The Fisher Effect and the Quantity Theory of Money

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The Fisher Effect and the Quantity Theory of Money

Eric Mahaney

4/7/13

EC-301-1

The Fisher effect and the Fisher equation were made famous by economist Irving Fisher. He created his equation by rearranging the equation for real interest rate, which is (r = i - π). Real interest rate equals the nominal interest rate plus inflation. This is a very basic equation. Fisher manipulated it to solve for i, in order to understand the effect that inflation has on nominal interest rate. The famous equation is i = r + π, nominal interest rate equals real interest rate plus inflation. This is basically saying that the nominal interest rate can be changed by a change in either the real interest rate or inflation. The Fisher effect is the one to one relationship between the inflation rate and the nominal interest rate. According to this model, as inflation increases, the nominal interest rate should also increase by the same proportion. The main concept behind the Fisher effect is that higher inflation causes higher nominal interest rate. (Mankiw, 91-92) By using the Fisher effect along with the quantity theory of money, the effect that money growth has on nominal interest rate can also be analyzed. The quantity theory of money is M*V=P*Y or the quantity of money multiplied by the velocity of money equals price multiplied by output. The velocity of money is assumed to remain constant in order to simplify the model. Therefore, PY is determined solely by the quantity of money. PY represents nominal GDP because prices times output is nominal GDP. Y is determined by the factors of production and the production function. Y is also used as real GDP. Because Y is considered exogenous and already determined by the production function and the factors of production, so a change in the quantity of money will affect only the price level and is therefore directly proportional. In other words, an increase in the money growth results in an equal growth of the price. An increase in prices is called inflation. According to the quantity theory of money, an increase in the money supply results in an equal growth of the inflation rate. This increase in the inflation rate in theory causes an equal increase in nominal interest rate. (Mankiw, 82-87) The fisher equation undergoes further manipulation to account for the lag time between the time that the nominal interest rates are set and the inflation that occurs during that time and the time that the interest rate is realized. Because the inflation rate is unknown at time onset of the interest rate the expected inflation rate is used in its place. The ex ante real interest rate is the real interest rate based on the expected inflation. The real interest rate that is realized at the maturity of the investment is called the ex post real interest rate. This affects the fisher equation because the nominal interest rate cannot be set by the actual inflation rate when it is unknown at the time that the nominal interest rate is set. The expected inflation rate (Eπ) is used to set the nominal interest rate. The Fisher effect can be rewritten as i = r + Eπ, interest rate equals real interest rate plus expected inflation. The borrowers and lenders who set the nominal interest can never be certain, however by analyzing the current markets and closely following indicators, they can make approximations about the future inflation rate. (Mankiw, 94) To examine the Fisher effect more, the graphs below show the relationship between the variables in the U.S. over the last fifty years.

(WorldBank)
The graph above shows the fisher effect occurring in the United States. Generally, the higher the inflation rate, the higher the nominal interest rate. The correlation is not perfect of course. This imperfectness can be attributed to other factors involved in the nominal interest rate. The Fed can adjust it using monetary and fiscal policy. The fed can keep the interest rate artificially low if they think...
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