. Since monetary policy changes made through the fed funds rate occur with a lag, policymakers are usually more concerned with adjusting policy according to changes in the forecasted or expected inflation rate, rather than the current inflation rate. In light of this, suppose that monetary policymakers employ the Taylor rule to set the fed funds rate, where the inflation gap is defined as the difference between expected inflation and the target inflation rate. Assume that the weights on both the inflation and output gaps are ½, the equilibrium real fed funds rate is 4%, the inflation rate target is 3%, and the output gap is 2%. a. If the expected inflation rate is 7%, then at what target should the fed funds rate be set according to the Taylor rule?

b. Suppose half of Fed economists forecast inflation to be 6%, and half of Fed economists forecast inflation to be 8%. If the Fed uses the average of these two forecasts as its measure of expected inflation, then at what target should the fed funds rate be set according to the Taylor rule?

c. Now suppose half of Fed economists forecast inflation to be 0%, and half forecast inflation to be 14%. If the Fed uses the average of these two forecasts as its measure of expected inflation, then at what target should the fed funds rate be set according to the Taylor rule?

d. Given your answers to parts (a)–(c) above, do you think it is a good idea for monetary policymakers to use a strict interpretation of the Taylor rule as a basis for setting policy? Why or why not?

Taylor's rule is a formula devised by John Taylor, an economist. It was created to provide "recommendations" on how a central bank, such as the Federal Reserve, should set short-term interest rates when economic conditions change in order to achieve both a short-run goal of economic stabilisation and a long-run goal of inflation. When predicted inflation differs from goal inflation and expected GDP growth differs from long-term GDP growth, it aids in estimating the target short-term interest rate.

According to Taylor's rule, the fed fund rate will be 7.5 percent. When projected inflation differs from goal inflation and expected GDP growth differs from long-term GDP growth, Taylor's formula can help determine the target short-term interest rate.

The formula for Taylor's rule is as follows:

Targeted Federal Funds Rate is

$\left(Inflationrate+Equilibriumrealfedfundrate+\frac{1}{2}Inflationgap+\frac{1}{2}Outputgap\right)$

$$\begin{gathered} =4\%+2\%+\frac{1}{2}·2\%+\frac{1}{2}·1\% \\ =7.5\% \end{gathered}$$

Hence, federal fund rate is 7.5%.

Average inflation rate

$$\begin{gathered} =\frac{3\%+5\%}{2} \\ =4\% \end{gathered}$$

Targeted Federal Funds Rate is

$\left(Inflationrate+Equilibriumrealfedfundrate+\frac{1}{2}Inflationgap+\frac{1}{2}Outputgap\right)$

$$\begin{gathered} =4\%+2\%+\frac{1}{2}·2\%+\frac{1}{2}·1\% \\ =7.5\% \end{gathered}$$

Inflation=0%

Half forecast inflation=8%

Average inflation rate

$$\begin{gathered} \frac{0\%+8\%}{2} \\ =4\% \end{gathered}$$

Targeted Federal Funds Rate is

$\left(Inflationrate+Equilibriumrealfedfundrate+\frac{1}{2}Inflationgap+\frac{1}{2}Outputgap\right)$

$$\begin{gathered} =4\%+2\%+\frac{1}{2}·2\%+\frac{1}{2}·1\% \\ =7.5\% \end{gathered}$$

No, these three scenarios are very different from one another. In situation a., it is assumed that there is little uncertainty about the level of inflation, hence a Taylor rule approach to policy may be appropriate. However, in cases b. and c., different economists have given different inflation values, demonstrating the uncertainty of the inflation rate. Using a mechanical rule to dictate policy without accounting for this uncertainty could be problematic.