Modeling of the Medium-Term Post-War Demographic Cycles in Russia

Demographic cycles are a fundamental mechanism for reproducing the population and regulating the number of inhabitants. The article simulates the medium-term birth cycles of the Russian population in the changing socio-economic conditions of the post-war period (1946–2017), and their interaction with the total fertility rate. The proposed mathematical model describes the cyclical demographic dynamics, distinguishing the fundamental endogenous factors from exogenousones and random phenomena. The authors apply a technique based on a combination of trigonometric approximation methods using finite Fourier series, adapted for the considered problems, and stepwise regression for model identification and optimization. Models for the entire, urban, and rural population during a specified period and in shorter periods of time are examined. It has been established that the frequency of the series of the number of births is associated with both the duration of women’s fertile age and the duration of entry into it. The results of the study show that the current demographic decline has an endogenous nature. The cycle lasts an average of 30 years, with the downward phase indicating the exhaustion of fertility growth resources within the current family model. A conclusion is made about the timeliness of additional measures of active demographic policy aimed at stimulating the birth rate, supporting large families and focused primarily on rural areas as well as small and medium-sized cities of Russia. However, the economy must adapt to demographic constraints.