A NECESSARY AND SUFFICIENT CONDITION FOR GREATER CONDITIONAL PROGRESSIVITY

Conditional progressivity is defined in terms of a (weakly) Lorenz-dom inating post-tax income distribution conditional upon a given pre-tax income distribution. This paper derives a condition that is both neces sary and sufficient for one income tax to be conditionally more progre ssive than another. It involves the odd number-crossing of normalized post-tax income functions together with certain integral (or summation ) conditions. Single-crossing, as a special case, is sufficient. If th e post-tax income functions are at least piecewise differentiable, an average rate progressivity condition is sufficient for the residual pr ogressivity condition which, in turn, is sufficient for single-crossin g.