Wednesday, May 14, 2014

From corporate bonds to a fiat CPI standard

Michigan Central Railroad 3.5% Bearer Bond with attached coupons, 1902

David Glasner is frustrated that there is no satisfactory theory of the value of fiat money, noting that "it's just a mess, a bloody mess, and I do not like it, not one little bit."

According to David, the core problem is the backward induction argument. Say that a valued fiat object provides no non-monetary services so that its price depends entirely on the expectation of future resale. This is a highly precarious situation since it it inevitable that someday no one will want to exchange for that fiat object. But if it is certain that no one will accept it at some point in the future, then why accept it in the first place? The explanation for the object's value rests on an "unlimited supply of suckers", as David puts it, hardly good fodder for a long term theory of asset prices.

David proposes tax acceptability as his way out of the problem, although he doesn't seem to be entirely convinced by this explanation. (I've never liked the tax-acceptability theory, as I wrote here. )

But there may be another solution to the backwards induction problem. I'm going to show that the market establishes the value of modern fiat money under a CPI standard in the exact same way that it establishes the value of a very familiar instrument; the standard corporate bond. Since corporate bonds are not subject to the backwards induction critique, then by analogy neither should fiat paper. What follows is a gradual progression from the one to the other with the aim of showing that if you can value a bond you can value a Federal Reserve note.

1. Start with a company, say Apple, that in addition to issuing corporate stock issues bonds. These are regular bonds. Each of them has a recurring quarterly claim on a nominal quantity of Apple income as well has the right to a final return of principal upon maturity. Should Apple be liquidated, bond holders get a first claim on whatever remains of the business. The market takes these terms and conditions into account and establishes a market price for the bonds. Pretty standard stuff.

2. A few years later Apple converts some of its bonds into bearer form, ie. they are printed on paper and transferable by hand, while leaving the rest unaltered. It issues these bearer bonds in both small denominations like 1/10, 1/4, 1, 5, and 10 units, as well as large 100 and 500 denominations. Attached to each bearer bond is a series of coupons. To receive interest, the bond owner detaches the coupon and brings it to Apple each quarter in return for a dollar payment.

Despite these changes, the market continues to value bearer bonds in the same way as the firm's regular bonds. Still pretty standard.

3. Next Apple ceases to periodically redeem its bearer bonds when they mature, converting them into perpetual bearer bonds. A perpetual is not as valuable as an equivalent series of redeemable Apple bonds, but the market can still establish a positive price for a perpetual debt instrument as easily as it can a fixed term bond.

4. Say that Apple begins to accept these perpetual bearer bonds as payment at Apple stores. Other merchants copy Apple. Bearer bonds become a highly liquid exchange medium. A liquidity premium develops, with Apple bearer bonds often trading at a higher price than Apple's regular bonds, despite the former being perpetual instruments. (Apart from the unusually large liquidity premium on bearer bonds, this is still pretty standard stuff.)

5. As the liquidity services thrown off by Apple's perpetual bearer bonds grows, Apple realizes that it can reduce the coupon rate it offers without losing too many investors. Apple eventually ceases paying any interest at all—owners of bearer bonds are sufficiently happy with the liquidity return provided by the bearer bonds that they do not require a pecuniary return. The bonds have effectively become "cash", or 0% yielding paper notes.

The market values these no-interest bonds in the same way they do the normal bonds. Both have first dibs come final liquidation of Apple. The difference is that whereas the regular bonds are fixed term, bearer bonds are perpetual; regular bonds pay interest while bearer bonds don't; and the bearer bonds carry a large liquidity premium whereas the regular bonds are illiquid.

6. The economy begins to spontaneously de-dollarize and Apple-ize. Merchants first set prices in terms of both "Apples" and dollars, and eventually just Apples. Debt contracts are redenominated into Apples. The market will continue to value both bearer and normal bonds in the same way as before.

