Tuesday, June 3, 2014

Scott Sumner vs. the Real Bills Doctrine

This is a guest post by Mike Sproul. Mike's last guest post is here.

Scott Sumner and I have argued about the backing theory of money (aka the real bills doctrine) quite a bit over the years, starting in 2009 and continuing to the present. (link 1, link 2, link 3, link 4, …) Scott rejects the backing theory, while I favor it. I think that printing more money is not inflationary as long as the money is adequately backed, while Scott thinks that printing more money causes inflation even if it is adequately backed. Our discussions in the comments section of his Money Illusion blog extend well over 50 pages, so I’m going to try to condense those 50+ pages into two key points that cover the main arguments that Scott and I have had over the backing theory. (That’s John Law on the right. He was an early proponent of the real bills doctrine, oversaw a 60% increase in French industry in the space of two years, and was the architect of the western world’s first major hyperinflation and stock market crash.)

The key points:
1. Scott thinks that the liabilities of governments and central banks are not really liabilities.

For example:

“In what sense is cash a liability of the Fed? I thought once we left the gold standard the Fed was no longer required to redeem dollars?” (July, 2009)

“Dollar bills are not debt. The government is not required to redeem them for anything but themselves. That's not debt.” (August, 2009).

It would be cheating if I were to point out that the Federal Reserve’s own balance sheet identifies Federal Reserve notes (FRN’s) as the Fed’s liability, and that a large chunk of the Fed’s assets are classified as “Collateral Held Against Federal Reserve Notes”. Scott already knows that. It’s just that he thinks that the accountants are wrong, and that FRN’s are not a true liability of the Fed or of the government.

Scott’s argument is based on gold convertibility. On June 5, 1933, the Fed stopped redeeming FRN’s for a fixed quantity of gold. On that day, FRN’s supposedly stopped being the Fed’s liability. But there are at least three other ways that FRN’s can still be redeemed: (i) for the Fed’s bonds, (ii) for loans made by the Fed, (iii) for taxes owed to the federal government. The Fed closed one channel of redemption (the gold channel), while the other redemption channels (loan, tax, and bond) were left open. For example, suppose that 10% of FRN’s in circulation were originally issued in exchange for gold, 20% of FRN’s were originally issued on loan, another 30% were given to the federal government, which spent them on office buildings, and the remaining 40% of FRN’s were issued in exchange for bonds. That would mean that 90% (=20+30+40) of circulating FRN’s could be redeemed through the loan, tax, and bond channels alone. Only after those channels were used up and closed would it matter whether the Fed re-opened the gold channel. Assuming that the Fed still cared about maintaining the value of the dollar, the Fed would finally have to start using its gold to buy back the remaining 10% of FRN’s in circulation. But as long as the loan, bond, and tax channels remain open, the mere suspension of gold convertibility does not make FRN’s cease to be the liability of the Fed or of the government.

So Federal Reserve Notes are a true liability, whether or not they are gold-convertible. And like any liability, they are valued according to the assets backing them, just like the backing theory says. In the case of a gold-convertible currency, this is not disputed by Scott or anyone else. For example, as long as the Fed maintained gold convertibility of the dollar at $1=1 oz, it would not matter if the Fed held assets worth 100 oz as backing for $100 in FRN's, or 300 oz worth of assets as backing for $300 in FRN's. The quantity of convertible FRN's can be increased by any amount without affecting their value, as long as they are fully backed. Once we understand that both convertible and inconvertible FRN's are a true liability of the Fed, it is easy to see that the quantity of inconvertible FRN's could also be increased by any amount, and as long as the Fed's assets rose in step, there would be no effect on the value of the dollar. (There is a comparable result in Finance theory: that the value of a convertible call option is equal to the value of an inconvertible call option.)

2. Scott thinks that if the central bank issues more money, then the money will lose value even if the money is fully backed.

For example:
“ That’s where we disagree. I think open market operations have a huge impact on the price level, even if they involve the exchange of assets of equal market value.” (April 2012)

“ I understand what the backing theory says, I just don’t think it has much predictive power. Nor do I think it matches common sense. If you increase the monetary base 10-fold, prices will usually rise, even if the money is fully backed.” (July, 2009)

The problem with supposing a 10-fold increase in the monetary base is that we must ask how and why the money supply increased. If the new money was not adequately backed, then I agree that it would cause inflation. So if every dollar bill magically turned into ten dollar bills, or if helicopters showered us with newly-printed dollar bills, or if the Fed issued billions of new dollar bills in exchange for worthless bonds or worthless IOU’s, then Scott and I would both expect inflation. It’s just that I would expect inflation because the quantity of Federal Reserve Notes was outrunning the Fed’s assets, while Scott would expect inflation because the quantity of FRN’s was outrunning the quantity of goods being bought with those FRN’s.

