Taylor Rule Calculator

What Is the Taylor Rule?

The Taylor rule is a simple formula that suggests where a central bank should set its short-term interest rate. It says the rate should go up when inflation is above its target or when the economy is producing more than its long-run level, and come down in the opposite cases. The Stanford economist John B. Taylor set it out in a 1993 paper as a description of how the United States Federal Reserve had been setting the federal funds rate.

No central bank follows the rule mechanically. It is used as a benchmark: a quick way to check whether the current rate looks high or low given inflation and output.

Taylor Rule Formula

This calculator uses the formula below:

• FFR: the federal funds target rate, in percent.
• r: the real interest rate, in percent.
• π: the current inflation rate, in percent.
• π*: the target inflation rate, in percent.
• y: the output gap.

Two of the parts are worked out from what you type:

Here i is the nominal interest rate, Y is current GDP and Y* is long-run GDP. Because r + π is the nominal rate again, the result is the nominal rate plus half of each gap.

How to Calculate the Taylor Rule

Inflation is 4.5%, the target is 2%, current GDP is 2,750,000, long-run GDP is 2,700,000 and the nominal rate is 5.25%:

1. Find the inflation gap. 4.5 − 2 = 2.5.
2. Find the output gap. log10(2,750,000) − log10(2,700,000) ≈ 0.007969.
3. Find the real interest rate. 5.25 − 4.5 = 0.75%.
4. Add the parts. 0.75 + 4.5 + 1.25 + 0.003984 ≈ 6.504%.

The target rate is about 6.504%, which is 1.254 points above the 5.25% nominal rate. The rule points to a higher rate.

The Taylor Rule in One Picture

The thin line keeps the real rate at 2% whatever inflation is. The Taylor rule line is steeper, so the real rate rises when inflation is above target and falls when it is below.

How the Output Gap Is Measured

The output gap compares what the economy produces with what it can produce in the long run. It is positive when current GDP is above long-run GDP and negative when it is below. There are two common ways to write it:

• Log gap: log10(Y) − log10(Y*). The main result of this calculator uses this form.
• Percent gap: (Y − Y*) ÷ Y* × 100. Taylor’s paper and most textbooks use this form.

The log gap is a much smaller number, so it moves the main result very little. To show the textbook version as well, the calculator adds two rows: the output gap in percent and the rate with that percent gap. For the example above:

Use the main result when your course or source uses the log form, and the “Rate with % gap” row when it uses the percent form.

The Real Interest Rate in the Rule

The calculator finds the real interest rate by taking current inflation away from the nominal rate you enter. Taylor’s 1993 version fixed the real rate at 2% (an estimate of the neutral rate, the real rate that neither speeds up nor slows down the economy) and the inflation target at 2%.

To use Taylor’s 2% real rate here, enter a nominal rate that is 2 points above current inflation. With inflation of 3%, a 2% target, GDP at its long-run level and a nominal rate of 5%:

Taylor Rule Examples

Low inflation and a weak economy. Inflation is 1%, the target is 2%, current GDP is 980, long-run GDP is 1,000 and the nominal rate is 3%:

The target is about 0.5 points below the 3% nominal rate, so the rule points to a cut. With the percent gap of −2%, the rate would be 3 − 0.5 − 1 = 1.5%.

Everything on target. Inflation is 2%, the target is 2%, GDP equals long-run GDP and the nominal rate is 4%. Both gaps are 0, so the target rate is 4% and the rule points to no change.

A negative result. Inflation is 0.5%, the target is 2%, GDP equals long-run GDP and the nominal rate is 0.25%. The real rate is −0.25% and the inflation gap is −1.5:

A rate below zero is hard to set in practice, which is one reason central banks turn to other tools when inflation is very low.

The Taylor Principle

In the formula, inflation appears twice: once on its own and once inside the inflation gap. Together they mean that when inflation rises by 1 point, the target rate rises by 1.5 points. This is called the Taylor principle: the nominal rate should rise by more than inflation, so that the real rate goes up and cools spending.

If the rate rose by less than inflation, the real rate would fall as prices sped up, which would push spending and inflation higher still.

Other Versions of the Rule

• Taylor (1993): weights of 0.5 on the inflation gap and 0.5 on the output gap. This calculator uses these weights.
• Balanced-approach rule: keeps 0.5 on the inflation gap and puts 1.0 on the output gap, so the rate reacts more to a weak or strong economy.
• Inertial rules: move only part of the way from last period’s rate toward the rule rate, so the rate changes gradually.

With a 2% real rate, inflation on a 2% target and a percent output gap of −2%, the 1993 rule gives 2 + 2 − 1 = 3% and the balanced-approach rule gives 2 + 2 − 2 = 2%.

Limits of the Taylor Rule

• Long-run GDP is an estimate. It cannot be observed, and estimates are revised.
• The neutral real rate is an estimate too. It changes over time and different methods give different values.
• Data arrive late. GDP and inflation figures are published with a delay and later revised.
• Which inflation measure? Headline and core measures can give different answers.
• Rates near zero. The rule can ask for a rate below zero, which is hard to deliver.

The result is for education and rough estimates. It is not a forecast of what any central bank will do.

Key Terms

Taylor rule

A formula that suggests a policy interest rate from inflation and output.

Federal funds rate

The rate at which United States banks lend reserves to each other overnight.

Inflation gap

Current inflation minus target inflation.

Output gap

How far current GDP is from long-run GDP.

Long-run GDP

The output an economy can sustain, also called potential GDP.

Real interest rate

The nominal rate minus inflation.

Neutral rate

The real rate that neither speeds up nor slows down the economy.

How to Use the Taylor Rule Calculator

1. Enter current and target inflation. Type the current inflation rate, such as 4.5, and the inflation target, such as 2. Both are percentages.
2. Enter current and long-run GDP. Type current GDP, such as 2,750,000, and long-run (potential) GDP, such as 2,700,000. Use the same unit for both.
3. Enter the nominal interest rate. Type the nominal interest rate as a percentage, such as 5.25.
4. Read and copy the result. The target rate appears as you type, with the working, both gaps, the real rate and whether the rule points to a rise or a cut. Press Copy to copy it, or Clear or Esc to start again.

Example: inflation of 3%, a 2% target, GDP equal to long-run GDP and a nominal rate of 5% give a target rate of 5.5%.

Who Can Use This Calculator?

Frequently Asked Questions (FAQs)

Sources

• Wikipedia. Taylor rule.
• Federal Reserve Board. Policy Rules and How Policymakers Use Them.
• Brookings. The Taylor Rule: A benchmark for monetary policy?.
• Federal Reserve Bank of Atlanta. Taylor Rule Utility.
• Wikipedia. John B. Taylor.
• Wikipedia. Output gap.
• Wikipedia. Federal funds rate.