Taylor Rule

The rules. Each rule sets a federal funds rate from the neutral real rate r*, inflation π over the past twelve months, an inflation target π*, and a measure of slack, the gap, in percent of potential output (an unemployment gap is converted to an output gap by the Okun coefficient). Taylor (1993): r* + π + 0.5(π − π*) + 0.5·gap. Balanced approach: the same with a coefficient of 1 on the gap, twice Taylor's, as the Federal Reserve Board's policy-rules page defines it. Balanced approach (shortfalls): the gap term counts only when output is below potential, the variant the Fed's Monetary Policy Report added in February 2021. First difference: last quarter's rate + 0.5(π − π*) + 0.5(gap now − gap a year ago), the Monetary Policy Report's first-difference rule written in output-gap terms (the Report writes it on the unemployment gap); it needs no r* at all. The Report's rule is quarterly, so between two meetings the step is scaled by the days between them over a 91-day quarter.

Inertia. With inertia the prescription is ρ × the rate going into the meeting + (1 − ρ) × the rule's own value. The featured setup, ρ = 0.85 on the balanced-approach rule, is the Board's own "inertial rule". ρ is quoted per quarter, as the Board quotes it, and converted to the gap between meetings (0.85 per quarter is about 0.93 per six-week meeting). For past meetings the rate going in is the actual target the day before (the previous month's effective rate before the target series begins, on September 27, 1982); on the forecast leg it is the rule's own prescription at the previous meeting, so the path is the rule's own dynamics.

Real-time timing, today's numbers. Each past meeting uses the latest unemployment month, inflation month and GDP quarter that had been released by the decision day, by ALFRED's record of when each number first appeared (the FRED release calendar stands in before that record begins: 1960 for unemployment, 1992 for GDP, 1997 for CPI, 2000 for PCE). A release that morning counts. Conference calls and unscheduled meetings appear only when they moved the target; the rows are every scheduled meeting plus those. The values are today's vintage: revised GDP and PCE, today's CBO potential and natural rate, today's New York Fed r* estimates, not what the committee saw then. The upcoming meeting is run on everything published as of the data date shown.

Slack. The featured measure is CBO's output gap for the latest quarter with a GDP estimate, moved month by month by the Okun coefficient times the change in the unemployment rate since that quarter's average, so the gap follows the jobs report between GDP releases. The unemployment gap is Okun × (u* − u). On the forecast leg the gap is carried forward by Okun's law from the chosen forecast's unemployment path alone, and r* and u* stay at their latest values, so where the FOMC projects steady unemployment the gap and the prescription stay high even as the FOMC's own rate path comes down; that divergence is the assumption, not a finding.

Forecasts. The FOMC's Summary of Economic Projections gives the medians for the fourth quarter of each year; the Survey of Professional Forecasters gives the next four quarters and then annual figures; CBO gives fourth-quarter values by year. Each is anchored at the middle of its period and interpolated to the meeting dates, starting from the latest actual reading. Where a forecast does not cover the chosen inflation measure (the SEP forecasts only PCE and core PCE; none of the three forecasts the trimmed mean), the forward leg uses the core PCE forecast and says so. Meeting dates beyond the Fed's published calendar are provisional, on the usual cadence.

The range. The two tables rerun the whole calculation, history and forward leg, once per cell, holding every setting a table does not vary at the rule above (so a change to the inflation measure, slack, r*, u* or target moves every cell). They read the rule at the next meeting or at the last meeting of a year; at the next meeting the forecast makes no difference, since that reading uses data already published. The "Rules × inertia" table leaves out the first-difference rule, which has no smoothing parameter, and adds a column for your own ρ when it is not one of the five shown. The median and range are over the cells shown.

The reaction-function updater. For each year both sets of projections cover, the change in the funds rate a rule implies is the change in the neutral rate (the longer-run funds rate, if you let it move) + the response to inflation × the revision to the inflation forecast + the response to the output gap × the revision to the gap. The gap revision is −Okun × (the revision to unemployment − the revision to the longer-run unemployment rate), or, on growth, the cumulated revisions to Q4/Q4 real GDP growth through that year less the revision to longer-run growth in each year. A year the earlier projections cover but the later ones no longer do is scored on what happened (Q4/Q4 inflation and growth, Q4 unemployment, the year-end target midpoint), today's vintage. There is no smoothing: the question is how far the committee moved its path, not how fast it gets there. Two caveats. The medians for each variable come from different participants, so they need not describe any one participant's view; and each forecast is conditional on the participant's own appropriate policy, so a higher rate path pulls the inflation forecast down and the rule-implied change understates the response to what was learned. The current year is also constrained by how many meetings are left, so later years are the cleaner read. The chart under the table repeats the comparison for one year-end from every earlier set of projections that covered it, so a single reading can be seen against the others.

Comparisons. The FOMC median is the SEP's "appropriate policy" median at each year-end, drawn at the December meeting. The market path is the CME FedWatch probability-weighted rate for each meeting it prices, from the chartbook's own engine. The u* options are CBO's noncyclical rate of unemployment and the SEP's longer-run unemployment rate; r* options are the New York Fed's Laubach-Williams (the house default) and Holston-Laubach-Williams one-sided estimates, the SEP's longer-run funds rate less the target, or a fixed value. SEP medians exist from September 2015, so SEP-based options fall back to CBO or Laubach-Williams before then. Historical readings that a rule could not compute (no r* before 1961, no trimmed-mean PCE before 1978) are left blank.