我国男女两性老龄人口死亡率联合建模与预测

老龄人口死亡率建模和预测是长寿风险度量和养老金风险管理的基础。在我国,退休年龄及以上老龄人口死亡数据稀少,随机波动大,构建能够捕捉老龄人口死亡率随性别、年龄和时间变动的动态预测模型成为难题。本文采用Logistic两人口死亡率模型研究我国老龄人口死亡率的建模与预测。首先,运用死亡率数据质量较好的我国台湾地区数据,对模型结构进行选择,并检验模型的稳健性和预测性能。其次,基于我国大陆地区死亡率数据对模型结构进行二次验证和选择,应用所选模型对大 陆地区老龄死亡率进行建模和预测。结果显示,对于我国男女老龄死亡率的拟合和预测,Logistic 两人口模型均优于单人口CBD模型。最后,运用Logistic两人口死亡率模型对死亡率在年龄和时间两个维度上外推和预测,计算出时期和队列老龄人口分年龄的预期余寿,为养老金精算评估和长寿风险分析提供更准确的数据支持。     

基于长寿背景下的企业年金风险评估

在死亡率不断降低,预期寿命不断提高的背景下,企业年金实现一定替代率目标的难度不断增大,面临的长寿风险越来越不容忽视。在中国人口死亡率最优模型基础上,通过企业年金比率模型评估了三种不同年龄结构企业年金的长寿风险,并在基于Bootstrap方法的VAR模型上考虑了投资风险,对企业年金进行综合风险分析。结果表明,当其他风险都能被完全对冲时,未来死亡率降低及预期寿命延长会对企业年金实现目标养老待遇产生较大影响,并且评估期越长,企业年金积累的长寿风险越大。     

有限数据下Lee-Carter模型在人口死亡率预测中的应用

Lee-Carter模型是当今世界上最流行的死亡率建模与预测模型,传统的Lee-Carter模型在样本量很大时才能得到较好的效果,而中国的死亡率数据量较少,且部分年限的数据缺失,从而难以达到较好的预测效果。本文基于Li等(2004)提出的有限数据死亡率建模方法,同时考虑样本量不足的影响,采用韩猛等(2010)提出的“双随机过程”建模,构建了有限数据下中国人口死亡率的预测模型,并用于对未来死亡率变动趋势和人口寿命的预测,最后将预测结果与保险公司采用的死亡率改善因子以及社会养老保险个人账户中采用的计发月数进行对比分析,给出了若干相关结论和有关死亡率风险管理的建议。     

基于均衡关系的中国人口死亡率预测模型

人口死亡率反映了人口的死亡程度,准确预测死亡率是人口科学及人口经济学研究的重点之一,同时也是长寿风险测量的重要数据基础。基于Lee-Carter模型,探索中国大陆与台湾地区死亡率的相关性,通过协整分析考虑两地死亡率的长期均衡关系,创新性地建立基于相关性的向量误差修正模型(VECM),克服传统自回归移动平均模型(ARIMA)使用有限数据进行预测的局限性;均方预测误差作为检验标准,结果表明:基于VECM模型的预测效果比传统的预测效果更佳;基于中国大陆地区和台湾地区的死亡率长期均衡关系,可以为两地联合长寿债券的定价提供重要参考。     

保险公司长寿风险度量

本文梳理了几种重要的动态死亡率预测模型,给出了长寿风险度量的三种方法,选取了保险公司及国家统计局公布的人口死亡率数据,度量了保险公司的两类长寿风险,对不同方法下长寿风险的度量结果进行比较,并分析了极限年龄与折现率变动对长寿风险影响的敏感性。研究发现：基于保险公司经营稳健性的视角,第一类长寿风险的度量应采用随机模拟法,第二类长寿风险的度量应采用标准公式法;极限年龄的变动对长寿风险的影响较小,保险公司无上调经验生命表极限年龄的必要;长寿风险对折现率的变动较为敏感,提高折现率,保险公司长寿风险显著降低。     

