# Asymptotic vs. bootstrap test statistic, size and power properties

I am running a VAR based Granger non-causality tests. I've obtained asymptotic and bootstrap $p$ values for Wald joint test of 0 restriction on a set of lagged variables. It appears that bootstrap based models fail to reject Granger non-causality more often than the models based on asymptotic theory.

My question is: How do I evaluate the size and power properties of these approaches/tests?

I know how to evaluate the size properties of the bootstrap based tests, but I'm not sure how to approach the asymptotic theory based tests.

• How do you evaluate the size of the bootstrap test? Can't you use the same approach for the asymptotic test, and if not, then why? – MånsT Apr 14 '14 at 7:21