So far, we have seen money mostly as a static measurement of value, almost like the kilogram and the meter. Since money is the unit in which accounting is done, this was a reasonable goal. After all, thinking about changing exchange rates between currencies (and thus prices of real goods going all over the place) is about as much fun as the meter changing in length.
Thus, ideally, we would like for money to be stable. That's easy to say, but everything floats. Obviously, if there was something—anything—that was more stable than money, we would already be using that to measure everything else (including money), right?
Where by domestic, regions using the same unit of account are meant. If a multitude of nations use a single unit of account, i.e. they are in a currency union, they are treated as though they were a single nation. On the other hand, different parts of a single nation using separate units of account are treated as international trading partners.
It is possible for there to be a separate unit of account and medium of exchange. In this case, while contracts and inventories would be denominated in terms of the unit of account, there might not actually exist any money denominated in it.
Furthermore, for the sake of simplicity, we are going to examine foreign trade later. For now, we will study either an isolated island, or the Spaceship Earth. No imports or exports whatsoever.
With that, the main theoretical problem is what I call the lambda problem. There is often no immediately apparent reason why the unit of account (or the medium of exchange) shouldn't be worth any λ times as much (λϵℝ+). This issue is especially pressing in the case of a "ghost money", a unit of account that does not exist as a medium of exchange.
The most solid case is (perhaps surprisingly) that of a scarce, unbacked unit. There is a definite real demand for it, and an inelastic supply. Consequently, its price is well-defined, though quite volatile. In the ideal case, there is no fundamental value to it, thus quantity theory fully applies: should its quantity e.g. double, its value would fall in half.
Popularly known as a gold standard. A currency issuer (including private banks) offers unlimited exchange between its liabilities and a defined quantity of e.g. gold. In practice, the issuer mostly owns assets (typically bonds) denominated in the unit of their own issuance. This—as far as the backing theory is correct—creates a very interesting mathematical situation.
For the sake of simplicity, have an example where the issuer has 100 units of the underlying asset (or denominated in it), 600 units of outstanding liabilities, and 500+x units of assets denominated in their issued unit. As long as x is positive, the bank has share capital of x units. But if x is negative, the issued liability must immediately be revalued downwards.
With a negative x, the bank has 100 units of underlying for a balance of 100+|x| units of its issue; it is bankrupt. Unless the issued unit is revalued to 100/100+|x| or below, the bank will stay bankrupt and will be run. This is why low fractions of underlying-denominated assets are considered risky: even a small loss, a negative share capital that is a small fraction of the whole balance sheet, can still cause great devaluation. In the limit case of no independently denominated asset whatsoever, the unit would immediately fall to zero.
Popularly known as fiat systems. While there is no direct conversion admitted (the issued liabilities do not include a put option), there is nearly always an indirect conversion pathway. In particular, rather than having a standing offer of exchanging liabilities into the underlying, and managing the composition of assets in the open market, modern issuers forgo the standing offer, keeping only the active managing around.
To me, this seems like a waste, and unnecessarily removing a failsafe from the system. Yet the system is still operable with direct passive conversion absent—it is merely easier to mismanage. In particular, central banks became engrossed in the idea of managing the nominal interest rate. The prime example of this is the Bretton Woods system, where a de facto absence of convertibility permitted a slight, but constant, deviation from parity.
While the two systems differ slightly in their vulnerability to mismanagement, as long as they work as designed, theoretically they are the same. And the crucial question in this case becomes: what is actually their behavior? Without loss of generality, I will use the example of a gold standard.
Classical economists, such as Ricardo, correctly described the case of an economy that is an infinitesimal part of the connected world. Issuing gold-denominated notes supplants the demand for liquidity that so far materialised as a demand for gold. Consequently, as much as the demand for gold was for the purpose of liquidity, it is exported from the country, with no effect on its price. Convertible notes issued beyond this quantity of gold reflux to the issuer. What happens, though, when there is nowhere for the gold to be exported to; such as, off the surface of the Earth?
In a (theoretical) world entirely using gold standard(s), the newly-issued notes would enter circulation and dilute the liquidity demand for gold. However, there would not be anywhere for the gold to be exported. In the limit case, gold could very well fall to its fundamental value—and with it, the unit of account.
And while specifically gold could well have such a fundamental value—it does have some practical uses, and its quantity is still limited—the general concept of "gold" ideally has no such fundamental value. Perhaps a more pure example is bitcoin. Demand for it is mostly speculative, with some small demand for pseudonymous liquidity; but a monetary system issuing bitcoin-denominated money on demand would drive its speculative demand to essentially zero.
