Fisher Equation Model

Evidence and data

Read nominal yields together with expected inflation, realized inflation, inflation-risk premia, and real-rate proxies such as inflation-indexed bonds.

Calibration or measurement

The exact multiplicative relation matters when inflation or rates are high. The linear classroom version is an approximation.

Boundaries

• Ex post real rates can differ from ex ante real rates.
• Credit and liquidity premia are outside the clean decomposition.
• Inflation-risk premia must not be confused with expected inflation.

Use guidance

When sufficient

Decomposing a nominal yield into its real-rate and expected-inflation components when a reliable measure of inflation expectations is available. TIPS breakevens, survey expectations, and inflation-swap rates each supply an expected-inflation estimate; the Fisher identity then backs out an implied real rate. The decomposition is arithmetically exact and valid regardless of the underlying theory.

When sketch only

Do not use to make causal claims about how policy moves the components. The identity is silent on whether a policy rate cut lowers the real rate, lowers expected inflation, or both. It also excludes inflation-risk premia and liquidity premia that empirically separate nominal yields from the sum of a clean real rate and clean expected inflation.

When to switch

Switch to a term-structure model (affine NKDSGE or Gurkaynak-Wright-type factor model) when risk premia and the full yield curve are the object of interest. Switch to a New Keynesian Phillips curve setup (theoretical:new-keynesian-phillips) when the question is how expected inflation is formed and what drives it.

Falsification signal

A sustained period in which the nominal policy rate moves by a large amount but neither the inferred real rate nor the measured inflation expectation moves by a corresponding amount points to a breakdown of the decomposition, usually because a time-varying liquidity or inflation-risk premium is doing the work. This is observable as a wedge between breakeven inflation and survey expectations that co-moves with the policy rate.