I like to say that everything is money, which is just another way of saying that all goods are liquid to some degree or other. Whether it be a house, a banknote, or ice cream, each of these items carries a liquidity premium. How large are these liquidity premia? It's difficult to get good measurements, but there are a few venues that offer a glimpse of this rare beast. One of them is equity markets. More specifically, we can use restricted stock studies to tease out liquidity premia.

Imagine that your shares in Microsoft, normally so easily exchanged on various stock markets like the New York Stock exchange or NASDAQ, were restricted for a period of time in a way that prevented you from trading them. Apart from this impairment, your illiquid Microsoft shares are exactly like any other Microsoft share: they provide you with a dividend, voting power, and a contingent claim on firm assets should Microsoft decide to wind up the business. The price you'd be willing to pay to own these rather unique shares would reflect their lack of liquidity. Or, put differently, the difference between the price of regular Microsoft shares and restricted Microsoft shares would precisely represent the value that you ascribe to the liquidity of regular Microsoft shares, or their liquidity premium.

Luckily for us, the practice of placing restricted stock, or unregistered stock, with investors provides an opportunity to measure this  difference. When you buy a blue chip stock on the NYSE you're purchasing registered stock—the issuer has registered the original offering of securities with the SEC. This is an expensive and time consuming process involving all sorts of lawyers and fees. If the issuer wishes to avoid these fees, it can choose to forgo registration and issue what are called unregistered shares, as long as the issue is presented to private accredited investors and not to the general public. However, securities law stipulates that investors who receive unregistered stock must accept a number of restrictions, all of which limit the liquidity of unregistered stock. In general, laws proscribe a holding period over which the owner of restricted stock cannot sell in public markets. After the holding period expires, unregistered securities can be sold in public transactions but only by complying with certain “dribble out,” or volume limit, provisions that may impede a stockholder from liquidating a position sufficiently fast. (For instance, an owner of restricted stock might not be able to sell more than x% of the stocks monthly trading volume).

Restricted stock studies measure the difference between the price at which a company has issued restricted stock and the publicly-traded price of that same company's non-restricted, or registered, stock . This difference represents the liquidity premium on the firm's registered stock; the very same liquidity that restricted stock owner forgo.

The chart below provides a partial listing of restricted stock studies and the average discount to market value displayed by restricted stock in each:

Source

The earliest restricted stock studies show a ~30% difference between the price of restricted stock and its publicly-traded equivalent. This implies that the liquidity premium over the combination of the holding period (initially set at two years) and dribbling out period on an average stock amounted to about 30 cents per each dollar of stock. That number doesn't include the value of liquidity after the holding period has expired and dribbling out rules have ceased to have a significant effect; if the entire lifespan of a stock were incorporated, we can imagine that 40-50 cents of each dollar worth of a typical stock might be due to liquidity. That's quite a lot!

As the chart shows, over time studies have found that the measured gap between the price of restricted shares and regular publicly-traded shares has steadily shrunk. This is due in part to changes in SEC rules concerning the sales of restricted shares. Owners of restricted shares initially faced a 2-year holding period, but this was reduced to 1-year in 1997 and then six months in 2008. Non affiliate owners (those who are not insiders and don't own controlling blocks of stock) initially faced an indefinite dribbling out period (ie. volume limitations) but this was reduced to 3 years of volume limitations in 1983, 2 years in 1997, and just six months in 2008. In 1990, something called the “tacking” rule was changed. Prior to this amendment, any sale of unregistered stock, even in privately negotiated transactions, would result in the required holding period restarting, a large inconvenience to the buyer. The 1990 amendment allowed non-affiliate purchasers to “tack” the previous owners’ holding period to their own holding period. Because all of these rule changes improved the liquidity of restricted shares, over time investors have needed less of an inducement to hold restricted stock relative to regular shares—thus the downward trend in average discount size.

Why so many restricted stock studies? In the field of business appraisal, evaluators are often called upon to estimate the values of illiquid assets in estates and divorce proceedings, typically small privately held company shares. One way to go about this is to apply an earnings multiple from a comparable publicly- traded companies trade to the privately held firm's earnings. But this assumes an "as if marketable" value for what is actually a very illiquid asset. A discount for lack of marketability (DLOM) must be applied to correct for this problem. A DLOM is the amount an appraiser deducts from the value of an ownership interest to reflect the relative absence of marketability. It will often be the single largest value adjustment than an appraiser will have to make. The results must be defensible in a court of law, necessitating a well structured argument backed by data. Restricted stock studies offer a way for an appraiser at a reasonable DLOM. Of course, an owner of an asset may want as large a discount as possible, usually for tax reasons. They therefore will be tempted to use a study with the highest discount, perhaps an older study that assumes 2-year holding periods, even though six month holding periods now prevail. The IRS has made efforts to shift the profession to using smaller DLOMs, for obvious reasons.

