Minimum Death Rates and Maximum Life Expectancy: The Role of Concordant Ages

Only five populations have achieved maximum life expectancy (or best practice population) more than occasionally since 1900. The aim of this article is to understand how maximum life expectancy is achieved in the context of mortality transition. We explore this aim using the concepts of potential life expectancy, based on minimum rates at each age among all high longevity populations, and concordant ages. Concordant ages are defined as ages at which the minimum death rate occurs in the population with the maximum life expectancy. The results show the extent to which maximum life expectancy could increase through the realization of demonstrably achievable minimum rates. Concordant ages are concentrated at increasingly older ages over time, but they have produced more than half of the change in maximum life expectancy in almost all periods since 1900. This finding is attributed to their quantity and position whereby concordant ages are concentrated at the ages that have the greatest impact on mortality decline in a particular period. Based on mortality forecasts, we expect that concordant ages will continue to lead increases in female maximum life expectancy, but that they will play a weaker role in male maximum life expectancy.     

The evolution of death rates and life expectancy in Denmark

From 1835 to date Denmark has experienced an increase in life expectancy at birth of about 40 years for both sexes. Over the course of the last 170 years, life expectancy at birth has increased from 40 to 80 years for women and from 36 to 76 years for men, and it continues to rise. Using a new methodology, we show that about half of the total historic increase can be attributed to the sharp decline in infant and young age death rates up to 1950. However, life expectancy gains from 1950 to date can be primarily attributed to improvements in the age-specific death rates for the age group from 50 to 80, although there is also a noticeable contribution from the further decline in infant mortality over this period. With age-specific death rates up to age 60 now at a very low absolute level, substantial future life expectancy improvements must necessarily arise from improvements in age-specific death rates for ages 60 and above. Using the developed methodology, we quantify the impact of further reductions in age-specific mortality. Despite being one of countries with the highest life expectancy at the beginning of the 20th century, and despite the spectacular historic increase in life expectancy since then, Denmark is, in fact, lagging behind compared to many other countries, notably the other Nordic countries. The main reason is an alarming excess mortality for cause-specific death rates related to ischaemic heart diseases and, in particular, a number of cancer diseases. Age-specific death rates continue to improve in most countries, and a likely scenario is that in the future Denmark will experience improvement rates at the international level or perhaps even higher as a result of a catch-up effect.     

Life Expectancy in 2040: What Do Clinical Experts Expect?

We use expert clinical and public health opinion to estimate likely changes in the prevention and treatment of important disease conditions and how they will affect future life expectancy. Focus groups were held including clinical and public health faculty with expertise in the six leading causes of death in the United States. Mortality rates and life tables for 2040 were derived by sex and age. Life expectancy at age 20 and 65 was compared to figures published by the Social Security Administration and to estimates from the Lee-Carter method. There was agreement among all three approaches that life expectancy at age 20 will increase by approximately one year per decade for females and males between now and 2040. According to the clinical experts, 70% of the improvement in life expectancy will occur in cardiovascular disease and cancer, while in the last 30 years most of the improvement has occurred in cardiovascular disease. Expert opinion suggests that most of the increase in life expectancy will be attributable to the already achieved reduction in smoking rates, especially for women.     

Die Gesundheitsausgaben in der letzten Lebensphase

The expenditures for healthcare in the last year of life fall with the age at death. According to this observation, the increase of the life expectancy should lead to a decrease of health expenditures. The available empirical data allows to verify this thesis. In the data, I find that the expenditures fall with the age at death at the same date. But, this does not lead to a decrease in healthcare expenditures as time goes by, because the declining effect of a growing live expectancy is much smaller than the increase of healthcare expenditures in every age at death.     

Probabilistic estate planning

Probabilistic estate planning is based on the principle of maximizing expected net present value commensurate with the risk assumed. Rather than assuming that death occurs at life expectancy, probabilistic estate planning treats death as a random variable. Compounded to randomly chosen ages of death, estate assets are taxed and distributed to heirs. The purpose of probabilistic estate planning is to find the estate plan and asset/liability combination that maximizes the expected net present value of assets passing to heirs and to convey some idea of the risk associated with that estate plan.     

Demographic change, social security systems, and savings

In theory, improvements in healthy life expectancy should generate increases in the average age of retirement, with little effect on savings rates. In many countries, however, retirement incentives in social security programs prevent retirement ages from keeping pace with changes in life expectancy, leading to an increased need for life-cycle savings. Analyzing a cross-country panel of macroeconomic data, we find that increased longevity raises aggregate savings rates in countries with universal pension coverage and retirement incentives, though the effect disappears in countries with pay-as-you-go systems and high replacement rates.     

