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 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.
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“Not only is time an essential component in causality (as causes precede effects [11]), but time can also influence whether or not something is causal.”
BackgroundMethod
- Authors
- Granger, C. W. J.
- Affiliations
- University of California San Diego (US)
- Corresponding author
- Granger, Clive W. J.
- Venue
- Essays in Econometrics
- Publisher
- Cambridge University Press
- Published
- 2010-07-02
- Pages
- 31-47
- OpenAlex
- W2101567517
- Cited by
- 4,762
- References
- 0
- Citations by year
- 2026: 11 · 2025: 109 · 2024: 154 · 2023: 201 · 2022: 175 · 2021: 154 · 2020: 140 · 2019: 137 · 2018: 145 · 2017: 111 · 2016: 209 · 2015: 338 · 2014: 382 · 2013: 371 · 2012: 295
- FWCI
- 689.58
- Type
- book chapter
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Social Sciences › Economics, Econometrics and Finance › General Economics, Econometrics and Finance › Monetary Policy and Economic Impact
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Diverse Scientific and Economic Studies
- Keywords
- causality testing, feedback, cross-spectral density, instantaneous causality, causal strength, two-variable model, spectral analysis, econometric models
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