Costs of the Gold Standard

Economists are often tempted to dismiss or criticise the gold coin standard because of the social costs of mining, minting, wear, and interest foregone. This post discusses these costs, and how they would be handled by market participants in a free market and evaluates their size under free banking.

(picture: a British Sovereign gold coin, depicting St George slaying the dragon, with 7.32235 grams of pure gold.)


Although there are social costs of having a gold standard, it is important to keep them in perspective. It is also worth looking into the economics of how these costs can be carried and managed, and how the related activities managed in a free market.

So firstly, what are the costs of a gold standard?

1. Mining the gold out of the ground and refining it into bullion
2. Minting costs, this is the cost of turning gold bullion into gold coin.
3. Wear of gold coin. Gold coin wears through abrasion, during normal handling through the life of the coin.
4. Interest foregone on the stock of gold coin during the life of the coin, and
5. Casual loss of coins.

Before considering the size of these costs, some comment is required on the how these costs can be carried.

The social cost of mining the gold out of the ground is not a social cost of a gold coin standard. Gold production is not the cost of holding a stock of gold coin, but the cost of replacing wear on the gold coin, and casual loss of gold coins. The cost of a holding a stock of gold coins is the foregone interest, and the cost of using a stock of gold coins for transactions is the wear and casual loss arising as a result of that use.

The minting of bullion into coin is a direct cost of the gold standard. This cost is avoided with a paper standard under the bullion exchange standard, for example, and also with an unanchored fiat money standard, although issuing and replacing worn bank notes has costs, too. This cost is used up over the life of the coin, when it is worn to the point that it is no longer serviceable and must be melted down and re-minted. The problem with this cost is that it is paid when the coin is minted, but the benefit of it is spread over the life of the coin. How can the free market solve this problem, and finance the cost of minting and wear? There are a few possible answers:

1. The coin could be legally valued at its depreciated cost, or a proxy for it. E.g. if it cost 0.5% to manufacture the coin, and the coin had an economic life of 0.5% wear, then the coin could have a legal value of face value less 2 times the mass loss, up to 0.5%, after which it would have no legal value, and would be commercially valued as scrap only. Note that the scrap value is the same as the legal value at the end of its economic life.
2. The coin could be legal tender for its face value, so long as the actual mass was not below the face value. E.g. the coin would originally be minted at 100.5% of face value, and after the additional 0.5% was worn off, it would no longer be legal tender and would be scrap. The commercial value of the coin could in this case be more than the face value (and legal value) up to the point the coin was worn to its face value. People who needed coin to discharge their debts would pay a premium to obtain it if they could not get others to tender it to them.
3. Under-mass coins could cease to be legal tender, but be accepted by some who did not discriminate, e.g. retailers who have good profit margins, who could carry the cost of re-minting it. Banks would only pay out legal tender coins, but would accept under-mass coins and charge the cost of re-minting them to the depositor. Thus holders of under-mass coins could pay a premium for goods or bear a discount on banking it.

Systems 2 and 3 are similar, in that they rely on different treatments by different traders, and they allow variable value coin to be accepted by tale (i.e. by only counting it) in many situations, while providing for it to be accepted by reference to exact mass in others. This allows for reduced transactions costs and allocation of minting and wear costs at the same time. System 1 has the advantage of allowing for a range of legal values through the life of the coin, and could be compatible with payment by tale where the seller or creditor chose to bear or pass on the cost.

Under a free market, traders and contractors could experiment with different terms they would offer to sell goods on, and different terms under which they would accept coins in settlement of debts. The law would fill any gaps in specifying what would be accepted as legal tender by reference to usage in trade. It is also likely that bankers and financial market participants would standardise the terms for settlement of debts using the banking system.

Foregone interest cost is offset, in a free market, by saved transaction costs. Holders of gold coin would only hold gold coin to the extent that its marginal benefits at least matched the returns they could earn on other assets. This implies that the foregone interest cost would be less than the social benefits provided by holding gold coin.

The social cost of casual losses of coins is difficult to analyse or estimate. Given that a single gold coin of 10 grams would be worth about NZ$500 or US$350, it is likely that people would look after them carefully.

Now that I have explained the types and nature of the social costs, I now turn to their size.