中国人口死亡率改善水平比较分析

 中国第六次人口普查数据如期公布,本文利用1981-2010年人口普查和人口抽样调查提供的死亡率数据,对四次人口普查期间中国人口死亡率改善水平进行深层次分析,分别按年龄、性别、城乡、是否投保等进行对比,并与其他国家的数据对比,旨在探讨中国人口死亡率变化趋势和不同分类人群死亡率改善的差异、成因及变动趋势,最终为长寿风险管理提供依据。主要结论是：建国以来,中国人口死亡率持续改善,死亡率改善程度随年龄的增长呈下降趋势,近十年来死亡率改善程度最高,特别是婴儿和55岁以上人口尤为明显。在大部分年龄组上,女性死亡率改善水平高于男性,市人口死亡率改善水平明显高于镇和乡,投保商业保险人口的死亡率改善水平高于全国人口,我国人口的死亡率改善水平高于对比国家,这反映了我国人民生活和医疗水平的实质提高,也表明未来死亡率还有较大的下降空间。     

基于VaR方法的长寿风险自然对冲模型

随着死亡率的下降与预期寿命的提高,保险公司面对着不容忽视的长寿风险。基于VaR方法探讨了长寿风险管理中的自然对冲策略,然后在对中国男性人口死亡率预测的基础上,给出了保险公司自然对冲长寿风险所需的最优产品结构,并进一步考查了利率、签单年龄、缴费方式等因素对最优产品结构的影响。     

A comparison of models for dynamic life tables. Application to mortality data from the Valencia Region (Spain)

The graduation of mortality data aims to estimate the probabilities of death at age x, q ( x ), by means of an age-dependent function, whose parameters are adjusted from the crude probabilities that are directly obtainable from the data. However, current life tables have a problem, the need for periodic updates due to changes in mortality over short periods of time. The table containing mortality rates for different ages in different years, q ( xt ), is called a dynamic life table, which captures mortality variation over time. This paper proposes a review of the most commonly used dynamic models and compares the results obtained by each of them when applied to mortality data from the Valencia Region (Spain). The result of the comparison leads us to the conclusion that the Lee-Carter method offers the best results for both sexes, while that based on Heligman and Pollard functions provides the best fit for men alone. Our working method is of additional interest as it may be applied to mortality data for a wide range of ages in any geographical location, allowing the most appropriate dynamic life table to be selected for the case at hand.     

Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections

Summary. The paper presents a reinterpretation of the model underpinning the Lee–Carter methodology for forecasting mortality (and other vital) rates. A parallel methodology based on generalized linear modelling is introduced. The use of residual plots is proposed for both methods to aid the assessment of the goodness of fit. The two methods are compared in terms of structure and assumptions. They are then compared through an analysis of the gender- and age-specific mortality rates for England and Wales over the period 1950–1998 and through a consideration of the forecasts generated by the two methods. The paper also compares different approaches to the forecasting of life expectancy and considers the effectiveness of the Coale–Guo method for extrapolating mortality rates to the oldest ages.     

Modelling Trends and Inequality in Small Area Mortality

This paper considers the modelling of mortality rates classified by age, time, and small area with a view to developing life table parameters relevant to assessing trends in inequalities in life chances. In particular, using a fully Bayes perspective, one may assess the stochastic variation in small area life table parameters, such as life expectancies, and also formally assess whether trends in indices of inequality in mortality are significant. Modelling questions include choice between random walk priors for age and time effects as against non-linear regression functions, questions of identifiability when several random effects are present in the death rates model, and the choice of model when both within and out-of-sample performance may be important. A case study application involves 44 small areas in North East London and mortality in five sub-periods (1986-88, 1989-91, 1992-94, 1995-97, 1998-2000) between 1986 and 2000, with the final period used for assessing out-of-sample performance.     

Trends in inequality in infant mortality in the north of England, 1921–1973, and their association with urban and social structure

Summary.  The paper analyses a time series of infant mortality rates in the north of England from 1921 to the early 1970s at a spatial scale that is more disaggregated than in previous studies of infant mortality trends in this period. The paper describes regression methods to obtain mortality gradients over socioeconomic indicators from the censuses of 1931, 1951, 1961 and 1971 and to assess whether there is any evidence for widening spatial inequalities in infant mortality outcomes against a background of an overall reduction in the infant mortality rate. Changes in the degree of inequality are also formally assessed by inequality measures such as the Gini and Theil indices, for which sampling densities are obtained and significant changes assessed. The analysis concerns a relatively infrequent outcome (especially towards the end of the period that is considered) and a high proportion of districts with small populations, so necessitating the use of appropriate methods for deriving indices of inequality and for regression modelling.     

