Fisher hypothesis

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The Fisher hypothesis is the proposition by Irving Fisher that the real interest rate is independent of monetary measures, especially the nominal interest rate. The Fisher equation is

r_r = r_n − π^e.

This means, the real interest rate (r_r) equals the nominal interest rate (r_n) minus expected rate of inflation (π^e). Here all the rates are continously compounded. For simple rates, the Fisher equation takes form of

r_r = (1 + r_n) / (1 + pi^e) − 1.

If r_r is assumed to be constant, r_n must rise when π^e rises. If an economic theory or model has this property, it shows the Fisher effect

Fisher Effect: The one for one adjustment of the nominal interest rate to the expected inflation rate.

According to the principle of monetary neutrality, an increase in the rate of money growth raises the rate of inflation but does not affect any real variable. An important application of this principle concerns the effect of money on interest rates. Interest rates are important variables for macroeconomists to understand because they link the economy of the present and the economy of the future through their effects on saving and investment.

To understand the relationship between money, inflation and interest rates you need to understand nominal interest rate and real interest rate. The nominal interest rate is the interest rate you hear about at your bank. If you have a savings account, for instance, the nominal interest rate tells you how fast the number of dollars in your account will rise over time. The real interest rate corrects the nominal rate for the effect of inflation in order to tell you how fast the purchasing power of your savings account will rise over time. The real interst rate is the nominal interest rate minus the expected inflation rate.

Real interest rate= Nominal Interest Rate - Expected Inflation Rate

Nominal Interest Rate= Real interest Rate + Expected Inflation Rate

If inflation permanently rises from a constant level, let's say 4%/yr., to a constant level, say 8%/yr., that currency's interest rate would eventually catch up with the higher inflation, rising by 4 points a year from their initial level. These changes leave the real return on that currency unchanged. The Fisher Effect is an evidence that in the long-run, purely monetary developments will have no effect on that country's relative prices.

International Fisher Relation
The international Fisher relation predicts that the interest rate differential between two countries should be equal to the expected inflation differential. Therefore, countries with higher expected inflation rates will have higher nominal interest rates, and vice versa.

Capital Market Integration
The generalized Fisher effect holds that real interest rates must be the same across borders. However, validity of the generalized Fisher effect requires capital market integration.

In order for the generalized Fisher theorem to hold, capital markets must be integrated. That is, capital must be allowed to flow freely across borders. In general, the capital markets of developed countries are integrated. However, in many less developed countries, we can observe currency restrictions and other regulation that inhibit integration.

Example

Suppose that the current spot exchange rate for U.S. Dollars into British Pounds is $1.4339 per pound. If the current interest rate is 5 percent in the U.S. and 7 percent in Britain, what is the expected spot exchange per pound rate 12 months from now according to the International Fisher Effect?

The International Fisher Effect estimates future exchange rates based on the relationship in nominal interest rates. Multiplying the current spot exchange rate by the nominal annual U.S. interest rate and dividing by the nominal annual British interest rate yields the estimate of the spot exchange rate 12 months from now ($1.4339 * 1.05) / 1.07 = $1.4071.