Granger causality tests whether one variable is useful in forecasting another from "summary" of Introduction to Econometrics by Christopher Dougherty
Granger causality is a concept that helps us determine the causal relationship between two variables in a time series context. In other words, it tests whether one variable can be used to forecast another variable. The idea is that if variable X Granger-causes variable Y, then the past values of X should contain information that helps predict the future values of Y. To conduct a Granger causality test, we typically use a regression framework. We regress the variable we want to forecast (Y) on both its own lagged values and the lagged values of the potential causal variable (X). If the coefficients on the lagged values of X are statistically significant, then we can say that X Granger-causes Y. This implies that knowing the past values of X helps us make better predictions about the future values of Y. It is important to note that Granger causality does not prove a true causal relationship between the variables. It simply tells us whether one variable is useful in forecasting another. The results of a Granger causality test should be interpreted with caution and in conjunction with other evidence to draw robust conclusions about causality. In empirical research, Granger causality tests can be used to investigate the direction of causality between variables, such as GDP and investment, inflation and interest rates, or stock prices and exchange rates. By understanding the causal relationships between economic variables, policymakers and researchers can make more informed decisions and predictions about the future.
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