In this paper, we investigate the properties of the Granger causality test in stationary and stable vector autoregressive models under the presence of spillover effects, that is, causality in variance. The Wald test and the WW test (the Wald test with White's proposed heteroskedasticity-consistent covariance matrix estimator imposed) are analyzed. The investigation is undertaken by using Monte Carlo simulation in which two different sample sizes and six different kinds of data-generating processes are used. The results show that the Wald test over-rejects the null hypothesis both with and without the spillover effect, and that the over-rejection in the latter case is more severe in larger samples. The size properties of the WW test are satisfactory when there is spillover between the variables. Only when there is feedback in the variance is the size of the WW test slightly affected. The Wald test is shown to have higher power than the WW test when the errors follow a GARCH(1,1) process without a spillover effect. When there is a spillover, the power of both tests deteriorates, which implies that the spillover has a negative effect on the causality tests.