Question

Suppose that actual inflation is 3 percentage points, the Fed’s inflation target is 2 percentage points, and unemployment is 1 percent below the Fed’s unemployment target. According to the Taylor rule, what value will the Fed want to set for its targeted interest rate?

Short answer

According to the Taylor rule, the Fed will set its targeted interest rate at 6.5%.

Step-by-step solution

Defining the inflation gap and unemployment gap

The inflation gap is the Current actual inflation rate minus the Inflation target, and the unemployment gap is the Current actual unemployment rate minus the Unemployment rate target.

Given the current actual inflation rate of 3%, with an inflation target of 2%. The inflation gap, from the definition, will be

Inflation gap = 3 – 2 = 1%

Since the actual unemployment is 1% below Fed’s unemployment target, it is equivalent to the unemployment gap in the US economy according to the definition. Thus,

Unemployment gap = -1%

Computing target interest rate

To obtain the target interest rate, Taylor’s formula is

Fed’s Target interest rate = real risk-free interest rate + current actual inflation rate + 0.5 (inflation gap) – unemployment gap

But based on historical data Fed’s real risk-free interest rate is 2 %.

Then,

Fed’s Target interest rate = 2 +current actual inflation rate + 0.5 (inflation gap) – unemployment gap.

$$\begin{gathered} targetinterestrate=2+3+\left(0.5\times 1\right)-\left(-1\right) \\ =5+0.5+1 \\ =6.5 \end{gathered}$$

Thus, according to Taylor’s rule, Fed’s target interest rate is 6.5%.