Backed Money, Fiat Money, and the Real Bills Doctrine



EMAIL FROM AARON FONTAINE 10/15/2003

Hello Mr. Sproul,

I am a self interested and self directing learner in

the field of economics and monetary theory. It has

become a recent obsession for the past year or so. In

trying to find the definition of the Real Bills

Doctrine I came across your paper: "Backed Money, Fiat

Money, and the Real Bills Doctrine". I did not fully

understand everything on the first read through, so

I'm going back through it again, slowly, writing notes

in the margins. Your paper has already helped me come

to many small realizations plus a fuller and more

appreciative understanding of the Real Bills Doctrine.

Although I don't fully agree with your refutation of

government money as fiat money, it's interesting I

never really thought of money as I do other financial

securities. I think that's what's going to finally

knock the Quantity Theory from my mind. I liked the

elegance of the Monetarist Theory when I first came

across it, but I always run into the problem of what

exactly do you define as money. How derivative can a

dollar be? Does corporate scrip count?

Anyway, all this brings me to another realization I

made while reading your paper. I noticed that in

section 1, "The Quantity of Money", the IOUs added to

the hypothetical bank had a *current market value* of

100 oz of gold. This is the first time I ever made the

distinction that the Federal Reserve values all of its

government securities at face value, not current

market value. Wouldn't that make all of the Treasury

Bills in its portfolio overvalued and thus reduce the

value of its credit? It's interesting since they have

to buy and sell the securities in the open market,

which means they are paying market value. Is this even

a concern? It's interesting to ask why gold is approx.

$370 an oz. when the Fed still holds a gold stock

valued at the statutory price of $42.22 an oz.

According to the Real Bills Doctrine, that implies

that the Fed is overvaluing the other assets it holds.

It would be interesting to do an analysis of the Fed

and see how much this can account for the devaluation

of the dollar. Unfortunately I don't know enough about

the Fed's other assets to know how to value them

properly in such a calculation. I tried some

rudimentary calculations with the equation G+xP=yP. G

is the quantity of gold held by the Federal Reserve

(261 or 263 million I think). x is the value in

dollars of the securities held by the Fed. y is the

liabilities in dollars of the Fed, and P is 1/(the

price per oz of gold ($370 or $380 I think)).

Depending on how I mess around with it I can get

market value roughly equal to between 87% and 93% of

face value. Is this making any sense? Can this at

least partially account for the loss of value of the

dollar? Am I even doing this right? I'd sincerely

appreciate your analysis and input on this.

Thank you,

Aaron Fontaine

COMMENTS FROM AARON FONTAINE 10/26/2003

Backed Money, Fiat Money, and the Real Bills Doctrine

Ok, first of let me start by saying I am in no a way an authority on monetary or economic matters. The extent of my formal education in economics consists of micro econ course from my freshman year of college. Nonetheless I have taken up a tremendous personal interest in these issues. Although my knowledge may have gaps and I may not fully understand everything, I’m always driven to complete this knowledge. I have done much studying, including several chapters of my old econ textbook, books ordered off the internet, and through websites.

I personally like your defense of the Real Bills Doctrine. It has a lot of intuitive appeal, much like the Monetarist Theory did to me when I first studied it. However, I see this paper more as a rebuttal of the arguments that defeated the Real Bills Doctrine in the first place. I find it a salient point that many of the arguments you dissect had assumed the validity Quantity Theory in their arguments for such validity. I’m not personally well versed in the debates and history of paper money, so there’s not much I can do to say you’ve represented both sides of the argument in historical fairness, but I feel I have gleaned much from your paper and that has even helped to grow and shape my understanding of the concept of money. Also, my lack of knowledge shouldn’t prevent from pointing out where the paper felt weak to me. I know this paper is very theoretical and even admits there is not enough appropriate historical data collected to verify its thesis. I also know I’ve spoken to you about the Federal Reserve and the possibility of analysis on such a central bank, but I concede such analysis is far beyond my ability at this point.

What I have for this discussion are two different goals. First is to examine the points brought up in your paper in relation to the Federal Reserve and see how perhaps their policies influence the value of money. The other is to examine the points of your paper in defense of the Real Bills Doctrine that were weak to me and discuss how perhaps the Real Bills Doctrine may only be a partial determinant of the value of money.

A few notes before I begin:

1st, check the labels of each section, I don’t think they are numbered/lettered correctly.

2nd, Friedman 1948, referenced on page 11, does not appear in the references.

3rd, “easy money” as you use the term, appears a biased distortion of the actual meaning. Easy money is generally means an expansion of the money supply and says nothing about “sufficient security” whereas you take it to specifically mean money created on insufficient security.

Now I will step through your paper section by section.