7. Initially the Apple price level moves around according to the whims of the market. Later, Apple decides to stabilize prices by targeting a 0% rate of growth in the price of a basket of consumer goods, a CPI basket. One way it can do so is by varying the quantity of Apple bearer bonds in the economy via open market operations. If Apple increases the amount of bearer bonds via open market sales, then the liquidity premium on bearer bonds is reduced and the price level rises. If it engages in open market sales, the amount of bearer bonds is decreased, their liquidity becomes more valuable on the margin and the price level falls.

Alternatively, Apple can vary the 0% coupon rate on bearer bonds. If the purchasing power of Apple bearer bonds is rising, i.e. the economy is characterized by deflation, Apple can counteract this by reducing the coupon rate (to the point of even introducing a negative Gesell tax), thereby making bearer bonds less attractive and forcing the price level back up. By increasing the fixed coupon payment, it can do the opposite and prevent inflation.

8. Now Apple decides to let bearer bonds fall at 2% a year, or allow them to purchase 2% less of the consumer basket each year. As in step 7, it varies the coupon rate or conducts open market operations to counteract any forces that would prevent it from hitting its target.

We have now arrived at a modern fiat CPI standard. What was once a standard bond has been converted into a highly liquid perpetual bearer instrument with a 0% coupon (flexible upwards or downwards) that falls in value by 2% a year, and also happens to be the economy's medium of account.  This modified bond is the equivalent of the so called "fiat money" issued by the likes of the Fed and the Bank of Canada, or what is otherwise known as cash. Since the market can easily value Apple's regular bonds without falling prey to the David's backwards induction problem, then surely it can value Apple's modified bond after taking into account all the extra bells and whistles that have been added in steps 1 to 8.

(With apologies to Nick Rowe)


  1. The only thing is there is this preceding currency in which Apples are denominated before Apples displace them. I think that is probably the solution though. The prior currency never becomes worthless. Apple buys up all it can and stores its value in its accounting balance sheet. Even though it ceases to be traded, it is never considered worthless and we have chain of currencies that never lose their value but are swallowed by subsequent ones, at least the successful ones. It may no longer provide monetary services but may provide collectible services.

    1. This would be my rebuttal to Glasner. For example, French francs are now essentially worthless. That doesn't mean that they were worthless in 1992. Between 1992 and now there was an event allowing unlimited conversion from soon-to-be-worthless francs into soon-to-be-valuable Euros. As long as we believe the conversions will continue, there is no induction problem.

      Even if we think that there *might* be a break in conversions we can still perform an expected value calculation and get a positive result. Add in that we think we might be able to convert some of our currency to real assets first, and we get a slightly higher positive result.

  2. Great job!

    Two things:
    1) It's strange that David Glasner, who sees the flaws of the theory of fiat money so clearly, nevertheless rejects the real bills doctrine:

    "The question I wish to address briefly in conclusion is whether the real-bills doctrine as applied to individual banks really does solve the problem that the law of reflux raises for them. Unlike the question of whether the version of the real-bills doctrine that applies to an entire banking system is valid (to which the answer is, of course, no), this question does not admit of a straightforward, logically compelling answer. "

    2) If Apple is able to issue currency that pay zero or negative interest, then Apple gets a free lunch. This will attract rival currencies, until Apple's gross profit on the currency is just enough to cover Apple's costs of printing and handling. At that point there is no more free lunch, and no more attraction for other firms to issue rival moneys.

    1. Thanks Mike. Hoping David gives this post a read, I'm curious what he thinks.

  3. This is very good, but I would add a few points.

    If the Apple bonds are perpetual and Apple is free to set the rate on them, then people do need to believe that Apple will try to stabilise their vale and not let it crash to nothing. In what you've described, this does require that Apple buys back bonds as required to support the value when demand for them falls. In the extreme, this means that Apple is willing and able (in principal at least) to buy back all the bonds should people decide that actually they don't want them after all. This means that nobody will ever find themselves in the position of holding bonds they can't pass on to someone else, so you avoid the bubble problem that people worry about with fiat currencies. This requires that Apple is actually able to purchase all the bonds back, which means that it must have enough real assets or earnings power to be able to do so. So, in as far as you've gone with this, the backing matters.

