Fedwire transactions and PT vs PY

Milton Friedman's alleged license plate, showing the equation of exchange

The excruciatingly large revisions that U.S. first quarter GDP growth underwent from the BEA's advance estimate (+0.1%, April 30, 2014) to its preliminary estimate (-1.0%, May 29, 2014) and then its final estimate (-2.9%, June 25m, 2014) left me scratching my head. Isn't there a more timely and accurate measure of spending in an economy?

One interesting set of data I like to follow is the Fedwire Fund Service's monthly, quarterly, and yearly statistics. Fedwire, a real time gross settlement interbank payment mechanism run by the Federal Reserve*, is probably the most important financial utility in the U.S., if not the world. Member banks initiate Fedwire payments on their own behalf or on behalf of their clients using the Fedwire common currency: Fed-issued reserves. Whenever you wire a payment to another bank in order to settle a purchase, you're using Fedwire. Since a large percentage of U.S. spending is transacted via Fedwire, why not use this transactions data as a proxy for U.S. spending?

Some might say that using Fedwire data is an old-fashioned approach to measuring spending. Irving Fisher wrote out one of the earliest versions of the equation of exchange, MV=PT, where T measures the "volume of trade" or "real expenditure" and P is the price at which this trade is conducted. Combined together, PT amounts to the sum of all exchanges in an economy. More specifically, Fisher's T included all exchanges of goods where his chosen meaning for a good was broadly defined as any sort of wealth or property. That's a pretty wide net, including everything from lettuce to publicly-traded equities to land.

Practically speaking, Fisher wrote that it was "utterly impossible to secure data for all exchanges" and therefore his statistical approximation of T was limited to the quantities of trade in 44 articles of internal commerce (including pig iron, rice, hogs, boots & shoes), 23 articles of import and 25 of export, sales of equities, railroad freight carried, and letters through the post office. This mishmash of items included everything from wholesale goods to securities to and consumption goods. Using Fedwire transactions to track total spending is very much in the spirit of Fisher, since any sort of transaction can be conducted through the interbank payments system, including financial transactions.

Nowadays we are no longer taught the Fisherian transactions version of the equation of exchange MV=PT but rather the income approach, or MV=PY. What is the difference between the two? Y is a much smaller number than T. This is because it represents GDP, or only those goods and services that are qualified as final, where "final" indicates items bought by a final user. T, on the other hand, includes not only the set of final goods and services Y but also all spending on second hand goods, stocks and bonds, existing homes, transfer payments, and more. Whereas GDP measures final goods in order to avoid double counting, T measures final and intermediate goods, thus counting the same good twice, thrice, or even more if the good changes hands more often than that.

A good illustration of the difference in size between Y and T is to chart them. The total yearly value of Fedwire transactions, which are about as good a measure of PT that we have (but by no means perfect), exceeds nominal GDP (or PY) by a factor of 40 or so, as the chart below shows. Specifically, nominal GDP came in at $17 trillion or so in 2013 whereas the total value of Fedwire transactions clocked in at $713 trillion.

So why do we focus these days on PY and not Fisher's PT? We can find some clues by progressing a little further through the history of economic thought to John Keynes (is it a travesty to omit his middle name?). In his Treatise on Money, Keynes was unimpressed with Fisher's cash transactions standard, as he referred to it, because PT failed to capture the most important human activities:

Human effort and human consumption are the ultimate matters from which alone economic transactions are capable of deriving any significant; and all other forms of expenditure only acquire importance from their having some relationship, sooner or later, to the efforts of producers or to the expenditure of consumers.

Keynes proposed to "break away from the traditional method" of tabulating the total quantity of money "irrespective of the purposes on which it was employed" and focus instead on the narrow range of trade in current consumption and investment output. Keynes's PY measure (the actual variables he chose was PO where O is current output) would be a "more powerful instrument of analysis than their predecessor, when we are considering what kind of monetary and business events will produce what kind of consequences."

And later down the line, Milton Friedman, who renewed the quantity theory tradition in the 1950s and 60s, had this to say about the shift from PT to PY:

Despite the large amount of empirical work done on the transactions equations, notably by Irving Fisher and Carl Snyder ( Fisher 1911 pp 280-318, Fisher 1919, Snyder 1934), the ambiguity of the concept of "transactions" and the "general price level", particularly those arising from the mixture of current and capital transactions—were never satisfactorily resolved. The more recent development of national income accounting has stressed income transactions rather than gross transactions and has explicitly and satisfactorily dealt with the conceptual and statistical problems of distinguishing between changes in prices and changes in quantities. As a result, the quantity theory has more recently tended to be expressed in terms of income rather than of transactions

So there are  evidently problems with PT, but what are the advantages? Assuming we use Fedwire transactions as the proxy for PT (and again, Fedwire is by no means a perfect measure of T, as I'll go on to show later) the data is immediate and unambiguous. It doesn't require hordes of government statisticians to laboriously compile, recompile, and check, but arises from the regular functioning of Fedwire payments mechanism. There are no revisions to the data after the fact. And rather than being limited to periods of time of a month or a quarter, there's no reason we couldn't see Fedwire data on a weekly, daily, or even real time level of granularity if the Fed chose to publish it.

Even Keynes granted the advantages of PT data when he wrote that the "figures are available promptly without the necessity for any special calculation." In Volume II of his Treatise, he took U.S. "bank clearings" data (presumably Fedwire data), and tried to remove those transactions arising from financial activity by excluding New York City, the nation's chief financial centre, thus arriving at a measure of final spending that came closer to PY.

What are the other advantages of PT? While PT counts second-hand and existing sales, might that not be a good thing? Nick Rowe, writing in favour of PT, once made the point that it's "not just new stuff that is harder to sell in a recession; it's old stuff too. New cars and old cars. New houses and old houses. New paintings and old paintings. New furniture and antique furniture. New machine tools and old machine tools. New land and old land." As for the inclusion of financial transactions, anyone who thinks asset price inflation or deflation is an important property of the economy (Austrians and Austrian fellow travelers no doubt) may prefer PT over PY since the latter is mute on the subject.

I'd be interested to hear in the comments the relative merits and demerits of PY and PT. Why don't the CNBC talking heads ever mention Fedwire, whereas they can spend hours debating GDP? Why target nominal GDP, or PY, when we can target PT?

For now, let's explore the Fedwire data a bit more. In the figure below I've charted the total value of Fedwire transactions (PT) for each quarter going back to 1992. I've overlaid nominal GDP (PY) on top of that and set the initial value of each to 100 for the sake of comparison.

