The Taylor rule is an equation John Taylor introduced in a 1993 paper that prescribes a value for the federal funds rate—the short-term interest rate targeted by the Federal Open Market Committee (FOMC)—based on the values of inflation and economic slack such as the output gap or unemployment gap. Since 1993, alternative versions of Taylor's original equation have been used and called "simple (monetary) policy rules" (see here and here), "modified Taylor rules," or just "Taylor rules." We use the last term in this web page.
This web page allows users to generate fed funds rate prescriptions for their own Taylor rules based on a generalization of Taylor’s original formula:
The subscript t denotes a particular quarter of a year while t-1 denotes the quarter before that. FFR denotes the quarterly average of the effective federal funds rate while the hat symbol on the left side of the equation denotes a prescribed value.
An overview of these and other variable and parameter choices are provided in the tab Overview of Data. A more detailed description of the data and sources is provided in the tab Detailed Description of Data.
Choose whether you'd like to use the chart or heatmap version of the Taylor Rule Utility.
The Taylor Rule Utility allows users to display prescriptions from alternative Taylor rules using either a time series chart, or a so-called heatmap. In the chart version, users can plot prescriptions for up to three rules. Under the default settings, "Alternative 3" in the chart corresponds closely with Taylor's original 1993 rule apart from utilizing a different inflation measure as well as a time varying estimate of the natural (real) interest rate instead of the 2 percent originally used by Taylor [either choice can be used by the user]. "Alternative 1" in the chart is the same as "Alternative 3" apart from using twice the unemployment gap as an approximation of the output gap as utilized in a 2015 speech by former Fed Chair Janet Yellen and using the median of the FOMC meeting participants' projections of the longer-run real federal funds rate in place of the estimate of the natural rate from the Laubach and Williams model. The unemployment gap is proxied in this rule by the negative of the difference between the (quarterly) unemployment rate and the midpoint of the central tendency of the FOMC meeting participants' longer-run projections of it. "Alternative 2" in the chart is identical to "Alternative 1" apart from using a larger coefficient on the resource gap that is described in a 1999 paper by Taylor and consistent with the "balanced approach" rule utilized in 2012 and 2017 speeches by former Fed Chair Yellen.
The heatmap displays a five-by-six table of Taylor rule prescriptions by varying the resource gap and natural (real) interest rate used in the rule. The prescription in the second row and first column of the heatmap uses the same rule as the default "Alternative 1" line in the chart, and the prescription in the fourth row and final column of the heatmap uses the same rule as the default "Alternative 3" line in the chart. The prescription consistent with the default "Alternative 2" line in the chart can be found in the second row and first column of the heatmap after doubling the user-chosen weight on the resource gap from the original "Taylor 1993" value of 0.5 to the "balanced approach" value of 1.0. The source data used for the Taylor Rule Utility is available here.
Alternative 1
Must be between 0 and 5.
Conventional values are 0.5 and 1.0.
Must be between 0 and 0.99.
Conventional values are 0 and 0.85.
Alternative 2
Must be between 0 and 5.
Conventional values are 0.5 and 1.0.
Must be between 0 and 0.99.
Conventional values are 0 and 0.85.
Alternative 3
Must be between 0 and 5.
Conventional values are 0.5 and 1.0.
Must be between 0 and 0.99.
Conventional values are 0 and 0.85.
Notes: In the default settings of the chart, "RStarFOMCMedian" refers to the difference between the medians of the longer-run federal funds rate and PCE inflation projections made by FOMC meeting participants. "LWRstar1side" is the most recent estimate of the natural (real) interest rate from the Laubach and Williams (2003) model regularly updated by the Federal Reserve Bank of New York. "U3gapFOMC" is twice the negative of the difference between the (quarterly) unemployment rate and the midpoint of the central tendency of the FOMC meeting participants' longer-run projections of it. "CBOGDPgap" is the percentage point difference between real GDP and the most recent estimate of potential real GDP made by the Congressional Budget Office. "CorePCEInflation" is the four-quarter inflation rate for the chained price index of personal consumption expenditures excluding food and energy. The default range of the chart starts at 1985:Q1, but users can zoom into a narrower plot range by selecting the area inside the chart they would like to display. To incorporate changes to the settings of the chart, click the "Draw chart" button.
Must be between 0 and 5.
Conventional values are 0.5 and 1.0.
Must be between 0 and 0.99.
Conventional values are 0 and 0.85.
Note on resource gap measures
The first column calculates the unemployment gap by using, or interpolating, the median longer-run unemployment rate projection(s) in the most recent one or two Summary of Economic Projections of Federal Reserve Board members and Federal Reserve Bank presidents. The remaining columns calculate resources gaps based on, or consistent with, estimates of the natural unemployment rate or potential real GDP from the Congressional Budget Office.
Note on r* measures
HLW denotes Holston, Laubach, and Williams; LW denotes Laubach and Williams; and LM denotes Lubik and Matthes
Note on the shading scheme
Let rTR be the prescription of the fed funds rate from a particular version of the Taylor rule.
