Taylor Rule Calculator
The Taylor Rule gives a formula-based prescription for where a central bank should set its short-term policy interest rate, given current inflation and the state of the economy relative to its potential. Enter your inflation rate, inflation target, output gap, and equilibrium real rate to get an instant policy rate recommendation. Switch between the original Taylor (1993) coefficients, the Balanced Approach, or enter your own. The result includes a full worked-step breakdown and an interpretation of whether the implied stance is accommodative, neutral, or restrictive.
What is the Taylor Rule?
The Taylor Rule is a monetary policy guideline introduced by economist John B. Taylor in a 1993 paper, "Discretion versus Policy Rules in Practice." It specifies a formula for setting a central bank's short-term nominal interest rate based on two key economic gaps: the difference between actual and target inflation, and the difference between actual and potential output (the output gap). The rule does not require a central bank to follow it mechanically; instead, it serves as a benchmark to evaluate whether policy is roughly appropriate given current economic conditions. The Federal Reserve and other central banks use it as one of many inputs to the policy-setting process.
The Taylor Rule formula explained
The general form is: i = r* + pi + alpha x (pi - pi*) + beta x (y - y*), where i is the recommended nominal policy rate, r* is the long-run equilibrium real interest rate, pi is current inflation, pi* is the inflation target, (pi - pi*) is the inflation gap, and (y - y*) is the output gap (actual GDP minus potential GDP, expressed as a percentage of potential). The term r* + pi equals the neutral nominal rate: the rate that would prevail if inflation were on target and output were at potential. The inflation gap term adds or subtracts depending on how far inflation deviates from target. The output gap term raises the prescription when the economy is overheating and lowers it when there is slack. In the original Taylor (1993) parameterization, both alpha and beta equal 0.5, r* equals 2%, and the inflation target equals 2%, giving a prescribed rate of 4% when inflation is on target and output is at potential.
Understanding the output gap
The output gap is the percentage difference between actual GDP and potential (or trend) GDP. A negative output gap, say -2%, means the economy is producing 2% less than its full-capacity level - typical in a recession or slow recovery. This signals labor market slack and downward pressure on inflation, so the Taylor Rule prescribes a lower rate to stimulate demand. A positive output gap means the economy is running above trend capacity, which tends to put upward pressure on prices; the formula responds by prescribing a higher rate to cool activity. In practice, measuring potential GDP is difficult: estimates from the Congressional Budget Office and the Federal Reserve differ, and revisions can be large. Uncertainty about the true output gap is one reason policymakers do not follow Taylor-type rules mechanically.
Taylor Rule variants: Balanced Approach and beyond
The original Taylor (1993) rule places equal weights of 0.5 on the inflation gap and the output gap. A variant often called the Balanced Approach Rule doubles the output gap coefficient to 1.0, giving greater emphasis to employment conditions. This variant gained prominence when then-Federal Reserve Chair Janet Yellen referenced it publicly. Another class of variants is the inertial (or smoothed) Taylor rule, which adds a weight on the lagged policy rate to capture central banks' tendency to move rates gradually rather than jumping to the formula prescription. The First Difference Rule, developed by Reifschneider and Williams, responds only to changes in inflation and the output gap rather than their levels, making it robust to uncertainty about the equilibrium real rate r*. The Atlanta Fed's Taylor Rule Utility tracks prescriptions from more than 30 variants simultaneously.
Common Taylor Rule variants and their coefficients
| Variant | Alpha | Beta | r* assumption | Notes |
|---|---|---|---|---|
| Original Taylor (1993) | 0.5 | 0.5 | 2.0% | Baseline benchmark; equal weights |
| Balanced Approach (Yellen) | 0.5 | 1.0 | 2.0% | Higher weight on employment/output |
| Price-level targeting | 0.5 | 0.5 | 2.0% | Targets cumulative price level, not rate |
| Inertial rule | 0.5 | 0.5 | 2.0% | Smooths changes; adds lagged rate term |
| First Difference rule | N/A | N/A | N/A | Responds to changes, not levels; robust to r* uncertainty |
| ECB-style rule | 1.5 | 0.5 | 1.0% | Stronger inflation weight; lower neutral rate |
Key variants used by the Federal Reserve and academic economists. Alpha is the inflation-gap coefficient; beta is the output-gap coefficient.
Frequently asked questions
What does a positive policy gap mean?
A positive gap means the Taylor Rule formula prescribes a higher rate than the current policy rate. In other words, the formula suggests the central bank is holding rates too low relative to current inflation and output conditions - an accommodative stance. A negative gap means the current rate is above the formula prescription, implying policy is relatively restrictive.
What is the equilibrium real interest rate (r*)?
The equilibrium real rate, often written r* or r-star, is the interest rate that would keep the economy growing at its potential with stable inflation over the long run. It is unobservable and must be estimated. For decades, many economists assumed r* was around 2%. After the 2008 financial crisis, research by Holston, Laubach, and Williams and others suggested r* had fallen to 0.5-1% in the US and even lower in other economies, implying a much lower neutral nominal rate. If you use a 2% r* when the true value is lower, the Taylor Rule will systematically prescribe rates that are too high.
How does the Taylor Rule handle recessions?
During a deep recession, the output gap becomes sharply negative and inflation often falls below target. Both effects push the Taylor Rule prescription down. In the 2008-2009 financial crisis, several Taylor Rule variants prescribed a rate well below zero - sometimes as low as -4% or -5%. Since central banks cannot (under normal operating procedures) cut nominal rates below zero, this situation prompted the use of unconventional tools such as quantitative easing and forward guidance.
Does the Federal Reserve actually follow the Taylor Rule?
Not mechanically. The Fed consults Taylor-type rules as one input among many. The Federal Open Market Committee (FOMC) is required by the Monetary Policy Transparency Act to publish an explanation when its rate differs from a simple rule benchmark. Academic research has found that the Fed's actual policy was reasonably consistent with a Taylor Rule from the mid-1980s through the 1990s - a period of low inflation and steady growth sometimes called the "Great Moderation" - but deviated from it notably after 2003 and again after 2008.
What is the difference between the Original Taylor rule and the Balanced Approach?
Both rules use an alpha (inflation gap coefficient) of 0.5. The key difference is the output gap coefficient (beta): 0.5 in the original Taylor rule versus 1.0 in the Balanced Approach. A higher beta means the formula responds more aggressively to economic slack or overheating. When the output gap is negative, the Balanced Approach prescribes a lower rate than the original rule; when the gap is positive, it prescribes a higher rate. The choice reflects a view about the relative importance of the price-stability and maximum-employment mandates.
Why might the prescribed rate be negative?
If the output gap is very negative (deep recession) and inflation is well below target, the formula can add large negative adjustments to the neutral rate baseline, pushing the prescription below zero. This is a real-world limitation: conventional monetary policy cannot easily achieve negative nominal rates, though some central banks (the ECB, Bank of Japan, Swiss National Bank) have experimented with mildly negative policy rates. When the prescription is negative, the Taylor Rule signals that alternative stimulus tools may be needed.