Friday, April 16, 2010

Austrian Business Cycle Theory 3: Public Finance

Many years ago, I read a paper by Richard Wagner that applied public finance principles to the Austrian Business Cycle theory. While there are many ideas in the paper, the key idea I took from the paper is that of course inflation impacts the allocation of resources. Why would a government run an inflationary policy if not to shift resources to its supporters?

I will describe an Austrian theory that is at least loosely based upon his argument. This is an equilibrium theory that allows for a sustainable change in the allocation of resources.

Contrary to the traditional exposition of the Austrian theory, I will begin by ignoring interest rates, consumption, and investment. Instead, I will describe malinvestment in the context of the market for tanks.

The economy in question is static. There is no economic growth. The money in the economy is a tangible, hand-to-hand fiat currency. The quantity of this currency has remained constant for some time. The currency is issued by the government, and it makes no commitment regarding its purchasing power or nominal quantity. The demand to hold this money has been unchanging as well. The price level has been stable.

The government determines that national security requires that it build up large force of tanks. Or perhaps a tank salesman has friends in high places. Further, imposing an explicit tax is politically impossible.

To solve this "problem" the government decides to print new money to to purchase the desired tanks. In other words, the government decides to use an inflation tax to fund government spending.

Suppose the government decides to impose an inflation tax of 10 percent each year. The government increases the quantity of money by 10 percent each year. In equilibrium, the price level rises at an annual rate of 10 percent.

This is called an inflation tax because it makes holding real money balances costly. The cost is the decrease in the purchasing power of money held . That is, of course, the same thing as the rate of increase in the price level. The cost of holding money balances is now 10 percent per year. (It is conventional to add to this the real interest rate to get the opportunity cost of holding money relative to financial assets.)

Because holding money balances is more expensive, the demand for real money balances will fall. This involves a shift to a higher price level. The new, lower level of real balances that people choose to hold forms the base of the inflation tax. The rate is 10 percent by assumption. The real revenue generated by the tax is found by multiplying the base times the rate. Again, this revenue is earmarked to the purchase of tanks.

While it is unlikely the economy will adjust immediately into this new equilibrium, for now, suppose that it does. Prices, including wages, instantly begin rising 10 percent a year. Nominal incomes begin rising 10% per year. The nominal quantity of money is rising 10 percent. The amount of real money balances that people hold remain constant. Real output remains constant.
However, the allocation of resources has changed. More tanks are produced. More resources are devoted to the production of tanks. Fewer resources are devoted to the production of other goods and services.

How is this possible? How does the tank industry capture additional resources from the rest of the economy?

The answer is simple. The inflation tax must be paid. In order to keep real balances unchanged, nominal money balances must be increased at the rate of inflation. This requires that nominal expenditures be less than nominal income. If all of nominal income were spent, nominal balances would be unchanged. With the rising price level, real balances would be falling.

For example, suppose Smith earned $50,000 per year and spent $50,000 on consumer goods and services and various securities. Smith held real money balances of $2,500. Suppose that prices and nominal incomes both rise 10%. Smith now earns $55,000. If Smith spends $55,000 on consumer goods and services and various securities, then Smith's nominal money holdings remain $2,500. Unfortunately, that purchases 10 percent less. To maintain the same command over goods and services, Smith needs $2,750 -- 10 percent more dollars. In order to obtain that, Smith must reduce nominal expenditures spending to $54,750.

Dividing through by the price level, these relationships imply that real expenditure must be less than real income. Goods and services are produced and incomes are earned, but households and firms in the private sector purchase fewer goods and services than they produce.

How is this consistent with equilibrium? The government's nominal and real expenditure on tanks closes the gap.

The decrease in real expenditures on various private goods and services reduces their demands. This frees up resources in order to produce the additional tanks. The government purchase of tanks creates a derived demand for the resources needed to produce the tanks.

If the economy really did immediately jump to the new equilibrium composition of demands, real expenditures on private goods and services would drop at the same time the real expenditures on tanks rises. This change in the composition of demand would result in structural unemployment. It will take time for workers to be absorbed in tank production from the other goods that are being sacrificed. Since the structurally unemployed workers aren't producing anything (other than leisure,) aggregate output is depressed until the workers are absorbed into tank production.

What about capital goods? Since capital goods are heterogeneous, the capital goods that had been built to produce the various private goods and services that are being sacrificed might be useless in producing tanks. Others might be helpful in producing tanks to some degree, but much less appropriate to tank production than for their previous employments.

Because the productive capacity of the economy depends on the particular goods being produced, the shift from private goods and services to tanks will result in temporarily lower aggregate output. That is, in the short run, the additional tanks that can be obtained will be less than what will finally be obtained once appropriate capital goods are constructed.

