What is money?  It turns out to be a surprisingly difficult question to describe a phenomenon that intuitively does not seem terribly complicated.  Even just pinning down money as a class of object is fraught with difficulty, as anthropologists and historians show that many different physical objects have been used as money in the past.  In various places and times, gold coins, shells, pieces of paper, beads, silver bracelets, and many other sorts of things have been used as cash.  After thinking about this for a long time, economists have determined that money is whatever is used in society that has the following three properties.

First, money is said to be the medium of exchange.  In other words, money is a special sort of good that can be exchanged for almost anything else directly.  As it says on the US dollar: “This note is legal tender for all debts, public and private”.  In fact, we have special words for transactions of this kind.  When a good or service is exchanged for money, it is said that we “sell” it, while the party that trades the money for the goods is said to “buy” or “purchase” it.  If you think about it, this is a little weird from a theoretical perspective (since whatever the money is, is an object just like anything else), but it makes intuitive sense.

Listed prices for all other goods are denominated in units of the medium of exchange.  This means that if one would like to find out how many oranges one can get for one’s stack of apples, one can do so much more easily by figuring out how many dollars can be gotten for your oranges, figure out what the price of apples is in dollars, and then compare the two.  Once everyone’s standardized, then it allows easy comparison like this for any conceivable pair or set of goods.  This is a pretty big deal.

Second, money is said to be the store of value.  What this means is that if you keep money around, you expect it to be “worth” about as much when you decide to eventually spend it as you do now.  The longer you can keep it around in the same state as before, the better it works.  So, for example, it might be theoretically possible for people to settle on using highly radioactive metals as a type of money, but it wouldn’t be a very good store of value because when you went to spend it you’d notice that a big fraction had decayed away while it was in storage.  Similarly, people don’t like to use a good as money that’s easily or cheaply replicable, since that has an equivalent effect.  In practice, people tend to demand that their money decay away at no worse than about 5% a year over a long period of time.  People start routing around any good that has worse properties than that.

Third, money is said to be the unit of account.  This means that if a person or firm is trying to figure out what they’re worth, how much they’re spending over time, or how much they’re yielding, this is the unit they resolve everything to internally.  There’s nothing from stopping any person from doing this using any unit they want, but when most people generally agree across firms (and this agreement is enshrined in law) then it’s fair to declare that good the unit of account in the society at large.

Now, notably, there’s strictly no reason why a given society couldn’t settle on distinct solutions for each of these.  So, for example, a place could use gold bars as the store of value, Monopoly-themed fun bucks as the medium of exchange, and acres of moon dust as the unit of account.  In this example system, all of the listed prices would be in fun bucks.  Any time a person wanted to go shopping, they’d take some stored gold bars down to the market, sell it for fun bucks, shop in the market buying anything else that they wanted, and then on the way out trade their excess fun bucks back to the moneychanger for gold bars.  Then, at home when they’re doing their budget, they’d mark down the value of what they bought or sold in moon-dust-equivalent units.  After all, the price of gold bars in fun bucks could fluctuate rapidly, but real estate on the moon is always a solid investment!

Admittedly, this is a pretty silly example.  But it shows just how complicated the idea of money can potentially be.  In practice, because these functions are pretty similar, most societies in the real world tend to standardize on the same good for all of these functions.  Hence, a single concept called “money” that works all right in most cases.

So, if much of the value of money in all three senses is bound up in the decision to coordinate on this specific good (or basket of goods) as special, then the student of game theory will naturally ask “What incentives encourage this coordination?”  After all, if the generally accepted form of money were to change one day, then there’d be a massive shift in wealth away from people who are holding the old good that used to be accepted as money and toward the holders of the new stuff.

To see how this works, let’s return to our toy example.  One day, the government of our toy society decides that it is stupid to maintain three different goods for money.  So they decide to standardize on seashells.  They publish a big registry explaining what makes for a particular grade of seashell (based on size, color, and general attractiveness) and then say that henceforth all legal contracts must be denominated in seashells.

The next morning, the moneychangers are stuck with a giant pile of useless fun bucks that nobody will want to trade their gold bars for, since seashells are now the medium of exchange.  Meanwhile, the few hobbyists who used to collect seashells for fun and have extensive supplies are suddenly the richest people around.  Note that this is a massive effect just because of this one-time shift – it would definitely be in the interest of seashell owners to get this law passed, while the people who own the “fun bucks” printing press would not be pleased.  So since there’s such a big incentive for some people to defect and switch the form of money, there has to be a correspondingly large incentive to maintain a particular standard.

