3
The Face of the U.S. Population in 2050

How will the population of the United States change on the way to the middle of the 21st century? How will immigration—current and future—contribute to that change? This chapter seeks to answer the second question, which in turn will help answer the first. It focuses on the characteristics of immigrants and their descendants and explores how they will change the demography of the United States over the next six decades.

Immigration is not the only force at work shaping the size and the structure of the United States in the coming years. It will interact with other demographic forces, already in place, that also play a large role in what the country will look like by the middle of the next century.

First, in the two decades following World War II, the baby-boom greatly increased the annual rate of U.S. population growth and provided birth cohorts from 1946 to about 1963 that were much larger than those of either the decade before or after. The baby-boom and the subsequent baby-bust will have major ramifications over the next half century: the population will age as the baby-boom generations become older; when they eventually retire, the number of retirees will be much larger than this country has ever seen.

Second, the future level of mortality among the elderly will have fundamental implications for their numbers. These changes, in turn, will affect their demand for private and public pensions and for health services. Because the small baby-bust generations will be the workers at that time, a relatively few income-producing residents will be providing for the older generations.

Finally, volatility in the volume and composition of immigration affects the U.S. population across many dimensions: its size and rate of growth, its age and sex composition, and its racial and ethnic makeup. In the future, a major source



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--> 3 The Face of the U.S. Population in 2050 How will the population of the United States change on the way to the middle of the 21st century? How will immigration—current and future—contribute to that change? This chapter seeks to answer the second question, which in turn will help answer the first. It focuses on the characteristics of immigrants and their descendants and explores how they will change the demography of the United States over the next six decades. Immigration is not the only force at work shaping the size and the structure of the United States in the coming years. It will interact with other demographic forces, already in place, that also play a large role in what the country will look like by the middle of the next century. First, in the two decades following World War II, the baby-boom greatly increased the annual rate of U.S. population growth and provided birth cohorts from 1946 to about 1963 that were much larger than those of either the decade before or after. The baby-boom and the subsequent baby-bust will have major ramifications over the next half century: the population will age as the baby-boom generations become older; when they eventually retire, the number of retirees will be much larger than this country has ever seen. Second, the future level of mortality among the elderly will have fundamental implications for their numbers. These changes, in turn, will affect their demand for private and public pensions and for health services. Because the small baby-bust generations will be the workers at that time, a relatively few income-producing residents will be providing for the older generations. Finally, volatility in the volume and composition of immigration affects the U.S. population across many dimensions: its size and rate of growth, its age and sex composition, and its racial and ethnic makeup. In the future, a major source

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--> of variation in population change may lie in the volume and characteristics of immigration. Population change inevitably has broad social and economic implications. Changes in the age composition of the population affect school enrollments and policies. The number and educational levels of the population in the early and middle adult years are critical for the future labor force and its productivity. And the numbers of elderly and how healthy they are become major determinants of pension needs and the health care system. Population change may also produce ripples across many other critical aspects of American life, in the needs for housing, the crime rate, savings, and voting. Immigration has consequences for all these aspects of population change. In its relatively large flows and wide variety, immigration as the United States experiences it adds both to the numbers of people in the nation and to their diversity. Immigration works its longer-term effects through other dimensions as well. First, not every group of immigrants into the United States bears children at the same rate. Immigrant groups with persistently high fertility rates will grow over time, absolutely and in relation to other immigrant groups. Second, not every group of immigrants has the same life span—that is, their mortality rates differ; these, too, may change over time and thus shift in their relation to one another. If immigrants have a higher fertility rate than does the resident population, the nation will grow younger on average. And if immigrants have a higher mortality rate—that is, if they die at an earlier age—that trend will be reinforced. Again, the differences among groups of immigrants also matter, and so do the shifts within-groups and between groups as the generations unfold.1 Previewing the U.S. population in 2050, then, calls for making assumptions about the numbers of people entering and leaving the country, about the numbers from various racial and ethnic groups within the totals, and about the fertility and mortality rates of individual groups. Moreover, it calls for assumptions about exogamy and ethnic affiliation— the degree to which groups intermarry and the way the descendants of intergroup marriages identify themselves. This chapter offers a view of how future immigration will alter the U.S. population.2 To paint that portrait, a framework is used to ensure consistency for 1   Even the apparently simple flow of immigrants into the country is not completely straightforward. The relevant concept is net immigration, the difference between the number of those entering the country and the number of those leaving it, whether foreign-born or native-born. These flows respond to various economic, political, social, and family concerns, in the United States as well as in the sending countries, that themselves may be volatile. 2   The panel is aware that our population projections may be of great interest to those with environmental concerns. Different immigration assumptions, as will be seen, have substantial influence on the future path of population size and growth for the United States. The panel was not charged with examining the environmental repercussions of population change and does not discuss these issues in this report. The panel does not have particular expertise in environmental studies and did not give special study to the effect of immigration on the environment.

