I recently received an e-mail asking about the price of gold. This person presented two gold-pricing models in the body of the e-mail along with an estimate of what price gold might command in the future in dollars.

Let’s examine the gist of what he wrote and provide an extended reply. He wrote

"We owe over 12 trillion dollars. At a $1000 per ounce gold price, that's 12 billion ounces of gold. According to estimates, only 4–5 billion ounces of gold have been produced since the beginning of time. This assumes either: a lot of Treasury debt is going to be defaulted on OR the dollar price of gold is going much higher than $1000. But how much higher? Does your analysis give you any inkling about what a proper dollar price is for gold? I read there are 20 trillion dollars of currency circulating around the world converted back into U.S. dollars. If there are 5 billion ounces, that's $4000 an ounce for all the currency to be fully backed by gold or $2000 to be 50% backed."

The writer here has given this matter some considerable thought and has come up with two very different models. The first one compares U.S. Treasury debt to be paid in dollars with ounces of gold and current gold price. The second one compares all the currency in the world (converted into dollar terms) to all the gold in the world. His serious thought and work deserve serious consideration.

There are many competing models that aim at estimating the worth of gold, now and in the future. They obviously give a range of different numbers. Bob Prechter has a model that predicts gold below $700. Paul van Eeden, last I looked, thought gold was fairly priced. Alf Field sees gold going to $6,000 or higher. The e-mail writer’s model looks for gold at $2,000 and higher. Which model or models should one choose? I’ll address only the two models that this writer presented.

No gold pricing model that comes up with a specific price for gold that I know of is complete. The most important missing factor is something that is not quantifiable. That factor is the degree of acceptance of the dollar in trade, exchange, and as a store of value versus the degree of acceptance of gold. This factor is qualitative. It depends on the behavior of those who use dollars and gold.

There is model risk in all endeavors. In this case, it means that no matter how carefully we think we understand pricing, we don’t fully understand all the factors that drive pricing. If we did, the only downside risk would be in predicting these factors, and the model would be worth more than gold. The fact is that we do not know all the factors that influence the pricing of an asset. We always have to bear model risk.

The writer is after a "proper" price or "fundamental" price. What this means concretely is a price toward which gold would gravitate if arbitrage or equilibrium forces were at work long and effectively enough.

Since acceptance or demand is a key variable in gold’s pricing, any fundamental price we come up with will only serve as an attractor to the actual price of gold if we can identify arbitrage forces that induce people to trade toward that price. I will come back to that after looking at the writer’s two models.

Model #1 relates U.S. Treasury debt to the world supply of gold. This model says that if all the U.S. debt were paid in gold and if the US possessed all the gold in the world and paid off its debt (in nominal terms), gold would have to be three times higher than at present. This method is badly flawed. Why stop at U.S. government debt? Why not use all debt? Why pay off the debt? And since the U.S. only has 1/20 or so of all the world's gold, wouldn't the price be twenty times higher? A basic problem with this model is that the gold price is not determined by the amount of debt in the world or in the U.S. or issued by the U.S. government. The value of the dollar in terms of gold is unaffected if the U.S. government issues a debt and then taxes citizens to pay it. It is unaffected if someone obtains a mortgage loan and then repays it over time. I will say no more about model #1. I won’t use it.

The writer’s model #2 is better conceived. The total of all currencies (in dollar terms) is a well-defined concept. The gold backing these currencies is a well-defined concept. The currencies are liabilities of the issuers. They hold various assets, including gold. Gold is what helps determine the acceptance of these liabilities and their use as money. It is what gives them value.

Many people mistakenly think that the paper dollars we use have nothing at all behind them or that the currency is a 100 percent fiat or unbacked currency. It should be understood that 100 percent pure fiat money does not last very long. It goes to zero value as in Zimbabwe because people do not accept it for long. The FED actually has 261.5 million ounces of gold that it carries as an asset (auditing issues aside). Its bank notes are not pure fiat money. What is true is that their wide use and acceptance depends on these notes being made into legal tender. If that law were abolished, rival currencies would have an easier time arising. It is also true that the FED is able to issue its bank notes ad infinitum, which is another fiat element. This in turn affects their acceptance, presumably lowering it.

