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Wolman, Alexander L.. "Zero inflation and the Friedman rule: a welfare comparison." Economic Quarterly. Federal Reserve Bank of Richmond. 1997. HighBeam Research. 20 Oct. 2018 <https://www.highbeam.com>.
Wolman, Alexander L.. "Zero inflation and the Friedman rule: a welfare comparison." Economic Quarterly. 1997. HighBeam Research. (October 20, 2018). https://www.highbeam.com/doc/1G1-20382407.html
Wolman, Alexander L.. "Zero inflation and the Friedman rule: a welfare comparison." Economic Quarterly. Federal Reserve Bank of Richmond. 1997. Retrieved October 20, 2018 from HighBeam Research: https://www.highbeam.com/doc/1G1-20382407.html
A distinct trend in recent years has been for central banks to emphasize low and stable inflation as a primary goal. In many cases zero inflation - or price stability - is promoted as the ultimate long-run goal (Federal Reserve Bank of Kansas City 1996). Economic theory also stresses the benefits of low inflation. However, in contrast to the current fashion among central banks, one of the most famous - and robust - results in monetary theory is that the optimal rate of inflation is negative: in many economic models in which money plays a role, welfare is maximized when the inflation rate is low enough so that the nominal interest rate is zero. Central bankers are certainly aware of this result, yet they never seriously advocate a long-run policy of deflation (negative inflation).
How much welfare is lost from a zero inflation policy as opposed to an optimal deflation policy? As shown below, the shape of the economy's money demand function with respect to nominal interest rates holds the key to answering the question. Lucas (1994) argues for a specification where real balances increase toward infinity as the nominal interest rate approaches zero. He finds that zero inflation is not much of an improvement over moderate inflation but that optimal deflation offers sizable benefits. The analysis in this article supports a different conclusion: reducing inflation from a moderate level to zero entails substantial welfare benefits, and the additional benefit achieved by optimal deflation is small. My analysis is based on estimating a general money demand function that nests the one preferred by Lucas. The estimates imply a satiation level of real balances, which proves to be important for the comparison of zero inflation and optimal deflation.(1)
The original analysis of the relationship between money demand and the welfare cost of inflation is credited to Bailey (1956). I review both Bailey's analysis and that of Friedman (1969), whose "Friedman rule" is the famous result previously mentioned. I then describe informally Lucas's (1994) recent work on quantifying the costs of deviating from the Friedman rule. Whereas Lucas's work is guided by inventory theory, my own estimates follow from a broader interpretation of the transactions-time approach to money demand. I use these estimates for welfare analysis similar to Lucas's. Although the analysis suggests that the Friedman rule may not offer much of a benefit in comparison to zero inflation, it does not explain why central banks do not choose to pursue deflation. I thus point out several channels absent from my analysis through which inflation may have welfare effects. These additional channels may help to explain why central banks seem content to shoot for zero inflation.
1. MONEY DEMAND AND THE WELFARE COST OF INFLATION
Bailey (1956) showed how a money demand relationship could be used to derive estimates of the welfare cost of inflation. He assumed a money demand function that gave real balances (M/P, where M is the nominal quantity of money and P is the price level) as a function of the nominal interest rate (R) and made a consumer surplus argument: just as the area under the demand curve for any good measures the total private benefits of consuming that good, so the area under a money demand curve represents the private benefit of holding money. At a nominal interest rate of 5 percent, since people are willingly giving up 5 cents per year per dollar of money held, the marginal benefit of holding the last dollar must be 5 cents per year. Similarly, at a nominal interest rate of zero, people are not giving up any interest payments to hold money, so the marginal benefit of holding the last dollar must be zero. At a social optimum, the marginal benefit to society of holding money should equal the marginal cost to society of producing money. With the reasonable simplifying assumption that the cost to society of producing money is zero, the optimal nominal interest rate is zero.(2) In a steady state the nominal interest rate is approximately equal to the real interest rate plus the inflation rate, so optimal policy, commonly known as the Friedman rule, involves deflation at a rate equal to the real interest rate.
With a nominal interest rate of zero as the optimal policy, it is possible to measure the cost of any inflation rate for a particular money demand function. Simply measure the area under the inverse money demand curve between the real balances corresponding to the Friedman rule and the real balances corresponding to the nominal interest rate in question.(3) That is, add up all of the marginal benefits that are foregone by following a suboptimal policy; those marginal benefits are measured by the nominal interest rate (the inverse money demand function) at each level of real balances.(4) At this point the term "cost of inflation" may seem misleading; according to the theory sketched above, it would be more appropriate to use the term "cost of positive nominal interest rates." Since the former term is so widely used, however, I will stick with it.
Particular theories of money may imply more complicated money demand relationships than the one assumed by Bailey; for example, the analysis in Section 3 will involve consumption and the real wage as arguments in the money demand function. However, it is still the case that the Friedman rule is optimal, and holding consumption and the real wage constant, the area under the inverse money demand curve still provides an approximate measure of the direct cost of inflation.(5)
While the optimality of the Friedman rule holds as long as real balances are a decreasing function of the nominal interest rate (subject to the caveats in Section 5), the welfare costs of inflation can vary with the money demand function in two ways. First, the overall benefit of reducing inflation from, say, 10 percent to the Friedman rule can vary. Second, the apportionment of that benefit may vary, in the following sense. According to one money demand function, reducing inflation from 10 percent to zero may generate 99 percent of the total welfare benefit, with the remaining reduction to the Friedman rule adding essentially nothing. Another function could reverse this; reducing inflation from 10 percent to zero might generate only I percent of the total welfare benefit, with the remaining reduction to the Friedman rule being crucial for generating any significant benefits. This article is concerned mainly with the latter issue.
Lucas (1994) contrasts the welfare implications of two particular money demand functions, both of which specify the ratio of real balances to real consumption as a function of the nominal interest rate. The ratio of real balances to consumption is used because the money demand functions discussed here are assumed to apply to long-run data, and in the long run real balances move roughly one for one with consumption.(6) In the first specification, semi-log, there is a fixed relationship between the change in the nominal interest rate and the percentage change in the real balances to consumption ratio. That is, if the nominal interest rate rises from zero to 1 percent, the percent decrease in real balances/consumption is the same as if the nominal interest rate rises from 5 percent to 6 percent. In the second specification, log-log, there is a fixed relationship between the percentage change in the nominal interest rate and the percentage change in the real balances to consumption ratio. Thus an increase in the nominal interest rate from zero to I percent will cause a much larger percentage drop in real balances/consumption than an increase in the nominal interest rate from 5 percent to 6 percent. Note that if the log-log relationship is taken literally, the ratio of real balances to consumption must be infinite when the nominal interest rate is zero.
How do the two specifications compare in terms of welfare? With the log-log function, a slight increase in the nominal interest rate near zero generates a tremendous decline in the ratio of real balances to consumption. …
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