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.

Kakwani 和 Lambert 在他们的开创性论文中（Eur J Polit Econ 14:369–380, 1998）阐述了公平税收制度应尊重的三个公理。他们通过提出一种基于税收、税率和税后收入重新排序指数的衡量体系，展示了如何评估公理违规对税收再分配效应的负面影响。通过考虑现实世界个人所得税的每个要素，即扣除额和税收抵免以及法定税率，在本研究中，我们通过分解所有这些税收要素产生的三个公理违规的程度，在理论上进一步迈出了一步。我们提出了两种互补的策略。第一个是“逐步”分解，计算税收的每个要素按顺序应用时对再分配效应的影响；第二种策略是“全面且同时”的分解，一旦所有三种税收工具同时应用，总是评估扣除额、税率和税收抵免的微小变化对税前收入分配的影响。这些策略可以更合适、更有效地衡量每个税收要素因违反公理而产生的再分配效应的损失。我们还表明，他们可以提供有关现有税收不平等的不同信息。最后，我们通过将其应用于现实世界的个人所得税来强调我们方法的优点。