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Una precisazione sulla scomposizione dell’indice di redistribuzione RE di Aronson-Johnson-Lambert e una proposta di estensione dell’indice di Plotnik
No full textAronson-Johnson-Lambert redistribution index RE can be correctly applied provided that after taxation incomes maintain the same pre-tax order in what it concerns (i) group average incomes and (ii) within group incomes. If this is not the case, R should be replaced by the transvariation index defined e.g. by Dagum (1997). Of course when R is different from the tranvariation index, in considering RE one neglects income rerankings between groups averages and within groups incomes. This note suggests how information on rerankings may be recovered, through a proper decomposition of Plotnick index. The decomposed Plotnick index might be a useful tool in choosing optimal interval bandwidth, controlling either for group-average reranking and within group reranking. Moreover minor suggestions are added which might be applied in analyzing taxation effects for incomes grouped according to socio-demographic or other criterion
Applying the Hadamard product to decompose Gini, concentration, redistribution and re-ranking indexes
Full text linkGini and concentration indexes are well known useful tools in analysing redistribution and re-ranking effects of taxes with respect to a population of income earners. Aronson, Johnson and Lambert (1994), Urban and Lambert (2008) decompose Gini and re-ranking indices to analyse potential redistribution effects and the unfairness of a tax systems. Urban and Lambert (2008) consider contiguous income groups which are created by dividing the pre-tax income parade according to the same bandwidth. However, earners may be very often split into groups characterized by social and demographic aspects or by other characteristics: in these circumstances groups can easily overlap. In this paper we consider a more general situation that takes into account overlapping among groups; we obtain matrix compact forms for Gini and concentration indexes, and consequently, for redistribution and re-ranking indexes. In deriving formulae the so called matrix Hadamard product is extensively used. Matrix algebra allows to write indexes aligning incomes in a non decreasing order either with respect to post-tax income or to pre-tax incomes. Moreover, matrix compact formulae allow an original discussion for the signs of the within group, across group, between and transvariation components into which the Atkinson-Plotnick-Kakwany (Plotnick, 1981) re-ranking index can split
Playing with the Hadamard product in decomposing Gini, concentration, redistribution and re-ranking indexes
Full text linkGini and concentration indexes are well known useful tools in analysing redistribution and re-ranking effects of taxes with respect to a population of income earners. Aronson, Johnson and Lambert (1994), Urban and Lambert (2008) decompose Gini and re-ranking indices to analyse potential redistribution effects and the unfairness of a tax systems. Urban and Lambert (2008) consider contiguous income groups which are created by dividing the pre-tax income parade according to the same bandwidth. However, earners may be very often split into groups characterized by social and demographic aspects or by other characteristics: in these circumstances groups can easily overlap. In this paper we consider a more general situation that takes into account overlapping among groups; we obtain matrix compact forms for Gini and concentration indexes, and consequently, for redistribution and re-ranking indexes. In deriving formulae the so called matrix Hadamard product is extensively used. Matrix algebra allows to write indexes aligning incomes in a non decreasing order either with respect to post-tax income or to pre-tax incomes. Moreover, matrix compact formulae allow an original discussion for the signs of the within group, across group, between and transvariation components into which the Atkinson-Plotnick-Kakwany (Plotnick, 1981) re-ranking index can split
4th International conference on social aspects of Market Economy
No full textAccording to Kakwani and Lambert (1998), an equitable income tax should respect three axioms related to each taxpayer’s tax liability, average tax rate and post-tax income: whenever taxation determines unequal tax treatments among equals or modifies pre-tax ordering, it influences the potential vertical effect of the tax through three types of inequity. Following the authors’ measurement system, we investigate axiom violations due to the 2007 Italian personal income tax reform. Our microsimulation model uses as input data those provided by the Bank of Italy in its Survey on Households Income and Wealth in the year 2008; estimates of the distribution of taxpayers are very close to the Ministry of Finance official statistics. The analysis focuses redistributive effects and re-rankings relations between different family types. Moreover we suggests an alternative way to measure violations of Kakwani and Lambert’s Axiom
The 2007 personal income tax reform in Italy : effects on potential equity, horizontal inequity and re-ranking
