Tax reform and progressivity

The established theory of tax progressivity cannot handle basic tax reform questions, such as whether an increase in personal allowances makes the tau system more progressive, because the core results assume that tax liabilit y is never zero. This paper generalises the core theory to allow for zero t ax payments, and applies the new framework to the analysis of allowances, i ncome-related deductions and tau credits. Log concavity of the tax schedule -a property quite distinct from any existing notion of progressivity-emerge s as the critical determinant of whether the distribution of die tau burden becomes more progressive as allowances are increased.