A major weakness of restricted stock studies is the assumption that the entire price gap between a restricted stock price and its publicly traded counterpart can be traced to the liquidity factor. But this isn't necessarily the case. Companies will often artificially underprice private offerings as a way to pay for services rendered (say to suppliers), to reward insiders, or to curry favor. This is the barter function of stock. We need to separate the portion of a restricted share discount that arises for liquidity reasons from that which arises due to this barter function. One way to do so is to compare the prices at which private offerings of restricted stock are carried out relative to private offerings of regular stock. Since both forms of private stock issuance are equally likely to be used for barter, the barter function can be canceled out, thereby leaving liquidity as the only explanation for the gap between the prices of restricted and non-restricted private stock issues.

Wruck (1989) found that the difference in average discounts between the restricted share offerings in her study and registered share offerings was 17.6%, while the difference in median discounts was 10.4%.  Bajaj et al found that private issues of registered shares were conducted at average discounts of 14.04% to their publicly traded price, while the average discount on placements of unregistered shares were conducted at 28.13% to their public price, 14.09% higher than the average discount on registered placements. This puts stock liquidity premiums at about 10-15 cents on the dollar, far below levels found in other studies.

Nevertheless, the fact that around 10 cents of each $1 worth of Microsoft stock can be attributed to the value that the market ascribes to one or two years of liquidity is still a significant number. And remember that restricted stock studies don't measure the long-term liquidity factor, only the value of liquidity foregone over the holding period and a dribbling out period. If the studies did isolate longer term measures of liquidity, we might find that 15-20 cents of each $1 of Microsoft stock is comprised of liquidity value.

All of this means that a share of Microsoft isn't a mere financial asset—a portion of any Microsoft share is providing its owner with a stream of consumable services, much like one's lawyer or neighborhood policeman or pair of shoes provides a service. If some sort of shock were to reduce the liquidity that Microsoft provides, then everyone would be made worse off. (All the more reason to adopt liquidity-adjusted equity analysis). Of course, all of this applies just as well to other securities like bonds and derivatives. And it also applies to consumer and capital goods, houses, land, and collectibles. Everything carries a degree of liquidity, and if we could compare the price of that asset to some illiquid copy of itself (restricted houses, restricted land, restricted paintings) then we'd have a pretty good idea for how much value the market ascribes to that liquidity.

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Other links worth exploring:

Blogs
Using Illiquidity Premiums on the Risk Free Asset to Measure Illiquidity Discounts by Joshua B. Angell

Papers
Revisiting the Illiquidity Discount for Private Companies by Robert Comment
Determining Discounts for Lack of Marketability: A Companion Guide to The FMV Restricted Stock Study
The Discount for Lack of Marketability by Reilly and Rotkowski
Market Discounts and Shareholder Gains for Placing Equity Privately by Hertzel and Smith (RePEc)

'...the peculiar feature of a money economy is that some commodities are denied a role as potential or actual means of payment. To state the same idea as an aphorism: Money buys goods and goods buy money but in a monetary economy goods do not buy goods. This restriction is - or ought to be - the central theme of the theory of a money economy.' -Robert Clower [A Reconsideration of the Microfoundations of Monetary Theory, 1967]

I started to sell some of my XRP yesterday, and the process of doing so brought to mind Robert Clower's famous quote. Clower's aphorism describes an idealized pure-money economy that exists only in theory. Were we to apply it to the real world, we'd be missing a lot. To begin with, Clower omits "money" for "money" transactions like the XRP trade I'm about to describe.

XRP is the cryptocurrency used to pay transaction fees in the Ripple system. In order to arrive at my end goal of holding Canadian paper, I have to enter into a surprisingly long line of transactions. Which underlines a point I've made before: we don't live in a monetary world characterized by one universal "money". Rather, we target a final state of liquidity appropriate to our goals, and then engage in a series of barter swaps across items with differing liquidity profiles in order to reach our target. Our final resting state may be XRP or bitcoin, it may be a bank deposit, it may be cash, or it might be an item in inventory destined for final sale. To get there requires a long monetary bartering process.