It's evident that the relative value of Fedwire transactions has been growing faster than nominal GDP. However, the financial crisis put a far bigger dent in PT than it did PY. Only in the last two quarters has PT been able to break to new levels whereas nominal GDP surpassed its 2008 peak by the second quarter of 2010. Is the financial sector dragging down PT? Or maybe people are spending less on used goods and/or existing homes?

Fedwire data is further split into price and quantity data. Below I've plotted the number of transactions, or T, completed on Fedwire each quarter. On top of that I've overlaid real GDP, or Y. The initial value of real GDP has been set to 16.6 million, or the number of transactions completed on Fedwire in 1992.

After growing at a relatively fast rate until 2007, the number of transactions T being carried out on Fedwire continues to stagnate below peak levels. In fact, last quarter represented the lowest number of transactions since the first quarter of 2012, a decline that coincided with the atrocious first quarter GDP numbers.

Finally, below I've plotted the average value of Fedwire transfer by quarter. On top of that I've overlaid the GDP deflator. To make comparison easier, I've taken the liberty of setting the initial value of the deflator at the 1992 opening value for Fedwire transaction size.

As the chart shows, the average size of Fedwire transfers really took off in 2007, peaked in late 2008 then stagnated until 2013, and has since re-accelerated upwards. In fact, we can attribute the entire rise in the quarterly value of transactions on Fedwire (the second chart) to the growth in transaction size, not the quantity of transactions. Fedwire data is telling us that inflation of the PT sort has finally reemerged.

A few technical notes on the Fedwire data before signing off. As I've already mentioned, Fedwire provides a less-than complete measure of PT. To begin with, it doesn't include cash transactions (GDP does, or at least those that have been reported). This gap arises for the obvious reason that cash transactions aren't conducted over Fedwire. Nor do cheque transactions appear on Fedwire, or at least they do so only indirectly. Check payments are netted against each other and canceled, with only the final amounts owed being settled between banks via Fedwire, these settlements representing just a tiny fraction of the total value of payments that have been conducted by check over any period of time.

The same goes for securities transactions. Fedwire data underestimates the true amount of financial transactions because trades are usually netted against each other by an exchange's clearing house prior to final settlement via Fedwire. The transfer of reserves that enables the system to settle represents a small percent of the total value of trades that have actually occurred.

Another limitation is that Fedwire data doesn't include wire payments that occur on competing payment systems. Fedwire isn't a monopoly, after all, and competes with CHIPS. I believe that once all CHIPS payments have been cleared, final settlement occurs via a transfer of reserves on Fedwire, but this final transfer is a fraction of the size of total CHIPS payments. And finally, payments that occur between customers of the same bank are not represented in the Fedwire data. This is because these sorts of payments can be conducted by a transfer of book entries on the bank's own balance sheet rather than requiring a transfer of reserves.

I'm sure I'm missing other reasons for why Fedwire data undershoots PT, feel free to point them out in the comments. Do Fedwire's limitations cripple its value as an indicator PT? I think there's still some value in looking at these numbers, as long as we're aware of how they might come up short.

Some links:
1. Canadian Large Value Transfer System Data, the Canadian equivalent to Fedwire
2. A paper exploring UK CHAPS data,the British equivalent to Fedwire: Income and Transactions Velocities in the UK

* 'Real time' means that payments are immediate and not subject to delay, while 'gross settlement' indicates that payments are not grouped together for processing but submitted individually upon being entered. Fedwire gets its name from the beginning of the last century, when payments were carried out over the wires, or the telegraph system. 

To recapitulate...

I'm going on holiday and don't have enough time to write anything new. At the risk of being repetitive, here's a recapitulation of what is one of this blog's major themes: the idea of moneyness. Most of the component parts are spread out over a couple of dozen posts written over many months—here I'll try and piece the whole quilt together in one spot.

Money vs moneyness

The initial point comes from one of my first posts (as well as a later one). There are two ways of thinking about monetary phenomena. The standard way is to draw a line between all things in an economy that are "money" and all those things which are not. Deposits typically go in the money bin, widgets go in the non-money bin, dollar bills go in the money bin, labour goes in the non-money bin and so forth.

The second approach, the one this blog takes, begins with the idea that all things in an economy are money-like. The line we are interested in here is the extent to which the value of each thing is determined by its money-like qualities, or its moneyness, versus the degree to which its value is determined by its non-money like qualities, say its ability to be consumed. We might say that deposits have more moneyness than labour, and labour is more money-like than a second-hand speedo and so forth.

(This second approach isn't without precedent, see Keynes, Hayek, and Friedman.)

Why is moneyness a valuable attribute?

It's all in this post, but here's a quick recap. The greater an item's degree of moneyness, the easier it is for its owner to mobilize that item in trade should some unanticipated eventuality arise. This quality of being easily liquidated provides the owner of that asset with a flow of uncertainty-alleviating services over time, or insurance.

Because moneyness, like insurance, is a valuable property, people must choose on the margin whether to sacrifice moneyness for either consumption or interest. In deciding whether to trade an item with high moneyness for a consumption good with low moneyness, an individual must weigh the present value of the flow of uncertainty-shielding services provided by the former against the one-time zing provided by the latter. In considering a potential exchange between an item with high moneyness and an illiquid interest-yielding asset, the tradeoff is between uncertainty-shielding services and an ongoing pecuniary return.

The supply of moneyness

Moneyness is a valuable good, but it also must be produced at a cost.

Certain characteristics of a good allow it to become more money-like, including durability, verifiability, fungibility, and portability. Network effects may promote an item's degree of moneyness.

The moneyness of an object can be improved by manufacturing these characteristics. Gold, for instance, is rendered more money-like by incurring coinage costs in order to promote verifiability. Adding copper to a gold coin increases its durability. Network effects can be harnessed through marketing. As long as the expected returns of boosting an object's moneyness are higher than the costs, liquidity providers will happily bear the costs.

Whereas only banks and central banks create money, the cast of characteristics involved in supplying moneyness is quite varied. Investor relations teams manufacture it as do hedge fund managers like Cliff Asness and roll-ups like Valeant Pharmaceuticals.

Difficulties in measuring moneyness

It's all here. To summarize, people often use bid-ask spreads and the frequency distributions of various assets in trade as a way to measure an asset's moneyness. But this comes up short. Bid-ask spreads and frequency distributions are objective measures of liquidity. We want to know the price that the market ascribes to things like tight bid ask spreads, not the bid ask spread itself. Moneyness, like value, is a subjective quality, not an objective one.