非稳态下公共养老金资产负债表的编制与精算平衡调整

公共养老金资产负债表是国家资产负债表的重要组成部分,也是政府实施养老金改革的重要依据。已有研究给出了稳态下公共养老金资产负债表的编制方法,但这些方法无法直接用于非稳态情形。当前我国面临经济、人口、制度调整等非稳态环境,因此构建适应我国实际的非稳态下的公共养老金资产负债表成为重要的研究问题。非稳态下公共养老金资产负债表编制的主要难题在于缴费资产的计算。本文在梳理公共养老金资产负债表编制原理的基础上,推导出非稳态下缴费资产的计算公式,给出我国公共养老金资产负债表的编制方法和实际应用,并进一步测算分析了降低养老金待遇指数、延迟退休、提高缴费等多项改革对公共养老金资产负债表的影响。结果显示：我国公共养老金的资产负债平衡过度依赖财政补贴,无法实现缴费资产与负债的平衡。适当调整养老金待遇指数、退休年龄、缴费水平等参数,有助于恢复资产和负债的平衡,减轻制度对财政补贴的依赖。     

养老保险个人账户参数设定错误与纠正

我国基本养老保险采取统账结合的制度模式。其中，个人账户采用记账方式建立了参保缴费与养老待遇之间的直接联系。理论上，公平和长期可持续的个人账户模式在记账利率、计发系数、余额继承等方面应遵循精算原则，但我国的个人账户参数设定存在不少违背精算公平和精算平衡原则的错误。本文结合国际经验，在剖析我国养老保险个人账户参数设定错误的基础上，基于精算平衡原理，探讨参数设定方法，检验纠正方案对制度精算公平和精算平衡性的效果，最后提出参数改革的具体建议。主要结论是：个人账户的记账利率应该是制度的内含回报率；名义账户的记账利率不是银行存款利率，而应随缴费工资增长率、人口预期寿命的变动等定期调整；养老金计发系数应基于动态生命表、养老金调整指数和个人账户内含回报率的变动而调整。由此确定的参数纠正方案将有效改善制度的精算公平与精算平衡性。因而建议我国基本养老保险个人账户应尽早明确现收现付的筹资模式和账户余额的权益归属，采用动态的记账利率和计发月数，引入自动平衡机制，实现制度的长期精算平衡。     

The multidimensional markov chain with prespecified asymptotic means,and (auto-)covariances

In this paper a method is presented to construct random time series which, starting from their present values, converge to stationary time series with a priori specified mean values, standard deviations, correlations and autocorrelations. The method is applied to simulate time series of price-inflation, wage-inflation, and interest rates, whose mean values, standard deviations, correlations and autocorrelations converge to the values which are estimated from historical data This application is a circular part of a Decision Support System which assists management of pension funds in analysing new methods of calculating pension premiums.     

收入、预期寿命和社会养老保险收入再分配效应

本文在考虑职工基本养老保险典型不同缴费基数参保者寿命存在异质性的情况下，通过内部收益率的计算考察典型不同缴费基数参保者之间的养老金收入再分配效应。首先根据省级宏观截面数据估计了职工基本养老保险典型不同缴费基数参保者退休时的平均余命，再据此分别计算和比较不同参保群体的内部收益率。 研究发现职工基本养老保险制度总体上呈现微弱的正向收入再分配效应。虽然低缴费基数参保者内部收益率略高于中、高缴费基数参保职工，但其内部收益率因相对较短的寿命而大大降低。这也提醒政策制定者在研究制定延迟退休、社会养老保险全国统筹等政策时需要充分考虑参保职工内部不同群体间的平均预期寿命差别，对低收入参保者予以特别关注。     