Here is the rather circuitous route I am currently taking in order to convert XRP into Canadian loonies.

Trades:
1. Sell XRP for bitcoin-denominated IOUs issued by Bitstamp. This is a floating exchange rate.
2. Sell bitcoin-denominated Bitstamp IOUs for actual bitcoin. This is at a fixed rate.
3. Sell bitcoin for bitcoin-denominated VirtEx IOUs. Fixed rate. VirtEx is Canada's largest bitcoin exchange.
4. Sell bitcoin-denominated Virtex IOUs for Canadian dollar-denominated Virtex IOUs. Floating rate.
5. Sell Canadian dollar-denominated Virtex IOUs for Canadian dollar-denominated Royal Bank of Canada IOUs. Fixed rate.
6. Sell Royal Bank IOU for loonies & Canadian currency. Fixed rate.

So after six transactions, I'll finally hold Canadian paper money in my wallet. It'll take at least 5 days to execute this chain of transactions, mainly because step 5 takes f.o.r.e.v.e.r. This is the fault of our legacy banking system. The cryptocurrency world, steps 1-4, is blazingfast.

Alternatively I could cut a few steps out:

1. Sell XRP for bitcoin-denominated IOU issued by Bitstamp.com. This is a floating rate.
2. Sell bitcoin-denominated Bitstamp IOU for bitcoin. This is a fixed rate.
3. Go to a local cafe where someone makes a market in bitcoin. Sell my bitcoins directly for cash at a floating rate.

We experience these long barter chains in the non-crypto world as well. When I am paid with a US dollar check (say for $50), I go to my bank and sell the check at par for $50 worth of USD deposits. Then I sell the bank my new USD deposits in return for $55 or so worth of Canadian deposits, depending on what the exchange rate at that moment.

My next monetary barter transaction depends on what I want to do after. If I want to get a haircut, I'll sell the $55 worth of deposits back to the bank for $55 worth of Canadian paper money. After all, my barber only takes cash. If I want to buy stock, say Blackberry, I'll sell my bank deposits for an equivalent amount of deposits at my broker, and then I'll be able to purchase Blackberry.

Behind the scenes, the bank's transaction chain continues. After buying the check from me, it sells it back to the issuing US bank in return for a deposit at the issuer. It then sells the issuer's deposit for central bank reserves/clearing balances. Long chains of monetary barter.

The other problem with Clower's simplification is that goods often do buy goods.

The word for this in a retail setting is barter. In a corporate setting it is countertrade. One example of countertrade are "soft dollar" practices in the financial industry. Fund managers or investment advisers promise to provide brokers with order flow. In return, managers and advisors enjoy various services such as the broker's internal research, third-party research, data, or exclusive access to new deals. Brokers will sometimes pay for the fund manager's rent, computers, electricity bills, or even vacation in return for trade flow. If the brokerage industry had to rely purely on hard dollar rather than soft dollar transactions, the whole industry would collapse (or so some people say).*

In sum, there is no rule that money must buy goods only, or goods money. The world is far more complex than this. Goods are more moneylike than we suppose, and so-called money is isn't a monolithic entity but a heterogeneous set of goods that get bartered for each other along long monetary chains.

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*Just as barter is often used to avoid leaving a paper trail, so are soft dollar trades used in the financial industry. Soft dollar expenses are not included in your mutual fund's management expense ratio (MER). You may think that the fund you own has low expenses, but until you back out soft dollar barter its engaged in you can't be sure. The more a fund manager can stuff into soft dollar, the cheaper his/her MER appears. Read the fine print. 

In his broad account of monetary economics, Nick Rowe points out that most modern economies are closer to being pure monetary exchange economies than pure barter economies. I'll argue that we're about half way between the two poles, although it's impossible to say for sure.

A helpful way to determine whether an economy is barter or monetary is to look at all trades made over a period of time and count the frequency of occurrence of each good in trade. In a pure barter economy, no good will appear more than any other. We'll see a flat, or uniform, distribution of media used in trade. In a pure monetary economy, a single good should appear in all trades. The distribution will be uneven. Nick describes it a bit differently but it's the same idea:

You could make a table, with a list of all the different goods for the columns, and the same list of all the different goods for the rows. So it's a square table, with n columns and n rows, if there are n different goods. If you observe someone exchanging apples for bananas, you put a tick in row A column B. (Obviously you can ignore the main diagonal, because people don't exchange apples for apples, unless they are different varieties of apples, and you can ignore everything North-East of the main diagonal, because it's just a duplicate.)