But if the Fed issued billions of new dollars in exchange for assets of equal value, then I’d say there would be no inflation as long as the new dollars were fully backed by the Fed’s newly acquired assets. I’d also add a few words about how those dollars would only be issued if people wanted them badly enough to hand over bonds or other assets equal in value to the FRN’s that they received from the Fed.

This is where things get sticky, because Scott would once again agree that under these conditions, there would be no inflation. Except that Scott would say that the billions of new dollars would only be issued in response to a corresponding increase in money demand. So while I’d say that there was no inflation because the new money was backed by the Fed’s new assets, Scott would say that there was no inflation because the new money was matched by an increase in money demand. It seems that for every empirical observation, he has his explanation and I have mine. We are stuck with an observational equivalence problem, with neither of us able to point to an empirical observation that the other guy's theory can't explain.

But what if the Fed lost some or all of its assets while the quantity of FRN’s stayed constant? The backing theory would predict inflation because the Fed would have less backing per dollar, and the quantity theory would predict no inflation, since the same number of dollars would still be chasing the same amount of goods. It looks like we finally have a testable difference in the two theories. But here again, it’s easy for both Scott and me to get weaselly. If inflation happened in spite of Scott’s prediction, he could answer that money demand must have fallen. If my expected inflation failed to materialize, I could answer that the government stands behind the Fed, so any loss of assets by the Fed would be compensated by a government bailout. Empirical testing, it turns out, is hard to do. But at least I can claim one small victory: Scott is clearly wrong when he says that the backing theory doesn't have much predictive power. It obviously has just as much predictive power as Scott's theory, since every episode that can be explained by Scott's theory can also be explained by my theory.

Scott is also wrong to claim that the backing theory doesn't match common sense. Clearly, it makes perfect sense. Everyone agrees that the value of stocks and bonds is determined by the value of the assets backing them, and the backing theory says, very sensibly, that the same is true of money. Actually, it's when we start to use our common sense that the backing theory gains the advantage over the quantity theory. There are many aspects of the quantity theory that defy common sense, but I'll focus on four of them:

(i) The rival money problem. When the Mexican central bank issues a paper peso, it will get 1 peso’s worth of assets in return. The quantity theory implies that those assets are a free lunch to the Mexican central bank, and that they could actually be thrown away without affecting the value of the peso. This free lunch would attract rival moneys. For example, if US dollars started being used in Mexican border towns, then the Mexicans would lose some of their free lunch to the Americans. As the dollar invaded Mexico, the demand for pesos would fall, and the value of the peso would fall with it. More and more of the free lunch would be transferred from Mexico to the US, until the peso lost all value. If the quantity theory were right, one wonders how currencies like the peso have kept any value at all.

(ii) The counterfeiter problem. If the Fed increased the quantity of FRN’s by 10% through open-market operations, the quantity theory predicts about 10% inflation. If the same 10% increase in the money supply were caused by counterfeiters, the quantity theory predicts the same 10% inflation. In this topsy-turvy quantity theory world, the Fed is supposedly no better than a counterfeiter, even though the Fed puts its name on its FRN’s, recognizes those FRN’s as its liability, holds assets against those FRN’s, and stands ready to use its assets to buy back the FRN’s that it issued.

(iii) The currency buy-back problem. Quantity theorists often claim that central banks don’t need assets, since the value of the currency is supposedly maintained merely by the interaction of money supply and money demand. But suppose the demand for money falls by 20%. If the central bank does not buy back 20% of the money in circulation, then the quantity theory says that the money will fall in value. But then it becomes clear that the central bank does need assets, to buy back any refluxing currency. And since the demand for money could fall to zero, the central bank must hold enough assets to buy back 100% of the money it has issued. In other words, even the quantity theory implies that the central bank must back its money.