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--> alternative assumptions about the future course of immigration and emigration and their associated demographic implications. This work has several purposes: To evaluate the assumptions concerning demographic developments in the years 1995 to 2050; To present alternative results so the sensitivity of assumptions can be assessed; To explore the national implications for population change from specific variations in immigration; and To use the population results to describe the implications for economic and social policies. On the basis of our population projection model, this chapter examines the effects of immigration on the future course of the U.S. population. We first examine why immigration is important for population change. Next, a model for population projection is briefly described, and the alternative assumptions used here to illustrate future population change are set out. Against this background, the heart of the chapter is a discussion of the main effects of immigration on the U.S. population over the next six decades. Background To Population Change The number and age structure of the population are determined by fertility, mortality, and migration. The last factor has attracted considerably less attention in formal models than the first two, which have been extensively examined by means of stable population models and their various extensions. At the simplest level, that of total population numbers, only net migration appears in the demographic balancing equation: population change = births deaths + net migration. Thus, net migration series are typically used to examine the effects of immigration on population structure. For most of its history, the United States has attracted large numbers of immigrants. In recent years, the estimated net inflow has been around 800,000 people, including illegal and legal immigrants and refugees. This figure reflects immigrant flows into the country and emigrant departures of both immigrants and native-born residents. Although the net figure is important from the demographic accounting perspective, gross inflows and outflows are necessary for many purposes of policy and analysis. To cite one example: immigrants who are not U.S. citizens are ineligible to vote, but emigrants who are U.S. citizens are eligible to vote by absentee ballot. Role of the United States in the World Population The world population has been growing at a historically unprecedented rate

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--> TABLE 3.1 World Population by Region: Actual Population, 1950-1990; Projected Population, 2010-2050   1950 1970 1990 2010 2030 2050 World total (in millions) 2,520 3,697 5,285 7,032 8,671 9,833 Percentage of world population World 100 100 100 100 100 100 Africa 9 10 12 15 19 22 Asia 55 58 60 60 60 58 Europe 21 17 14 10 8 7 Latin America and the Caribbean 7 8 8 9 9 9 North America 7 6 5 5 4 4 United States 6 5 4 4 4 4 Other Countriesa 1 1 1 1 0 0 Oceania 1 1 1 1 0 0 a Other North American countries, by United Nations definitions, include Bermuda, Canada, Greenland, and St. Pierre and Miquelon. Source: United Nations (1995:Tables A.1 and A.2); population projections by the panel for the United States, 2010-2050. for the past century and numbered an estimated 5.8 billion in 1996. In 1990, the U.S. population accounted for 4 percent of the world's population (see Table 3.1). Since 1950, the U.S. population has been declining as a proportion of the world's population, decreasing from 6 percent in 1950. If we rely on the world population projections prepared by the United Nations (1995), anticipating results for the United States that are discussed later, the population of the world and the United States will grow through the year 2050. Because we project that the United States will experience moderate population growth for the next six decades, its proportion of the world's population will remain constant at 4 percent. Some other regions, such as Europe, will account for a diminishing proportion of the world's population over the next six decades, and regions such as Africa are likely to increase their relative proportion. Although not everyone outside the United States wishes to or realistically will seek to emigrate to the United States, these results also provide evidence that the number of potential U.S. immigrants will increase in the future.