Let FFR be the value of the fed funds rate being compared to the prescription.
For example, FFR could be the current midpoint of the target range for the funds rate.
The general cell shading scheme is:
rTR - FFR > 1.25%
0.75% < rTR - FFR <= 1.25%
0.25% < rTR - FFR <= 0.75%
-0.25% < rTR - FFR <= 0.25%
-0.75% < rTR - FFR <= -0.25%
-1.25% < rTR - FFR <= -0.75%
rTR - FFR <= -1.25%
Inflation measure: πt
In his 1993 paper, Taylor used the trailing four-quarter inflation rate for the gross domestic product (GDP) deflator. Since the FOMC has used the price index for personal consumption expenditures (PCE) for its longer-run inflation objective in recent years, we include the trailing four-quarter PCE and core PCE inflation rates in the Taylor Rule Utility. The four-quarter inflation rate for the core PCE price index, which excludes food and energy prices, is the default choice in the Taylor Rule Utility chart and heatmap. Users can also choose real-time measures of PCE and core PCE inflation—the observed published values of inflation policymakers would have seen at past FOMC meetings—for the Taylor Rule Utility. A measure of expected PCE inflation from the Federal Reserve Bank of Philadelphia's Survey of Professional Forecasters (SPF) can also be chosen as the inflation measure.
Inflation target measure: π*t
Taylor used a target of 2 percent inflation for the rule in his 1993 paper. In its annual statements on longer-run goals and monetary policy strategy since 2012, the FOMC has announced its judgment that an annual rate of 2 percent PCE inflation "is most consistent over the longer run with the Federal Reserve's statutory mandate." The default option for the Taylor Rule Utility chart and heatmap is a 2 percent inflation target for the current and previous quarters. The midpoint of the central tendency of FOMC participants' longer-run PCE inflation projections is another option for the inflation target. These midpoints, included in the Summary of Economic Projections (SEP), were either 1.80 or 1.85 percent prior to 2012.
Natural (real) interest rate measure: r*t
This is the steady-state value of the real federal funds rate prescribed by the Taylor rule when inflation equals its targeted value and the resource gap is zero. Taylor calibrated this at 2 percent in his original paper, and this is one of the available choices in the Taylor Rule Utility chart. For the chart, a user can also choose one of two versions of the natural rate based on the difference of FOMC meeting participants' longer-run projections for the federal funds rate and PCE inflation under appropriate monetary policy. Finally, for the chart, users can choose measures of the natural (real) interest rate estimated from models by (a) Thomas Laubach and John C. Williams, (b) Kathryn Holston, Thomas Laubach, and John C. Williams, and (c) Thomas Lubik and Christian Matthes.
Resource gap measures: gapt
Each resource gap used in the Taylor Rule Utility is a measure of the deviation of an indicator of economic or labor market activity from an estimate of its potential, sustainable, longer-run, or natural value. In his original rule, Taylor used the percentage point deviation between real GDP and an estimate of its trend as his measure of the resource gap. A GDP gap is also used in the default setting for the "Alternative 3" line of the Taylor Rule Utility chart, with the Congressional Budget Office's (CBO) estimate of potential real GDP as the measure of the trend. Output gaps derived from two alternative measures of potential real GDP from a model designed by Federal Reserve Board of Governors (BOG) economists Charles A. Fleischman and John M. Roberts can also be used in the chart. A commonly used rule of thumb called Okun's law posits that the unemployment rate gap—the negative of the difference between the unemployment rate and its natural rate—is typically half as large as the output gap. We implement Okun's law by allowing users to choose twice the unemployment gap as the resource gap in the chart. Various unemployment gaps are calculated from estimates of the natural rate of unemployment from the CBO, the Survey of Professional Forecasters, and the aforementioned Fleischman and Roberts' (BOG) model. FOMC meeting participant projections of the longer-run unemployment rate, provided in the SEP, are also used as a proxy of the natural rate of unemployment. The default settings for the "Alternative 1" and "Alternative 2" lines in the chart utilize this proxy from the SEP. Real-time versions of the CBO's output and unemployment gaps can also be used in the chart. Users can also utilize a measure of the employment-population ratio gap in the chart, based on the CBO's estimates of the natural unemployment rate and the potential labor force participation rate. Finally, for the chart, we also allow users to choose resource gaps based on two measures of labor utilization called U-6 and ZPOP. These gaps are consistent with the unemployment gap derived from the CBO's underlying long-term rate of unemployment; the method used for constructing them is described here.
Interest-rate smoothing parameter: ρ
In the original Taylor rule, there is no interest-rate smoothing, and this parameter value is set to 0. The default settings of the Taylor Rule Utility chart and heatmap also have no interest-rate smoothing. However, some have argued that an "inertial Taylor rule," where ρ is set between 0 and 1, should be used for policy prescriptions to avoid excessive volatility in short-term interest rates or account for uncertainty regarding the value of the natural (real) interest rate. Federal Reserve Bank of Philadelphia economists Michael Dotsey and Keith Sill set the smoothing parameter to 0.85 for the inertial Taylor rule in their 2015 paper. A smoothing parameter of 0.85 is also used in the inertial Taylor rule in one of the Federal Reserve Board's workhorse macroeconometric models called FRB/US.