And let's not forget that the fundamental, commodity value—even if strongly positive—is subject to change of technology. Aluminium, initially more expensive than gold, suffered a thousandfold collapse in its price when the Hall-Héroult process for its manufacture was widely implemented. Gold, as an industrial commodity, is subject to technological development finding either a replacement or a new use.
In general terms, fouding the unit of account on a scarce, unbacked commodity is a poor idea. The very process of establishing currency boards to it would upend the foundations. And the fundamental price of a single commodity with inelastic supply, even if not subject to supply shocks (like gold and bitcoin), is still subject to demand shocks.
A different idea is to completely forgo scarce commodities ("gold"). In this case, the backing is entirely provided by assets denominated in the issued unit. This is a terrible gamble, because if the issuing bank goes bankrupt, the backing equation immediately returns a zero. Treacherously, this can come about due to a deflation that strains the debtors to such degree they are unable to repay their debt.
On the other hand, while inflation does not contain such an instant-death trap, there is no fundamental reason for it not to proceed at nearly infinite pace. In the absence of redeemability, never mind redeemability into something not denominated in the same unit, the fundamental value of money is questionable.
In effect, the fundamental question to be solved is the λ problem. Why the unit of account and/or the currency isn't worth any λ times as much (λϵℝ+)?
In the absence of unlimited redeemability, it is possible for the values of money and the backing assets to diverge. This is analogous to a closed-end fund trading above, or occasionally below, NAV. Because the central bank is not under obligation to issue money on demand, it can create a liquidity premium on its notes. Due to a definite real liquidity demand, despite the initial apparent circularity, there is a unique, positive solution for money's value.
In other words, the liquidity attached to the money is the foundation of its value. This behaves as an unbacked, scarce commodity, and as a consequence, quantity theory is operative on it. Unlike ideal gold, however, the supply of liquidity can be infinitely elastic. Such a supply curve doesn't exist in nature, but can be synthesized by the monetary authority's policy. As such, the price can be kept stable even in the face of demand shocks for liquidity.
This is like the Baron Münchhausen lifting himself out of the swamp by pulling on his own hair. And because the unit of account owes its value to the fact that money is more liquid than the bonds used to back it, the bonds are valuable because they are less liquid than the money they back. Phrased this way, the statement is bizarre—but not untrue, strictly speaking.
Unlike a commodity-based system, liquidity is not subject to either replacement or a sudden increase in demand by technological development. Yet exogenous disturbances, such as improvements in the stock market supplying an excess quantity of liquidity, would mess with the price level—or the quantity of money, at least.
Somewhat more troublingly, the system rests on an effective monopoly of liquidity creation by the monetary authority. If this monopoly breaks down—particularly, if something more liquid than central bank-issued money is developed—control is lost over the system, as the liquidity premium on money falls to nothingness. Shortly afterwards, a rapid drop to 0 is expected.
To the extent the issuing bank has independently denominated assets, and is willing to act like a currency board through them, it can shore up the value of its liabilities. This is at the price of transitioning to a different system, explored above.
The above description gives a nearly universal tool for setting the value of money. In some way, it is too universal, in that it can be used to set any arbitrary value, and doesn't set any particular value as special. Thus there are several ideas about what should the value of money follow.
One quite popular option is to make nominal GDP stay a certain fixed number, or follow a defined path. The obvious problem with this is that GDP growth is somewhat erratic—or at the very least, variable. A good time (in real terms) would translate into deflation, while a stagnant or even shrinking economy would bring with itself severe inflation.
If the NGDP targeting economists were right in their apparent belief that monetary policy is the only thing influencing GDP, this would be perfect. Unfortunately perhaps, this is simply false. Any number of things from technological progress to fiscal policy can—and do—impact GDP growth.
The mainstream option is to create a large basket of goods and services, the CPI index, and keep its price on a certain path. A key problem with this approach is that many goods in the basket are immobile or nearly so, and subsequently there is no law of one price on them. Consequently, the CPI series of different countries diverge over time.
The above observation also betrays the fact that as a country improves its capital to labor ratio, wages rise, and many labor-heavy components of the CPI rise in value. As a result, there is a minor deflation. Though perhaps no more than 0.5%/year, this is still undesirable.
My take is that money should do its best at being neutral in the short run as well as the long. We already saw that in a modern system, in the long run the quantity theory does apply, and money is neutral. It would be a boon if it stayed a constant value, and would thus be neutral in the short run as well.
