Populations with constant immigration

"We consider a Leslie-type model of a one-sex (female) population of natives with constant immigration. The fertility and mortality schedule of the natives may be below or above replacement level. Immigrants retain their fertility and mortality, their children adopt the fertility and mortality of the natives. It is shown how this model may be written in a homogeneous form (without additive term) with a Leslie-type matrix. Reproductive values of individuals in each age group are discussed in terms of a left eigenvector of this matrix. The homogeneous form of our projection model permits the transformation into a Markov chain with transient and recurrent states. The Markov chain is the basis for the definition of genealogies, which incorporate immigration. It is shown that genealogies describe the life histories of individuals in a population with immigration. We calculate absorption times of the Markov chain and relate them to genealogies. This extends the theory originally designed for closed populations to populations with immigration." (SUMMARY IN FRE)     

How responsive is U.S. population growth to immigration? A situational sensitivity analysis

There has been public concern about the effect of immigration on population growth in the U.S. But how responsive is population growth to immigration? This paper examines the sensitivity of intrinsic population growth to immigration and situates such sensitivity in fertility and survival changes. The application of second derivatives on a modified Leslie matrix facilitates the analysis of situational sensitivity of U.S. population growth to immigration. The results show that the sensitivity to immigration is not as influential as the sensitivity to fertility, and that the sensitivity to immigration further depends on changes in fertility and survival.     

人口预测的随机方法:基于Leslie矩阵和ARMA模型

本文探讨了人口预测的一种随机方法。文章回顾了经典的Leslie矩阵并结合中国的人口统计数据,用时间序列的ARMA模型对未来的生育率、死亡率进行估计,并由此构造Les-lie矩阵,经时间序列的数据中心化,根据自相关函数、偏自相关函数的截尾性或拖尾性,以及贝叶斯信息准则函数方法对模型定阶,实现对ARMA模型的识别。在中国人口预测方面的应用证明,基于Leslie矩阵和ARMA模型的人口随机预测方法是稳健的,具有很强的适用性。由于统计数据可获得性的局限,对模型做了不少假设和近似。随着人口数据的积累,未来将会在此方面有所改进。     

The multistate stable population model with immigration

This paper outlines the discrete‐time and continuous‐time formulations of the stable population model with immigration, showing their commonality. It then illustrates how the model can be extended to include multiple interacting populations, and goes on to consider a multistate version of reproductive value that further illuminates the evolutionary dynamics of an “open”; model of multistate population growth and redistribution. Attention is restricted to results arising from a fertility regime that is below replacement level.     

Population growth with variable family size

The Sharpe‐Lotka continuous time deterministic model of population growth is developed to take account of some possible forms of mother‐daughter fertility association, characterised here by a bivariable measure, A. This leads to a linear double integral equation for which, subject to certain conditions, a finite time solution can be found by Laplace transform methods and thus also model specific results relating the intergenerational fertility effect to the long term population growth rate and magnitude are established. The quantitative implications of the theory are illustrated by a consideration of a general bilinear form of A and in this context numerical results illustrating the finite time growth and also the long term distribution of fertility levels in the stable female population are obtained. In particular, it is shown that different fertility specific subpopulations can coexist indefinitely.     

Compensating changes in fertility and mortality

This paper illustrates a method of studying changes in vital rate schedules which have no effect on the intrinsic rate of population growth. These changes are described as compensating changes in fertility and mortality. The analysis proceeds from the discrete perspective of Leslie matrices, wherein the central idea is to establish the set of all compensating changes by identifying that class of Leslie matrices which possess the same positive eigenvalue, λ₁. A root-squaring technique is adapted for the purpose of estimating λ₁. Finally, a variety of compensating fertility and mortality changes is illustrated using data from Japan.     

