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The Monetary Policy Response to Uncertain Inflation Persistence Accessible Data
Figure 1: Economic Losses as a Function of Inflation Persistence (optimized Taylor rule; simple model example)
Figure 1 is a double-scaled chart with three lines in the body of e chart. Two of the lines are curves showing "relative" economic losses, as measured by a quadratic loss function described in the text of the Note, and where "relative" is taken to mean normalized such that the loss under the mean value of the uncertain parameter, beta, is taken to be the true value. Relative loss is measured on the left-hand scale and ranges from zero to ten. A red, solid line shows the relative losses under the assumption that policymakers know the true value of the parameter of interest, beta, and choose the optimal Taylor rule coefficients using that knowledge. The red line starts toward the lower-left of the chart where it is associated with the lowest value of beta in the range, 0.76 and the loss is about 0.8. It then rises slowly with beta, reaching a value of one, by construction, at the expected value of beta, which is 0.88. From there is turns up more sharply until it reaches its maximum value of about 3.8 at the upper bound for beta of 1.00. A green, dashed line shows the same relative loss, but in this case under the assumption that the value of policy rule coefficients that are optimal for the expected value of beta are used in all circumstances. The curve starts in the lower left at nearly the same values as does the red red line. It rises close-to-identically with the red line until it gets to values for beta of a bit over 0.9, then it becomes steep at a more rapid pace than does the red line, reaching a maximum value when beta = 1.00 of nearly 10.
The right-hand scale measures the probability of a given value of beta, measured in discretized units. The probabilities of values of beta are assumed to be uniform, so a blue solid line at the bottom of the chart turns out to be a simple rectangle.
Figure 2: Optimized Taylor Rule Coefficients as a Function of Inflation Persistence (simple model example)
Figure 2 shows policy rule coefficients that have been optimized for the values of beta over the allowable range. These coefficient values are the ones that correspond with the relative losses shown by the red solid line in figure 1. Two lines are shown, one for the optimized coefficient on the output gap, a red dashed line; the other for the optimized coefficient on inflation, a red solid line. The scale of coefficient values is shown on the left, and runs from about one to more than five. The optimized coefficients for both inflation and the output gap are small for lower values of beta, at around 1.2 to 1.6. Then as beta rises, the optimized coefficient on the output gap barely changes, while the optimized coefficient on inflation rises first relatively gently but then quite steeply as beta approaches unity. At the upper bound for beta of unity, the optimized coefficient on inflation is about 4.6.