If we succeeded in reaching this goal, what would that look like? Firstly, if the money started to circulate outside the country—perhaps being unofficially adopted abroad due to its superior stability?—its quantity would increase, while its value would stay constant. Second, if the country developed, wages and the price of immovable, labor-heavy goods and services would rise.
Unfortunately, the latter is easiest to see if our economy is an infinitesimal part of the connected world. In this case, there are easily-movable goods whose price is anchored by the rest of the world, and whose value can serve as a benchmark for the rest. If, on the other hand, our economy is the entire world, then the prices of these goods will move all over the place.
It is easy to say that money should be stable, but everything floats. If there were anything more stable than money, we would already be using that to measure everything, including money. It is possible that comparisons between a wide variety of industries and technologies could give a good value for the average productivity of labor, but I'm not certain about its feasibility.
Even some famous economists, such as Milton Friedman, had their own, often ridiculously stupid ideas on the topic. Friedman, for instance, tried to fix the quantity of money. This would turn the currency into an inelastic-supply commodity. We have examples of that, such as bitcoin. Their prices are very volatile.
Other, mainstream economists fiddle with the interest rates. If you are mathematically inclined, you might notice that some variables—the quantity and value of money, interest rates—are not at all independent. A few can be set by the monetary authority freely, but the others are determined by them. Ideally, you would want to fix value, and adjust quantity to go along with it.
Do note that monetary variables are also affected by real factors. Suppose the central bank fixed the value, and this determined the quantity. What about interest rates? Those also depend on the situation of the economy. If there are a great number of new ideas on how to use capital, far in excess of the stock of capital, interest rates will be high. On the other hand, if there is a glut of capital in comparison to productive uses, interest rates will be very low.
I have not yet described how a "disembodied" unit of account can work. In the case of a foreign currency serving this role, then the case is very simple: it is not disembodied at all, and there is a well-defined foreign exchange ratio. As the foreign money exists abroad, and has high value density, the law of one price is operational.
On the other hand, a completely immaterial unit of account works differently. Because the unit is defined by the monetary authority in terms of another money of its own issuance, the units combined work by the self-denominated backing mechanism described above.
In the simplest world, inter-currency trade would work as barter. International traders would hold as much foreign-denominated liquidity as they received in payment for their goods, and would soon spend on buying goods for the return leg.
In this case, a country trying to be a net importer of wealth would soon see its currency become worthlessin the international market. Traders would receive plentiful amounts for imported goods, but there would be less exports for them to spend it on. The former increasing the quantity in their hands, the latter decreasing real demand for it, its price plummeting would be the result.
Naturally, a country fortunate enough to export more than it imports would face the opposite situation, as its currency would appreciate. This is called the Dutch disease.
But our world is not this simple. Not only physical goods, but also securities can flow internationally. In particular, a monetary authority facing the Dutch disease can purchase foreign securities, putting its money in the hands of foreign traders. Thus the stock of this money held by traders is replenished, and there is no appreciation of the currency. Netting out the international currency flow, the holders of the excess money finance the exportation of the real goods.
Interestingly, traders holding an increased quantity to conduct an increased volume of trade, and the assumed increase in liqudity demand of the exporting economy do not necessarily grow the demand for the money to the same degree as required by keeping its international parity. If an economy suddenly decided to save and export a massive fraction of its "luxury" consumption, it is entirely possible for it to simultaneously experience deflation abroad (appreciation of the currency), and inflation at home (the excess liquidity causing a depreciation).
You might remember Say's law. There we saw that money—and the liquidity carried by it—is just another commodity, and that there cannot be a surplus of everything including money, but there can be a surplus of everything except money. And obviously, there can be entirely too much money being produced, diluting its liquidity premium.
What, then, if we tied the value of money to that of everything else? To per-person productivity; the value added by each person's labor. And this makes sense, too. After all, you could barter this for something else of equal value. Money is only there to ease the trade, by being a token of purchasing power. And this is why it makes sense to only discuss the real economy, and not get tangled up in monetary affairs.
Money is only the shadow that the real economy casts. Thus if you ever feel confused by what happens with money, you can always frame it in terms of the real economy, and a transfer of purchasing power. Taxes? The government—on behalf of society, hopefully—takes some purchasing power, and has others do some services for it. This is how the economy contains not just agriculture, manufacturing and services, but also people spending time and effort on military service, for example.
With the exception of a few systems, money derives its value from its liquidity, and thus behaves according to the quantity theory. In this case, money is neutral in the long run.