The other problem is that the value of a good is usually derived from not only its moneyness, but also its 1) consumability and 2) its ability to yield pecuniary returns (like interest and capital gains). Stripping out the moneyness component from these others poses some thorny problems.

Here's how to do it

As I pointed out in this post, the trick is to poll people about how much they expect to be compensated if they are to forgo the ability to sell an asset for some a period of time, say one year, while still enjoying the pecuniary and consumption yields provided by that asset. The question goes something like this:

"How much would I have to pay you in order for you to relinquish all rights to trade away your holdings of asset x for one year?"

The price that an individual lists represents the value they ascribe to that asset's moneyness stripped of its other valuable attributes. It represents how much value they put on that asset's foregone bid-ask spread and other objective liquidity data.

On a larger scale, we want to create a moneyness market

The previous paragraph solves for each individual's assessment of moneyness, but we want to know the value that the market as a whole ascribes to a given asset's moneyness. In this post, I imagined what these markets would look like. We'd want to create a financial product that requires investors to set a price on how much they need to be paid if they are to relinquish the right to trade away asset x for a period of time. Buyers and sellers of these rights would establish a market price for the moneyness of all sorts of assets.

A few practical uses of moneyness and moneyness markets

Right now, equity analysts include an equity's moneyness in their valuation metrics, which is a big mistake. I go into this in plenty of detail here and here. If an analyst wants to accurately value an equity's price relative to its earnings, they need to have a measure of moneyness. That way they can strip out that part of an equity's price that is due to its moneyness and compare the non-monetary residual to earnings. A moneyness market would provide them with the missing data.

To properly value bonds and housing, we should probably do the same. See here and here.

And as I wrote here, financial assets like stocks are 2-in-1 deals meaning that you've got to buy an asset's moneyness along with its pecuniary return. Investors may prefer to have the one without the other. A moneyness market allows investors to split off and sell (or buy) each component separately, resulting in a more optimal allocation of moneyness and pecuniary returns.

Moneyness and monetary policy

Monetary policy is more of a sideline, but here are a few posts on the subject. A central bank issues liabilities with a high degree of moneyness. By increasing the quantity of outstanding liabilities, a central bank can reduce the marginal value that people are willing to pay for that moneyness, thereby lowering the purchasing power of central bank liabilities and increasing the price level. By tightening the supply of liabilities, it increases their marginal value, boosting their purchasing power and lowering the price level.

So in short, a central bank manipulates the moneyness of its own liabilities.

However, once it reduces the moneyness of its liabilities to zero across all time frames, a central bank can't create more inflation. This is the zero-lower bound from a moneyness perspective, which I go into here.

And in the future

I'm hoping to write a few posts on liquidity crisis and moneyness markets, and how moneyness markets can displace central banks as lenders of last resort (or at the very least help central banks improve).

It was the best of times, it was the worst of times

You may know by now that the final revision of U.S. first quarter GDP revealed a shocking 2.9% decline while its mirror image, gross domestic income (GDI), was off by 2.6%.

As Scott Sumner has pointed out twice now, the huge decline in GDI is almost entirely due to a fall in corporate profits. Whereas employee compensation, the largest contributor to GDI, rose from $8.97 to $9.04 trillion between the fourth quarter of 2013 and the first quarter of 2014, corporate profits fell from $2.17 to $1.96 trillion (see blue line in the above chart) This incredible $198 billion loss represents a 36% annualized rate of decline!

A number of commentators have pointed out the difficulty in squaring this data bloodbath with reality. After all, Wall Street has not been announcing 36% quarter on quarter profit declines. Rather, earnings per share growth has been pretty decent so far this year. If earnings were off by so much, then why are equity markets at record highs? Why have there been no layoffs? It's hard to believe that a bomb has gone off when there's no smoke and debris. Investors are patting themselves down to make sure they had no wounds or broken body parts and, coming up clean, are shrugging and buying more stocks.

I'm going to argue that the odd disjunction between the numbers and reality may have arisen due to something called money illusion. We live in a historical-cost accounting world in which stale prices are used as the basis for much of our profit and loss calculations. But the gunshot rang out in a different universe, one in which accountants rapidly mark costs to market. At some point we in the historical-cost world will feel the repercussions of the gunshot since everything is eventually marked to market. For now, however, no one seems to have noticed because we're all caught up in an the illusion created by accountants focused on the ghost of prices past.

More specifically, the folks at the Bureau of Economic Analysis who compile GDI report a different corporate profit number than the profit numbers being bandied around on Wall Street during earnings season. Wall Street profits are by and large paid out after depreciation expenses, and these have been accounted for on a historical-cost basis. This is the red line in the above chart. The BEA's number, represented by the blue line in the chart above, represents the profits that remain after depreciation expenses have been marked to market. The choice between mark-to-market depreciation accounting and historical-cost accounting can result in large differences in bottom-line profit, as the last data point in the chart illustrates.

For instance, consider a manufacturing company that earns revenues of $100 per year from a machine that it bought for $600. It depreciates the machine by $60 each year over 10 years, earning a steady $40 in profits ($100 - $60). Now imagine that all over the world machines of this type are suddenly sabotaged so that, due to their rarity, the cost of repurchasing a replica doubles to $1200. If the manufacturing company uses historical cost deprecation, it will continue to bring in revenues of $100 a year, deducting the same $60 in depreciation to show $40 in earnings. All is fine in the world. But if the firm uses mark-to-market depreciation, the cost of using up the machine will now reflect the true cost of replacing it: $120 a year ($1200/10 years). Subtracting $120 from the annual $100 in revenues means the company is losing $20 a year, hardly a sign of health.

It's easy to work out an example that shows the opposite, how a glut in machinery supply (which would drive the replacement cost of the machine down) is quickly reflected in a dramatic improvement in earnings after mark-to-market depreciation expenses, but earnings after historical-cost depreciation show nothing out of the ordinary.

Thus we can have one profit number that tells us that all is fine and dandy, and another that indicates the patient is on death's door. An individual's perception of the situation depends on which universe they live in, the historical cost universe or the mark-to-market one. The GDI explosion has gone off in the latter (the BEA uses a mark-to-market methodology), but since we experience only the former (the Wall Street earnings parade is entirely a celebration of historical-cost earnings per share data) we haven't really felt it... yet.

