Ronald Lee

Modeling and Forecasting U.S. Mortality

Abstract Time series methods are used to make long-run forecasts, with confidence intervals, of age-specific mortality in the United States from 1990 to 2065. First, the logs of the age-specific death rates are modeled as a linear function of an unobserved period-specific intensity index, with parameters depending on age. This model is fit to the matrix of U.S. death rates, 1933 to 1987, using the singular value decomposition (SVD) method; it accounts for almost all the variance over time in age-specific death rates as a group. Whereas e 0 has risen at a decreasing rate over the century and has decreasing variability, k(t) declines at a roughly constant rate and has roughly constant variability, facilitating forecasting. k(t), which indexes the intensity of mortality, is next modeled as a time series (specifically, a random walk with drift) and forecast. The method performs very well on within-sample forecasts, and the forecasts are insensitive to reductions in the length of the base period from 90 to 30 ...

The Demographic Transition: Three Centuries of Fundamental Change

Before the start of the demographic transition, life was short, births were many, growth was slow and the population was young. During the transition, e rst mortality and then fertility declined, causing population growth rates e rst to accelerate and then to slow again, moving toward low fertility, long life and an old population. The transition began around 1800 with declining mortality in Europe. It has now spread to all parts of the world and is projected to be completed by 2100. This global demographic transition has brought momentous changes, reshaping the economic and demographic life cycles of individuals and restructuring populations. Since 1800, global population size has already increased by a factor of six and by 2100 will have risen by a factor of ten. There will then be 50 times as many elderly, but only e ve times as many children; thus, the ratio of elders to children will have risen by a factor of ten. The length of life, which has already more than doubled, will have tripled, while births per woman will have dropped from six to two. In 1800, women spent about 70 percent of their adult years bearing and rearing young children, but that fraction has decreased in many parts of the world to only about 14 percent, due to lower fertility and longer life. 1 These changes are sketched in Table 1. These trends raise many questions and controversies. Did population grow so

Evaluating the Performance of the Lee-Carter Method for Forecasting Mortality

Lee and Carter (LC) published a new statistical method for forecasting mortality in 1992. This paper examines its actual and hypothetical forecast errors, and compares them with Social Security forecast errors. Hypothetical historical projections suggest that LC tended to underproject gains, but by less than did Social Security. True e0 was within the ex ante 95% probability interval 97% of the time overall, but intervals were too broad up to 40 years and too narrow after 50 years. Projections to 1998 made after 1945 always contain errors of less than two years. Hypothetical projections for France, Sweden, Japan, and Canada would have done well. Changing age patterns of mortality decline over the century pose problems for the method.

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.

Rethinking the evolutionary theory of aging: Transfers, not births, shape senescence in social species

The classic evolutionary theory of aging explains why mortality rises with age: as individuals grow older, less lifetime fertility remains, so continued survival contributes less to reproductive fitness. However, successful reproduction often involves intergenerational transfers as well as fertility. In the formal theory offered here, age-specific selective pressure on mortality depends on a weighted average of remaining fertility (the classic effect) and remaining intergenerational transfers to be made to others. For species at the optimal quantity–investment tradeoff for offspring, only the transfer effect shapes mortality, explaining postreproductive survival and why juvenile mortality declines with age. It also explains the evolution of lower fertility, longer life, and increased investments in offspring.

Coherent mortality forecasts for a group of populations: An extension of the lee-carter method

Mortality patterns and trajectories in closely related populations are likely to be similar in some respects, and differences are unlikely to increase in the long run. It should therefore be possible to improve the mortality forecasts for individual countries by taking into account the patterns in a larger group. Using the Human Mortality Database, we apply the Lee-Carter model to a group of populations, allowing each its own age pattern and level of mortality but imposing shared rates of change by age. Our forecasts also allow divergent patterns to continue for a while before tapering off. We forecast greater longevity gains for the United States and lesser ones for Japan relative to separate forecasts.

FACTORS REGULATING THE BIOSYNTHESIS OF VARIOUS PROSTAGLANDINS

the Karolinska Institute working in collaboration with Professor B. Samuelsson. At that time we were able to develop thin-layer techniques which allowed quantitative measurement of the many different products appearing during prostaglandin biosynthesis. This led to the identification of the unusual pros t ag land in , l l -ke to -PGFl , , f rom reaction mixtures(Granstr8m et a1,1968),and a recognition that the oxidative cyclization most probably occurs after the liberation of the essential acid(Lands & Samuelsson,l968),by action of an acylhydrolase. Last year I began again to use those methods to examine in more detail the regulation of prostaglandin biosynthesis. A useful review of the factors in the biosynthesis of prostaglandins recognized up to that point was provided by Samuelsson in that years Progress of Biochemical Pharmacology(Samuelsson,l969).

