The Bullseye Chart
When there is only one goal for policy, a comparison of the current value against its target is a straightforward gauge of progress. However, evaluating results when there are two goals is more complicated. The bullseye chart provides a means of visualizing the simultaneous progress toward each goal.
Each circle plots the combinations of inflation rates and unemployment rates that represent an equivalent "policy loss" when equal weight is placed on deviations of core inflation from 2 percent and the unemployment rate from the SEP long-run median (un). The smaller the circle, the smaller the policy loss.
The unemployment rate is displayed on the horizontal axis and the core PCE inflation rate is on the vertical axis. The black vertical line shows FOMC participants' estimate of the longer-run normal rate of unemployment that is consistent with full employment. The black horizontal line indicates the 2 percent inflation target. The two goals together form the cross hairs of the bullseye. The black circle in the center is where the two monetary policy goals are met.
Any combination of unemployment and inflation can be represented as a distinct dot on the chart. The plot can be divided into four quadrants. Dots that lie to the southeast of the bullseye have an unemployment rate above its estimated goal and an inflation rate below the 2 percent objective. Dots that lie to the northeast of the bullseye have both unemployment and inflation above desired levels. Dots that lie to the southwest of the bullseye have both unemployment and inflation below the FOMC's stated aims. Lastly, dots that lie to the northwest of the bullseye have unemployment below the estimated rate consistent with full employment but inflation above the 2 percent objective.
For dots that are in the southeast and northwest quadrants, monetary policy actions that support progress toward one goal of the dual mandate also support movement toward the other objective. For example, when the unemployment rate exceeds the FOMC's objective and inflation is less than 2 percent, appropriate monetary policy calls for a more accommodative stance that will support movement toward the bullseye. The two goals do not present a conflict for policymakers. However, dots that are in the southwest and northeast quadrants are more challenging: Policy prescriptions that support moving toward the bullseye by making progress on one goal are in conflict with achieving the other goal. For example, a point in the northeast quadrant has both too high unemployment and too high inflation relative to the FOMC's respective targets. In this case a more accommodative policy that would reduce unemployment toward its longer-run normal rate runs the risk of increasing inflation further above the FOMC's target. When the objectives are not complementary, the FOMC has explicitly stated that it will take a "balanced approach" to policy that weighs the costs of policy misses.
The distance from the center of the bullseye to any given dot provides a means of measuring how far from the dual mandate objectives the economy stands at that particular combination of unemployment and inflation. Any point that is further away indicates that the miss is greater, as is the economic cost associated with that miss.
The concentric circles drawn around the target show all the points that are equally distant from the center. These circles can be thought of as all the different combinations of inflation and unemployment that produce the same degree of economic loss. Consequently, the circles provide a means for policymakers to evaluate and compare the losses associated with different possible situations. For example, having an unemployment rate at target but an inflation rate that is 1 percent below our goal generates the same degree of loss as a situation in which the inflation rate is at target but the unemployment rate is 1 percent higher than its long run goal. The loss is also identical to a situation in which the unemployment rate is at its target but the inflation rate is 1 percent above the 2 percent goal, placing it at 3 percent.
In calculating the degree of economic loss associated with any particular divergence from our dual mandate goals, three assumptions are made. First, losses are symmetric so that undershooting a goal is just as harmful as overshooting that goal by the same margin. Second, larger misses entail larger losses. Third, each objective carries the same weight. Consequently, losses generated from missing on one objective of our dual mandate are the same as losses occurring from an equal miss on the other objective. These three assumptions are embodied in the following loss function
L = (π-2)2 + (u-un)2
where L is the calculated loss, π is the inflation rate with an objective of 2 percent and u is the unemployment rate with an objective of un percent.