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--> Population Projections The population projections reported in this chapter take the 1995 U.S. population and calculate future growth by making assumptions about the level of births, deaths, and net immigration. The initial 1995 population is characterized by age, sex, race/ethnicity, and immigrant generation—whether the person is of the first generation (foreign-born) or is its descendant. We examine four racial or ethnic groups of primary affiliation: Asian and Pacific Islander (taken together and referred to as Asian in this chapter), black, Hispanic, and white.3 In federal government statistics, Hispanic status is defined for purposes of establishing a Hispanic population, which may be reported in any of the four races. In practice, the Hispanic population mainly reports itself as either white or "other" race (the latter includes individuals who do not check a specific, listed race but write in such responses as "Mexican"). The official current classification is based on an arbitrary separation of race and ethnicity, defining Asians, blacks, and whites as "races'' and not ethnic groups. We refer to the four groups broadly as ethnic groups in this chapter. The main implication of the official classification system is that population projections for the Hispanic population overlap with the overall projections for the main race groups in official government projections. For the projections presented here, we calculate a base population in which the white, black, and Asian groups do not include any Hispanic component.4 This avoids a double-counting of Hispanic persons. We rely on a population projection model that makes assumptions about several parameters: immigration and emigration; mortality, fertility, and exogamy; and ethnic attribution. In the next sections, we set out the model we used to make our projections and the demographic assumptions that underlie them. For a technical, detailed description of the model and additional information about the assumptions used in the projection model, see Appendixes 3.A and 3.B, respectively. 3   Government statistics include Native Americans as a fifth racial group. The size of this group is relatively small and, because immigrants include few Native Americans, we have excluded them from presentation in this report. Data for the total population, however, includes separate estimates for the three Native American groups—American Indians, Eskimos, and Aleuts. 4   One needs to remember that the Asian and Hispanic populations are very diverse. In addition, white and black populations are diverse and represent different ethnic origins. Immigrants may report themselves with a primary racial or Hispanic affiliation, but they include persons from many quite distinct countries. Some Asian and Hispanic ethnic groups, of different origins and cultures, have variations in fertility and mortality levels, as well as in propensities for emigration. For example, the Asian population includes immigrants from China, Korea, India, Vietnam, and Japan, among others, and the Hispanic population includes immigrants from Mexico, Guatemala, the Dominican Republic, Argentina, Chile, and many other countries. These within-group differences may be as important as the across group differences we model in this volume. We do not, however, attempt to model these within-group demographic differences in this report.

