A two-part series by Kevin L. Kliesen of St Louis Fed.

The first part presents the original Taylor Rule which shows that Fed Funds rate should be much higher than it is today:

*In its basic form, the Taylor rule states that the monetary authority (e.g., the Federal Reserve) should set its policy rate in the following manner:*

*i _{t} = r^{*} + π_{t} + α(y_{t} – y^{*}) + β(π_{t} – π^{*}),*

*where i _{t} is the nominal federal funds interest rate; r^{*} is the equilibrium real interest rate; π_{t} is the current inflation rate, measured from a year earlier; y_{t} is real gross domestic product (GDP) and y^{*} is real potential GDP, the difference between the two being the output gap; and π^{*} is the Fed’s inflation target, which is currently 2 percent for the personal consumption expenditures price index.^{2} *

*Three key principles are embedded in the Taylor rule. First, the Fed should raise its federal funds target rate proportionally more when inflation increases. This is known as the Taylor principle. Second, the interest rate should be adjusted in response to the output gap, a measure of “slack” in the economy. This is known as the Phillips relationship, whereby inflation decreases (increases) if real GDP decreases (increases) relative to real potential GDP. In Taylor’s original specification, the coefficients on the output and inflation gaps, α and β, respectively, were each 0.5. Third, Taylor stipulated that the equilibrium real interest rate, r ^{*}, should be fixed over time at 2 percent. Although Taylor believes that r^{*} should remain invariant over time, other policymakers have instead adopted the position that r^{*} is time varying and depends importantly on the underlying growth rate of the economy and other factors, such as the demand for risk-free Treasury securities (i.e., “safe assets”).^{3}*

*To illustrate the Taylor principle noted above, the figure shows how the Taylor rule would evolve under higher- and lower-inflation scenarios between now and the end of 2020. In the former, inflation would increase by 12.5 basis points per quarter (0.5 percentage points per year) from the third quarter of 2018 to the fourth quarter of 2020. In the latter, inflation would slow by 12.5 basis points per quarter. Each scenario assumes that the output gap remains constant at the value that prevailed in the third quarter of 2018. As expected, under the higher-inflation scenario, the rule indicates that the Federal Open Market Committee should continue to raise its target rate. It indicates the opposite if inflation were to slow—again, under the assumption of an unchanged output gap. *

*Interestingly, the figure also shows that during the current expansion, the actual federal funds target rate has been consistently below the rate suggested by the Taylor rule. Using actual data through the third quarter of 2018, the actual federal funds target rate is 1.88 percent, while the rule indicates that the rate should be about 4.75 percent. ^{4}*

In Part Two, a modified version of Taylor Rule is discussed:

*In a recent speech, Federal Reserve Bank of St. Louis President James Bullard presented an alternative version of the Taylor rule that reflects three developments that today’s monetary policymakers routinely confront. First, the economy has entered an economic regime of low interest rates that reflects, importantly, weak productivity growth and a strong demand for safe assets. ^{2} Second, the Fed appears to have successfully engineered a regime of low and relatively stable inflation expectations that are anchored near the Fed’s inflation target. Third, the Phillips relationship that posits a negative relationship between inflation and the current level of the unemployment rate and a measure of the “natural rate” has all but disappeared.^{3} Accordingly, this development means falling levels of the unemployment rate relative to its natural rate will have a very small effect on inflation. *

*Given these developments, Bullard proposes an alternative, what he terms a “modernized” version, of the Taylor rule:*

*i _{t} = ρi_{t}_{–1} + (1 – ρ)(r_{t}^{*} + π^{*} + ϕ_{π}π_{t}^{GAP} + ϕ_{u}u_{t}^{GAP}).*

