Wednesday, November 20, 2013

Friends, not enemies: How the backing and quantity theories co-determine the price level

Kurt Schuler was kind enough to host a Mike Sproul blog post, which I suggest everyone read.

I think Mike's backing theory makes a lot of sense. Financial analysis is about kicking the tires of a issuer's assets in order to arrive at a suitable price for the issuer. If we can price stocks and bonds by analyzing the underlying cash flows thrown off by the issuer's assets, then surely we can do the same with bank notes and bills. After all, notes and bills, like stocks and bonds, are basically claims on a share of firm profits. They are all liabilities. Understand the assets and you've understood the liability (subject to the fine print, of course), how much that liability should be worth in the market, and how its price should change.

Mike presents his backing theory in opposition to the quantity theory of money. But I don't think the two are mutually exclusive. Rather, they work together to explain how prices are determined. By quantity theory, I mean that all things staying the same, an increase in the quantity of a money-like asset leads to a fall in its price.

We can think of a security's market price as being made up of two components. The first is the bit that Mike emphasizes: the value that the marginal investor places on the security's backing. "Backing" here refers to the future cash flows on which the security is a claim. The second component is what I sometimes refer to as moneyness—the additional value that the marginal investor may place on the security's liquidity, where liquidity can be conceived as a good or service that provides ongoing benefits to its holder. This additional value amounts to a liquidity premium.

Changes in backing—the expected flow of future cash flows—result in a rise or fall in a security's overall price. Mike's point is that if changes in backing drive changes in stock and bond prices, then surely they also drive changes in the price of other claims like bank notes and central bank reserves. Which makes a lot of sense.

But I don't think that's the entire story. We still need to deal with the second component, the security's moneyness. Investors may from time to time adjust the marginal value that they attribute to the expected flow of monetary services provided by a security. So even though a money-like security's backing may stay constant, its price can still wobble around thanks to changes in the liquidity premium. Something other than the backing theory is operating behind the scenes to help create prices.

The quantity theory could be our culprit. If a firm issues a few more securities for cash, its backing will stay constant. However, the increased quantity now in circulation will satisfy the marginal buyer's demand for liquidity services. By issuing a few more securities, the firm meets the next marginal buyer's demand, and so on and so on. Each issuance removes marginal buyers of liquidity from the market, reducing the market-clearing liquidity premium that the next investor must pay to enjoy that particular security's liquidity. In a highly competitive world, firms will adjust the quantity of securities they've issued until the marginal value placed on that security's liquidity has been reduced/increased to the cost of maintaining its liquidity, resulting in a rise or fall in the price of the security.

This explains how the quantity theory works in conjunction with the backing theory to spit out a final price. In essence, the quantity theory of money operates by increasing or decreasing the liquidity premium, Mike's backing theory takes care of the rest.

P.S. Kurt Schuler's response to Mike.


  1. Yep. If the demand curve for an asset is perfectly elastic wrt the spread between the interest rate asset on that asset and the interest rates on other assets, we get the backing theory.

    If the demand for an asset is perfectly inelastic wrt that spread, we get the old quantity theory.

    In the general case, where the elasticity is between zero and infinity, we get the modern quantity theory, where expected future printing of money affects the expected future price of money and hence the expected rate of return on holding money and hence the current price of money.

    But the assets of a central bank give us very little information about future printing of money, unlike the assets of a firm which uses the returns on those assets to buy back shares. Because most of the returns on the central bank's assets will not be used to buy back money, but will be given to the government.

    Imagine if you held shares in a company, and you liked holding those shares because you could wear them as jewelry to flaunt your wealth, so your utiliity depended on the real value of the shares you owned, and you had a downward-sloping demand curve for that jewelery. But the company gave most of its profits to charity, not to the shareholders. We would use the modern quantity theory to explain the value of those shares. We wouldn't pay much attention to its assets.

    1. Put it another way: we should be using the modern quantity theory to explain the price of any firm's shares, if that firm's shares are unique in some way, and if the firms' managers choose how much of the profits to give away to charity. We need to know the demand function, and we need to know how many new shares they will issue or retire in future.

