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FRBSF Economic Letter

97-27; September 19, 1997

What is the Optimal Rate of Inflation?

  • The Friedman Rule
  • Seignorage and Other taxes
  • Other Considerations
  • References

  • Central banks are now placing greater emphasis on maintaining low inflation, and this raises the question: How low should inflation be? Some say that the current level of inflation is acceptable, while others argue that inflation should be pushed toward zero. There are a number of ways to think about this problem, and one approach focuses on conditions for the optimal quantity of money. This Economic Letter summarizes the lessons which this literature contains.

    The Friedman Rule

    Milton Friedman (1969) provided a simple rule for determining the optimal rate of inflation. He started with the observation that money provides valuable services, as it makes it easier and more convenient for consumers to execute transactions. For example, while many establishments accept both money and credit cards as payment for goods and services, others accept only cash. A consumer could probably get by with credit cards alone, but this would entail spending more time seeking out establishments that accept them. Having some money in one's pocket saves the time and inconvenience of doing so.

    While money is useful for carrying out transactions, it is also costly to hold. Monetary instruments generally earn less interest than securities such as Treasury bills. In fact, some forms of money, such as currency, earn no interest at all. The decision to hold more money means investing less in securities that pay more interest, and the cost of holding money depends on how much interest income is forgone. In order to decide how much money to hold, consumers must trade off the benefits of ease and convenience in carrying out transactions against the cost in terms of forgone interest earnings. In the end, people strike a balance between the two factors, holding more money when the cost is low and less when it is high. But as long as monetary instruments pay less interest than other securities, money will be costly to hold and consumers will have an incentive to economize on its use.

    But economizing on money is somewhat wasteful from society's point of view. For while money is costly to hold, it is essentially costless for central banks to produce. Thus, by increasing the quantity of real balances (i.e., the nominal quantity of money divided by the price level), the central bank could make everyone better off at no cost to itself. That is, consumers would benefit from additional real balances because they would make it more convenient to carry out transactions, and it would cost the central bank nothing to provide this service. Robert Lucas (1987) writes that this is "one of the few legitimate 'free lunches' economics has discovered in 200 years of trying." Pursuing this idea to its logical conclusion, Friedman argued that the optimal policy involves eliminating incentives to economize on the use of money. To do so, the central bank should seek to eliminate the difference between interest rates on monetary instruments and on other securities, because then money would be costless to hold.

    At the time Friedman wrote, money paid no interest, and the optimal policy called for setting nominal interest rates on bonds equal to zero. To a first approximation, the nominal interest rate equals the real interest rate plus expected inflation. To set the nominal interest rate to zero, it follows that the inflation rate must equal minus the real interest rate. If the latter were around 2 to 3%, Friedman's arguments suggest that the central bank should seek to deflate at a rate of 2 to 3%. This would involve reducing the nominal quantity of money, but this would fall at a slower rate than the price level, and the quantity of real balances would increase.

    An alternative way to eliminate the interest differential between money and bonds would be to pay interest on money. While monetary instruments such as checkable deposits now earn interest, narrow measures such as currency do not, and it is difficult to imagine a low-cost way to begin paying interest on cash. But since currency is still essential for some purchases, it would still be optimal for the central bank to make it costless to hold. And since no interest is paid on currency, the Friedman rule carries through.

    Seignorage and Other Taxes

    Edmund Phelps (1973) criticized the Friedman rule on the grounds that it ignores considerations related to taxation. Phelps pointed out that inflation is a source of tax revenue for the government and that if inflation were reduced other taxes would have to be increased in order to replace the lost revenue. He also argued that some inflation would be desirable if distortions associated with inflation taxes were less costly than distortions associated with other taxes to which the government might resort.

    Phelps's argument raises a number of important issues. First, in what sense is inflation a source of tax revenue? The government can finance its purchases in three ways: by levying direct taxes, by borrowing from the public, and by printing money. When the government pays for goods and services with newly printed money, it increases the money supply, which raises the price level, and the increase in the price level diminishes the real value of pre-existing money held by the public. Thus, inflation works like a tax on people who hold money: the newly printed money enables the government to buy goods and services at the expense of everyone who held pre-exisiting money balances, which fall in real value as a consequence of the increase in the price level. Revenue raised in this manner is called "seignorage."

    If a central bank were to follow the Friedman rule, it would reduce inflation and force the government to rely on other taxes to pay its bills. Phelps argued that those taxes introduce distortions of their own, which may outweigh the benefits of reduced inflation. What is the nature of these distortions?

