Results well known in the actuarial community about closed-form expressions to Gompertz and Gompertz-Makeham life expectancies for a person aged x are still being independently rediscovered to this day. This note seeks to acknowledge previous results about closed-form expressions to Gompertz-Makeham life expectancies, especially in the actuarial science field, hoping to stimulate interdisciplinarity and provide the background for further developments, especially since the derivation of closed-form expressions for life expectancy (and annuities) based on particular mortality laws are matters of interest for multiple fields such as actuarial science, biology, demography, statistics among others.
Ideally, life expectancy should be a decreasing function of age. When this fact is not observed, this situation is known as the life table paradox. This paper investigated the timing (and health metrics at the time) in which Brazil and its Federation Units (FU) overcame (or are expected to overcome) this paradox. The data were gathered from the Brazilian Institute of Geography and Statistics and contained 3,416 sex-specific abridged life tables, from 2000 to 2060. At national level, females and males overcame the paradox in 2016 and 2018, respectively. However, when the FU were examined separately, much heterogeneity was observed. Through the decomposition analysis of the change over time in the difference between life expectancy at birth and at age one, we found that Brazil and most of its FU are expected to have both changes declining over time and the total change is expected to be decreasing and greater than zero. Nevertheless, for some Northeastern states the total change is expected to pass from a positive to a negative value; and for two Northern states the total change is expected to be neither decreasing nor increasing. In a public planning perspective, we understand that achieving balancing in the life tables is a goal to be pursued, especially because having an imbalanced table means that life expectancy at birth is still strongly influenced by high levels of infant mortality. Therefore, this knowledge could help planners to properly define strategies to accelerate the balancing process and revert unequal scenarios.
O estudo objetivou aplicar modelos atuariais (dinâmicos e estáticos) para calcular as alíquotas previdenciárias equilibradas para o benefício de aposentadoria programada (na idade mínima) para o Regime Geral de Previdência Social, tomando como base o texto original e o substitutivo da reforma proposta pelo Governo Michel Temer. Mesmo ante os aumentos regulares da expectativa de vida e o caráter de longo prazo das análises, os estudos nacionais sobre previdência tipicamente se apoiam na hipótese de mortalidade estática. A relevância deste estudo é evidenciada devido às mudanças demográficas, particularmente o aumento da expectativa de vida, vivenciadas pela população brasileira nas últimas décadas e que põem em dúvida a sustentabilidade do sistema previdenciário nacional. O uso de modelos atuariais dinâmicos possibilita discussões mais acuradas sobre o futuro da previdência, além de contribuir para uma literatura nacional ainda escassa. Foram aplicados modelos atuariais estáticos e dinâmicos para um indivíduo representativo, ajustando tábuas de mortalidade das Nações Unidas entre 1950 e 2100. Constatou-se que as alíquotas atuarialmente justas calculadas pelo modelo atuarial dinâmico são tipicamente maiores do que aquelas obtidas por meio do modelo estático, sobretudo para as mulheres. Espera-se que tal diferença aumente à medida que os ganhos na expectativa de vida passem a sofrer maior influência da redução da mortalidade nas idades mais avançadas. Adicionalmente, pelo modelo dinâmico, sendo aprovada a reforma da previdência (pelo texto original ou substitutivo), há indícios de que as alíquotas cobradas atualmente seriam demasiadas para os homens. Por sua vez, essas seriam demasiadas para as mulheres pelo texto original e mais próximas do valor atuarialmente justo pelo texto substitutivo. Recomenda-se, ainda, o desenvolvimento, a divulgação e a revisão regular de tábuas dinâmicas oficiais (seja para a mortalidade ou outras premissas biométricas). ; 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.
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.
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.
Com o objetivo de reformar o sistema previdenciário brasileiro, o Governo Federal enviou para a Câmara dos Deputados a Proposta de Emenda à Constituição nº 287/2016, a qual, dentre outras medidas, propõe instituir uma idade mínima progressiva de aposentadoria. Este trabalho avaliou os aspectos distributivos que esta medida pode gerar aos contribuintes, a partir do cálculo das alíquotas atuarialmente justas frente à heterogeneidade da mortalidade da população brasileira. Como principal resultado, constatou-se que haverá uma redistribuição negativa, em que os indivíduos com menor expectativa de vida, que ingressaram no mercado de trabalho mais jovens e que têm baixo crescimento salarial irão financiar as pensões daqueles mais longevos, que ingressaram no mercado de trabalho mais velhos e com maior perspectiva de crescimento salarial.