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--> A Projection Model This report uses a new demographic model for population projections. Similar to standard cohort-component models, this model forecasts an initial population under certain assumptions about fertility, mortality, and international migration.5 Our interest in projecting the future population, however, places special emphasis on the size of the foreign-born population and the ethnicity of its descendants. In an important innovation, therefore, the model arrays the population by generation: a foreign-born first generation (the immigrants), a second generation (sons and daughters of immigrants), a third generation (grandsons and granddaughters of immigrants), and fourth and later generations. Because the model requires fertility, mortality, and migration by generation, it takes a somewhat different form from that of conventional demographic models. Standard cohort-component projection models do not distinguish immigrant generations. Such a model has several limitations for our projections. First, it does not incorporate the changes in fertility and mortality that occur within a generational framework (Werner, 1986). Second, its specification of emigration is inadequate, usually assuming a fixed number of emigrants or a number based on a certain percentage of the total number of residents (Miltenyi, 1981). Finally, it provides no information on such important aspects of ethnic groups as the number who are foreign-born and native-born (Tabah, 1984). In particular, it has questionable assumptions about rates of intermarriage and ethnic attribution. The new model presented in this chapter overcomes some of these limitations. By distinguishing the population by immigrant generation, it improves the description of population dynamics influenced by immigration. With the model used here, we make no attempt at a pinpoint prediction of future population. Rather, the implications of a credible set of assumptions about basic demographic processes are examined on the basis of state-of-the-art research. Projections for the immediate future—say, 15 to 25 years, for which current research provides credible parameters—have much higher analytical credibility. Beyond that, population projections must be seen as much more uncertain. The simulations of the model reported here are designed to generate the racial/ethnic distribution of the U.S. population implied in assumed interactions of the basic demographic process. Except for arithmetic errors, the projections presented here must, in a special sense, be accurate because they derive logically 5   Among various methods for making population projections, cohort-component approaches are commonly used for making projections by age and sex. Cohort-component methods involve making separate assumptions for the components of fertility, mortality, immigration, and emigration. The method is usually applied to separate birth cohorts, by sex. The total population is obtained by combining the projections for age-sex groups.

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--> from the assumptions of the demographic model. Hence, it becomes all the more necessary to explicate the new generational model and to buttress the assumptions we have made. We stress that the projections for ethnic groups are not necessarily accurate predictions for the future course of the population.6 Supported as they are by the latest evidence, our assumptions about fertility and mortality are reasonable, yet leading researchers vigorously debate the dynamics of these demographic processes. Furthermore, immigration and emigration may follow a variety of plausible courses in the coming decades. Recent history suggests, for example, that one or more new countries may be the source of a major surge of immigration, whose size, composition, and origin are uncertain. An Immigrant-Generation Approach Standard cohort-component population projections move a population through time by estimating its survival under the conditions of mortality (its survival from one period to the next), fertility (the births to the population and their survival during the projection period), and migration (the survival of immigrants during the projection period and the survival of the population until emigration). Such projections take into account the age and sex distribution of the population, but they do not treat immigrants and their descendants explicitly. The population projections presented here are distinguished by their explicit treatment of the generations of the immigrant population. They address the four generations of each racial or ethnic group defined above. Characterized from this perspective, the population includes a foreign-born component (the first generation) and a native-born population (the second and later generations). A generational perspective has several advantages for examining the future population of immigrant groups and their influence on the nation. First, the generations themselves may be useful numbers. Those in the first generation speak the language and hold many of the cultural values of their countries of origin. Their children typically grow up speaking their parents' native language at home and adhering to many of their parents' cultural values, even while speaking English and absorbing U.S. culture. To know the generational distribution of a racial or ethnic group, therefore, is to know a lot about its acquisition of the English language and of U.S. values. Second, generational characteristics refine the modeling of immigrants, who usually enter the United States as first-generation, foreign-born individuals, and 6   Population projections have had a long history of debate about viewing their results. In general, most demographers emphasize the analytical credibility of the projection model, the plausibility of the assumptions, and the usefulness of a range of assumptions for understanding future population change (Romaniuc, 1990).