    To a first approximation, taxes on income, consumption, capital gains, and so on are levied on a proportional basis. Thus, for example, workers who earn higher levels of income pay higher income taxes. This distorts private economic decisions because it creates incentives to alter behavior in order to avoid the tax. For example, a tax on labor income raises the pre-tax wage that firms have to pay but lowers the after-tax wage that workers receive. An increase in the pre-tax wage reduces the quantity of labor that firms want to hire, and a fall in the after-tax wage reduces the quantity of labor that workers are willing to supply. The tax makes firms worse off because they pay higher wages but employ fewer workers and produce less output. The tax also makes workers worse off because they earn lower wages and work fewer hours. The government collects revenue from the tax and uses it to provide public goods and services, but the losses of those who pay the tax generally exceed the revenue collected. The difference between the losses of those who pay the tax and the revenue raised is known as the "deadweight loss" or "excess burden" of the tax, and one principle of public finance is that taxes should be administered in a way that minimizes these losses.

    The Friedman rule would certainly not be optimal if seignorage revenue were replaced by other tax increases that were even more distortionary. On the other hand, the fact that governments must choose among distortionary taxes does not necessarily invalidate the Friedman rule. The optimal mix depends on how distortionary the various taxes are. Phelps argued that at low rates of inflation, distortions associated with the inflation tax might be minor and that substituting other taxes for the inflation tax might result in greater deadweight losses. But contrary to Phelps's argument, there are reasons to believe that the inflation tax is highly distortionary.

    One is related to the fact that money is an intermediate good rather than a final good. Intermediate goods are those goods which are used in the production of other goods and services, and taxes on these commodities are regarded as undesirable because they introduce two sets of distortions. On the one hand, they reduce production efficiency and increase the cost of producing final goods. And on the other, since this increase in cost is reflected in final goods prices, they distort final goods markets as well. Alternatively, the government could raise the same amount of revenue by taxing final goods directly, and while this would still distort final goods markets, it would not distort production efficiency.

    V.V. Chari, Lawrence Christiano, and Patrick Kehoe (1996) apply this principle to the inflation tax. They point out that money is intrinsically useless and should not be classified as a final good. Instead, since money is useful for facilitating transactions, it should be regarded as an intermediate good. This line of reasoning suggests that the inflation tax is really an indirect tax on other goods and that taxing those goods directly might be more efficient. In fact, Chari, et al., construct a number of theoretical examples in which this is so. In their examples, the Friedman rule remains optimal even though seignorage revenue must be replaced by distortionary taxes on labor income or consumption. That is, although the replacement taxes are distortionary, their calculations suggest that the inflation tax is even more distortionary.

    Furthermore, even when the Friedman rule isn't strictly optimal, there are two reasons why it is likely to be nearly so. First, Robert Lucas (1994) estimates that even low rates of inflation involve substantial welfare costs. Second, seignorage accounts for only a small fraction of tax revenue raised in the U.S., usually less than 3%, and the adjustments in other taxes needed to replace lost seignorage revenue are likely to be minor. Taken together, these two facts suggest that the optimal inflation tax is not likely to be far from the Friedman rule. For example, Casey Mulligan and Xavier Sala-i-Martin (1997) estimate that taking replacement taxes into account raises the optimal inflation rate by perhaps as much as 1%. R. Anton Braun (1994) estimates that tax considerations raise the optimal inflation rate by between 1 and 6%. Taking the average of Braun's estimates and subtracting a real interest rate of, say, 2.5% yields an optimal inflation rate of 1%. Thus, one can rationalize a goal of (approximate) price stability by appealing to optimal tax arguments.

    Other Considerations

    Other factors might further increase the optimal rate of inflation. For example, the underground economy uses cash intensively and is difficult to reach with other tax instruments. Some additional inflation might be desirable as a tax on activity in this sector. Similarly, much of the stock of U.S. currency is held abroad, and it might be desirable to collect seignorage from foreigners. Quantitative information on the amount of money held abroad or used in the underground economy is sparse, however, and it is difficult to say how much these factors might raise the optimal inflation rate.

    Timothy Cogley
    Senior Economist


    Braun, R. Anton. 1994. "How Large Is the Optimal Inflation Tax?" Journal of Monetary Economics 34, pp. 201-214.

    Chari, V.V., Lawrence J. Christiano, and Patrick J. Kehoe. 1996. "Optimality of the Friedman Rule in Economies with Distorting Taxes." Journal of Monetary Economics 37, pp. 203-223.

    Friedman, Milton. 1969. The Optimal Quantity of Money and Other Essays. Chicago: Aldine.

    Lucas, Robert E., Jr. 1987. Models of Business Cycles. Oxford: Basil Blackwell.

    _____. 1994 "On the Welfare Cost of Inflation." CEPR Working Paper No. 394.

    Mulligan, Casey B., and Xavier X. Sala-i-Martin. 1997. "The Optimum Quantity of Money: Theory and Evidence." NBER Working Paper No. 5954.

    Phelps, Edmund S. 1973. "Inflation in the Theory of Public Finance." Scandinavian Journal of Economics 75, pp. 67-82.

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