohibitions against usury weren't so misguided after all! Instead, real returns arise from the gain in capital value of the shares. Thus, borrowers make repayments with shares worth more than when they borrowed them; depositors make withdrawals of shares worth more than when they deposited them.

So how does the bank make its profits? The simple answer is that it doesn't; it is a mutual organisation owned by its customers, the holders of its share money; the usual conflict of interest between a bank's owners and its customers is lacking. However, even a mutual bank has expenses. How should they be met? Perhaps the fairest and most straightforward way would be by means of a modest annual fee for maintaining an account, plus a specific charge for each transaction, covering its actual cost to the bank. Unless the bank is hopelessly inefficient, these charges should be small.

Admittedly, it is usual today to charge borrowers a higher rate of interest than is offered to savers. But this is to conflate interest payments with fees, expenses and premiums that really have nothing to do with interest at all. Arranging a loan is a valuable service that costs time and money, and so should naturally command a fee up-front. Borrowers may want their loan insured against death, disability or unemployment, and lenders will want the loan insured against the borrower's default, so appropriate premiums should be levied to cover these risks. Maintaining a mortgage account and making payments also involve costs. However, none of these charges is strictly equivalent to a fixed rate of interest and in general ought not to be subsumed to one; it is better to make the charges explicit and allow them to find their market level. It should be noted in passing that in a just ultraminimal state there will be very little risk of default for most loans, since the courts will provide effective and cost-free enforcement of all debts.

15. Competitive Share Banking

So far, in this discussion of share banking, I have implicitly assumed that there is only one issuing bank. What happens if there is more than one? Each bank issues its own bearer shares, granting an equity stake in the assets of that bank. Each bank's loans and deposits are denominated in the shares of that bank. Thus each bank's shares comprise a competing currency. Each currency is freely valued by the market. That is, it has an exchange rate (against each other currency) set by the market value of that bank's shares (against the value of the other banks' shares).

Although each bank account is denominated only in that bank's own currency, there is nothing to prevent the competing banks from accepting each other's shares for exchange at the prevailing rates. Interestingly enough, the banks can themselves continue to hold each other's shares as assets; they don't have to send them back to the issuing bank. They can also spend or sell them. This is quite different from the case of partial reserve private banking.

Now each competing currency can be expected to appreciate at approximately, but not exactly, the same market rate, depending on the profitability of their respective asset portfolios. A currency that outperforms its rivals has a competitive advantage; demand for that currency will increase, adding a further premium to its value. The bank in question can then profitably expand its issue by purchasing additional assets. This is the mechanism, discussed in section 11, that leads to rapid hypertransfer among competing fiat currencies. Here the effect is much weaker and transfer occurs without subjecting any share holders to more than marginal loss; nevertheless, the tendency is towards a single dominant currency within each territory.

This tendency is strengthened by the natural desire of the public for a uniform general purpose currency. Multiple currencies within a single economy are clearly inconvenient for the consumer, who will consequently be inclined to obtain his cash only from the market leader, just as retailers will mostly prefer to mark their prices and take payment in the market leader's currency. A (near) monopoly should result. This is not to say that other banks and businesses will not continue to issue bearer shares, but that outside specialised circles they will lose liquidity and cease to have widespread circulation as currency. For practical purposes, then, they will cease to be thought of as "money".

This monopoly should not cause us any loss of sleep. First, because mutual ownership removes the dreaded conflict of interest between monopolist and customer. Second, because potential competition from other banks or businesses should keep the dominant currency reasonably efficient (or risk losing its dominant position as the public transfers savings to the bearer shares of those other organisations). Third, because of the background competition from the share currencies of foreign countries (already dominant in their own territories) to which the public can turn if their local currencies prove unprofitable.

