A Note on the Relation between the Rate and Variability of Inflation

TL;DR: In this paper, the authors examined the relationship between the rate and predictability of inflation by examining the past experiences of a large number of countries during the postwar period and found that there is a systematic relationship between average rates of inflation and their variability or unpredictability, and that the calculations of a country's optimum target rate of inflation should be revised upward or downward to take into account the difference in uncertainty costs that might be expected to accompany different target rates.

Abstract: In recent years there has been considerable interest in the concept of the optimum rate of ancitipated inflation-that rate which taxes the holding of cash balances such that the marginal excess burden from the inflation tax equals the marginal cost of the most efficient alternative method of raising government revenue. (For recent discussion, and references to the earlier literature by Bailey, Freidman and others, see Tower (1971), Tower and Willett (1972) and Barro (1972).) This and related ideas have been used not only as intellectual exercises but also have been the basis of suggestions concerning macroeconomic policies. However, as Harry Johnson has noted, "Contrary to the assumptions of the 'inflation tax' model, inflation does not proceed at a steady and well anticipated rate, but proceeds erratically with large politically determined variations in the rate of price increase" (Johnson, 1967, p. 290). Such unanticipated inflation or deflation may entail considerable welfare cost. (On such costs, see the surveys by Bronfenbrenner and Holzman (1963) and Johnson (1967, pp. 104-142) and the references cited in these works.) Of course, recognition that actual inflation rates will not in general be perfectly anticipated does not by itself call for a modification of calculations of optimum rates of inflation. If the variability of inflation is independent of its average rate, then the situation of a particular target rate of inflation will not influence the cyclical variability of inflation and hence this consideration need not be taken into account in the calculation of optimum rates of inflation. If however a higher rate of inflation were expected to yield also a higher degree of variability of inflation, then the marginal costs of this additional uncertainty would have to be subtracted from the marginal net benefits of the corresponding degree of perfectly predicted inflation. Thus, if there is a systematic relationship between average rates of inflation and their variability or unpredictability, the calculations of a country's optimum target rate of inflation should be revised upward or downward to take into account the difference in uncertainty costs that might be expected to accompany different target rates of inflation. In addition, we note that the relevant measure of the variability of inflation is an absolute rather than relative one (see Logue and Willett, 1975). In this paper we seek information on the relationship between the rate and predictability of inflation by examining the past experiences of a large number of countries during the postwar period. Of course past experience is not always a safe guide to future performance. This is especially true in the present case because much of the observed variability of past inflation rates may have been induced by deliberate government policies aimed at stabilizing the price level rather than stabilizing expectations.