The answer is that, in practice, the government usually serves as the coordinating agent.  This is why in most places the power to coin and print money is typically reserved to the government.  Accordingly, the government’s powers are used to enforce money-based contracts and to demand taxation in the form of the supported money.  It turns out that this, in itself, can be sufficient to maintain the standard.

Historically, most state-issued currencies had a commodity backing of some sort.  Either they were physically made of precious metals (gold or silver coins, for example) or they were legally exchangeable for some fixed amount of a backing commodity.  This helped to establish the efficacy and reliability of the currency in people’s minds.  Whatever the government might say or do, the coins still contain the same fraction of gold (or whatever).  In the worst case scenario of a standards-switch, the money can’t be worth any less than the backing material.  This means that a more inherently (or stably) valuable commodity for the currency establishes a floor in people’s minds about the value of the currency.

But this isn’t actually necessary.  Within the past fifty years, most countries in the world have moved to what is called a “fiat system of money”.  Basically, it means that the government issues notes at whatever rate and denomination it chooses, without regard to any physically-limited commodity, and just declares that it be used as money within the jurisdiction.  Everyone has largely gone along with this without much complaint.  And, surprisingly, the world didn’t implode.  It turns out that a modern government is powerful and influential enough to ensure this level of coordination by dictate alone.

OK, so far we’ve basically just briefly surveyed theoretical monetary economics 101.  Now let’s take it to the next level.  Basically all of economics assumes that money is the important thing to track – utility functions are defined in dollars, national income is defined in dollars, net worth is measured in dollars, etc., etc.  Even your crankier goldbug economists will measure everything in grams of gold instead.  But they all follow the money.  Which makes total sense, since money is both the medium of exchange and the unit of account.

But most everyone also agrees – if pressed – that what’s actually important in the real world isn’t the money itself.  It’s the goods or services that are exchanged for the money.  We’re only looking at money transactions in the first place because it is a sign that both: one, something interesting happened; and two, it gives some sense of what the value of the transaction was in some broader context.

I like to think of this with an analogy to the history of the discovery of the electric current.  Back in the day, people knew that there were two different kinds of electric charge.  The same kinds repelled and the opposite kinds attracted.  So, arbitrarily, they picked one kind and called it positive and called the other kind negative.  Then, when people realized that these charges could be induced to flow in a metallic medium, they called the direction that the positive charges were going the positive current.  When physicists got a more accurate view of what was happening, it turned out that the positive charges are actually fixed in the material and it’s the negative charges on the electrons that are really moving.  This meant that the positive current that was being traced was actually the “holes” being revealed as the negative charges flowed past in the opposite direction.  Still, after that discovery, nobody thought it was worthwhile to change the established convention.  After all, the math still all works out.  It’s just that the signs are a little strange.

Money is sort of like that.  At every point when we trace a transaction conventionally, we’re actually following the reverse of the flows of interest.  Most of the time, since the flows work out the same either way, it doesn’t matter so much.  Only the sign is different.  But when it comes to actually understanding what’s going on in order to generate deeper insight, having an accurate picture of what’s going on is invaluable.

If that’s the case, then it can be profitable to think about the entire situation from a computer science perspective.  Let’s start by modeling the entire economy as a simplified distributed algorithm for allocating scarce resources through time and space so as to maximize overall output.  What exactly is meant by “overall output” can be set aside for the moment, but it is worth keeping in mind as an open issue.

So our economy is made up of a collection of agents.  Each agent (which could be a person, household, or firm), is an economic actor.  By that, we mean that they can hold an inventory of goods, exchange goods or services with another actor, and can physically transform inputs into outputs.  We can model an agent pretty simply in the following fashion.

1) Each agent has an inventory.  This is nothing more than the list of goods that they currently have on hand, available for exchange.  In order to model services (like labor), we can add a term that says how long the item can stay in inventory unused before expiring.  That’s set to t=1 for services and can be set to a finite number if we care about modeling perishable goods, like food.

2) Each agent has a list of functions that describe the transformations they can physically perform during any given time slice.  So, for example, you could have an agent that has a function that looks like: f(2 coal, 1 iron) => 1 steel.  This would mean that during this time slice, the agent can turn 2 coal units and 1 iron unit into 1 steel unit, but only if it has the coal and iron already in inventory.  For simplicity, we can say that only at most one function can be executed at any time slice, but it can be executed any number of times (inventory permitting).

