Methodological issues: gender related indices

Abstract

Gender related Index (GRI) is a singled valued function combining selected dimensions containing different number of components. Measurement of multidimensional GRIs involves measurement issues for meaningful aggregations and comparisons over time and space. The paper proposes gender inequality through multiplicative aggregation ({GRI}_{GM}) and gender similarity index (GSI) by cosine similarity, avoiding scaling, finding weights and satisfying desired properties. Inverse relationship derived between {GRI}_{GM} and GSI. Each proposed index reduces level of substitutability, effect of outliers. Each facilitates aggregation of country-wise scores to find world average, statistical testing of equality of mean of two countries or mean of a country at two time-periods using Y-scores obtained from each measure by linear transformations where Yin [0, 100] and Ysim N (mu , {sigma }^{2}). Each index can be used for ranking and classification of countries. GSI can indicate current distance of a country from the goal of zero gender inequality. {GRI}_{GM} can assess progress/decline in successive periods for women and separately for men. {GRI}_{GM} is preferred for satisfaction of time-reversal test, easy identification of critical areas and contribution of the components or dimensions to the index. Empirical verification of the proposed indices and their properties including robustness could be taken as future studies.