Those matters behind us, the model #2 comparison of the total of all currencies to the gold total makes sense. The writer’s application of these ideas is flawed. Should we compare all the gold, held by anyone anywhere to the currency total? Most of that gold is not being used to back up the currency. A central bank issues currency in a way that is analogous to Bank of America issuing stock. To value the stock, we’d examine the assets of Bank of America, including all of its branches. We would not get the total of all the branches of all banks anywhere. We should use only the gold held by those central banks that issue the currency in valuing the currency. They hold perhaps 20 percent of all the above-ground gold. That means comparing total currency dollars to 0.8 to 1 trillion ounces of gold. That amount is a reasonable estimate of the gold held by central banks.

The writer has a second error. The total currency ounces is not $20 trillion. It is about $3.5 trillion. I think the writer here is perhaps using an estimate of all forms of money, not just currency issued by central banks the world over. He’s including demand deposits and time deposits in non-central banks or some such construct. However, the latter deposits are not a liability of the issuers of bank notes, which are the central banks. The deposits used as money are a derivative money that is created when a non-central bank makes a loan and creates a corresponding demand deposit. It is true that this bank uses the currency of the central bank as a base for making such loans and creating such deposits, but the backing for these deposit liabilities is not gold. It is the loans the bank holds as its assets.

If the reader sees this matter differently than I do and wishes to use 20 trillion rather than 3.5 trillion, then this will raise the model price of gold by a factor of 20/3.5 = 5.7. Instead of getting $7,000 an ounce, the user of 20 trillion will get $39,900 an ounce. You tell me if that is reasonable. I don’t think it is. And I don’t think gold is the backing for all that derivative money.

So then what we find using model #2 and appropriate data inputs is $3.5 trillion currency/0.8 trillion ounces of gold = $4,375 per ounce; or we get $3,500 using the 1 trillion ounce figure. The mean of these two estimates is $3,938. This assumes that every dollar of currency is 100 percent backed by gold. It may be of interest to know that before the U.S. went off gold, the FED was mandated by Congressional law to maintain 40 percent gold backing of the dollar. At 40 percent backing, the estimate we are getting here is $1,575.

This method has the flaw that every currency issued by central banks is not equally backed by gold, as it assumes. In fact, the euro has a much larger backing than the U.S. dollar. Clearly, the Zimbabwe currency will have a much higher gold price in its local currency because its backing is zilch.

Model #2 also assumes that these exchange rates are rates that will prevail indefinitely into the future. Exchange rates change all the time, however. If the dollar strengthens versus other currencies, this will cause the gold price in dollars to decline, holding constant the world price of gold.

This is an important economic fact that is verifiable and not clearly understood, and so I digress slightly. The fact of the matter is that an identity holds. Let the term forex stand for an index of foreign currencies. Then the domestic gold price is $/gold oz = ($/forex) x (forex/gold oz). The term (forex/gold oz) is the world price of gold. The term ($/forex) is the exchange rate between the dollar and the world currency basket.

A stronger dollar means that it takes fewer dollars to buy a unit of forex. This means that $/forex is lower. This means that $/gold oz is lower, as long as the world price of gold does not change. These statements can be verified using actual data.

Model #2 is not bad at all. But I’d be strongly inclined to improve it by examining each currency separately. When I do that with the U.S. dollar, I find that the 100 percent backing gold price estimate of $3,938 per ounce may get up to as high as $7,151 an ounce.

For the U.S. data, the monetary base is currently $1.87 trillion. The monetary base changes every week. Per ounce of gold held by the FED, this is $7,151. That represents 100 percent backing by gold. The dollar is now at less than 15 percent backing (using gold at $1,050). This is the same low level it had in the late 1990s.

About half of the monetary base is in place because of the FED’s extraordinary credit expansion, and the permanence of that component is an open question. If the extraordinary component of the monetary base is simply ignored, then the backing percentage of the remainder is a much more respectable 28.6 percent. If it were even 40 percent of this reduced amount, gold would be $1,400 an ounce. If the backing were 40 percent of the total monetary base, gold would be $2,865.

Numbers such as these surely give the impression that gold can go higher, but we knew that already. Any asset can go higher. These numbers give the illusion of certainty and necessity, or in other words they suggest that gold will go higher. But the model has no reasoning in it to say why this has to happen, if it has to happen at all.

The real problem of the gold speculator is predicting the degree of acceptance or non-acceptance of gold versus the dollar and its changes over time. Having an idea of levels is nice, but we also need a model of what causes current levels to change so that they eventually arrive at what we think is a level that will prove to be an attractor for actual price.

