Fisher Equation Model

The Fisher Equation links nominal interest rates, real interest rates, and expected inflation. It is the bridge between market quotes and real borrowing costs.

The exact relation is 1 + i = (1 + r)(1 + pi^e). The familiar i = r + pi^e form is a small-rate approximation, often good enough for classroom and policy discussion but not exact when rates or inflation are high.

The distinction between ex ante and ex post real rates matters. Borrowers and lenders contract on expected inflation, but realized inflation determines the actual redistribution after the fact.

The nominal rate compensates lenders for the real return they require plus the expected loss of purchasing power over the contract horizon.

An inflation-risk premium can sit on top of the clean Fisher relation when inflation uncertainty is material. That premium is not expected inflation; it is compensation for risk around the forecast.

If the real rate is anchored by saving and investment fundamentals, higher expected inflation should pass into nominal rates. If policy represses nominal rates, expected inflation lowers the ex ante real rate instead.

Bond-market analysis starts with the Fisher decomposition. A rise in Treasury yields may reflect higher real rates, higher expected inflation, or a larger inflation-risk premium.

Central banks care about the real rate because spending responds to inflation-adjusted borrowing costs. A nominal rate held constant while expected inflation rises is an easing in real terms.

Emerging-market debt analysis must add credit and currency premia. The Fisher Equation isolates inflation compensation but does not explain sovereign risk.