(iv) The last period problem. I’ll leave this one to David Glasner:
“For a pure medium of exchange, a fiat money, to have value, there must be an expectation that it will be accepted in exchange by someone else. Without that expectation, a fiat money could not, by definition, have value. But at some point, before the world comes to its end, it will be clear that there will be no one who will accept the money because there will be no one left with whom to exchange it. But if it is clear that at some time in the future, no one will accept fiat money and it will then lose its value, a logical process of backward induction implies that it must lose its value now.”
Taken together, I think these four problems are fatal to the quantity theory. Scott is welcome to bring up any problems that he thinks might be similarly fatal to the backing theory, but it will be a tough job. It’s easy to make the quantity theory fit the data. It’s harder to reconcile it with common sense.

Addendum: Scott Sumner responds.And Mike Freimuth comments. Over at Scott's blog, Mike Sproul writes a rejoinder to Scott. And now David Glasner has chimed in.


  1. In the counterfeiter example, I take it that the quantity theorists would base that position on an assumption that everyone believed the counterfeit notes to be real. So everyone would believe that they would therefore be accepted for all normal uses for FRNs. But if everyone thought they were real, why would they not also believe the relative backing had reduced, under a backing theory explanation?

  2. I'm incredibly sympathetic to the backing theory as I come from a finance perspective, but there's one thing I haven't been able to square away yet, and that is wherefore all this secular inflation? If all the liabilities of the Fed are sufficiently backed, then how is it we get on average 2% inflation each year?

  3. Nick:
    The assumption is that everyone knows that counterfeiters have increased the quantity of notes by 10%, but nobody can tell them from the real notes. So each note has 10% less backing, and we get 10% inflation.

  4. John:
    Two explanations:
    1) The quantity of FRN's outruns the Fed's assets by 2%/year on average. This might happen because the Fed issued $100 while getting a bond that is only worth $98 (after transaction costs), or maybe the Fed's printing and handling costs exceed its interest earnings by 2%/year.
    2) The Fed has enough assets to fully cover all its FRN's with zero inflation, but through habit, ignorance, or painful experience of deflation, the Fed chooses to maintain inflation at 2%, in effect, defaulting on 2% of its obligations per year.

    Interesting to note that the old Bank of Amsterdam, which maintained 100% coin reserves against its (deposit) money, charged about 2% storage fees per year, effectively accomplishing the same thing that the Fed does with its 2%/yr inflation.

  5. Somehow i don't really understand this "backing" theory of yours, at least doesn't seem to be the same as the real bills doctrine, I learned about.

    Do you really think, that it enough to "back" the money with some assets in order to prevent inflation, regardless of the size of these assets and the corresponding size of the monetary base. Then you should take a look at tne balance sheet of the Reichsbank (german central bank) anno 1923, all the gargantuan monetary base was "backed" at the time by some assets, mostly german government bonds, and still the were a hyperinflation? How do you explain that?
    Of course the "real" real bills doctrine, as opposed to yours, differentiates between good or "real" assets, which are allowed as backing, and somehow less real assets, which are not. So, perhaps the german government bonds weren't "real" at the time, but then, why are the US Treasury bills today? I don't understand the difference, do you?

  6. Alex:
    You raise some important points, and they justify several posts. Here's an outline of the answers to your concerns:

    1. The RBD asserts that the best monetary policy is for banks (central and private) to issue money (usually meaning bank notes) in exchange for
    a) short term
    b) real bills
    c) of adequate value.

    (c) is the most important. Obviously a bank should not issue $100 of new notes to someone who only offers stuff worth $99 in exchange. Unfortunately, textbook statements of the RBD usually neglect to mention (c), for the simple reason that it is too obvious to mention. Any banker that needs to be told not to issue $100 of notes for $99 worth of stuff, has no business being a banker. The trouble is that historically, most economists thought the RBD consisted of only (a) and (b), and wrongly thought that the RBD claimed that (a) and (b) alone were enough to prevent inflation, when of course you need (c).

    2. Yes, it's really enough to back money with assets of ADEQUATE VALUE. If you issue $100, and back them with assets worth 100 oz of silver, then $1=1 oz. Of course, if you do what the Reichsbank did, and try to back $1 billion of currency when the bank's assets are worth only 100 oz, then of course your currency will lose value, because it has inadequate backing. The Reichsbank episode also gave the RBD an undeserved black eye, since people thought that the Reichsbank was following the RBD when it was in fact neglecting the most important rule, which was for the bank to get assets of adequate value.