1. THE QUANTITY OF MONEY

I am very much in agreement with you in this part. The price of money should not change relative to gold. However we know this is not the case with the Federal Reserve, so that naturally leads to the question, why is this so? As I mentioned previously, I believe the Fed overvalues its holdings of government securities. In your paper, you were careful to use the current market value of the IOUs held by the bank in question. I have found it difficult to determine the exact operational model of the Fed but I believe they are not using the current market value of their securities. As evidence I refer you to their statistical release: Factors Affecting Reserve Balances.

Scroll down to the 2nd table: Consolidated Statement of Condition of all Federal Reserve Banks. Notice that all Securities Held Outright, except Inflation Compensation are value at face value, according to footnote 2. For bills, this is obviously more than current market value. From the Bureau of Public Debt: “You buy T-bills for a price less than their par (face) value, and when they mature we pay you their par value.” Also I contend that notes and bonds are overvalued as well, because although the Fed is collecting interest on these items, the public sector holding the dollars they back is not. For the most part, this is not a genuine concern amongst the public since they can simply convert their base dollars into derivative forms, such as demand deposit accounts, which do pay interest. This would seem however, to drive the value of base money to zero, the only mitigating factor being that base money is the only form of money acceptable for taxes. If the Fed were to reestablish convertibility, I contend that a vast majority of people would redeem their notes for the bonds held by the Fed so that they could realize the interest for themselves and perhaps deposit them for notes at their own local banks in the hopes of realizing a better interest rate than they were receiving on accounts consisting of derivative dollars.

I will contend also at this point that I recognize a tradeoff between security and liquidity and the expected rate of return. So the base money, being the most secure and liquid type of financial security available, would naturally have the lowest expected rate of return. However, its tough to say whether a properly organized system would realize a negative real rate of return on its base money, as US dollars do. But then again, what lies at the heart of this discussion also lies at the heart of inflation, so who knows?

2. THE CONVERTIBILITY OF MONEY

This is where I draw my biggest contention with your paper. The question I initially asked myself here is, if dollars are not convertible, now or ever, what difference does it make whether they are backed or not? If the dollar is never going to be exchangeable in your lifetime, does it matter that the Fed is holding assets against it? Now I grant that I am not this skeptical. If the Fed were ever to get rid of its assets, I’m sure the value of the dollar would drop to zero. You compare FRNs to shares of stock, so let’s analyze that. The main difference I see here is that normally stocks pay dividends, and the main value of stocks comes from the total future expected return of all dividend payments. FRNs pay no interest and no dividends, but even still, a stock that paid no dividends would still be worth something, simply because there are assets backing it. I have enough faith in the government that if the Fed ever were dissolved that the assets backing its notes would remain. So it’s a fair contention that although not convertible, dollars may still maintain some of their value. I would like also to look at non-convertibility from a different angle. In your paper, “no such thing as fiat money”, you gave the current value of a bank note to be ((1+C)^n)/((1+R)^n). Where n is the number of years until convertibility, C is the marginal cost per year to maintain notes in circulation, and R is the current expected rate of interest. Now this is an interesting an equation, for if we make n infinity, as the Fed has done, then the value either drops to 0 or rises to infinity, depending on whether C is less then or greater than R. This however may be too difficult to analyze meaningfully and I wouldn’t be surprised if they were close. My skepticism tells me that C is probably less than R though, which again would bring us back to the question, why do the FRNs have any value if they are never convertible and never pay any returns?

3. MONEY DEMAND

In this section you denounce the acceptance of paper money as taxes as a possible reason for its value, yet in your paper on the history of paper money, you recognize taxes collectible as a perfectly valid asset behind the value of paper money. I would contend then that in the case of the US dollar that taxes collectible on the part of the federal government is at least partially responsible for its value. This could be then a kind of double backing on top of the assets held by the Federal Reserve. Also I believe the statement that money has value because others value it is valid. That’s what a medium of exchange is about. In this case its being valued for its facility in increasing liquidity and efficiency in the market.

4. THE QUANTITY OF DERIVATIVE MONIES

My main contention here is that derivative monies are less distinguishable from actual money than derivative stocks are from actual stock. I hope most people recognize how banks and financial institutions really work, but the line is still blurry. Look at a bank statement. It will say you have x dollars in your account when in reality they are holding bonds and loans worth that amount. Look at a statement for a mutual fund account. It will say you have x dollars in your account when in reality they are holding stocks and bonds worth that amount. This all serves to make it appear as if there is more money than there really is. Now from a purely monetarist standpoint, there are two ways of looking at this. First you can say well yeah, such accounts really do count as money and you get into a big hassle making different definitions, such as M1, M2 and M3. Or you can recognize these accounts as increasing the efficiency of the base money and thereby increasing its velocity, which is the viewpoint I favor.