If we go back to the English system of metallic currency of the 19th Century, we can use this as an example of the costs of minting gold coins. Jervons wrote in 1876:

The English sovereign is the principal legal tender and the standard of value. It is defined as consisting of 123.27447 grains (7.98805 grams) of English standard gold, composed of eleven parts of fine gold, and one part of alloy, chiefly copper. The sovereign ought, therefore, in theory, to contain 113.00160 grains, or 7.32235 grams, of pure gold.

He also details the costs of minting sovereigns:

it may still be considered that the cost of converting gold bullion into sovereigns is about ¼ per cent.

Note that this does not include the difference between the original mass and least current mass that allows for the economic life of the coin. In the case of the Sovereign, the original mass of standard gold was 7.98805 grams, and :

Every sovereign issued from the mint in accordance with these regulations, and bearing the impress authorized by the Queen, is legal tender, and must be accepted by a creditor in discharge of a debt to that amount, provided that it has not been reduced by wear or ill-treatment below the weight of 122.50 grains (7.93787 grams).

This provided for 0.05018 grams of wear during the coin's economic life, which is 0.628% of the original mass of the coin.

Jervons also details his own analysis of studies to determine the rate of wear on English sovereigns. 

Some attention must be given to the abrasion which coins suffer in use. In the case of gold coins the loss of metal thus occasioned is of importance, and leads, as we have seen (p. 111), to a gradual depreciation of the currency. As coins pass frequently from hand to hand, the amount of metal abraded will be nearly the same as regards each coin of the same type, and each year of circulation. The loss will be proportional to length of wear. Now the English law allows a sovereign to be legal tender so long as it weighs 122.5 grains, or more; and the difference between this and the full standard weight, or 0.774 grain, represents the margin allowed for abrasion. Now, from experiments described in a paper read to the London Statistical Society in November, 1868 ("Journal of the Statistical Society," Dec., 1868, vol. xxxi. p. 426), I estimated the average wear of a sovereign for each year of circulation at 0.043 grain (0.00276 gram). It would follow that a sovereign cannot in general circulate more than about eighteen years without becoming illegitimately light. This length of time, then, would constitute what may be called the legal life of a sovereign. It has since been shown by Dr. Farr, that certain considerations overlooked in my calculations would reduce this estimate of the legal life to fifteen years. Mr. Seyd, on the other hand, thinks that twenty years might be adopted as the legal age of the sovereign.

So this is a rate of wear of about 0.035% p.a. Jervons also quotes a Swiss study that found that the rate of wear on 20 franc gold coins was only 0.02% p.a.

We can add the cost of re-minting (0.25% per re-minting) to the of wear (0.628% over its life) to get the total cost of 0.878% over its life of 18 years, or 0.05% per year.

The cost of interest foregone is simply the interest rate, which would typically be something like 3% p.a. and this cost is about 60 times the cost of minting and wear. In accounting terms, the costs of minting and wear are not material.

Under a free banking system, bank notes and current accounts with banks provide an alternative means of mediating trade and settling debts without carrying the full notional amount in metal. This allows the interest cost (being the major cost) of a gold standard to be economised. As mentioned before, and outlined by Lawrence H White in his bank profit maximisation model in Free Banking in Britian (p. 5) the banks and other traders will only hold gold coin to the extent that the marginal benefits of holding it exceeds the cost of the interest foregone:

in profit-maximising equilibrium, the marginal net revenue from holding bills (yield minus net marginal operating costs of bill holding) is equated with the marginal net benefit from holding specie (reduction in expected liquidity cost minus the marginal operating cost of holding specie). The bank must be indifferent at the margin between holding extra bills and holding extra specie of the same market value, since it can exchange one for the other on the market.

I also wish to highlight how the costs of metallic currency compare with the costs of accepting cash (whether in the form of bank notes or coins). According to this news article, the costs of accepting and handling cash are 2% of the transaction value. According to the Bank of Canada, Canada's central bank, the cost of accepting and handling cash for a C$36.50 transaction are C$0.25 which is 0.68%. The fee costs of accepting credit cards are around 1-2% of the transaction value (sometimes much higher, for less significant volumes and values of transactions).

Suppose, for the sake of argument, a gold coin in a gold standard would be transacted twice a month, and that the interest rate is 3% p.a. The annual costs of maintaining the coin, are 3.05% p.a. divided by 24 to give a per transaction cost of just 0.13%.  So, compared with typical retail cash and credit card transaction costs of, say 0.68-2%, the costs of gold coin are not very great.

