# R - Testing for Granger causality when OLS assumption are violated

I am using the vars package to estimate a VAR-model. Since it seems, that the residuals of my model are neither homoscedastic or uncorrelated I computed Newey West Standard Errors to perform the t-tests for the individual coefficients of every model. Obviously the test results are different using the robust standard errors. Now I want to test for granger causality in the model.

I will try to structure my questions,

## How is the F-Test of causality() improved by using a robust covariance estimator?

According to the documentation of the vars package the causality() function divides the endogenous variables of the model in two groups and then tests whether one variable granger causes all the other variables in the model (as has been explained here). It does so by utilizing an F-Test.

The function offers to add a specification of the covariance matrix of the estimated coefficients using the parameter vcov to allow for specifically using a robust covariance-matrix estimator. However, in this thread it is mentioned, that the F-statistic is not influenced by Newey West Standard Errros.

How does the use of a robust covariance matrix improve the F-Test for granger causality then?

## Can I use grangertest() even though it is not directly connected to my VAR-model?

Furthermore in the thread cited above, it is advised to use the Wald Test instead of the F-Test, when the OLS assumptions for the error terms are violated.

The function grangertest() of the lmtest package is simply a Wald Test according to the documentation. However, the function is not capable of checking for models with more than two dimensions. However, it also allows to set a robust covariance matrix estimatior as a parameter.

Since I am also interested in the pairwise relation between the variables, would it still be correct to simply use the corresponding variables in pairs of two to test for granger causality between them?

I am a little hesitant to simply use grangertest(), because as far as I can see it would not be related to my VAR-model.

If grangertest() cannot be used to test for pairwise causality between the variables, can the causality() function be adapted to do the same?

• The $F$-statistic itself is not affected by using robust standard errors, but the reference distribution from which you take the critical values is. – Richard Hardy Jun 24 '18 at 13:26