The Fisher equation reflects the relationships and differences between the real interest rate the nominal interest rate and the expected inflation rate. Nominal interest rates (i) are calculated in accordance with the commitment of monetary value without considering the inflation factor. On the other hand, the real interest rates (r) are the modified version of nominal rates considering the changes in the purchasing power of money. As inflation rate cannot be known in advance, the expected inflation rates (π) are based on historical experience, which may be differ with different investors and may give rise to errors.

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Considered a situation where price level is constant, the nominal interest rates should be equal to the real interest rates; however this is not likely and not realistic in the present world. Due to the fact that both borrowers and lenders are more concerned with the real purchasing power of the currency, rather than the nominal value of the currency, the real interest rates can more accurately measure the cost of borrowing and benefits for saving. While the nominal interest rates denominated in units of currency, comparatively the unit of account for the real interest rates are standardised basket of goods and services.
If we assume the non-existence of inflation factor, saving 1 pound will result in (1+i) future value in a year. Recalling the nature of real interest rate and nominal interest rates are equal without inflation, (1+i) would be equal to (1+r). Taking the influence of expected inflations into consideration, the real purchasing power of this future value would only be equivalent to (1+i)/(1+π), thus we can derive this into the equation: (1+r)=(1+i)/(1+), which could be rearranged into (1+r)(1+π)=(1+i) , expanded into the equation: 1+rπ+r+π=1+i, and finally simplified into r+π+rπ=i. In a situation involving high rate of inflation, the cross product of real interest rates and inflation rates must be taken into account. However, in the normal situation without extreme hyperinflation, the expected rate ofπshould be less than around 5%, thus the resulting product of rπwould be minimal and insignificant. This allows us to remove this cross product and comes to the Fisher’s equation r ≈i-π -the real interest rate is approximately equal to the difference of nominal interest rates and inflation rates.
According to the Loanable Funds Theory by Knut Wicksell in the 1900s, economic fundamentals such as growth potential and private savings determined the long term real interest rate equilibrium. In order words, real interest rates are contended to be stable over the long run as a result of the interaction between the society’s time preference and productivity of capital assets. As a result, the adjustment of nominal interest rates can be used to maintain a stable real interest rate when the expected inflation rate is fluctuating. As described in the lecture notes of topic 7 ‘the nominal interest rates reflect the stability of the real interest rates plus a premium that tracks the expected rate of inflation, this is the Fisher effect’ (Fisher, 1907). This shows the positive link between the nominal interest rates and the expected inflation rates; as the expected inflation rates goes up, the nominal rates must also be raise to the similar level, as the difference of the two rates would resulting in the final real interest rates.
This relationship could also be elaborated from the circumstances that, if lenders and borrowers can perfectly predict the future price level movement- the expected inflation rates, it would be rational for them to react by adjusting the interest rates for their own good. For example, lenders would fight against changes in the real purchasing power of their loans by adding the percentage changes in price level to their interest charges. In contrast, borrowers who expect their income to change in proportion to price level would be more willingly to accept a higher interest rate. (Yoshinomi, 1979)
Still, Fisher had noticeably differentiated between full equilibrium and the transition period. He specifies that the nominal interest rate adjustments according to expected inflation rate that keeps the real interest rate constant, is only valid during a period of full equilibrium. In other words, in steady state equilibrium nominal interest will adjust following the exact rate of inflation, and real interest rate would be stable. While during the transition period, inflation’s impact is majorly on the real interest rates.
Despite this hypothesis is widely known and applied to economic studies, there is no empirical evidence that may prove or denied this theory. A recent studied of Fatima N and Shamin A. (2012) had conducted to determine the short term and long term relationship between the variables of money supplies, interest rates and inflation rates of Pakistan for the period 1980-2010. They concluded that Fisher effect prevails in Pakistan and the authors suggested that monetary policies should carefully deal with the changes in these variables as they are highly interrelated, both in short run and long run. (Fatima N., 2012) On the other hand, an empirical study from Japan at 1979 showed that the Fisher effect has not been working as the real interest rates are not stable over time. (Yoshinomi, 1979) This may due to the fact that Japan was during the ‘transition period’ as mentioned before, during the decades of the time of this study.
There are also critiques that argue the notion of real rate is not theoretically relevant and thus cannot be applied to macroeconomics problems or microeconomic problems. Problems included the inability of the underlying arbitrage to carry out, and the lack of protection against loss of purchasing power. An article by Tymoigne, E. (2006) interpreted empirical literatures and studies to research over the correlation between interest rates and inflation. He argued that the inflation does not tend to affect nominal interest rates unless monetary authorities, such as the central bank moves the interest rates artificially, thus concluding that what really matters is not so much inflation but monetary policies instead. His also argued that the notion of ‘real’ interest rates defined in Fisher’s theory is inappropriate, as nominal variables matter more than real variables. For instance, higher inflation does not necessarily decrease the debt burden of debtors, that only wage rate changes will affect the burden of the debts. The comparison between nominal value of income inflow to nominal value of income outflows is more important than simply relying on changes in ‘real’ purchasing power of money. The importance of purchasing power of money should not be overlooked indeed, however in most cases of economic system with normal level of inflation the ‘real purchasing power’ had already been included in nominal considerations. (Tymoigne E., 2006)
In conclusion, the Fisher’s equation estimates the relationship between nominal interest rates, real interest rates and expected inflation. Despite the disagreement of the notions of real interest rates, one does not simply argue over the fact that there is a positive link between the nominal interest rates and inflation rates. The control of nominal interest rates has always been an effective channel for central banks such as the Europe Central Banks to carrying out their inflation targeting policies.