Structural waves of the population of Russia and its regions: issues of assessment and comparison

The article deals with methodological and methodological issues of comparative analysis of age structures of the population, identification of the level of their unevenness due to structural demographic waves. The benchmark for comparison is the age structure of the population, built on the series of "Numbers living in this age interval" from the "Tables of mortality and life expectancy" of Rosstat. The coefficients existing in the practice of socio-economic analysis for measuring the structural differences of the series are considered. These coefficients are studied from the standpoint of the possibility of their application for measuring structural demographic waves in Russia as a whole and in its regions. These coefficients are necessary not only to measure and compare the degree of differences, unevenness of the age structures of the population of separate territories, but also to monitor this situation over time. The latter is necessary to develop policies to smooth out the structural demographic waves. The index (1-R) proposed in the article, showing the residual value of covariance not described by the coefficient of determination, can be used at the stage of preliminary analysis of the differences in structures, since it is instantly calculated using application programs and gives a general picture of the level of unevenness of the series, ranks them on this basis. In our opinion, the most adequate measure of differences in structures is the coefficient of unevenness (Kn), calculated by analogy with the coefficient of variation. It is preferable at the main stage of comparative analysis, as it reveals the average relative measure of the unevenness of pairs of series, is simple and understandable in interpretation. Three other similar coefficients (Gatev, Salai, Ryabtsev) can be used as a supplement to confirm the adequacy of the comparative analysis, as well as for an overall assessment of the degree of discrepancy between the series using the scale familiar to the end user from zero to one. All five coefficients for measuring the degree of unevenness of structural series are suitable not only for studying the age structural waves of the population of the country and its regions, but also for comparing the age structures of the population of different territories with each other. The conclusions to the article contain recommendations for building a path for the most effective smoothing of the demographic structural waves in Russia with the help of differentiated in time and regional demographic policy in the field of fertility and immigration.