Yet? Even a company that lives in a historical cost accounting universe will eventually have to face the market price music. Imagine our sabotage example again. If our company uses mark-to-market accounting, it will immediately know it is facing a problem since its $100 revenue stream is failing to offset the $120 cost of machinery depreciation. However, if it uses historical cost accounting then our company continues to enjoy what it perceives to be a revenue stream that more than offsets its historically-fixed $40 cost of machinery. However, once that machine inevitably breaks down and needs to be replaced with a $1200 machine, a new historical cost base will be established and depreciation will suddenly rise to $120. Several quarters too late the company will realize that it is now operating in the red. Had it marked deprecation to market, that realization would have come much sooner.

If I had to speculate, here's a more detailed story about the last quarter. US corporate revenues were particularly underwhelming between Q4 2013 and Q1 2014 due to the cold weather. At the same time, we know that a number of government stimulus acts that had introduced higher than normal historical cost depreciation allowances (this allows firms to protect their income from taxes) were rolling off. Flattish revenues were therefore offset by smaller deprecation costs, resulting in a decent bump to headline earnings numbers, as the red line in the chart shows. Everything looked great to majority of us who inhabit the historical cost accounting universe.

However, mark-to-market depreciation accounting used by the BEA strips out the effect of the expiring depreciation allowances, thereby removing the bump. The combination of flattish revenues and higher market-based depreciation expenses (perhaps due to some inflation in the cost of capital goods) would have conspired to create a fall in the blue earnings series, and therefore a groaningly bad quarter in our mark-to-market universe.

In any case, the crux of the issue is that Wall Street's headline numbers indicate that corporate America did a better job in the first quarter of 2014 generating the cash necessary to replace worn out capital than it did in Q4 of 2013. The BEA numbers are telling us the opposite, that corporate America did a poorer job of covering the costs of wear & tear. Neither of the two numbers is wrong per se, but as I've already point out in my example, mark-to-market methodology is the first to reveal problems while historical cost accounting will follow after a lag.

As I've already hinted, the fact that Wall Street hasn't yet noticed that it just lived through a miserable quarter can be attributed to money illusion: a phenomenon whereby people focus on nominal rather than real values. In this specific instance, investors are so obsessed with headline changes in earnings that they fail to adjust that number for the true cost of using up machinery. Irving Fisher himself described a version of this mistake in his book The Money Illusion:

...during inflation the cost of raw materials and other costs seem to be lower than they really are. When the costs were incurred the dollar was worth more than it is later when the product is sold, so that the dollars in the original cost and the dollars in the later sale are not the same dollars. The manufacturer is deceived just as was the German shopkeeper or the Austrian paper manufacturers who thought they were making profits.

How likely is it that Wall Street, full of so many bright individuals, is being fooled by money illusion? It's not inconceivable. Even Scott Sumner volunteers that he doesn't believe the BEA's numbers due to soaring stock prices and strong earnings, thus falling prey to that very same affliction that serves as his blog's namesake. Money illusion can happen to the best of us.

The monetary economics of the roll-up

The so-called corporate "roll up" lies at the conjunction of finance and monetary economics. For those monetary economists who aren't familiar with the term, a roll-up is a company that tries to consolidate an entire industry by serially acquiring competitors, usually using its own stock as currency. Valeant Pharmaceuticals, currently in the midst of a battle to take over botox-maker Allergan for $53 billion, is one of the more well-known roll-ups in the world of finance these days, having acquired around 75 companies in the specialty pharmaceutical niche over the last six years. But there have been many others over the years who have pursued the roll-up strategy.

Plenty of analysts dislike the corporate roll-up. They criticize it for not creating value organically but merely accumulating other people's castaway businesses. Roll-up equity is generally viewed as ridiculously overvalued and destined to implode. Valeant, for instance, has been variously described as a house of cards, Kool Aid, and something from the Wizard of Oz.

I'm going to argue in this post that a roll-up is less nefarious than some people think. A roll-up does the same thing that a bank does—it is a liquidity provider. In the same way that a bank expects to be compensated for turning the illiquid into the liquid, a roll up deserves to be paid a fee for doing the same. Like banks, roll-ups are monetary phenomena.

Let's build a roll-up from scratch. Our roll-up begins its life as a regular business, say a fishing store. Like all other fishing stores in the area, the store yields its owner, Bob, about $10 a year. Fishing stores generally distribute all their earnings to their owners so that nothing is retained in the business. A store can generally be bought and sold for around 5 times earnings, or $50 ($10/year x 5), although due to their illiquidity it may take a lot of time and effort to match buyers of fishing stores with sellers.

Bob's first task is to make the ownership position in his store more liquid. He decides to divide his $50 stake into 100 shares, each worth 50 cents, thus rendering it easier for people to purchase bite-sized positions in his business rather than being required to gulp the thing whole. He hires a store manager to take care of day-to-day business, buys himself an Armani suit, and begins to canvas the land marketing his shares. He may even take the time and effort to list on a public stock exchange.

Eventually, shares in Bob's store will have attracted a large crowd of buyers and sellers. Whereas all the other fishing stores in the area remain relative illiquid, an ownership stake in Bob's store has become more moneylike. A liquidity premium attaches to the value of the shares. Each of the 100 shares is now priced at 75 cents which puts a $75 valuation on Bob's business ($0.75 x 100 shares), twenty-five bucks higher than the $50 price tag that was originally placed on Bob's store and is currently being placed on competing fishing stores. Since Bob's store continues to earn the same $10 a year that other stores make, the twenty-five buck premium is entirely related to the superior ease that owners of Bob's business enjoy in transacting with their shares. Both Bob's Armani and his hard work have paid off.

Here's another way of looking at the scenario. Whereas all fishing stores trade at around 5 times earnings, Bob's shares trade at 7.5 times earnings due to their superior liquidity.

Bob now embarks on the next stage of executing his roll-up strategy—issuing new stock to buy up his competition. He begins by printing up 66.6667 new shares and offers to buy Joe's fishing store down the street for a total value of $50 (66.6667 shares x $0.75/share) . This is where the magic of the roll up strategy begins. If Joe accepts, Bob will now have two stores earning a combined $20, each share earning $0.12 ($20 / 166.667 shares). Notice that this is an improvement over the $0.10 per share being earned prior to the deal with Joe ($10/100 shares). Since the market continues to value Bob's shares at 7.5x earnings due to their excellent liquidity, each share will now trade for 90 cents (7.5 x $0.12 earnings per share), higher than their pre-purchase price of 75 cents (7.5 x $0.10). Thus Bob's shareholders enjoy an immediate 15 cent pop in the share price once Joe's store is bought! Not bad for a day's work. This is what is called an accretive acquisition.