Weight on the resource gap: β
The default value used in the Taylor Rule Utility heatmap is the value of 0.5 used in Taylor's original 1993 rule. A very commonly used alternative value, utilized as the default setting for the "Alternative 2" line in the chart, is 1.0. Versions of this rule are often called "Taylor 1999" from a paper by Taylor that considered a rule with this larger weight on the resource gap.
Use (employment) shortfalls option
In its August 27, 2020, update to its Statement on Longer-Run Goals and Monetary Policy Strategy, the FOMC stated that "[i]n setting monetary policy, the Committee seeks over time to mitigate shortfalls of employment [emphasis added] from the Committee’s assessment of its maximum level and deviations of inflation from its longer-run goal." The previous version of the statement declared that "[i]n setting monetary policy, the Committee seeks to mitigate deviations of inflation from its longer-run goal and deviations of employment [emphasis added] from the Committee's assessments of its maximum level." This notion of mitigating shortfalls, rather than deviations of employment from its maximum level was incorporated in the "balanced-approach (shortfalls) rule" introduced in the box titled "Monetary Policy Rules and Shortfalls from Maximum Employment" in the February 2021 Monetary Policy Report (MPR) to the Congress. While the standard version of the "balanced-approach rule"—which is included in the same MPR box—prescribes a higher federal funds rate when the unemployment rate falls below its longer-run value, the shortfalls version of the rule does not. Under the default settings, the “Alternative 1” line is the "balanced-approach (shortfalls) rule" in the February 2021 MPR, while the "Alternative 2" line is the standard "balanced-approach rule" from the same report.
Detailed description of data and sources
The Taylor Rule Utility chart allows the user to select each of the four variables used in the version of the rule provided on our website. The variables in the rule are the inflation target, the measure of current inflation, the natural (real) interest rate, and the resource gap. We describe the available choices for each of these variables in the sections below.
Inflation target measures
In the Federal Open Market Committee's statement on longer-run goals and monetary policy strategy released after the January 2012 FOMC meeting, the Committee announced its judgment "that inflation at the rate of 2 percent, as measured by the annual change in the price index for personal consumption expenditures, is most consistent over the longer run with the Federal Reserve's statutory mandate." The Committee has renewed this judgment at every subsequent January FOMC meeting. Consequently, the default option for the inflation target used in the Taylor Rule Utility is the FOMC's 2 percent objective.
The alternative inflation target option for the Taylor Rule Utility is the midpoint of the central tendency of the FOMC meeting participants' longer-run inflation projections for the price index for personal consumption expenditures (PCE). The central tendency is the midpoint of the range of projections that excludes the three highest and three lowest values. Since 2012, these projections have been submitted in conjunction with four scheduled FOMC meetings a year, and the central tendencies of the projections have been released with the FOMC statement. Additional information regarding the projections have been released with the FOMC meeting minutes in the so-called Summary of Economic Projections (SEP).
FOMC meeting participants first provided their longer-run inflation projections at the January 2009 FOMC meeting. Through the end of 2011, the central tendency of the longer-run PCE inflation projections was always 1.6 to 2.0 percent or 1.7 to 2.0 percent. Beginning with the announcement of the longer-run 2 percent PCE inflation objective in January 2012, both the range and the central tendency of these has been 2.0 percent. For the Taylor Rule Utility, the central tendency midpoints of longer-run PCE inflation projections are assigned to the month of the FOMC meeting. Linear interpolation of the midpoints is used to assign values for months without FOMC projections. Quarterly averages of the actual and interpolated longer-run inflation projections are used for the Taylor Rule Utility. For months beyond the last FOMC forecast submission, it is assumed that longer-run inflation projections will remain at 2 percent.
Inflation measures
The default inflation measure in the Taylor Rule Utility is the four-quarter inflation rate for the price index for personal consumption expenditures excluding food and energy, also known as the core PCE price index. The US Bureau of Economic Analysis (BEA) constructs the index. As former Fed Chair Yellen noted in a March 2015 speech, the current inflation rate for the Taylor (1993) rule is "usually measured using a core consumer price index." The four-quarter core PCE inflation rate was also used for the Taylor (1993, 1999) rule prescriptions in the December 2015 Tealbook B, Monetary Policy: Strategies and Alternatives provided to FOMC participants for the meeting that month. (Transcripts and historical confidential material like the Tealbook for FOMC meetings are released to the public after to five to six years.) Users can also use the BEA's trailing four-quarter PCE inflation rate for the Taylor rule. Projections of PCE and core PCE inflation for the most recent quarter are constructed using forecasts from the Federal Reserve Bank of Cleveland's Inflation Nowcasting website.
