Granger causality test is a technique for determining whether one time series is useful in forecasting another.[1] Ordinarily, regressions reflect "mere" correlations, but Clive Granger, who won a Nobel Prize in Economics, argued that there is an interpretation of a set of tests as revealing something about causality.
A time series X is said to Granger-cause Y if it can be shown, usually through a series of F-tests on lagged values of X (and with lagged values of Y also known), that those X values provide statistically significant information about future values of Y.
The test works by first doing a regression of ΔY on lagged values of ΔY. Once the appropriate lag interval for Y is proved significant (t-stat or p-value), subsequent regressions for lagged levels of ΔX are performed and added to the regression provided that they 1) are significant in and of themselves and 2) add explanatory power to the model. This can be repeated for multiple ΔXs (with each ΔX being tested independently of other ΔXs, but in conjunction with the proven lag level of ΔY). More than one lag level of a variable can be included in the final regression model, provided it is statistically significant and provides explanatory power.
The researcher is often looking for a clear story, such as X granger-causes Y but not the other way around. In practice, however results are often hard-to-interpret. For instance no variable granger-causes the other, or that each of the two variables granger-causes the second.
Despite its name, Granger causality does not imply true causality. If both X and Y are driven by a common third process with different lags, their measure of Granger causality could still be statistically significant. Yet, manipulation of one process would not change the other. Indeed, the Granger test is designed to handle pairs of variables, and may produce misleading results when the true relationship involves three or more variables. A similar test involving more variables can be applied with vector autoregression. A new method for Granger causality that is not sensitive to the normal distribution of the error term has been developed by Hacker and Hatemi-J (2006).[2] This new method is especially useful in financial economics since many financial variables are non-normal.
This technique has been adapted to neural science.[3].
Software implementation
Here is an example of the function grangertest() in the lmtest library of the R package:
Granger causality test Model 1: fii ~ Lags(fii, 1:5) + Lags(rM, 1:5) Model 2: fii ~ Lags(fii, 1:5) Res.Df Df F Pr(>F) 1 629 2 634 5 2.5115 0.02896 * --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Granger causality test Model 1: rM ~ Lags(rM, 1:5) + Lags(fii, 1:5) Model 2: rM ~ Lags(rM, 1:5) Res.Df Df F Pr(>F) 1 629 2 634 5 1.1804 0.3172
The first Model 1 tests whether it is okay to remove lagged rM from the regression explaining FII using lagged FII. It is not (p = 0.02896). The second pair of Model 1 and Model 2 finds that it is possible to remove the lagged FII from the model explaining rM using lagged rM. From this, we conclude that rM granger-causes FII but not the other way around.
References
- ^ Granger, C.W.J., 1969. "Investigating causal relations by econometric models and cross-spectral methods". Econometrica 37 (3), 424–438.
- ^ R. Scott Hacker & Abdulnasser Hatemi-J, 2006. "Tests for causality between integrated variables using asymptotic and bootstrap distributions: theory and application," Applied Economics, Taylor and Francis Journals, vol. 38(13), pages 1489-1500, July.
- ^ "Scientists Adapt Economics Theory To Trace Brain's Information Flow", Science Daily, October 10, 2008
See also
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