For demand shocks, this assmnes that the costs of moderate inflation variabilitj- is

low.

because the first-order condhion does not depend on i or tf, the optimal policy is to go directly to the inflation rate that satisfies (9.28) regardless of the current state of the economy. Indeed, if policymakers respond to high inflation by creating an extended recession that brings inflation down to the level satisfying (9.28) only slowly, the total amount of unemployment will be no different than it would have been if they had reduced inflation aU at once. Thus they will have subjected the economy to an extended period of above-normal inflation for no benefit.

This baseline case implies that policymakers should not attempt to stabilize unemployment in the face of supply shocks. It also implies that the benefits of using policy to offset aggregate demand shocks come only from reducing the variability of inflation. The linearity of aggregate supply implies that if policymakers allow demand shocks to cause fluctuations in unemployment and inflation, average unemployment is unaffected; and the linearity of social welfare implies that fluctuations in unemployment do not affect welfare. Thus the only costs of the fluctuations come from the costs of the variation in inflation. If inflation variabiUty has low costs over the relevant range, policymakers should attach little importance to offsetting demand shocks.

Is There a Case for Stabilization Policy?

The key assumptions behind these results are the linearity of the social welfare function, (9.27), and of the aggregate supply curve, (9.26). Thus for there to be a substantial benefit to stabilization policy, one of these functions must be significantly nonlinear.

Consider first social welfare. Lucas (1987) shows that in a representative-agent setting, the potential welfare gain from stabihzing consumption around its mean is small; that is, he suggests that social welfare is not sufficiently nonhnear in output for there to be a significant gain from sta-bUization. His argument is straightforward. Suppose that utility takes the constant-relative-risk-aversion form:

U(C) = f, > 0, (9.29)

I -

where is the coefficient of relative risk aversion (see Section 2.1). Since l/"(C) = -ec" a second-order Taylor expansion of U(-) around the mean of consumption implies

E[U(C)] - f- - C--l, (9.30)

where V and cr are the mean and variance of consumption. Thus eliminating consumption variability would raise expected utility by approximately (e/2JC~~ac. Similarly, doubling consumption variability would lower welfare by approximately that amount.

To translate this into units that can be interpreted, note that the marginal utility of consumption at is . Thus setting to zero would raise expected utility by approximately as much as would raising average consumptionby(e/2)C~V/C " = (e/2)C~Vc. As a fraction of average consumption, this equals (6i/2)C"V/C, or (6>/2)(ctc/C)2.

Lucas argues that a generous estimate of the standard deviation of consumption due to short-run fluctuations is 1.5% of its mean, and that a generous estimate of the coefficient of relative risk aversion is 5. Thus, he concludes, an optimistic figure for the maximum possible welfare gain from more successful stabilization policy is equivalent to (5/2)(0.015)2, or 0.06%, of average consumption-a very small amount.

At first glance, it appears that Lucass conclusion rests critically on his assumption that there is a representative agent. Actual recessions do not reduce everyones consumption by a smaU amount, but reduce the consumption of a small fraction of the population by a large amount; thus their welfare costs are larger than they would be in a representative-agent setting. Atkeson and Phelan (1994) show, however, that accounting for the dispersion of consumption decreases rather than increases the potential gain from stabilization. Indeed, their analysis suggests a basis for the linear social welfare function, (9.27), where there is no gain at aU from stabihzing unemployment. Suppose that individuals have one level of consumption, Ce, when they are employed, and another level, Cu, when they are unemployed, and suppose that Cf and Cv do not depend on the state of the economy. Since is the fraction of individuals who are unemployed, average utility from consumption is uU{Cu) + (1 - u)U(Ce)- Thus expected social welfare from consumption is E[u]U(Cu) + {1 - E[u])U{Ce)- social welfare is independent of the variance of unemployment. Intuitively, in this case stabilizing unemployment has no effect on the variance of individuals consumption; individuals have consumption Ce fraction 1 -£[u] of the time, and Cv fraction £[u] of the time.

Consumption variability is not the only cost of fluctuations, however. The variability of hours of work may have much larger costs than the variability of consumption. The cyclical variability of hours is much larger than that of consumption; and if labor supply is relatively melastic, utility may be much more sharply curved in hours than in consumption. BaU and D. Romer (1990) find that as a result, it is possible (though by no means clear-cut) that the cost of fluctuations through hours variabiUty is substantial. Intuitively, the utility benefit of the additional leisure during periods of below-normal output may not nearly offset the utility cost of the reduced consumption, whereas the disutility from the additional hours during booms may nearly

Targets, Indicators, and Instruments

Pohcy actions affect the economy with a lag. In addition, pohcymakers have imperfect information about the current condition of the economy, about the path it would follow if policy did not change, and about the effects

Just as with the argument for the cost from consumption variability. Ball and Romers argument concerning the cost from hours variability requires that not all of the variation in aggregate hours take the form of movements between employment and unemployment.

See De Long and Summers (1989) for one attempt to argue for important nonlinearit> of the form that makes stabihzation policy beneficial. Ball (1994b), on the other hand, finds evidence of nonlinearity of the opposite form, which implies that stabihzation policy could actually increase average unemployment.

offset the beneht of the higher consumption. Thus if there is a substantial direct welfare gam from reducing the variance of output, it is likely to be through the impact on hours rather than on consumption.

It is also possible that stabihzation policy has important indirect benefits. One natural mechanism is through investment: investment may be higher when the economy is more stable. As a result, stabihzation policy could raise income substantially over the long run (see, for example, Meltzer, 1988). As Section 8.6 describes, however, the effect of uncertainty on investment is complicated and not necessarily negative. Thus whether stabilization policy has important benefits through this channel is not known.

There has been little work on nonlinearities in the aggregate supply curve. Many textbook formulations assume that the increase in inflation triggered by a fall in unemployment below the natural rate is larger than the decrease in inflation caused by a comparable rise in unemployment above the natural rate. If this is correct, reducing the variance of unemployment reduces the average increase m mflation, and thus makes a lower average unemployment rate feasible.

In fact, however, most researchers working on aggregate supply have found that a linear specification provides an adequate description of the data (see, for example, Gordon, 1990, and BaU and Mankiw, 1995). There is certainly no strong evidence of any large nonlinearity over the relevant range.2

If social welfare or aggregate supply is nonlinear in output, the optimal response to an unfavorable supply shock that raises inflation is to reduce inflation gradually rather than all at once. Thus a supply shock could give rise to an extended period of inflation. At the same time, however, such non-linearities would also imply that the optimal response to a positive supply shock is to bring inflation back up to its initial level only gradually. Thus although nonlinearities may provide grounds for stabilization policy, they do not provide a simple explanation of high average inflatioiL