Finally, users have the option of using a forecasted value of four-quarter PCE inflation three quarters hence. The forecasted value comes from the Federal Reserve Bank of Philadelphia's Survey of Professional Forecasters (SPF). It is constructed by taking the median forecasts of the quarterly PCE inflation rates for the current and subsequent three quarters and aggregating them to a four-quarter rate. The SPF is typically released in the middle of a quarter about two to three weeks after an "advance," or first, GDP estimate. When a Taylor Rule Utility update occurs within this two- to three-week interval between an "advance" GDP estimate and an SPF release, we aggregate the latest Cleveland Fed model nowcast of PCE inflation for the current quarter with the PCE inflation forecasts for the subsequent three quarters from the most recent SPF release published about 11 weeks earlier. Prior to 2007, the SPF did not elicit forecasts of PCE inflation. So pre-2007 values are obtained by taking expected four-quarter CPI inflation—analogously constructed—and subtracting 0.3 percentage points. In a January 2010 speech, former Fed Chairman Ben Bernanke used expected PCE inflation in a version of the Taylor rule.
Natural (real) interest rate measures
The natural (real) interest rate—also called the equilibrium real rate, or r*—is the intercept in the Taylor rule. The rate is usually just called the natural interest rate, but we add the word "real" in parentheses to avoid any confusion with the nominal federal funds rate that the FOMC targets. In John Taylor's 1993 paper introducing the Taylor rule, the intercept was calibrated at 2 percent. This became the standard value used in many subsequent implementations of the rule. Taylor noted in his paper that his choice was close to the 2.2 percent trend growth rate of real GDP from 1984:Q1 to 1992:Q3 estimated at the time of his writing.
However, as former fed Chair Yellen noted in a March 2015 speech, the Taylor rule can give a very different prescription for the federal funds rate if an estimate of the natural (real) interest rate from a model is used in place of 2 percent. In her speech, Chair Yellen cited the Laubach-Williams (LW) model estimate of r*, which was just below 0 percent at the time. Updated estimates of r* from Thomas Laubach and John C. Williams's model, and a similar model from Kathryn Holston, Laubach, and Williams (HLW), are maintained at the Federal Reserve Bank of New York here. The Taylor Rule Utility allows the user to choose three of the LW and two of the HLW model estimates of the natural (real) interest rate as the intercept in the rule. The one-sided LW and HLW estimates use data only through the quarter of the Taylor rule prescription to determine the value of r*. The two-sided LW estimate uses all the available data through the second quarter of 2020 to estimate the current and past values of r*. Users can also choose to use real-time LW and HLW estimates of r* for the last quarter for which the data were available at the time of the estimation. These estimates will differ from the aforementioned one-sided estimates computed with the latest data vintage because of revisions to the source data and changes in the model's estimated parameter values. Due to the extreme volatility in GDP in the first three quarters of 2020, the New York Fed suspended publication of the LW and HLW estimates of r* in November 2020 after releasing estimates for the second quarter of 2020 in August 2020. Beyond the second quarter of 2020, we assume that the LW and HLW estimates of r* remain at their last published values.
Federal Reserve Bank of Richmond economist Thomas A. Lubik and former Richmond Fed economist Christian Matthes constructed an alternative model of r* in a short 2015 paper. In their model, r* is the five-year-ahead forecast of the real federal funds rate from a time-varying parameter vector autoregressive model. The median estimate of r* from their model—available here—is included in the Taylor Rule Utility. For quarters beyond the most recent Lubik and Matthes estimate of r*, we assume that r* will remain at its last value.
Finally, the Taylor Rule Utility includes two measures of r* constructed from the FOMC meeting participants' longer-run projections of the federal funds rate and inflation for the price index for PCE under appropriate monetary policy. In particular, the longer-run PCE inflation measure described in the section on inflation target measures is subtracted from either the median or the midpoint of the central tendency of the FOMC meeting participants' longer-run projections of the federal funds rate. (The central tendency is the range of projections that excludes the three highest and three lowest values.) The fed funds rate medians and central tendency midpoints are assigned to the month of the meetings. Linear interpolation is used to fill in values for months without FOMC projections. For months beyond the last FOMC meeting forecast submission, it is assumed that the FOMC meeting participant-based measures of r* will remain at their last readings. Quarterly averages of r* are used in the Taylor Rule Utility. We are not the first to use the longer-run FOMC meeting participant projections to construct a proxy for r*; Federal Reserve Governor Lael Brainard provided a similar calculation in a December 2015 speech. For the default settings of the "Alternative 1" and "Alternative 2" lines in the Taylor Rule Utility chart, the implied estimates of r* are constructed with the median of the FOMC meeting participants' longer-run projections of the federal funds rate. For "Alternative 3," the (non-real-time) one-sided LW model estimate of r* is used.
