Solving non-linear, stochastic differential equations with Uhlig algorithms
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Stochastic, dynamic models are frequently used in modern economic analyses. In macroeconomic models resting on microeconomic bases, for instance, the conditions for solving general equilibrium models can be described using a non-linear, stochastic system of differential equations. This prescription-like article shows that the simpler systems - thanks to advances in computer technology - can be solved and analysed with graduate-level knowledge of economics. The algorithm in Blanchard and Kahn's 1980 study presents, as a solution to a matrix-equation system, the recursive form of such models. This the German economist Harald Uhlig transformed in 1999 for the purpose of computerization, so that he is often cited by users. There are two important restrictive criteria for applying the method: that the models should exist in their permanent state, and that they should be susceptible to linear approach. Two examples illustrate how the means necessary for solution do not exceed the level of fairly complex multiplicator analyses. With the model of real business cycles (RBC), the steps are given in detail. This is followed by a brief introduction to a sticky-price model representing a short-term application.
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