Taylor Rule Calculator — a policy rule, not a forecast

The Taylor rule calculator evaluates a family of simple monetary policy rules that map four macroeconomic quantities — inflation, an inflation target, a neutral real interest rate and an output gap — onto a single prescribed nominal interest rate. It is a teaching and analysis instrument. It takes every number from you, publishes no economic data of its own, and produces an arithmetic prescription rather than a prediction of what any central bank will actually do.

Arb Digital publishes this alongside the rest of its free economics tools because the Taylor rule is one of the most widely quoted and most widely misread objects in macroeconomics. People cite “the Taylor rule says rates should be X” as though the rule were a measurement. It is not. It is an equation with contested coefficients fed by inputs that are themselves estimates, and the honest way to use it is to see how far the answer moves when you change the assumptions.

What This Taylor Rule Calculator Does

You supply the current inflation rate, the central bank's published inflation target, an estimate of the neutral real interest rate, and an output gap. You also choose the two response coefficients, either by picking a named variant or by typing your own. The calculator returns the nominal policy rate the rule prescribes, and breaks that number into its parts so you can see which input is doing the work.

The four supporting figures are the inflation-gap term, the output-gap term, the real interest rate implied by the prescription, and the prescription after an effective lower bound is applied. That last figure matters because a rule can prescribe a deeply negative nominal rate in a severe downturn, which no central bank can straightforwardly deliver in cash-based economies. Seeing the unconstrained and constrained numbers side by side is the point.

Everything is a model output. Nothing here is a statement about what any interest rate should be, and nothing here is investment or financial advice.

How to Use It

1. Pick a rule variant. The original 1993 weights are 0.5 on the inflation gap and 0.5 on the output gap. Choose “Custom” if you want to set your own.
2. Enter inflation and the target. Use the same measure the central bank you are studying uses, and take both figures from that bank or your national statistics office.
3. Enter a neutral real rate. This is an estimate, not a measurement. Try more than one value.
4. Enter the output gap as a percentage of potential output, negative when output is below potential.
5. Set a lower bound if you want to see the constrained prescription, then read the breakdown to see which term drives the result.

The Formula

The rule in its original published form is written as a nominal interest rate equal to the neutral real rate, plus current inflation, plus a weighted inflation gap, plus a weighted output gap:

i = r* + π + a(π − π*) + b(y − y*)

Here i is the prescribed nominal policy rate, r* the neutral real rate, π current inflation, π* the inflation target, and (y − y*) the output gap in percentage points. The coefficients a and b are the response weights. The US Federal Reserve sets out this exact form, together with several alternative rules, in its published note Policy Rules and How Policymakers Use Them, which cites John B. Taylor's 1993 paper Discretion versus Policy Rules in Practice as the source.

A worked example makes the arithmetic concrete. Take a neutral real rate of 2%, inflation of 3%, a target of 2%, an output gap of −1%, and the original 0.5 and 0.5 coefficients. The inflation-gap term is 0.5 × (3 − 2) = 0.5. The output-gap term is 0.5 × (−1) = −0.5. The prescription is 2 + 3 + 0.5 − 0.5 = 5.0%. The implied real rate is 5.0 − 3 = 2.0%, exactly the neutral rate, because in this example the two gap terms cancel.

Why the Coefficients Are Disputed

The 0.5 and 0.5 weights were not derived from first principles. They were chosen because they described the behaviour of one central bank over one historical window reasonably well. Every serious treatment since has produced different numbers. The so-called balanced-approach variant doubles the output weight to 1.0. The Federal Reserve Bank of Cleveland publishes a running comparison of several such rules under the title Simple Monetary Policy Rules, and the spread between them is routinely wide. Estimated rules fitted to different countries, different decades and different inflation measures return a wide spread of coefficients, and a rule fitted to a period of high and volatile inflation will not resemble one fitted to a period of persistent disinflation.

This is not a defect that better estimation will fix. The coefficients encode a preference about how much output volatility a policymaker is willing to accept in exchange for inflation stability. That is a value judgement expressed as a number, which is precisely why the tool asks you to choose it rather than choosing for you. Run the same inputs through 0.5/0.5 and 0.5/1.0 and note that the two prescriptions diverge by half the output gap. In a deep recession that is a difference of whole percentage points.