The Census Bureau on Prospects for US Population Growth in the Twenty‐First Century

The U.S. Census Bureau periodically releases projections of the US resident population, detailed by age, sex, race, and Hispanic origin. The most recent of these, issued 13 January 2000, for the first time extend to the year 2100 and also include information on the foreign‐bom population. (Earlier projections were carried up to 2080.) The extensive tabulations presenting the new set, and detailed explanation of the methodology and the assumptions underlying the projections, are accessible at the Census Bureau's web site: http://www.census.gov . A brief summary of some of the main results of these projections is reproduced below from United States Department of Commerce News, Washington, DC 20230. (The Census Bureau is an agency of the Department of Commerce.) Uncertainties as to future trends in fertility, mortality, and net migration over a period of some 100 years are very great, as is illustrated by the massive difference in the projected size of the population for 2100 in the three variants produced. The “middle” projected population figure of 571 million (which represents a growth of some 109 percent over its current level) is bracketed by “lowest” and “highest” alternative projections of 283 million and 1.18 billion, respectively. With somewhat lesser force, the point also applies to the 50‐year time span considered in the well‐known country‐by‐country projections of the United Nations. These projections are also detailed in three variants: low, middle, and high. The UN projections (last revised in 1998) envisage less rapid growth in the United States during the first part of the twenty‐first century than do the Census Bureau's. The projected population figures for 2050 in the three variants (low, middle, and high) are as follows (in millions):

Immigration and the stable population model

This paper reports on work aimed at extending stable population theory to include immigration. Its central finding is that, as long as fertility is below replacement, a constant number and age distribution of immigrants (with fixed fertility and mortality schedules) lead to a stationary population. Neither the level of the net reproduction rate nor the size of the annual immigration affects this conclusion; a stationary population eventually emerges. How this stationary population is created is studied, as is the generational distribution of the constant annual stream of births and of the total population. It is also shown that immigrants and their early descendants may have fertility well above replacement (as long as later generations adopt and maintain fertility below replacement), and the outcome will still be a long-run stationary population.     

On the distribution of completed parities when fertility is heritable

Over the last one hundred years, there has been, in many developed countries, a demographic convergence towards the two child family. The possible implications for population growth of such a tendency are considered in this paper in terms of both family limitation and also the intergenerational transmission of fertility. These two effects interact so that as the proportion of two‐child families increases, the possible influence of mother‐daughter fertility associations on population growth decreases, though even now it could override otherwise significant changes in either or both of the birth and death intensities. In particular, it is shown that according as to how fertility is transmitted through generations, it is still possible to have zero growth rates consistently with a widely dispersed stable distribution of family size as well as a typical mortality regime.     

The Future Composition of the Canadian Labor Force: A Microsimulation Projection

This article charts the future transformations of the Canadian labor force population using a microsimulation projection model. The model takes into account differentials in demographic behavior and labor force participation of individuals according to their ethnocultural and educational characteristics. As a result of a rapid fall in fertility, the Canadian population is expected to age rapidly as baby boomers start to retire from the labor market in large numbers. In response to declining fertility, Canada raised its immigration intake at the end of the 1980s, and immigration is now the main driver of Canadian population growth. At the same time, immigrants to Canada are becoming more culturally diversified. Over the last half century, the main source regions have shifted from Europe to Asia. Results of the microsimulation show that Canada's labor force population will continue to increase, but at a slower rate than in the recent past. By 2031, almost one third of the country's total labor force could be foreign‐born, and almost all its future increase is expected to be among university graduates, while the less‐educated labor force is projected to decline.     

Long‐Term Contribution of Immigration to Population Renewal in Canada: A Simulation

We analyze the direct and indirect demographic contribution of immigration to the foreign‐origin composition of the Canadian population according to various projection scenarios over a century, from 2006 to 2106. More specifically, we use Statistics Canada's Demosim microsimulation model to assess the long‐term sensitivity to immigration levels and the frequency of mixed unions of the share of immigrants in Canada and of persons who have at least one ancestor who arrived after 2006. The results of the simulations show that the population renewal process through immigration happens at a fast pace in a high immigration and low fertility country such as Canada. Under the scenarios developed, immigrants who entered after 2006 and their descendants could form the majority of the population by 2058 at the earliest and by 2079 at the latest and could represent between 62 percent and 88 percent in 2106. They also show that mixed unions are a key element of the speed at which the changes are likely to occur in the long run.     