    2. Hi Nick,

      Your share/jewellery argument makes sense. The shares would be like curio zimbabwe dollars or rare art prints. If they aren't "unique" and can be replicated by competitors, their price would be competed down to the cost of printing and shipping them. If they are unique, we care about the producers future intentions concerning quantity since those will set the price, as you point out.

      If an artist promises to maintain the value of his art prints, he may do so by promising to repurchase them at a certain rate, at which point he has accepted a liability on himself. We'd be interested in looking at the assets on his balance sheet in order to determine how credible his promise is. The price of prints will now be jointly determined by their commodity value and their liability value.

      "In the general case, where the elasticity is between zero and infinity, we get the modern quantity theory"

      In your "general case", we get both, not just the QTM. Expected future printing and expected future changes in backing affect the future price of money-like assets and hence the expected return and hence the current price.

      "But the assets of a central bank give us very little information about future printing of money, unlike the assets of a firm which uses the returns on those assets to buy back shares."

      I wouldn't look at the returns on a firm's assets for for information about future printing/unprinting -- I'd look at the spread. A firm will buy back shares if they've fallen to a discount to perceived fundamental value and issue more shares when they're at a premium.

  2. JP:
    When we've talked about this before, you seem to think that the liquidity premium is in the 3% range. Taking that as a starting point, that means the BT is 97% of monetary theory, while the QT is 3%. But Nick Rowe says the BT is completely wrong; George Selgin calls it poppycock, and Scott Sumner says he utterly rejects it. Looks like the QT and the BT are a long way from being friends.

    I'm fine with gold and other commodities (even bit coin) having a liquidity premium, but paper/credit moneys are fundamentally different, in that they are liabilities of their issuers, whereas commodities are nobody's liability. It's a pretty obvious distinction, but you sure never hear quantity theorists talk about it. The words "backing theory" don't even appear in any of their textbooks!

    1. Hi Mike,

      Plenty of people say its wrong, but don't the fiscal-theory of the price level (FTPL) folks and people like Andolfatto/Williamson agree with some version of the backing theory? Wallace/Sargent's "Real Bills vs the Quantity Theory" paper, for instance, says:

      "The purpose of this paper is to represent and compare the real-bills doctrine and the quantity theory in a simple model that is compatible with the principle of finance theory that assets are valued according to the streams of returns that back them."

      "BT is 97% of monetary theory, while the QT is 3%."

      I'm not entirely sure what the size of the liquidity premium is. But I do think that US monetary policy has usually been executed by changing the liquidity premium via quantity changes, and since the unit of account is defined in terms of US dollars, those minute alterations to the liquidity premium have had economy-wide effects. So the quantity theory has an important role to play.

      However, the marginal value people are willing to pay for the liquidity services provided by base money is so low now that we are approaching a pure backing theory world.

    2. Hi JP:

      Exactly right about FTPL. Here's the conclusion of my paper on the subject:

      "The fiscal theory of the price level is an overly narrow special case of the backing theory of money. The backing theory recognizes that money is an ordinary liability of its issuer, and as such is valued according to the total assets and liabilities of its issuer. This broader perspective leads us to give proper consideration to cases where newly-issued money is backed by newly-acquired assets, or by the net worth of the money issuer.

      The backing theory implies that money is valued according to the same rules by which we value stocks, bonds, and other liabilities. While consideration must be made for differences in seniority, risk, and time to maturity, money is no different in this respect from stocks and bonds.

      The backing theory yields a determinate price level based on the money-issuer’s assets and liabilities. The price level does not depend on wealth effects, and is only indirectly related to whether the central bank is tough or soft. "

