Sunday, April 18, 2010

Where Did Mises Go Wrong?

The public finance approach to inflation starts with an "inflation tax" and reasons that the revenue generated from that tax can persistently impact the allocation of resources. In the example where the revenue is used to purchase tanks, the number of tanks a given inflation rate will allow the government to purchase in long run equilibrium can be characterized in terms of the price elasticities of supply and demand for tanks, the inflation rate, the quantity of real balances and how the demand for real balances responds to changes in the inflation rate. Working in reverse then, it should be possible to choose how many tanks the government would like to purchase, and then work out the necessary inflation rate to allow that many to be purchased in equilibrium.

Suppose that instead the procedure is to posit that the government would like to purchase a certain quantity of tanks using money creation, and then describe what happens to the rate of money creation and the rate of price inflation during the adjustment process. Ignoring that the short run elasticity of supply of tanks is likely to be lower than the long run, and assuming there is already some kind of market for tanks, it would be possible to imagine that the government purchases the needed number of tanks at their current market price. Because the money is spent before it has lost any purchasing power, the government gets a bargain.

Interestingly, this traditional Austrian argument that those receiving the money relatively early, before prices have risen, benefit, can be related to a joint effect of the disequilibrium and public finance effects of inflation. If the quantity of money rises faster than prices, the real quantity of money rises. That is an increase in the base of the inflation tax. A given revenue can be generated with a lower tax rate if the base is larger. Again, leaving aside problems with short run price elasticity of supply of tanks, a smaller rate of money growth is needed to purchase the needed quantity of tanks if the expansion of the quantity of money creates an excess supply of money.

Of course, any such excess supply of money will be ephemeral. And once the real quantity of money has adjusted to the real demand to hold money, the base is smaller and so a greater rate of money growth and price inflation is needed to obtained the desired number of tanks.

But the process doesn't stop there. Price inflation makes holding real money balances more costly, and so, the demand for real money balances falls. This raises the rate of money growth and the rate of price inflation needed to obtain sufficient real revenue to purchase the desired number of tanks.

And so, we see at least two reasons why obtaining the desired number of tanks requires that the government expand the rate of money growth and so the rate of inflation. However, in the end, we are left with the same inflation calculated from the long run elasticities of supply and demand for tanks and the elasticity of demand for real money balances with respect to the inflation rate. That inflation rate and the tank purchases can persist as long as money holders/taxpayers put up with the program.

Mises on the other hand, was constantly drawn to describing a process by which the rate of money creation and price inflation must rise higher and higher until the demand for real money balances falls to zero, and money has no value. Where did he go wrong?

The "laffer curve" may be a subject of some derision, but it is an implication of basic public finance. Tax revenue is found by multiplying the tax rate by the tax base. And typically, the tax base is negatively related to the tax rate. A low rate then, allows for a high base but a low revenue. A very high rate that results in a very low base and also a low revenue. There should be some intermediate tax rate that results in some intermediate base that generates the maximum amount of revenue.

Applying this concept to the inflation tax, a low inflation rate results in a very large demand for real money balances, but the low rate and high base generates a low revenue. A very high inflation rate results in in a very low demand for real money balances. The high rate and low base also generates a low revenue. At some intermediate inflation rate and some intermediate level of real balances, the maximum revenue is generated.

Assuming that the inflation tax is earmarked to the purchase of tanks, the maximum revenue that can be generated by the inflation tax, along with the price elasticities of supply and demand determines a maximum quantity of tanks that the government can purchase from the inflation tax.

Suppose that the government decides to use the inflation tax to purchase a number of tanks that is greater than that maximum? Suppose that the government can obtain that number of tanks in the short run because of the increase in the tax base resulting from a temporary excess supply of money, or else, because the demand for real money balances only gradually responds to the higher cost of holding balances. The short run elasticity of demand for real money balance with respect of inflation becomes more elastic over time.

