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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

Expert Solution & Answer
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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 −

    Federal Funds Rate Target = Inflation Rate + Equilibrium Real Fed Funds Rate + ½ (Inflation Gap) + ½ (Output Gap)

Given that:

Inflation rate = 4%

Equilibrium Real Fed Funds Rate = 2%

Output Gap = 1%

    Federal Funds Target Rate = 4% + 2% + ½ (4%2%) + ½ (1%) = 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%

      Federal Funds Rate Target = Inflation Rate + Equilibrium Real Fed Funds Rate + ½ (Inflation Gap) + ½ (Output Gap)

Given that:

Inflation rate = 3%

Equilibrium Real Fed Funds Rate = 2%

Output Gap = 1%

      Federal Funds Target Rate = 3% + 2% + ½ (3%2%) + ½ (1%) = 6%

Given that:

Inflation rate = 5%

Equilibrium Real Fed Funds Rate = 2%

Output Gap = 1%

    Federal Funds Target Rate = 5% + 2% + ½ (5%2%) + ½ (1%) = 9%

Average of these two forecasts will be

    = ½ (6% + 9%) = 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%

    Federal Funds Rate Target = Inflation Rate + Equilibrium Real Fed Funds Rate + ½ (Inflation Gap) + ½ (Output Gap)

Given that:

Inflation rate = 0%

Equilibrium Real Fed Funds Rate = 2%

Output Gap = 1%

    Federal Funds Target Rate = 0% + 2% + ½ (0%2%) + ½ (1%) = 1.5%

Given that:

Inflation rate = 8%

Equilibrium Real Fed Funds Rate = 2%

Output Gap = 1%

    Federal Funds Target Rate = 8% + 2% + ½ (8%2%) + ½ (1%) = 13.5%

Average of these two forecasts will be

    = ½ (1.5% + 13.5%) = 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%

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