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### The Relationship Between Real and Nominal Interest Rates and Inflation

The Fisher effect states that in response to a change in the money supply the nominal interest rate changes in tandem with changes in the inflation rate in the long run. For example, if monetary policy were to cause inflation to increase by five percentage points, the nominal interest rate in the economy would eventually also increase by five percentage points.

It's important to keep in mind that the Fisher effect is a phenomenon that appears in the long run, but that may not be present in the short run. In other words, nominal interest rates don't immediately jump when inflation changes, mainly because a number of loans have fixed nominal interest rates, and these interest rates were set based on the expected level of inflation. If there is unexpected inflation, real interest rates can drop in the short run because nominal interest rates are fixed to some degree. Over time, however, the nominal interest rate will adjust to match up with the new expectation of inflation.

In order to understand the Fisher effect, it's crucial to understand the concepts of nominal and real interest rates. That's because the Fisher effect indicates that the real interest rate equals the nominal interest rate less the expected rate of inflation. In this case, real interest rates fall as inflation increases unless nominal rates increase at the same rate as inflation.

Technically speaking, then, the Fisher effect states that nominal interest rates adjust to changes in expected inflation.

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### Understanding Real and Nominal Interest Rates

Nominal interest rates are what people generally envision when they think about interest rates since nominal interest rates just state the monetary return that one's deposit will earn in a bank. For example, if the nominal interest rate is six percent per year, then an individual's bank account will have six percent more money in it next year than it did this year (assuming of course that the individual didn't make any withdrawals).

On the other hand, real interest rates take purchasing power into account. For example, if the real interest rate is 5 percent per year, then money in the bank will be able to buy 5 percent more stuff next year than if it was withdrawn and spent today.

It's probably not surprising that the link between nominal and real interest rates is the inflation rate since inflation changes the amount of stuff that a given amount of money can buy. Specifically, the real interest rate is equal to the nominal interest rate minus the inflation rate:

Real Interest Rate = Nominal Interest Rate - Inflation Rate

Put another way; the nominal interest rate is equal to the real interest rate plus the inflation rate. This relationship is often referred to as the Fisher equation.

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### The Fisher Equation: An Example Scenario

Suppose that the nominal interest rate in an economy is eight percent per year but inflation is three percent per year. What this means is that, for every dollar someone has in the bank today, she will have \$1.08 next year. However, because stuff got 3 percent more expensive, her \$1.08 won't buy 8 percent more stuff the next year, it will only buy her 5 percent more stuff next year. This is why the real interest rate is 5 percent.

This relationship is particularly clear when the nominal rate of interest is the same as the inflation rate - if money in a bank account earns eight percent per year, but prices increase by eight percent over the course of the year, the money has earned a real return of zero. Both of these scenarios are displayed below:

real interest rate = nominal interest rate - inflation rate
5% = 8% - 3%
0% = 8% - 8%

The Fisher effect states how, in response to a change in the money supply, changes in the inflation rate affect the nominal interest rate. The quantity theory of money states that, in the long run, changes in the money supply result in corresponding amounts of inflation. In addition, economists generally agree that changes in the money supply don't have an effect on real variables in the long run. Therefore, a change in the money supply shouldn't have an effect on the real interest rate.

If the real interest rate isn't affected, then all changes in inflation must be reflected in the nominal interest rate, which is exactly what the Fisher effect claims.