What is the Granger causality test?

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AcadiFi · Accepted Answer

The Granger causality test checks whether past values of variable x help predict variable y beyond y's own past. It is a test of predictive content, not philosophical causation. We say x Granger-causes y if lagged x has significant explanatory power for y after controlling for lagged y.

The procedure: estimate a restricted model y_t equals sum of lagged y only. Then estimate an unrestricted model y_t equals sum of lagged y plus lagged x. Run an F-test on the joint significance of the lagged x coefficients. Reject the null of no Granger causality if F exceeds the critical value.

Example: analyst Sarai Eidelman-Porsch at Havelund Quantitative tests whether crude oil futures returns Granger-cause airline stock returns. Using daily data, the F-test on four lags of oil returns in the airline equation yields F equals 6.73, p-value 0.001. Reject — oil returns Granger-cause airline returns. Reverse test fails, consistent with airlines being price-takers in oil markets.

Caveats: (1) Granger causality is bivariate by default; a third variable could drive both. (2) Both series must be stationary or appropriately transformed. (3) The choice of lag length matters — use AIC or BIC. (4) Instantaneous (within-period) causation is not captured.

Granger causality is commonly paired with VAR analysis and is a staple of both academic research and practical market microstructure work, for instance in testing whether futures markets lead spot markets or vice versa.

What is the Granger causality test?

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