3) Each agent can exchange goods for money or money for goods with any other agent, but they cannot trade anything that wasn’t in their inventory at the beginning of the time slice.  This rule means that middlemen require time to move goods.  We could modify this to model transportation by making it so that agents can only trade with other agents within a certain radius, but that isn’t necessary at first.

4) For each good that we model other than money, an agent has an internal list of prices denominated in the unit of account.  Each price is the value they currently place on the good.  So they’ll sell if they have the item in inventory and are offered an exchange at a price above that number; equivalently, they’ll buy if they have enough cash in inventory and the price is less than the value.

We’ll treat time as discrete, like in a circuit.  When our clock is high, the agents can transform goods and revalue goods.  When the clock is low, exchanges occur based on the previously established valuation.  Then we’ll cycle over and over.

Note that we can handle deposits of raw materials in this model by initializing certain agents with inventories of unprocessed material and a transformation function that combines this unprocessed material with labor to make refined material.  This models that agent owning the rights to the fruits of the land.

This model is sufficient to discover all sorts of interesting phenomena.  The laws of supply and demand jump out immediately, as does the principle of comparative advantage.  But the most fascinating thing for me from this thought experiment is that the true nature of money arises into stark relief.  Money itself is as much a signal as a listed price.

To clarify that statement, notice that when an agent has money, goods flow towards it on the next tick to be transformed accordingly.  Consistently profitable agents are ones that take less valued inputs and turn them into more valuable outputs, as determined by the broader consensus.  From the algorithmic perspective, profitability is a signal that says “Push more resources to this agent.  It is doing something right!” and unprofitability is the reverse.  Notably, the signal contains a magnitude as well as a direction.  In fact, the difference in value between that which was consumed and that was produced is exactly equal to the profit, which is by definition exactly the amount of money that the agent has to buy more inputs in the next cycle.

But the above analysis assumes that the value of the money remains constant.  And we actually know that that isn’t going to be true.  If the sum total of all of the transformations across the economy mean that there is more stuff available, which we’d expect after a few cycles as more and more of the productive capacity of the economy is routed through the most efficient nodes, then with a fixed amount of money available we’d expect to see some deflation.  That’s because each unit of money is now more scarce compared to the amount of stuff around.  Notably, this benefit is distributed amongst the various agents weighted by the amount of cash that they are currently holding.  And these are explicitly not the profitable agents that drove this change, since they don’t get to exchange their newly produced goods for money until the next cycle.

The effect goes in reverse if the real economy suddenly contracts.  There’s the same amount of money in circulation, but now there are fewer goods available.  In this case, the prices of all the various goods get bid up over the next few clock ticks until a new equilibrium is reached.  And, again, the benefit of this is spread throughout the economy based on cash holdings – agents with real resources come out ahead compared to the ones that are holding money.

As we alluded to before, what we really care about when analyzing the system is the real flow of goods and services.  Not the money itself.  So the part of the price-and-money signal that corresponds to underlying profitability is the true signal, while the part that just reflects the relative scarcity of money itself is noise.  To the degree that exchanges are made based on the latter, goods and services are being sent to the wrong nodes.

Coming back to the real world, we see that the historical record matches this deduction from our model.  Periods where there was either inflation or deflation to a large degree correlate with massive economic dislocation and chaos.  For instance, the Spanish experience in the 16th and 17th centuries was of massive inflation as the new gold from their American empire overwhelmed the national capacity for production, leading to economic malaise.  Similarly, the Panic of 1873 and the Great Depression of the 1930s correlate with significant deflation experienced in the USA at these times.

This need for a clean-enough money signal for the system to function properly is often called “price stability”.  Under a gold or a silver standard, the amount of money available to the economy is determined based on how much of the precious metal is mined.  There’s a physical limit to the growth, which is good, but there’s no guarantee that the mining operations generate enough to keep up with the growth of the economy.  And, similarly, if the economy contracts, there is no available mechanism by which gold in circulation will be returned to the Earth.  In the historical record, regimes like this have a pretty good record of success.  But it’s certainly not unblemished.

Which leads us to the blessing and the curse inherent in a fiat monetary standard.  If the money signal is attached to something easily created and destroyed, and in the limit worthless in and of itself (like paper notes or Bitcoins), then it is theoretically possible to have the growth or contraction of the money supply roughly track the real economy.  Hooray for real price stability!

