Sequential Stochastic Dominance, Principles and implementation. An application to the assessment of the French and German tax system

This paper presents the principles of stochastic dominance which is a powerful tool that enables to have a generalized approach for the measure of poverty and inequalities. This paper first summarizes the literature on stochastic dominance with all its latest developments. We then present how to apply stochastic dominance to the assessment of the redistribution of a tax system and discuss of the constraints that are bound to it. A tax system is designed to address equity concerns, but two dimensions have to be taken into account. The first one is the redistribution between high income and low income (vertical redistribution) and the second one is the redistribution from small families towards large families (horizontal redistribution). Therefore, we study and discuss the uses of sequential stochastic dominance (Atkinson and Bourguignon (1989)) and restricted dominance (Chambaz and Maurin (1998)) that seem well suited to the assessment of a tax system. We finally provide SAS macros with the computations of all the stochastic dominances that are contained in the paper. We also provide an example of how to use the macros to compare the tax systems between France and Germany.