      I had sent a copy to Christopher Sims, and here's his reply:Mike: I think it's you, not me, that has it wrong. Here's a passage that I think shows your misunderstanding.
      > Since writers on the fiscal theory often say that money is valued like stock, a stock market analogy might help to explain the flaws in Sims’ statement. We all recognize that a firm that issues new shares of stock will normally get equal-valued assets in exchange for those new shares, and so the price per share will not change. By applying this stock analogy to wealth effects, we could paraphrase Sims as follows:
      > " New shares in the hands of the public that are not accompanied by expected future earnings or a fall in stock prices will leave the public with apparently increased wealth. Thus they will spend their new shares until the share price falls enough, or expected future earnings rise enough, to make them scale back spending.
      > The trouble with this statement is that when investors buy a dollar’s worth of newly-issued stock, they pay a dollar to the corporation in exchange for the stock, and their wealth is unaffected. The investors do not feel wealthier, because they are not wealthier. Meanwhile, the corporation’s assets rise in step with its shares of stock, so stock prices are unaffected."
      > The analogue to the government's issuing debt without a commitment to increase future taxes is for the firm to sell shares to the public without using the proceeds to purchase productive assets. This happens. Sometimes it is a matter of the company simply having bad judgment, with investors realizing the company is making a bad decision about how to use the proceeds, but it can also be a deliberate "watering" of the stock. The analogy I use in one or more of my papers is to a company that sells stock and uses it to finance unjustified compensation for executives, country club memberships, corporate jets, etc. If the company does this and investors realize it is happening, one does not find that the company cannot sell shares at all --- it's just that the stock price declines, so that the total value of outstanding shares after the sale matches the (unchanged) value of the firm.
      > The reverse transaction is even more widely recognized to work this way. A company that buys back some of its outstanding shares, but does not sell productive assets to finance the share purchase, raises its stock price, so again the total value of outstanding shares does not change. That such a share buyback is equivalent to issuance of a dividend (except possibly for tax implications, which is why the IRS takes an interest in these transactions) is well understood.
      > Chris Sims

    3. I should probably point out that a government can in fact issue more debt (including money) as long as its net worth is sufficiently positive. In my post at, this is shown in line 2, where 20,000 new livres are spent, but are covered by the 30,000 livres in coins coming from France. The story about buying back shares is similarly flawed, but that's a longer story.

      I guess I had figured that this would be obvious, so I didn't explain it when I commented last night. But if it wasn't obvious to Sims, it wouldn't be obvious to the average reader.

    4. Mike, I'm not really sure how the backing theory differs from Sim's FTPL. Sim's reply seems to make sense to me. If a firm issues new shares and uses the proceeds to pay the wrong price for something, its future per share profits will decline and the shares should fall in value.

    5. JP:
      Looking back, I did make kind of a mess of things. Let's see if this untangles it:

      Money is valued more like bonds than like stock. If the company is already profitable, and its prospects improve, then its bonds won't rise; they will stay the same. But if a company is unprofitable, and it becomes less profitable, its bonds will fall. So bonds (and money) are priced like a written put.

      So my paraphrasing of Sims should have said: " New BONDS in the hands of the public that are not accompanied by expected future earnings or a fall in BOND prices will leave the public with apparently increased wealth. Thus they will spend their new BONDS until the BOND price falls enough, or expected future earnings rise enough, to make them scale back spending."

      Now, assuming the company is profitable, so that its bonds are significantly 'in the money', issuing new bonds, not accompanied by expected future earnings, might not have any effect on bond values, just like issuing new money might not have any effect on the value of money. But if the company issued $100 worth of bonds to the public, the public would have paid $100 for those bonds, so the public is not wealthier and there is no wealth effect. If we switch to talking about money, then the public would have paid $100 worth of their stuff for the newly-issued $100, so again no wealth effect.

      What if an unprofitable firm, whose bonds are out of the money, issues new bonds without future earnings? Then the bonds will fall in value, not because people spend them, but because the bonds have less backing. But still, people would have paid market price for those bonds, so their wealth would have been unaffected. Still no wealth effects.

      But what if people paid less than market price for those bonds? Now they are wealthier, but the company is less wealthy, so still no wealth effects.

      Jeez! I’m not very happy with the way I phrased that, but I have to get to class. I’ll try again later.

  3. Nick:

    1. For practical purposes, the central bank is part of the government, so transferring the central bank's assets to the government is just moving assets from one of the government's pockets to another. Most of us think, for example, that if the central bank blew up tomorrow, the dollar would still be backed by the government's assets. Besides, the central bank's bonds were already backed by the 'taxes receivable' of the government anyway.

    2. I don't know why this didn't really jump out at me before, but you put interest rates on the vertical axis of the money demand/supply curves, and I don't think that way. If I think about money demand/supply at all, I put oz./$ on the vertical axis. For the sake of argument, try it that way.

