Mortality dynamics and the statutory retirement age proposal: an actuarial view

ABSTRACT This paper aimed to apply (dynamic and static) actuarial models to calculate the balanced contribution rates for the planned (at the minimum age) retirement benefit of the General Social Security System, based on the original and substitutive texts of the reform proposed by Michel Temer’s government. Even with the regular increases in life expectancy and the long-term nature of the analyses, national studies on social security are typically based on the static mortality hypothesis. The relevance of this study is evident due to the demographic changes, particularly the increase in life expectancy, experienced by the Brazilian population in recent decades and which put in question the sustainability of the national pension system. The use of dynamic actuarial models allows for more accurate discussions about the future of social security, besides contributing to the still scarce national literature. Static and dynamic actuarial models were applied to a representative individual, adjusting mortality tables from the United Nations covering 1950 to 2100. It was verified that the actuarially fair rates calculated by the dynamic actuarial model are typically higher than those obtained by the static model, especially for women. This difference is expected to increase as gains in life expectancy become more influenced by the reduction in mortality at more advanced ages. Moreover, if the social security reform is approved (in accordance with either the original or the substitutive text), there are indications from the dynamic model that the contributions rates currently charged would be excessive for men. In turn, these rates would be excessive for women considering the original text, and closer to the actuarially fair value considering the substitutive text. The development, disclosure, and regular updating of official dynamic tables (whether for mortality or other biometric assumptions) are also recommended.

摘要
本研究基于米歇尔·特梅尔（Michel Temer）政府提出的社保改革原文本与替代文本，运用动态精算模型(dynamic actuarial models)与静态精算模型(static actuarial models)，测算巴西通用社会保障体系(General Social Security System)最低领取年龄下的退休待遇均衡缴费率。尽管人口预期寿命持续提升且分析具备长期性特征，巴西国内社会保障领域的现有研究通常仍采用静态死亡率假设。鉴于近几十年来巴西人口经历的人口结构变迁——尤以预期寿命增长为甚——正对本国养老金体系(pension system)的可持续性提出挑战，本研究的现实意义与学术价值不言而喻。相较于当前国内该领域研究仍较为匮乏的现状，动态精算模型的应用不仅能够更精准地研判社会保障体系的未来走向，还能为国内相关学术研究提供有益补充。本研究以典型代表性个体为研究对象，分别应用静态与动态精算模型，并采用联合国1950年至2100年的死亡率表(mortality tables)进行参数校准。研究证实，动态精算模型测算得到的精算公平缴费率(actuarially fair contribution rates)通常高于静态模型的结果，女性群体的这一差异尤为显著。随着预期寿命的提升更多源于高龄段死亡率的下降，该缴费率差异预计将进一步扩大。此外，若社保改革（无论是原文本还是替代文本版本）获得通过，动态模型的测算结果显示，当前针对男性征收的缴费率或已过高；若采用原文本标准，当前女性缴费率也将偏高，但若采用替代文本标准，该缴费率则更接近精算公平值。研究同时建议，官方应制定、公布并定期更新涵盖死亡率及其他生物特征假设在内的官方动态统计表格。