### Discussion Paper

Country Inequality Rankings and Conversion Schemes

## Abstract

Two conversion schemes are usually employed for assessing personal-income inequality from household equivalent incomes: to weight household units by size or by needs. Using data from the Luxembourg Income Study, the authors show the sensitivity of country inequality rankings to conversion schemes and explain the finding by means of inequality decomposition. A bootstrap approach is implemented to test for statistical significance of the results.

## Comments and Questions

The subject of the article is timely and important in the light of the last social movements. I like the technical side of the work.

The paper deals with the interesting issue of measurement aspects within distributional anal-yses. Concretely, the authors scrutinize two conversion schemes: weighting household in-comes by household size and, alternatively, by (more elaborated) equivalence scales, i. e., by needs. These conversion schemes are applied with respect to empirical data from the Luxembourg ...[more]

... Income Study (LIS) for 20 countries (partly supplemented by stochastic ele-ments in terms of bootstrap estimates). On this basis and referring to decompositions via several Generalized Entropy indicators, the authors evaluate the rankings between all con-sidered countries generated by both conversion schemes, by different inequality indicators, and by varying equivalence scales.

I have the following comments on the paper:

• Ever since Anthony B. Atkinson (1983) has published the 2nd edition of his famous textbook “The Economics of Inequality” it has been known that, on principle, three populations’ weighting schemes exist in inequality analyses: weighting by households, by individuals, and by equivalent units. In terms of Buhmann et al.’s (1988) simplifying scale formula, which only depends on household size, these weights correspond with alternative values for the Buhmann et al. parameter θ: θ = 0 in the case of weighting by households, θ = 1 in the case of a per-capita weighting, and θ values between these two extreme cases when weighting by equivalent units. Thus, on principle, each of these three cases can be interpreted as a kind of needs-based weighting because all three weighting schemes arise from a general equivalence scale formulation reflecting different degrees of economies of scale (extremely high economies of scale in the case of households’ weighting, extremely low economies of scale in the case of a per-capita weighting). In this context, it is well-known that differences between households’ and per-capita weighting exist with respect to means and dispersions of income distributions.

• Apart from this, Schröder and Bönke gaze at another connection: at the relationship between well-being variable (income) and weighting scheme. Again referring to At-kinson (1983), nine combinations can be differentiated from each other by combining the three weighting schemes sketched above with household, per-capita or equivalent income (i. e., in terms of the Buhmann et al. formula, household income divided by 1, by the number of household members, or by values between 1 and household size). Schröder and Bönke merely concentrate themselves on two combinations: Equivalent household disposable income combined with household size and with (elaborated) equivalence scale values (alternatively using Buhmann et al.’s θ = 0.5 and θ = 0.25). This procedure appears to be sufficient to illustrate the consequences which arise from differences in the divisors of household incomes on one hand and in the weighting factors on the other hand. Whereas divisors and weighting factors coincide in the case of needs-weighting (by elaborated equivalence scales), they differ from each other in the case of pure size-weighting. Hence, only the first kind of needs-weighting is consistent with adding up the individual equivalent incomes towards total equivalent income. However, this finding in Schröder and Bönke’s paper is well-established in the literature on equivalence scales. More important than this rather theoretical aspect is for distributional analyses that equivalent units do not correspond with real well-being units and that size-weighting expresses an individualistic perspective which seems more appropriate for considering welfare issues (as the au-thors even admit on page 2).

• The statement “Particularly, some authors advocate a weighting of households by needs, i. e. by households’ equivalence scales.” on page 3 is not substantiated by corresponding references. This seems unfortunately since I do not know former elab-orated empirical studies on income distribution which refer to this kind of needs-weighting.

• The authors draw socio-political conclusions at the end of their paper by referring to different household types. Insofar it is somewhat curious that the authors only use a size-based equivalence scale formula and not a general formula which, additionally, takes into account differences in needs between different age groups (like differences between adults and children; see, in this context, e. g., Citro and Michael 1995).

• Mainly, the authors use two Buhmann et. al scales (θ = 0.5 and θ = 0.25) which are, typically, connected with a rather high level (θ = 0.25) and a (very) low level of ine-quality (θ = 0.5; see, e. g., Figures 2a-2c in the paper). The corresponding scale val-ues are out of the value range of wide-spread equivalence scales used in international analyses on income distribution, e. g., of the modified OECD scale (θ = 0.6) and of the “traditional” OECD scale (θ = 0.8).

Despite the afore-mentioned points of critique, the paper presents interesting and valuable insights into the sensitivity of distributional settings.

References:

Atkinson, A. B. (1983): The Economics of Inequality, 2nd edition, New York.

Buhmann, B., et al. (1988): Income, Well-Being, Poverty, and Equivalence Scales: Sensitivity Estimates Across Ten Countries Using the LIS Database. In: Review of Income and Wealth, 34, pp. 115 142.

Citro, C. F., and R. T. Michael (1995): Measuring Poverty – A New Approach, Washington (D. C.).

The paper provides an empirical analysis based on LIS data, which is aimed at showing whether the Generalized Entropy family of inequality measures is sensitive to the choice of the weighting scheme. Though there is no methodological contribution, the empirical applications are well done and accurate. The paper is well-written ...[more]

... and easy to follow. However, the manuscript should be improved in some parts; in particular, in the introduction the authors should discuss more carefully the pro's and con's of the two alternative weighting scheme. Also, the notation at pages 6-8 should be reviewed. Some results should be commented more deeply and, finally, the conclusions should provide a clearer authors' opinion about the usage of the alternative weighting scheme.

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