Under a free banking system with today's technology we would of course expect EFTPOS systems and bank notes (whether in the form of paper or polymer documents, or base metal discs) to dominate retail payments. Such banks notes would be expected to displace silver and copper subsidiary coinage, leaving gold coin only as an option for high value (NZ$500+ in today's money) transactions.

At this point I'll address the question of small gold coins. What is the smallest practical and effective gold coin that can be made? Jervons addresses this question as follows:

There appear to be pretty well defined limits of size within which we should confine ourselves in the striking of money. Coins must not be so small that they can be easily lost, or can with difficulty be picked up. The rule seems to be that the coin should cover the whole area of contact between the points of the thumb and first finger; and though, of course, this area will differ with men, women, and children, we should err rather in excess than defect. On this ground I should condemn the English threepenny silver piece as too small, and, on the same ground, the Swedish ten-öre piece, the American one-dollar gold piece, the former Papal one-scudo piece, must be pronounced inconveniently small. The French five-franc gold piece of the later type, the English fourpenny piece, the Canadian five-cent piece, or the new silver piece of twenty pfennigs, now being introduced into the German Empire, must be considered the smallest coins to be tolerated. 

The French five franc gold piece had a diameter of 16mm and a mass of 1.6129 grams and 90% gold content, and would be worth about NZ$72. To appreciate just how tiny such a coin was, the smallest coin used in New Zealand today, the new 10c piece, has a diameter of 20.5mm and a mass of 3.3 grams, and is made of steel. The mass density of steel is 7.8 g/cm3, whereas the mass density of gold is 19.3 g/cm3, so if this coin made from 90% gold and 10% copper, it would have a mass of about 8 grams, about the same as the sovereign, and would be worth about NZ$400. So, it appears to me that gold coin would have a limited role under a modern gold standard in mediating transactions, due to limits on divisibility, and the availability of bank notes in small and convenient denominations, and the availability of cheques, EFTPOS and internet banking transfers. It is likely that gold coin would converge to a single denomination of, say, 5g (NZ$250) or 10g (NZ$500). Note that the largest bank note issued by the Reserve Bank of New Zealand now is the $100 note, and $100 notes make up about 38% of the value of bank notes held by the public.

EFTPOS systems offer lower costs for merchants and consumers alike. In New Zealand almost all merchants accept EFTPOS and neither consumers nor merchants pay per transaction fees (unlike the Bank of Canada costings for 'debit cards'), and the facility only costs merchants about $15/month (or, if they do pay per transaction fees, these are normally about NZ$0.20 per transaction). Yet for higher value transactions, where gold coin is a payment option, cheques, bank cheques, and internet banking transfers are almost universal today. Of course high denomination bank notes can be a good substitute for gold coin for the few transactions like buying a second hand car in a private sale where bearer forms of money desirable. One can only conclude that the use of gold coin under a free banking gold standard would be quite limited.

Banks would still hold significant stocks of gold coin in order to honour such demands for payment in gold as occur, and to settle payments between their customers. Historical cases of free banking have indicated low ratios of specie reserves e.g. 3% of demand liabilities. We can use this to estimate the approximate cost of holding gold coin under a free banking gold standard. For an economy with output Y, the banking system would issue notes and demand deposits equal to some ratio of Y, we will call that ratio a, and the banking system will maintain reserves in some ratio to its demand debts, we will call this ratio b. The banking system holds a proportion of the gold coin stock, we will call this proportion c. Finally we will call the ratio of interest, minting and wear costs on the gold coin stock d. So the social costs of the gold standard (SCGS), as a proportion of output is:
SCGS=d*a*b/c

Now, to estimate the values for a, b,c and d. To do this we will use New Zealand GDP and banking figures.

New Zealand GDP in the year to March 2009 was $183,737m. This is the Y in our formula.

ANZ National bank, New Zealand's largest bank with about one third of the banking market, will give us estimates of banking system variables, by way of multiplying by three. Note 31 (page 85) of the financial statements in the General Disclosure Statement for the year ending 30 September gives a contractual maturity analysis of the bank's assets and liabilities, and gives a total 'at call' liabilities figure of $27,466m. Multiply by three gives a banking system figure of $82,398m. This figure is similar to the $73,254 RBNZ figure for M2, which excludes inter-bank call funding. Divide this by GDP of 183737 gives a ratio of 45%, which is our estimate of a.