After there has been a complete adjustment to the new composition of demand, unemployment and output return to their previous level. The government is getting tanks. Those using money bear the cost of inflation. The price level is rising 10 percent a year. There is no economic reason why this situation cannot be permanent.

The situation is little different from any other tax. Suppose that the tanks were funded by an income tax. Real income and output will be depressed a bit and leisure increased. The lower level of output and income is the tax base. Revenue is found by multiplying the rate times the base. After tax income is found by subtracting the revenue from income. Because of lower-after tax incomes, nominal and real expenditure on private goods and services is lower than nominal and real income. The government closes that gap by spending on the tanks. The lower demand for private goods and services and higher demand for tanks requires a reallocation of resources. Structural unemployment and the need to produce capital goods appropriate to tank production implies lower output and employment during the transition. While the lower level of output would presumably lower money demand and slightly raise the price level, there would be no persistent inflation in this scenario.

Returning the the inflation tax, suppose the taxpayers determine that whatever increase in national security the tanks provide is simply not worth the cost. Further, suppose they can influence politicians so that the inflation stops and tanks are no longer purchased.

The demand for tanks falls (to zero.) There will be layoffs in the tank producing industry. However, the inflation tax now disappears. Since holding money balances is now less costly, the demand for real balances expand. This requires a slightly lower price level. After that adjustment, the price level is stable.

No longer do household and firms need to constantly build their nominal money balances to maintain their real money balances. Prices are stable. Constant nominal money balances provide for constant real money balances. Nominal and real expenditures can now be increased to match nominal and real incomes. Whatever it is that households and firms choose to purchase with that part of real income no longer needed to pay the inflation tax enjoy increased demand.

Assuming the economy had fully adjusted to the previous composition of demand, structural unemployment will be associated with the shift in the allocation of resources. With heterogeneous capital goods, there may be a total loss in equipment suitable only to the production of tanks and partial loses with capital that is only slightly appropriate to whatever private goods and services households prefer. The result will be a temporary reduction in output and employment. Fortunately, as labor shifts and appropriate capital goods are constructed, real output should recover.

Notice that this equilibrium approach to the Austrian theory is symmetrical. There is structural unemployment in both the "boom," and in the "bust." Both the implementation of the inflation tax/government expenditure scheme, and its repeal, result in structural unemployment, losses for specific capital goods, and a transition period where output is depressed.

Suppose that political story is slightly different. The politicians implement a very low inflation tax. They purchase only a few tanks. Finding that low inflation tax creates little political opposition, they try a slightly higher tax and purchase more tanks. The tank industry is gradually expanding. As resources shift from various private goods and services towards tanks over the years, the somewhat higher structural unemployment and lower level of output becomes the new normal.

Once inflation reaches 10 percent, the people rebel. They begin listening to those who claim that inflation is everywhere and always a monetary phenomenon. They begin to doubt the stories of the politicians that prices are rising due to growing greed in the private sector. Or perhaps they no longer value the tanks.

The politicians suddenly decide that inflation is politically unacceptable. They stop at once. The tank industry, after years of slow growth has grown quite large. Suddenly, it drops to zero. Since the inflation tax has dropped to zero as well, there is a substantial increase in the real demands for various private goods and services. Still, this sudden large change in the composition of real demand involves a substantial increase in structural unemployment. Combined with the complete or partial losses associated with capital goods more or less specific to the tank industry and the gradual build up of capital goods more appropriate to the production of private goods and services, the transitional decrease in output and employment looks sudden and large.

If the analysis is shifted from a static to a growing economy, there are many complications that must be added. The demand for real money balances is presumably growing. The government can issue money without there being price inflation. But rather than deal with all of those complications here, consider just the following change in the analysis. Suppose that the gradual build up in the inflation tax never required any reduction in the production of private goods and services or in the employment of labor in those sectors. Instead, real and nominal expenditures on private goods and services simply grew more slowly and employment in those areas grew more slowly. Some new entrants into the labor force began to produce tanks. Some of the new capital goods being produced were devoted to tanks. During the entire period of growing inflation, the rest of the economy is expanding, more people are hired, and more capital goods are produced. The composition of final demand and output, and of composition of the capital stock and the allocation of labor between sectors are all changing over time, but it is sufficiently gradual that there is never any absolute decrease in the demand or production of the private goods and services being sacrificed to pay the tax.

And now, suppose the voters demand an end of inflation, and the tank industry suddenly collapses. While the gradual build up of the tank industry and the gradually rising inflation tax simply implied that employment, investment and production in the private sector grew less than they would have, the shut down of the tank industry requires that workers find new jobs. Rather than simply not building fewer or no capital good specific to the tank industry, existing capital goods specific to tank production become worthless.