The objective of this work was to compare the actuarially fair social security rates for the General Social Welfare Policy (GSWP), based on the social security factor rules and the minimum age proposal present in Proposed Constitutional Amendment n. 287/2016. The demographic changes that have taken place in Brazil in recent years raise questions about the sustainability of the national social security system and approving social security reform has been a government priority. Therefore, there is an undisputed need for an actuarial study that calculates actuarially fair rates and compares the current scenario with the reform proposals. Multiple decrement actuarial models were used to calculate the fair rates considering a standard family (25-year-old worker, spouse, and two children), in which the man is three years older than the woman. The IBGE 2015 Extrapolated (mortality) and Álvaro Vindas (disability) tables were adopted as biometric assumptions, and a real wage growth rate of 2% p.a. and real interest rate of 3% p.a. were used. It has been shown that under the social security factor rule current contribution rates are insufficient to cover social security benefits, since the actuarially fair rates are 30.69% and 35.27% for men and women, respectively. However, if the social security reform were approved as submitted, the fair rates would be reduced to 22.25% and 21.60%, respectively. Besides the minimum age, part of this reduction is due to the proposed rules allowing pension values lower than the minimum wage. ; O objetivo deste trabalho foi comparar as alíquotas previdenciárias atuarialmente justas para o Regime Geral de Previdência Social, tendo como base as regras do fator previdenciário e da proposta de idade mínima, presente na Proposta de Emenda à Constituição n. 287/2016. As mudanças demográficas ocorridas no Brasil nos últimos anos chamam a atenção para a questão da sustentabilidade do sistema previdenciário nacional, e aprovar a reforma previdenciária tem sido prioridade do governo. Logo, é indiscutível a necessidade de um estudo atuarial que viesse calcular alíquotas atuarialmente justas e comparar o atual cenário com as propostas de reforma. Utilizaram-se modelos atuariais com múltiplos decrementos para o cálculo das alíquotas justas, considerando uma família padrão [funcionário(a) de 25 anos, cônjuge e dois filhos], sendo o homem três anos mais velho que a mulher. Adotaram-se como premissas biométricas as tábuas IBGE 2015 – Extrapolada (mortalidade) e Álvaro Vindas (invalidez), a taxa real de crescimento salarial de 2% a.a. e a taxa real de juros de 3% a.a. Concluiu-se que, pela regra do fator previdenciário, as alíquotas vigentes são insuficientes para cobertura dos benefícios previdenciários, uma vez que as alíquotas atuarialmente justas são 30,69% e 35,27% para homens e mulheres, respectivamente. Contudo, caso a reforma da Previdência fosse aprovada em seu texto original, os percentuais justos seriam reduzidos para 22,25%, e 21,60%, respectivamente. Além da idade mínima, grande parte dessa redução deve-se às regras propostas para cálculo da pensão, que admitem valor abaixo do salário mínimo.
Abstract It has been shown that under the social security factor rule current contribution rates are insufficient to cover social security benefits, since the actuarially fair rates are 30.69% and 35.27% for men and women, respectively. However, if the social security reform were approved as submitted, the fair rates would be reduced to 22.25% and 21.60%, respectively. Besides the minimum age, part of this reduction is due to the proposed rules allowing pension values lower than the minimum wage. These results served the objective of this work, which was to compare the actuarially fair social security rates for the General Social Welfare Policy (GSWP), based on the social security factor rules and the minimum age proposal present in Proposed Constitutional Amendment n. 287/2016. The demographic changes that have taken place in Brazil in recent years raise questions about the sustainability of the national social security system and approving social security reform has been a government priority. Therefore, there is an undisputed need for an actuarial study that calculates actuarially fair rates and compares the current scenario with the reform proposals. Multiple decrement actuarial models were used to calculate the fair rates considering a standard family (25-year-old worker, spouse, and two children), in which the man is three years older than the woman. The IBGE 2015 Extrapolated (mortality) and Álvaro Vindas (disability) tables were adopted as biometric assumptions, and a real wage growth rate of 2% p.a. and real interest rate of 3% p.a. were used.
Abstract It has been shown that under the social security factor rule current contribution rates are insufficient to cover social security benefits, since the actuarially fair rates are 30.69% and 35.27% for men and women, respectively. However, if the social security reform were approved as submitted, the fair rates would be reduced to 22.25% and 21.60%, respectively. Besides the minimum age, part of this reduction is due to the proposed rules allowing pension values lower than the minimum wage. These results served the objective of this work, which was to compare the actuarially fair social security rates for the General Social Welfare Policy (GSWP), based on the social security factor rules and the minimum age proposal present in Proposed Constitutional Amendment n. 287/2016. The demographic changes that have taken place in Brazil in recent years raise questions about the sustainability of the national social security system and approving social security reform has been a government priority. Therefore, there is an undisputed need for an actuarial study that calculates actuarially fair rates and compares the current scenario with the reform proposals. Multiple decrement actuarial models were used to calculate the fair rates considering a standard family (25-year-old worker, spouse, and two children), in which the man is three years older than the woman. The IBGE 2015 Extrapolated (mortality) and Álvaro Vindas (disability) tables were adopted as biometric assumptions, and a real wage growth rate of 2% p.a. and real interest rate of 3% p.a. were used.