Estimating b, the metallic reserve ratio, is a little more difficult, using today's banking data because:

1. metallic standards are not presently in use,
2. today's banks hold interest bearing central bank balances as reserves, in addition to non-interest bearing central bank notes as reserves (both are able to be immediately used to meet the bank's liabilities, and the bank has a right to convert between the two forms of central bank liabilities), and
3. today's banks hold central bank notes partly to serve demands that the bank could service with its own notes if it were allowed to issue them (i.e. to meet the demand for bearer forms of bank liabilities rather than the meet redemption demands).

Nevertheless, today's bank's holdings of non-interest bearing central bank notes as reserves is like bank holdings of non-interest bearing metallic reserves under free banking and a gold standard.

ANZ National bank as at 30 September 2009 held $2 373 m in 'cash and balances with central banks' which included $2 207m in central bank balances, implying that the difference, $166m, was held in the form of non-interest-bearing vault cash. Compare this with the $27,466m at call liabilities gives a cash reserve ratio of 0.6%. This can be used as an  estimate of b.

Estimating the proportion of the total metallic currency stock that would be held by the banking system is not easy. In New Zealand today, the RBNZ, New Zealand's central bank, is the only issuer of bank notes, and the total bank notes and coins held by the public, excluding holdings by banks, was $3,339m in September 2009. This gives a bank reserve note holding ratio of $166m * 3 /($3,339m+3*$166m) which is 13%. However, the non-bank holdings of bank notes is partly the demand for bearer money and partly the demand for base money. Under a free banking system, banks would issue bank notes that would serve as bearer money, alongside metallic base money. As mentioned before, on a gold standard, a 10 gram gold coin would be worth about NZ$500, and thus gold coin would only serve for high value transactions. For fractional bearer money, without, or in place of, the institution of bimetallism or subsidiary coinage of silver and copper, small denomination bank notes would serve this function.

For lack of any other basis, we will have to make a guess as to the proportion of bearer money holdings that would be served by bank notes and by gold coin, under a modern free banking gold standard. As previously noted, about 38% of bank notes held by the public today is in the form of the highest denomination, $100 notes. We could consider this an upper bound of the demand to hold gold coins which would be worth NZ$250-500 each. It is likely that a significant amount of the demand for holding high denomination bank notes is for the underground economy, where the chief concern of the holders is anonymity rather than avoiding the risk of bank failures or needing legal tender to satisfy debts, and would therefore be served by bank notes rather than gold coin under a modern gold standard. Also, non-underground holdings of and commerce with $100 notes is likewise, in large portion, not likely to be significantly motivated by concern with bank failures, and we can assume that bank notes would continue to serve best the needs of many users of $100 notes. So, for the purpose of estimating c, the proportion of the gold coin stock that would be held as bank reserves rather than by the public, we will guess that 50% of the outstanding $100 notes would continue to be served by bank notes, and that the other 50%, would be demand for gold coin.  This gives a total demand for gold coin as being $705m held by the public (50% of $1411m in $100 notes held by the public), out of total holdings of $1203m ($705m held by the public + 3 times $166m held by ANZ National Bank), a ratio, c,  of 41.4%.

So this allows us to estimate the social costs of a modern gold standard, as a proportion of output:
SCGS=d*a*b/c
         =3.05%*45%*0.6%/41.4%
         =0.02% (or $36.55m out of GDP of $183,737m)

It also allows us to indicate the level of holdings of gold coin in relation to economic output: a*b/c = 0.65%.