    To complete the analogy, we need to imagine that banks start to operate accounts denominated in Apple bonds, including accounts that can be used for payments. These may be close substitutes for the bearer bonds themselves. Bank lending will also expand the gross long and short positions in Apple bonds, so that in time the actual bonds themselves represent only a tiny part of the open position. In keeping with dollars, settlement of long and short positions in bank accounts would be done by netting - there would be no need for physical delivery of Apple bonds. In fact, as the bank payment system got more efficient, people might never actually need to hold Apple bonds at all.

    At this point, Apple may account for a vanishingly small part of the actual open position in its bonds. However, it will retain control over the exchange value, provided that banks are committing to convert Apple bond denominated accounts into actual Apple bonds at par. Apple can then raise market interest rates whenever it likes by increasing the coupon on the bonds. Banks will then need to follow suit to avoid having all their customers convert their deposits into Apple bonds. Note that Apple does not need to pay its coupon in dollars or real goods - it can just give holders more of the Apple bonds. Obviously for a normal perpetual that would be useless, but here it makes a difference because of all the debt contracts denominated in Apple bonds. Giving people more bonds alters the position of creditors and debtors.

    Once we have a large network of Apple bond denominated claims, the dynamics change. People will accept and hold such claims because they bear an interest return. Overwhelmingly, this is a return which represents a real transfer of resources from debtor to creditor. Only in the case of the actual bonds themselves does it not represent a transfer from debtor to creditor, but it doesn't make any difference to the holder of the bonds, and it makes little difference overall as the bonds represent such a small part of the overall open position.

    1. continued..

      This key point is that this return is different to the return on something like Bitcoin. That return depends wholly on an increase in its exchange value, so a continual return depends on people wanting to hold a greater and greater total value of it. Once demand slows, the return falls. When the Apple bonds are widely used for creating debt relationships, the return on Apple bond denominated debts is an actual transfer of resources. People can get paid a return, even while the nominal stock is shrinking.

      So people will hold Apple bond denominated positions because of the real return, which is not at all dependent on Apple's balance sheet. Against this, people have to weigh the risk that, one day, everyone may abandon Apple bonds as the medium of exchange. In that event, some people may be left with the actual Apple bonds and those people may then care about Apple's balance sheet. But for someone holding a long position in those bonds now, it is a very small chance that they will be the unlucky person holding them in the end, given that the bonds represent such a small share of the total long position. This percentage chance of loss will be easily outweighed by their interest return. With something like Bitcoin, you can't separate the chance of loss from the return.

      So once you have an extended network of claims, Apple's commitment to maintaining the exchange value of Apple bond denominated remains crucial, but its balance sheet no longer plays a material role.

    2. Nick, I agree with a lot of what you say. Just a quick comments.

      "In what you've described, this does require that Apple buys back bonds as required to support the value when demand for them falls"

      I'm not sure that Apple has to be permanently "on the bid" to support the value of bearer bonds when the demand for them falls. Like a regular bond, bearer bonds have a terminal or fundamental value (albeit a fluctuating one), so that at some lower price value investors will purchase the bearer bonds and support their value, effectively doing Apple's job for it. If Apple wants to maintain a stable price level, however, I do agree that it needs to have a permanent bid out for bearer bonds so as to enforce its target.

      "Apple's commitment to maintaining the exchange value of Apple bond denominated remains crucial, but its balance sheet no longer plays a material role."

      Doesn't Apple's commitment to maintain the exchange value of Apple bearer bonds require that it have a sufficiently strong set of assets on its balance sheet that it can mobilize for repurchases?

    3. I don't think so. We are at the stage here, where Apple doesn't need any resources to pay coupons on the bonds, because it can pay them in kind - just handing out more bonds. If the bonds were the only money used, this would be meaningless - the holders would have received nothing of value. But once there is a significant network of claims denominated in Apple bonds, it is very meaningful. Now the holders have received something valuable (at the expense of everyone else holding long positions in Apple bonds).