Statistical modeling of selected aspects of the childbearing process with application to world fertility survey countries∗

The childbearing process should be monitored in developing countries experiencing high population growth rates and high levels of maternal and infant mortality. A mathematical model for estimation of certain aspects of the childbearing process, which requires only data on age‐specific fertility rates, is developed. Synthetic maternal childbearing indices, namely, mean ages at first and last birth, length of reproductive life span, inter‐birth spacing, and proportion of childless women, in addition to the well‐known mean age at childbearing, for the WFS countries are obtained using the proposed model. The indices are free from age truncation effects, and, under certain assumptions, provide information about a cohort's completed fertility before the women stop reproducing. The effects of women's residence and education on fertility are also examined.     

Population dynamics in Germany: the role of immigration and population momentum

The effects of changes in rates of mortality, fertility, and migration depend not only on the age-specific patterns and levels of these rates, but on the age structure of the population. In order to remove the influences of the age structure and concentrate on the effects of the demographic rates themselves, a common practice is to analyze the influences of the rates for a standard age structure. This paper analyzes current and future population changes in Germany, using a stationary population equivalent model (SPE) that shows long-term effects of current fertility, mortality, and international migration patterns. Results indicate that the German population will eventually decline because of below replacement fertility, if net immigration does not counteract this decrease. This means, for instance, that the long-term stationary population levels for Germany will decrease by approximately 6.5 million during a decade in which current fertility, mortality, and international migration levels prevail. The paper also reports how various other assumptions for mortality, fertility, and international migration affect the SPE model for Germany.     

Leslie matrix models

A review of the Leslie matrix model theory and its literature 1941–1987 is presented. The point of view is that of a mathematician who focuses on the parts of the theory which are relevant to demography. Works of a decidedly applied nature are not dealt with.     

Turbulent dynamics in a Xviith century population

A reconstruction of the population of the Pays de Caux (1589–1700) yields the time series of a fertility behavior indicator, the overall Coale index If. In spite of the noisy appearance of its evolution, the trajectory of If looks ordered, as if it were confined alternatively to two given zones, looping in each of them for a while, then suddenly jumping from the low one to the higher one, or slowly whirling down from the high to the low one.

An attempt is made to explain this general temporal structure by using a simulation model based on the autoregulation model (the so‐called European Marriage Pattern), putting into play a choice of the spouse function, a fertility function, modalities of marriage and remarriage, under the environmental forcing of the reconstructed mortality conditions.

The correspondence between reconstruction and simulation turns out to be quite good, not only for the population size or the Coale index, but also for the marriage series, quite independently of the reconstructioa

A second simulation with simulated mortality conditions shows a bifurcation point: as the mean frequency of crisis increases, the state of the system leaves the lower level and concentrates more and more in the higher level.

Thus, not only does the autoregulator model appear validated by empirical data, but its bi‐modal structure is revealed, depicting the dynamic response of a traditional community both to the environment and to the endogeneous demographic process.     

Should the US have locked heaven��s door?

This paper examines the economic impact of the second great immigration wave (1945–2000) on the US economy. Our analysis relies on a computable general equilibrium model combining the major interactions between immigrants and natives (labor market impact, fiscal impact, capital deepening, endogenous education, endogenous inequality). Contrary to recent studies, we show that immigration induced important net gains and small redistributive effects among natives. According to our simulations, the postwar US immigration is beneficial for all natives cohorts and all skill groups. Nevertheless, the gains would have been larger if the US had conducted a more selective immigration policy.     

Stochastic Population Forecasting Based on Combinations of Expert Evaluations Within the Bayesian Paradigm

This article suggests a procedure to derive stochastic population forecasts adopting an expert-based approach. As in previous work by Billari et al. (2012), experts are required to provide evaluations, in the form of conditional and unconditional scenarios, on summary indicators of the demographic components determining the population evolution: that is, fertility, mortality, and migration. Here, two main purposes are pursued. First, the demographic components are allowed to have some kind of dependence. Second, as a result of the existence of a body of shared information, possible correlations among experts are taken into account. In both cases, the dependence structure is not imposed by the researcher but rather is indirectly derived through the scenarios elicited from the experts. To address these issues, the method is based on a mixture model, within the so-called Supra-Bayesian approach, according to which expert evaluations are treated as data. The derived posterior distribution for the demographic indicators of interest is used as forecasting distribution, and a Markov chain Monte Carlo algorithm is designed to approximate this posterior. This article provides the questionnaire designed by the authors to collect expert opinions. Finally, an application to the forecast of the Italian population from 2010 to 2065 is proposed.     

