Taylor Rule

Definition

The Taylor rule (Taylor 1993) is a monetary policy reaction function that specifies the central bank's target for the short-term nominal interest rate $i_t$ as a function of the output gap and the deviation of inflation from target:

$i_t = r^* + \pi^* + \phi_\pi (\pi_t - \pi^*) + \phi_y (y_t - y_t^*)$

where $r^*$ is the long-run real interest rate, $\pi^*$ is the inflation target, $\phi_\pi > 0$ is the inflation response coefficient (Taylor's original value: 1.5), $\phi_y \geq 0$ is the output gap coefficient (Taylor's original value: 0.5), and $y_t - y_t^*$ is the output gap.

Key Ideas

Taylor principle: for the rule to ensure a determinate equilibrium and stabilise inflation, $\phi_\pi > 1$ (the real rate must rise when inflation rises). Rules with $\phi_\pi < 1$ are associated with indeterminacy and sunspot equilibria.
Observational equivalence: different parametrisations of the Taylor rule can imply identical interest rate paths, making structural identification of policy preferences difficult without additional restrictions.
Forward-looking variants: New Keynesian Dynamic Stochastic General Equilibrium (DSGE) models typically use $E_t[\pi_{t+1}]$ rather than $\pi_t$ in the rule, capturing the forward-looking nature of central bank decisions.
Instrument rules vs. targeting rules: the Taylor rule is an instrument rule specifying how to set the policy rate; targeting rules (flexible inflation targeting) describe the loss function the central bank minimises.

How It Works

The rule is embedded in Vector Autoregression (VAR) models as an identifying restriction for monetary policy shocks: the "recursiveness assumption" (Christiano-Eichenbaum-Evans 1999) places the policy instrument last in the Cholesky ordering, effectively assuming the central bank responds to contemporaneous macro variables. See Monetary Policy Shocks and Sign Restriction Identification for identification strategies.

Why It Matters

The Taylor rule provides a benchmark for evaluating central bank behaviour and for identifying monetary policy shocks in structural VARs. Deviations from the rule have been used to assess whether policy was "too loose" (as argued for the pre-2007 period) or "too tight."

Open Questions