The key criterion for a monetary regime is to maintain monetary equilibrium and avoid monetary disequilibrium. First, a good monetary regime should not generate changes in the quantity of money if there is no change in the demand to hold money.
For example, creating money for the government to spend should be avoided, assuming the existing quantity of money matches the demand to hold money. Similarly, creating money for the private sector to borrow should be avoided, again, assuming that the existing quantity of money matches the demand to hold money. And, combining these two notions, creating money for the government to borrow, when the existing quantity of money matches the demand to hold money, should be avoided. Perhaps more importantly, reducing the quantity of money when the government runs a budget surplus or the private sector or government wants to borrow less, when the demand to hold money is unchanged, should be avoided.
Why? Disturbing monetary equilibrium and creating monetary disequilibrium disrupts economic activity until the money prices of goods and services, (including resources prices like wages) adjust so that the real quantity of money returns to the demand to hold money. Because money does not have its own price and market, those specializing in the provision of all of the other goods and services, (again including resources like labor) must simultaneously try to make judgments about what what money prices are needed to keep the real quantity of money equal to the demand to hold money. With the lack of specialization in that activity, it is no wonder that substantial problems develop.
While a fixed quantity of money fulfills this first criterion well, it must be noted that any monetary regime that seeks to fix the quantity of money must carefully determine what counts as money and fix that. Too narrow, and those monetary assets not included can change in quantity, so that the total quantity of money varies. Too broad, and while an outer limit on the quantity of money is created, then true quantity of money can vary, and drop off significantly, while the total remains fixed.
However, a fixed quantity of money is only desirable if the demand to hold money is unchanging. The second criterion for a good monetary regime is that the quantity of money should always change with the demand to hold money. If the demand to hold money rises, the quantity of money should rise an equal amount. If the demand to hold money falls, the quantity of money should fall an equal amount.
Of course, if the nominal quantity of money fails to adjust to match the demand to hold money there is a market process that will bring about the necessary adjustment in the real quantity of money. All that is necessary is for the money prices of all goods and services, including resource prices like wages, to adjust. But because those setting prices specialize in the provision of other goods and services and not money, depending on this process is likely to be disruptive.
A monetary regime should allow for specialization in maintaining monetary equilibrium. While the money price of money is always one, the interest rate paid on money and the nominal quantity of money can both be adjusted. That money does not have its own market can hardly be avoided if it is to serve as medium of exchange. Still, those creating money can specialize and vary the yield on money that takes the form of deposits and the quantity of all types of money to keep the total quantity and each type of money equal to the demand to hold it.
Further, if the monetary regime adjusts the quantity of money to the demand to hold money, finding the perfect definition of money is not very important. For example, suppose the quantity of overnight commercial paper is wrongly excluded from the quantity of money. A loss in confidence in the issuers results in a drop in the "true" quantity of money. Those who where holding overnight commercial paper have to compete to obtain the limited quantity of conventional bank deposits. But this amounts to an increase in the demand for that narrower conception of money. If the quantity remains unchanged, there is a shortage of money even though the quantity of what is wrongly counted as money remains fixed. But if the quantity of that narrow conception of money rises to meet this added demand, then monetary disequilibrium is avoided.
Since the market process that brings the real quantity of money into balance with the demand to hold money ends with changes in the price level, it is certainly plausible that maintaining monetary equilibrium and avoiding monetary disequilibrium would amount to avoiding changes in the price level. This would be true if the only way that the price level changed was in response to monetary disequilibrium. Unfortunately, this is not correct.
Imagine a realistic scenario where there are many firms purchasing resources, such as labor, and producing a variety of products. Each firm sets money prices based upon expected demand and cost conditions. If the supply of one good should decrease, then firms producing and selling that good will raise its price enough to clear expected supply and demand conditions. As a matter of arithmetic, this raises the price level.
A monetary regime that stabilizes the price level would need to offset this price increase by forcing down the prices of other goods and services. Those specializing in the production and sale of the good with the decrease in supply can make appropriate adjustments in the price and quantity of that particular good, and those adjustments provide adequate signals and incentives to conserve the use of this good and expand its production (the increase in quantity supplied.) With a monetary regime that stabilizes the price level, not only does all other firms need to make adjustments in their prices to keep some index number at an arbitrary level, even the firm facing the decrease in supply must account for this indirect effect when setting its price.
How is it that a monetary regime would cause these adjustments in prices? It would be by generating an excess demand for money and reduced expenditures on all of the goods and services, forcing the price level back down. This would be inconsistent with having a monetary regime that maintains monetary equilibrium and avoids monetary disequilibrium.
Since in real market economies, stabilizing the price level implies creating monetary disequilibrium when the supply of some particular good changes, what is the alternative? Consider the process by which excess supplies or demands for money lead to a new equilibrium price level. For example, an excess supply of money leads to additional expenditures on goods and services. Of course, other things being equal, this added demand results in shortages of goods and services and higher prices. But why wait for the higher prices? When the excess supply of money leads to growing expenditures on output, adjust the quantity of money to stop and reverse the excess spending, returning to monetary equilibrium.
Rather than watching price indices for signs of monetary disequilibrium, it is better to watch measures of aggregate expenditure--nominal GDP. Consider again the impact of a decrease in the supply of some product. While those specializing in the production and sale of that product raise the price, they also reduce the amount produced and sold. The increase in price and reduction in quantity of offsetting consequences on spending on the particular product and so on total spending on output.
Only if the demand for the good with a change in supply is unit elastic will nominal GDP targeting leave total spending in the rest of the economy undisturbed. If demand is inelastic, spending will fall in the rest of the economy. If the demand is elastic, spending in the rest of the economy will rise. So, the argument isn't that nominal GDP targeting is perfect, but rather that it is better than price level targeting.
Nominal GDP targeting, like price level and quantity of money targeting, prevents changes in the quantity of money motivated by changes in the desire by government to spend or changes in the desire of the government or private sector to borrow. Nominal GDP targeting, like price level targeting, but unlike quantity of money targeting, accommodates changes in the demand to hold money without generating changes in spending on output and the price level. And finally, Nominal GDP targeting, like quantity of money targeting, limits the damage caused by price level targeting in the face of shifts in the supplies of particular goods.
Would it be nice to write down a model that exhibits these characteristics? I think so. Go to it.