U. von Kalckreuth, Economic Research Centre of the Deutsche Bundesbank, Deutsche Bundesbank, P.O. Box 10 06 02, D-60006 Frankfurt a.M., Germany, e-mail: ulf.von-kalckreuth@bundesbank.de; M. Krtscha, Institute for Mathematical Stochastics, University of Karlsruhe, Englerstr. 2, D-76128 Karlsruhe, Germany, e-mail: manfred.krtscha@mathematik.uni-karlsruhe.de
Abstract: In economic systems, reactions to external shocks often come with a delay. On the other hand, agents try to anticipate future developments. Both can lead to difference-differential equations with an advancing argument. These are more difficult to handle than either difference or differential equations, but they have the merit of added realism and increased credibility. This paper generalizes a model from monetary economics by von Kalckreuth and Schroder. Working out its stability properties, we present a general method for determining the stability of any solution to a homogeneous linear difference-differential equation with constant coefficients and advancing arguments.
Keywords: linear difference-differential equations, stability, monetary transmission
Classification (MSC 2000): 39A11, 39B99, 91BC2
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