Fisher Effect

The Fisher Effect , named after the economist Irving Fisher , is a relationship between the inflation rate , nominal and real interest rate , which states that increases in the inflation rate are reflected in proportional increases in the nominal interest rate.

In mathematical terms, the Fisher effect can be expressed as follows:

${\displaystyle {\mathit {\Delta i=\Delta \pi }}}$

with = change in nominal interest and = change in inflation rate ${\displaystyle \Delta i}$ ${\displaystyle \Delta \pi }$

The basis of the Fisher effect is the following relationship:

${\displaystyle (1+i)=(1+\pi )\cdot (1+r)}$

with i = nominal interest rate, = inflation rate, r = real interest rate ${\displaystyle \pi }$

If and r are sufficiently small, the well-known Fisher equation can be derived from ${\displaystyle \pi }$

${\displaystyle 1+i=1+\pi +r+\pi \cdot r}$ as

${\displaystyle i\approx \pi +r}$( Fisher equation )

The strict separation of the monetary and real spheres ( classic dichotomy ) is important in Fisher's theory . According to this, the real interest rate in the capital market is determined as the interest rate that balances the demand for capital goods and savings. Monetary influences play no role in determining the real interest rate. This means that changes in the inflation rate cannot affect the real interest rate ( ) and are therefore directly reflected in the nominal interest rate. ${\displaystyle \Delta r=0}$

The above formulation of the Fisher effect assumes that the inflation rate is known. In reality, however, the actual inflation rate is only known with a time lag. In this respect, a more realistic formulation of the Fisher effect includes the change in the expected inflation rate.

${\displaystyle {\mathit {\Delta i=\Delta \pi ^{e}}}}$

${\displaystyle i\approx \pi ^{e}+r}$ (Fisher equation with inflation expectations)

In this form, changes in inflation expectations are already having an impact on today's nominal interest rate.

International Fisher Effect

The International Fisher Effect (also: Fisher Open) transfers the statements of the Fisher Effect to international relationships. The following assumptions are fundamental:

• The real rates of return of the countries under review (h: home; f: foreign) are identical (freedom from arbitrage).
• The Fisher relationship applies in both countries.

With

• ${\displaystyle r\!\,}$ : Real interest rate
• ${\displaystyle n\!\,}$ : Nominal interest
• ${\displaystyle \pi \!\,}$ : Inflation rate

this implies that the following relationship holds:

${\displaystyle {\frac {1+n_{h}}{1+\pi _{h}}}=(1+r_{h})=(1+r_{f})={\frac {1+n_{f}}{1+\pi _{f}}}}$.

Hence, the extended Fisher relationship applies:

${\displaystyle {\frac {1+n_{h}}{1+n_{f}}}={\frac {1+\pi _{h}}{1+\pi _{f}}}}$.

This equation also implies that currencies with higher (expected) inflation rates should have higher interest rates. Deviations can be justified by:

• Capital markets not fully integrated (real rates of return do not match).
• Political Risks.
• Currency risks.
• Different reasons.

If the (relative) purchasing power parity theory is valid , it also follows as the exchange rate in price quotation and the time index : ${\displaystyle e}$ ${\displaystyle t}$

${\displaystyle {\frac {1+n_{h}}{1+n_{f}}}={\frac {(1+\pi _{h})}{(1+\pi _{f})}}={\frac {e_{t+1}}{e_{t}}}}$.

This equation is known as the Fisher Open or International Fisher Effect . It implies that currencies with low nominal interest rates tend to appreciate against those with high nominal interest rates. (The high nominal interest rates are due to high inflation rates.)