Deep money, the coexistence puzzle, and the legal restrictions hypothesis

WWI Liberty bonds, which according to Neil Wallace circulated alongside Federal Reserve notes [source]

What follows are some thoughts on the coexistence puzzle as well as the folks who find it interesting.

There is plenty of hyperbole over the difference between freshwater and saltwater economists, but one peculiarity that surely distinguishes a freshwater economist from his saltier cousin is that they tend to be interested in the underlying motivations guiding monetary exchange, the so-called microfoundations of money. (Saltwater economists tend to be content with broad assumptions about monetary phenomena). Representatives of the microfounded approach, which includes the blogosphere's own David Andolfatto as well as Stephen Williamson—who has anointed his approach New Monetarism—like to refer to their models as "deep models of money".

One of the classic questions that continues to interest deep money types is the so-called coexistence puzzle. Zero-yielding financial assets like central bank-issued banknotes are "dominated" in terms of rate of return by interest-yielding financial assets created by governments. The puzzle that needs explaining is why these dominated instruments can continue to coexist with the instruments that do the dominating.

A quick answer is that a lower-yielding asset can coexist with the higher-yielding asset because the first is more liquid than the second. In an uncertain world, the stream of liquidity services that an asset provides over its lifetime is a valuable service. An asset that provides a little less income can still be demanded in the marketplace as long as it provides a little more liquidity. Deep money folks would say that my answer is a bit shallow. It avoids exploring both the qualities of the assets being used and the frictions that characterize the world in which those assets trade that might render one asset more liquid than the next.

Let's explore the setup of the coexistence problem in more detail. In a 1982 paper, deep money pioneer Neil Wallace defined the problem thusly; if the government were to issue small denomination bearer bonds, say in units of $5, $10, and $20, and these instruments were to yield interest, just like their larger denomination relatives, why would anyone carry 0% Federal Reserve notes in their wallets when they might own an interest-yielding replica instead? These two instruments shouldn't coexist—cash should be driven out of existence or, if they are to coexist, then bearer bonds should yield no more than the 0% rate on cash.

One aspect of the problem, Wallace noted, was that for some obscure reason, governments typically choose not to issue small denomination bearer bonds. The large denomination size of t-bills and t-bonds inhibits their use in trade, thus preventing at the outset any sort of direct competition between government bonds and zero-yielding cash.

However, Wallace pointed out that this doesn't explain why private issuers don't simply buy high denomination government bonds and create their own government bond-backed small denomination bearer notes. If they did so, Wallace believed that two things might happen. These private issuers, by virtue of paying interest on their notes (more specifically by issuing bearer bonds at a discount to face value and allowing them to appreciate in price till maturity, much like treasury bills) would drive inferior 0% yielding banknotes out of existence so that only interest-bearing notes circulate.

Alternatively, the public would allow privately-issued bearer bonds to circulate at par with existing currency. Par acceptance would mean that private bearer bonds no longer paid interest in the form of a steadily rising price. However, Wallace stumbled upon an interesting side effect of par acceptance: nominal rates on government bonds would have to fall to zero. Why? According to Wallace, arbitrage dictates that as long as the rate on long term government bonds is above zero, competing private issuers will flock to buy those term bonds with which to back their 0% bearer notes, putting upward pressure on bond prices and downward pressure on yields. It makes sense for banks to do so because they earn the spread between the 0% notes that they issue and the interest-yielding bonds they purchase. According to Wallace, the arbitrage window will only be shut when banks have driven long term rates close enough to zero that the the opportunity for excess profits disappears. In a free market, the term structure of interest rates disappears. All we have is a flat yield curve.

Here is Wallace: "Thus, my prediction of the effects of imposing laissez-faire takes the form of an either/or statement; either nominal interest rates go to zero or existing government currency becomes worthless."

Of course in the world we live interest-yielding bearer currencies have not kicked out 0% notes nor have private notes driven long term bond rates to zero. Wallace attributed this to various legal restrictions against banks from entering the small denomination bearer bond line of business. Take away these legal restrictions and he believed that his conclusions followed.

Even if we removed these legal restrictions, I'm not convinced by Wallace's arguments. Given free competition in note markets, I don't think that positive-yielding small denomination bearer bonds (issued either by a private bank or a government) must necessarily drive cash into exile, not do I think their coexistence means that the term structure of interest rates must be flat.

