Financial
Taylor Rule formula: central bank policy interest rate & ZLB floor
Explore a Taylor-style policy-rule benchmark with supplied neutral rate, inflation target and output gap, plus an optional zero-floor scenario.
Understand the 1.5x Taylor Principle on inflation and 0.5x output-gap response
This teaching version uses i=r*+inflation+0.5*(inflation-target)+0.5*outputGap. The 2% neutral real rate and 2% target are example assumptions, not current universal central-bank settings. Potential output and the neutral rate are estimated and uncertain; policymakers consider more information than this rule.
Holding other inputs fixed, a 1 percentage-point rise in inflation raises the rule result by 1.5 percentage points. This is a model sensitivity, not a prediction of the next policy decision. MAX(0,rate) imposes a chosen scenario floor; negative nominal rates are possible and the effective lower bound need not be zero.
| Macro Regime (r* = 2.0%, Target pi* = 2.0%) | Inputs (pi, OutputGap) | Prescribed Taylor Rate |
|---|---|---|
| Overheating Boom | pi = 3.6%, Gap = +1.0% | 2% + 3.6% + 0.8% + 0.5% = 6.90% |
| Balanced Steady State | pi = 2.0%, Gap = 0.0% | 2% + 2.0% + 0% + 0% = 4.00% |
| Mild Recession | pi = 1.4%, Gap = -3.0% | 2% + 1.4% - 0.3% - 1.5% = 1.60% |
| Deflationary Slump (ZLB) | pi = 0.0%, Gap = -6.0% | Raw = -2.0% -> MAX(0, i) = 0.00% |
Unconstrained Taylor Rule policy interest rate
A2=NeutralRealRate r* (0.02), B2=Inflation pi (0.036), C2=TargetInflation pi* (0.02), D2=OutputGap (0.01).
Enter rates and the output gap as decimals: 0.01 means 1%. Use a consistently defined inflation measure and output-gap series. Negative inflation and output gaps are allowed.
=IF(COUNT(A2:D2)<>4,"Invalid inputs",ROUND(A2 + B2 + 0.5 * (B2 - C2) + 0.5 * D2, 4))Optional zero-floor scenario
This scenario floors the computed benchmark at zero. It does not model unconventional policy, an actual central-bank reaction function or the effective lower bound in every jurisdiction.
=IF(COUNT(A2:D2)<>4,"Invalid inputs",MAX(0, ROUND(A2 + B2 + 0.5 * (B2 - C2) + 0.5 * D2, 4)))Try the example
Use the original values or change them to test your understanding.