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A Simple Dynamic-Control Macro Model to Examine the Behavior of International Reserves for Selected Economies

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  • James P. Gander

Abstract

The purpose of the paper is to show the construction of a simple dynamic-control macromodel, using an economy-wide preference (utility) function as the objective function with two variables, national income and international reserves. National income is the control variable and reserves is the state variable. The first-order equilibrium condition at each instant of time, t, shows that the two variables optimally must grow at different rates for it to be satisfied. The model is applied to the empirical data on income and reserves by examining the behavior of the ratio of income to reserves for a selected number of mature and developing economies over the time period 1970 to 2011. For both types of economies, the model shows that there is a trade-of f between income and reserves based on the utility function. However, for mature economies the trade-off is such that the ratio of income to reserves is trending upwards while for the developing economies the ratio is trending downwards. In either case, the model fits the data. The policy implications are briefly discussed within the context of the existing literature on international reserves.

Suggested Citation

  • James P. Gander, 2013. "A Simple Dynamic-Control Macro Model to Examine the Behavior of International Reserves for Selected Economies," Working Paper Series, Department of Economics, University of Utah 2013_11, University of Utah, Department of Economics.
    • Handle: RePEc:uta:papers:2013_11
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    References listed on IDEAS

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    1. Maurice Obstfeld & Jay C. Shambaugh & Alan M. Taylor, 2010. "Financial Stability, the Trilemma, and International Reserves," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(2), pages 57-94, April.
    2. Bar-Ilan, Avner & Marion, Nancy P. & Perry, David, 2007. "Drift control of international reserves," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3110-3137, September.
    3. Guillermo Calvo & Alejandro Izquierdo & Rudy Loo-Kung, 2013. "Optimal Holdings of International Reserves: Self-insurance against Sudden Stops," Monetaria, Centro de Estudios Monetarios Latinoamericanos, CEMLA, vol. 0(1), pages 1-35, January-j.
    4. Arnaud Costinot & Guido Lorenzoni & Iván Werning, 2014. "A Theory of Capital Controls as Dynamic Terms-of-Trade Manipulation," Journal of Political Economy, University of Chicago Press, vol. 122(1), pages 77-128.
    5. Petar Vujanovic, 2011. "Understanding the Recent Surge in the Accumulation of International Reserves," OECD Economics Department Working Papers 866, OECD Publishing.
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • F3 - International Economics - - International Finance
    • F4 - International Economics - - Macroeconomic Aspects of International Trade and Finance

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