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1

Some Considerations on Measuring the Progressive Principle Violations and the Potential Equity in Income Tax Systems

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Mazurek E., Vernizzi A.

Statistics in Transition new series

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2014

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vol. 15

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issue 3

467-486

EN

Kakwani and Lambert (1998) state three axioms which should be respected by an equitable tax system; then they propose a measurement system to evaluate at the same time the negative influences that axiom violations exert on the redistributive effect of taxes, and the potential equity of the tax system, which would be attained in absence of departures from equity. The authors calculate both the potential equity and the losses due to axiom violations, starting from the Kakwani (1977) progressivity index and the Kakwani (1984) decomposition of the redistributive effect. In this paper, we focus on the measure suggested by Kakwani and Lambert for the loss in potential equity, which is due to violations of the progressive principle: the authors’ measure is based on the tax rate re-ranking index, calculated with respect to the ranking of pre-tax income distribution. The aim of the paper is to achieve a better understanding of what Kakwani and Lambert’s measure actually represents, when it corrects the actual Kakwani progressivity index. The authors’ measure is first of all considered under its analytical aspects and then observed in different simulated tax systems. In order to better highlight its behaviour, simulations compare Kakwani and Lambert’s measure with the potential equity of a counterfactual tax distribution, which respects the progressive principle and preserves the overall tax revenue. The analysis presented in this article is performed by making use of the approach recently introduced by Pellegrino and Vernizzi (2013).

2

DECOMPOSITION AND NORMALIZATION OF ABSOLUTE DIFFERENCES, WHEN POSITIVE AND NEGATIVE VALUES ARE CONSIDERED:APPLICATIONS TO THE GINI COEFFICIENT

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Ostasiewicz K., Vernizzi A.

Metody Ilościowe w Badaniach Ekonomicznych

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2017

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vol. 18

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issue 3

472-491

EN

We show how the absolute differences approach is particularly effective to interpret the Gini coefficient (G) when a distribution includes both positive and negative values. Either in erasing units having negative values, or in transforming negative values into zero, a significant variability fraction can be lost. When including negative values, instead of correcting G, to maintain it lower than 1, the standard G should be kept to compare the variability among different situations; a recent normalization, Gp, can be associated to G, to evaluate the variability percentage inside each situation.

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Preliminary notes on Palma’s measure of inequality

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Ostasiewicz K., Vernizzi A.

Śląski Przegląd Statystyczny

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2020

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issue 18 (24)

183-196

EN

Based on Palma’s observation that for empirical distributions within the range of the 4th and 9th deciles there are – with a good approximation – 50% of all goods, a new measure was introduced that is in a strong relationship to the Gini index, thus – supposedly – including all the information that it provides. In this paper this relationship is investigated more deeply for cases of some theoretical distributions as well as the relationship of a lower bound of a slightly differently defined ‘middle class’ on the Gini index.

PL

Nowa miara nierówności, zaproponowana na podstawie spostrzeżeń Palmy, iż dla empirycznych rozkładów dochodów pomiędzy czwartym a dziewiątym decylem zawarte jest – z dobrym przybliżeniem – 50% wszystkich dóbr, okazuje się ściśle związana z indeksem Giniego, niosąc tyle samo co on informacji. W niniejszym artykule zależność ta analizowana jest dla pewnych rozkładów teoretycznych. Badana jest również zależność dolnej granicy „klasy środkowej”, zdefiniowanej nieco odmiennie od analogicznej klasy według Palmy, od współczynnika Giniego.

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1 Metody Ilościowe w Badaniach Ekonomicznych

1 Statistics in Transition new series

1 Śląski Przegląd Statystyczny

3 Vernizzi A.

2 Ostasiewicz K.

1 Mazurek E.

1 2020

1 2017

1 2014

Some Considerations on Measuring the Progressive Principle Violations and the Potential Equity in Income Tax Systems

DECOMPOSITION AND NORMALIZATION OF ABSOLUTE DIFFERENCES, WHEN POSITIVE AND NEGATIVE VALUES ARE CONSIDERED:APPLICATIONS TO THE GINI COEFFICIENT

Preliminary notes on Palma’s measure of inequality