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--> of emigrants, whose rate of leaving the United States varies greatly with the number of foreign-born members of a racial or ethnic group. The model also permits varying the assumptions about fertility and mortality rates by generation. Conventional population projection models generally make the unreasonable assumption, for example, that childbearing patterns are the same for all generations—that, in other words, immigrants acquire the fertility levels of the resident population upon arrival in the United States. Demographic research, however, suggests that fertility differences exist for immigrants but that they diminish with later generations. A Generational Perspective To sum up, our modified cohort-component approach adds a generational perspective to the characterization of the initial population by age, sex, and ethnicity used by standard population projections. The base population is moved forward in five-year intervals, with successive application of the demographic dynamics: births are added to the population. Deaths are subtracted. And net migration is added, depending on the combination of immigration and emigration. Thus, the model requires assumptions about the fertility, mortality, and migration flows for the age-sex groups in each generation. For our approach, assumptions made about the generational dynamics are also important, inasmuch as they affect the results and interpretation of the projection. Most users of population projections need to be able to regard them as plausible. "Plausible," in this context, means that the conditions for demographic dynamics could be regarded as likely for the future course of fertility, mortality, and international migration. Thus, a critical aspect of population projections is scrutiny of the assumptions made about the demographic dynamics. Our approach assumes a relatively general model for each of the demographic processes on a generational basis (the formal model is presented in Appendix 3.A). For mortality, each age and sex group in each generation experiences its own schedule of death rates. Deaths in a generation reduce its numbers. For fertility, births to a generation add to the next generation.7 Births to foreign-born immigrants (the first generation) are members of the second generation and will thus, given the time intervals used in the model, add to the 0-4 age group in the second generation in the next interval of the projection. In our approach, the latest generation is the fourth and their descendants. Births to the third generation and to the fourth or later generations will, by definition, become members of the last generation group. 7   The discussion here assumes that the generation membership of the parents is unique—that is, either both parents always have the same generation or only the mother's generation is considered. We discuss mixed generational models in a later section.

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--> International migration also calls for assumptions about the generational composition of migrants. Immigrants to a population are almost exclusively foreign-born.8 Emigrants from the United States are predominantly members of the first generation: people who have emigrated to the United States and then decided to return to their country of birth. A relatively small number of native-born residents, second or later generation, also emigrate from the United States. Base Population The base populations were defined for July 1, 1995, and rely on information from April 1, 1990, the date for the 1990 U.S. Census of Population, and post-census estimates made by the U.S. Bureau of the Census (1996a). The age-sex distributions for the four immigrant generations in each ethnic group were taken from fitted projections of the U.S. population for the years 1880 to 1990. To obtain their numbers by generation, the projections were scaled, by ethnic group, to the 1970 census (for the first, second, and third and later generations) and the 1980 and 1990 censuses (for the native- and foreign-born). Finally, the population figures were scaled to the post-census age-sex distributions for the total population, by ethnic group, estimated by the U.S. Bureau of the Census (1996a). For this chapter, we include estimates for the 1995 population by single and multiple-ancestry. We consider two types of births in these projections: single-ancestry births are those to parents who have the same racial or ethnic identification; multiple-ancestry births are births to parents whose racial or ethnic identifications differ. Single ancestry, in the context of this chapter, means that a person reports a racial or ethnic ancestry that is the same as his or her primary racial or ethnic identification. To obtain estimates of single and multiple-ancestry, we used the 1990 census to divide persons in each of the four main racial/ethnic groups into two groups: (1) single-ancestry persons, who reported that both ancestries were the same as their racial/Hispanic-origin identification and (2) multiple-ancestry persons, who reported one or more ancestries that differed from their racial/Hispanic-origin group identification. Overall, the proportion of multiple-ancestry for the four main racial/ethnic groups varies a lot. About 7 percent of the U.S. population reported multiple-ancestry in the 1990 census. Of those who reported their primary ethnic affiliation as white, about 6 percent reported one or more ancestries that were not white. Of those reporting themselves as black, about 7 percent reported one or more 8   There are small numbers of immigrants to the United States who are native-born persons with foreign citizenship who immigrate. For example, a foreign-born couple residing in the United States may have children born in the United States and, subsequently, return to the country of their own birth. If their children later return to the United States, they would be immigrants from the second generation.

