  The problem of testing instantaneous causality between variables with
time-varying unconditional variance is investigated. It is shown that the
classical tests based on the assumption of stationary processes must be avoided
in our non standard framework. More precisely we underline that the standard
test does not control the type I errors, while the tests with White (1980) and
Heteroscedastic Autocorrelation Consistent (HAC) corrections can suffer from a
severe loss of power when the variance is not constant. Consequently a modified
test based on a bootstrap procedure is proposed. The relevance of the modified
test is underlined through a simulation study. The tests considered in this
paper are also compared by investigating the instantaneous causality relations
between US macroeconomic variables.