      So rather than repurchase bonds if demand falls, Apple only has to increase the coupon it pays, which costs it nothing.

      I confess I'm still thinking through this.

    4. Some further thoughts on this.

      First, I am interested in the situation where there are private banks which are committing to doing two way par exchanges of Apple bonds for Apple bond denominated deposits and the number of actual Apple bonds is several magnitudes smaller than the net equity of those banks.

      In general, I don't think the balance sheet of Apple then matters. In a wind-up of all Apple bond denominated contracts, the actual Apple bonds would all end up being held by the equity owners of banks through repayment of bank loans. So even if Apple has no assets to distribute on a liquidation, the banks are committing themselves to playing the greater fool. If people suddenly learned that Apple has no assets, it might affect the value of bank equity, but it shouldn't affect the value of the bonds themselves in the hands of the general public.

      However, Apple's balance sheet might matter in the event that Apple bonds ceased to carry any special benefits over private bank money (including things like fulfilling reserve requirements). In that case, the bonds would need to pay a coupon equivalent to the rate on commercial bank money. As I mentioned before, paying a coupon itself is not a problem, because Apple can pay it in bonds themselves. However, if the required return exceeds the growth rate of the economy (and assuming accumulation of Apple bonds by the state does not compensate), then the stock of bonds relative to GDP is going to grow. Eventually this will violate our assumption about the size of the stock relative to the size of private banking.

      So in this case, I think it would matter if Apple did not have the balance sheet to repurchase bonds.

      Apologies for the long comments here. I'm still trying to work out what I really think on all this, so it's useful to play around with your thought experiment.

    5. "because it can pay them in kind - just handing out more bonds. If the bonds were the only money used, this would be meaningless - the holders would have received nothing of value."

      I don't think I'm following you here. Why would this be meaningless? Why would these bearer bonds not be of value? By issuing more bearer bonds in lieu of interest, Apple is reducing the claim that existing shareholders have upon Apple's assets (come dissolution) by allowing a new set of bonds to step in front them and take over that claim.

    6. Good point. I was thinking in QTM terms there and comparing it to giving someone one extra dollar for each dollar they held. But when the bonds are the only money used - i.e. there is no private bank money, then I can see that Apple's balance sheet will be more relevant. So I agree it's not meaningless. I do think though that it is meaningful for a different reason.

  4. A question: why wouldn't this mechanism result in a system where the price level (P) is directly proportional to the supply of "Apples" (A) -- i.e. the pure quantity theory of money? It seems like an increase in the supply of "Apples" should cause a proportional increase in the price level P = k A, or at least a log linear-relationship log P = α log A + k.

    1. It has to do with something called Wallace Neutrality. Apple's liabilities trade close to their fundamental value, ie. a discounted stream of cashflows. Google's do so too. As in my post, assume that Apple's liabilities are used to represent the economy's unit of account. If Apple creates new liabilities to purchase Google's liabilities (and buys them at market prices), the fundamental values of each respective firm's liabilities are not being altered in any way by the transaction. Therefore the economy's price level doesn't change, despite the fact that the quantity of Apple's liabilities may have increased dramatically.

    2. I'm confused by why Jason asked this question and why JP answered it the way he did given that JP writes in the post, under step 7:

      "One way it can do so is by varying the quantity of Apple bearer bonds in the economy via open market operations."

    3. Sorry for being confusing. Open market operations do have an effect on prices because they alter the liquidity premium (otherwise known as the convenience yield) on Apple shares. The narrower (wider) the premium the lower (higher) the Apple price level. Once that premium has hit 0 then open market operations no longer have any effect and we are in a world characterized by Wallace neutrality. So the quantity theory is relevant for a while at least, but it isn't the the ideal quantity theory whereby an increase of x dollars (or Apples) always causes a proportional increase in prices.