To start with, the necessity of calculating interest payments throws a wrench in the smooth transfer of a bearer asset, a point made by Larry White. Say that the bearer bonds are printed with a $10 face value but sold by the government at a discount to face so that their price appreciates over time until maturity, the capital gain being a stand-in for interest payments. Should someone wish to use their unmatured bearer bond to pay for something, they will have to calculate how much of a discount to face to apply to the bond. Such a calculation imposes a burden on the transactors since it will take time to crunch the numbers or require a costly technology to speed up the process. As White has noted, a $20 note held for one week at 5% interest would yield less than 2 cents. Is it really worth it for a banknote user to take the time and trouble to compute and collect such a small amount?

The interest rate feature of bearer bonds also precludes the simple summations that round numbers allow. An owner of a $10, $5, and $20 bearer bond doesn't have $35 in purchasing power. Rather, discounting the bonds will show that their purchasing power is composed of inconvenient sums like $9.33, $4.89, and $19.60. This makes it harder to know how much purchasing power is in one's wallet prior to going to market, thereby inhibiting the usefulness of bearer bonds as a liquid medium. Carrying around 0% currency which trades at its face value allows for certainty of purchasing power, a feature that may more than compensate for lack of a pecuniary yield.

Even worse, having inconvenient non-round bonds in one's wallet or till makes the process of obtaining or providing change a nightmare. If you buy a $10 bottle of wine with an unmatured bearer bond worth $11.56, what are the odds that the cashier will have a $1.56 bearer bond to give you as change? 0% cash may not offer interest payments, but at least the standardized even denominations in which it is available (combined with small change) allow for hassle-free transactions.

Lastly, all transactions in bearer bonds face capital gains taxes. That means on each exchange, the owner of bearer bonds must fish back into their records to find the original price at which they received the bond, determine the price at which it was sold, compute the profit, and then submit all this information to the tax authority. Payments made with 0% banknotes are not taxed, saving those who choose to transact with banknotes time and energy.

So in a nutshell, the previous factors may explain why interest-yielding small denomination bearer bonds will always be less liquid relative to 0% yielding cash, thus preventing the former from kicking the latter out of circulation.

If Wallace's first point is wrong and the payment of interest on banknotes doesn't drive existing 0% cash out of existence, what about his second prediction? Assuming that privately issued bearer bonds are accepted at par, what prevents profit-hungry banks from issuing 0% bankotes and accumulating interest-bearing bonds, eventually arbitraging bond rates down to zero?

As I've already illustrated, interest yielding instruments (especially large and ungainly ones like t-bills) will always be less liquid than cash. This gives rise to an un-arbitrageable wedge between the yield on cash and that on bonds, or a liquidity premium. Note-issuing private banks eager to earn more spread income may be able to temporarily push rates down through bond purchases. However, at these lower bond rates the marginal bond investor will be dissatisfied. They are now holding an asset that offers the same inferior liquidity return as before but less interest. These investors will sell their bonds, in the process pushing interest rate right back up to so that bonds once gain offer an attractive return on the margin. In short, bond-buying banks can't push long term bond rates down to zero because the rest of the liquidity-buying public won't let them.

But if long term rates won't budge when banks buy them, doesn't that mean that banks can continuously earn excess profits by perpetually issuing 0% notes and purchasing risk-free long term bonds? Free dollar bills left on the floor are, after all, the biggest no-no in economics. This ignores the fact that even if rates don't fall to zero, other costs will rise instead as banks compete to enjoy the spread. Larry White refers to this as non-price competition. It might include any number of costly strategies used to attract note-holders, including longer bank operating hours, more tellers, increased advertising expenses to make notes more trusted, and special engraving of notes to make one's bills more attractive relative to the competitions'. Thse mounting costs will soon counterbalance the fat spread income, thereby reducing the window for excess profits.

So contra Wallace, laissez faire doesn't reduce the risk-free bond yield curve to a flat line. Because liquidity differentials between bonds and notes will continue to exist free market or not, bond rates will always have to provide a sufficiently high nominal interest rate in order to attract holders.

What makes Wallace's conclusion about the yield curve in a free market interesting is its pleasing counter-intuitiveness. Many of the theories that deep money people come up with have this same quality, including one of my favorites: the irrelevance of open market operations, or what some call Wallace Neutrality. Stephen Williamson's odd theory that central bank's need to fight inflation by lowering rates, not increasing them, is in this same tradition, although in this case I think he's probably wrong.

Empirical evidence is the best way to test deep money theories. In the case of Wallace's legal restrictions theory, reality is not kind. For instance, we know that in the 18th and 19th centuries Scottish banks were not burdened by legal restrictions on the issue of notes, yet the Scottish yield curve was not a flat one. Indeed, interest bearing bills-of-exchange circulated freely with notes. Despite dominating notes, bills of exchange did not drive them to oblivion. Makinen and Woodward report on the coexistence of small-denomination interest-paying "bons" in 1920s France with the franc currency, and Wallace himself points to evidence that Liberty bonds circulated concurrently with Fed cash during WWI. (I should note that David Andolfatto is skeptical of these instances since they are commonly associated with periods of fiscal distress.)

