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.