Dimension reduction for measuring the multidimensional demographic convergence

We aim to measure the demographic convergence of the populations towards a common pattern in a multidimensional perspective, considering several variables together at one time. Recently, we proposed some normalized indices of multiple variability that are useful for this aim. We applied them for measuring the convergence of European populations, using the yearly series of the crude birth rates, crude death rates, infant mortality rates and aging index. However, that procedure shows some drawbacks. Firstly, the crude birth rates and crude death rates could be not the most appropriate variables for studying reproduction and survival, due to the fact that these rates depend on the age structure of the population. Secondly, if the variables are correlated each other, some indices of multiple variability could take low values even with not significant demographic convergence. Here, we introduce some developments to overcome these drawbacks. We use also other variables that do not depend on the age structure of the population. Moreover, we apply a suitable statistical technique to the original dataset for defining new uncorrelated variables to use for testing the demographic convergence.