The Taylor rule
Taylor's 1993 formula, what each term means, and why a simple rule described Fed policy so well.
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 (Taylor, 1993).
The rule
In Taylor's notation the federal funds rate \(r\) is set as
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 \(x_t\):
Definition 1 (Reading the rule)
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
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 (Taylor, 1993).
- 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 (Taylor, 1999).
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.
Linked from
- Real-time data and the Taylor rule · Monetary Policy Rules and the Policy Stance
- The natural rate of interest · Monetary Policy Rules and the Policy Stance
- Variants of the Taylor rule · Monetary Policy Rules and the Policy Stance
- The Taylor principle and determinacy · Monetary Policy Rules and the Policy Stance
- Why rules? Time inconsistency and the case for commitment · Monetary Policy Rules and the Policy Stance
References
- Taylor, J. B. (1993). Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy, 39, 195–214. https://doi.org/10.1016/0167-2231(93)90009-L
- Taylor, J. B. (1999). A historical analysis of monetary policy rules. Monetary Policy Rules, 319–341.
Cards (5)
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question
Write the Taylor (1993) rule with named constants and state the values Taylor used.
Answer
\(i_t = r^* + \pi_t + 0.5(\pi_t - \pi^*) + 0.5\,x_t\) with \(r^* = 2\) and \(\pi^* = 2\) percent; \(x_t\) is the percentage output gap and \(\pi_t\) inflation over the previous four quarters.
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gap
In the Taylor rule a one-point rise in inflation raises the nominal rate by […] points and therefore the real rate by […] points.
Answer
In the Taylor rule a one-point rise in inflation raises the nominal rate by 1.5 points and therefore the real rate by 0.5 points.
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question
Inflation is 4 %, the output gap is −1 %, \(r^* = \pi^* = 2\). What rate does the Taylor rule prescribe?
Answer
\(2 + 4 + 0.5(4-2) + 0.5(-1) = 6.5\) percent.
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question
What is the neutral nominal rate implied by the Taylor rule when inflation is at target and the gap is closed?
Answer
\(r^* + \pi^*\); with Taylor's numbers, 4 percent.
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gap
Taylor presented the rule as a […], not as a formula to be followed mechanically; it tracked the Fed's decisions over […] closely.
Answer
Taylor presented the rule as a benchmark for judging policy, not as a formula to be followed mechanically; it tracked the Fed's decisions over 1987–1992 closely.
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