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--> ancestries that were not black. The comparable figures were 8 percent for Asians and 9 percent for Hispanics. Fertility Assumptions Fertility is the starting point of any demographic projection model. Higher fertility rates will make the future population larger, and subgroups with higher than average fertility will grow relative to others. Since 1971, the Census Bureau has published fertility estimates in a special supplement to the Current Population Survey (CPS) in June of each year. The survey asks women several fertility questions, including how many children they have ever borne and whether they have had a child within the past year. Starting in 1994, the CPS has also asked about the nativity of the respondent and the parents of the respondent. Using the CPS nativity data, we tabulated the population for the foreign-born (first generation), sons and daughters of the foreign-born (second generation), and native-born of native-born parents (third and later generations).9 There is apparently some underreporting of births in the CPS, when compared with vital statistics for registered number of births. Births are registered for a calendar year, whereas CPS data on reported births are from July of the preceding year to June of the survey year. We tabulated the number of births from vital statistics and the CPS by race/ethnicity, along with the adjustment factors to scale CPS data to the known level of births by race of mother.10 Age-specific fertility rates for the four major racial/ethnic groups were estimated using recent fertility data from the June 1994 CPS and the tabulations for 1994 of the National Center for Health Statistics (NCHS). Separate estimates were made for the first, second, and third and later immigrant generations (fertility levels for the third and fourth and later generations were assumed to be the same). Overall, the following total fertility rates were assumed for the starting period of 1995 to 2000:1.81 for the white population, 2.33 for Asians, 2.34 for blacks, and 2.63 for Hispanics. As the generational composition shifts, the pro- 9   The CPS has two important limitations for fertility estimates: undercoverage of the population and underreporting of births. The first results from omitted households and from missing persons within sample households. Although the CPS has lower rates of undercoverage than do other large federal household surveys, its undercoverage is about 8 percent lower than that of the 1990 census (Shapiro et al., 1993). Undercoverage rates vary with age, sex, and race. For some groups, such as black males aged 20 to 29, the rate is estimated to be as high as 34 percent compared with that of the 1990 census. Although the CPS is adjusted for undercoverage, the extent to which the weighting procedure corrects for fertility reporting bias due to undercoverage is unknown. 10   Fertility estimates derived from the CPS are subject to sampling variability. To provide a range of the variability, we calculated standard errors for some of the fertility estimates. For the native-born white population, we calculated that the total fertility estimate of 1.81 has a standard error of ± 0.04.

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--> TABLE 3.2 Fertility Estimates for U.S. National Population Projections by Race/Ethnicity and Immigrant Generation, 1995-2050   Immigrant Generation Race/Ethnicity Overall First Second Third+ Total 1.98       White 1.81 1.82 1.82 1.81 Asian 2.33 2.54 2.17 1.80 Black 2.34 2.76 2.53 2.31 Hispanic 2.63 3.23 2.63 2.04   Source: Panel estimates based on June 1994 Current Population Survey data and 1994 National Center for Health Statistics birth registration data. jection shows declining overall total fertility levels for the heavily immigrant-oriented groups, such as Asians and Hispanics. We used the June 1994 CPS to make fertility estimates for the major racial/ethnic groups for the first, second, and third-plus generations, using the adjustment factor described above (see Table 3.2). In a number of important ways, our fertility assumptions are not very different from those used by the Census Bureau in their demographic modeling. The overall estimate of the fertility rate of the population, 1.98, is only slightly lower than the 2.02 assumption made for the 1995 Census Bureau's baseline population projection. The new estimate for the white population of 1.81 is also similar to the previous assumption of 1.83. There is little difference in the fertility levels by immigrant generation for the non-Hispanic white population. The fertility estimate for the black population from the June 1994 CPS is slightly lower than the Census Bureau's projections. Reductions appear as the generations progress, with a decline to 2.3 children per woman by the third and later generations. The 2.33 fertility estimate for the Asian population is considerably higher than the assumption of 1.92 used in the 1995 Census Bureau projections. We assume different fertility levels for each immigrant generation, with higher fertility for first-generation immigrants and a decline to 1.80 for the third and fourth generations. Fertility rates for Asians three or more generations out are similar to those for the white population. Fertility estimates in the June 1994 CPS for the Hispanic population appear to be lower than those assumed in the Census Bureau's projections. 11 Moreover, 11   From the June 1994 CPS special supplement on fertility and from births to Hispanic women reported in 1994 to the National Center for Vital Statistics, we estimate total fertility rates of 3.23 for foreign-born women and 2.31 for native-born women, yielding an overall total fertility rate of 2.63.