No full textAccording to Kakwani and Lambert (1998), an equitable income tax should respect three axioms related to each taxpayer’s tax liability, average tax rate and post-tax income: whenever taxation determines unequal tax treatments among equals or modifies pre-tax ordering, it influences the potential vertical effect of the tax through three types of inequity. Following the authors’ measurement system, we investigate changes in axiom violations due to the 2007 Italian personal income tax reform, that introduced significant changes in the tax structure. Our microsimulation model uses as input data those provided by the Bank of Italy in its Survey on Households Income and Wealth in the year 2006; estimates of the distribution of taxpayers are very close to the Ministry of Finance official statistics. The analysis considers both the individual and equivalent household gross income distribution and evaluates the decomposition with and without surtaxes. Main findings suggest that both in the 2006 and 2007 tax system most of the overall violations concern the axiom demanding the average tax rate to be a non decreasing function with respect to the gross income; the axiom requiring richer taxpayers to pay higher tax liabilities than poorer ones and the axiom requiring the tax to do not introduce re-rankings in the pre-tax income order present minor violations. The 2007 reform enhances both the potential redistributive effect, that is the one that could be obtained without axiom violations, and the axiom violations: the net result is a small positive variation of the actual redistributive effect. These phenomena appear more relevant for taxpayers than those for equivalent households. For what concerns taxpayers, the 2007 reform has modified also the composition of the three axiom violations, that remains almost the same whenever equivalent households are considered. Finally, focusing on each decile of the income distribution, regressivities are concentrated in the bottom five deciles of the income distribution both for taxpayers and equivalent household
On measuring violations of the progressive principle in income tax systems
No full textKakwani 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
On the Aronson-Johnson-Lambert decomposition of the redistributive effect
Full text linkRecently van De Van, Creedy and Lambert (2001) and Lambert and Urban (2005) have reconsidered the original Aronson, Johnson and Lambert (1994) decomposition of the redistributive effect in order to properly evaluate personal income tax reforms, when sequential income groups do not concern exact equals. Lambert and Urban (2005) decompose the Atkinson-Plotnick-Kakwani index into three terms. We utilize this decomposition in choosing the optimal bandwidth and suggest to consider not only the highest vertical contribution to the redistributive effect, but also the horizontal inequity due to the reranking of the mean post-tax income among groups. Findings are applied to Italian data with respect to both individual nominal incomes and equivalent household income
On determining "Close equals groups" in decomposing redistributive and reranking effects.
Full text linkRecently van De Van, Creedy and Lambert (2001) and Lambert and Urban (2005) have reconsidered the original Aronson, Johnson and Lambert (1994) decomposition of the redistributive effect in order to properly evaluate personal income tax reforms when sequential income groups do not concern exact equals. Lambert and Urban (2005) discuss a set of further possible decompositions of the redistributive effect together with a decomposition of the Atkinson-Plotnick-Kakwani index into three terms. If the issue is to chose the optimal income bandwidth which splits the pre-tax income parade into contiguous sets, we suggest combining the information given by the latter decomposition with those concerning the highest vertical contributions to the redistributive effect. We show that the horizontal inequity due to the reranking of the mean post-tax income among groups plays a crucial role in choosing the optimal bandwidth either within the van De Van, Creedy and Lambert (2001) methodology or in pursuing coherent measures for the potential redistributive effect
Equivalence scales for biological type of households empirical research
No full textThe main goal of this work is to estimate general equivalence scales for six biological types of households. The estimation was made using Engel’s method. In this method the share of food is used as an indirect indicator of welfare of the households. Equivalence scales were defined using data from 1993-2000. Besides, other approaches to estimating equivalence scales and some generalizations of Engel’s method were presented
Estimating the cost of children through Engel curves by different good aggregates
Full text linkEquivalence scales for the cost of children are estimated for one of the most developed Italian region (Lombardia) through the Engel approach. The data set is obtained from the survey on household consumption expenditures, which is hold by the Italian Central Institute for Statistics (ISTAT) in 1997, 1998, 1999 and 2000. The estimation of equivalence scales is not restricted to the share devoted to food. Besides the usual share of food and non-alcoholic beverages, 1w, we specify four further shares of necessities. The results obtained in this research show that in estimating equivalence scales through Engel curves it is very important to specify in control variables to take account for heterogeneity among families. Though the food share can still be a valid indicator to compare family welfare and then to estimate equivalence scales, in some situations it results to be misleading. The experiment of adopting broader good aggregates as indicators gives interesting results and more likely estimates in correspondence of some family typologies
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