    3. As to "real" assets. The purpose of part (b) is not to prevent inflation. That's accomplished by part (c). The reason that old time bankers preferred to issue notes in exchange for "real" bills is that they found that it helped their notes to remain in circulation, as opposed to returning to the bank the very next day. Bankers found, through centuries of experience, that if they issued new notes to carpenters and farmers (engaged in "real" activity), then those notes would stay in circulation. The reason was that this procedure automatically helped the banks to issue more notes when the carpenters and farmers were busy, and fewer notes when times were slow. But the bankers also found that if they issued new notes to gamblers and tourists (people who were not engaged in productive activity) then the notes that the banker printed and issued on Monday would return to him the very next day.

    1. So you think, the crucial point is, that the backing assets have to be of the "adequate value" in order to prevent inflation and german bonds were not adequate while US treasuries are. The logical next question then, how do you define this "adequateness".

      For example, let's assume, that the only asset a central bank is allowed to hold is silver, like in your examples (100% silver standard). Let's further assume some revolutionary innovation in the siver mining occurs and suddenly the silver miners are able to quadruple the the amount of the silver in the country. The public converts the new silver at the central bank into new notes (or balances), so its balance sheet and the monetary base quadruple too.

      Do you really think, this sudden quadrupling wouldn't produce any inflation because the monetary base continues to be solidly backed by silver? I, for my part, very doubt this.
      If you think otherwise, then it seems, that after the quadrupling the silver backing isn't adequate anymore. But why? What changed exactly?

    2. Alex:

      If the supply of silver quadruples, then 1 oz of silver will buy much less at the grocery store. Since the dollar is pegged to silver, the dollar will buy just as much less at the store. But of course $1 will still buy 1 oz of silver.

  7. Sorry, why can't we have no-arbitrage backing? Central bank balance sheet assets versus currency/reserve liabilities is entirely valid -- there is backing -- but if there is no arbitrage or deliverable, then backing is practically moot.

    In the case of the Fed, the fixed income assets that back the currency are now structurally inferior -- Treasury bonds mature, are unsecured, have duration mark-to-market risk, and are denominated in the liability. Currency is infinite, zero duration, and market-risk-free (always 1:1 numeraire).

    Gold is a superior counterparty-risk-free asset: gold itself is the numeraire, but through the magic of the balance sheet can be transformed into (inverse) currency liabilities.

    The major advantage to holding gold is that gold fairly well automatically increases in price with growth in the monetary base, even in the absence of central bank holdings. That is, there is a positive association between the value of assets and the value of liabilities. Printing more currency typically raises the value of outstanding gold (think about how Bretton Woods broke down.)

    Fixed income is the most bizarre thing a central bank can hold. The asset mark-to-market goes down when liabilities rise: asset value is negatively correlated with liabilities. Backing matters, but it must have the proper characteristics (convertibility and correlation).

  8. Anonymous:

    The Fed's 'deliverable' is bonds, taxes, loans, and, last but not least, gold. Of course the gold won't be delivered for 100 years or so, but the fact that the gold is in the fed's vaults, as opposed to lost on the bottom of the ocean, means that it is still a genuine asset of the Fed.

    You're right that it's a bad idea for the Fed to hold bonds denominated in dollars, since it can result in inflationary feedback: A loss of assets causes the dollar to fall, which causes the (dollar denominated) assets to fall still more, which makes the dollar fall more, etc. Holding physical assets (like gold) anchors the dollar and reduces the feedback effect.

    Gold is a perfectly good money, but maintaining gold convertibility is dangerous. All that has to happen is the bank becomes insolvent, people see that the bank can't redeem all its money in gold at par, and so they rush to the bank to get the gold before it runs out. Say a bank pegs $1=1 oz, and has issued $100, backed by assets worth 100 oz. Then $1=1 oz and everything's fine. But if assets drop to 99 oz while the public still holds $100, then maintaining gold convertibility at $1=1 oz just invites a bank run. On the other hand, suspension of convertibility will let the dollar float, and people will naturally value $1=.99 oz. Not a great result, but better than a bank run.

  9. Mike, I understand how the deliverable can be seen as some 1/17,101,300,000,000 of current activity, but again, the deliverable is denominated in the numeraire. There's no arbitrage, just ouroboros.

    Bond assets are only financial contracts to deliver the numeraire (meaning currency for non-banks as you and I), and are not a secured claim on assets. The government's tax rights are senior-secured, but the governments liabilities are entirely unsecured -- they do not pass on the secured rights to bondholders.

