Investigating Causal Relations by Econometric Models and Cross-Spectral Methods
Abstract:There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalisation of this result with the partial cross spectrum is suggested.
摘要:在某些情况下,很难确定两个相关变量之间的因果关系的方向,也很难确定是否有反馈。提出了因果关系和反馈的可测性定义,并用简单的双变量模型进行了说明。讨论了表观瞬时因果关系这一重要问题,认为这个问题往往是由于记录信息的速度慢或没有使用足够广泛的可能的因果变量而引起的。结果表明,两个变量之间的互谱可以分解为两个部分,每个部分都与反馈情况的单个因果臂有关。然后,可以构建因果滞后和因果强度的度量。提出了用部分交叉谱对这一结果的推广。
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