Interest rates and inflation : A continuous time stochastic approach
AbstractThis paper investigates the theoretical foundations of Fisher's equation which expresses the nominal interest rate as the sum of the real interest rate and the expected rate of inflation. To emphasize Fisher's (1930) original formulation and Sargent's (1973) recent suggestion that nominal interest rates and inflation are simultaneously determined rather than having the causation go from inflation to interest rates, we develop a two-equation continuous time stochastic model to build a more solid theoretical foundation of Fisher's equation. Assuming that the nominal interest rate and the rate of inflation follow Itô processes we derive an Itô equation that allows us to express and compute the expected real interest rate and its volatility. These two equations generalize the traditional Fisher equation and an illustration using US long data from 1865–1972 shows the usefulness of our results.
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