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Stable solutions to homogeneous difference-differential equations with constant coefficients: Analytical instruments and an application to monetary theory. (English) Zbl 1099.39009
The paper generalizes a model from monetary economics by U. von Kalckreuth and J. Schröder [Review of Economics 53, 125–141 (2002)]. It is a monetary macroeconomic model which includes homogeneous linear differential-difference equations with constant coefficients. The paper deals with a method of determining the stability of solutions for such equations using a theorem by E. Hilb [Math. Ann. 78, 137–170 (1917; JFM 46.0707.02)]. The resulting method is rather general and can be applied to a large class of dynamical problems. In the paper the method is applied just to the dynamic model of monetary transmission at hand and some conclusions are drawn.
MSC:
39A11 Stability of difference equations (MSC2000)
39B99 Functional equations and inequalities
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References:
[1] R. Bellman, K. L. Cooke: Differential-Difference Equations. Academic Press, New York-London, 1963.
[2] R. Dornbusch: Expectation and exchange rate dynamics. Journal of Political Economics 84 (1976), 1161-1176.
[3] R. D. Driver: Ordinary and Delay Differential Equations. Springer-Verlag, New York-Heidelberg-Berlin, 1997.
[4] J. K. Hale, S. M. Verduyn Lunel: Introduction to Functional Differential Equations. Springer-Verlag, New York, 1993.
[5] W. H. Fisher, S. J. Turnovsky: Fiscal policy and the term structure of interest rates: an intertemporal analysis. Journal of Money, Credit and Banking 24 (1992), 1-26.
[6] M. R. Gray, S. J. Turnovsky: The stability of exchange rate dynamics under perfect myopic foresight. Int. Econ. Rev. 20 (1979), 643-660. · Zbl 0427.90022
[7] A. de la Fuente: Mathematical Methods and Models for Economists. Cambridge University Press, Cambridge, 2000. · Zbl 0943.91001
[8] K. P. Hadeler: Mathematik f?r Biologen. Springer-Verlag, Heidelberg, 1974. · Zbl 0286.92001
[9] E. Hilb: Zur Theorie der linearen funktionalen Differentialgleichungen. Math. Ann. 78 (1918), 137-170. · JFM 46.0707.02
[10] U. von Kalckreuth, J. Schr?der: Monetary transmission in the new economy: service life of capital, transmission channels and the speed of adjustment. Jahrbuch f?r Wirtschaftswissenschaften (Review of Economics) 53 (2002), 125-141.
[11] M. Krtscha: Short-term and long-term interest rates in a monetary model of a closed economy. Operations Research 91. Physica Verlag Heidelberg, 1991.
[12] M. Krtscha: The dependence of the price level on the expansion of the money supply in closed economies. Mathematical Modelling in Economics. Springer-Verlag, Berlin, 1993, pp. 249-259. · Zbl 0849.90030
[13] J. H. McCulloch: Measuring the term structure of interest rates. The Journal of Business 44 (1971), 19-31.
[14] T. Sargent, N. Wallace: The stability of models of money and growth with perfect foresight. Econometrica 41 (1973), 1043-1048. · Zbl 0278.90011
[15] C. A. Wilson: Anticipated shocks and exchange rate dynamics. Journal of Political Economicy 87 (1979), 639-647.
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