In a pure barter economy, where any good can be exchanged against every other good, you would have ticks everywhere. With n different goods, there are n(n-1)/2 functioning markets.

In a pure monetary exchange economy, where apples (say) were the medium of exchange, there would be ticks everywhere in the A column or row, and no ticks anywhere else. With n different goods, there are n-1 markets, where in each market apples are exchanged for one of the other goods.

A monetary exchange economy has a lot fewer markets operating than a pure barter economy, for n > 2. Most economies are a lot closer to the pure monetary exchange economy than they are to the pure barter economy.

If there was such a thing as a universal dollar and all trade in an economy contained this item, then we'd certainly be living in a pure monetary economy. But in the real world, there is no such hypothetical item as "the" dollar. Dollars are heterogeneous. There are multiple types, brands, issuers, and denominations.  To get to where we want, we often have to engage in a long chain of dollar-for-dollar barter transactions. Only when we've managed to acquire the right form of dollar can we buy the things we want.  This means that no single type of dollar appears in 100% of an economy's trades. Using Nick's wording, we have ticks everywhere, not just in the A column/row.

Types of dollars

In Canada we have the $1 dollar coin, or the loony, which is issued by the Royal Canadian Mint. If you try using loonies to pay for something worth over $100, say a washing machine, there's a good chance that you'll be turned away by the shopkeeper. To buy the washing machine, you'll first have to barter your loonies for larger-denomination paper dollars. Banks typically engage in this sort of barter. They'll either sell you paper dollars for your coins, or they'll sell you an electronic bank deposit. If you buy the paper dollars you can head back to the store and get the washing machine.

Canadian paper banknotes, created by the Bank of Canada (BoC), are accepted in a wider range of trade than loonies. But like the Mint's coins,  BoC notes are not generally accepted. Say you need to get your clothes washed at the local laundromat. Since the washing machines are coin-operated, you'll have to sell notes and buy loonies in order to get them to work. Alternatively, say you want to buy the local laundromat, which the owner is selling for $2 million. The laundromat owner won't accept your offer of notes since having a few suitcases full of paper is awkward. Rather, you'll first have to barter away your notes for some medium more appropriate to the context. If you take your notes to a bank and purchase deposits, then you can transfer your deposits to the owner in return for the car wash. The owner will likely accept deposits, since holding $2 million at the bank will be safer for him than $2 million under his bed.

You could also offer to pay the owner with a personal IOU. If the laundromat owner accepts your IOU, he'll want to barter it away at some point. In the old days, he might have sold it on to another merchant in return for, say, a convenience store (see bills of exchange). Nowadays, the most popular form of IOU is probably the cheque. If the laundromat owner accepts your offer, he'll take your cheque to his bank and sell it for $2 million in deposits. His bank will in turn sell your $2 million IOU back to your bank in return for a $2 million deposit. Your bank will in turn sell your IOU back to you in return for a deposit.

You're in trouble if you don't have a sufficient deposit balance to buy back your IOU. It's for this reason that cheques are not generally accepted. If the writer of the cheque fails to settle their end of the bargain, the entire chain of dollar-for-dollar trades risks being unwound.

Nor are direct transfers of bank deposits generally accepted in trade. In order to purchase an exchange-traded stock or bond, for instance, you'll have to first sell your bank deposit for a deposit at a brokerage house. Now you can buy the stock. You're in trouble if you change your mind and decide that you want to buy a couch instead of a stock. Dollars in your brokerage account are useful only in financial market transactions, not retail transactions. You'll have to sell your brokerage deposit for a bank deposit, and only then will you be able to buy your couch.

I've left out another major type of dollar—deposits held at the Bank of Canada. A commercial bank that owns a deposit at another bank will often sell this deposit back to the issuer in return for a deposit held at the Bank of Canada. Deposits at the Bank of Canada can be used by banks to engage in all sorts of transactions with other banks.

But Bank of Canada deposits are not generally accepted. A bank, for instance, can't purchase a box of donuts from Tim Hortons with a central bank deposit—corporation or individuals aren't permitted to have accounts at the BoC and therefore can't accept BoC deposits as payment. To buy the box of donuts, the bank will have to sell some Bank of Canada deposits to Tim Hortons's bank, say the Royal Bank of Canada, in return for RBC deposits. It can then sell these deposits to Tim Horton's and get donuts.