Given an effective monopoly of issue, is it possible for other banks to offer competing banking services based on the dominant bank's currency? So long as each bank retains 100% reserves against all liabilities (demand deposits, secondary note issues or electronic cash) in the form of bearer shares in or on deposit with the dominant bank or fully insured loans denominated in that currency, there can be no objection. Since reserves of bearer shares yield real returns (unlike reserves of commodity money) this is no great burden. Such banks will normally be unable either to charge interest on loans (because borrowers would go elsewhere) or offer interest to depositors. However, they will be free to compete with the dominant bank on transaction charges, service and convenience, all the banks thereby keeping each other efficient. They might also gain custom by supplying other financial services as well.

16. From Fiat to Share Money

How can we get from the present use of fiat money to a currency based upon bearer shares? Consider the following scenario:

The government ceases to draw seigniorage from the central bank, which then proceeds to spend large amounts of new fiat money on the purchase of a portfolio of assets, including a network of branches throughout the country. The expansion of the currency supply leads to its progressive depreciation, until the value of the newly purchased assets matches the value of the currency in circulation, which will obtain once the cumulative inflation has reached 100%. If all the purchases could be put through simultaneously, this would mean a fall in the value of the currency by a factor of two; in practice, later purchases have to be bought with partially inflated money (that is, after prices have already started to rise), so more fiat money must be printed and its value will fall somewhat further (by an overall factor of 2.7321). I here assume that the initial assets of the central bank are negligible.

Once the bank's assets and issue are matched, its fiat rights are abolished and existing notes and deposits are exchanged at par for bearer shares in the newly independent national bank. The country's legal tender now takes the form of shares in a mutually owned institution. Since these shares will progressively appreciate in value over time, demand will exceed the previous demand for fiat currency; the bank will meet this demand by purchasing further assets with additional bearer shares. Once the transfer is complete and demand has stabilised, the government lifts the prohibition on competing currencies, whilst ensuring that the courts are given the necessary powers to preclude all dishonest forms of private banking.

The disadvantage of this scenario is the substantial inflation the changeover entails. There are several ways of avoiding this. First, the assumption that the central bank has no significant assets to begin with is likely to be false; foreign currency and gold reserves may be considerable; asset purchases can then be on a correspondingly smaller scale. Second, the government can transfer public assets to the bank prior to the changeover. If sufficient publicly owned assets are available the inflationary currency expansion can be eliminated (though this may not always be politically or economically desirable). Either way, it is clear that changing from the existing system of government-controlled fiat currency to one based upon privately owned bearer shares presents no insurmountable obstacles.

17. Share Money and Electronic Cash

In the past, economists considered cash as consisting of notes and coins passed from hand to hand. However, as money becomes embodied more and more in electronic form, the definition of cash needs to be extended and the workings of electronic cash considered. I say "electronic cash", or "e-cash" for short, but any method of transferring the numerical information that is money would work. It doesn't have to be electronic, or even electrical; we could also use semaphore, pneumatic pipes, telepathy, men on horseback, trained bees, or even printed writing on pieces of paper or metal disks. The key is the reliable transfer of a unique number.

Bearer shares will be issued in the form of certificates like bank notes, denominated not as "money" but as a certain number of shares. Each share will have its own unique serial number. Thus, a Clodhopper's Bank 1 clod note might have a serial number 1,234,567,891 while a 10 clod note might own all the serial numbers between 1,432,765,980 and 1,432,765,989 and be labelled with the former; 5 clod notes would have serial numbers ending in 0 or 5; and so on. Smaller denominations could add a decimal point; a tenth clod note or coin might have the serial number 243,657,109.8 for instance.

Counterfeiting by unlawful duplication of serial numbers is comparatively easy for banks and other organisations to detect by cross-checking; with N notes in circulation and a fraction f duplicated, examination of on the order of (N/f)^1/2 notes should detect the duplications. With say a billion notes of one denomination, a million of them counterfeit, about a million must be checked to spot a duplication, but the bank will take in ten times as many over the counter every day.