Human Survival at Older Ages and the Implications for Longevity Bond Pricing

Abstract

Governments are concerned about the future of pension plans, for which increasing longevity is judged to be an important risk to their future viability. We focus on human survival at age 65, the starting age point for many pension products. Using a simple model, we link basic measures of life expectancy to the shape of the human survival function and consider its various forms. The model is then used as the basis for investigating actual survival in England and Wales. We find that life expectancy is increasing at a faster rate than at any time in history, with no evidence of this trend slowing or any upper age limit. With interest growing in the use of longevity bonds as a way to transfer longevity risks from pension providers to the capital markets, we seek to understand how longevity drift affects pension liabilities based on mortality rates at the point of annuitization, versus what actually happens as a cohort ages. The main findings are that longevity bonds are an effective hedge against longevity risk; however, it is not only the oldest old that are driving risk, but also more 65-year-olds reaching less extreme ages such as 80. In addition, we find that the possibility of future inflation and interest rates could be as an important a risk to annuities as longevity itself.     

How to prepare a life expectancy report for an attorney in a tort case

The purpose of this methodology article is to describe a suitable format for a legally acceptable report on the life expectancy of the principal in a tort case that is being advocated or defended by an attorney. Life insurance medical directors and underwriters are clearly skilled and experienced in mortality risk classification for life insurance. However, the judicial system is accustomed to measuring excess mortality only in terms of reduced life expectancy. The analyst preparing the report must convert the excess mortality into a figure for reduced life expectancy and compare this with the life expectancy of persons matched by age, sex and race in the latest Decennial US Life Tables. This process is different from the life insurance underwriting process. A life table projected to age 109 must be constructed as an essential part of the report, and the entire process must be presented clearly and convincingly. There are good reasons why the excess death rate (EDR) should be used as the index of excess mortality in constructing the life table, in preference to the mortality ratio (MR), which is used most of the time in life insurance risk classification. All of these considerations are discussed in this article, which is based on a sample of 40 cases handled by the author, a retired life insurance medical director.     

Estimation of future mortality rates and life expectancy in chronic medical conditions

Estimates of old-age mortality are necessary for the construction of life tables and computation of life expectancy, and are essential in the growing area of life insurance for the elderly. Two common assumptions are that either the excess death rate (EDR) or the relative risk (RR) stays constant with increasing age. It is known, however, that for most medical conditions the former underestimates the risk and the latter overestimates it. A third popular method is that of rating up: a subject is said to be "rated up k years" if his future mortality rates are assumed to be those of a person in the general population who is k years older. It is shown here that this method generally leads to gross overestimates of old-age mortality. We consider two less-commonly used models, log-linear declining relative risk (LDR) and constant proportional life expectancy (PLE), and compare them to the methods of constant EDR, constant RR and rating up. Although slightly more complicated to employ than the other methods, both LDR and PLE generally give better estimates of mortality and life expectancy. When mortality rates for chronic conditions are known within a certain age range, and estimates outside of the range are required, the LDR and PLE methods may be preferable to the more familiar methods of constant EDR, constant RR, or rating up.     

How long might the younger-old live: A predictive model

Life expectancy amongst older people in industrialised countries has been improving over an extended period and still continues to do so. This has ramifications for providers of services to this population, thus necessitating a level of forward planning. Predictive models of remaining life expectancy for older age groups can assist long-term planning processes. This paper presents an extrapolative approach to forecasting remaining life expectancy. Based on logistic modelling of historic mortality and survivorship for the “younger-old” male population of England and Wales over the period 1970-2005, a parsimonious two-parameter model is derived. This model provides a close correspondence to published period life table data. Trends in these parameters are then fitted and extrapolated to enable projections of life expectancy up to 40 years into the future. Alternative assumptions are used to determine a range of future life expectancy trajectories for a 65-year-old male. Occupational pension scheme provision is identified as an area of particular concern in the context of increasing longevity. As an illustration, the life expectancy trajectories are combined with differing discount rate assumptions to generate a number of alternative pension liability scenarios for the extrapolation period.     