    There is some small question of the claims on the Fed's gold, also -- convertibility was only "suspended" while the price was some $35. There is some question over how this affects potential realizable value on the balance sheet. The ECB is a case of where they let gold holdings get marked-to-market on the asset side of the balance sheet. What's also intriguing is how the stated collateral for the currency includes gold and sdrs -- it is not backed exclusively by Treasury or mortgage bonds (or Maiden Lane!)

    Part of the problem is "in exchange for assets of equal value" is the common numeraire problem. The Fed sets the price level in the economy: if it bought 1oz bags of dirt for $1,000 each, it could carry those "assets" on their balance sheet at that price and the price level would rise to meet that new equilibrium -- i.e. the abundance of the numeraire is linked to the abundance of the underlying asset.

    Central bank asset quality has been degraded on the gold-to-dirt scale through Treasury-and-mortgage-and-maiden-lane standards. There's also the question of the monetary base composition: it's drastically non-uniform now between currency and reserves. Currency circulates and is the actual numeraire for price levels in the real economy; while reserves mostly affect the price of financial contracts (interest rates).

    Also, if convertibility is dangerous, then why can't economies simply go to an ounce standard instead of mucking around with constantly-defaulting convertibility pegs?! You'd have to borrow real assets out of real surplus, and you'd end up with real market-demand-driven interest rates rather than this circa-1914-and-arguably-now-obsolete Fed system. Have the Fed lend out real gold and collect it back during and after panic bank runs: far superior to our "heads I get a bonus tails you get the bill" banking system.

  10. Mike,

    So then my question is which way do the accountants say that the inflation occurs? 1 or 2? Or is it ambiguous? My guts say the answer is 1, though 2 would be interesting but harder to pin down.

  11. John:
    I'd say that inflation can happen for both of those reasons. Just depends on the time and place. The world's hyperinflations look like a clear case of base money far outrunning central bank assets, while the more moderate inflations look more like #2.

  12. Anonymous:
    Thanks to you and google, I now know what ouroboros means: a snake eating its tail.

    Start with a bank issuing $100 in exchange for 100 oz of silver. Clearly, $1=1 oz. No feedback or other complications. Then the bank issues another $200 in exchange for bonds worth $200 (denominated in dollars). Define the exchange value of the dollar as E. The dimension is oz/$. The bank's assets consist of 100 oz plus bonds worth 200E. The bank's liabilities are 300E. Setting assets=liabilities yields 100+200E=300E, or E=1 oz/$. In other words, it actually works to back a dollar with another dollar, as long as there are some physical assets (the gold) anchoring things.

    Now suppose the bank is robbed of 30 oz, which is 10% of its assets. The equation becomes
    70+200E=300E, or E=0.7 oz/$. The 10% loss of assets has caused 30% inflation. That's the inflationary feedback effect at work, but notice that the dollar did not lose ALL value, because there is still a gold anchor (=70 oz.). It's still OK to back a dollar with another dollar.

    In real life, the anchor can be the Fed's gold, or office buildings owned by the government, or the government's ability to take real assets from people as taxes. Clearly, both the Fed and the government have some physical assets, and that can easily be enough to offset the gold-to-dirt asset-degradation you mentioned.

    About the ounce standard: It's workable until something goes wrong and the Fed becomes insolvent. Then the only choice is to maintain convertibility and face a bank run, or suspend and let the dollar float a little lower. Almost every country that has faced this choice (and that's just about all of them) has chosen to suspend. Interesting though, that private banks hardly ever suspend, except during bank runs, and as soon as the run is over, they resume convertibility.

  13. Mike,

    Obviously, MV = PT is just an identity. If M/P is determined by the backing, how would you expect V and T to respond to changes in that backing?

    (I'm not defending the QTM - I'm just interested in your view.)

  14. Nick:
    My knee-jerk answer is that the algebra tells us all we need to know. If M/P rises, then T/V will rise as well.

    My not-so-knee-jerk answer is that MV=PT is a meaningless identity. If we tried to use it to describe the value of GM stock, then M=# of shares, V=# times/yr a share is spent buying the goods represented by T; P= the # of shares it takes to buy a unit of T, and T= the # of units of goods bought with the money represented by M.

    The equation will always be "correct" for GM stock, in the sense that the left side will always equal the right side, but there is no sense in which the equation explains the value of GM stock. That's why stock market analysts don't use that equation. They spend their time looking at GM's balance sheet instead.

