Life lived equals life left in stationary populations

The average age of the individuals in a population is equal to the average remaining life expectancy when the population is stationary.

How Late Can First Births Be Postponed? Some Illustrative Population-level Calculations

I shift, stretch, and transform the observed cohort age-schedule of first birth for Danish women born in 1963 to see how late the mean age at first birth could plausibly shift. Constraints of two kinds are placed on the ultimate distribution of first births. First, no more than one-third of first births can occur after age 35. This constraint allows postponement without radical changes in childlessness or parity distribution. Second, I preserve some variability in the age at first birth by keeping the standard deviation of first birth above 4 years, the minimum value observed for Denmark during the baby boom years. Under these constraints, I find that mean ages at first birth of at least 33 years are plausible. This would represent a further increase of about 4 years in the mean age at first birth seen in recent periods. I conclude that the depressed levels of fertility seen due to postponement could continue for decades before limits are reached.

Formal Relationships: Introduction and Orientation

In 2009, Demographic Research will be publishing short reports on mathematical relationships in formal demography in a new Special Collection called "Formal Relationships". This first publication outlines the goals and procedures for publications in the collection. The guest editors of the collection are Joshua R. Goldstein and James W. Vaupel.

How slowing senescence changes life expectancy

Mortality decline has historically been a result of reductions in the level of mortality at all ages. The slope of mortality increase with age has been remarkably stable. A number of leading researchers on aging, however, suggest that the next revolution of longevity increase will be the result of slowing down the rate of aging, lessening the rate at which mortality increases as we get older. In this paper, we show mathematically how varying the pace of senescence influences life expectancy. We provide a formula that holds for any baseline hazard function. Our result is analogous to Keyfitz's "entropy" relationship for changing the level of mortality. Interestingly, the influence of the shape of the baseline schedule on the effect of senescence changes is the complement of that found for level changes. We also provide a generalized formulation that mixes level and slope effects.

Cohort postponement and period measures

We introduce a new class of models in which demographic behavior such as fertility is postponed by differing amounts depending only on cohort membership. We show how this model fits into a general framework of period and cohort postponement that includes the existing models in the literature, notably those of Bongaarts and Feeney and Kohler and Philipov. The cohort-based model shows the effects of cohort shifts on period fertility measures and provides an accompanying tempo-adjusted measure of period total fertility in the absence of observed shifts. Simulation reveals that when postponement is governed by cohorts, the cohort-based indicator outperforms the Bongaarts and Feeney model that is now in widespread use. The cohort-based model is applied to fertility in several modern populations.

East Germany overtakes West Germany: recent trends in order-specific fertility dynamics

Some 20 years after unification, the contrast between East and West Germany provides a unique natural experiment for studying the persistence of communist-era family patterns, the effects of economic change, and the complexities of the process of fertility postponement. After unification, fertility rates plummeted in the former East Germany to record low levels. The number of births per year fell 60 percent. The period total fertility rate (TFR) reached a low of 0.8. Since the middle of the 1990s, however, period fertility rates have been rising in East Germany, in contrast to the nearly constant rates seen in the West. By 2008, the TFR of East Germany had overtaken that of the West. In this paper, we explore why fertility in the East is higher than in West Germany, despite the severe economic situation in the East, whether the East German TFR will increase even further in the future, and whether the West German rate will remain at the constantly low level that has prevailed since the 1970s. This article seeks to shed some light on these questions by (a) giving an account of the persisting East-West differences in attitudes towards and constraints on childbearing, (b) conducting an order-specific fertility analysis of recent fertility trends, and (c) projecting completed fertility for the recent East and West German cohorts. In addition to using the Human Fertility Database, we draw upon Perinatal Statistics, which enable us to conduct an order-specific fertility analysis. This new data source allows us to calculate a tempo-corrected TFR for East and West Germany, which has not been available previously.Germany, fertility

Probabilistic forecasting using stochastic diffusion models, with applications to cohort processes of marriage and fertility

We study prediction and error propagation in Hernes, Gompertz, and logistic models for innovation diffusion. We develop a unifying framework in which the models are linearized with respect to cohort age and predictions are derived from the underlying linear process. We develop and compare methods for deriving the predictions and show how Monte Carlo simulation can be used to estimate prediction uncertainty for a wide class of underlying linear processes. For an important special case, random walk with, we develop an analytic prediction variance estimator. Both the Monte Carlo method and the analytic variance estimator allow the forecasters to make precise the level of within-model prediction uncertainty in innovation diffusion models. Empirical applications to first births, first marriages and cumulative fertility illustrate the usefulness of these methods.

Culture revisited: a geographic analysis of fertility decline in Prussia

In this paper, we re-introduce geography into the analysis of fertility decline in the first demographic transition in Europe. We reanalyze Galloway et al.'s (1994) Prussian data, fitting structural models similar to those of Galloway et al. to the data and to map the residuals. Our findings give evidence both of the predictive effect of economic as well as cultural variables. However, although testing different non-spatial model specifications, a significant unexplained geographic clustering of fertility decline always remains. Indeed, adjacency to an area of large fertility decline and location along communication and transport corridors seem to be important predictors of fertility decline beyond what one would expect from structural models. This gives support to the cultural diffusion hypothesis of the Princeton European Fertility Project.German Empire, culture, diffusion of innovations, economics, fertility decline, spatial analysis

An editorial on plagiarism

In January this year, we were confronted with a case of plagiarism. One paper that had been submitted last year by a certain person turned out to be written by three other persons. It was presented by the three true authors at a conference in 2010, where they distributed copies of their paper. One of the reviewers of the paper informed us about that fact. We asked the three authors for a copy, which turned out to be identical with the submission, except for a few minor details. When confronted with these facts, the person who had submitted the paper was unable to give us a satisfactory explanation. This is a case of serious scientific misconduct. The editors and the publisher of Demographic Research cannot and will not accept any form of plagiarism. Nor will we accept any other form of misconduct in science, including fabrication, falsification, or other practices that seriously deviate from those that are commonly accepted within the scientific community for proposing, conducting, or reporting research. With Long et al. ("Responding to possible plagiarism", Science 6 March 2009), we are of the opinion that the responsibility for research integrity ultimately lies in the hands of the scientific community: educators, students, authors, and those who provide peer reviews. Journal editors must take appropriate action and verify the originality of suspected manuscripts. The Office of Research Integrity provides useful guidelines (http://ori.dhhs.gov/). We have decided that any future submission to Demographic Research that lists the plagiarist as an author or co-author will be rejected automatically.