Wealth and Partial Wealth

Abstract

The currently discussed increase in inequality within many countries arise not only from higher poverty rates but also from the growing population at the upper end of the distribution and the resulting tensions between rich and poor. The rise of wealth in several dimensions was coming back as an issue for quality-of-life applications. Although achieving comfortable living conditions is a common goal, the shape of the distributions may have direct impacts on well-being, even for the broad majority of the population that does not fall into the high-wealth category. This is because most people below the wealth line experience at least some degree of prosperity, which I refer to here as partial wealth.

The major innovation in the measurement approach proposed here lies in the framework of partial wealth. The partial wealth approach offers a parameter-based measure to model degrees of wealth as a counting approach for fuzzy areas of prosperity. It can be integrated into a generalized FGT-measure of wealth. The proposed methods for considering wealth can be applied to any wealth concept, including multidimensional settings. The empirical applications used in this paper refer to economic wealth (income and assets) and subjective wealth (satisfaction).

Appendix

The modelling of partial deprivation follows a similar measurement approach as for partial wealth, based on parameters tau (τ) and epsilon (ε) to define and shape the baseline function. The identification function for partial deprivation is:

$$ pd_{i} = exp\left(\varepsilon \left[1-{\left(\frac{y_i}{z}\right)}^{\tau\left({y}_i/z\right)}\right]\right)\ \mathrm{for}\ y_i\ge z $$

with

pd_i :

individual score of partial deprivation for indicator y_i

y_i :

individual value of deprivation in indicator y

z:

threshold of poverty/deprivation for indicator y

τ:

parameter for the type of the baseline identification function

ε:

parameter for the shape of the identification function.

The partial deprivation measures can be also further integrated into a generalized FGT framework for unidimensional and multidimensional poverty applications.