Abstract: 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.

Keywords: Cohort Fertility Rate, Fertility Patterns, Fertility Projection, Total Fertility Rate, Period-Cohort-Period (PCP) Method

摘要： 本文设计了总和生育率预测的Period-Cohort-Period(PCP)方法：利用历次全国人口普查和1%人口抽样调查的时期生育率数据建构队列生育率分布，再由队列分布反转预测时期生育率分布，从而求取未来年份的总和生育率。PCP方法要求生育模式模拟函数具备高精度和显性、灵活的可控参数。为此，本文从现有的Gompertz生育模型出发，推导出广义Gumbel生育模式。基于此，本文解析了1981年以来中国时期生育率分布变化的阶段性特征，并通过时期转队列分析揭示了1965~1990年出生队列妇女的生育率分布及其参数演变，然后通过参数变动趋势分析，按高、中、低方案预测了1991~2030年出生队列的生育率分布，进而得到2025~2050年时期总和生育率的可能演变轨迹。研究发现，“十五五”后期中国的总和生育率有可能出现缓慢回升趋势。若要在21世纪中叶走出“低生育率陷阱”、回归正常生育模式，国家既应积极实施生育支持政策，又应尊重生育价值的多元性，避免因过度焦虑导致政策偏激。

关键词: 队列生育率, 生育模式, 生育率预测, 总和生育率, PCP方法