# What is Granger Causality and how to determine it?

For example, we have $VAR(2)$:

$Y_t := \begin{pmatrix}GNP_i \\M2_i \\ IR_i \\ \end{pmatrix}\\ = \begin{pmatrix}2\\1\\0\\ \end{pmatrix}\ + \begin{pmatrix} 0.7 & 0.1 & 0 \\0 & 0.4 & 0.1\\ 0.9 & 0 & 0.8\\ \end{pmatrix} *\begin{pmatrix} GNP_{i-1} \\ M2_{i-1} \\IR_{i-1}\\ \end{pmatrix} + \begin{pmatrix} -0.2 & 0 & 0 \\ 0 & 0.1 & 0.1 \\ 0 & 0 & 0\\ \end{pmatrix} * \begin{pmatrix} GNP_{i-2}\\ M2_{i-2}\\IR_{i-2}\\ \end{pmatrix} + \begin{pmatrix} u_{1t} \\ u_{2t}\\ u_{3t}\\\end{pmatrix}$

How do I check if $M2$ Granger-causal for the vector $(GNP,IR)$ or if $IR$ is Granger-causal for the vector $(GNP,M2)$?

And what is 2-step causal? (For example, how can we determine if $IR$ is 2-step causal for $GNP$?)

• Possible duplicate of Granger causality and non-linear regression – luchonacho Mar 21 '17 at 20:35
• @luchonacho, the OP has a standard linear model, nothing nonlinear. While the post is likely to be a duplicate of some earlier question, I do not think the one you suggest is the relevant one. – Richard Hardy Mar 22 '17 at 7:36