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).

Thus, while the long-run price level is not being stabilized, expected reductions in future inflation more than offset the initial increase in the price level. This stands in sharp contrast to the other rules reported in the table. For these rules, this coefficient exceeds one so that increases in the current price level lead to even larger increases in the long-run price level. This means that, on average, increases in inflation are followed by further inflation. This clearly destabilizes the long-run price level. In addition, because expected future inflation leads price setters who can change their prices at t to raise their prices by more, it also means that inflation at t is increased by policies that follow inflation at t with further inflation. For this reason, policies with high values of (З^ have both variable inflation and large variances in the innovation of the long run price level.

The remaining columns of Table 1 report statistics that measure various components of the utility-based measure of deadweight loss derived in the previous section. The columns labeled var(7r), var(7r — Ett) and var{£(F — Ys)} report the values of the three unconditional variances that receive positive weights in expression (1.33) for the loss measure L. The third column from the right then reports the implied value for L. This is our summary measure of the deadweight losses due to variability of inflation and output, in units of the variance of inflation. We scale inflation so that 7r = 1 corresponds to a 1% inflation per year. Hence, L = 1 indicates the same degree of deadweight loss as results from this inflation rate. The next-to-last column reports the minimum value of 7r* consistent with the degree of funds rate variability required by the policy rule, using (1.39) to derive this. Finally, the last column reports the implied value of L + 7Г*2, our total measure of deadweight loss.

One interesting fact about the table is that the ranking of alternative rules according to their implications for the variability of Y — Ys is quite different from their ranking according to their implications for the variability of output relative to its deterministic trend path. The Henderson-McKibbin (1993) rule Do, that minimizes var(Y) among those considered in the table, implies the highest degree of variability of output relative to the natural level Ys. This indicates that responding to deviations of output from a deterministic trend, while perhaps successful as a way of stabilizing output around that trend, may well be counter-productive if one is interested in keeping output close to its natural level. (Compare Figures 6 and 8 below, for further illustration of this point.)