Thus, Jackendoff's analysis of Aspectual Auxiliaries as Specifiers which expand V-bar into V-double-bar seems to have some empirical support (though we should point out that by no means all X-bar syntacticians are happy to treat Aspectuals as Specifiers which expand V-bar into V-double-bar: some prefer to treat them as Verbs which head their own VP, for reasons which you can work out for yourself when you come to Exercise VII).