I have a panel data regression with fixed effects, but for simplicity it is such that a lagged explanatory variable is significantly correlated with the dependent variable, which I believe is causation as well as correlation. I want to test this by how I understand the Granger causality test to work; by also adding future lagged variables to the same regression.
My understanding is, if these future lags are found to be insignificant in explaining the dependent variable, then this adds strength to the direction of causality which I originally believed: i.e. that the lagged explanatory variable causes the dependent variable, and not vice versa. (There are theoretical arguments that could argue for both directions of causality, hence the interest in testing for this.)
My question is, is this a Granger causality approach? And if so, I notice on Stata there are specific Granger commands; however, can I instead not simply add future lags and do this manually?
Also, can this sort of causality test only be interpreted based on the significance of the coefficient of the additional future lagged variable or can I also say something about how the additional of this future variable influences the coefficient of the original explanatory variable? i.e. if the coefficient of the future lagged variable is insignificant but also the coefficient of the original explanatory variable falls, what does this mean?