Intuitively what is happening here is that Joe's illiquid ownership rights are being brought under Bob's umbrella. They are immediately rendered just as liquid as Bob's ownership position, and since liquidity is a service that the market is willing to pay a premium for, Joe's ownership rights will now be worth more than before.

It makes sense for Bob and his shareholders to push for the deal with Joe since they enjoy an immediate gain. But what about Joe? Why would he agree to the deal? Consider that before the agreement was struck, Joe was comfortably earning $10 a year selling rods and hooks. After the transaction is over, he'll own 66.6667 shares of Bob's business, each share yielding $0.12 in earnings, for a total of just $8 a year vs $10 before. So if he signs on the dotted line, he'll be earning $2 less each year. A terrible deal for Joe, right?

Not necessarily. The reason Joe may very well take the deal despite earning less finds an answer in Carl Menger. For finance types, Menger was a 19th century economist who pretty much nailed down the idea of liquidity, or what he preferred to call marketability, the fact that "different goods cannot be exchanged for each other with equal facility." Menger gives the example of a black smith who, when going to market with his newly made armour, has difficulties locating someone willing to trade food and fuel. Rather than seeking to directly trade, it is in the smith's interest to take an indirect route by accumulating some good that though useless to him, has greater marketability than the armour he has produced. In this way, the smith gives up his less saleable commodity for others of greater marketability since "possession of these more saleable goods clearly multiplies his chances of finding persons on the market who will offer to sell him the goods that he needs."

Returning to our story, let's say that Joe is tired of working and wants to retire so that he can travel around the world. Travel will require cash, but Joe's business isn't very easy to sell. In a strategy that Menger would approve of, Joe may choose to give up his shares in exchange for other, more saleable, shares, even if he doesn't not need them, because it brings him closer to the final position he desires. So while Joe doesn't get cash when he signs the bottom line, he does get the next best thing, Bob's liquid shares, which are far easier to turn into cash than his own. The amount that Bob asks as a fee for superior liquidity is the forfeiture of $2 a year in potential earnings, hardly a large price for Joe to stump up if he is desperate for a getaway from the fishing industry.

After gobbling up Joe's store, Bob continues rolling up the fishing store industry by constantly printing up new shares to buy out folks like Joe who want an exit. Bob and his merry band of shareholders are content to fabricate this desired liquidity as long as they get a portion of each exiting store owners' earnings and the ensuing boost to the share price. The Joe's of the world are happy to give up a bit of earnings to Bob for a bit of his liquidity.

This is exactly what a bank does. Just like Bob buys up illiquid ownership positions in fishing stores, banks buy up illiquid IOUs that have been issued by individuals and businesses. Where Bob issued new shares in exchange, a bank offers a different sort of financial asset; the bank's own highly-liquid IOUs, or deposits. Bankers don't engage in liquidity creation for free. In the same way that Bob requires that Joe give up some earnings in return for the liquidity benefit of Bob's shares, bankers require that the person who initially receives the bank's deposits pays an ongoing fee to enjoy the benefits of their superior liquidity, a fee that is otherwise known as interest. The only difference between a banker and Bob is that one is using debt, or bank deposits, as their liquidity carrot, while the other is using equity.

Banks spend large amounts of capital to ensure the superior liquidity of their deposits. Branch networks, ATMs, card payment infrastructure, and secure internet systems must all be built and maintained. Should a bank's deposits lose their liquidity advantage, the benefit of owning those deposits will diminish to the point that no one will willingly pay a fee to purchase them. Individuals will costlessly convert their illiquid deposits into liquid deposits of competitors (banks typically offer free 1:1 conversion among each others deposit brands). If this continues indefinitely, the bank will eventually go bankrupt.

Bob too faces these same sorts of limitations. His roll-up strategy can only continue as long as his shares are more liquid than those of his universe of targets. Once they are no longer special, folks like Joe won't see it worthwhile to forfeit a bit of their earnings to Bob for his shares. Put differently, Bob can continue rolling-up fishing stores only as long as the multiple that the market is willing to pay for his earnings remain significantly elevated relative to those stores that he wants to buy.

Like banking, rolling-up an industry requires continued investment in the mechanisms that promote share liquidity. Bob must buy ever fancier suits, travel ever further afield to advertise the quality of his shares, and list on more stock markets. One of the threats he must constantly face is that of competing roll-ups who also spend to promote the liquidity of their own shares. If the cost of suits is driven too high by the roll-up competition, it may no longer be profitable for Bob to maintain his shares' liquidity.

Roll-ups will also compete for acquisition opportunities. When folks like Joe who want to exit the fishing business receive multiple bids from roll-ups like Bob interested in buying him out, Joe can play Bob off against his competition so that Bob must sell Joe liquidity for less than he would otherwise prefer, perhaps below his cost of creating that liquidity.

When competition among roll-ups creates too much liquidity then investors will start to cut the liquidity premium that they attach to Bob's shares. Bob's acquisition targets will no longer be willing to forfeit as large a piece of their earnings to Bob as they once did in order to enjoy the liquidity of which he was once the only provider. As a result, acquisitions provide ever small returns, the immediate increase in per share earnings and the good old jump in the share price that Bob once enjoyed is increasingly a thing of this past . At some point, it makes no sense for Bob to continue his roll-up strategy. His business will have lost its banking function and now operates like any other fishing store chain—it grows in line with population growth and the market's desire for fishing products.

If investors had been pricing Bob's shares on the assumption of further growth in its banking function, upon the realization that acquisitions are no longer worthwhile they will all sell in earnest, a large decline in Bob's share price being the result. The roll-up game is officially over, as are Bob's days as a banker.

But let's say that Bob successfully guards the liquidity premium that his shares have always enjoyed against the competition. At some point he'll run up against another limitation; there are only so many fishing stores he can buy. Once he has purchased every shop around him, he runs out of accretive acquisitions and the banking function he once profited from suddenly comes to an end.

If he wants to continue his roll-up strategy, one option is for Bob to expand into another line of business, say gun shops. But here he faces a disadvantage in the fact that he has no natural talent in appraising hunting stores. Where his knowledge of the fishing store industry insured him against buying lemons, the odds of him making mistakes as he rolls-up this new industry increases. This risk isn't unique to Bob. A banker who specializes in construction loans faces this same risk when he or she expands into consumer lending, or auto loans. Just like an accumulation of bad loans may cause a run on a bank, bad gun store purchases may cause a run on Bob's shares. The value of both deposits and shares as media of exchange is jeopardized when the underlying assets are in doubt.

