INTEREST-RATE RULES: Consequences of Simple Policy Rules 4

Another fact that is apparent from the table is that the ranking of different rules according the value achieved for L is essentially the same as their ranking in terms of the variability of inflation. Thus our utility-based welfare criterion L+7T*2 leads to conclusions that are similar to those that would be reached by giving some weight to the reduction of both the variability of inflation and the variability of the funds rate. In both these respects, the rules labeled Ei: Giy and I are better than the others. We turn now to a more systematic exploration of the consequences of parameter variations, in order to clarify why this is so.
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INTEREST-RATE RULES: Consequences of Simple Policy Rules 3

The regression coefficients Д*, of the innovation in the long-run price level on the current price level innovation reported in Table 1 help to explain this finding. This coefficient is obviously zero for the price-level rules, since these equilibria involve no change in the forecast of the long-run price level at any time. For the Ег rules as well as for the rule marked /, which is the rule that minimizes L + 7Г*2 among all possible rules, this coefficient is actually smaller than -1. This means that increases in the contemporaneous price level eventually lead to a lower price level, and indeed, to a lower price level by an amount that is even greater than the size of the initial price-level innovation (but with an opposite sign).
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INTEREST-RATE RULES: Consequences of Simple Policy Rules 2

The first column of Table 1 serves as a key for Figures 1, 2 and 3, where the consequences of these rules for the variability of output, inflation, interest rates and long-run price-level forecasts are plotted. The first of these figures has a certain similarity to the policy frontier shown in Taylor (1979), in that rules that have smaller standard deviations of inflation tend to involve larger standard deviations of output and vice versa. The only rules that appear to be “dominated” in this plot are the rules with labels in the series C* and Д. These are simple “Taylor Rules” that make the funds rate a function only of current inflation and output, and they respond much more strongly to output fluctuations than does our optimal rule in that family (labeled F0).
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INTEREST-RATE RULES: Consequences of Simple Policy Rules

When we study rules that can be described by only a small number of parameters, we study the consequences of parameter variation for two sorts of issues. First we analyze the range of parameter which ensure that a determinate rational expectations equilibrium exists; as an extensive prior literature has stressed, determinacy of equilibrium cannot be taken for granted in rational expectations models, especially in the case of a monetary policy defined by an interest-rate rule. (See, e.g., Bernanke and Woodford, 1997, for general discussion of this issue, and illustrations in the context of a model similar to the one that we use here.) Next we study the effect of parameter variation within the range of parameter values for which equilibrium is determinate.
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INTEREST-RATE RULES: The Welfare Loss from Price-Level Instability 6

While minimizing the welfare losses of the agents in the economy is a rather obvious objective for policy, it is worth looking more generally at the effect of different monetary policy rules on the variances of output, inflation, and interest rates. This analysis has several benefits. First, it provides intuition for our results concerning the effects of different rules on L + 7Г*2. Second, because this analysis is not as dependent on the subset of parameters that we calibrate, it remains valid even if some our calibrations are inappropriate. Feel free to come by whenever your find yourself in need of some money, easy pay day loans to get as much as you need for solving your temporary financial troubles without embarrassing yourself in front of your friends and relatives. Visit us right now at www.easyloans-now.comto see how we can help you out

Finally, the model may be incorrect in ways that maintain the validity of our estimates of the structural parameters but vitiate our welfare analysis. We do not know the precise range of variations on the model for which this would be true. One simple example would be if there are changes over time in the elasticity of substitution of different goods for each other. This would imply that the Dixit-Stiglitz aggregator varies over time. The resulting changes in the elasticity of demand faced by each firm would lead firms to desire changes in the ratio of price to marginal cost.
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INTEREST-RATE RULES: The Welfare Loss from Price-Level Instability 4

For some Л > 0, assumed in many analyses of optimal monetary policy (e.g., Taylor (1979), Bean (1983)). Our utility-based derivation, however, allows us to assign a specific numerical weight to the relative importance of stabilization of output around У5, as opposed to inflation stabilization. It also clarifies the kinds of stabilization that are important. Because of the lags involved in pricing, it turns out to be desirable to reduce the variability of both expected inflation and unexpected inflation. Moreover, the variability of unexpected inflation deserves somewhat greater weight, unlike what the ad hoc loss function above would imply.
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