In sum, the dollar is not some homogeneous entity. There are hundreds of thousands of implementations of the dollar. A list of all trades done in Canada over a period of time will show various types of dollars being exchanged for various goods & services and also being exchanged for each other. The distribution of appearance of each type of dollar in total trade is probably flattish, much as in theoretical barter. Liquid stocks and bonds and popular goods like coffee could very well appear in more trades than various types of dollars. The occurrence of cell phone minutes in trade, for instance, probably exceeds that of travelers' checks. The market value of transactions in which coins participate is probably exceeded by the market value of transactions in which S&P/TSX60 stocks participate. Our economy is less monetary and more barter-like than we commonly suppose.

I've been playing the game of Settlers of Catan for ages. Over time I've gotten less cutthroat and more philosophical about the game. What I've come to realize is that Settlers is a great tool for both thinking about monetary phenomena and building different sorts of monetary economies. In this post I'll assume a basic knowledge of Settlers—if you haven't played the game by now, you're living on the moon.

1. Catan isn't a barter economy

The first thing worth noting is that Catan is not a barter economy—it's a monetary economy. This might seem like an odd thing to say. After all, the trades that we see in a typical Settlers game are all commodity-for-commodity trades.

To see why it's a monetary economy, imagine the case of autarky, or a Catan in which trade is prohibited. Here, players can only build structures using cards earned from tiles on which they have a settlement. The value of a lumber card in an autarkical economy is derived solely from its use-value, or its ability to help build settlements and roads.

The moment autarky is lifted and players are allowed to trade resources amongst each other, resource cards provide their owners with a whole new range of services. Not only is a lumber card valuable for the settlements and roads it yields, but also for its ability to purchase things from others. It has become a medium-of-exchange. Given the unpredictability of dice rolls, owning a stock of readily-tradeable exchange media provides players with wiggle room, or monetary optionality. Because an option is valuable, resources that provide optionality earn liquidity premia. The more liquid the resource card, the broader the option it provides and the larger its premium.

Monetary phenomena like monetary optionality begin to emerge the moment we exit from autarky—we don't have to wait till some hypothetical item called "money" appears on the scene in Catan, nor for so-called barter to disappear. All media-of-exchange, whether they exist in our simple Catan economy or the real economy, have money-like properties. In fact, I'll show later that there is no such thing as "money" in our modern economy, only a universe of media-of-exchange that differ along a spectrum of liquidity.

2. Patterns of resource monetization in a Catan economy

The Catan universe is a well-balanced monetary economy. By well-balanced, I mean that we tend to observe an even distribution of trade. Put differently, since Catan's five resources are all equally marketable, none of them earns a superior liquidity premia.

There are ways to tilt the rules of Settlers so that trade patterns get more skewed. One way to do this is to penalize trade in certain goods. For instance, say we institute a rule that continues to allow for full trade in sheep, brick, ore, and wheat but only permits lumber to be traded when a six has been rolled (limited autarky in lumber markets). This inhibits lumber cards from serving as full media of exchange. As a result, lumber loses some of its optionality and will trade at a discount to its prior price. The distribution of trade will now be skewed away from lumber towards the other four resources. If we penalize all resources but one, we would skew the pattern of trade dramatically in this resource's favor.

Another way to affect the distribution of trade is to endow certain resources with unique properties. Let's say that ore is more storeable than the other commodities. The rule in Settlers is that when a 7 is rolled, any player with eight or more cards must lose half their hand. If ore cards don't count to the total when a 7 is rolled (they are storable, after all) then players will be able to hold larger hands as long as they cushion their hand with ore. Players will begin to trade for ore not because they wish to build a city with it, but to protect their hands from 7s. This could increase the incidence of ore cards in trade relative to other cards. The more liquid ore cards become, the more will their monetary optionality increase, as will their liquidity premium.

There are all sorts of ways to tilt the distribution of monetary trade. Be creative.

3. Let's try Settlers chartalism

The idea behind chartalism is that some external monopolizer, say a gang or a king, sets an obligation upon citizens that can only be discharged with a certain type of settlement media. This media doesn't have to be a commodity. It might be an intrinsically useless token.

Let's imagine that the robber in Settlers requires a bribe from all players whenever a 7 is rolled. If a player doesn't pay the bribe, then they must sacrifice two cards. Say that the bribe must be paid in the form of an intrinsically useless $100 Monopoly bill. Players can only purchase the Monopoly bills from the robber on their turn for one resource card. Presumably players will purchase $100 bills since the 1 card cost exceeds the potential loss of 2 cards.