The central question is what incentives there are for those who use and accept dollars to demand fewer dollars and demand more gold as time passes. It is the operation of these incentives over time that will determine the price of gold, not the numbers generated by models like the above.

The two major groups of players in this drama are members of the public and the governments of the world. A few short years ago, gold was $255 an ounce. Gold was not afforded a high degree of acceptance. Dollars were accepted. This has changed dramatically. Now gold is much higher.

The attempt to get out of dollars en masse and into gold cannot lower the total supply of dollars in the world unless the central banks contract that supply, and they haven’t. Shareholders cannot lower the supply of shares of Bank of America stock outstanding by intense selling. They can only make the price fall to ration the existing supply at a lower price. In the same way, if demand for gold is more intense, the existing supply will be rationed via a higher price. The number of dollars in existence need not change any more than the number of shares of Bank of America stock needs to change in order to observe a price change.

Several major facts lie behind this gold price rise, which has been, by the way, a rise in the world price of gold. To recount these facts is to give a qualitative model for gold price changes, not levels as in model #2. This is really model #3.

The first fact is that the central banks have increased the supply of currencies (and bank reserves), so that the gold backing per unit of currency issued has fallen. This is of prime importance. In model #2, this causes the warranted price of gold to rise.

The second is that the returns provided by investments in dollar-denominated securities have declined. This too is of prime importance, but it is not in model #2. If safe securities pay little or no interest and if there is price inflation to boot, then holding currency or these safe securities is a losing proposition. There is a very strong economic incentive to shift out of these securities and into assets that maintain their value, such as gold. Gold is a convenient asset for this purpose because it trades in a highly liquid and low-cost market. As long as interest rates stay low, this factor operates to pull funds out of safe securities and into gold.

The third factor is that the banking system of the U.S. (and perhaps some other countries) is insolvent. The loans that back the derivative money have been sliced in half or more in value. The government guarantees are being called into play. This results in more pressure upon the central bank to create credit for the government.

In addition, the FED has responded to this pressure and to the worries of foreign debt holders like China by making immense purchases of mortgage-backed securities. This policy expands FED credits (the monetary base) and dilutes the dollar’s backing as each week passes and more of these securities are absorbed by the FED and paid for with newly-created FED money.

The deep recession and the resulting government issuance of debt have the same effect of pressuring the central bank. In the future, the immense debts that are in prospect due to promises to pay off on programs like Medicare and Social Security are going to pressure the government to inflate.

Fourth, foreign governments and central banks are discovering that their policy of piling up dollar reserves has high costs that did not prevail when they began this policy in the 1970s. Why did they not tell Nixon to kiss off when he closed the gold window in 1971? Why didn't they play hard ball right there and then? Why did they go along with this when it could hurt them directly and when it was a repudiation? There are several reasons. They felt in a weak position. They wanted to sell goods to the U.S., which was the big market. The U.S. applied various pressures. The U.S. was the big power with the big military that operated as an umbrella over the non-Communist world. But the foreign governments did not take much coercing at first. They liked the idea of having some control over their own currencies. That was another reason they went for the inconvertible dollar. They could have more power to manipulate their own economies, or so they thought, until they discovered that the U.S. dollar policy really called the tune. Furthermore, at that time, the gold backing of the dollar was substantial, even if it was not convertible.

So they accepted dollars that were not convertible into gold. What this acceptance did was to relegate gold to a distinctly secondary and inferior status of non-acceptance. Subsequently, the U.S. inflated merrily in the 1970s and gold made a serious comeback due to public buying of gold, since the public is the other major player that can turn away from dollars if it chooses. Gold ran up far beyond even its 100 percent backed value. Very high U.S. interest rates scotched the gold bubble. Consequently, gold fell to an extremely large discount to its fundamental value during an extremely long and tiring bear market. Gold appeared to be almost entirely a relic. But even during this period, gold was still a basic anchor to currency values. It was and is the basic unit of account of the world’s monies, even though that important role is not mentioned very often or emphasized. If gold were not present in central bank reserve asset holdings, the paper currency system would not last long.

Because these political economic matters have acted very slowly, this acceptance of the inconvertible dollar has gone on now for almost 40 years. But that's long enough for the relative strengths of the economies to change, and for foreign governments to want more independence, both in terms of economic impact and political power. They are now groping for a new relationship.