5. FISCAL POLICY

What I see here is a distinction being made between fiscal policy and monetary policy. I observe the open market operations as an important part of the fiscal and monetary processes. It means that the government can’t create more debt than the public is willing to hold to begin with, which means money can never be created beyond the government’s available credit.

I had hoped to talk about more at this point, but I’ve written on and analyzed this stuff enough for now. I will get back with more later.

SPROUL-FONTAINE DISCUSSION 11/09/2003

10/26/03-11/05/03

Hi Aaron:

I’ll try replying right in your document. Thanks very much for all this input. It is really hard to find an economist who is interested enough in this subject to give any useful feedback, and you’ve given it in spades.

Backed Money, Fiat Money, and the Real Bills Doctrine

Ok, first of let me start by saying I am in no a way an authority on monetary or economic matters. The extent of my formal education in economics consists of micro econ course from my freshman year of college. Nonetheless I have taken up a tremendous personal interest in these issues. Although my knowledge may have gaps and I may not fully understand everything, I’m always driven to complete this knowledge. I have done much studying, including several chapters of my old econ textbook, books ordered off the internet, and through websites.

I personally like your defense of the Real Bills Doctrine. It has a lot of intuitive appeal, much like the Monetarist Theory did to me when I first studied it. However, I see this paper more as a rebuttal of the arguments that defeated the Real Bills Doctrine in the first place. I find it a salient point that many of the arguments you dissect had assumed the validity Quantity Theory in their arguments for such validity. I’m not personally well versed in the debates and history of paper money, so there’s not much I can do to say you’ve represented both sides of the argument in historical fairness, but I feel I have gleaned much from your paper and that has even helped to grow and shape my understanding of the concept of money. Also, my lack of knowledge shouldn’t prevent from pointing out where the paper felt weak to me. I know this paper is very theoretical and even admits there is not enough appropriate historical data collected to verify its thesis. I also know I’ve spoken to you about the Federal Reserve and the possibility of analysis on such a central bank, but I concede such analysis is far beyond my ability at this point.

A good starting point to understand both sides in historical fairness would be David Laidler’s entry on the real bills doctrine in the Palgrave Dictionary of Economics. David is anti-RBD, and you might have noticed the discussion with him that I posted on my website. He gives about as intelligent an exposition of the anti-RBD view as you can find nowadays, and he’s not that hard to get hold of thru email.

When I first started thinking about this stuff in 1989, I kept a journal of random observations about money as they occurred to me. It took 5 years before I was able to first put my thoughts into a cogent paper in 1994. During that time I discovered, as you no doubt have, that modern economic textbooks have NOTHING to say about the RBD. Not just nothing intelligent—I mean the words “real bills doctrine” don’t even appear in 99% of the textbooks out there--even the advanced ones. Very true. Most books don’t discuss the history of economic thought. They especially seem to omit Smith’s RBD, which is interesting considering how much emphasis is placed on Smith’s other theories as being basic. An excellent online resource can be found at the “History of Economic Thought Homepage” []. Their page on monetary theory can be found at []. The essays at this website (amongst many other things) cover the RBD and QT, the bullionist debates, and the views of people such as Thornton, Ricardo, and Wicksell. In the few cases where it does appear the coverage is a few sentences (e.g., Mishkin’s Money and Banking book).

This got me looking up old books. The first was Knut Wicksell’s “Lectures on Political Economy”, which was anti-RBD. I didn’t know there was such a thing as the RBD at the time. Anyway, from there I read Thomas Tooke’s “Inquiry into the Currency Principle”, which read at the time like a foreign language, although nowadays I can read it easily. Probably the book I liked best was John Fullarton’s “Regulation of Currencies of the Bank of England”. Both of these books were pro-RBD, and they really kept me going. Then I read the anti-RBD books: Henry Thornton’s “Paper Credit”, Mises’ “Money and Credit”, Lloyd Mints’ “History of Banking Theory”, etc. It’s a few years’ worth of reading, but there it is. Thanks for the references. The only book I’m familiar with in this list is Mises’ “Money and Credit”, which is available online at []. I have intended to read the entire work, but it is so incredibly long-winded I find it difficult. Considering what I think of Rothbard and Mises, I don’t consider it a great loss.

What I have for this discussion are two different goals. First is to examine the points brought up in your paper in relation to the Federal Reserve and see how perhaps their policies influence the value of money. The other is to examine the points of your paper in defense of the Real Bills Doctrine that were weak to me and discuss how perhaps the Real Bills Doctrine may only be a partial determinant of the value of money.

A few notes before I begin:

1st, check the labels of each section, I don’t think they are numbered/lettered correctly.

2nd, Friedman 1948, referenced on page 11, does not appear in the references.

