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147 Potential Benefits of Inflation So far we have considered only costs of inflation. But inflation can have benefits as well. Tobin (1972) observes that if it is particularly difficult for firms to cut nominal wages, real wages can make needed adjustments to sectorspecific shocks more rapidly when inflation is higher. Summers (1991) notes that since nominal interest rates cannot be negative, low inflation (by causing usual nominal rates to be low) may limit the Federal Reserves ability to stimulate aggregate demand in response to contractionary shocks. And just as inflation above some level can disrupt longterm planning and increase uncertainty, so too can inflation below some level. Given that average inflation has been significantly positive over the last several decades, it is not If these costs of inflation variability are large, however, there may be large incentives for individuals and firms to write contracts in real rather than nominal terms, or to create markets that allow them to insure against inflation risk. Thus a complete account of large costs of inflation through these channels must explain the absence of these institutions. Moreover, the estimates of Fischer and of Rudebusch and Wilcox suggest that at moderate inflation rates, a 1percentagepoint reduction in inflation is associated with roughly a 0.2percentagepoint increase in growth. This association is so large that it is difficult to identify plausible ways that it can represent an effect of inflation on growth. "This argument is due to Allan Meltzer. ones." And finally, highly variable inflation (or even higher average inflation alone) can also discourage longterm investment because hrms and individuals view it as a symptom of a government that is functioning badly, and that may therefore resort to confiscatory taxation or other polices that are highly detrimental to capitalholders. Empirically, there is a strong negative association between inflation and investment, and between inflation and growth (Fischer, 1991, 1993; Rudebusch and Wilcox, 1994). At this point, however, there is little evidence concerning whether these relationships are causal. It is not difficult to think of reasons that the associations might not represent true effects of inflation. In the short run, negative supply shocks are associated with both higher inflation and lower productivity growth. In the long run, governments that foUow pohcies detrimental to growthprotectionism, large budget deficits, and so onare likely to also pursue policies that result in inflation (SalaiMartin, 1991b).3 For high inflation rates, one can argue that the issue of whether the association between inflation and growth represents an effect of inflation on growth is of limited relevance. For a coimtry to reduce inflation from very high levels, it is likely to need to adopt a broad range of budgetary and policy reforms. Thus growth is likely to rise, even though it may be the other reforms and not the reductions in inflation that bring it about.* In contrast, inflation can be reduced from moderate to low levels without fimdamental policy reforms. Thus for moderate and low inflation, the issue of causation is crucial.
Concluding Comments As this discussion shows, research has not yet yielded any firm conclusions about the costs of inflation and the optimal rate of inflation. Thus economists and policymakers must rely on their judgment in weighing the different considerations. Loosely speaking, they fall into two groups. One group views inflation as pernicious, and believes that pohcy should focus on eliminating inflation and pay virtually no attention to other considerations. Members of this group generally believe that policy should aim for zero inflation or moderate deflation. The other group concludes that extremely low inflation is of httle benefit, or perhaps even harmful, and beUeves that policy should aim to keep average inflation low to moderate but should keep other objectives in mind. The opinions of members of this group about the level of inflation that policy should aim for generally range from a few percent to close to 10 percenL Problems 9.1. Consider a discretetime version of the analysis of money growth, inflation, and real balances in Section 9.2. Suppose that money demand is given by m,  Pr =  b{E,PmPt), where m and p are the logs of the money stock and the price level, and where we are imphcitly assuming that output and the real interest rate are constant (see 9.36]). (a) Solve for Pt in terms of and Etp,+\. (b) Use the law of iterated projections to express £tPt+i in terms of Eim,+j and EtPt+2 (c) Iterate this process forward to express p, in terms of mt, , ,\, E,mt+2, .... (Assume that lim, „oo E,[{b/(1 + )] , ] = 0. This is a nobubbles condition analogous to the one in Problem 7,7 ) clear that zero inflation minimizes uncertainty and is least disruptive. Finally, as described above, inflation is a potential source of revenue for the government; under some conditions it is optimal for the government to use this revenue source in addition to more conventional taxes. In addition, it is possible that the publics aversion to inflation represents not some deep imderstanding of the costs of inflation that has eluded economists, but a misapprehension. For example, Katona (1976) argues that the pubhc perceives how inflation affects prices but not wages. Fhus when inflation rises, individuals attribute only the faster growth of prices to the increase; they therefore incorrectly conclude that it has reduced their standard of living. Alternatively, individuals may dislike inflation just because times of high inflation are also times of low real growth; but if the high inflation is not in fact the source of the low growth, again inflation does not actually make them worse off.
(d) Explain Intuitively why an increase in E,m,+, for any i > 0 raises p,. (e) Suppose expected money growth is constant, so Etmt+, = m; + gi. Solve for Pt in terms of mt and g. How does an increase in g affect p,? 9.2. Consider a discretetime model where prices are completely unresponsive to unanticipated monetary shocks for one period and completely flexible thereafter. Suppose the IS and LM curves are =  ar and mp=b+hyki, where y, m, and p are the logs of output, the money supply, and the price level; r is the real interest rate; / is the nominal interest rate; and a,h, and are positive parameters. Assume that initially m is constant at some level, which we normalize to zero, and that is constant at its flexibleprice level, which we also normalize to zero. Now suppose that in some periodperiod 1 for simplicitythe monetary authority shifts unexpectedly to a policy of increasing m by some amount g > 0 each period. (a) What are r, , (, and p before the change in policy? (b) Once prices have fully adjusted, " = g. Use this fact to find r, j, and p in period 2. (c) In period 1, what are i, r, p, and the expectation of inflation from period 1 to period 2, Eiipz]  Pi? (d) What determines whether the shortrun effect of the monetary expansion is to raise or lower the nominal interest rate? 9.3. Assume, as in Problem 9.2, that prices are completely unresponsive to unanticipated monetary shocks for one period and completely flexible thereafter. Assume also that = car and mp b + hyki hold each period. Suppose, however, that the money supply follows a random walk: m, = mti + Ut, where u, is a meanzero, serially uncorrelated disturbance. (a) Let E, denote expectations as of period f. Explain why, for any , £([£(+![Pt+2]  Pt+i] = 0, and thus why E,mt+i  EtPt+i = b + hy  kr. (b) Use the result in part (a) to solve for yt, Pt, U, and rt in terms of mt i and Uf. (c) Does the Fisher effect hold in this economy? That is, are changes in expected inflation reflected oneforone in the nominal interest rate? 9.4. Suppose you want to test the hypothesis that the real interest rate is constant, so that changes in the nominal interest rate reflect changes in expected inflation. Thus your hypothesis is i, = r + frt+i (a) Consider a regression of i, on a constant and + Does the hypothesis that the real interest rate is constant make a general prediction about the coefficient on T7f+i? Explain. (Hint: for a univariate OLS regression, the coefficient on the righthandside variable equals the covariance between the righthandside and lefthandside variables divided by the variance of the righthandside variable.) (b) Consider a regression of 7 +] on a constant and U. Does the hypothesis that the real interest rate is constant make a general prediction about the coefficient on 7 Explain.
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