    Suppose the interest rate on bonds is 5%, and the CB issues convertible dollars, which say "IOU 1 oz anytime during the next year", and inconvertible dollars, which say "IOU 1 oz at year-end". Assume no printing/handling costs. The inconvertible dollars will start the year at .95 oz and rise to 1 oz at year-end. The best the issuing bank could hope for is to issue the dollar in january, get .95 oz for it, lend the .95 oz at 5% for 1 year, get back 1 oz in december, and use the 1 oz to buy back his dollar, making zero profit. But the convertible dollar could be issued for 1 oz in january. Lend the 1 oz at 5% and get back 1.05 oz in december, then buy back the dollar for 1 oz and make a profit of .05 oz. This profit of .05 oz will attract rivals.

    The first rival will come out with an improved convertible dollar that says "IOU .99 oz+ 1% interest, payable anytime". This dollar could be issued in january for .99 oz. Lend the .99 oz for 1 year and get back 1.04 oz in december, then use 1 oz to buy back the dollar, keeping .04 oz as profit. Rivals will still be attracted. The next guy will issue a new convertible dollar that says "IOU .98 oz anytime +2% interest". This will earn him a profit of .03 oz. Rivals will keep introducing new dollars until the convertible dollar finally says "IOU .95 oz. +5% anytime". Now profit is zero, but note that the convertible and inconvertible dollar are now priced the same: .95 oz in january and 1 oz in december. This shouldn't be much of a surprise, since american calls sell for the same price as european calls anyway.

    Now throw in printing/handling costs of 3%/year. Both kinds of dollars must now yield only 2%, and will be worth .98 oz in january and 1 oz in december. People tolerate the 2% return because of moneyness.

    Now we finally get to money supply/demand. The supply is perfectly horizontal at .98 oz, since if the issuing banks could get .99 oz they would issue huge amounts, and if they could get .97 oz they would not issue any. Money demand is also horizontal at .98 oz, since buyers would want huge amounts at .97 oz and zero at .99 oz. Even if we allowed the demand curve to slope down, the dollar would still be worth .98 oz with that horizontal supply curve. But of course the supply and demand curves are just shadows, whose position is entirely determined by backing of .98 oz. Change the backing to .85 oz, and both curves would be horizontal at .85.

  4. JP, I've been thinking about a crazy alternative reality. Imagine a flow-through economy. Corporations do not need (tangible) assets, owning factories is just a preference to leasing them; competition is perfect so there are no excess profits. Households do not have assets, which is in fact partially true for some countries which allow infinite or intergenerational mortgages (and interest only). This would essentially be a pure credit economy where the government setting the interest rate is the equivalent of taxation. There are no (tangible) assets backing the flows (no Backing Theory). Quantity is just a side effect of some government policy (i.e. quantity of money is just an arbitrary observable; one could just as easily have the `toilet paper theory of money`etc.). Tell me I'm crazy.

    1. jt26:

      JP is too nice to tell you that, so it's up to me. Trouble is, you're not crazy. You might be describing an economy where everyone's net worth is zero, where their future production is just enough for their future consumption flows. Massachusetts in 1690 matched this pretty well, and they issued paper shillings to pay their soldiers, backed by future tax collections. Since their net worth was already zero, this reduced their future consumption. But the backing theory still worked, in the sense that if the issued 20,000 Mass. pounds, backed by future taxes with a present value of 20,000 pounds sterling, then 1 Mass. pound=1 pound sterling.

      Please explain how government setting of the interest rate=taxation.

    2. Thanks for your comment Mike! I forgot to clarify one point; in this CrazyLand there is no taxation. A monopoly public bank just sets the interest rate (to change the flow of income between debtors and savers) as a monetary policy, and in fact they will try to discourage saving (net worth>0). Assuming the bank makes somewhat ideal lending decisions, any incremental lending may increase the quantity of total money, but the value increases proportionately. Anyways, thanks for entertaining a crazy guy.

    3. jt26, I'm not exactly sure where you're going with your story. But one nitpick: "There are no (tangible) assets backing the flows (no Backing Theory)."

      A security can have no tangible assets and still be valued. Intangibles like human capital, patents, monopolies etc serve as "backing".