When it comes to electronic cash there is an apparently inescapable conflict between security and anonymity. Gold and silver are intrinsically costly, and bank notes have traditionally proved difficult to counterfeit, but since e-cash is simply a number it is highly vulnerable to fraudulent reproduction. A dishonest person can copy and spend the same item of cash many times over. The use of special sealed hardware that automatically deletes the information during transfer might seem a possible solution, but unless we can somehow make use of an intrinsic quantum indeterminacy whereby detection at the receiver necessarily destroys the information at the transmitter (and I am not at all sure that this is possible, even in principle), reverse engineering can always produce a version of the hardware which does not delete the cash, and which will therefore appear an attractive investment to criminals. If e-cash is to be secure it must be possible to refer back to the issuing bank for confirmation of its validity and to trace unlawful duplications; absolute anonymity cannot then be guaranteed.

Here I describe a system of electronic cash using public key encryption. It is well suited to private share money but could also be used for fiat or fiduciary money. I will not describe the various mechanisms of public key encryption in any detail here; all you need to understand is that we can generate a private key K* which by means of an essentially irreversible "trapdoor function" can easily be transformed into a public key K, but that someone who knows only the public key K cannot get back to the private key K*. If we encrypt a message with one of the keys it can then only be decrypted with the other (we can write this as KK*P=K*KP=P, where P is the plaintext).

The bank, which has a private key KB* and public key KB, issues an element of e-cash with serial number N. It also calculates KB*N and attaches it to the data-packet, thus: (N,KB*N), before sending it out to a customer, who verifies that KBKB*N=N. Only the bank can issue a valid packet, because only the bank has the private key KB*.

Suppose a person P wishes to pay this packet to a recipient R. He sends out the encrypted packet KRKP*(N,KB*N). Only R can decrypt it, thus: KPKR*KRKP*(N,KB*N) =(N,KB*N), before verifying that KBKB*N=N. If R trusts P and wishes to preserve anonymity that may conclude the transaction. Otherwise, R checks the continuing validity of the cash packet by sending the bank an encrypted query KB(KR,KR*N). The bank decrypts this and checks its records to see whether N is still valid or has been cancelled. If N is invalid the bank warns R with the false packet KR(N,KB*E), in which the verification KBKB*E=N fails and E may contain information on how and when the cash was cancelled. But if N is valid the bank cancels it and sends R a new cash packet KR(N',KB*N'), which R decrypts with KR* and stores as (N',KB*N') after verifying that KBKB*N'=N'. If R is satisfied he can then send P an encrypted receipt KPKR*(N,KB*N), which P decrypts as KRKP*KPKR*(N,KB*N)=(N,KB*N), before storing the receipt KR*(N,KB*N) and deleting the spent packet (N,KB*N).

In communicating with the bank, R can remain anonymous by including a session specific public key KR in his query (unfortunately, no two-way Internet communication can be truly anonymous, since there is always an electronic trail back to the source). R and P each have the option of using either publicly posted keys (identified at least by pseudonym) or nonce keys generated specifically for that session. However, the bank's public keys must be publicised permanently at trusted sites.

R may prefer to deposit the cash in his account. Even here it is not essential for the bank to know his identity; an anonymous numbered account may be created and accessed as follows. The customer generates a private account key KA* and a public key KA, which he sends to the bank as KBKA. The bank decrypts and retains KA, then sends back the account number A, encrypted as KB*KAA. The customer decrypts with KA*KB to obtain his account number A. To access the account he sends KB(A,KA*A); the bank decrypts with KB* then verifies that KAKA*A=A.

There are other features and other more subtle uses. For example, if P finds he has been defrauded by R or believes his cash has been wrongfully copied, he can revalidate the packet or trigger an alert by sending the bank the encrypted query KB(KP,KP*N). R may also ask the bank for change by sending KB(KR,KR*(N1,N2,N3...;D1,D2,D3...)), where D1,D2,D3... is a list of requested denominations, receiving back KR((N1',KB*N1'),(N2',KB*N2'),(N3',KB*N3')...). The system can also be used to seal documents, or to send and validate signatures.

