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87 A large literature, pioneered by Barro (1977a, 1978) and significantly extended by Mishkin (1982, 1983), tests Lucass predictions concerning the impacts of observed and unobserved monetary policy using the money stock as the measure of policy. In Barros formulation, the basic idea is to regress output on measures of forecastable and unforecastable money growth and a set of control variables. Unfortunately, these tests suffer from the same difficulties as regressions of money on output (see Section 5.6). For example, a positive correlation between unexpected changes in the money stock and output movements can reflect an impact of output on money demand rather than an impact of money on output. Similarly, the absence of an association between predictable movements in money and changes in output can arise not because observed monetary changes have no real effects, but because the Federal Reserve is adjusting the money supply to offset the impact of other factors on output. See also Problem 6.3. on consumption was considerably smaller than was expected on the basis of the statistical relationship between disposable income and spending (see, for example, Dolde, 1979). Anticipated and Unanticipated Money The result that only unobserved aggregate demand shocks have real effects has a strong imphcation: monetary pohcy can stabilize output only if policymakers have information that is not available to private agents. Any portion of policy that is a response to publicly available informationsuch as interest rates, the unemployment rate, or the index of leading indicatorsis irrelevant to the real economy (Sargent and Wallace, 1975; Barro, 1976). To see this, let aggregate demand, m, equal m * + v, where m * is a policy variable and v a disturbance outside the governments control. If the govemment does not pursue activist pohcy but simply keeps m * constant (or growing at a steady rate), the unobserved shock to aggregate demand in some period is the realization of v less the expectation of v given the information available to private agents. If m * is instead a function of public information, individuals can deduce m *, and so the situation is unchanged. Thus systematic pohcy rules cannot stabiUze output. If the government observes variables correlated with v that are not known to the pubhc, it can use this information to stabihze output: it can change m * to offset the movements in v that it expects on the basis of its private information. But this is not an appealing defense of Keynesian stabihzation policy, for two reasons. First, a central element of conventional stabilization policy involves reactions to general, publicly available information that the economy is in a boom or a recession. Second, if superior information is the basis for potential stabilization, there is a much easier way for the government to accomphsh that stabihzation than foUowing a complex pohcy rule: it can simply announce the information that the public does not have. BaU (1991), building on the work of Sargent (1983), argues that the Lucas models predictions concerning observed policy can be tested by looking at
Empirical Application: International Evidence on OutputInflation Tradeoffs In the Lucas model, suppliers responses to changes in prices are determined by the relative importance of aggregate and idiosyncratic shocks. If aggregate shocks are large, for example, suppliers attribute most of the changes in the prices of their goods to changes in the price level, and so they alter their production relatively little in response to variations in prices (see [6.20]). The Lucas model therefore predicts that the real effect of a given aggregate demand shock is smaller in an economy where the variance of those shocks is larger. To test this prediction, one must find a measure of aggregate demand shocks. Lucas (1973) uses the change in the log of nominal GDP. For this to be precisely correct, two conditions must be satisfied. First, the aggregate demand curve must be unitelastic; in this case, changes in aggregate supply affect P and Y but not their product, and so nominal GDP is determined entirely by aggregate demand. Second, the change in log nominal GDP must not be predictable or observable; that is, letting x denote log nominal GDP, Ax must take the form + , where is white noise. With this process, the change in log nominal GDP (relative to its average change) is also the unobserved change. Although these conditions are surely not satisfied exactly, they may be accurate enough to be reasonable first approximations. Under these assumptions, the real effects of an aggregate demand shock in a given country can be estimated by regressing log real GDP (or the change in log real GDP) on the change in log nominal GDP and control variables. The specification Lucas employs is yt = V 7t V t ixt V \, (6.34) where is log real GDP, t is time, and Ax is the change in log nominal GDP. Lucas estimates (6.34) separately for various countries. He then asks whether the estimated tsthe estimates of the responsiveness of output to aggregate demand movementsare related to the average size of countries times of announced sfiifts to tigliter monetary policy to combat inflation. The Lucas model predicts that there should be no systematic relationship between real variables and any publicly known information about monetary policy. Thus it imphes that output growth should not be on average different from normal following such announcements. But Ball argues that when policymakers do not carry through with the announced policy, inflation typically changes little and output growth generally remains about normal, and that when they do carry through, inflation typically declines and output growth usually falls below normal. Thus, he concludes, output growth is on average below normal following the announcements, which is not consistent with Lucass model.
T, = 0.388  1.639  ,,, (0.057) (0.482) = 0.201, (6.36) s.e.e. = 0.245, where the numbers in parentheses are standard errors. Thus there is a highly statistically significant negative relationship between the variabihty of nominal GDP growth and the estimated effect of a given change in aggregate demand, just as the model predicts. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3,     +* +       +++    >  + + +    1 1 1  1 1 
0 0.1 0.2 0.3 0.4 Standard deviation of nominal GNP growth FIGURE 6.1 The outputinflation tradeoff and the variability of aggregate demand (from Ball, Mankiw, and Romer, 1988) aggregate demand shocks. A simple way to do this is to estimate T, = a + /  ,,, (6.35) where , is the estimate of the real impact of an aggregate demand shift obtained by estimating (6.34) for country z and  ,1 is the standard deviation of the change in log nominal GDP in country i. Lucass theory predicts that nominal shocks have smaller real effects in settings where aggregate demand is more volatile, and thus that p is negative. Lucas employs a relatively small sample. His test has been extended to much larger samples, with various modifications in specification, in several studies. Figure 6.1, from BaU, Mankiw, and D. Romer (1988), is typical of the results. It shows a scatterplot of against cr\x for 43 countries. The corresponding regression is
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