Thanks. It might be too late to fix it, since the paper’s already out there.

3rd, “easy money” as you use the term, appears a biased distortion of the actual meaning. Easy money is generally means an expansion of the money supply and says nothing about “sufficient security” whereas you take it to specifically mean money created on insufficient security.

Personally, I think that’s the best definition of easy money. For one thing, if the Fed offered $100 cash for a bond worth $101, nobody would sell bonds to the Fed and the money supply wouldn’t expand. If the fed offered $100 for bonds worth $99, everyone would take the offer and the money supply would expand. There’s a problem that comes up: What if the Fed is offering $100 for bonds worth $99, but the Fed then rations credit, meaning that it will only buy a fraction of the bonds offered, so as to keep the money supply from skyrocketing. On the one hand you might say the fed is being tight, and on the other easy. It’s the same problem that comes up with price ceilings. If the natural price of gas is $1.70/gal, and the ceiling price is $1.40, then sellers won’t sell as much as buyers want. The $1.40 price is “easy”, but the restricted output is “tight”. Economists handle this by distinguishing between “scarcity” (price>0) and “shortage” (Qd>Qs). I didn’t delve into this in the paper for obvious reasons, but you probably get the idea of how it can be applied to money. I do delve into this in my “Quick History” paper, as well as in chap 29 of my online text. I agree with you on this point, and I like the extra perspective you added. I was just picking nits because biased language can so easily degrade a conversation. So can ambiguous language. It’s an interesting point you make though that although the Fed may believe they are being tight, they are in fact exacerbating inflation.

Now I will step through your paper section by section.

1. THE QUANTITY OF MONEY

I am very much in agreement with you in this part. The price of money should not change relative to gold. However we know this is not the case with the Federal Reserve, so that naturally leads to the question, why is this so?

I’ll just classify myself as “confused” on this point. I always think of that time in the 70’s (I think) when the price of gold shot up to $800/oz. and then shot back down again. This should have played havoc with the value of the dollar but it didn’t, and I don’t have a good explanation for why, except that maybe the public figured they wouldn’t be able to get gold for their dollars for a hundred years or more, and they figured the price of gold would return to a normal level by then, so the temporary volatility of gold didn’t translate into a volatile dollar. Anyway, for most of recorded history the price of gold has been stable—remarkably stable in fact. I would have to assume the 70s era you are thinking of is when Nixon ended gold convertibility to foreign nations. I’ve actually never heard of it, but it’s a very interesting phenomenon. I’m guessing the reason it didn’t reak havoc is because much of that overvaluation was due to speculation. Such bubbles are typical of other financial markets, such as stocks and real estate, but was not possible for gold as long as dollars remained convertible on demand. But one thing about such large fluctuations: economists like to talk about them more than they actually affect any other sectors of the economy. Speculation is different than a real and sustained market response. For example, the day convertibility was abandoned for US currency in the 1930s, the stock market rose nine percent. It rose another six the day after. [See Jeremy Siegel’s “Stocks for the Long Run” for more on this.]

As I mentioned previously, I believe the Fed overvalues its holdings of government securities. In your paper, you were careful to use the current market value of the IOUs held by the bank in question. I have found it difficult to determine the exact operational model of the Fed but I believe they are not using the current market value of their securities. As evidence I refer you to their statistical release: Factors Affecting Reserve Balances.

Scroll down to the 2nd table: Consolidated Statement of Condition of all Federal Reserve Banks. Notice that all Securities Held Outright, except Inflation Compensation are value at face value, according to footnote 2. For bills, this is obviously more than current market value. From the Bureau of Public Debt: “You buy T-bills for a price less than their par (face) value, and when they mature we pay you their par value.”

Correct. But if the Fed starts its life by taking in 100 oz of silver and issuing 100 paper dollars, and then issues another $100 to buy a bond with a current market value of $100, then the public will correctly value each dollar at 1 oz. of silver. If time passes, then normally not much would change and it’s possible that the dollar will still be worth 1 oz. 90 years later. If someone then noticed bookkeeping irregularities at the Fed, it might not even matter because the public was correctly valuing the dollars the whole time. The reason I was making such quibbles is because I am looking for an explanation of the difference in the market price of gold over its statutory price. The idea here is that if the Fed has been following your definition of “easy money” for decades, then that combined with the reinforcement effect of holding assets demonitated in your own credit (government securities greatly outnumber gold in the Fed’s asset table) might largely, if not wholly account for the devaluation of the dollar against gold.

Also I contend that notes and bonds are overvalued as well, because although the Fed is collecting interest on these items, the public sector holding the dollars they back is not.