Resource gap measures
The default option for the resource gap used in the "Alternative 3" line of the Taylor Rule Utility chart is the output gap derived from theCongressional Budget Office's (CBO) estimate of potential real gross domestic product. The output gap is the number of percentage points that real GDP is above or below an estimate of potential. For the most recent quarter used in the Taylor Rule Utility, the Atlanta Fed's GDPNow model forecast is used to forecast real GDP and derive the output gap. This default option does not use real-time data on actual and potential real GDP, but real-time CBO output gaps using either the US Bureau of Economic Analysis's (BEA) first, second, or third estimates of real GDP can be used in the Taylor Rule Utility chart. For each of the first three estimates of real GDP, the output gap is constructed with the CBO's latest estimate of potential GDP that was available at the time of the GDP release. For dates when the CBO's latest estimate of potential GDP was released before the BEA's last benchmark or comprehensive revision of real GDP, it's not clear what the best way to compute the output gap is. In such cases, we do the following. For the release date of the CBO's last estimate of potential real GDP, we calculate what the output gap was using the BEA's latest estimate of real GDP at the time of the CBO release. We maintain the output gap at its previous level for the quarter of this earlier GDP release. For quarters beyond this, we assume the potential real GDP grows at the same rate the CBO estimated it would be growing at in its last estimate of potential real GDP. This uniquely pins down the output gap.
An alternative measure of potential real GDP is constructed using a model designed by Federal Reserve Board of Governors (BOG) economists Charles A. Fleischman and John M. Roberts. This BOG model is used to construct potential output for the Federal Reserve Board's FRB/US macroeconometric model. We estimate potential real GDP for the Fleischman and Roberts' model using the EViews code and input data available at the website for the FRB/US model. The source data for the Fleischman and Roberts' model are revised and/or extended to the most recent quarter used for the Taylor Rule Utility by using the most recently released data from the original sources (the BEA, the US Bureau of Labor Statistics, and others) and our own calculations. We also "nowcast" the input data as necessary using both standard econometric techniques like vector autoregressions and publicly available forecasts. None of these nowcasts incorporates our own judgment.
The Fleischman and Roberts' BOG model estimates of potential real GDP are used to construct alternative measures of the output gap. As with the LW model of the natural (real) interest rate, the Fleischman and Roberts' model estimates of potential real GDP come in one-sided and two-sided varieties (see the previous section on the natural [real] interest rate measures). The one-sided and two-sided output gaps derived from the Fleischman and Roberts' model are available in the Taylor Rule Utility.
An alternative measure of the resource gap can be constructed using the difference between an estimate of the natural rate of unemployment and the civilian unemployment rate from the US Bureau of Labor Statistics (BLS; both measured as quarterly averages). We put the so-called "unemployment gap" on about the same scale as the output gap by multiplying this difference by negative 2 as former Federal Reserve Chair Janet Yellen did in a March 2015 speech. For the most recent quarter, when necessary, the monthly unemployment rate is forecasted using a projection from the Wall Street Journal Economic Forecasting Survey. To construct the forecasts, we linearly interpolate the shortest horizon monthly unemployment rate from this survey with the most recent estimate of the monthly (unrounded) unemployment rate. The published (rounded) monthly unemployment rates extended with the forecasts for the most recent quarter available in the Taylor Rule Utility are then averaged.
An alternative measure of the resource gap can be constructed using the difference between the civilian unemployment rate from the US Bureau of Labor Statistics (BLS) and an estimate of the natural rate of unemployment (both measured as quarterly averages). We put the so-called unemployment gap on about the same scale as the output gap by multiplying this difference by negative 2 as former Federal Reserve Chair Janet Yellen did in a March 2015 speech. For the most recent quarter, when necessary, the monthly unemployment rate is forecasted using a projection from either the Wall Street Journal Economic Forecasting Survey, or the Federal Reserve Bank of Philadelphia's Survey of Professional Forecasters (SPF). Both surveys are conducted once a quarter, with the Wall Street Journal (WSJ) survey released in the first half of the first month of each quarter and the Philly Fed survey released near the middle of the second month of each quarter. When the WSJ survey has been released after the most recent employment report, we forecast the unemployment rate for the remainder of the current quarter by linearly interpolating the shortest horizon monthly unemployment rate forecast from this survey with the most recent estimate of the monthly (unrounded) unemployment rate. When the Philly Fed SPF has been released after the most recent employment report, we determine the constant monthly rate of change in the unemployment rate that would result in the average (unrounded) unemployment rate in the subsequent quarter equaling the median projection of the unemployment rate from the survey, and assume the unemployment rate changes by that constant monthly rate for the remainder of the current quarter. Finally, when the most recent employment report has been released after the latest WSJ survey or SPF, we assume the unemployment rate changes at the same constant rate it was forecasted to have changed based on the near-term unemployment rate forecast in the most recent SPF or WSJ survey and the latest (unrounded) estimate of the unemployment rate that was available before the survey took place. The published (rounded) monthly unemployment rates extended with the forecasts for the most recent quarter available in the Taylor Rule Utility are then averaged.