  5. "As the liquidity services thrown off by Apple's perpetual bearer bonds grows, Apple realizes that it can reduce the coupon rate it offers without losing too many investors. Apple eventually ceases paying any interest at all—owners of bearer bonds are sufficiently happy with the liquidity return that the bearer bonds provide that they do not require a pecuniary return. The bonds have effectively become "cash", or 0% yielding paper notes."

    I must say that at this stage I think you are assuming your conclusion.

    This stage depend very much on whether there is a competing medium of exchange and what the comparison of the two services looks like at that point and which one wins and why. And if there isn't a competing medium of exchange, the assumption is the conclusion.

    1. Does it help if I add that in addition to making bonds acceptable for payment at its own stores, Apple would also have to spend significant resources on both the infrastructure necessary to promote the liquidity of its bearer bonds as well as advertising and whatnot to promote their use as currency. This outlay might not make Apples as liquid as paper dollars, but it would get them closer.

    2. That helps.

      I wonder if the question needs more clarification. There's a difference between how a currency retains its value and how a currency retains its pre-eminence as the medium of exchange. The mechanisms of money and interest rate control can go to explaining the first. But they don't explain the second. Google can compete with Apple and both can compete with the US government. Given that all three can pursue the iteration strategy you describe in your post, what is it that determines who the victor is? Resource and infrastructure investment? Maybe.

      The taxation argument is nice in that it explains the outcome by way of a monopoly control mechanism.

      MMT has this hokey parable about somebody standing at the door with a "nine millimetre" forcing people to work in order to "earn" business cards. They have to pay cards ("taxes") to get out of the room. It's a dumb parable because the same guy with the gun can just force people to use cards as currency quite apart from tax obligations. The government has a monopoly not only over tax obligations but over the employment of an army.

      So there's something about government power that is the ultimate explanatory variable in my view. That's why Apple and Google would lose. And that's why Bitcoin will lose in my view.

      I like your iteration story because its elegant and continuous, but I think it is describes a process of voluntary economic adoption which may in fact not be necessary when the victorious issuer has an underlying monopoly power of some sort.

    3. I don't doubt that monopoly power has a large impact on the success of certain media of exchange. But monopoly power isn't a necessary condition for success as a medium of exchange.

      For instance, BMO and TD compete to make their deposit media of exchange as liquid as possible versus competing banks (and the Bank of Canada's notes). They do so by investing in their bank networks and properly placing their ATMs. Desjardin is a poor competitor with the big banks in Toronto because its banking infrastructure is so inferior, but it is strong in Quebec because there's a branch on every corner. So the creation of a good medium of exchange requires real investment, with banks competing to promote the liquidity of their deposits.

      In Scotland in the 18th and 19th centuries, banks issued notes in addition to deposits. The promotion of one's notes as a good medium of exchange required investment in design, anti-counterfeiting, bank networks to allow for easy convertibility into gold, and processes for the removal of damaged notes.

      So I don't think that we don't need government to explain why certain media of exchange rise above others, although that isn't to say that various policies like the granting of unique powers to the Bank of Canada don't have some influence.

  6. I noticed this commenter at Nick Rowe's site touting something called "Ripple." Is anybody familiar with that here?


    2. Thanks JP. I should have remembered that one.

  7. Why can't we just forward induct based on faith? Of course the faith needs to be built incrementally and validated (in the present and future). Liquidity can be broken down into long and short-term. In the short-term, given a transparent exchange, we can test the faith, for e.g., can Bitcoin be used for short-term small $ payment? Yes, the Bitcoin liquidity service is given by hourly volatility and volume and can be assessed. For the long-term liquidity service, we need to see some evidence of longer duration contracts denominated in Bitcoin (and at growing volume), because looking forward, they are the transactions that we would see on the exchange.

  8. This is exactly why gift cards are actually worse for the general public, it would be a fascinating experiment to attach a gift card value to some rolling benchmark pricing mechanism (a song in itunes? a small coffee at sbux??) obviously this isn't good or easy for the corporation and they are making plenty on the gift cards themselves, but would be an interesting competitive advantage idea for someone bold to try..