So to wrap this up (roll it up?), there's nothing mysterious or nefarious about roll-ups. They are merely entities that provide banking services to the industries in which they operate, namely swapping illiquid assets for liquid ones. They earn a return for producing liquidity in the form of an accretive earnings bump on each acquisition. Once they reach certain natural limits, a roll-up will cease providing banking services to the industry and return to being a normal company.

The larger point I'm trying to make, however, is that there are monetary phenomena at play in all sorts of  situations that don't involve money proper. Monetary economists, those folks who study monetary phenomena, focus laser-like on a narrow range of goods they consider to be money, usually central bank notes and private deposits, thus excluding all other objects from the study of monetary phenomena. This is too bad. When we allow ourselves to think of money not as an either/or proposition but as an adjective that applies more or less to all valuable goods, then you'll see fascinating monetary phenomena all around you, such as the corporate roll-up.

When the good drives out the bad

There's a fairly regular monetary phenomenon that needs a name. It's similar in nature to Gresham's law, yet the inverse version.

Gresham's law is commonly stated as the phenomena by which "bad money drives out the good". But as any economist will tell you, that's not quite it. Bad money chases out the good, but only if authorities have chosen to enforce a fixed exchange rate between the two moneys. When the market ratio diverges from the fixed ratio, the undervalued money—the "good" one—will disappear from circulation while the overvalued money —the bad one—will become the exchange medium of choice. Bad money drives out good money because they pass by law at the same fixed price.

That's the classic Gresham's law. However, it's possible to show how an authority can set a fixed price between two moneys yet rather than the bad coin chasing out the good, the opposite happens: the good coin chases out the bad.

Before I show how, let's first give an example of Gresham's law. Say that new full-bodied silver coins and debased silver coins with the same face value circulate concurrently. If authorities set a law requiring that all coins must be accepted by the populace at face value, buyers and debtors will only settle their bills in debased silver coin (the "bad" money). Full-bodied coins (the "good" money) will be held back as hoarders clip off a bit of each coin's silver content, converting the entire full-bodied coinage into debased coinage. After all, why spend x ounces of silver on goods when a smaller amount will suffice? Thus the bad chases out the good.

Now let's vary our example to have good money chase out the bad. Say authorities promise two-way conversion between all silver coins at face value. Everyone will bring debased silver coins, the "bad" money, to the authorities for conversion into full bodied coins, the "good" money. In essence, they are bringing in x ounces of silver and leaving with x + y silver. This will continue until every bad coin has been deposited into the authority's vaults so that only the good money circulates.

So why in the first case does bad silver coin chase out good yet in the second good chases out bad?

When coins circulate at face value while their true market price differs, a mispricing is created. Any mispricing provides an arbitrage opportunity. In our first example, the arbitrage is such that all those holding full-bodied coin can take a full-bodied coin, file off some silver, and purchase the same amount of goods as before with the now debased coin, all the while keeping the silver clippings to themselves. A different sort of arbitrage opportunity arises in our second example. Because the authorities offer a two-way conversion feature, everyone holding debased coins gets to enjoy a risk-free return by bringing those coins in for conversion into full-bodied coins. They get more silver with less.

So the way that the arbitrage opportunity is structured will either incentivize the population to switch to bad money or to good. We get Gresham's law if people switch en masse to bad coins, and we get an inverse-Gresham effect if they take advantage of conversion and switch en masse to good coins. Since I'm not feeling especially creative, I'll call this effect Mahserg's law (Gresham spelt backwards).

My favorite modern example of Gresham's law is the proliferation of credit cards. In the same way that an owner of a full bodied coin could clip a bit of "bonus" silver off the coin while still being guaranteed the same purchasing power, payment with a credit card allows its owner to maintain their purchasing power while getting rewards to boot.

There are a few modern examples of Masherg's law. In 1978 U.S. authorities created a situation in which two different exchange media with the same denomination circulated concurrently, the Susan B. Anthony dollar and the good old $1 US bill. Because it was novel and untrusted, the Susan B. Anthony was considered to be "bad" money. The dollar bill, which enjoyed network externalities that had been established over a century of use, was the "good" money. The Federal Reserve offered two-way conversion between coin and paper. The inevitable result was that whatever Susan B. Anthony dollars were emitted into the economy were quickly brought back to the Fed to be converted into paper dollars. The good money drove out the bad. To this day Susan B. Anthony dollars are nowhere to be seen.

Another example of Masherg's law is a good old bank run. Take the intra-Eurosystem bank run that began after the credit crisis. There exist many different brands of euros, some issued by Germany, some by Greece. As a condition of membership in the Eurosystem, all nations are required to accept each other's euros at par. With the spectre of euro breakup growing in 2010 and 2011, Greek euros came to be viewed as inferior to German euros. Since it was possible to convert the bad into the good at par, everyone leaped at the opportunity. The quantity of bad Greek euros rapidly contracted while the quantity of good German euros grew, a process that would have eventually resulted in the complete extinction of Greek euros if Mario Draghi hadn't stepped in to short-circuit the run.

My favorite modern example of Masherg's law is the zero-lower bound. A central bank issues two media, dollar bills and dollar deposits. It allows free conversion between the two at par. Say that the central bank reduces the interest rate it pays on reserves to a negative rate so that reserves are inferior, or "bad", relative to 0%-yielding bills, which are now good. Anxious to avoid the negative rate penalty, everyone will race to convert their reserves into cash at the central bank until reserves no longer exist. The good has chased out the bad.

The zero-lower bound can be thought of as the lowest rate that a central bank can institute before setting off Masherg's law. Modern central banks are petrified of encountering this particular law—that's one reason that they aim for a positive inflation target

And what about Gresham? Say our central bank reduces rates below zero. If the central bank ceases allowing convertibility between dollar notes and deposits but continues to require merchants to accept the two media at par, then the incentives change such that the good no longer chases out the bad. With no conversion outlet for bad currency, people will hoard notes while only deposits will circulate. After all, why use good cash to pay for groceries when a negative yielding deposit will suffice? We're back at Gresham's law, or the chasing out of the good by the bad.

Why loonies circulate but Susan B. Anthony dollars don't

What causes a new currency to survive while others fail? Why do some cryptocoins never see the light of day while others enjoy successful launches? This post explores these questions by looking at the story of the Susan B. Anthony dollar, one of the great modern monetary failures.

