The Taylor Rule and Miles's Triple-Strength Taylor Rule

Notation and the Fisher Equation

i = nominal interest rate

r = real interest rate

r* = natural interest rate (a.k.a. “neutral interest rate”)

pi = inflation

pi* = inflation target

r = i - pi (Fisher equation—the definition of the real interest rate)

i = r + pi (Fisher equation, rearranged)

Sometimes people think of the Fisher equation in terms of expected inflation. But since inflation is sticky, over a one-year horizon or less, expected inflation (at least for sophisticated folks) is very close to actual inflation.

The Taylor Rule

eople often state the Taylor rule in terms of nominal interest rates, but I’ll state it in terms of the real interest rate. To state it in terms of the nominal interest rate, put i instead of r on the left-hand side and add pi to the right-hand side. I’m also stripping away some complications people sometimes put into the Taylor rule to strip it to the essentials.

In what follows, the output gap in percent is equal to ln(Actual Output) - ln(Natural Level of Output)

=ln(Y) - ln(Y^n).

The a %Delta measure of how far output is from the natural level of output.

The Taylor Rule is:

r =r*+ (.5/year) [Output gap in %] + .5 (pi - pi*)

Sometimes it is stated in terms of nominal interest rates. In that case, just add pi:

i = r*+pi + (.5/year) [Output gap in %] + .5 (pi - pi*)

Note that the first occurence of pi is just to convert from the real to the nominal rate. The second occurrence is about how far you are from the inflation target.

The Triple-Strength Taylor Rule

The Triple-Strength Taylor Rule is:

r =r*+ (1.5/year) [Output gap in %] + 1.5 (pi - pi*)

Sometimes it is stated in terms of nominal interest rates. In that case, just add pi:

i = r*+pi + (1.5/year) [Output gap in %] + 1.5 (pi - pi*)

Note that the first occurence of pi is just to convert from the real to the nominal rate. The second occurrence is about how far you are from the inflation target.

Exercise

Open this Excel file. The first sheet is the task: to fill in the last 4 columns for the real and nominal rates recommended by the Taylor Rule and the real and nominal rates recommended by the Triple-Strength Taylor Rule. I suggest doing 5 rows or so before looking at the first 5 rows of answers. Then do the last 15 rows before you look at the last 15 rows of answers.