A player who has already bought enough Monopoly money to satisfy the robber should a 7 come up may wish to sell excess bills to players desperate for protection. Monopoly paper bills thereby join the five existing resources as a media of exchange in Catan. We might be able to tilt the distribution of trade in favour of the chartal medium if we encourage its marketability through rule changes discussed in section two.

4. Credit-based settlers

The existing rules of Settlers prohibit credit transactions. Relaxing these rules allows us to introduce a whole new range of resources that can be used in trade—each player's future earnings power.

There are infinite ways to structure credit transactions in Catan. Informal verbal promises are one way. I tell my trading partner that I'll buy a lumber from them now for an IOU of two sheep in the future. Due to their informality, these promises are unlikely to become liquid.

To really tilt the distribution of trade towards credit, we probably want to create standardized paper credit contracts. Standardization allows for quick appraisal, and this lowers transaction costs. Transcribing the promise onto paper will encourage its negotiability, or exchangeability from player to player. The more we streamline the process, the more likely that credit will become Catan's most liquid traded resource. The simplest IOU I can think of is a one-time paper promise to pay out all production from a 6 or 8 tile. The issuer can easily satisfy this obligation since they don't have to trade away for the media to settle it—they produce the media themselves.

When we allow for credit, players are acting simultaneously as bankers. The player that succeeds in getting his or her credit to circulate from player to player has effectively increased their purchasing power relative to everyone else and will be able to advance through the game much quicker. Players that push too close to the sun will find themselves unable to meet their outstanding promises and will default. They'll lose the trust of fellow players and will find it difficult to issue credit again, their advancement in the game slowing.

5. The social contrivance of a fiat Catan dollar

Paul Samuelson famously described how the contrivance of fiat money would allow members of an economy to efficiently solve the problem of passing on savings over time. Through a "grand consensus," worthless "oblongs of paper" would be accepted into circulation. This sort of paper is different from chartal Monopoly paper since the latter discharges a particular obligation. Samuelson's oblongs are merely bits of paper. They have no non-monetary use whatsoever.

Could we get players to accept mere paper? Our first guinea pig will only do so if they know for sure that the next player will accept it. Absent a significant amount of negotiation and coordination ahead of time, its difficult to imagine why the first player will ever trust the future negotiability of paper. Far safer for him or her to just refuse any fiat paper trades. Might players spontaneously negotiate a set of rules to encourage the circulation of Samuelsonian paper? Perhaps, but if the game already allows people several trading technologies—trade in resources, trade in chartal Monopoly money, and trade in credit—will players want to devote resources negotiating an expensive institution like fiat paper? I doubt it.

6. Catan Money?

Can the rules of Settlers be manipulated so that Catan approximates our modern world in which there seems to be one universal medium-of-exchange called money? Could we get ore to appear in all of Catan's trades, or Monopoly money, or the circulating credit of one trustworthy player?

As I pointed out earlier, we don't have to. In the real world, there's no such thing as a universal medium of exchange. Rather, we have an almost an infinite range of media that vary in terms of liquidity. The "dollar", for instance, refers to a number of different exchange media: paper dollars printed by the Fed, electronic dollars created by the Fed, private savings account dollars, chequing account dollars, eurodollars, traveller's cheques, credit card dollars, and more. Private chequing account dollars can be broken down into Bank of America dollars, Wells Fargo dollars, Citi dollars etc. The fact that these various media are denominated in the same unit should not confuse us into consolidating them into one universal medium-of-exchange. A US paper dollar, for instance, is a far more liquid instrument than a hamburger patty, but it still only appears in a small percentage of total US trades. As long as we can manipulate a game of Settlers to show a skewed distribution of trades, then we've sufficiently approximated the real world.

7. Catan economics vs. modern economics

Setting up a stylized Catan environment in order to explore monetary phenomena is akin to the approach taken by modern monetary economists. Economists realized long ago that exchange media simply had no role to play in a stylized Walrasian environment. In a world with an omniscient auctioneer who calculates the prices and quantities of all trades, and in which all trades are cleared at a central clearing house, there's no room for monetary phenomena like media of exchange or liquidity premia to arise.

To get "money" into an economy, modern economists start by introducing various refinements into a Walrasian environment. Rather than have individuals meet at a centralized market, Kiyotaki and Wright (1993) have traders meeting randomly and pairwise. Wright, Trejos, and Shi (1995) replace the auctioneer with traders who are capable of negotiating prices bilaterally. Our simple Settlers environment easily captures decentralized search and bargaining.