*Bullard’s modernized version of the Taylor rule embeds several changes from Taylor’s original specification. ^{4} First, there is a one-quarter lag of the federal funds target rate (i_{t}_{–1}) with a fixed coefficient of ρ. This “smoothing” parameter is used by many in the policy rule literature. In this case, Bullard assigns ρ a value of 0.85. This assignment means that the past period’s policy rate is extraordinarily important for setting the current period’s policy rate. Second, the output and inflation gaps remain in the policy function, but they are measured a bit differently. The output gap (u_{t}^{GAP}) is instead measured as the difference between the current unemployment rate and the Congressional Budget Office’s natural rate of unemployment. The inflation gap (π_{t}^{GAP}) is measured as the difference between a market-based measure of inflation expectations and the Fed’s inflation target. Specifically, inflation expectations are measured as the difference between the nominal yield on a 5-year (5Y) Treasury security and the yield on an inflation-adjusted (real) 5Y Treasury inflation-protected security (TIPS).^{5} This difference is sometimes called the breakeven inflation (BEI) rate. Third, r_{t}^{*} now varies over time instead of being set at a fixed 2 percent. In this case, r_{t}^{*} is measured as the trend interest rate estimated from a Hodrick-Prescott filter of the 1-year nominal constant maturity Treasury yield less the four-quarter change in the Federal Reserve Bank of Dallas’s trimmed mean measure of the personal consumption expenditures (PCE) inflation rate. Fourth, the current inflation rate, π_{t}, is replaced by the Federal Open Market Committee’s (FOMC’s) inflation target (π^{*}), which is set at 2 percent. Finally, Bullard reduces the coefficient on the unemployment rate gap (ϕ_{u}) to 0.1, to reflect the flatness of the Phillips curve. The coefficient on the inflation gap (ϕ_{π}) is equal to 1.5 and consistent with the 1993 Taylor rule. Since ρ equals 0.85, this value means that the rule is very inertial in setting policy—that is, the past period’s federal funds target rate is important for setting the current period’s target rate. *

Based on these changes/modifications, the actual Fed funds rate is closer to the one shown by Bullard-Taylor rule:

*The figure plots five versions of Bullard’s modernized Taylor rule that are based on five different measures of inflation expectations. Four of the five measures of inflation expectations are market-based measures calculated as the difference between the yield on a nominal Treasury security and the yield on a TIPS. The first market-based measure is Bullard’s preferred measure: the 5Y BEI less 30 basis points (the adjusted 5Y BEI). The second is the market’s predicted average inflation rate over the next five years without this adjustment: the 5Y BEI. The third market-based measure is the inflation rate that is expected to prevail over the five-year period beginning five years from today: the 5Y, 5Y forward BEI (5Y5Y BEI). The fourth market-based measure is the average inflation rate that is expected to prevail over the next 10 years: the 10Y BEI. The final inflation expectations measure is based on the Federal Reserve Bank of Philadelphia’s quarterly Survey of Professional Forecasters. Specifically, each participant in the survey is asked to forecast the average PCE price index inflation rate expected over the next 10 years. ^{6}*

*The figure also plots the federal funds rate calculated from the 1993 Taylor rule, as described above and plotted in Part 1 of this Economic Synopses essay. To see how these two rules differ in their policy prescriptions, consider the prescription for the fourth quarter of 2015, when the FOMC lifted its federal funds target rate for the first time in a decade. The 1993 Taylor rule indicated that the rate should be set at 0.88 percent. The average of the five rules cited above was 0.12 percent, which was pretty close to the actual average of 0.16 percent. Over the next four quarters, real GDP growth remained close to 2 percent, the unemployment rate fell from 5 percent to 4.7 percent, and inflation increased from 1.6 percent to 2 percent. In the fourth quarter of 2016, the 1993 Taylor rule indicated that the target rate should be 2.9 percent, while the average of the five modernized Taylor rules was 0.46 percent. The actual target rate in the fourth quarter of 2016 was 0.42 percent. A key difference between the two rules during this period is that the 1993 Taylor rule assumes a fixed r ^{*} equal to 2 percent. In the modernized rule, r_{t}^{*}was equal to –1.12 percent in the fourth quarter of 2015 and then –0.72 percent four quarters later.*

Hmm..

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