What Is the Taylor Rule? Formula and Use in Central Bank Policy

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The Taylor rule is a formula that prescribes a level for a central bank’s short-term policy rate based on two conditions: how far inflation is from the bank’s target and how far output is from its potential. Economist John Taylor of Stanford University proposed it in 1993 in the paper “Discretion Versus Policy Rules in Practice.” The rule calls for raising the federal funds rate when inflation runs above target or the economy runs above capacity, and lowering it in the opposite case. Central banks do not set rates by plugging numbers into it. They use it as a benchmark for checking whether policy looks too tight or too loose.

The Taylor Rule Formula

In its original form, the equation is:

r = p + 0.5y + 0.5(p - 2) + 2

• r = the nominal federal funds rate
• p = the inflation rate over the previous four quarters
• y = the percent deviation of real GDP from its long-run trend (the output gap)

The first p keeps the real policy rate constant: if inflation rises by one point and the nominal rate rises by the same amount, the real rate does not change. The final 2 is the assumed equilibrium real rate, often called the neutral rate, at which policy neither stimulates nor restrains the economy. Together, p + 2 is the neutral nominal rate.

The two 0.5 terms are the policy response. The 0.5(p - 2) term raises the rate by half a point for every point inflation exceeds the 2% target and lowers it when inflation falls short; the 0.5y term does the same for output, so growth above potential pushes the prescribed rate up and a shortfall pulls it down. Taylor chose the 0.5 weights because the resulting rule tracked actual Fed policy closely over the several years before 1993. They are not derived from theory, and he described the rule as a concept for guiding policy rather than an algebraic formula to follow mechanically.

The Taylor principle

Collecting the inflation terms gives an equivalent form: r = 1 + 1.5p + 0.5y. The coefficient of 1.5 expresses the Taylor principle: to restrain rising prices, a central bank must raise its nominal rate by more than one for one so that the real rate goes up. A bank that lifts rates by less than inflation rises is effectively easing policy. The principle is separate from the rule itself, since many policy rules with different weights satisfy it as long as the inflation response exceeds one.

Worked Examples

These examples use hypothetical inputs, not actual economic data.

Example 1: overheating economy. Inflation is 4% and output is 1% above potential.

r = 4 + 0.5(1) + 0.5(4 - 2) + 2 = 4 + 0.5 + 1 + 2 = 7.5%

Inflation two points over target adds 1 point, the positive output gap adds 0.5, and the neutral nominal rate contributes 6.

Example 2: weak economy. Inflation is 1% and output is 3% below potential.

r = 1 + 0.5(-3) + 0.5(1 - 2) + 2 = 1 - 1.5 - 0.5 + 2 = 1.0%

Example 3: deep recession. Inflation is 0.5% and output is 10% below potential.

r = 0.5 + 0.5(-10) + 0.5(0.5 - 2) + 2 = 0.5 - 5 - 0.75 + 2 = -3.25%

The third result cannot be carried out with ordinary rate cuts, which leads to the rule’s main practical weakness.

How the Taylor Rule Is Used

Policymakers and analysts use the Taylor rule as a yardstick. An actual policy rate well below the prescription means policy is looser than the rule suggests, and one well above means it is tighter. The Federal Reserve’s semiannual Monetary Policy Report to Congress has presented prescriptions from several Taylor-type rules alongside the actual federal funds rate.

The rule also suits academic models and forecasting. Because it states a systematic reaction to inflation and output, economists use it to represent central bank behavior in macroeconomic models, and markets use it to reason about where rates may head as inflation data change.

Limitations and Critiques

The zero lower bound. The basic rule can prescribe negative policy rates, as Example 3 shows. During the short, deep COVID-19 recession, the Taylor rule and its variants called for a sharply negative federal funds rate, while the actual rate was constrained near zero, a point the Fed made in its June 2022 Monetary Policy Report.

Missing tools. When rates hit that floor, central banks turned to other instruments, such as large-scale asset purchases (quantitative easing) and forward guidance. The basic rule has no term for any of them.

No risk management. The formula treats inflation and the output gap as known quantities and weighs deviations the same way regardless of circumstances. In a crisis, policymakers may focus on downside risks that the formula does not capture.

Unobservable inputs. Neither the output gap nor the neutral real rate can be observed directly. Both are estimated, and models such as Laubach-Williams produce neutral rate estimates that can differ from the fixed 2% assumption. Data revisions also mean the gap measured in real time can differ from later figures. Small changes in these inputs move the prescription noticeably.

Choice of measure. The result depends on which inflation index is used. The Fed prefers the Personal Consumption Expenditures (PCE) price index to the Consumer Price Index, and core versus headline measures give different answers.

Taylor criticized the Fed for keeping rates too low before the 2007 to 2009 financial crisis. Former Fed Chair Ben Bernanke replied that rigid formulas miss too much of what policymakers must weigh, and joked that robots would not replace the Federal Open Market Committee anytime soon.

Variations of the Rule

Balanced-approach rule. Janet Yellen, while Fed vice chair, discussed a version that gives equal weight to inflation and output deviations. Bernanke has written that a rule with a coefficient of 1.0 on the output gap, double Taylor’s original 0.5, fits the Fed’s dual mandate of stable prices and maximum employment better. Applied to Example 1, it prescribes 4 + 1.0(1) + 0.5(2) + 2 = 8.0%.

Unemployment-gap versions. Fed variants often replace the output gap with the difference between the long-run unemployment rate and the current rate, in line with the employment side of its mandate.

Shortfall-adjusted rule. The June 2022 Monetary Policy Report also showed a version that delays rate increases after a period at the lower bound, making up for the accommodation the floor prevented.

What the Taylor Rule Is Not

• Not inflation targeting itself. Inflation targeting is a policy framework built around a stated inflation goal. The Taylor rule is one way to set rates within such a framework, and it adds an output term.
• Not a mandate. No central bank is legally required to follow it.
• Not a money-supply rule. It sets an interest rate directly, unlike rules that target growth in money aggregates.
• Not the Taylor curve. That separate concept describes a trade-off between the variability of inflation and the variability of output.

FAQs

The Bottom Line

The Taylor rule matters to anyone judging whether Federal Reserve policy looks too tight or too loose. It works as a benchmark, and no central bank sets rates by plugging numbers into it. Its prescriptions depend on estimated inputs like the output gap and neutral rate, on the inflation measure chosen, and on the zero lower bound. Readers should compare several variants and treat any single result with caution.