Jervons also tried to estimate these costs in his own day, when there was a gold standard, but banking freedom was not as well established as it could have been, e.g. Bank notes less than 5 pounds were outlawed, leaving only gold coins for the 1 pound denomination, and subsidiary coinage was silver and copper rather than bank notes (they were, in effect, bank notes issued by the Royal Mint, since their metallic value was less than their face value and the Mint would redeem them for their face value, but they did contain most of their face value in metal (for silver but not copper coins)). Also the banking system in Britain at the time was not dominated by a few large strong banks, and bank failures were fairly common, giving more motive for holding gold coin rather than bank notes and bank deposits. Let's examine his figures:

The cost of the currency is made up of four principal items: the loss of interest upon the capital invested in the money, the loss by the abrasion of gold coins, the expenses of the mint, and lastly the casual loss of coins. The last item is of wholly unknown amount; the other items may be estimated as follows. We may, roughly speaking, assume the gold currency of the kingdom to consist of 84,000,000 of sovereigns and 32,000,000 of half-sovereigns, the total value being 100,000,000 sterling. The sovereigns lose annually on the average 0.043 grain each, giving an annual loss of about £30,000; the half-sovereigns lose 0.069 grain each, producing a loss of £18,000. The loss of interest, however, is a far more serious matter. The whole value of the metals employed in the currency is, roughly speaking, as follows:—

Gold coin in circulation . . . .	100	millions.
Bullion in the Bank of England . .	15	"
Silver coin . . . . . . . .	15	"
Bronze coin . . . . . . . .	1 1/8	"
Total . . . . . . . . .	131 1/8	millions.

The interest on this sum at 3¼ per cent. is no less than £4,262,000.

XIII.21

The cost of the mint establishment is about £42,000 annually. The following statement, then, show the aggregate cost of the metallic currency so far as it can be estimated.

Loss of interest . . . . . .	£4,262,000
Wear of coin . . . . . . .	48,000
Mint establishment . . . . .	42,000
	£4,352,000

 The figures he gives can be compared with UK GDP figures in 1876: 1,229 million . The costs as measured by Jervons (i.e. 4.352m pounds) are 0.35% of GDP, much higher than the 0.02% of GDP figure I estimated above. This is due to the much higher holdings of metallic currency and monetary metal, in relation to GDP, i.e. 10.67% of GDP in Jervon's 1876 Britain, vs. 0.65% of GDP in my modern NZ based estimate.

How can we account for this difference?

Firstly, we can subtract the bullion, silver and copper coinage, leaving only the gold coins (i.e. sovereigns and half sovereigns).  This would leave the 100m pounds figure and reduce the ratio to 8.14%. 

Secondly, the lack of any 10 shillings (half pound) and 1 pound and 2 pound notes (other than 1 pound notes in Scotland), due to Bank Notes Acts of 1826, restricted availability of bank notes for the key gold coin denominations of 10 shillings and 1 pounds (as well as for amounts of 2 pounds), leaving no bearer form of money that did not require the expense of holding gold metal. The smallest bank note, other than in Scotland, was the 5 pound note, and 5 pounds in those days was a lot of money (GDP per capita in 1876 in the UK was 37 pounds per year). Likewise the lack of small denomination bank notes (trader's tokens were suppressed) requires the cost of holding silver and copper coins as fractional currency.

Thirdly, banks were not financially strong and bank failures were common, so public confidence in bank deposits and notes was not as strong as would be the case under free banking where the banks, as in New Zealand today, are extremely large and strong.

Fourthly, the development of bank accounts, cheques, EFTPOS and the like was not as advanced as it is today, or did not even exist. Merchants did not have the facilities to reference-check the drawer of a cheque to see if the account exists and if the account has had dishonoured cheques before (these days, merchants can use telephone, fax or internet to do this). Merchants could not accept EFTPOS payments.

For all these reasons, I argue that a modern gold standard and free banking would involve costs closer to 0.02% of GDP than 0.65% of GDP.

Against these costs, the benefits of the gold standard should also be counted. As argued above, no one is obliged to hold gold coin, the only situation when you need gold coin is when you have contracted yourself to provide it in satisfaction of debt. Normally creditors will accept payment by cheque or EFTPOS or bank notes or bank transfer, but if the creditor wants to be paid gold coin, he can insist on it. The marginal benefits of holding gold coin, must, for every holder, not be less than the marginal cost of holding it, and so, whatever the level of gold coin holdings the public and banks wish to hold, the costs are more than offset by benefits. But even if these benefits are not counted, the costs of the gold coin standard are very modest. 0.02% of GDP or $36.55m can be compared with, $11m for example, for the Reserve Bank of New Zealand's monetary policy formulation expense in 2009. Another way to put this into perspective is to express it as a per person cost: for a population of 4 million, this is $9.14 per person per year.