    The same thing is true of money.

  15. Mike, great post. It seems to me that once folks like Sumner grant your third point (as he does in his reply... "But what about when they are successfully targeting inflation at 2%? In that case they’d need some assets to do open market sales, but they might well get by with far less than 100% backing...) they are admitting a version of the backing theory in through the back door. How many assets must it hold? At least enough that it can support the market price of their issued dollars. Which means that if the market believes that backing assets are not sufficient, it will bid the price of dollars down. Of course that belief could very well be dashed if the bank does indeed have appropriate assets and it conducts open market sales to punish speculators.

    Nick brings up the quantity equation. I don't see why we can't fit all of into the MV = PT framework. Here the debate pivots around what influences velocity. Traditional quantity theorists like Milton Friedman would say that velocity V is constant so that any change in the money supply M directly increases the price level P. Your point tends to be that V is largely dependent on backing. An increase in M will always be matched by a decrease in V as long as it is a well-backed increase. Changes in backing without corresponding changes in M will cause V to change independently of M, and therefore push the price level higher or lower. So in sum, maybe we can rethink this as an argument between you and Scott over the determinants of V.

    I'd argue that in the stock market we do sometimes think in terms of MV=PT. Consider the inverse of V, or 1/k. This is the "Cambridge K" take on the quantity equation, where k represents the demand to hold money (or stock). When a firm does a good job of issuing new stock, the increase in M will be matched by an improvement in k, or the desire to hold the stock, so that the price level P stays constant. If the underwriter botches the issue then the k will not increase sufficiently to offset the rise in M so that P will fall. This is what happened with the Facebook issue, for instance.

    1. I think, for stock market valuations, that we can't get away from taking demand into account. We value a stock by looking at its expected future pay-out (which comes from the backing) and then discounting it at an appropriate rate. The discount rate depends on the extent to which the stock complements the rest of the investor's portfolio. The greater the amount of stock held relative to the overall size of the portfolio, the less complementary it is. So the valuation given to the stock depends on the total assets of investors (amongst other things) and not just on the characteristics of the issuer.

    2. "It seems to me that once folks like Sumner grant your third point..."

      Though Scott Sumner apparently didn't thought about that while writing his reply, there is indeed a possibility for a central bank to manage the size of the monetary base without sifficient assets: it can issue it's own (long term) bonds, in effect converting some of it's very liquid liabilities (money) into very iiliquid liabilities (long term bonds). In the extreme such a central bank wouldt need assets at all and still would be able to manage the monetary system properly through changes of the composition of it's liability portfolio (bonds vs. money).

    3. JP (and Nick):
      " they are admitting a version of the backing theory in through the back door."

      Excellent point. I had the same argument with Nick Rowe a few years back, with him saying that a central bank can get by with maybe enough assets to buy back 30% of its currency, and me saying the central bank needs 100%. It seems clear that arbitragers would be all over any central bank with less than 100% assets, but I don't seem to convince the skeptics with this argument. I've started thinking about some small country with GDP=$20 billion of so,1 billion pesos in circulation, and they only hold 99% backing. There should be some scenario where Bill Gates comes along and arbitrages at their expense.

      Also, of course, there's no such thing as a bank that holds 30% assets or anything close. By their nature, banks always hold 100% assets.

      I agree about V and K. My usual thought experiment starts with some firm (GM) whose only asset is $60 mil in the bank, and the only thing on the right side of their balance sheet is 1 million shares of stock. In that case, share price must be $60, regardless of V or K. It's when assets and liabilities are complicated and uncertain that V and K start to matter, and we are forced to talk about supply and demand of stocks and of money.

    4. I think JP characterizes the issue correctly in terms of the equation of exchange but I just want to say that I think the stock comparison is a dead end. The assumption underlying the equation is that all goods traded in the economy are traded using money. That is what makes it meaningful. This means that if we don't think that T changes wildly with changes in the money supply, we have to explain how the equation holds through some combination of changes in V and P. (Or if T does change, then we have monetary non-neutrality which is even more interesting.).

      In the case of a stock, if we use T to represent whatever people trade the stock for, that is not anchored in any meaningful way. The price can change all over the place with practically no shares changing hands (low V) or with tons of shares changing hands (high V) and T just changes along with it to fill in the equation. But this tells us nothing interesting about the way the stock is valued (or for that matter about the total amount of other goods "purchased" with the stock).

