On measuring violations of the progressive principle in income tax systems

Kakwani and Lambert (1998) state three axioms which should be respected by an equitable tax system. Using the Atkinson-Plotnick-Kakwani re-ranking indexes of taxes, tax rates and post-tax incomes, calculated with respect to the ranking of pre-tax income distribution, they then propose a measurement system to evaluate the negative influences that axiom violations exert on the redistributive effect of taxes. In this paper we reconsider the way Kakwani and Lambert measure violations of their second axiom, which concerns the re-ranking of tax rates. We construct a non-negative index which is strictly faithful to Kakwani and Lambert’s commands; we show that the Authors’ measure does not exactly fit the statements made in their second axiom. Both Kakwani and Lambert’s original measurement system and the modified one are then applied to Italian personal income tax in 2008. According to the modified measurement system, the average tax rate seems to play a smaller role than that suggested by the results gained using Kakwani and Lambert’s original methodology.