Tax progression and inequality of income distribution

Eichhorn, Wolfgang; Funke, Helmut; Richter, Wolfram F.

doi:10.1016/0304-4068(84)90012-0

Cited by 84 publications

(31 citation statements)

References 4 publications

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“…Sufficiency of the condition on g for F x L R F y to hold for all F z was recognised by Fellman (1976) and Kakwani (1977). Eichhorn, Funke and Richter (1984) and Arnold (1987) extend this result to drop the assumption that φ x and φ y are continuous and increasing.…”

Section: Inequality-reducing Policiesmentioning

confidence: 95%

Inequality and income gaps

Preston¹

2006

Working Paper Series

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This paper discusses inequality orderings based explicitly on closing up of income gaps, demonstrating the links between these and other orderings, the classes of functions preserving the orderings and applications showing their usefulness in comparison of economic policies. JEL: D31, D63 Keywords: Inequality, income distribution * I am grateful for helpful comments from Tim Besley, Chris Gilbert, Terence Gorman, Chris Harris, Peter Lambert, James Mirrlees, Stephen Nickell, Hyun Shin, seminar participants and an anonymous referee. The paper draws in large part upon my doctoral thesis, for the funding of which I am grateful to the Economic and Social Research Council.† Address: Ian Preston, Department of Economics, University College London, Gower Street, London WC1E 6BT, UK. Email: i.preston@ucl.ac.uk 1 Executive SummaryIt is a truism to say that inequality is about gaps between incomes and that reducing inequality is about closing these gaps up.Common means of comparison between income distributions all use criteria which do show inequality as falling when gaps close. However explicitly asking whether the gaps reduce throughout the whole distribution in concertina-like fashion is a rare criterion to apply. This paper seeks to investigate the related orderings. The most common criteria for inequality comparison are those based on Lorenz curves, made plausible most persuasively as indicators of inequality by their link to progressive transfers of income. Progressive transfers are often seen, since the arguments of Pigou and Dalton, as uncontentiously inequality reducing but this view could be challenged if there are more than two people. A transfer from the top to the middle of the income distribution reduces inequality between the top and the middle but increases it between the middle and the bottom. Regarding inequality as having fallen overall involves giving priority to the former effect -the effect on the gap between incomes of those involved directly in the transfer -for which there may be good reason, but it is not obvious that it would not be sensible to say inequality simply could not be compared. A minor function of the current paper is to bring some overlooked but highly germane mathematical literature to the attention of inequality theorists. The major function, though, is to tell a rounded story about the ratio and difference dominance concepts, and associated orderings and welfare properties.

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Section: Inequality-reducing Policiesmentioning

confidence: 95%

Inequality and income gaps

Preston¹

2006

Working Paper Series

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“…Using this definition in our setting would amount to require that the ratio s j /ω j of the per capita net subsidy over the jurisdiction's per capita wealth to be decreasing with respect to per capita wealth. The justification usually given to this common definition of progressivity lies in the fact, apparently first established by Jakobsson (1976) (see also Eichhorn, Funke and Richter (1984), Moyes (1994) and Thon (1987)) that it is equivalent to requiring the relative Lorenz curve associated to the post-tax income distribution to be everywhere above that associated to the before-tax income distribution. As is well-known, the relative Lorenz curve associated to an income distribution is the graph of the function that maps every household's rank in the ordering of incomes to the fraction of the aggregate wealth held by all households in (weakly) lower ranks.…”

Section: Conditions For a Progressive Equalization Payments Schemementioning

confidence: 99%

The progressivity of equalization payments in federations

Gravel¹,

Poitevin

2006

Journal of Public Economics

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We investigate the conditions under which an inequality averse and additively separable welfarist constitution maker would always choose to set up a progressive equalization payments scheme in a federation with local public goods. A progressive equalization payments scheme is defined as a list of per capita net (possibly negative) subsidies -one such net subsidy for every jurisdiction -that are decreasing with respect to jurisdictions per capita wealth. We examine these questions in a setting in which the case for progressivity is a priori the strongest, namely, all citizens have the same utility function for the private and the public goods, inhabitants of a given jurisdiction are all identical, and they are not able to move across jurisdictions. We show that the constitution maker favors a progressive equalization payments scheme for all distributions of wealth and all population sizes if and only if its objective function is additively separable between each jurisdiction's per capita wealth and number of inhabitants. When interpreted as a mean of order r social welfare function, this condition is shown to be equivalent to additive separability of the individual's indirect utility function with respect to wealth and the price of the public good. Some implications of this restriction to the case where the individual's direct utility function is additively separable are also derived. * We are indebted to Chuck Blackorby, Robin Boadway and Philippe Michel for helpful discussions. We acknowledge financial support from CRSH, the CIREQ and the Département de scienceséconomiques, Université de Montréal. JEL classification numbers: D630, H100, H200,H210, H410, H700, H730, H770.

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“…Jakobsson [8] was the first to recognize that the result could be stated as an equivalence. His proof however contained a number of flaws that were corrected by Eichhorn et al [5] and Thon [27]. Furthermore, the fact that he restricted his attention to populations of fixed sizes as well as to non-decreasing taxation schemes actually made him unable to point at a number of interesting features of an equalising scheme.…”

Section: Inequality Reduction and Elementary Taxation Schemesmentioning

confidence: 99%

“…For instance G(u) :=ln(1+exp(uÂ2)) is convex and progressive over V :=[0, uÄ ]. 5 For differentiable taxation schemes, condition (a) in Proposition 3.1 is equivalent to G$(u) uÂG(u) 1, all u # (u Ä , uÄ ). In the public finance literature, the elasticity of the taxation scheme is actually known as the residual income progression (see Lambert [11,Chap.…”

Section: Inequality Reduction and Elementary Taxation Schemesmentioning

confidence: 99%