“做实做小”个人账户对个人养老金水平的影响

 本文引入养老保险金记账利率和工资增长率，测算了在不同初始缴费工资和缴费年限条件下实施“做实做小”个人账户政策对参保人养老金水平的影响。通过分析得出：1.政策调整后，养老金给付结构较调整前更能体现缴费积累与养老金水平的内在经济联系； 2.政策调整后个人养老金水平普遍不如政策调整前的水平，政策调整后养老金水平高于政策调整前均出现在缴费年限较长以及初始缴费工资较高的情况下；3.政策调整对不同的参保人影响不同。政策调整加大了低初始缴费工资人群的生活压力；拉大了男、女职工退休养老金的差距，不利于当前社会男女平等和贫富分化问题的解决。     

The Increasingly Mixed Proportional Hazard Model: An Application to Socioeconomic Status,Health Shocks,and Mortality

We introduce a duration model that allows for unobserved cumulative individual-specific shocks, which are likely to be important in explaining variations in duration outcomes, such as length of life and time spent unemployed. The model is also a useful tool in situations where researchers observe a great deal of information about individuals when first interviewed in surveys but little thereafter. We call this model the “increasingly mixed proportional hazard” (IMPH) model. We compare and contrast this model with the mixed proportional hazard (MPH) model, which continues to be the workhorse of applied single-spell duration analysis in economics and the other social sciences. We apply the IMPH model to study the relationships among socioeconomic status, health shocks, and mortality, using 19 waves of data drawn from the German Socio-Economic Panel (SOEP). The IMPH model is found to fit the data statistically better than the MPH model, and unobserved health shocks and socioeconomic status are shown to play powerful roles in predicting longevity.     

Longevity and concentration in survival times: the log-scale-location family of failure time models

Evidence suggests that the increasing life expectancy levels at birth witnessed over the past centuries are associated with a decreasing concentration of the survival times. The purpose of this work is to study the relationships that exist between longevity and concentration measures for some regression models for the evolution of survival. In particular, we study a family of survival models that can be used to capture the observed trends in longevity and concentration over time. The parametric family of log-scale-location models is shown to allow for modeling different trends of expected value and concentration of survival times. An extension towards mixture models is also described in order to take into account scenarios where a fraction of the population experiences short term survival. Some results are also presented for such framework. The use of both the log-scale-location family and the mixture model is illustrated through an application to period life tables from the Human Mortality Database.     

养老保险可持续发展调整机制研究

在人口老龄化压力下,各国公共养老金体系普遍面临逐步增大的支付压力,为维持系统的可持续发展,各国纷纷引入了自动调整机制。本文对公共养老金自动调整机制的国际经验做了比较分析,总结了自动调整机制的机理、特点和类型,结合我国社会养老保险的实践,测算分析了不同调整机制对制度可持续性和待遇充足性的影响,探讨了自动调整机制在我国的适用性。最后给出我国建立养老保险调整机制的建议。     

A progressive rise in stomach cancer-related mortality rate during 1970–1995 in Japanese individuals over 85 years of age

A large number of studies have shown a gradual fall in stomach cancer-related mortality rate during the last decade. Here we analyzed the pattern of stomach cancer-related mortality rates in Japanese aged>85 years from 1970 to 1995. We used data for the entire population of Japan. The magnitude of change was measured by relative risk and cause-elimination life tables to distinguish time trends in mortality rates of stomach cancer for individuals over 85 years of age compared with other age groups (55–84 years). In the over-85 age group, stomach cancer mortality increased from 374 in 1970 to 662 in 1995 per 100,000 (77%) for males and from 232 to 296 per 100,000 (27%) for females. Using the 55–59 years group as the reference category, the relative risk increased from 2.3 to 9.9 and from 2.8 to 11.1 in men and women, respectively. The effects of mortality on life expectancy also increased 1.5 times and 1.1 times, respectively. Our results showed a rise of stomach cancer mortality in Japanese aged over 85 years, which paralleled the increase in relative risk and negative contribution to life expectancy. While the mortality of younger age groups is decreasing, the change over from increase to decrease in the over-85 age group is only just beginning.