On measuring axiom violations due to each tax instrument applied in a real-world personal income tax

In their seminal paper, Kakwani and Lambert (Eur J Polit Econ 14:369–380, 1998) state three Axioms an equitable tax system should respect. By proposing a measurement system based on re-ranking indexes of taxes, tax rates and post-tax incomes, they show how to evaluate the negative influences that Axiom violations exert on the redistributive effect of a tax. By considering each element of a real-world personal income tax, i.e. deductions and tax credits as well as statutory tax rates, in this study we take a theoretical step further by decomposing the magnitude of the three Axiom violations produced by all these tax elements. We propose two complementary strategies. The first one is a ‘stepwise’ decomposition computing the effect of each element of the tax on the redistributive effect when they are sequentially applied; the second strategy is an ‘overall and simultaneous’ decomposition always evaluating the effect of small changes in deductions, tax rates and tax credits with respect to the pre-tax income distribution, once all the three tax instruments have been simultaneously applied. These strategies can be more suitable and effective in measuring the loss of the redistributive effect produced by each tax element because of axiom violations. We also show that they can give different information on the existing inequities of the tax. We finally emphasize the goodness of our approach by applying it to a real world personal income tax.