Investigating causal relations by econometric models and cross-spectral methods
Investigating causal relations by econometric models and cross-spectral methods
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DOI：
10.1017/cbo9780511753978.002
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发表时间：
1969-08
期刊：
影响因子：
--
通讯作者：
C. Granger
中科院分区：
文献类型：
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作者：
C. Granger
在某些情况下，很难决定两个相关变量之间因果关系的方向，也很难决定反馈是否发生。因果关系和反馈的可测试的定义提出和说明使用简单的两个变量模型。表观瞬时因果关系的重要问题进行了讨论，并建议，这个问题往往会出现由于缓慢的recordhag信息或因为一个足够广泛的类可能的因果变量尚未使用。可以表明，两个变量之间的交叉谱可以分解为两个部分，每个部分与反馈情况的单个因果臂相关。然后可以构建因果滞后和因果强度的度量。本文的目的是阐明某些类含有反馈的计量经济模型与谱分析中出现的函数之间的关系，特别是交叉谱和部分交叉谱。因果关系和反馈在这里被定义在一个明确的和可测试的方式。它表明，在两个变量的情况下，反馈机制可以分解为两个因果关系，交叉谱可以被认为是两个交叉谱的总和，每个密切相关的原因之一。本文接下来的三个部分简要介绍了谱方法、模型构建和因果关系等方面的内容。第四节介绍了两个变量的情况下的结果和第五节推广这些结果为三个变量。
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 recordhag 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 generalization of this result with the partial cross spectrum is suggested.The object of this paper is to throw light on the relationships between certain classes of econometric models involving feedback and the functions arising in spectral analysis, particularly the cross spectrum and the partial cross spectrum. Causality and feedback are here defined in an explicit and testable fashion. It is shown that in the two-variable case the feedback mechanism can be broken down into two causal relations and that the cross spectrum can be considered as the sum of two cross spectra, each closely connected with one of the causations. The next three sections of the paper briefly introduce those aspects of spectral methods, model building, and causality which are required later. Section IV presents the results for the two-variable case and Section V generalizes these results for three variables.