This is handled because of the cost of issuing paper dollars. If you say the Fed gets interest on the bonds while paying no interest on the paper dollars, you’re saying the Fed is getting a free lunch. You’re also saying the same thing for every other country. It’s not plausible to think that the government of Bolivia gets a free lunch from issuing paper money, when there are obviously so many rival moneys that would prevent it from getting the free lunch. It’s only a little less plausible for the U.S. government. What is plausible is that the value of any paper currency is (1+C)^n/(1+R)^n. Agreed, but let’s make the distinction here between base money and credit money. Base money consists of FRNs and accounts held by member banks at the Federal Reserve. Obviously FRNs are more expensive to maintain so that should imply that as technological advances cause people to keep more of their money in the bank and use other systems of payment, then the cost of maintaining the same amount of base money should drop.

For the most part, this is not a genuine concern amongst the public since they can simply convert their base dollars into derivative forms, such as demand deposit accounts, which do pay interest. This would seem however, to drive the value of base money to zero,

Not if the liquidity service the public gets from paper dollars is enough to compensate them for the interest they sacrifice by holding paper dollars instead of derivative dollars. Eventually alternative methods of payment will drop the demand for cash practically to zero. I have trouble seeing it going away entirely though.

the only mitigating factor being that base money is the only form of money acceptable for taxes.

But the government accepts derivative dollars for taxes, and spends derivative dollars when it builds roads and buys fighter jets. In fact, I’ll bet government tax officials rarely handle green paper dollars. That’s true at the federal, state, and local levels. True at state and local levels, not at the federal level. The Treasury’s account is maintained at the Federal Reserve which means that it necessarily is base money. When a check is drawn from a bank to pay taxes, the reserves must be transferred from the bank’s account at the Fed to the Treasury’s account. In reality this is true for any payment or check drawn from an account, but it all tends to balance out in the end amongst the public sector. Anything that doesn’t is handled by interbank lending and the Federal Funds rate. The Treasury on the other hand, recognizes that at tax collecting time its increase in reserves means a corresponding decrease of reserves in the public sector, which is equivalent to a contraction of the money supply. To compensate they will hold extra reserves at various regular banks across the country until it can be spent.

You’re viewing taxes as if they give value to paper money by creating a demand for paper money. I view taxes as giving money value by giving backing to the money. Sorry, I didn’t mean to imply taxes give it value by creating demand. I recognize “Taxes Collectible” to be the backing in such a case.

If the Fed were to reestablish convertibility, I contend that a vast majority of people would redeem their notes for the bonds held by the Fed so that they could realize the interest for themselves and perhaps deposit them for notes at their own local banks in the hopes of realizing a better interest rate than they were receiving on accounts consisting of derivative dollars.

There’s some confusion here. Right now the Fed conducts open market operations with the goal of keeping the dollar stable. That means if the public wants fewer dollars, and they start depositing them at banks, then paper dollars will start piling up in bank vaults. The Fed, in trying to hold up the value of the dollar, will give the banks bonds (sell securities in the Open Market thereby reducing the supply of base money) for those paper dollars. In this way the supply of paper dollars grows and shrinks according to the public’s demand for paper dollars (“the needs of business”). That means people are holding as many dollars as they currently want for conducting business, so if they were suddenly able to take a dollar to the Fed and get a dollars worth of gold for it, they’d have no desire to do so. After all, they can go to a coin store right now and get a dollar’s worth of gold for a paper dollar any time they want. Elaborate on this more please. I haven’t read enough about the Fed’s current monetary policy to know how the demand for currency affects its open market operations. Basically what I do know is that they will buy and sell securities to keep bank reserves steady during seasonal variations in the demand for currency (i.e. Christmas).

I will contend also at this point that I recognize a tradeoff between security and liquidity and the expected rate of return. So the base money, being the most secure and liquid type of financial security available, would naturally have the lowest expected rate of return.

I don’t think of it this way. I’d say that paper money is the most costly form of money to maintain in circulation, so it has the lowest rate of return. At the MARGIN, the overall return to holding money (including liquidity services as well as interest yields) should be the same for all kinds of money. Please elaborate on this. I’m not sure what you mean by margin. Are you saying that market value of liquidity services plus market value of interest yields should be the same for all forms of money? That would mean you trade interest yields for liquidity services as the money gets more liquid, which is what I was trying to say. I think this is perfectly natural. For example, consider the following list of accounts: checking account, savings account, money-market fund, mutual fund. Notice it is ordered both in terms of increasing interest yield and decreasing liquidity service.

However, its tough to say whether a properly organized system would realize a negative real rate of return on its base money, as US dollars do. But then again, what lies at the heart of this discussion also lies at the heart of inflation, so who knows?

