Multidimensional affluence: theory and applications to Germany and the US

Abstract

This article suggests multidimensional affluence measures for the top of the distribution. In contrast to commonly used top income shares, they allow the analysis of the extent, intensity and breadth of affluence in several dimensions within a common framework. We illustrate this by analysing the role of income and wealth as dimensions of multidimensional well-being in Germany and the US in 2007 as well as for the US over the period 1989–2007. We find distinct country differences with the country ranking depending on the measure. While in Germany wealth predominantly contributes to the intensity of affluence, income is more important in the US.

Keywords:

• top incomes
• multidimensional measurement
• richness
• wealth
• in-equality

JEL Classification:

• D31
• D63
• I31

View correction statement:

Erratum

Acknowledgements

Andreas Peichl is grateful for financial support from Deutsche Forschungsgemeinschaft (DFG). We thank the editor as well as an anonymous referee for their valuable comments and suggestions. Moreover, we thank Joachim R. Frick, Markus M. Grabka, Thomas Piketty, Christoph Scheicher and Sebastian Siegloch, seminar participants in Bonn (IZA), Leuven and Verona as well as participants of the ECINEQ (Catania), New Directions in Welfare (Paris) and Social Choice and Welfare (Moscow) conferences.

Notes

1. In principle, it would be possible to combine both income and wealth into an extended income measure by annualizing the stock of wealth (Smeeding and Thompson, 2011). However, this implies the assumption that a stock of assets has the same characteristics as income.

2. An individual i can be affluent in one or more dimensions and, at the same time, not be multidimensionally affluent (when it holds that ), while an affluent person by definition is always affluent in at least k dimensions. We assume equal weighting of dimensions.

3. The concave measure is normalized between zero and one, while the convex measure is not. Although one would prefer to have normalized measures, this is not possible in the convex case without violating the monotonicity axiom.