Granger Causality Test
Also known as: Granger test, GC test, predictive causality test, Granger non-causality test
The Granger causality test is a statistical hypothesis test that determines whether past values of one time series help predict future values of another, beyond what that series' own past already explains. Introduced by Clive Granger in 1969, it is the standard approach for assessing predictive causality in VAR-based time-series analysis.
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When to use it
Use the Granger causality test when you have two or more stationary time series and you want to determine whether one variable has predictive precedence over another. It is well-suited to macroeconomic and financial research questions such as whether money supply leads inflation, or whether trading volume predicts returns. Do not use it on non-stationary (integrated) series without first differencing them or applying the Toda-Yamamoto extension; spurious causality results otherwise. It is also not appropriate when sample sizes are very small (fewer than ~50 observations), as the F-test has poor finite-sample properties, and it cannot distinguish genuine economic causation from mere correlation driven by a common third variable.
Strengths & limitations
- Grounded in a clear, operationalizable definition of predictive causality with a formal F-test.
- Straightforward to implement in any VAR framework; widely supported by statistical software.
- Bidirectional testing is simple: run the test in both directions to detect feedback loops.
- Easily extended to multivariate settings (block Granger causality in a full VAR system).
- The underlying concept is intuitive and communicable to non-technical audiences.
- Detects predictive precedence, not structural or economic causation; results depend on the information set included.
- Sensitive to lag length selection: too few lags omit relevant dynamics, too many reduce power and inflate type-I error.
- Requires stationary series; applying it to integrated variables without correction produces spurious results.
- Cannot handle nonlinear causal relationships; linear VAR may miss threshold or asymmetric effects.
- Common-cause confounding (a third variable driving both series) can produce spurious Granger causality.
Frequently asked
Does Granger causality imply true economic causation?
No. Granger causality is a statement about predictive precedence — variable x Granger-causes y if x's past values contain information about y's future beyond y's own history. It does not rule out spurious correlation from a common third factor, and it does not establish structural or policy-relevant causality.
What should I do if my series are non-stationary?
If the series are integrated but not cointegrated, difference them to achieve stationarity before running the standard Granger test. If they are cointegrated, use a VECM-based causality test or the Toda-Yamamoto procedure, which works with levels regardless of integration and cointegration order.
How do I choose the lag length?
Use an information criterion such as the Akaike (AIC) or Schwarz/Bayesian (BIC) criterion applied to the VAR system. BIC tends to select more parsimonious models; AIC may select longer lags. Always report results under alternative lag choices as a robustness check.
Can Granger causality run in both directions simultaneously?
Yes. Bidirectional Granger causality (feedback) occurs when x Granger-causes y and y simultaneously Granger-causes x. This is common in macroeconomic systems and simply means both variables contain predictive information about each other.
How does the Granger test differ from the Toda-Yamamoto procedure?
The standard Granger test requires stationary data and loses its asymptotic chi-squared/F distribution when series are integrated. The Toda-Yamamoto procedure estimates a VAR in levels augmented by extra lags equal to the maximum order of integration, then applies a Wald test to the original lag coefficients — this preserves standard asymptotic theory regardless of integration or cointegration status.
Sources
- Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, 37(3), 424–438. DOI: 10.2307/1912791 ↗
- Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press. ISBN: 978-0691042893
How to cite this page
ScholarGate. (2026, June 3). Granger Causality Test. ScholarGate. https://scholargate.app/en/econometrics/granger-causality-test
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