There is one less than elegant feature — the necessity for the bank to maintain a record of every cash packet issued. This is a lot of data, which will normally need to be kept centrally at the head office or communications centre. If a hundred million people hold about ten units each of about twenty denominations with serial numbers 512 bits long the validating computers will need some 10¹³ bits of RAM (hard disks are too slow, except as backup) costing around £1 million as of 2000 AD. Not negligible, but acceptable for a national currency (and of course the price should fall with advancing technology).

However, the demand for very small denominations (less than a penny) for on-line micropayments (say a tenth penny or less per accessed page, or as little as a thousandth of a penny per second of low-priced TV) may be much larger, perhaps hundreds or thousands per person, and may end up dominating the validation traffic, though it may be possible to develop mitigating protocols. For example, your television set could download one micropayment a second from your bank account, just in time to upload it to the programme provider in exchange for the next second's programme decryption; since the programme provider promptly deposits it in his account only a few units of e-cash are needed at any one time. Moreover, it should be possible to set up anonymous nonce accounts with a bank or a trusted escrow agent, or simplest of all directly with the programme provider, by depositing e-cash of larger denominations and drawing out micropayments as required.

More worrying is the dependency upon a single central site. Fortunately, the e-cash will remain useable even if the bank's validation site goes down or cannot be contacted, though the risk of fraud is increased. It may also be possible for local branches to take over some of the validation work (especially if most transfers take place within the locality) and to issue replacement packets flagged with the issuing branch's identity. Alternatively, it may be possible to hold the data in distributed and redundant form across a network, so that no single-point failure could disrupt the system.

Before leaving the subject of electronic cash, I should point out that of the various proposals and e-cash experiments to date, most fail to meet acceptable criteria for security, anonymity and non-reproducibility. It is important that we scrutinise carefully any form of electronic cash introduced by today's multinational companies, major banks or governmental organisations. They are likely to have agendas that conflict with the interests of individual customers; it is particularly likely that personal privacy or anonymity will be compromised unnecessarily.

Having devised a system of electronic cash, we can see that bank notes can easily be fitted into the same scheme. The first 64 bits (or 16 hexadecimal digits) of N can constitute the ordinary serial number, visibly printed on each note or stamped on each coin. The remaining 448 bits, say, may be randomly chosen, unique to each packet, providing the necessary cryptographic security. A magnetic stripe in each bank note (like the present aluminium strip) could then hold the full 512 bits of N and 512 bits of KB*N. When the bank note is passed through a reader at the point-of-sale terminal, a validation message can be sent to the bank in the usual fashion and the returning (N',KB*N') loaded back onto the magnetic stripe.

Coins could be manufactured with an embedded chip fulfilling the same function as a magnetic stripe, but for small change it probably wouldn't be worth the bother; occasional checks on the ordinary serial number stamped on each coin would be sufficient to make counterfeiting uneconomical. Trying to shift a bagful of bad pennies would be very hard work indeed. However, if ever we decided to replace flimsy bank notes with hard-wearing coins of high denomination, embedded chips could provide the necessary security.

18. Conclusions

We have seen that money is the information that mediates the exchange of goods and services on the market, and that currencies are embodiments of that monetary information. We have seen that commodity money is economically inefficient but otherwise sound, that fiduciary money is basically untrustworthy and unstable, that fiat money is necessarily monopolistic and liable to government abuse. We have seen that neither central banking nor private banking can be guaranteed to provide honest money unless the courts are willing strictly to enforce the law against fraud and to hold the bankers fully liable for all risks and losses wrongfully imposed upon other people.

We have seen that bearer shares can provide the basis for an efficient and honest currency that offers not only full liquidity and ease of use, but also the opportunity for effortless saving and profitable investment. We have seen how the existing system of fiat money under state control could be transformed into a system of share money under the control of the note holders and depositors. And we have seen how share money can be issued in the form of electronic cash utilising cryptographically secure transactions and a high degree of privacy. In short, bearer shares are the ideal embodiment of money in a free market.

© Paul Birch, 20th Oct. 2000

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