11.6 The Taylor rule

Motivation

Desks do not forecast the RBI or the Fed from speeches alone. They anchor on a policy-rule benchmark and ask why the central bank is above or below it.

11.6.1The rule and its calibration#

Statement (Taylor 1993)

i = r^* + \pi + a_\pi(\pi-\pi^*) + a_y\,x, \tag{11.15}

where:

$i$ is the policy rate;
$r^*$ is the neutral real rate, the real rate consistent with full employment and stable inflation;
$\pi$ is inflation over the past four quarters and $\pi^*$ the target;
$x$ is the output gap, actual minus potential output in percent of potential.

Taylor's calibration for the US was $r^*=2$ , $\pi^*=2$ and $a_\pi=a_y=0.5$ (Taylor, 1993, Carnegie-Rochester Conf. Series on Public Policy 39:195–214 [V]). Rearranged, the nominal rate moves $1+a_\pi = 1.5$ for one point of inflation.

11.6.2The Taylor principle#

Proposition 11.6Taylor principle

Consider a minimal accelerationist economy:

\pi_t = \pi_{t-1} + \kappa x_t,\qquad x_t = -\sigma\,(i_t - \pi_t - r^*),\qquad \kappa,\sigma>0,

with policy set by (11.15). Then $\pi_t-\pi^* = \lambda^{-1}(\pi_{t-1}-\pi^*)$ with $\lambda = 1 + \kappa\sigma a_\pi/(1+\sigma a_y)$ . Inflation converges monotonically to target if and only if $a_\pi>0$ . Equivalently, the nominal rate must move more than one-for-one with inflation.

Proof

From (11.15), the real rate gap is $i_t-\pi_t-r^* = a_\pi(\pi_t-\pi^*) + a_y x_t$ . Substitute into the IS equation:

x_t = -\sigma a_\pi(\pi_t-\pi^*) - \sigma a_y x_t,

so $x_t = -\dfrac{\sigma a_\pi}{1+\sigma a_y}(\pi_t-\pi^*)$ . Substitute into the Phillips curve, writing $\hat\pi_t = \pi_t-\pi^*$ :

\hat\pi_t = \hat\pi_{t-1} - \frac{\kappa\sigma a_\pi}{1+\sigma a_y}\hat\pi_t \;\Longrightarrow\; \hat\pi_t\,\lambda = \hat\pi_{t-1}.

If $a_\pi>0$ then $\lambda>1$ and $\hat\pi_t = \lambda^{-t}\hat\pi_0 \to 0$ monotonically. If $a_\pi=0$ then $\lambda=1$ and any inflation shock is permanent. If $a_\pi<0$ but small in magnitude, $0<\lambda<1$ and deviations explode. A very negative $a_\pi$ with $\lambda<-1$ gives oscillating convergence, which is economically irrelevant.∎

The intuition: if the nominal rate rises less than inflation, the real rate falls when inflation rises. That stimulates demand and pushes inflation up further. This is the core argument for why central banks in 2026 hiked into a supply shock: once inflation is high, keeping rates unchanged is an easing.

Inertial rule Central banks move gradually, which is well described by

i_t = \rho\,i_{t-1} + (1-\rho)\,i^{\text{Taylor}}_t,\qquad 0\le\rho<1. \tag{11.16}

With constant inputs, $i_t$ converges geometrically to $i^{\text{Taylor}}$ at rate $\rho$ (tested in test_m11_taylor.py).

11.6.3Applying the rule in 2026#

Worked example 11.5: the Fed, inputs as of late Oct 2026

Inflation: August 2026 core PCE 3.0% (the Fed's preferred gauge). September headline CPI was 3.7% y/y and core CPI 2.6%¹; core PCE was 3.0% y/y in August and 3.1% in September²; energy CPI was reported at +20.4% y/y³.
Output gap: US real GDP (FRED GDPC1) against CBO potential (GDPPOT) gives +1.70% for 2026Q3⁴.
$r^*$ : the NY Fed's Holston–Laubach–Williams estimate is 1.01% and the Laubach–Williams one-sided estimate is 1.65%, both for 2026Q2⁵.

With $r^*=1.01$ , $\pi=3.0$ , $\pi^*=2$ and $x=1.7$ :

i = 1.01 + 3.0 + 0.5(1.0) + 0.5(1.7) = 5.36\%.

The fed funds midpoint is 3.875% (range 3.75–4.00%, held on 28 Oct 2026 [V]). The policy rate is therefore about 150 bp below this version of the rule. The answer is sensitive to choices:

using headline CPI instead of core PCE adds 1.05 pp;
using Taylor's original $r^*=2$ adds about 1 pp;
the LW estimate of the output gap (+1.20%) instead of the CBO gap subtracts 0.25 pp.

This sensitivity is why two analysts can both "use the Taylor rule" and disagree by 200 bp. Markets price about a 75–85% chance of another 25 bp hike on 9 Dec 2026, and futures imply about 4.7% by Sep 2027⁶. The market is pricing a path that closes part of the gap.

Worked example 11.6: the RBI

Inflation: September 2026 CPI 5.54% [V]. The RBI's FY27 projection is 5.2% [V].
Target: 4%, with a tolerance band of 2–6%, renewed for April 2026 to March 2031 (gazette notification of 25 Mar 2026)⁷.
$r^*$ for India: estimates are model-dependent and roughly in the 1–2% real range. I take $r^*=1.5\%$ as an assumption. An RBI Bulletin estimate in this range is widely cited but was not re-verified here.
Output gap: no official series. I take $x=0$ as an assumption. With GDP growth projected at 7.1% for FY27⁸, the gap is unlikely to be strongly negative.

i = 1.5 + 5.54 + 0.5(1.54) + 0 = 7.81\%.

Using the 5.2% projection gives 7.30%. Both are well above the 5.50% repo.

Why might the RBI rationally sit 180–230 bp below the rule?

Much of the inflation is imported energy and food, a supply shock that monetary policy affects only through second-round effects.
The rule ignores the exchange rate. An open-economy Taylor rule adds a term in currency depreciation. Hiking also supports the rupee, which was one stated motive in October.
Reaction-function inertia, (11.16) with $\rho\approx0.8$ , describes most central banks.
The parameters for India are uncertain. With $r^*=1.0$ the prescription is 7.31%, and with a −0.5% gap it is 7.56%. All variants stay above 5.50%, so the qualitative conclusion is robust: Indian policy is accommodative relative to a Taylor benchmark.

Practitioner notes

The Taylor rule is a benchmark, not a forecast. Its value to a trader is in the change in the gap: a rising gap means the market should price more hikes.
Indian MPC decisions are announced on the morning of the last day of the meeting (check the RBI's schedule for the exact time). Bond and rupee desks trade the statement's stance language ("neutral", "withdrawal of accommodation", "calibrated tightening") as much as the rate.