Study by Ottó Hajdu published in the new issue of Social Indicators Research
The paper suggests a new generalized variance concept for measuring multidimensional inequality, GVIP (Generalized Variance Inequality and Poverty), and then to give an out-group in-group decomposition of inequality for a stratified, segmented society and to apply the principle to the measurement of poverty. The method is based on a multivariate measure of dispersion, called Generalized Variance. The Wilks' lambda ratio is used to measure the efficiency of inter-group decomposition, allowing numerical calculations to be computed using standard statistical software, thus providing the GVI (Generalized Variance Inequality) metric. The GVI concept is based on the determinants of two new matrices defined by the author, where the two matrices are, on the one hand, a variance-based "Inequality Covariance Matrix" and, on the other hand, an information-theoretic-based "Entropy (Theil-type) Covariance Matrix". The GVI, however, takes into account the correlation system and the asymmetric frequency distribution of the dimensions, which are loaded with extreme outliers, and uses a multivariate method even in the univariate case, exploiting its numerical advantages. For example, if the dimension is the income factor, the manifest variables can be either per capita, per household, gross, net, annual, etc.
In summary, the study published in the June issue of the Social Indicators Research proposes a new inequality methodology, the application of which could lead to new methodologies in other fields such as poverty analysis, information theory, data mining, risk analysis, etc. In essence, the method measures the variance of a cloud in a multidimensional "oblique space" in a composite way, with inequality content, also linked to Entropy Theory.
The key formula is the "Generalized Variance" measure of multivariate statistics, which applies to a specific Entropy Covariance Matrix in our case. Since the covariance matrix can be disaggregated - in general - into a sum of internal and external factors in the case of groups, the proposed inequality measure can also be given as the resultant of external and internal effects.
In measuring poverty, the so-called censored distributions (where the incomes of those above the threshold are replaced by the threshold value itself) are used to produce GVI as a generalized poverty measure (GVP). Thus, the proposed method can be used to investigate the discriminatory effect of poverty thresholds of different dimensions on the poverty rate, or the predictive power of a given socio-economic grouping. In addition, the relative impact of each group within internal inequality can be analyzed.
Since its foundation in 1974, Social Indicators Research has become the leading journal on problems related to the measurement of all aspects of the quality of life. The journal continues to publish results of research on all aspects of the quality of life and includes studies that reflect developments in the field. It devotes special attention to studies on such topics as sustainability of quality of life, sustainable development, and the relationship between quality of life and sustainability. The topics represented in the journal cover and involve a variety of segmentations, such as social groups, spatial and temporal coordinates, population composition, and life domains. The journal presents empirical, philosophical and methodological studies that cover the entire spectrum of society and are devoted to giving evidence through indicators. It considers indicators in their different typologies, and gives special attention to indicators that are able to meet the need of understanding social realities and phenomena that are increasingly more complex, interrelated, interacted and dynamical. In addition, it presents studies aimed at defining new approaches in constructing indicators.
Source: ELTE GTK