As for some of the more modern deep money efforts like Stephen Williamson's, reality remains a hard customer. One wonders how Rudolph Havenstein's tight interest policy would have created the Wiemar hyperinflation, for instance. While I'm being tough on the deep money folk, I want to sign off on a positive note. Figuring out the underlying nature of monetary exchange is no doubt an important endeavor. Anyone who wants to learn more about monetary phenomena and central banking should probably be reading what the deep money people have to say.

Scott Sumner: Damned if markets are efficient, damned if they're not

Last week I wrote a post that attempted to dehomogenize Scott Sumner from Krugman. I left a similar but more precise comment on Bob Murphy's blog. Sumner seemed to endorse it. But there's something that doesn't make sense.

Open market operations can really only have an effect if markets are not efficient. Yet Sumner is a great believer in efficient markets (as commenter Max notes on RM's blog). See Scott here and here. How can Sumner reconcile those two positions?

First, some definitions. I'll define efficiency as the idea that financial assets trade in the market at the discounted value of their future cash flows. Any deviation from this value will be fleeting as investors arbitrage it away. Another word for discounted value is fundamental value.

Here's the logic for why open-market operations need an inefficient market to work.* Say reserves are currently plentiful and yield 0%. Twenty-year 2% bonds are trading in the market at their fundamental value of $115 and an implied interest rate of about 1%. If the Fed announces it's going to buy a bunch of 20-year bonds, how can it increase their price above fundamental value? Any attempt to bid bond prices above $115 will cause rational traders to quickly sell every bond they own to the Fed so as to take advantage of the overvaluation. Bond prices don't change, nor does the 1% yield. Same goes for stocks and other assets. QE-style open market operations can't get a "bite" on asset prices.

But as market monetarists like to point out, even in today's environment of plentiful reserves, open market operations do seem to have an effect on asset prices. See Lars Christensen's chart, for instance. So if purchases have demonstratively pushed up asset prices, that means traders aren't selling those assets at their fundamental value, and therefore markets aren't efficient.

Ok, here's a way for Scott to have his cake and eat it to - he can be a believer in efficient markets and accept the relevance of open market operations. Let's redefine the efficient price of a some asset to be composed of not only its fundamental value (the discounted value of future cash flows), but also a liquidity premium. Assets have differing liquidity premiums depending on the expected ease of buying or selling them. Marketable assets have large liquidity premiums and, as a result, their efficient price is higher than if they were illiquid. It's worthwhile for rational traders to own liquid assets because in an uncertain world, the ability to sell or hypothecate some asset provides a set of options that an illiquid asset doesn't.

Having redefined efficient, when the Fed announces it will buy 20-year bonds, their fundamental value still doesn't change. Instead, the liquidity premium on 20-year bonds rises. After all, with the Fed wading into the pool, these bonds have become much more liquid. As a result, the efficient price of 20-year bonds will rise. In this way, prices can rationally diverge from their fundamental value without the assumption of efficiency being dropped. That's why open market operations can have bite, even in an environment like ours.

*I get this from Eggertson and Woodford, who get it from Neil Wallace, who got it from the efficient market crowd, Miller, Modigliani, and the rest.

Would Warren Buffett buy green pieces of paper?

Noah Smith has an interesting post in which he asks: "Is money fundamentally worth nothing more than the paper it's printed on?"

He goes into some soul searching on the definition of "fundamental." His concern with definitions is helpful. The recent debt super-debate was largely blown out proportion due to definitional differences, in my opinion.

If anyone is worthy of describing the word fundamental, it's the sage of Omaha. In deciding whether to purchase a stock or not, Warren Buffett conceptualizes the problem by imagining that he'll never be able to sell it again. He's stuck with it forever. If you abstract from an asset's ability to be exchanged onwards, what you're left with is pure fundamental value. This applies to commodities and consumer goods as well as it does to financial assets.

The definition of fundamental having been dealt with, we're left with a thorny problem. The word money is still undefined. As Neil Wallace pointed out, "monetary theories should not contain an undefined object labeled money." Is Noah talking about gold, cattle, gold-backed bank notes, bitcoin, yap stones, Federal Reserve notes?