We allow users to choose the unemployment gap implied by a number of estimates of the natural rate of unemployment. One estimate comes from the Congressional Budget Office (CBO). Technically, the measure from the CBO that we use is called the "underlying long-term rate of unemployment." The CBO has a second natural rate of unemployment measure, which was higher than the former measure from 2008 to 2014 due to structural factors such as extended unemployment insurance benefits. Apart from the 2008 to 2014 period, the CBO's estimates of the "underlying long-term rate of unemployment" and the natural rate of unemployment are identical. We use the former for the Taylor Rule Utility because the CBO says it's consistent with its measure of potential output. Users can also choose real-time measures of the unemployment rate derived from real-time measures of the CBO's "underlying long-term rate of unemployment" and either the first, second, third, or fourth release of the unemployment rate. The real-time data come from the CBO and the Federal Reserve Bank of St. Louis's Archival FRED (ALFRED) database. The gap is computed using the CBO's most recent estimate of the "underlying long-term rate of unemployment" available at the time of the unemployment rate release. In almost all cases, only the nth estimate of quarterly PCE inflation will be available at the time of the (n+1)st estimate of the quarterly unemployment rate.
A second measure of the unemployment gap is derived from the median estimate of the natural rate of unemployment in the Federal Reserve Bank of Philadelphia's Survey of Professional Forecasters (SPF). The SPF natural rate estimates are collected in the third quarter of each year. These estimates are assigned to the third quarter of their survey year and linearly interpolated to fill in estimates for other quarters besides the third. Whenever the SPF natural rate is not available for one or more recent quarters, we assume that natural rate remains at its last estimate from the survey. The Taylor Rule Utility uses the BLS's most recent estimate of the unemployment rate time series when calculating the SPF-based unemployment gap.
A third measure of the unemployment gap is derived from themidpoint of the central tendency of the FOMC meeting participants' longer-run unemployment rate projections that are published in the Summary of Economic Projections (SEP).The midpoint projections are assigned to the month of the FOMC meeting and linearly interpolated to assign values for months without FOMC projections. For recent months covered by the Taylor Rule Utility where an estimate of the longer-run unemployment rate is not yet available, it is assumed that the longer-run rate remains at the same reading from the most recent SEP. Quarterly averages of the actual, interpolated, and extended longer-run unemployment rate projections are used for the unemployment rate gap calculations in the Taylor Rule Utility. The BLS's most recent estimate of the unemployment rate time series is used when calculating the SEP-based unemployment gap. This measure of the unemployment gap is the default setting used for the "Alternative 1" and "Alternative 2" lines in the Taylor Rule Utility chart.
A final measure of the natural rate of unemployment, used to calculate the unemployment gap, comes from theFleischman and Roberts' (BOG) model described above. As with potential real GDP, the natural unemployment rate from this model comes in one-sided and two-sided varieties.
For the chart, we also allow users to choose resource gaps based on one of the BLS's alternative measures of labor underutilization, called U-6, and a measure of labor utilization called ZPOP. ZPOP, the utilization-to-population ratio, was constructed by Atlanta Fed researchers John Robertson and Ellyn Terry and described in a September 2015 macroblog entry. It is the share of the working-age population that is working full-time, is voluntarily working part-time, or doesn't want to work any hours. To translate ZPOP into a labor underutilization measure like the unemployment rate and U-6, we use 1 minus ZPOP for the Taylor Rule Utility. As with the unemployment rate, when necessary, we construct forecasts of U-6 and ZPOP through the last month of the most recent quarter used in the Taylor Rule Utility. The forecasts are derived from small vector autoregression models conditioning on the aforementioned unemployment rate forecasts based on the Wall Street Journal Economic Forecasting Survey or the Federal Reserve Bank of Philadelphia's Survey of Professional Forecasters. The forecast padded measures of U-6 and 1 minus ZPOP are aggregated to the quarterly frequency and converted into gaps consistent with the CBO's underlying long-term rate of unemployment. The relatively simple method used for constructing these gaps is described here. These gaps are not constructed with real-time data.
Finally, we allow users to choose an employment-population gap for the chart, defined as the difference between the employment-population ratio and its potential level. The potential employment-population ratio is derived by simple arithmetic from the Congressional Budget Office's estimate of the quarterly natural unemployment rate and its estimate of the quarterly potential labor force participation rate. The employment-population gap is multiplied by 2 to put it on about the same scale as the output gap.
How frequently is the source data for the Taylor Rule Utility updated? When are the updates?
The source data are updated twice a month. We update the source data on the day of, or the business day after, the monthly releases of each of the Consumer Price Index and personal income and outlays reports. The source data used for the Taylor Rule Utility are available here.
How do you construct Taylor rule prescriptions for the most recent quarter when the source data are not released yet?
We use a combination of publicly available model-based forecasts like GDPNow and the Federal Reserve Bank of Cleveland's Inflation Nowcasting website, projections derived from surveys of professional forecasters like the Wall Street Journal Economic Forecasting Survey, and standard econometric forecasting models like vector autoregressions. For each variable, the forecasting method used is described in the tab Detailed Description of Data and Sources. We do not incorporate our own judgment in the forecasts.
