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A sufficient condition for the existence and the uniqueness of a solution in macroeconomic models with perfect foresight

机译:具有完美远见的宏观经济模型中解的存在性和唯一性的充分条件

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Macroeconomic models with perfect foresight have become easy to simulate because of the recent development of powerful algorithms. However, a priori, the existence and the uniqueness of a solution for these models are not warranted. Blanchard and Kahn established local conditions for these properties in terms of eigenvalues computed at the steady state of the model. These are easy to check. However, these conditions can be used only in linear models with coefficients independent of time. To overcome this difficulty, the usual practice has been to write a model which does not share these properties in reduced variables, to compute its linear approximation in the neighbourhood of a reference steady state and to apply Blanchard and Kahn's conditions to this approximation. However, this practice assumes that the reduced variables must converge to steady-states values. There are good reasons, both practical and economical, to question this condition and prefer the assumption that the original variables must converge to balanced growth paths. This paper provides sufficient conditions for the existence and uniqueness of a solution satisfying this last condition of convergence.
机译:由于近来功能强大的算法的发展,具有完美预见力的宏观经济模型变得易于模拟。但是,对于这些模型的解决方案,先验地存在和唯一性是不能保证的。 Blanchard和Kahn根据在模型稳态下计算出的特征值,为这些属性建立了局部条件。这些很容易检查。但是,这些条件只能在系数与时间无关的线性模型中使用。为了克服这一困难,通常的做法是编写一个模型,该模型在缩减变量中不共享这些属性,在参考稳态附近计算其线性近似值,并将Blanchard和Kahn条件应用于该近似值。但是,此实践假定减少的变量必须收敛到稳态值。有充分的理由,既实用又经济,对此条件提出质疑,并倾向于假设原始变量必须收敛于平衡的增长路径。本文为满足最后收敛条件的解决方案的存在性和唯一性提供了充分的条件。

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