Fertility, Human Capital, and Economic Growth over the Demographic Transition

Do low fertility and population aging lead to economic decline if couples have fewer children, but invest more in each child? By addressing this question, this article extends previous work in which the authors show that population aging leads to an increased demand for wealth that can, under some conditions, lead to increased capital per worker and higher per capita consumption. This article is based on an overlapping generations (OLG) model which highlights the quantity–quality tradeoff and the links between human capital investment and economic growth. It incorporates new national level estimates of human capital investment produced by the National Transfer Accounts project. Simulation analysis is employed to show that, even in the absence of the capital dilution effect, low fertility leads to higher per capita consumption through human capital accumulation, given plausible model parameters.RésuméLes basses fécondités et le veillissement de la population conduisent-ils au déclin économique si les couples ont moins d’enfants, mais investissent plus dans chaque enfant? La présente étude explore cette question, dans le prolongement d’un travail antérieur des auteurs, dans lequel ils avaient établi que le vieillissement des populations suscite une demande accrue de richesse qui peut, sous certaines conditions, entraîner un accroissement du capital par travailleur et une consommation par habitant plus élevée. La méthode employée est basée sur une modèle à générations imbriquées qui met en évidence le compromis entre quantité et qualité et les liens entre investissement en capital humain et croissance économique. L’analyse intègre de nouvelles estimations nationales de l’investissement en capital humain produites par le National Transfer Accounts Project (projet des comptes de transfert nationaux). Une simulation permet de montrer que, même en l’absence d’effet de dilution du capital, une basse fécondité conduit à une consommation par habitant plus élevée à travers une accumulation de capital humain, avec des paramètres de modélisation plausibles.

The Outlook for Population Growth

Projections of population size, growth rates, and age distribution, although extending to distant horizons, shape policies today for the economy, environment, and government programs such as public pensions and health care. The projections can lead to costly policy adjustments, which in turn can cause political and economic turmoil. The United Nations projects global population to grow from about 7 billion today to 9.3 billion in 2050 and 10.1 billion in 2100, while the Old Age Dependency Ratio doubles by 2050 and triples by 2100. How are such population projections made, and how certain can we be about the trends they foresee?

Population dynamics of humans and other animals

Human population dynamics, at least until the past century, have probably been governed by homeostasis and in this resembled those of other animals. Because human population homeostasis was probably substantially weaker than among large mammals, its operation has been less obvious. Nonetheless, the empirical evidence for advanced agriculturalists is compelling. Unlike animals, the human population has tended toward equilibria that have been tending upward at an accelerating rate. The acceleration might reflect long-run positive feedback between density and technological progress, as Boserup has suggested. Because homeostasis was weak, its role in shorter run historical explantation is limited; its force was gentle and easily overwhelmed by other particular influences. Malthusian oscillation, in the sense of distinctive medium-run dynamics arising from homeostasis, probably did not occur. And because homeostasis was weak, density dependence can in principle explain only a minute proportion of the annual variation in population growth rates. Yet homeostasis plays an essential role in demographic theory. Without it, we are incapable of explaining population size and change over time except by recounting a mindless chronology of events back to the beginning of humanity--whenever that was. Without it, we cannot explain the response of population growth to economic growth. Without it, we cannot explain recovery from catastrophe or the rapid natural increase in many frontier regions. Without it, we cannot properly analyze the influence of climatic variation and other partially density-independent factors. Our basic understanding of human history requires a grasp of what homeostasis can explain and what it cannot. A homeostatic approach to population dynamics also leads to questions about the roles of reproductive norms and institutions, not just whether they encourage high or low fertility, but whether they make natural increase responsive to resource abundance. And if they do, whether they strike the balance of population and the means of subsistence at a relatively prosperous or impoverished level. Such considerations may contribute to an understanding of broad preindustrial differences among the regions of the world in densities, average levels of vital rates, and living standards--which was very much how Malthus viewed the matter. Ordinary homeostatic tendencies essentially vanish in the course of economic development, and they were probably all but gone from much of Europe by the end of the 19th century.(ABSTRACT TRUNCATED AT 400 WORDS)