The Two Unobservable Inputs

Two of the four inputs cannot be measured at all. The neutral real interest rate is defined as the real rate consistent with output at potential and stable inflation, which means it is defined by a counterfactual. Estimates of it are model outputs with confidence bands wide enough to cover most of the plausible policy range. Because r* enters the rule with a coefficient of one, an error in r* passes straight through to the prescription with no damping whatsoever.

Potential output is the second. The output gap requires knowing what the economy could have produced, which is again a counterfactual estimate built on a measured output series whose own construction is documented at length — for the United States, in the Bureau of Economic Analysis NIPA Handbook — and it is routinely revised years after the fact. Real-time output-gap estimates have historically been revised by margins comparable to the gaps themselves. A rule evaluated with the data available at the time can therefore prescribe something quite different from the same rule evaluated with the revised data later, and both are “the Taylor rule”. If you want to see how measurement conventions shape a headline macro number, the same problem appears in the unemployment rate calculator and the GDP calculator.

Nominal, Real and the Inflation Term

A frequent misreading is to treat the standalone π term as if it were part of the response to inflation. It is not. It is the conversion from a real rate to a nominal one. The rule says: start from the neutral real rate, add inflation to express it in nominal terms, and only then respond to the gaps. Dropping that term produces a rule that never keeps up with inflation at all.

The consequence is the Taylor principle: because inflation appears once as a conversion and once inside the gap term with coefficient a, the total response of the nominal rate to inflation is 1 + a. With a positive a, the nominal rate rises by more than one-for-one with inflation, so the real rate rises too. If a were zero, the nominal rate would track inflation exactly and the real rate would never move. You can check the arithmetic behind that distinction with the real interest rate calculator, and see the compounding side of it in the inflation calculator.

What the Rule Deliberately Leaves Out

Simple rules are simple on purpose, and the omissions are large. There is no financial stability term, no exchange rate, no credit condition, no term structure and no allowance for policy transmitted through anything other than the short rate. There is no interest-rate smoothing, so the rule can prescribe large jumps between periods where actual central banks move gradually. There is no forward-looking element in the original form, though many later variants substitute forecast inflation for current inflation and get materially different answers.

The rule is also silent on the effective lower bound. A prescription of −4% is arithmetically fine and operationally meaningless in a cash economy, which is why the calculator reports the constrained figure separately. Periods when the unconstrained prescription sits far below the bound are exactly the periods when central banks reached for balance-sheet policies that a short-rate rule cannot represent.

Reading the Output Honestly

The useful question is never “what does the rule say the rate should be”. It is “how wide is the range of prescriptions across reasonable assumptions, and where does the actual policy rate sit inside that range”. Vary r* by a percentage point in each direction, vary the output gap by a percentage point, and run two coefficient sets. That produces a spread rather than a point, and the spread is the honest answer. A single number quoted without its assumptions is the most common way this rule is misused in public argument.

It is also worth remembering what the rule was for. Taylor's original contribution was descriptive: a demonstration that a simple equation summarised past policy decisions surprisingly well. Turning a description into a prescription is a step the arithmetic does not license by itself.

Common Mistakes to Avoid

• Quoting one prescription as “the” Taylor rule rate when a different but equally standard coefficient set gives a materially different number.
• Treating r* as known. It is an estimate that enters with a coefficient of one, so its error passes through undamped.
• Mixing inflation measures. Using headline inflation against a target defined on a core measure quietly changes the gap term.
• Using revised output-gap data to judge a real-time decision that was made with figures later revised away.
• Ignoring the lower bound and reporting a large negative prescription as though it were implementable.

Related Free Tools From Arb Digital

Pair this with the Okun's law calculator for the empirical link between the output gap and unemployment, the velocity of money calculator for the equation of exchange, the money multiplier calculator for the reserve side, and the interest rate calculator for the arithmetic of rates themselves. The free online tools hub lists every economics calculator we publish.

Frequently Asked Questions

This page is an educational model, not financial, investment or policy advice. The Taylor rule is a simple equation with disputed coefficients and unobservable inputs; nothing it produces is a forecast of any interest rate or a recommendation about any financial decision. Take every input from your central bank or national statistics office and cite it.