The concept of tax progressivity at a point (local progressivity) is well defined and accepted, but the concept of overall progressivity of a tax schedule (global progressivity) is not as precise and clearly defined, even though it is an important concept and is widely used in evaluating the redistributive impact of tax policies. Public finance economists have been comparing tax schedules and making statements on one as 'more progressive' than another without being very precise about the basis of comparison. In my earlier paper in the May 1985 issue of this JOURNAL (Liu, 1985), I attempted to unify the two concepts of local and global progressivity. Two requirements are imposed when a tax schedule is characterized as globally progressive, one of which is structural and the other redistributive and hence normative in nature. Drawing on the earlier work of Jakobsson (1976), Musgrave-Thin's measure was shown to satisfy both requirements. Two recently proposed measures by Suits (1977) and Kakwani (1976) were shown to be unappealing from both a positive and a normative viewpoint. In their comment on my paper Formby, Smith, and Sykes pointed out an error in a proposition by Jakobsson, thereby showing that the link between the pointwise concept of residual progression and the global concept of Lorenz domination is weaker than indicated by Jakobsson and me. This reduces the appeal of Musgrave-Thin's global measure as structurally consistent with pointwise progressivity everywhere in the tax schedule. The implication is that if we insist on this structural consistency, the basis for comparison of tax schedules will be too restrictive, since comparison will require one post-tax income distribution to Lorenz dominate another for all (instead of for any) pre-tax income distributions. Hence, despite my earlier effort, the device of a global measure of tax progressivity that is consistent with pointwise