A number of things are coming to a head among Russia, China, Brazil, and the Gulf states, including their own growth, the FED's policies, the troubled US banking system and economy, the extended US military positions, and the impossible debt obligations of the US government for social programs. Other countries as well have greater incentives to lower their acceptance of the dollar and increase their acceptance of gold and/or other currencies that have higher gold backing. This fourth factor is incipient but growing.

The preceding are forces of arbitrage that make or induce abandonment of the dollar. Their presence means that we can be more certain that this will actually happen. Now let’s mention a few general considerations that have less immediate but perhaps more long-run applicability.

One such force is the incentive that a nation has to grow economically. Economic growth is stimulated when the currency is stable, for then interest rates will tend to be low and stable and businesses can undertake long-term investments with greater assurance. Economic growth is also stimulated when a society eschews a welfare and warfare state. And it is stimulated when property rights are secure. The U.S. government has retarded this nation’s progress by diminishing these policies that it once had in place before most of us were born.

If any major nation or group of nations adopt these growth policies, they will grow relative to the U.S. and then they will gain political power. If they even move in the direction of these policies, they will grow stronger. That is a strong inducement, based on solid grounds, to move away from the dollar. In other words, political and economic competition at the level of the nation-state can undermine the dollar. That may, if it happens, then force the U.S. to alter its policies.

Another such force is rival privately-based currencies that are stable. Whatever enterprise or group of enterprises that succeed in producing a private competing money system with a stable money will be extremely profitable. This is not unattainable, but it is very difficult given the privileged role of the dollar as legal tender and in the nation’s payment systems. If this happens, it will compete with the dollar. In fact, if another major nation succeeds in constructing a stable gold-based currency, then this will provide very significant competition to the dollar and impel other countries to move toward gold as well.

A third force stems from the domestic political economic policy. The U.S. federal government has impossible dollar obligations and promises that it cannot meet in the next ten to twenty years, short of a productivity miracle or two. Who is going to pay these obligations? Some combination of scaling back, more borrowing, reneging, and higher taxes is necessary, such as the value-added tax mentioned by Speaker Pelosi only a few days ago. The wealth redistributions are going to slow the economy and raise prices. The effect of all this is likely to be increased pressure on the central bank to inflate.

There is a fourth force, which is increased acceptance of gold as a component of diversified investment portfolios. Gold has remained the world’s monetary unit of account, even when it was very unpopular. It did not serve widely among many people either in everyday exchange or as a store of value. That is changing. By definition, the nonmonetary shocks to real economic activity are uncorrelated with the monetary shocks that impact the price of gold. Hence, over long periods gold’s price changes tend to show a low contemporaneous correlation with the returns of stocks. As more and more research has advertised the portfolio benefits of holding gold in a portfolio, more and more investors are seeking it out. This requires bidding gold away from other holders, which makes the price rise. That reduces the diversification attractiveness, but the net result is still greater acceptance of gold as a store of value.

What’s the bottom line? Gold’s price depends on the main factors mentioned above, of which I place interest rates and monetary inflation of the currency as the two of prime importance. I am not here speaking of changes in the money supply, which have to do with the derivative monies produced by non-central banks, and I am not speaking of changes in consumer prices or any set of prices in the economy. I am speaking of that which is under the control of the central bank, which is its inflation of its balance sheet liabilities. That inflation, in turn, is affected by government policies and domestic political factors.

The model prices of gold are substantially higher than the present price. Gold looks very attractive from that point of view. But there is a proviso. There is no mathematical relation between the price of gold in the market and estimates one obtains from a model, even a sound model. Over the years, the dollar has been accepted and used while having widely varying amounts of gold backing, no matter what a model like model #2 says. The degree of dollar acceptance and backing varies through time, so that there is a large area of price uncertainty of gold.

As people reduce dollar acceptance, they demand more backing and they bid the price of the dollar down in terms of gold, so that the gold price rises. As the gold price rises, the value of any gold held by a central bank rises and this automatically increases the backing. The market determines the dollar’s worth.

A model like that relating currency to gold holdings gives levels of gold price. As speculators, we need to judge the future acceptance of the dollar. Arithmetic does not suffice. We need to judge changes in order to speculate profitably in gold. We need to look for and judge real incentives that induce people to leave the dollar and replace it with gold.

Michael S. Rozeff

Michael S. Rozeff is a retired Professor of Finance living in East Amherst, New York. He publishes regularly his ideas and analysis on www.LewRockwell.com . Copyright © 2009 by LewRockwell.com.