Canada came out with a $1 coin in 1987 that remains in circulation to this day. We affectionately refer to it as the loonie as it carries a picture of a loon swimming on its reverse side. (The obverse side of a coin is the one that usually carries a portrait, the reverse side is opposite to the obverse side). The U.S. came out with a $1 coin in 1979, popularly known as the Susan B. Anthony dollar due to the appearance of the social reformer's face on the obverse side of the coin. Oddly, to this day the Susan B. Anthony is nowhere in sight. Americans don't hold it in their wallets or purses, nor do retailers keep them in their tills for change. Why did one monetary experiment fail and the other succeed?

The reason for introducing $1 coins is to replace relatively more expensive $1 bills. While notes are cheaper to produce than coins, the upkeep costs of a note issue are far higher than coin, especially as velocity increases. In general, higher value monetary instruments will circulate at slower velocities than lower value instruments. It makes more sense to use coins at the low-value/high velocity end of the circulation spectrum than bills because coins are both easier to sort and more durable—coins must be replaced every few decades whereas bills deteriorate within a year or two if they are used often. As the price level steadily inflates, what would have once been considered to be a high-value note that circulated only slowly enters the low value/high velocity end of the spectrum. Replacing that note with a durable metallic token makes sense... but that which makes sense isn't always that which succeeds.

One of the more popular reasons the has been put forward for the Susan B. Anthony's failure is that it was too similar to the already existing quarter in shape, size, and colour. This prevented consumers from quickly differentiating between the two coins. The loonie, on the other hand, was gold coloured due its bronze plating as well as having been minted with eleven edges to allow for differentiation when groping in one's pocket or purse. Apart from that, the weight and thickness of the loonie and Susan B. Anthony are almost identical.

I don't buy the argument that insufficient differentiation caused one coin to succeed and the other to fail. In 2000 the U.S. took another shot at debuting a dollar coin with the introduction of the so called "golden dollar" (due to yellowish tint provided by manganese brass), otherwise known as the Sacagawea dollar thanks to the appearance of this Native American interpreter and guide on its obverse.  Despite having the same golden sheen as the loonie, the Sacagawea dollar does not circulate in the U.S. Rather, huge amounts of these coins are held along with their predecessor Susan B. Anthony in the vaults of the Federal Reserve as Fed officials wait in vain for demand to pick up. (See Lotz and Rocheteau for a good explanation of this event). That's two failed monetary experiments and counting.

$1 coins languishing in a vault at the Federal Reserve Bank of Richmond's Baltimore branch
Source: NPR

Could it be that the loonie's eleven edges (the Sacagawea was smooth) were a sufficiently unique feature that the loonie stood out from the quarter and thereby successfully circulated? I don't buy it. That something so cosmetic as the shape of a coin's edge could push it into continued circulation seems silly to me. In all likelihood the Sacagawea dollar would have failed even if it replicated the loonie in every way.

The best explanation for the failure of $1 coins in the U.S. comes from Caskey and St. Laurent (pdf). They point to the network effects that must be overcome in introducing a new monetary instrument:

The benefit an individual attains from the use of a particular currency form depends on how many others are also using that currency form. For example, a new high-denomination coin can increase the range of vending machine transactions open to individuals, but only if vending machine owners convert the machines to accept the coin. Vending machine owners can increase sales from converting their machines to accept the coin, but only if the public commonly carries the coin. Similarly, retailers who learn to distinguish quickly the new coin can make small transaction more rapidly, but only if their customers have also learned to distinguish the coin quickly.

In the presence of these network externalities, anyone who doubts that a new coin will be used by others won't bother spending the time and effort to familiarize themselves with the coin and make the necessary adjustments. If everyone behaves this way, the coin will never get off the ground. We get the unfortunate consequence that even though the substitution of notes by coin makes society better off, a set of perverse self-perpetuating beliefs prevents that solution from ever being selected.

So why did the loonie survive? Caskey and St. Laurent point out that the government stepped in to ensure that the network externalities that would surely have prevented the loonie's success were removed. In 1988, the year after the loonie's debut, the Bank of Canada announced that it would be withdrawing the $1 note from circulation. Consumers and retailers were given no choice but to adapt to the loonie's arrival. U.S. authorities, on the other hand, never tried to dash the existing network effects that favoured the status quo by withdrawing the $1 note. Because $1 bills and coins co-circulated, the public was given a choice between a perceived "good" currency, the existing and comfortable note, and a "bad" currency, an unfamiliar coin. They took the less costly route and stuck with the "good" notes.

Unfortunately this left the U.S. in the worst possible situation. Having failed to arrive at the welfare maximizing solution—the replacement of notes with coins—it was stuck not only with its existing and expensive $1 note circulation but it now had to pay ongoing costs for storing the unwanted coin.

This makes me think about the mad dash to create new cryptocurrencies. I remember a time when there were only five or six of them, but now there are around 313 cryptocoins according to Coin Market Cap. Many of the newer coins that have debuted over the last year are no doubt technically superior to Bitcoin, and the welfare of the universe of cryptocurrency users would surely be improved by the phasing out of bitcoin and the adoption of the best of these new coins. However, as the incumbent, bitcoin enjoys tremendous network effects. The public is already familiar with the various bitcoin wallets and client as well as the markets in which it trades and all the related bitcoin jargon that goes with it. Why bother spending the time and effort to understand a new cryptocoin if there is no guarantee that it will ever be widely accepted? Because everyone thinks this way, the cryptocurrency world has locked itself into an inferior currency structure. While it should be using something like SusanBAnthonyCoin, it still clings to bitcoin.

Or consider the current system. We could make the argument that the world would be better off it stopped using bank deposits, wire transfers, and cash and instead adopted bitcoin due to the latter's superior speed and low cost of maintenance. However, absent the cooperation of a large actor like the U.S. government to overcome the network effects that the existing system enjoys, it is unlikely that the technically superior option will ever be selected. Just like Susan B. Anthony dollars drift around as little more than a curiosity some 34 years after their debut, bitcoin may be no more than a neat curio in 2044 if the network effects that it faces are not overcome.

As for the $1 coin, at some point you can be sure that the U.S. will take its third swing at the bat. Let's hope that when the time comes they won't make the same mistake.

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.