In nomadic societies, cattle were highly liquid. What was a cow's fundamental value? Assume that it could never be exchanged again. What remains is the cow's fundamental value — it might be eaten, it could be used to make clothing, it can help rear more cows, it can help in the fields etc. Take another form of "money". In the 1800s, most bank notes were issued with gold redemption clauses. What was a gold-backed bank note's fundamental value? Assume that a note can never be exchanged onwards, and you're left with a security with some fine print on it that says that the issuing bank will redeem it for gold. Its fundamental value is the value of the underlying metal.

I'm going to assume that by green pieces of paper, Noah is specifically interested in the fundamental value of fiat money, perhaps Federal Reserve notes. Assume that a specific FR note, say the one in your wallet, can never be exchanged onwards. What is it worth?

This isn't an economic question. It's a question of security analysis. What does the fine print of your FR Note say? FR notes are liabilities of the Federal Reserve. They carry a "first and paramount lien" on the assets of the Federal Reserve. Having a first lien means that an FR note holder ranks higher than all other Federal Reserve creditors. In other words, your note is an excellent claim. What are the Fed's assets? They have a bunch of government bonds, some gold,* and a few foreign currency denominated assets. These assets aren't paid out on demand. Rather, as a note holder you'd have to wait for the Federal Reserve to be wound up before you could get their hands on these assets. So the fundamental value of an non-exchangeable FR note is the distant possibility that the note holder gets to exercise their senior claim on underlying Federal Reserve assets. That possibility is worth some non-zero value.

see chart in scribd.

This all reminds me of an old conversation I had with Nick Rowe. See here. In that conversation, Nick uses the same Buffetian concept of fundamental value as I use in this post, and argues that fiat money has no fundamental value. I argue the opposite.

Ok, that's my answer to Noah's question.

An interesting thought game is to consider what would happen if all FR notes are no longer exchangable. Say that for some reason or other, no one will accept notes anymore. The price of FR notes would immediately plunge towards their fundamental value. But a large component of a note's fundamental value is derived from the underlying value of the bonds which the Fed holds on its balance sheet. Because these bonds promise to pay a fixed quantity of dollars, the bonds themselves would simultaneously plunge in value along with the notes. And as the bonds plunge in value, the notes do too. And as the notes fall in value, the bonds plunge again etc. etc. until they both spiral to zero.

What halts this spiral is that the Fed holds more than just nominal bonds. It also owns some US dollar assets that pay an inflation-linked return, namely Treasury Inflations Protected notes. At the same time they hold gold. Lastly, they hold foreign denominated bonds whose value would be protected. At some much lower price for FR notes, the Warren Buffetts of the world calculate that the value of a note's senior claim on gold, TIPS, and forex is probably worth more than the market price of notes, and they step in to buy. The death spiral ends.


*the Fed doesn't actually own gold. It owns claims to gold. See this article. 

Wallace Neutrality... don't fight the Fed

Miles Kimball gave me some help on understanding Wallace Neutrality, which in turn might help me understand more where Stephen Williamson is coming from when he says QE is irrelevant. I asked Miles:

I'm not sure if I entirely understand the Wallace neutrality argument.

If I may paraphrase, does it mean something like... the Fed could buy a bunch of stocks on the NYSE, and they might be able to push their prices up (their dividend rates down). But if they did so, the price of these stocks would rise above their intrinsic value and profit-seeking agents would immediately take the opposite side of the trade, thereby pushing the purchased stocks' value back to their intrinsic value. So in order for the Fed to permanently increase stock prices above their intrinsic value, there must be some sort of "friction" that prevents profit-seeking agents from taking the other side of the trade. Is that what it means?

Miles:

Yes... You said it very well.

That's a relief. Sometimes I have troubles translating the somewhat Spockian language of formal economics into words that are more comfortable to me, that being the daily lingua of the marketplace, trading, and investing.

To further re-translate, I'd say the idea of Wallace Neutrality falls in the same boat as the old trader's adage... don't fight the Fed. If traders believe the Fed is all-powerful and too strong to trade against, then the Fed can effectively change assets prices above or below what they should otherwise be. If traders think they can fight the Fed, then the Fed can't change asset prices - traders will collectively take the other side of any Fed action, canceling out any Fed-induced price changes. What "friction" motivates traders to believe they can or can't fight the Fed?

Here is my older post on Stephen Williamson's QE irrelevance. The frictions I point to in that post are the Fed's size relative to other actors in asset markets and the Fed's ambivalence to profits/losses in a environment in which all other actors are hypersensitive to profits/losses. In other words... don't fight the Fed. It's massively big and doesn't care if it loses on the trade.

Brad DeLong had a comment on the idea of Wallace Neutrality here. Miles goes into the idea of Wallace Neutrality again here.