Theory-Based Models

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Theory-Based Models

Introductoryscatter trend

Phillips Curve

A reduced-form inflation-unemployment relationship used to study slack, inflation expectations, and supply disturbances.

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

Sections

Setup and notation

The route uses a reduced-form inflation relation around an anchored inflation level and a natural unemployment benchmark.

\pi = \pi^e + \nu - \kappa(u - u^n)

Short-run Phillips relation

Inflation rises when unemployment falls below the natural rate and falls when slack runs above it.

\frac{\partial \pi}{\partial u} = -\kappa

Expectations and shifts

Changes in expected inflation or a supply shock shift the entire curve.

\frac{\partial \pi}{\partial \pi^e} = 1

\frac{\partial \pi}{\partial \nu} = 1

Comparative statics

The model’s message is directional: tighter labor markets raise inflation pressure, while cost shocks shift the whole relation upward.

\pi - \pi^e - \nu = -\kappa(u - u^n)

Theory-Based Models

Theory-Based Models

Introductoryscatter trend

A reduced-form inflation-unemployment relationship used to study slack, inflation expectations, and supply disturbances.

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

Sections

Setup and notation

The route uses a reduced-form inflation relation around an anchored inflation level and a natural unemployment benchmark.

\pi = \pi^e + \nu - \kappa(u - u^n)

Short-run Phillips relation

Inflation rises when unemployment falls below the natural rate and falls when slack runs above it.

\frac{\partial \pi}{\partial u} = -\kappa

Expectations and shifts

Changes in expected inflation or a supply shock shift the entire curve.

\frac{\partial \pi}{\partial \pi^e} = 1

\frac{\partial \pi}{\partial \nu} = 1

Comparative statics

The model’s message is directional: tighter labor markets raise inflation pressure, while cost shocks shift the whole relation upward.

\pi - \pi^e - \nu = -\kappa(u - u^n)