Of course, if the owners of the printing press wanted, they could run them full bore and cause inflation on virtually any scale one desires.  Inflation on the order of millions of percent a year has been seen in fiat regimes in the historical record.  Why would a government ever want to do this?  The answer lies in the fact that it takes time for prices to adjust.  If a bunch of new money is created by the government and exchanged for real goods and services – say to fund an ongoing war or social program – it takes place at the current, uninflated prices.  So the overall effect is a net flow of resources toward the new money, dissipating over time and through more exchanges, until the system reaches equilibrium again.  This benefit is traditionally referred to as “seignorage” and, among other things, it is the big reason why most governments take such a poor view of counterfeiters.

In the modern world, most countries have tried to solve this incentive problem by the creation of an independent central bank to whom is given the sole power to create new money.  In theory, these banks are not responsible to the official government, so once the officers are appointed, government officials have no way to encourage them to inflate (or, less likely, deflate) the currency in order to accomplish short-term political goals like getting re-elected.  Then, ideally, they can do the hard work of figuring out how much money to produce and inject into the economy.

Unfortunately, they aren’t very good at it.  Over the course of the past hundred years, the US Federal Reserve (the central bank of the country) has repeatedly missed their inflation targets.  Sometimes they’re too high; sometimes they’re too low; and sometimes they’re so far off that they cause chaos and serious economic dislocation.  The Great Depression, the inflation of the 1970s, and the deflation seen around the deep recession of 2008-9 and the slow recovery are all signs of fundamental trouble with the model.  Even the best disinterested experts with all of their knowledge aren’t able to accomplish the goal.

This is such a problem that one of the best ideas right now among macroeconomists for a rule to ensure price stability is what is called Nominal Gross Domestic Product targeting (or NGDP targeting for short).  Basically, the idea is that the central bank should set the expected GDP growth rate at some percent (like 5% a year) and then ensure that it happens.  A publicly announced target backed by printing enough money to make this work is potentially possible.  And at least we’d be sure that the central bank could at least hit its target.

There are two main issues with this idea, though.  The first is that there is no guarantee that the real economy is going to expand at this predetermined rate.  If it doesn’t, then there will be inflation or deflation to the degree that this guess misses the mark.  In the event of a real contraction, the inflation could be pretty severe.

The second issue is that it invalidates a key measure of economic health.  As it stands, NGDP is a decent proxy of the overall real economy.  It’s not perfect, but it correlates pretty well to the underlying real economy.  It’s certainly better in many ways than measures of real GDP, which take NGDP and apply a fudge-factor to try to cancel out any inflation in the given time period.  In the world where NGDP growth is fixed, then all the signal in the measure is now hidden in the fudge-factor.  That’s a real problem.

It’s worth noting that Bitcoin is intending to solve this problem from a different angle.  As a purely virtual peer-to-peer currency, it enables a monetary regime to come into being that is not under the control of any central bank.  Therefore, there’s no risk that the officers of the central bank can make a mistake.  The real problem with it is that, as designed, it suffers from the reverse problem as NGDP targeting: it is inherently deflationary.  At some point soon, virtually all of the valid bitcoins that can possibly exist will be found (or “mined” as they say in the business).  This means that the money supply for anyone using Bitcoin as a monetary regime is fixed.  Since the Bitcoin economy will almost assuredly not remain static, this is not a desirable property.

What is really needed is a solution for the money signal that will naturally track the underlying productive capacity of the economy that’s wired to the signal.  Ideally, the only way to create more money would be to add value to the economy as a whole.  As is so often the case, Sid Meier’s Alpha Centauri leads us to the answer: energy credits!  As we did in God, Gold, and Glory, we can measure a real economy in the black-box thermodynamic sense through overall energy capture.  Then all we need to do is to somehow fix the price of energy in terms of money.

For example, the central bank could set the value of a dollar as equal to 1 kilowatt-hour delivered to the national electrical grid.  Additions to the grid are metered and then every month the monetary base can be set accordingly.  Ideally, the seignorage benefits could be routed directly to energy producers based on the output to the grid, without regard to the price of the energy itself to consumers, as an additional subsidy.  But that isn’t strictly necessary to make the scheme work.

Once this is done, then we know with certainty that the supply of money available to the system as a whole is matching the real productive capacity of the economy.  We can still see inflation or deflation if there is a rapid change in the real value generated by the electricity in that month, but insofar as growth in the economy feeds back in as increased energy capture, the monetary base will track it accordingly.  In particular, it means that if there is another real shock to the economy (like the energy crisis of the 1970s), the system will immediately respond correctly by removing a bunch of money from circulation, cushioning the blow.

That’s pretty neat!  We managed to start from the definition of money and ended up devising the kernel of a superior monetary policy, based mostly on the insight that money qua money is best interpreted as a signal in a distributed resource-allocation algorithm.