Granger causality
The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969.[1] Ordinarily, regressions reflect "mere" correlations, but Clive Granger argued that causality in economics could be tested for by measuring the ability to predict the future values of a time series using prior values of another time series. Since the question of "true causality" is deeply philosophical, and because of the post hoc ergo propter hoc fallacy of assuming that one thing preceding another can be used as a proof of causation, econometricians assert that the Granger test finds only "predictive causality".[2] Using the term "causality" alone is a misnomer, as Granger-causality is better described as "precedence",[3] or, as Granger himself later claimed in 1977, "temporally related".[4] Rather than testing whether X causes Y, the Granger causality tests whether X forecasts Y.[5]
A time series X is said to Granger-cause Y if it can be shown, usually through a series of t-tests and F-tests on lagged values of X (and with lagged values of Y also included), that those X values provide statistically significant information about future values of Y.
Granger also stressed that some studies using "Granger causality" testing in areas outside economics reached "ridiculous" conclusions.[6] "Of course, many ridiculous papers appeared", he said in his Nobel lecture.[7] However, it remains a popular method for causality analysis in time series due to its computational simplicity.[8][9] The original definition of Granger causality does not account for latent confounding effects and does not capture instantaneous and non-linear causal relationships, though several extensions have been proposed to address these issues.[8]
Intuition[edit]
We say that a variable X that evolves over time Granger-causes another evolving variable Y if predictions of the value of Y based on its own past values and on the past values of X are better than predictions of Y based only on Y's own past values.
Limitations[edit]
As its name implies, Granger causality is not necessarily true causality. In fact, the Granger-causality tests fulfill only the Humean definition of causality that identifies the cause-effect relations with constant conjunctions.[14] If both X and Y are driven by a common third process with different lags, one might still fail to reject the alternative hypothesis of Granger causality. Yet, manipulation of one of the variables would not change the other. Indeed, the Granger-causality tests are designed to handle pairs of variables, and may produce misleading results when the true relationship involves three or more variables. Having said this, it has been argued that given a probabilistic view of causation, Granger causality can be considered true causality in that sense, especially when Reichenbach's "screening off" notion of probabilistic causation is taken into account.[15]
Other possible sources of misguiding test results are: (1) not frequent enough or too frequent sampling, (2) nonlinear causal relationship, (3) time series nonstationarity and nonlinearity and (4) existence of rational expectations.[14] A similar test involving more variables can be applied with vector autoregression.
The validity of the Granger causality test has been challenged in the academic literature,[16] in a paper claiming that “not even the most fundamental requirement underlying any possible definition of causality is met by the Granger causality test... any definition of causality should refer to the prediction of the future from the past... we find that Granger also allows one to ‘predict’ the past from the future.”