2. THE CONVERTIBILITY OF MONEY

This is where I draw my biggest contention with your paper. The question I initially asked myself here is, if dollars are not convertible, now or ever, what difference does it make whether they are backed or not? If the dollar is never going to be exchangeable in your lifetime, does it matter that the Fed is holding assets against it? Now I grant that I am not this skeptical. If the Fed were ever to get rid of its assets, I’m sure the value of the dollar would drop to zero. You compare FRNs to shares of stock, so let’s analyze that. The main difference I see here is that normally stocks pay dividends, and the main value of stocks comes from the total future expected return of all dividend payments. FRNs pay no interest and no dividends, but even still, a stock that paid no dividends would still be worth something, simply because there are assets backing it. I have enough faith in the government that if the Fed ever were dissolved that the assets backing its notes would remain. So it’s a fair contention that although not convertible, dollars may still maintain some of their value. I would like also to look at non-convertibility from a different angle. In your paper, “no such thing as fiat money”, you gave the current value of a bank note to be ((1+C)^n)/((1+R)^n). Where n is the number of years until convertibility, C is the marginal cost per year to maintain notes in circulation, and R is the current expected rate of interest. Now this is an interesting an equation, for if we make n infinity, as the Fed has done, then the value either drops to 0 or rises to infinity, depending on whether C is less then or greater than R. This however may be too difficult to analyze meaningfully and I wouldn’t be surprised if they were close. My skepticism tells me that C is probably less than R though, which again would bring us back to the question, why do the FRNs have any value if they are never convertible and never pay any returns?

To begin with, n probably isn’t infinite. I’d personally put it around 100. For example, as new forms of money are invented, people will demand fewer paper dollars. They return their dollars to banks where they pile up. The Fed buys the dollars with government bonds. Assume the Fed unloads all its bonds in this way, and even after that there are still 100 billion paper dollars laying claim to $100 billion in gold held by the Fed. If the public still keeps returning dollars to private banks, and if the Fed still conducts open market operations with an eye to stabilizing the dollar, the Fed would (or at least could) start selling its gold for dollars, until the public once again holds as many paper dollars as it wants. Once again I will need to ask for elaboration on current monetary policy. Would the Fed really give up a great portion of its bonds if the FRNs they back were returned? Either way, I doubt this would happen since the vast majority are held overseas and are out of the picture of the US economic system for all intents and purposes. You might say that inconvertibility doesn’t matter as long as the public prefers dollars to gold, but if the day comes that people prefer gold to dollars (Great Depression), the Fed would probably relent and let go of the gold. Interesting then that ending the Gold Standard is widely recognized as one of the actions that helped lead us out of the Great Depression. I need to do more studying on this topic. At least people probably expect this to happen, and as long as they expect it the public will value dollars on the expectation of eventual convertibility.

As for C and R, a good historical example is the Bank of Amsterdam, which Adam Smith discussed. People would deposit 100 silver coins (guilders, let’s say) and would be given 100 guilders of bank credit. I think the B of A didn’t issue paper money. They just issued credits on their books. These credits were a convenient form of money, and people used them in spite of the fact that the bank charged service fees. My memory is bad but I think a guy with 100 guilders on deposit would have paid 2 guilders a year for the bank’s services in storing his coins and recording his transactions. Note that in principle, the B of A could have issued paper guilders to its customers and it wouldn’t have made any real difference. Customers can buy things with paper guilders or with deposit guilders.

So we have a case where C=2%/year, and since the bank didn’t lend its coins, R was effectively 0. The B of A has two ways of charging its fees: (1) take 2% out of each deposit account each year, but keep each deposit guilder worth one silver guilder, or (2) let the value of each deposit guilder fall 2% each year relative to silver guilders. Either method will work, though for bookkeeping purposes it’s easier to keep the deposit guilders constant in value.

For our purposes, let’s say the B of A chose to let the deposit guilders fall at 2%/year. Now look at your statement above:

Now this is an interesting an equation, for if we make n infinity, as the Fed has done, then the value either drops to 0 or rises to infinity, depending on whether C is less then or greater than R.

People deposited their silver guilders, probably knowing that it would be centuries before they would actually want their silver back. (Adam Smith mentioned that the coins in the B of A’s vaults still had burn marks from a long-ago fire, indicating that once coins were deposited, they seldom if ever left the bank.) Taking your statement literally would have us imagining that as a customer deposits his silver guilder, he gets a deposit guilder in exchange which instantly falls in value to almost nothing.

The fact is that when the customer deposits his silver guilder, he gets a paper guilder that starts out worth 1 silver guilder, but which falls in value at 2%/year. The trick here, I think, is that you must understand that the customer is willing to put up with this negative rate of return because of the guilders’ liquidity services. (Tradeoff between liquidity services and interest yield, already discussed.) But nobody gets a free lunch. The bank’s fees just cover its costs, and at the margin, the customer’s liquidity services just cover his bank fees. Not that the customer gets no consumer surplus from the guilders—he does, and to that extent there’s a free lunch. But that’s no more surprising than the fact that I get consumer surplus (=free lunch) when I buy apples at the store.

