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Interest rates and inflation: A continuous time stochastic approach

In: Economic Uncertainty, Instabilities And Asset Bubbles Selected Essays

Author

Listed:
  • A. G. Malliaris

    (Loyola University of Chicago, Chicago, IL 60611, USA)

  • Walter F. Mullady

    (Loyola University of Chicago, Chicago, IL 60611, USA)

  • M. E. Malliaris

    (Loyola University of Chicago, Chicago, IL 60611, USA)

Abstract

This 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.

Suggested Citation

  • A. G. Malliaris & Walter F. Mullady & M. E. Malliaris, 2005. "Interest rates and inflation: A continuous time stochastic approach," World Scientific Book Chapters, in: Economic Uncertainty, Instabilities And Asset Bubbles Selected Essays, chapter 4, pages 23-28, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812701015_0004
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    Cited by:

    1. Hakan Berument & Zubeyir Kilinc & Umit Ozlale, 2005. "The Missing Link Between Inflation Uncertainty And Interest Rates," Scottish Journal of Political Economy, Scottish Economic Society, vol. 52(2), pages 222-241, May.

    More about this item

    Keywords

    Asymptotic Economic Growth; Inflation; Interest Rates; Asset Pricing; Equity Markets; Foreign Currency; Monetary Policy; Crash;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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