A balanced normalization for cross-sectional and longitudinal composite indices in Mexico, 2000-2020

Implicit weighting in the normalization of aggregate variables generates distorted composite indices (CI). This distortion is associated with the uneven range of each distribution, the fact that the maximum and minimum values differ from one variable to another, and the asymmetry of each variable. Controlling implicit weighting is a pending issue. All normalization procedures reviewed in this research counteract the influence of implicit weighting only partially. The balanced standardization proposed in this study achieves the triple purpose of simultaneously matching the ranges between variables, matching the maximum and minimum between them, and controlling the asymmetry in each distribution. This new procedure neutralizes implicit weighting in the cross-sectional or longitudinal aggregation of variables. The variables of educational backwardness in Mexico illustrate this procedure. The methodological proposal of this research is applicable to any subject where space-time normalization is necessary.