One thing that might be confusing you about that C and R equation is an incorrect use of present value. Let’s say C=5% and R=4%, and let a person deposit 1 ounce of silver in a bank today for 1 paper dollar. Let’s say convertibility will be possible after 1 year. Right now, the value of a paper dollar must be 1 oz., or why would the customer have deposited the ounce in the first place? At the end of 1 year according to the equation, a paper dollar will be worth .99 0z. But it would be wrong to then turn around and take the present value of that .99 oz. and claim that a dollar would be worth .99/1.05=.94 oz. I think that might be what you’re doing when you say the dollar can drop to nothing when n is infinite. While the dollar will steadily fall in value over time, eventually reaching zero when n is large, it’s still true that the dollar is worth 1 oz. today. I was using that equation to calculate backward to the present value of the dollar. Take your example: n=1, C=5, R=4, and the final value of the dollar is .99oz. Then .99oz((1.05^1)/(1.04^1)) = current value of the dollar = 1oz. So when I did the same thing for the Federal Reserve, using n=infiniti and assuming a positive non-zero amount at the end of infiniti years, that’s what got me into trouble. But obviously the dollar is worth neither zero nor infiniti. I was mainly hoping for a resolution to this dilemma which I think you provided when you estimated n to be about 100 and your reasoning for that estimation makes a lot of sense to me. Also I made a sort of mathematical error here that I just realized. If C is greater than R, then the value of the dollar when convertibility is restored approaches zero as n approaches infiniti. Therefore it is not correct to assume a non-zero value when convertibility is restored for n=infiniti. If the dollar->0 as n->infiniti, then that implies the dollar could be worth any amount now, and the equation would still balance. Basically I was being careless and not following the proper mathematical rules for when there is an infiniti in the equation, which isn’t actually (and can’t be treated like) a real number.

3. MONEY DEMAND

In this section you denounce the acceptance of paper money as taxes as a possible reason for its value, yet in your paper on the history of paper money, you recognize taxes collectible as a perfectly valid asset behind the value of paper money. I would contend then that in the case of the US dollar that taxes collectible on the part of the federal government is at least partially responsible for its value.

Depends. The Fed backs dollars with US bonds. The bonds are backed by taxes, so the dollar is backed by taxes. But if you contend that the dollar had value because tax collections increase the demand for dollars, then I’d disagree. First because it creates a free lunch for money issuers, and second because the government rarely collects or spends paper dollars.

This could be then a kind of double backing on top of the assets held by the Federal Reserve. Also I believe the statement that money has value because others value it is valid.

That’s where you get in trouble with a free lunch. If the dollar was valued because others valued it, then any money-issuer earns a free lunch by issuing dollars, because the dollars will necessarily be worth more than their backing.

That’s what a medium of exchange is about. In this case its being valued for its facility in increasing liquidity and efficiency in the market.

4. THE QUANTITY OF DERIVATIVE MONIES

My main contention here is that derivative monies are less distinguishable from actual money than derivative stocks are from actual stock. I hope most people recognize how banks and financial institutions really work, but the line is still blurry. Look at a bank statement. It will say you have x dollars in your account when in reality they are holding bonds and loans worth that amount. Look at a statement for a mutual fund account. It will say you have x dollars in your account when in reality they are holding stocks and bonds worth that amount. This all serves to make it appear as if there is more money than there really is. Now from a purely monetarist standpoint, there are two ways of looking at this. First you can say well yeah, such accounts really do count as money and you get into a big hassle making different definitions, such as M1, M2 and M3. Or you can recognize these accounts as increasing the efficiency of the base money and thereby increasing its velocity, which is the viewpoint I favor.

Well, sort of. But I’d deny that velocity has anything to do with the value of money—any more than the velocity of GM stock affects the value of GM stock.

And I suppose you could talk about derivative dollars increasing the “efficiency” of paper dollars, but I don’t look at it that way. A checking account dollar is just as real as a credit card dollar is just as real as a Disney dollar is just as real as a Federal reserve dollar. People find those other forms of dollars convenient to hold, so firms issue them, and people find they can get by with fewer Federal reserve dollars. Let’s not think of paper dollars here, but reserves or base money, which would be paper currency plus bank accounts held at the Federal Reserve banks. When a check is drawn from an account, whether that account exists due to a loan (bank created credit money), or due to a deposit of paper dollars, the banks assets, liabilities, and reserves all decrease by an equal amount (assuming the check is deposited in a different bank). This is how all transactions work, so in a sense, all purchases are made with base money. This is how I was thinking of the efficiency of the dollar. Just like you were saying that the value of gold due to its use as a medium of exchange drops as derivative monies increase its efficiency, I see the same thing as likely being true for Federal Reserve credit. This means that as paper currency is useful now for many of the payments we need to make, base money still derives some extra value from this use. As payment systems become more advanced and the demand for base money for its use as a medium of exchange drops, the base money should more appropriately approach its proper value.

