Abstract
This paper presents a decomposition of inflation and its volatility. According to the traditional quantity theory of money, the rate of inflation is decomposed into three components: the rate of change in the money supply, plus the rate of change in the velocity of circulation, minus the rate of change in real output. We derive a generalization of this decomposition by postulating that the rate of change of money supply, velocity, and output follow diffusion equations. Using stochastic calculus techniques, two expressions are obtained decomposing inflation and its volatility as a sum of several economically important terms. We also use two sets of U.S. data to illustrate these decompositions with actual numbers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bronfenbrenner, M. and F. Holzman, “A Survey of Inflation Theory.”American Economic Review 53, 593–611, (1963).
Cox, John C. and Mark Rubinstein,Options Markets. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1985.
Den Haan, Wouter J., “The Optimal Inflation Path in a Sidrauski-Type Model with Uncertainty.”Journal of Monetary Economics 25, 389–409, (1990).
Fischer, S., “The Demand for Index Bonds.”Journal of Political Economy 83, 509–534, (1975).
Fisher, I.,The Purchasing Power of Money. Augustus M. Kelley, 1963.
Friedman, Milton, “Quantity Theory of Money.”The New Palgrave: A Dictionary of Economics, vol 4. New York: The Stockton Press, 1987.
Friedman, Milton and Anna J. Schwartz,Monetary Trends in the United States and the United Kingdom. Chicago: University of Chicago Press, 1982.
Gertler, M. and E. Grinols, “Monetary Randomness and Investment.”Journal of Monetary Economics 10, 239–258, (1982).
Gikhman, I. and A.V. Skorokhod,Introduction to the Theory of Random Processes. Philadelphia: Saunders, 1969.
Gordon, Robert J.,Macroeconomics, 5th Ed. Boston: Little, Brown and Company, Inc., 1990.
Grinols, Earl L. and Stephen J. Turnovsky, “Risk, the Financial Market, and Macroeconomic Equilibrium.”Journal of Economic Dynamics and Control 17, 1–36, (1993).
Lucas, Jr., Robert E., “Two Illustrations of the Quantity Theory of Money.”The American Economic Review 70, 1005–1014, (1980).
Malliaris, A.G., “Itô's Calculus in Financial Decision Making.”Society for Industrial and Applied Mathematics 25, 481–496, (1983).
Malliaris, A.G., “Itô's Calculus: Derivation of the Black-Scholes Option-Pricing Model.” In C.F. Lee, J.E. Finnerty, and D.H. Wort,Security Analysis and Portfolio Management. Glenview, IL: Scott, Foresman and Company, 1990.
Malliaris, A.G. and W.A. Brock,Stochastic Methods in Economics and Finance. Amsterdam: North Holland Publishing Company, 1982.
Merton, R.C., “Theory of Finance from the Perspective of Continuous Time.”Journal of Financial and Quantitative Analysis 10, 659–674, (1975).
Merton, R.C., “On the Mathematics and Economic Assumptions of Continuous Time Models.” In W.F. Sharpe and C.M. Cootner, eds.,Financial Economics: Essays in Honor of Paul Cootner. Englewood Cliffs, NJ: Prentice-Hall, 1982.
Parkin, M., “Inflation.”The New Palgrave Dictionary of Economics, vol. 2. New York: The Stockton Press, 1987.
Sidrauski, M., “Inflation and Economic Growth.”Journal of Political Economy 796–810, (1967a).
Sidrauski, M., “Rational Choice and Patterns of Growth in a Monetary Economy.”American Economic Review: Papers and Proceedings 57, 534–544, (1967b).
Tobin, J., “Money and Economic Growth.”Econometrica 33, 671–684, (1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Malliaris, A.G., Malliaris, M.E. Decomposition of inflation and its volatility: A stochastic approach. Rev Quant Finan Acc 5, 93–103 (1995). https://doi.org/10.1007/BF01074854
Issue Date:
DOI: https://doi.org/10.1007/BF01074854