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Wealth and Partial Wealth

Measurement Approaches for Economic and Subjective Well-Being

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Part of the Social Indicators Research Series book series (SINS,volume 76)

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).

Keywords

  • Partial wealth
  • Fuzzy zones of prosperity
  • FGT-measures for wealth
  • Multidimensional application

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Notes

  1. 1.

    SOEPv33L, https://doi.org/10.5684/soep.v33.1

  2. 2.

    This might be useful for very small q-values resulting from large differences between the upper and lower bounds of the prosperity zone (w-line/l-line).

  3. 3.

    The identification function for partial deprivation is described in the Appendix.

  4. 4.

    The use of the ninety-ninth percentile as a defined maximum instead of the original maximum value reduces the impact of fluctuations in the highest value over time and therefore provides more robust results for comparisons across time. Values above the defined maximum are recoded. As partial wealth rates (usually) include standard wealth measures, the maxima are the same.

  5. 5.

    Higher values for the parameter alpha may of course catch this effect in the FGT framework. But higher alpha values with more sensitivity to top values appear to be more volatile empirically due to the fluctuations in extreme values.

  6. 6.

    As the subjective wealth rates are derived from an ordinal scale (life satisfaction, 0–10), the use of cardinal methods has to be evaluated. All checks have confirmed that such applications provide meaningful results. Nevertheless, such applications are used here to further check the robustness of trends to confirm additional results derived from ordinal ones.

  7. 7.

    This may be partly related to the higher correlations in the income indicators; the indicators for subjective wealth include a wider variety of different domains.

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Acknowledgements

I would like to thank Arnd Scheel for his advice on the identification function and Jan Reher for his suggestions on the aggregation functions and implementations in STATA.

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Correspondence to Peter Krause .

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Appendix

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

pdi :

individual score of partial deprivation for indicator yi

yi :

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.

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Krause, P. (2019). Wealth and Partial Wealth. In: Brulé, G., Suter, C. (eds) Wealth(s) and Subjective Well-Being. Social Indicators Research Series, vol 76. Springer, Cham. https://doi.org/10.1007/978-3-030-05535-6_5

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