5. FISCAL POLICY

What I see here is a distinction being made between fiscal policy and monetary policy. I observe the open market operations as an important part of the fiscal and monetary processes. It means that the government can’t create more debt than the public is willing to hold to begin with, which means money can never be created beyond the government’s available credit.

Yes; except that when governments do issue more currency than they can back, the value of the currency will fall in proportion as the money supply outruns its backing.

I had hoped to talk about more at this point, but I’ve written on and analyzed this stuff enough for now. I will get back with more later.

A couple of afterthoughts here. First we have some alternative views to inflation than the ones put forth in my economics textbook. That book presented in the typical manner as the tradeoff between unemployment and inflation. The basic explanation is this: as employment approaches zero and the economy gets close to reaching its full production capacity, prices begin to rise prematurely due to the inefficiencies within the marketplace. It’s a fair explanation, but it leaves some questions unanswered. For example, how could inflation keep happening if the money were tied to a certain commodity? That would imply that that commodity’s value in the market was constantly dropping, simply due to an arbitrary selection to use it as backing. Analyzing that more closely, one realizes there wasn’t much inflation before the end of the gold standard, and that after that CPI closesly correlates with the increase in reserves created by the Fed. This sounds like proof positive of Quantity Theory regardless of the direction of causation because couldn’t the just not increase reserves if they wanted to hold the value of the dollar steady? So let’s say causation goes from CPI to reserves. Let’s say the textbook explanation is correct and the CPI was inflated. Without a corresponding increase in reserves, that implies there could be a deflationary drop in CPI with a corresponding bout in unemployment. So the value of the dollar can be subject to speculatory bubbles and booms and busts just like any other financial market. Perhaps this is what was happening with the Great Depression. In this case the Fed’s job should be to enact countercyclical measures, expanding credit when the economy slows down and restricting it when the economy heats up, but always increasing the amount of reserves because like the textbook says, you must be willing to put up with a continuously increasing CPI if you want the economy to remain near full employment. But this is all still a Quantity Theory view of money. Notice it all still agrees about a correlation between CPI and the amount of reserves and none of it says anything about the actual backing of the dollar. So what of that? How does the Real Bills Doctrine fit in with all this when theory has been fitting in with practice for this operating model for decades already?

An alternative view of inflation: now as we’ve already come to realize, inflation is also perfectly plausible under the Real Bills Doctrine. It’s simply a tradeoff between interest yield and liquidity service. Like with your example of the Bank of Amsterdam, at the highest liquidity service available, the money actually has a negative yield, whether its represented by a continuous decrease in its value or by periodic reductions in a persons account. When it’s the former, this is essentially the same thing as inflation. Inflation is the price of the liquidity service of money. If you don’t want to pay that cost, then you should be holding as much money possible in higher yield, less liquid accounts. But there’s still a problem here. Let’s assume C is greater than R. Then we’ll say the interest on bonds R is payed into the Fed’s Capital Account CA. And the cost of maintaining the money supply C is payed out of CA. If C is greater than R, then CA should eventually drop to zero and assets should eventually fall below liabilities, and the decrease in the value of the dollar should be due to a smaller nominal value in assets backing the same amount of liabilities. This is not the case.

Then there is perhaps yet another explanation? From your paper No Fiat Money: “As long as demand intersects supply to the right of point L, the banks can maintain the value of the dollar at 1 oz./$ simply by conducting ordinary open market operations, buying bonds with dollars whenever dollars rise above 1.0 oz./$, and selling bonds for dollars whenever dollars fall below 1.0 oz./$. It is not necessary for the dollars to be convertible into silver at the issuing banks.” So if the Fed’s job were to maintain the value of the dollar, that would mean they’ve conducted bad policy and bought way too many bonds, thereby inundating the public with more money than it really demands. If the price of gold really is representative of the demand for the dollar, then that should indicate supply is far exceeding demand and the Fed should set out selling its overabundance of bonds post haste. However, it’s interesting to note that if one also believes the long term goal of fiscal policy should be to maintain a balanced budget, then there’s not much power any central authority has in coaxing a lagging economy back to full employment.

I wish I could correlate these three different views on inflation, that is bring them all into some overriding context that can explain them all and why they differ, but I think that is too difficult for me at this point. There still seem to be some missing links here that I’m not seeing. But at least it’s food for thought.

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