The effect of variability in the fertility schedule on numbers of kin

The kinship formulas developed by Goodman, Keyfitz, and Pullum (1974) are extended to encompass populations in which fertility varies among women. An expression is derived to determine the amount by which the number of sisters in a heterogeneous population exceeds that in a population with homogeneous fertility. This expression, which is a function of the variance in the gross reproduction rate of the population, can readily be applied to numbers of other kin, such as aunts and cousins. Several trial calculations indicate that calculations of average numbers of sisters based on an assumption of uniform fertility could result in an underestimate of about 13 percent.     

An Italian Statement on International Migration

Increasing realization of the implications of persisting below‐replacement fertility in Europe—shrinking absolute numbers combined with a rising proportion of the elderly—is giving new salience to policy considerations regarding immigration in the countries most affected by low fertility. The recent United Nations report on “replacement migration” (see the Documents section in the June 2000 PDR) highlighted the issue through illustrative calculations showing the size of immigrant streams that would be needed for achieving specified demographic targets in selected lowfertility countries, given continuation of present fertility and mortality trends. For example, the UN report suggested that in Italy—which has one of the lowest fertility rates in the world—maintaining a constant population over time would require a net influx of some 12.6 million immigrants during the next 50 years, and maintaining a constant labor forceage population (ages 15–64) would require a net inflow of 18.6 million. Yet immigration policy in Western Europe has become increasingly restrictive during the last quartercentury, and the official policy stance that regulating immigration is strictly within the domain of a country's sovereign right has been assiduously maintained. (International treaty obligations qualify that right in the case of bona fide asylum seekers; however, the definition of that category is also subject to the discretion of the receiving countries.) Thus, although within the European Union national borders are open to EU citizens, the power of regulating immigration from outside the EU is retained by the individual countries rather than subject to EU‐wide decisions. Suggestions coming from the developing countries to follow up the 1994 International Conference on Population and Development with an intergovernmental conference on international migration and development were set aside by the potential immigrant‐receiving countries as overly contentious. A statement by the Minister of Foreign Affairs of Italy, Lamberto Dini, delivered at the 55th General Assembly of the United Nations, 13 September 2000, may be a sign of a notable shift in official approaches to immigration policy by at least one EU member state. The statement, in a departure from the practice of touching lightly upon a wide range of issues in international affairs, typical in high‐level ministerial speeches given at that UN forum, is devoted essentially to a single topic: international migration. It characterizes migration “between or within continents” as an international problem and advocates “coordinated and integrated” instruments in seeking a solution. It suggests that “today, with a declining birth rate and an aging population, Europe needs a strategy that embraces the complex process of integrating people from different regions of the world.” The rules for international migration, the statement claims, should be set in a global framework, such as provided by the United Nations. In the “age of globalization,”“a solidarity pact is needed to find the best and most effective way of balancing the supply and demand of labor.” With the omission of opening and closing ceremonial passages and a brief comment on the problem of debt relief, the statement is reproduced below.     

Sweden faces zero population growth

In this discussion of Sweden as it approaches zero population growth, focus is on the following: population growth in perspective, fertility trends (childbearing concentrated and cohort versus period fertility), marital status (non-marital cohabitation, out-of-wedlock births, and divorce), women's changing status (increasing education and increasing employment), constraints and supports for women's dual role (family allowances and housing), birth control (contraceptive methods and practice and abortion), mortality trends, changing age structure and the elderly (average population age and proportion of elderly and cost of elderly support), international migration (from emigration to immigration and demographic impact of immigration), immigration policy, recent population debate (immigration issues and facing zero population growth). Since 1900 the primary features of Sweden's demographic history are a continuing decline in the birth rate to very low levels -- relieved by some upward movement in the 1940s and 1960s -- and a marked shift in the migration balance from emigration to immigration. It is almost entirely because of immigration that Sweden's population growth rate has not yet turned negative. If Swedish women were to continue to bear children at the rate that all women in the reproductive ages actually did in 1978, each women would end up with an average well below the level necessary to exactly replace each adult in the population leaving migration out, an annual total fertility rate of 2.1 children per woman would have to be sustained for births and deaths to be in balance under the low mortality conditions prevaling in Sweden.