Theory-Based Models

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Theory-Based Models

Introductoryrule line

Taylor Rule

A policy rule linking the nominal interest rate to inflation and output gaps, giving a compact view of monetary reaction functions.

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Proof

Read the derivation as a document, with the math typeset directly and the intermediate chains tucked behind expandable steps.

Sections

Setup and notation

The Taylor rule is written as a benchmark reaction function rather than a fully optimal policy problem.

i = r^n + \pi + \phi_{\pi}(\pi - \pi^*) + \phi_y y_{gap}

Taylor-rule specification

The rule raises the policy rate when inflation overshoots target or when the output gap is positive.

\frac{\partial i}{\partial \pi} = 1 + \phi_{\pi}

\frac{\partial i}{\partial y_{gap}} = \phi_y

Taylor principle

The standard Taylor-principle intuition requires the policy response to inflation to be strong enough that the nominal rate rises more than one-for-one with inflation.

\phi_{\pi} > 1

Comparative statics

A more hawkish rule rotates the policy line upward; a positive output gap moves the active point along that line.

\frac{\partial i}{\partial \phi_{\pi}} = \pi - \pi^*

Back to explore Open compare

Theory-Based Models

Loading Theory-Based Models

Theory-Based Models

Introductoryrule line

Taylor Rule

A policy rule linking the nominal interest rate to inflation and output gaps, giving a compact view of monetary reaction functions.

Catalog Overview Explore Proof Compare

Proof

Read the derivation as a document, with the math typeset directly and the intermediate chains tucked behind expandable steps.

Sections

Setup and notation

The Taylor rule is written as a benchmark reaction function rather than a fully optimal policy problem.

i = r^n + \pi + \phi_{\pi}(\pi - \pi^*) + \phi_y y_{gap}

Taylor-rule specification

The rule raises the policy rate when inflation overshoots target or when the output gap is positive.

\frac{\partial i}{\partial \pi} = 1 + \phi_{\pi}

\frac{\partial i}{\partial y_{gap}} = \phi_y

Taylor principle

The standard Taylor-principle intuition requires the policy response to inflation to be strong enough that the nominal rate rises more than one-for-one with inflation.

\phi_{\pi} > 1

Comparative statics

A more hawkish rule rotates the policy line upward; a positive output gap moves the active point along that line.

\frac{\partial i}{\partial \phi_{\pi}} = \pi - \pi^*

Back to explore Open compare