The Lee-Carter Method for Forecasting Mortality,with Various Extensions and Applications

Abstract

In 1992, Lee and Carter published a new method for long-run forecasts of the level and age pattern of mortality, based on a combination of statistical time series methods and a simple approach to dealing with the age distribution of mortality. The method describes the log of a time series of age-specific death rates as the sum of an age-specific component that is independent of time and another component that is the product of a time-varying parameter reflecting the general level of mortality, and an age-specific component that represents how rapidly or slowly mortality at each age varies when the general level of mortality changes. This model is fit to historical data. The resulting estimate of the time-varying parameter is then modeled and forecast as a stochastic time series using standard methods. From this forecast of the general level of mortality, the actual age-specific rates are derived using the estimated age effects. The forecasts of the various life table functions have probability distributions, so probability intervals can be calculated for each variable and for summary measures such as life expectancy. The projected gain in life expectancy from 1989 to 1997 matches the actual gain very closely and is nearly twice the gain projected by the Social Security Administration’s Office of the Actuary. This paper describes the basic Lee-Carter method and discusses the forecasts to which it has led. It then discusses extensions, applications, and methodological improvements that have been made in recent years; considers shortcomings of the method; and briefly describes how it has been used as a component of more general stochastic population projections and stochastic forecasts of the finances of the U.S. Social Security system.     

Temporal Evolution of Mortality Indicators

Abstract

In Spain, as in other developed countries, significant changes in mortality patterns have occurred during the 20th and 21st centuries. One reflection of these changes is life expectancy, which has improved in this period, although the robustness of this indicator prevents these changes from being of the same order as those for the probability of death. If, moreover, we bear in mind that life expectancy offers no information as to whether this improvement is the same for different age groups, it is important and necessary to turn to other mortality indicators whose past and future evolution in Spain we are going to study. These indicators are applied to Spanish mortality data for the period 1981–2008, for the age range 0–99. To study its future evolution, the mortality ratios have to be projected using an adequate methodology, namely, the Lee-Carter model. Confidence intervals for these predictions can be calculated using the methodology that Lee and Carter apply in their original article for expected lifetime confidence intervals, but they take into account only the error in the prediction of the mortality index obtained from the ARIMA model adjusted to its temporal series, excluding other sources of error such as that introduced by estimations of the other parameters in the model. That is why bootstrap procedures are preferred, permitting the combination of all sources of uncertainty.     

Emergence of Supercentenarians in Low-Mortality Countries

Abstract

The exponential increase in the number of centenarians, which started just after World War II, is well documented in Europe and Japan. Much less is known about the population of extremely old persons reaching age 105—the semisupercentenarians—or age 110—the supercentenarians. The first cases of validated supercentenarians appeared in the 1960s, and their numbers have steadily increased since the mid-1980s. The current prevalence of known supercentenarians in low-mortality countries involved in the International Database on Longevity (IDL) is approximately 10 times higher than in the mid-1970s. In roughly 20 years, from 1980 to 2000, the maximum reported age at death, which was once assumed to indicate the maximum life span of the human species and seen as a stable characteristic of our species, has increased by about 10 years from 112 to 122 years. The annual probability of death at age 110 is about 50% and stays at that level through age 114. Our results strongly support the finding that mortality does not increase according to the Gompertz curve at the highest ages, and the results are consistent with a plateau between ages 110 and 115. The data after age 115 are so sparse that they are not analyzed here, but an earlier study suggested that mortality may fall after age 115. We intend to investigate this question in subsequent research.     

Modeling disease elimination

The effect of the elimination of mortality from heart disease and cancer was modelled mathematically to allow for the effect of other competing causes of death. The model allows for potential dependence between heart disease or cancer and other causes of death by using cupola functions, which analyse the individual risk itself and the dependence structure between causes of death by using correlation coefficients. As the strength of these risk associations is unknown, the study investigated both full positive and negative dependence and compared this with no dependence. Depending upon the degree and type of correlation assumed, positive or negative, the life expectancy at birth is increased by between 3 months and 6.5 years if cancer mortality was eliminated, and between 5 months and 7.5 years in the case of heart disease. In addition, estimates of these effects on life insurance premia can be made with the greatest reduction for women with the elimination of cancer mortality. These figures provide a range of improvements in life expectancy and the consequent effect on life insurance risk premium rates which elimination of either of these important diseases would produce.     

Diverging Mortality Inequality Trends among Young and Old in the Netherlands*

We analyse the trends in inequality in mortality across poverty groups at different ages over the period 1996–2016 in the Netherlands. In addition, we examine whether these trends are related to unequal changes in avoidable mortality, separated by preventable and treatable causes of death. We find that while inequalities in mortality have decreased at ages up to 65, inequalities increased for the oldest age groups. The decline in inequality at the younger ages can, to a large extent, be explained by a strong decrease of mortality from preventable and cardiovascular causes among the poor. The link between inequality and avoidable mortality at the oldest ages is less straightforward. The increasing inequality at old age might be the result of the inequalities shifting from the young to the older age groups, or of the rich benefiting more from the recent health (care) improvements than the poor.     

