Granger causality

Estimating correlations between historical time series gives us an idea of the co-movements of variables (returns of financial instruments, macro-economic factors, etc…).

But macroeconomist are more interested in establishing cause-effect relationships, in determining the impact of changes in the economic environment or political decisions.

There is an endless debate about the very sense of causality and the way to test it. Clive Granger (2003 Nobel Prize in Economics for his work on cointegration) introduced in 1969 the concept of Granger causality¹, an idea that originates from the work of Norbert Wiener².
The idea of Granger causality is the following: a variable X Granger-causes Y if Y can be better predicted using the historical values of both X and Y than using the historical values of Y alone.


Testing Granger-causality

Granger causality can be assessed by regressing each variable on lagged values of itself and the other:



and then using an F-test to test the null hypothesis that X does not Granger-cause Y. In other words, the F-test determines whether using past information on X improves significantly the fit to the Y observables.

The choice of the lags J and K is crucial: insufficient lags imply autocorrelated errors, while excessive lags reduce the power of the test.


Causality does not imply control

In 1972, Christopher Sims presented the first application of Granger causality³: he showed that money Granger-caused nominal GNP, apparently strengthening the monetarist idea that fluctuations in money are the major cause of business cycles.

But the concept of Granger causality is based on predictability and not control: the fact that money Granger-causes GNP does not imply that the Fed has an effective instrument to control the economy! While Granger used the term “causality” in his early work, his concept is now referred to as Granger-causality to distinguish it from “control-based” causality. Granger causality measures whether one thing happening before another thing helps predict it - and nothing else.


References

[1] Granger, C.W.J., 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37 (3), 424– 438

[2] Wiener, N., 1956. The theory of prediction. In: Beckenbach, E. (Ed.), Modern Mathematics for Engineers. McGraw-Hill, New-York.

[3] Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-52, September.