Some environments created by modern monetary economists are downright odd. The modern work-horse Lagos/Wright model sets up an environment with day and night markets. Day markets are bilateral and anonymous while night markets are centralized. Dror Goldberg imagines different cities which specialize in a certain good. Traders must trek between cities to secure a consumption good. Settlers, of course, will appear odd to anyone seeing it for the first time. Manipulating the rules of Settlers to see how we can generate monetary patterns is very much like letting rational agents loose in an Lagos/Wright sci-fi environment. The advantage of the former is that it's fun and real people are testing out the model, not imaginary agents.

Try experimenting with some of these rule changes the next time you play Settlers and tell me what happens. Even if you don't get around to it, hopefully I've convinced you that Settlers provides a great model for thinking about monetary economic phenomena.

For diligent readers who have trudged through my first two post on Yap stones (here and here), I promise this will be my last on the subject.

There is an interesting exchange between historian Cora Lee Gillilland, the author of The Stone Money of Yap: A Numismatic Survey (pdf), and critic David M. Schneider in the December 1976 issue of the American Anthropologist. Schneider was a well known anthropologist and contributor to The Micronesians of Yap and their depopulation.

In response to Gillilland's survy, Schneider issues a warning that:

Suffice it to say that traditional Yap does not have “money” in any technical sense of the word. None of the objects listed on page 1 [of Gillilland], like yar, gau, ma, or mbul, are money in any proper sense. It is certainly true that rai has been called “stone money” and that the literature which is cited (all of which is very far out-of-date) calls it “money.” And indeed, the Yapese themselves call rai “stone money.” But to call a “cow” a “dog” does not make the cow a dog. Even if the traditional European name of the object called rai is “stone money,” the most rudimentary scholarship could have established that it is not money.

Gillilland replies:

He [Schneider] has postulated a definition of "money" I know not whether exclusively his or one generally accepted by his discipline. For my part I am a historian, not an anthropologist, and as stated in the title and introduction of my work I take a numismatic view. Schneider's definition of the English word "money" is too narrow and traditional to be acceptable. I am not alone and would cite scholars such as Melville J. Herskovits, Alison H. Quiggin, and Paul Einzig who have all discussed this issue and have concluded that primitive media, including rai, are within the perimeters of "money."

The above quarrel is a great example of the sorts of debate one sees amongst those who have adopted the standard money-view the world. The money-view dictates that before embarking on a monetary exploration of Yap, all valued items on the island must be split into money or non-money. This is always a controversial process. Do we add yar, gau, ma, or mbul to our "money" category, all of which Gillilland lists as media of exchange? (See first post, #5). Furness too reports that for "small change", Yapese used yar (pearl shells), and that when used in exchange, mbul, or banana fibre mats, were valued at the same rate as a rai stone three hands spans in diameter. What about coconuts? Furness writes about a trade in which "Old Ronoboi paid twenty thousand coconuts for a cooking stove 'made in Germany' of thin sheet-iron". Or should we only add rai stones to the money category, relegating coconuts and the rest to the non-money category? If so, then monetary analysis of the island of Yap begins and ends with rai.

On the other hand, if we adopt Schneider's categorization, then nothing appears in the money category, in which case we can't do monetary analysis at all since all we've got is a barter economy. This argument over the contents of the category called "money" is never-ending.

The moneyness view starts its monetary analysis of Yap from a different perspective. Rather than splitting Yap's commodities into money and non-money, we try to analyze the monetary nature, or moneyness/liquidity, of all items that were traded on Yap. According to Gillilland and Furness, this list of traded items includes not only the famous stones, but also yar, mbul, gau, and ma. We can also add a few trade commodities like bêche-de-mer (sea cucumber), turmeric, coconuts, and copra (dried coconut meat) to our list, as well as local commodities like housing materials, fishing equipment, canoes, bananas, yams, taro, and fish. Non-commodities like labour, war indemnities, funeral expenses, women, and dances were also all traded by the Yapese and find their way onto our list.

In adopting the view that the monetary nature of any item is a function of its liquidity, or its ability to be exchanged away, we shift monetary analysis from a focus on one (or a few) item(s) categorized as pure money to analyzing the relative liquidities of all items on our list. How often did each good appear in Yapese exchange? Would we see a flat distribution in which all items appear in roughly the same amount of trades, or a sloped distribution in which certain items appear in more trades? How does this distribution change over time? What sort of liquidity premia would each item have carried? For instance, if a yap stone could never be traded onwards, for how much less would the Yapese have valued that stone? What about the premia on mbul, coconuts, and labour?

