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The Taylor rule
What if a simple formula told the central bank where to set its policy rate?
i = r* + π + 0.5(π − π*) + 0.5·GDP gapProblem / motivation
In 1993, John Taylor noticed that the Fed's decisions, supposedly a matter of judgement, in fact followed a simple equation. Can monetary policy be reduced to a formula?
A central bank pursues two objectives in tension: bringing inflation back towards its target (2%) and keeping output close to its POTENTIAL — the sustainable level when the economy runs at full tilt, without overheating (the “potential” already met in the course “Okun's law”). The Taylor rule weighs those two gaps and draws from them a numerical prescription for the policy rate — the lever whose cascade the course “The policy rate and transmission” set out.
Its power is twofold: DESCRIPTIVE (it reproduces the Fed's observed rates strikingly well) and NORMATIVE (it says where the rate ought to be). A lasting departure from the rule is a signal — the Fed judged “too low” in 2003-2005 is the classic example. This course builds the formula piece by piece, PROVES its principle in three lines, then points the compass at a real decision: the ECB facing the inflation of 2022.
Assumptions
In your view, which assumptions are needed for this model to hold? Jot down your ideas — no lead is wrong, this is your worksheet.
Your worksheet is still empty. Go for it: propose at least one idea.
0 idea(s) proposedFormalization
Start from the neutral question: what advertised rate NEITHER brakes NOR stimulates? Assumption 2 answers: the real rate is about the nominal minus inflation — turn it over, and to obtain a neutral real rate r*, you need a nominal rate of r* + π. At r* = 2% and π = 5%, it ALREADY takes 7% just to be neutral: the largest piece of the formula is not a punishment, it is the conversion of real into nominal. Forget it and you will wrongly find central banks “brutal”.
Around the base, the rule corrects for each of the two objectives (assumption 1). Inflation above target? +0.5 point of rate per point of gap (π − π*). Output above potential — the GDP gap, as a % of potential? +0.5 point per point: overheating calls for the brake, languor for the accelerator (a negative gap → a negative correction). The two 0.5s are Taylor's CHOICE: round weights, set down in 1993, which he found reproduced the Fed of 1987-1992 well — a reasonable setting, not a law of nature. (Taylor himself proposed a variant in 1999, doubling the weight on output to 1.0: more attentive to employment, it prescribes lower rates in a recession. Hold on to the idea: the “Taylor rule” is a FAMILY of rules, of which you choose the setting.)
The course's great claim can be checked on the back of a ticket. Write the prescribed REAL rate: i − π = r* + 0.5(π − π*) + 0.5·GDP gap (the π of the base has cancelled out). Raise π by 1 point: i rises by 1.5, so i − π rises by +0.5 — the brake GENUINELY tightens. With a weight of 1 instead of 1.5, i − π would stay frozen: the bank would run after inflation without ever catching it. There is the Taylor principle, proved.
Finally, the rule reads BACKWARDS: compare the central bank's ACTUAL rate with the prescribed rate. Below it → accommodative policy; above it → restrictive. This is the formula's real use today — a marker for judging, not an autopilot (the interpretation points it at the ECB of 2022). One last point of honesty: for Taylor, “π” means the inflation of the GDP deflator; in practice the rule is read with the CPI or core inflation — and the choice changes the prescription. Click each term:
Solving / calculation
π = 5%, target π* = 2%, output gap = +1%, neutral rate r* = 2%. Let's unroll the prescription, then check that it really DOES brake. Handle it afterwards.
- The base: the nominal rate that makes the real rate neutral (1st beat)
r* + π = 2 + 5= 7% - Inflation correction: 3 points above target
0.5 × (5 − 2)= +1.5 pt - Output correction: mild overheating
0.5 × 1= +0.5 pt - The prescribed rate
i = 7 + 1.5 + 0.5i = 9% - Cross-check: does the resulting REAL rate exceed r*?
i − π = 9 − 5 = 4% > r* = 2%yes: the policy really is braking
The rule prescribes 9% — a real rate of 4%, two points above neutral: restrictive, as it should be with inflation at 5%. At equilibrium (π = π* = 2%, zero gap), everything falls back onto r* + π* = 4%, the neutral nominal rate. The simulator now shows the real rate alongside the prescribed one — and warns you when the rule steps outside its own domain (a negative prescription).
i = r* + π + 0.5(π − π*) + 0.5·GDP gapSet inflation, the target, the output gap and the neutral rate: the prescribed rate AND the resulting real rate are computed — push inflation into negative territory to meet the zero lower bound of limit 2.
Economic interpretation
A proved formula, a compass in hand: what remains is to use it — on real decisions, and knowing its place in the toolbox.
The principle (3rd beat) guarantees that the REAL rate rises when inflation rises. And a higher real rate brakes through the cascade of the course “The policy rate and transmission”: dearer loans, fewer borrowers, demand slowing — until prices ease. Without the 1.5 over-adjustment, inflation would always keep a head start on its own brake.
In late 2022, euro area inflation peaked at around 10.6%. A naive compass reading: i = 2 + 10.6 + 0.5 × 8.6 ≈ 17%. The ECB, for its part, took its rates towards 4% — thirteen points below the prescription! A shameful gap? No, an instructive one: the shock was largely IMPORTED (energy — a rate does not bring the price of gas down), expectations stayed anchored near 2%, and core inflation was running well below 10.6. The compass SIGNALS; judgement decides — exactly “descriptive, not autopilot”.
The Phillips curve promised that central banks “watch the gap u − u* and set their rate accordingly”: here is the formalisation. The rule uses the OUTPUT gap rather than the unemployment gap — the two are cousins through Okun's law (output below potential ⇔ unemployment above the natural rate): same thermometer, two scales.
An actual rate durably BELOW the prescription: accommodative policy (the Fed of 2003-2005, accused of having fed the housing bubble); above it: restrictive. Modern central banks CONSULT the rule — the Fed publishes its prescriptions in its report — without chaining themselves to it: the limits say why.
Limits / critiques
Exercises
π = 3%, π* = 2%, output gap = −2%, r* = 2%. What policy rate is prescribed (in %)?
An economy at equilibrium (π = π* = 2%, zero gap), r* = 2%. What nominal rate does the rule settle on?
π = 4%, π* = 2%, zero gap, r* = 2% (so i = 7%). What is the resulting REAL rate (in %)?
Late 2022: π ≈ 10%, π* = 2%, gap ≈ 0, r* = 2%. What rate did the rule prescribe (in %)?
True or false: according to the Taylor principle, when inflation rises by one point, the prescribed rate rises by more than one point.
The rule prescribes 6%; the central bank posts 3%. Its policy is…
Deflation and recession: π = −1%, π* = 2%, gap = −4%, r* = 1%. The rule prescribes i = −3.5%. What does the central bank do?
True or false: if the total weight of inflation in the rule were 1 (instead of 1.5), the real rate would not move when inflation rises.