In other words, there is no symmetry in adjustment costs if the time taken for the adjustment isn't symmetrical. Consider the opposite scenario. Suppose their was a crash program to build up a tank force funded by inflation. And then, the inflation tax was gradually reduced. The workforce in the tank industry shrinks by attrition. Tank specific capital goods are not replaced. As resources are freed up to produce private goods, the inflation rate is lowered, and the private expenditures can expand because their is less build up nominal balances to maintain real balances. In that situation, there could be large reductions in the real demand for private goods and services and structural unemployment and losses in capital goods specific to those industries during the buildup. On the other hand, the gradual end of the inflation tax, there could be little obvious disruption in the transition. (Of course, the taxpayers give up private goods and services to get additional tanks.)

The Austrian theory has not been about tanks. While the most abstract approaches, about money entering the economy at one place and impacting relative prices and so output, is consistent with the story about tanks, generally, the Austrian theory has focused on interest rates, saving and investment.

Suppose that rather than using the revenue created from the inflation tax to purchase tanks, the government provides a subsidy for the provision of loans. Think of it as a subsidy for production and sale. The private sector generates a loanable fund market with the interest rate being the price of those loans. Lenders receive a payment from the government equal to some fraction of the interest rate. As usual with such a subsidy, the lenders are willing to supply more loans. The equilibrium interest rate paid by the borrowers is lower. While the amount lenders receive from borrowers is less, the equilibrium net interest rate the lenders receive is higher--what is paid by the borrowers plus the subsidy. The equilibrium quantity of loans is higher.

To the degree that an inflation tax on real money balances generates a revenue that is used to subsidize the provision of loans, a persistent shift in the allocation of resources is possible. Such a tax and subsidy scheme can be permanently sustainable. If it is instituted only gradually, then the transitional disruption caused by the change in the allocation of resources could be small, and more or less nonexistent in the context of a growing economy. If, however, the inflation tax became politically unacceptable, and it suddenly dropped, then the readjustment as interest sensitive industries sharply contracted could be wrenching.

Finally, can the revenue from an inflation tax be shifted to borrowers, not by providing lenders with a subsidy for the loans made, but rather by simply lending the funds created by the central bank out in competition with other lenders? I believe that the answer is yes, and that this equilibrium process has been often mixed in with the disequilibrium process described in my previous post.

In my view, the disequilibrium process--an excess supply of money generating an increase in the real supply of credit--is likely too ephemeral to generate any significant malinvestment. On the other hand, the equilibrium process by which an inflation tax on real money balances is used to subsidize lending, can be persistent. And if it is gradually introduced, and then suddenly removed, the result can be the sudden appearance of significant structural unemployment and what it hindsight appear to be inappropriate capital goods.

The problem with the equilibrium process is that the base of the inflation tax is the monetary base. Before the current crises, the monetary base was approximately $800 billion. The inflation "tax" was perhaps 5 percent. (The price inflation rate was 2 percent and the demand for real balances was growing about 3 percent.) That generates a $40 billion revenue. Nominal income is currently $14 trillion. Gross investment is about $1.6 trillion. While a $40 billion tax and subsidy scheme almost certainly impacts relative prices, the composition of output, and the allocation of labor and other resources, even reducing this "tax" all the way to zero would seem unlikely to generate significant adjustment costs.

In my judgment, both the disequilibrium and equilibrium processes are unlikely to generate significant malinvestment. I am not saying that there would be no malinvestment. In my judgement, liquidation of malinvestments generated by monetary policy do not significantly contribute to the decrease in production and increase in unemployment in recessions.

It is my view that too many single family homes were produced in the U.S. during the naughties. I think the structural unemployment and the need to construct appropriate capital goods to replace some that were specific to housing construction is a significant source of unemployment and may have absolutely reduced the productive capacity of the economy. But I don't believe that persistent excess supplies of money in the early naughties are a plausible source of the problem. And there certainly has not been an intentional decrease in the inflation tax.


  1. I feel guilty for not paying tuition fees when reading these posts. This is great stuff.

  2. Bill: Yes, that makes sense. Back of the envelope calculations: assume currency = 10% of GDP, and inflation is 10%, then the tax is 1% of GDP. So tank production is 1% of GDP. Suppose tanks are very capital intensive, and require specialised capital. What would be a ballpark figure for the amount of malinvestment? Maybe 5% of GDP, on a stock basis?

  3. @Nick, so is this a dead weight loss resulting from inflation?

  4. Doc: no, unless we say the tanks weren't needed. The deadweight loss should be thought of as the distortions to the demand for real money, plus to real income, from the inflation tax.

    There are 2 margins on which people can avoid the inflation tax: higher velocity of circulation for given amount of real market transaction; make a smaller amount of real market market transactions. The first distortion is the traditional deadweight loss, the area under the money demand curve. The second is like the distortion created by an income tax. And that's why the inflation tax has a higher deadweight cost than an income tax.

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