So by shifting the axis of what we consider to be "monetary" from money to moneyness, we can ask ourselves a range of different questions. Nor do we need to follow Schneider and halt our monetary analysis when so-called barter prevails, since even then all goods will be liquid to some degree.

Enough yapping away about Yap (sorry, I couldn't resist).

There is a century's old debate between metallists and chartalists on the origin of money. The metallist view is that the first spark of money emerged through barter and matured when the use of precious metals as money was discovered. The chartalists disagree. According to them, the use of credit preceded the use of precious metals as money.

At its core, the metallist/chartalist debate is a battle over the definition of the word money. In a moneyness world, there is no such thing as money. All we have are numerous media of exchange with varying ranges of liquidity. Whether moneyness first gets attached to credit or precious metals is really not important.

Imagine that a hunter encounters a trapper. The hunter has a deer. The trapper wants the deer but isn't sure what to offer. On the one hand, he can exchange the two rabbits in his belt for the deer. On the other he can offer his credit. In offering to exchange away his credit, the trapper is simply capitalizing his future earning power and bringing it forward for use in trade. Metallists and chartalists put tremendous importance on this first choice of credit versus rabbits, since one or the other will represent the so-called origins of money.

From a moneyness perspective, there are more interesting forces at play. Say that the trapper learns that the hunter will accept either his credit or his rabbits. The trapper next arrives at the realization that both items now have a degree of liquidity, or moneyness. He begins to attach a liquidity premium to both, for not only are the trapper's inventory of rabbits useful to him as food, but they can also be resold to the hunter, thereby providing the trapper with an extra range of liquidity services. The same goes for his credit. The trapper's future earning power is one of his key possessions. Now that it is tradeable, his future earnings power provides an extra margin of liquidity services. Over time the trapper will learn which one of his trade items is more liquid  and will favor that item with a larger liquidity premium. A monetary economy has now emerged in which traded goods are appraised according to their degree of liquidity and carry varying liquidity premiums.

If we split the world into money and non-money, then debates over the what items make it into the money category will often be heated. The origins debate gets especially intense because it tries to define modern money by looking back to its so-called debut. Taking inspiration from gold's barter origins, modern day metallists want a pure real/commodity based money. Modern day chartalist, who advocate state-issued inconvertible paper, look back to money's credit origins to support their view that the essential nature of money is credit.

From a moneyness perspective, the money-or-not debate is distracting. The origins of liquidity and liquidity premia is complex and probably not subject to study. There never was a single dominant instrument that could claim the mantle of money, only multiple goods and forms of credit, each with different degrees of moneyness. As for the metallists and chartalists, a pox on both their houses.

The response to the above question will usually be a barter economy. But I want to show you that this is a tougher question than it seems. The answer depends on whether you're starting from a money view of the world or a moneyness view. (See Why Moneyness? in which I explain these ideas).

1. The money view, which is the standard view, begins by classifying all things in an economy into either money (M) or non-money. Any economy that has M in it is a monetary economy. All exchange in a monetary economy is achieved by trading non-money into M and back into a different non-money. When there is no M, then a non-monetary economy is said to exist. In a non-monetary economy, exchange occurs by trading non-money for non-money, our word for this being barter. So a non-monetary economy is a barter economy.

2. Things are different from a moneyness perspective. An isolated household living in a cave values their inventory of goods solely for its use-value—how each good satisfies the household's needs. The household's goods become liquid the moment that it realizes that other people are willing to exchange for them. Their inventory is now worth more to them than before because it provides them with a greater range of options. As once-isolated households trade with each other, goods will be graded according to their relative liquidities. Depending on its ranking, each good earns a smaller or larger premium over use-value. ie. a liquidity premium. Liquidity/moneyness don't exist in a world without trade. We call such a state autarky.

So depending on one's method of classifying the world, a non-monetary economy can be either a barter economy or an autarkic economy.

This conclusion may seem somewhat odd at first. Take what we would typically consider to be a barter economy, say a world in which people barter deer for beaver. This setup is actually monetary in nature, insofar as both deer  and beaver earn a monetary premium for their potential to be bartered. In other words, its possible to start monetary analysis way before we ever exit from so-called barter.