Taylor Rule: Central Bank Interest-Rate Stability

Taylor Rule Weights

Inflation response a_π 1.50

Output-gap response a_y 0.50

Starting Shock

Initial inflation shock 4.0%

Initial output gap 2.0%

Live Readouts

Policy rate i

5.00%

Quarter

Inflation π

4.00%

Output gap

2.00%

Taylor principle: a_π = 1.50 > 1 → stabilizing. Real rates rise faster than inflation, so overheating gets choked off.

How it works

The Taylor Rule is the standard textbook formula for how a central bank sets its short-term policy rate from two gaps — how far inflation sits above target, and how far output sits above its sustainable trend:

i(t) = r* + π(t) + a_π·(π(t) − π*) + a_y·gap(t)

r* = 2% (neutral real rate), π* = 2% (inflation target). Once a rate is set, the simplified economy reacts one quarter later through two textbook relationships — an IS curve (tight real rates cool demand) and a Phillips curve (a weak economy cools inflation):

gap(t+1) = gap(t) − σ·(i(t) − π(t) − r*)     [σ = 0.5]
π(t+1)   = π(t) + κ·gap(t)                    [κ = 0.3]

The Taylor principle: this feedback loop only converges back to target if a_π > 1 — the policy rate must rise by more than one point for every point inflation rises, so the real rate (i − π) actually tightens. Push a_π below 1 and the same shock spirals outward instead of decaying: nominal rates chase inflation but never catch it in real terms.

The bar surface plots the rule's recommended rate over every combination of inflation gap and output gap at your current weights — a static map of the policy.
The glowing marker and trail are the actual simulated economy: each quarter it computes a rate from the surface, then the IS/Phillips equations move it to a new point, which is plotted again next quarter. A trail that spirals inward and stays near the target dot is stable; one that grows outward is not.

This is the same instability John Taylor pointed to in 1993 and central banks still cite today: reacting to inflation less than one-for-one in nominal terms quietly loosens policy in real terms exactly when it should tighten.

Rate surface (bar height = i) Economy trajectory Target (π*, gap=0)

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