The long-term projection of changes in the total fertility rate (TFR) is a crucial basis for assessing population development trends, as well as a persistent challenge in demographic research. This paper designs a Period-Cohort-Period (PCP) method for TFR projection: it utilizes period fertility data from successive censuses to construct cohort fertility distributions, and subsequently inverts these cohort distributions to project period fertility distributions, thereby deriving the TFR for future years. The PCP method requires the fertility pattern simulation function to have high precision and parameters that are explicit and flexibly controllable. This study discusses the relationship between the Gompertz fertility model and the standard Gumbel function, revealing shortages in the Gompertz model such as ambiguous parameter interpretations, parameter redundancy, and inflexibility in shape control. By addressing these limitations, we derive the Generalized Gumbel fertility model, which surpasses all previous models in goodness of fit.

Applying the Generalized Gumbel model, we fitted and analyzed data from successive population censuses since the 1980s. The results reveal that the peak fertility points across different periods exhibit a “C-shaped” trajectory, which can be broadly divided into three stages: the “early marriage and early childbearing” stage in the early 1980s driven by the post-peak effect, the rapid plunge stage of the fertility peak during 1986-2005, and the delayed childbearing stage with a broad peak since 2010. The period-to-cohort analysis reveals that the cohort total fertility rate (CTFR) experienced an initial increase followed by a decline, with the magnitude of change being much more moderate than that of the period TFR. Specifically, the CTFRs for 1965-1974 cohorts slightly increased from 1.93 to 2.17, while the CTFRs for 1974-1985 cohorts dropped from 2.17 to 1.87. In terms of the fertility distribution shape, this manifests as a vertical plunge in fertility peaks, with an ongoing trend of the right tail of the fertility curve lengthening and rising. For cohorts born since 1985, the rightward shift of the peak fertility age has accelerated, while the magnitude of the peak decline has narrowed.

By referring to the changing trends of indicators such as lifetime childlessness rates and TFRs in other countries, this study analyzed the parameter variation trends of China's future fertility patterns. We projected the fertility distributions for 1991-2030 cohorts by parity under high, medium, and low scenarios, thereby extrapolating the potential evolutionary trajectories of the period TFR from 2025 to 2050. The findings indicate that China’s TFR may exhibit a slow recovery trend during the latter half of the 15th Five-Year Plan period. On the one hand, this is a result of the diminishing tempo effect of fertility; on the other hand, it reflects the self-correction of diverse groups within a massive population. To escape the “low fertility trap” and return to a normal fertility pattern by the mid-21st century, the state must not only actively implement fertility support and pro-natalist policies but also trust and protect the rich diversity of fertility values, maintaining confidence in the future and avoiding extreme policies driven by excessive anxiety.

A three-group age structure can be designated as a point in the triangular diagram, while the routine of the points in time series traces the age structure evolution. The paper classifies the age structure evolution patterns of countries (areas) in the world and provinces in China, and discovers the general and ergodic age structure transition (AST) pattern which experiences three stages: the “bonus raising” stage (i.e., from the traditional fertile young population to fewer children-more labors population), the “debted ageing” stage (i.e., from fewer children-more labors population to fewer labors-more aged population), and the stage in between (i.e., turning stage). While developed countries are primarily in the middle of stage three, most developing countries are in the late phase of the first stage, and many least developed countries in Africa are still in the early stage one or even in the traditional position. Started in the 1950s and accelerated since the 1980s, the AST in China is now just passing the turning stage with diversifying decreasing bonuses at turning points from coast to inland provinces. According to a simulation scenario, China will approach the equilibrium position near 2100, with 15% children, 55% labor forces, and 30% older people, which is probably the common end of all countries in the future.