---
title: "The Taylor rule"
author: "@econcortex"
url: https://www.econcortex.com/knowledge/@econcortex/the-taylor-rule/
collection: "Monetary Policy Rules and the Policy Stance"
visibility: public
tags: [taylor-rule, fed, monetary-policy]
updated: 2026-09-22
summary: "Taylor's 1993 formula, what each term means, and why a simple rule described Fed policy so well."
---

# The Taylor rule

In 1993 John Taylor proposed a rule that has since become the reference point for every discussion of the interest-rate stance. He did not claim central banks should follow it mechanically; the point was to show that a simple formula tracked the Federal Reserve's actual decisions between 1987 and 1992 remarkably well, and that it could serve as a benchmark for judging policy [@taylor1993].

## The rule

In Taylor's notation the federal funds rate $r$ is set as

\begin{equation}
r = p + 0.5\,y + 0.5\,(p - 2) + 2, \label{eq:taylor93}
\end{equation}

where $p$ is inflation over the previous four quarters and $y$ is the percentage deviation of real GDP from its trend. Two constants are hidden in the formula: an inflation target of 2 percent and an equilibrium real interest rate of 2 percent. Taylor chose both as round numbers that fitted the period; he did not derive them.

It is clearer to write the rule with the constants named. With the nominal policy rate $i_t$, inflation $\pi_t$, the inflation target $\pi^*$, the equilibrium real rate $r^*$ and the output gap $x_t$:

\begin{equation}
i_t = r^* + \pi_t + \phi_\pi\,(\pi_t - \pi^*) + \phi_x\, x_t, \qquad \phi_\pi = \phi_x = 0.5. \label{eq:taylor}
\end{equation}

!!! definition "Reading the rule" #def:terms
    The first two terms, $r^* + \pi_t$, are the nominal rate that keeps the *real* rate at its equilibrium value when inflation is at target. The third term raises the rate when inflation exceeds the target, the fourth when output is above potential. With $\phi_\pi = 0.5$ the total response of the nominal rate to inflation is $1 + \phi_\pi = 1.5$: a one-point rise in inflation raises the nominal rate by 1.5 points and therefore the real rate by 0.5 points.

That last observation is the *Taylor principle*, the subject of [[The Taylor principle and determinacy]]. Here it is enough to note that the rule reacts to inflation *more than one for one*, so the real rate leans against inflation rather than accommodating it.

## A worked example

Suppose inflation is running at 4 percent, the output gap is $-1$ percent, and $r^* = \pi^* = 2$. Then

$$
i = 2 + 4 + 0.5\,(4 - 2) + 0.5\,(-1) = 6.5\ \text{percent}.
$$

Inflation two points above target adds one point; a mild recession subtracts half a point. Compare the case of inflation at target and a closed gap: $i = 4$ percent, which is just $r^* + \pi^*$, the *neutral* nominal rate.

## What made the rule persuasive

- **It is transparent.** Anyone with two published series can compute the prescription and compare it with the actual rate. This turned the abstract case for rules from [[Why rules? Time inconsistency and the case for commitment]] into something operational.
- **It fitted.** Taylor showed that the prescription tracked the funds rate closely over 1987–1992, with the deviations explainable by events such as the 1987 stock market crash [@taylor1993].
- **It is robust.** Later work found that rules of this form perform well across a range of models, even when they are not optimal in any single one [@taylor1999].

## What the rule leaves open

Every ingredient except the current policy rate is measured with error or has to be estimated: which inflation index, which measure of potential output, and above all what $r^*$ is. Lessons [[The natural rate of interest]] and [[Real-time data and the Taylor rule]] show that these choices change the prescription by percentage points, not decimals. The rule is a benchmark, not an oracle.

## References

- [taylor1993] Taylor, John B. (1993). *Discretion versus policy rules in practice*. Carnegie-Rochester Conference Series on Public Policy, 39, pp. 195--214. https://doi.org/10.1016/0167-2231(93)90009-L
- [taylor1999] Taylor, John B. (1999). *A historical analysis of monetary policy rules*. In Monetary Policy Rules, pp. 319--341.