Financial Plumbing: Europe and the Fed's Interdistrict Settlement Account

One of this blog's most recurrently popular posts is a 2012 ditty entitled the Idiot's Guide to the Federal Reserve Interdistrict Settlement Account. The Interdistrict Settlement Account, or ISA, is a highly esoteric "plumbing" mechanism that lies at the centre of the Federal Reserve System. After a century of being ignored, it suddenly became a popular topic for discussion in late 2011 and 2012 as the breakup of the euro became a real possibility. Groping for a fix, European analysts turned to the world's other large monetary union, the U.S. Federal Reserve System, to see how it coped with the sorts of monetary problems that Europe was then experiencing.

Here's a short explanation of the ISA. Consider that there is no such thing as a unified Federal Reserve dollar. Rather, both the paper dollars that you hold in your wallet and the electronic reserves that a private bank holds in its vaults are the liability of one of twelve distinct Federal Reserve district banks. Thanks to the convention among these Reserve banks of accepting each others dollars at par, a 1:1 exchange rate between each of these twelve U.S. dollar brands prevails. This gives rise to the useful mental short cut of assuming that there is one homogeneous dollar brand. But to do so ignores the heterogeneity at the core of the system —we can imagine worlds, for instance, in which one district's dollars, say those of the St Louis Fed, are considered to be so inferior to the rest that the other Reserve banks will only accept "St. Louis's bucks" at a discount.

All inter-district flows between Reserve banks must be settled, which is where the ISA comes into the picture. The ISA is a ledger that tracks the various imbalances that accrue between Federal Reserve banks. Each April that imbalance is settled by a transfer of assets from debtor to creditor Reserve banks, so that if St. Louis is owing and San Francisco is owed, then bonds will flow from the former to the latter, reducing each district's respective ISA balance (or increasing it) to a sufficient level.

I'm happy to say that my ISA post was useful to a number of researchers, including Karl Whelan (pdf), Kevin H. O’Rourke and Alan M. Taylor, and most recently, Alexander Wolman (pdf), who all made reference to it in recent papers. I like to think that this demonstrates the second purpose of the econblogosphere. The first purpose, of course, is to swarm over polished work by those like Piketty and Reinhart/Rogoff searching for chinks in the armour. The second is to act as an advance scout of sorts. When a completely new problem crops up, a blogger can quickly pump out a few posts, establishing a beachhead from which the main army—academics with time, money, and resource—can begin to launch a larger-scale attack.

While scouts can provide useful hints on where to launch initial sorties, they will always make a few errors, and I want to draw attention to one error I made in my ISA post. I speculated that the Federal Reserve banks may not have bothered to settle the ISA in 2011. Given a visual inspection of the various imbalances that had arisen between several of the Reserve banks, it appeared that the Richmond Fed in particular had been allowed to carryover a large deficit while the New York Fed (FRBNY) was stuck with an outstanding credit. Luckily for the small group of folks interested in the ISA, Federal Reserve researcher Alexander Wolman has recently provided some clarity on this issue.

Wolman has written the definite explanation of how the ISA functions and it is well worth your time if you want to discover how this fascinating mechanism works. (In defense of my old Idiot's Guide, note that I did manage to incorporate the destruction of the Death Star scene into it — I doubt Alex's editors would let him get away with that). He also goes through the data to show how the ISA settled in April 2011. I had originally focused on the New York Fed's ISA balance as the basis for my suspicion that settlement may not have occurred—the FRBNY's ISA balance had not fallen by the proper amount over the settlement month. But if you look at the FRBNY's securities balance on its balance sheet, you'll see that it rose by $100-$150 billion, an amount sufficient to settle the debts that other Reserve banks owed it. If you care to explore more deeply, Alex deals with this on page 135 of his article. I'm tickled pink that he managed to "settle" this bit of trivia since it has been a recurring topics on this blog. (See here and here).

I should point out that the 2011 episode interested me because if non-settlement had occurred, then the ISA would impose very weak constraints on payments imbalances arising between the various district Reserve Banks. European analysts, who were looking to the U.S. for inspiration, needed to know whether the ISA imposed stern limits on imbalances or lenient ones.

Like the Fed, the ECB is composed of a number of member banks, or national central banks (NCBs). Each issues their own brand of Euro while accepting all other Euros at par, thereby ensuring a smooth 1:1 exchange between the various Euros. Unlike the Fed, the ECB has no settlement mechanism. Imbalances that arise between member banks can continue growing perpetually. This is what appeared to be happening between 2008 and 2012 as European depositors, wary of a break up the Eurozone, fled the GIIPS banking systems for safe havens like German and Dutch banks, resulting in the emergence of massive deficits and credits between the various member NCBs. The chart below illustrates the size of these imbalances, which have since shrunk.

Source: Euro Crisis Monitor, Osnabrück University

A number of analysts, led by Hans Werner Sinn, felt that a U.S.-style ISA settlement mechanism should be grafted on to the European payments system. In theory, this would impose strict discipline on NCBs and prevent imbalances from emerging. Many, including myself, felt that this sort of discipline might be a bad idea.

But a better rebuttal of the proposed European ISA is that the Federal Reserve ISA was never the stern mechanism that folks like Sinn made it out to be. Though my point about 2011 non-settlement is false, other features of the ISA provide for long settlement delays, including the "rediscounting mechanism" that I mentioned in my Idiot's Guide. However, the best person to learn from on this topic is economic historian Barry Eichengreen who, in the video that I've linked to below, provides a definitive historical overview of the ISA.

While the whole video is worth watching, I'm going to draw attention to a chart that Eichengreen shows at around minute 14-15 which I reproduce below.

Source: Federal Reserve Bulletin, 1922

During 1920 and 1921, large and persistent imbalances between Federal Reserve banks emerged, much like the imbalances that have plagued the Eurosystem since the credit crisis. It would seem that the Fed, just a young pup at the time, faced the very same problem that the ECB began to face just nine years after its debut and, much like the ECB, it chose to handle it by allowing for non-settlement. Eichengreen (and Mehl, Chitu & Richardson) has an upcoming paper that explores the long history of Reserve bank "mutual assistance", although for now you'll have to be content with the video.

The European payment imbalances debate (or Target2 debate) has long since died out. Germany's ever-growing creditor position halted in 2012 and has been shrinking ever since while debtors like Italy, Spain, and Greece have seen their negative positions return towards zero. No one talks about intra-Eurosystem imbalances or Euro breakup anymore, at least not on the blogosphere. But I have no doubt that somewhere in the ECB's deepest catacombs a group of European monetary architects are debating if, how, and when to import an ISA-style settlement mechanism into Europe. Let's hope that they are very careful in their approach and consider the softest possible solution.

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

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

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.