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Theory-Based Models

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Macro by Mark

U.S. macro data with release timing, boards, and macro context.

Public U.S. data from agencies and market feeds.

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Theory-Based Models

Taylor Rule

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

Introductoryrule line
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Theory-Based Models

Proof

Route section

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

Sections

Setup and notationTaylor-rule specificationTaylor principleComparative statics

Setup and notation

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

i=rn+π+ϕπ(π−π∗)+ϕyygapi = r^n + \pi + \phi_{\pi}(\pi - \pi^*) + \phi_y y_{gap}i=rn+π+ϕπ​(π−π∗)+ϕy​ygap​

Taylor-rule specification

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

∂i∂π=1+ϕπ\frac{\partial i}{\partial \pi} = 1 + \phi_{\pi}∂π∂i​=1+ϕπ​
∂i∂ygap=ϕy\frac{\partial i}{\partial y_{gap}} = \phi_y∂ygap​∂i​=ϕy​

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.

ϕπ>1\phi_{\pi} > 1ϕπ​>1

Comparative statics

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

∂i∂ϕπ=π−π∗\frac{\partial i}{\partial \phi_{\pi}} = \pi - \pi^*∂ϕπ​∂i​=π−π∗

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Introductory

Taylor Rule

How aggressively should the policy rate react to inflation and output gaps?

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