Chapter 19, Problem 25AP

To determine

1. Fed target funds rate according to Taylor rule when inflation rate is 4%
2. According to Taylor rule when inflation rate is 3% and 5%, Fed target funds rate on average of these two forecasts
3. According to Taylor rule when inflation rate is 0% and 8%, Fed target funds rate on average of these two forecasts
4. Suitability of Taylor’s Rule

Explanation of Solution

According to Taylor rule the federal funds rate target = 7.5%

According to Taylor rule the federal funds rate target is calculated using the following formula −

$\begin{array}{l}FederalFundsRateTarget=\\ InflationRate+EquilibriumRealFedFundsRate+\mathrm{½}\left(InflationGap\right)+\mathrm{½}\left(OutputGap\right)\end{array}$

Given that:

Inflation rate = 4%

Equilibrium Real Fed Funds Rate = 2%

Output Gap = 1%

$FederalFundsTargetRate=4\%+2\%+\mathrm{½}\left(4\%-2\%\right)+\mathrm{½}\left(1\%\right)=7.5\%$

Requirement 2:

According to Taylor rule when inflation rate is 3% and 5%, Fed target funds rate on average of these two forecasts

Answer:

According to Taylor rule the federal funds rate target = 7.5%

  $\begin{array}{l}FederalFundsRateTarget=\\ InflationRate+EquilibriumRealFedFundsRate+\mathrm{½}\left(InflationGap\right)+\mathrm{½}\left(OutputGap\right)\end{array}$

Given that:

Inflation rate = 3%

Equilibrium Real Fed Funds Rate = 2%

Output Gap = 1%

  $FederalFundsTargetRate=3\%+2\%+\mathrm{½}\left(3\%-2\%\right)+\mathrm{½}\left(1\%\right)=6\%$

Given that:

Inflation rate = 5%

Equilibrium Real Fed Funds Rate = 2%

Output Gap = 1%

$FederalFundsTargetRate=5\%+2\%+\mathrm{½}\left(5\%-2\%\right)+\mathrm{½}\left(1\%\right)=9\%$

Average of these two forecasts will be

$=\mathrm{½}\left(6\%+9\%\right)=7.5\%$

Requirement 3:

According to Taylor rule when inflation rate is 0% and 8%, Fed target funds rate on average of these two forecasts

Answer:

According to Taylor rule the federal funds rate target = 7.5%

$\begin{array}{l}FederalFundsRateTarget=\\ InflationRate+EquilibriumRealFedFundsRate+\mathrm{½}\left(InflationGap\right)+\mathrm{½}\left(OutputGap\right)\end{array}$

Given that:

Inflation rate = 0%

Equilibrium Real Fed Funds Rate = 2%

Output Gap = 1%

$FederalFundsTargetRate=0\%+2\%+\mathrm{½}\left(0\%-2\%\right)+\mathrm{½}\left(1\%\right)=1.5\%$

Given that:

Inflation rate = 8%

Equilibrium Real Fed Funds Rate = 2%

Output Gap = 1%

$FederalFundsTargetRate=8\%+2\%+\mathrm{½}\left(8\%-2\%\right)+\mathrm{½}\left(1\%\right)=13.5\%$

Average of these two forecasts will be

$=\mathrm{½}\left(1.5\%+13.5\%\right)=7.5\%$

Requirement 4:

Suitability of Taylor’s Rule

Answer:

It is necessary to interpret Taylor’s rule strictly because even at varied inflation rates it gives the same target rate.

Economics Concept Introduction

Introduction:

Taylor’s rule is a proposed guideline which describes the interest rate decisions of central banks. It is based on the following three factors:

1) Targeted versus actual inflation levels;

2) Full employment versus actual employment levels;

3) The short-term interest rate appropriately consistent with full employment

Requirement 1:

Fed target funds rate according to Taylor rule when inflation rate is 4%