    5. Mike F:

      "The assumption underlying the equation is that all goods traded in the economy are traded using money."

      But that never happens. Some goods are bought with FRN's, some with checking account dollars, some with credit card dollars, some with gift cards, or bitcoins, or foreign money, or barter. The guy who originally popularized the equation (Lubbock, I think, back around 1880) recognized this, and the left side of his equation contained M1V1+M2V2+M3V3....., for n different kinds of money and n different velocities. I forget what he put on the right side.

      " if we use T to represent whatever people trade the stock for, that is not anchored in any meaningful way."

      Exactly. Because it's not meaningful.

    6. But it is meaningful for money, you are just saying that money takes different forms. That's fine, but you can still think of the quantity of all of those things together. I think it is misleading to claim that because it is meaningless with respect to stocks it must be meaningless with respect to money.

    7. Incidentally, I wrote some more thoughts on the matter for anyone who is interested.


      Short version: Money is "backed" but I think you are missing the true nature of the backing by looking only at the CB's balance sheet. Also, the fact that it is backed doesn't mean that the price level is independent of the quantity of money.

    8. Mike F.: Thanks! I'll check it out.

    9. I think it's valid to apply the equation of exchange to stock. In words we can describe the equation as saying that the amount of shares spent on buying money over a period of time (P*T) should be equal to a firm's total shares outstanding times their velocity (M*V).

      Whether it's meaningful is a different question since we are talking about a tautology. We need to think about the behavior underlying the equation.

      The perfect markets assumption means that P adjusts instantaneously to news. So if MV rises (because people want to get rid of a stock, thus pushing up V) then P will quickly jump i.e. the purchasing power of the stock will fall. But if the purchasing power of stock P fails to fall (say a large institution supports the market) then the equation can only be balanced by a rise in T. We can think of the inability of the purchasing power of shares to fall as an incredible arbitrage opportunity that creates a large volume of transactions in that stock, or a rush to sell while the selling is good. This transactions glut will only cease when the institution imposing the friction that prevents P from rising caves in, or it owns every stock ever created.

      So yeah, I like the quantity equation applied to stock. I also like Assets = Liabilities.

  16. Mike F.:
    I posted my reply over at your blog.

  17. I'm not sure whether the GM stock analogy is useful or not.

    GM stock is valued overwhelmingly on the basis of the cashflow it is expected to yield, rather than any ancilliary benefit such as its suitability as collateral for borrowing. The cashflow clearly depends on the backing - the earning power of GM.

    The value of central bank money depends much more on the non-pecuniary benefits it yields, such as liquidity and fulfilment of regulatory requirements. The cash yield (if there is any) plays less of a role. Any link between the non-pecuniary benefits and the backing is more tenuous.

    1. You don't think that the cash yield plays a role in the valuation of central bank money? If I'm an international bank I can keep a deposit at the Bank of Canada and earn 0.75% overnight or I can keep it at the Fed and earn 0.25%. I'd be willing to take a slightly smaller return if one of the banks is less risky and has better earnings power.

    2. I think it must play some role. Just less of a role. I guess if the real yield on FRNs were zero, say, any value must come from non-pecuniary benefits, right?

    3. I'd say that people are willing to accept an inferior pecuniary return on cash because the non-pecuniary return is higher than on competing assets. If cash suddenly lost all its non-pecuniary benefits, it would crash in price to some lower plateau at which point its return would be provided entirely in the form of a pecuniary return, or an expected capital gain.

    4. I can see that, but I think that fits with what I'm saying. That crash in value would be entirely due to external factors (its liquidity benefits say), rather than anything to do with the backing assets. Could a comparable crash in the value of GM stock happen for reasons unrelated to the expected underlying performance of GM? (I don't think that a general market crash counts here, but I'm not sure.)

    5. I think we could generate a crash in the value of cash due to a deterioration of backing assets too... say the sovereign decides to confiscate a large chunk of a central bank's gold or other assets in the central bank's vaults. Or the sovereign insists on getting cash from the bank in return for a sovereign bond that yields a below-market interest rate.

      I also think we can generate drops (perhaps not crashes) in GM stock due to changes in its liquidity benefits and not its earnings power. GM stock earns a liquidity premium (not as big a premium as cash earns) and if for some reason that liquidity premium is doubted then GM shares will drop.