The rational expectations equilibrium for this scenario is that money loses all value and the government purchases absolutely no tanks using the inflation tax. However, it is possible to imagine a gradual process by which the government obtains a large amount of tanks initially, but that it as it raises the rate of money creation and inflation to try to continue this volume of purchases, inflation becomes higher and higher, and the real demand for money falls, until this futile process results in money having no value.

Mises, of course, didn't describe this in the context of the use of the inflation tax to purchase tanks. Rather, he described it in terms of the use of money creation to lower real interest rates. The reason to lower interest rates was to stimulate the production of capital goods. Or mpore precisely, to shift production of consumer goods to the more distant future. Rather than think about how a particular rate of money creation would impact the composition of demand and the allocation of resources, the assumed rate of money creation is allowed to vary to maintain the desired impact on real interest rates and the demand for capital goods.

If the only process at work is the creation of an excess supply of money, then no persistent impact is possible. But even including the public finance effect, if the initial size of the targeted change in real interest rate and the demand for capital goods is beyond what can be stimulated by subsidies funded by the maximum revenue that can be generated by the inflation tax in the long run, then a futile effort to raise the inflation rates to maintain the effect on interest rates and the demand for capital goods will eventually destroy the value of money.


  1. Question Bill: have you read my macro book? I mean that seriously.

  2. Steve:

    No. I guess, "I was getting to it" is a bet stale after a decade.

    It looks like I have electronic access. I will get to it now.

  3. Steve:

    Any particular section you want to suggest? Or was this a suggestion I need to start at the beginning? :)

  4. Actually, it was genuine curiosity, mostly driven by the fact that I really do try to bring the ME/MD perspective into the ABCT in a way I think you'll like. All of these recent posts on ABCT seem to be going after a 1970s/80s version of the story.

  5. This isn't talked about much, but there is a completely different (microeconomic) way to look at ABCT when a central bank targets inflation.

    You start with money as a good that has certain high substitutability with some goods (we will call these financial assets) and very low substitutability with other goods (we will call these consumer goods).

    Note: financial assets have a utility that has the first derivative wrt the first derivative of its expected price wrt time > 0. (More utility for things that are expected to increase in price).

    In times of very high productivity increase, the price of consumer goods goes down. The central bank as it is targeting price level growth, will increase the money supply in response. So, people who are savers rationally shift their savings from money to other financial assets. The way you can save in a house is by getting a mortgage and then paying it every month.

    Eventually the monetary expansion reaches a point where the change in price level becomes high enough that the central bank raises the interest rate. Other goods then become more attractive, and financial goods prices fall. Now, if the system was leveraged (as housing is) then a small change in rates causes a massive (and very quick) drop in asset prices.

    This isn't quite the same story as usually told with ABCT, but I think it applies to our case, because our central bank targets changes in price level of a basket of goods that includes both consumer goods and assets. This means that when productivity is high, they will be expanding the money supply too much, which will make people look for alternatives to money (that aren't as liquid or useful), eventually leading to a crash.

  6. Doc:

    I think you need to translate your argument into more ordinary language.

    The rate of return of financial assets isn't usually described as "utility." It is a source of income that can fund future consumption which will provide utility.

    If the initial cause is increased productivity and so increased supplies of consumer goods, and the central bank is using its policy to keep prices from falling, then why isn't holding money just as a attractive as it was before the improved productivity?

    What has happened is that holding money didn't get more attractive by deflation.

    The argument appears to identify money with currency. Much of the effect should be people shifting from currency holdings to deposit holdings.

    Then you explain that this central bank that is keeping the price level stable has somehow causes prices to start rising.

    You shift to interest rate analysis at the end. The central bank increases the interest rate and home prices fall alot. That higher interest rates will change the prices of long live assets a good bit is true.

    I'm not sure that there isn't something of value here, but I think you should work on the exposition a bit.

  7. The description that Mises gives of ABCT is quite closely tied to the Gold Standard.

    Accelerating inflation is quite reasonable in that situation. It isn't with modern fiat currencies though.

    Mises would say (I think he did say it somewhere) that if a currency is officially revalued then the inflation problem can be solved if caught at an early enough stage.

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