# Fisher Equation

This paper examines the effects of negative real interest rates and talks about developments in Taiwan. For the calculation of the real interest rates the Fisher equation and Fisher effect is examined first. In the end suggestions for the further management of interest rates in Taiwan by the central bank is given. 1. Fisher effect and equation

Fisher equation

The Fisher equation links the nominal interest rate (i), the real interest rate (r) and the expected or real (ex- ante or ex- post) inflation (Π) The main concept is the composition of the nominal interest rate (i) out of the real (expected) interest rate (ra) and the expected inflation rate (Πe). Ex post this equation is adjusted, so as the nominal interest rate (i) is composed out of the real interest rate (r) and the real inflation (Π).

i ~ ra + Πe -> ra ~ i - Πe (ex ante)

and

i ~ r + Π -> r ~ i - Π (ex post)

Implications

The Fisher equation has some important implications regarding the real interest rate, that are described in Horn, 2008, p5: 1. If Π = 0, then i = r.

In this case the value of money is constant. The cost of holding money is the same as the opportunity costs of investment. Under this condition r cannot be negative, as i >= 0.

2. If Π > 0, then i > r. In the case of a positive inflation rate, nominal interest rates will always be higher than real interest rates.

3. If Π < 0, then i < r. In the case of a negative inflation rate (= an expected deation), real interest rates will always be higher than nominal interest rates.

4. For a given i, the higher Π, the lower r.

This case is particularly relevant if an economy is in a liquidity trap where i cannot

be influenced by the central bank anymore. In the case of increasing inflation such a situation will eventually lead to negative real interest rates.

The Fisher effect

The Fisher effect now states a 1:1 linear relationship between i and Π (Πe). This is also what the logic tells us, that the nominal interest rate in a country has to go up with increasing (expected) inflation.

For a more comprehensive discussion of the Fisher effect see Levich, 2001, p. or Horn, 2008, pp2. 2. Negative Interest Rates

Nominal Interest Rates

Negative nominal interest rates are practically not occuring. Such a rate would mean that it is profitable to borrow money. No rational credit institute would accept these conditions. It would also mean that holding money is more lucrative than any kind of investment. Therefore the nominal interest rate is usually positive. There are only a few examples in history when such a situation actually happened (Switzerland 1970's; Hong Kong 1990's) (HKTDC, 2007).

Real Interest Rate

The real interest rate can and actually does become negative quite frequently. If i >= 0 (what we can assume based on the previous subsection), it also means that r >= . Therefore it is always more profitable to invest than to hold money (except in a situation of r=0 and = 0. Hence, investments and the spending of money increases, which in turn increases the inflation rate.

Interest Rate development in Taiwan

Table 1: sources: nominal interest rate (yearly average; except 2010: March and September rates): see [1]; inflation (2010: September index): see[2]; real interest rate computed by the author

We clearly see that during the period of increased inflation (Consumer Price Index) of 2008, as well as in the beginning of 2010, the real interest rate was negative. The drivers of inflation were sharp increases in food and energy prices. Meanwhile the CPI peaked as high as 5.8 %.

Effects of negative real interest rates

If the real interest rate is negative (i.e. the interest rate is lower than the inflation rate) it means that actually banks are paying their customers for having a loan. This provides an incentive to speculation with real...

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