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The Taylor Rule

The Taylor rule describes how a central bank sets its policy rate in response to the inflation gap and the output gap. Its defining feature is the Taylor principle. When inflation rises, the nominal rate is raised by more than one-for-one so the real rate climbs and actually cools demand.

Try it yourself

The Taylor rule

The rule sets the policy rate from the inflation gap and the output gap: i = r* + π + 0.5(π − π*) + 0.5ỹ. The slope on inflation is 1.5, steeper than the 45° line i = π. That extra steepness is the Taylor principle, so the real rate rises with inflation.

Prescribed policy rate i3.0%
-1%3%7%12%16%0%2%4%6%8%10%Inflation π (%)Policy rate i (%)3.0%Taylor rule (slope 1.5)45° line, i = π
Implied real rate r = i − π 1.0%Inflation gap π − π* +0.0%
Inflation π2.0%
Inflation target π*2.0%
Output gap ỹ+0.0%
Neutral real rate r*1.0%
Because the slope (1.5) exceeds 1, the implied real rate r = i − π = 1.0% rises when inflation rises. A higher real rate cools demand, which is how the rule stabilises inflation.

Why it matters

The rule is a simple reaction function, not a law the bank obeys. It captures the idea that policy should lean against both excess inflation and a weak economy, and that fighting inflation requires a real, not just nominal, tightening.

Formulas

Taylor rule
i=r∗+π+0.5(π−π∗)+0.5 y~i = r^* + \pi + 0.5(\pi - \pi^*) + 0.5\,\tilde{y}
r∗r^* is the neutral real rate, π\pi inflation, π∗\pi^* the target, and y~\tilde{y} the output gap. The coefficient on π\pi is effectively 1.5. Because it exceeds 1, the real rate rises when inflation rises, which is the Taylor principle.

Worked examples

Scenario

With a neutral real rate of 2%, inflation at 4%, a 2% target, and a zero output gap, what rate does the rule prescribe?

Solution

i = 2 + 4 + 0.5(4 - 2) + 0.5(0) = 7%. On target (inflation 2%, no gap) it gives 4%, and in a recession (inflation 1%, output gap -2%) it gives 1.5%.

Common mistakes

  • ✗Central banks mechanically obey the formula. It is a benchmark that describes and guides policy, not a rule the committee is bound to follow.
  • ✗Matching the rate to inflation one-for-one controls it. The Taylor principle needs the nominal rate to rise by more than one-for-one, so the real rate rises and demand actually cools.

Revision bullets

  • •Policy rate reacts to the inflation gap and the output gap
  • •Taylor principle: raise the nominal rate more than one-for-one
  • •A reaction function, not a binding rule

Quick check

The Taylor principle says that when inflation rises by 1 percentage point, the central bank should raise the nominal policy rate by

Connected topics

Bond MarketPolicy ToolsInflation Targeting

Sources

  1. Mishkin (2018), Ch. 17
    Mishkin, F. S. The Economics of Money, Banking, and Financial Markets. 12th ed. Pearson, 2018. ISBN 978-1-292-26885-9.
    The Taylor rule and the Taylor principle in the conduct of monetary policy.
How to cite this page
Dr. Phil's Quant Lab. (2026). The Taylor Rule. Derivatives Atlas. https://phucnguyenvan.com/concept/mb-taylor-rule
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