Versteilerung der alters- und geschlechtsspezifischen Ausgabenprofile von Krankenversicherern

It is well-known for a long time, that health care expenditure of elder people are a lot higher than expenditure of younger people, we call this correlation of average per-capita-expenditure and age expenditure profiles. If health care expenditures for the elderly grow faster than for younger people, the expenditure profiles become ?steeper“. Data of a German private health insurer are used to investigate the phenomenon growing steepness of profiles over a period of 18 years. In the article three instruments for measuring the phenomenon of growing steeper expenditure profiles are proposed. None of them is perfect, but the more or less common trend shows that the profiles of the investigated health insurance plans did grow steeper. The health plans of men do reflect this phenomenon clearer than those of women and the inpatient plans do show a stronger effect than the outpatient plans. Research of causes by data is not possible because of the given data structure. But neither the correlation between health expenditure and time til death nor the improving life expectancy can help to explain the phenomenon.     

Extreme Value Analysis of Mortality at the Oldest Ages: A Case Study Based on Individual Ages at Death

In this article, the force of mortality at the oldest ages is studied using the statistical tools from extreme value theory. A unique data basis recording all individual ages at death above 95 for extinct cohorts born in Belgium between 1886 and 1904 is used to illustrate the relevance of the proposed approach. No leveling off in the force of mortality at the oldest ages is found, and the analysis supports the existence of an upper limit to human lifetime for these cohorts. Therefore, assuming that the force of mortality becomes ultimately constant, that is, that the remaining lifetime tends to the Negative Exponential distribution as the attained age grows is a conservative strategy for managing life annuities.     

Do abnormal accruals affect the life expectancy of audit engagements?

We examine the cross-sectional determinants of audit engagement length, paying particular attention to abnormal accruals as a potential driver. We are interested in how the potentially incongruent incentives of managers and auditors can cause frictions, and in turn affect the audit engagement’s life expectancy. We estimate a hazard model in the form of a multi-period logit model, allowing us to estimate (the inverse of) the life expectancy of audit engagements. We find that audit engagement life expectancy at any age decreases when firms make relatively large positive or large negative abnormal accruals. One interpretation of these results is that large positive (negative) abnormal accruals make the auditor (client) more likely to terminate the engagement. Conversely, smaller abnormal accruals reflect a compromise which extends the life of the engagement. Our results are robust to several alternative specifications and controls. However, because there is no complete theoretical model that explains audit engagement length, our results should be interpreted with caution.     

The Cost of Firearm Deaths in the United States: Reduced Life Expectancies and Increased Insurance Costs

The United States remains far behind most other affluent countries in terms of life expectancy. One of the possible causes of this life expectancy gap is the widespread availability of firearms and the resulting high number of U.S. firearm fatalities: 10,801 homicides in 2000. The European Union experienced 1,260 homicides, Japan only 22. Using multiple decrement techniques, I show that firearm violence shortens the life of an average American by 104 days (151 days for white males, 362 days for black males). Among all fatal injuries, only motor vehicle accidents have a stronger effect. I estimate that the elimination of all firearm deaths in the United States would increase the male life expectancy more than the total eradication of all colon and prostate cancers. My results suggest that the insurance premium increases paid by Americans as a result of firearm violence are probably of the same order of magnitude as the total medical costs due to gunshots or the increased cost of administering the criminal justice system due to gun crime.     

Natural Exchange Rate and Its Implications for the Purchasing Power Parity Puzzle

The notion of purchasing power parity has been an important building block in the theory of nominal and real exchange rates and for many theoretic models in international economics, leading to the purchasing power parity puzzle. The central issue of the puzzle is how to reconcile volatile short-term movements of real exchange rates (defined as nominal exchange rates adjusted for differences in national price levels) with very slow convergence to the parity condition. The main emphasis of this article is to show that the slow adjustment of the natural exchange rate is responsible for the well-known slow convergence of the real exchange rate to the long-run parity condition. The novel element of this article is to identify the relative importance between the financial channel and output gap channel of the purchasing power parity puzzle. The empirical findings of this article suggest that the financial channel is a dominant factor to explain persistent deviations of the real exchange rate from its long-run level.