Taylor Rule Calculator

Quick Calculator

Inflation π (%)

Inflation target π* (%)

Gap type Output gap (%) Unemployment gap (u - u*) (pp)

Gap value

Okun coefficient

Used only for unemployment gaps.

Equilibrium real rate r* (%)

α (inflation gap weight)

β (output gap weight)

Smoothing λ (0–1)

Policy inertia; 0 uses unsmoothed rule.

Previous rate i_t-1 (%)

Compute Compute instantly Instant compute uses client-side calculations.

Example data

Editable rows are also preloaded above.

Formula used

i = r* + π + α(π − π*) + β(ygap)

• i: implied nominal policy rate.
• r*: equilibrium real interest rate.
• π: current inflation; π*: target inflation.
• α, β: response weights to inflation and output gaps.
• y_gap: output gap (%). For unemployment gaps, output gap ≈ -Okun × (u - u*).
• Optional smoothing: it = λ it-1 + (1-λ) iTR.

Defaults mirror a common specification: r* = 2%, α = 0.5, β = 0.5. Adjust as appropriate for your framework.

How to use this calculator

1. Enter inflation, target, gap type, and gap value.
2. Set r*, α, β. Optional: set smoothing λ and previous rate.
3. Click Compute instantly for a single result.
4. Use the Scenario Table to model multiple periods or cases.
5. Press Compute all to fill implied and real rates.
6. Export your table to CSV or PDF for documentation.
7. Use the graph to compare paths across scenarios.

Taylor Rule reference

What is the Taylor Rule?

The Taylor Rule links the policy rate to inflation and real activity. A common form is i = r* + π + α(π − π*) + β(ygap). When inflation exceeds target, the rule recommends higher nominal rates. When the output gap is negative, the rule recommends lower rates.

Output gap vs unemployment gap

If the unemployment gap is used, convert to an output gap via Okun's relation: ygap ≈ −κ (u − u*) where κ is the Okun coefficient (often around 2). Example: if u − u* = 0.5 pp and κ = 2, then the output gap is approximately −1.0%.

• Positive output gap → economy above potential → higher rate.
• Negative output gap → slack → lower rate.
• Signs matter: unemployment gap positive implies negative output gap.

Smoothing, calibration, and interpretation

Policymakers often smooth changes using it = λ it−1 + (1−λ)iTR. Higher λ increases inertia and reduces abrupt moves between meetings. Typical coefficients might start at α = 0.5 and β = 0.5, then be tuned to local conditions and data definitions.

Interpreting results: the real implied rate equals nominal implied minus π. Consider bounds, measurement uncertainty, and structural changes in r*.