Isn't there only one Taylor rule?
In his commentary, John Taylor has endorsed calling the version of his rule he made famous in his 1993 paper the Taylor rule and referring to this version for a benchmark for monetary policy (see here, here, and here). However, former Fed Chairs Ben Bernanke and Janet Yellen have stated they prefer other versions of the rule to the so-called Taylor (1993) rule (see here, here). Both former Chairs have called alternative rules to Taylor (1993) "modified Taylor rules" (see here and here). Part two of the Federal Reserve Board of Governors' July 2021 Monetary Policy Report includes a section on various types of Taylor rules and their role in the Fed's monetary policy process.
Although we refer to both the Taylor (1993) rule and other variants as "Taylor rules" without any disclaimers, one should keep the above paragraph in mind.
How does the Taylor Rule Utility handle the zero lower bound?
The zero lower bound (ZLB) is based on the observation that interest rates should not be negative because an investor could hold cash rather than accept a negative return on an asset. Although some foreign central banks like the Bank of Japan and the European Central Bank have adopted negative policy rates, the Federal Open Market Committee has not targeted the federal funds rate below 0 percent. Nevertheless, many of the rules one can construct with the Taylor Rule Utility will prescribe a negative fed funds rate during or after the 2007–09 recession. We do not constrain these prescriptions to be nonnegative to satisfy the ZLB constraint. Rules that prescribe negative fed funds rate can be compared with either shadow short-term (see here and here) or measures of the stance of monetary policy that account for stimulus provided by large-scale asset purchases (see, for example, here and here).
One should keep in mind that the ZLB can impact the prescriptions of rules with a large amount of interest-rate smoothing (for example, r close to 1.0 in the Taylor Rule Utility). Because these rules put a large weight on the (positive) lagged fed funds rate, these rules generally will not prescribe rates much below 0 percent.
Are there versions of the Taylor rule that cannot be implemented with the Taylor Rule Utility?
Yes. The Taylor Rule Utility does not allow for nominal GDP targeting. Nor does it allow for the fed funds rate prescription to depend on more than one lag of the federal funds rate. Quarterly Taylor rules with two lags of the federal funds rate can capture the empirical property that increases (declines) in the fed funds rate have historically tended to be followed by subsequent increases (declines). See the outcome-based rule on numbered page 37 of the December 2010 Tealbook B, Monetary Policy: Strategies and Alternatives. The Taylor Rule Utility does not incorporate "difference rules" where the funds rate prescription depends on an estimate of a change in a resource gap rather than the size of the gap itself or account for the zero lower bound (ZLB) on the federal funds rate with an “adjusted” rule that eventually makes up for the shortfall of accommodation during the ZLB period. These rules are discussed in the July 2019 Monetary Policy Report. Finally, there are a number of inflation or resource gap measures not incorporated. For example, the Taylor Rule Utility does not include inflation measures based on the Consumer Price Index or the GDP deflator.
Where can I learn more about the Taylor rule?
John Taylor's seminal 1993 and 1999 papers are good resources both for the basics on the Taylor rule and historical investigations of monetary policy and macroeconomic outcomes. The work of Athanasios Orphanides—in particular here, here, and here—also provides historical analysis as well as treatments of theoretical issues such as robustness of particular rules to mismeasurement of unobserved variables like the resource gap. A Brookings Institution blog post by former Fed Chairman Ben Bernanke provides a fairly gentle analysis of the Taylor rule and its consistency with actual monetary policy outcomes in recent years. The online appendix to the Cleveland Fed's Simple Monetary Policy Rules web page provides broad descriptions, references, and analysis of the data and parameters used in the Taylor rule.
How does the Atlanta Fed's Taylor Rule Utility differ from similar tools?
A number of organizations have tools similar to the Taylor Rule Utility. One of the nicer versions available is on the Cleveland Fed's Simple Monetary Policy Rules web page. The Cleveland Fed's application provides policy prescriptions of seven versions of the Taylor rule, starting from the previous quarter through two years in the future using outside forecasts and the Cleveland Fed's own statistical model. The Cleveland Fed also has an Excel file that lets you customize your own rule. Our Taylor Rule Utility generates policy prescriptions from 1985 through the quarter after the most recent one for which the US Bureau of Economic Analysis has released an estimate of GDP. Our Excel file allows you to construct prescriptions for before 1985.
The Federal Reserve Bank of St. Louis also has web pages—here and here—with charts of Taylor rule prescriptions generated with its FRED application.
Why are the resources gaps associated with labor underutilization rates multiplied by 2?
A commonly used version of Okun's law states that the unemployment rate tends to be 1 percentage point above its natural rate for every 2 percentage points that real gross domestic product (GDP) is below its potential level. Defining the unemployment gap as an estimate of the natural rate of unemployment minus the actual rate, this version of Okun's law implies that in a Taylor rule, twice the unemployment gap can be used to proxy the output gap. This conversion factor from the output gap to the unemployment gap was used, for example, by former Federal Reserve Chair Janet Yellen in a 2015 speech. However, it's not the only conversion factor used. The original version of Okun's law implies that output tends to be 3 percentage points above potential for every 1 percentage point the unemployment rate is below its natural rate. And the conversion factor used in the Federal Reserve Bank of Cleveland's simple monetary policy rules spreadsheet implies that the unemployment rate tends to be 3 percentage points above its natural rate for every 2 percentage points real GDP is below potential.
Users who want to use the unemployment gap with a different Okun's law conversion factor than the default also used in former Chair Yellen's speech can implement this by setting the appropriate weight on the gap. For example, users who want to implement the Taylor (1993) rule with the unemployment gap and Okun's original conversion factor should set the weight on the gap equal to 0.75 = (3.0/2.0)*0.5.
Finally, users should note that the U6 and ZPOP resource gaps described here are translated to be on the same scale as twice the unemployment gap. Users who want to use these gaps with a Taylor (1993) type rule and the default Okun's law conversion factor of 2 should leave the weight on the resource gap at its default setting of 0.5.
What is the heatmap? How does it differ from the chart in the "Create Your Calculation" tab?
The heatmap shows prescriptions from 30 monetary policy rules using different combinations of resource slack and the (real) natural interest rate for either the latest quarter or the quarter before that. Other settings applied to each of the 30 rules—such as the inflation measure or the weight on the resource gap—are chosen by the user. The chart displays three time series of historical prescriptions from policy rules—chosen by the user—back to the first quarter of 1985 or the earliest available date.
How should I interpret the cell colors in the heatmap? Does green mean the Federal Open Market Committee (FOMC) should raise the target range for the fed funds rate? Does red mean the FOMC should lower it?
Roughly speaking, a white shaded cell means that the prescribed fed funds rate is within 25 basis points of the current fed funds rate. (The user has some flexibility how the latter rate is defined.) Green shaded cells imply the prescribed fed funds rate is more than 25 basis points above the current fed funds rate, while red shaded cells imply the prescribed rate is at least 25 basis points below the funds rate. Darker shaded colors correspond to larger deviations between the prescribed and actual fed funds rate. The coloring scheme is nonjudgmental and is not intended to provide support for a particular view on the stance of monetary policy. It will sometimes be the case that there are both red and green shaded cells in the heatmap.
How is the actual fed funds rate in the heatmap determined?
Color shading is determined by comparing the prescribed fed funds rate with the "actual" fed funds rate. If the user chooses the "latest quarter," which is always the quarter after the most recent quarter with an official estimate of gross domestic product published by the US Bureau of Economic Analysis, then it will often be the case that the effective fed funds rate for the quarter has not been published because the quarter has not ended. In this case, the user has three distinct choices for the fed funds rate in the "latest quarter."
1.) Predicted effective fed funds rate assuming no change in target range. For months in the "latest quarter" where monthly readings on the effective federal funds rate have been published in the Federal Reserve Board's H.15 Selected Interest Rates release, those readings are used. For a month where some, but not all, daily readings on the effective federal funds rate from the Federal Reserve Bank of New York have been published, those daily readings are used. For the remaining days of the month, the predicted effective fed funds rate is the lower bound of the FOMC's current target range for the fed funds rate plus the average difference between the effective fed funds rate and the beginning-of-day lower bound of the FOMC's target range for the fed funds rate over the previous 90 days. The average of the actual and predicted daily effective federal funds for the month is used (carrying over actual or predicted effective federal funds rate from the previous business day on weekends and holidays). For months where no daily readings on the effective fed funds rate have been published, the same predicted effective fed funds rate described above is used. The quarterly effective fed funds rate is the simple average of the actual and predicted monthly effective fed funds rates.
2.) Futures market prediction of average effective fed funds rate. Monthly readings on the effective fed funds rate, described above, are used whenever they are available. For months in which they are not available, rates implied by last price quotes from 30-day federal funds futures contracts on the Chicago Mercantile Exchange website are used. The quarterly effective fed funds rate is the simple average of the actual and futures market predictions of the effective fed funds rates for the three months in the quarter.
3.) Current target fed funds rate, midpoint of range. If the "latest quarter" has ended, then the rates determined by choices 1.) and 2.) will be identical.
If the user chooses the "penultimate quarter"—the quarter before the "latest quarter"—then the average effective fed funds rate for that quarter is used. It is the simple average of the monthly readings on the effective federal funds rate published in the Federal Reserve Board's H.15Selected Interest Rates release.
We plan on generally updating the Taylor Rule Utility by the close of business on the days of these releases after the Federal Reserve Bank of Cleveland updates its inflation nowcasting model forecasts. Upon occasion, an update may occur on the business day after one of these releases.
Additionally, whenever the Federal Open Market Committee changes the target range for the federal funds rate, we plan on updating the utility on the current or subsequent business day.
** Because of holidays, update may be delayed more than usual.