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--> Passel, J.S., and B. Edmonston 1994 Immigration and race: Recent trends in immigration to the United States. In B. Edmonston and J.S. Passel (editors), Immigration and Ethnicity: Immigration and the Adjustment of America's Newest Immigrants. Washington, D.C.: The Urban Institute. Romaniuc, A. 1990 Population projection as prediction, simulation, and prospective analysis. Population Bulletin of the United Nations 29:16-31. Shapiro, G.M., G. Diffendal, and D. Cantor 1993 Survey undercoverage: Major causes and new estimates of magnitude. Pp. 638-663 in Proceedings of the 1993 Bureau of the Census Annual Research Conference. Washington, D.C.: U.S. Department of Commerce. Tabah, L. 1984 Population Projections: Methodology of the United Nations. Papers of the United Nations Ad Hoc Expert Group on Demographic Projections, United Nations Headquarters, 16-19 November 1981. Population Studies Number 83. Department of International Economic and Social Affairs, United Nations, New York. United Nations 1995 World Population Projections. New York: United Nations. U.S. Bureau of the Census 1989 Projections of the population of the United States, by age, sex, and race: 1988 to 2080. Prepared by Gregory Spencer. Current Population Reports, Series P-25, No. 1018. Washington, D.C.: U.S. Department of Commerce. 1996a Population projections of the United States by age, sex, race, and Hispanic origin: 1995 to 2050. Current Population Reports, P25-1130. Washington, D.C.: U.S. Department of Commerce. 1996b Statistical Abstracts of the United States, 1996. Washington, D.C.: U.S. Department of Commerce. Werner, B. 1986 Family building intentions of different generations of women: Results from the General Household Survey, 1979-83. Population Trends 44 (Summer): 17-23. Appendix 3.A Population Projection Model The panel's population projection model forecasts a population by age, sex, and four generation groups for a period of five-years, using survival rates by five-year age groups for each sex and generation, five-year age-specific fertility rates for each generation, and the number of migrants by age, sex, and generation during the five-year period. The projection handles four generations: the foreign-born (the first generation), the sons and daughters of the foreign-born (the second generation), the grandsons and granddaughters of the foreign-born (the third generation), and all higher-numbered generations lumped together. A FORTRAN program, designed for use on microcomputers, implements the basic immigration generation model. The program displays results for each generation as well as the total native-born (the second and higher generations) and the total population. Although a special procedure handles each five-year projection, the main population projection program can make projections for a period of 5 to 100 years.

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--> The model requires the following data: (1) initial female population in five-year age groups, by generation, (2) initial male population in five-year age groups, by generation, (3) five-year survival rates for females during each five-year period, by generation, (4) five-year survival rates for males during each five-year period, by generation, (5) annual age-specific fertility rates (for five-year age groups) for the beginning and end of each five-year period, by generation, (6) female immigrants and emigrants by five-year age groups during each five-year period, by generation, (7) male immigrants and emigrants by five-year age groups during each five-year period, by generation, and (8) sex ratio at birth. In addition, several parameters control various options of the computer program and permit alternative input data (such as using Coale-Demeny model life tables instead of age-specific survival rates). Consider a population defined with the following characteristics: population size for age x at time t, rates for population age x surviving to age x+5 during the period from t to t+5, and age-specific fertility rates for women age x at time t. Survival rates are derived from the life table person-years lived values in the standard fashion, with We assume five-year age groups here, so the population age x represents the age group x to x+4. Model With No International Migration. For a population projection with no international migration, the closed population is affected only by fertility and mortality processes. The survival of the population at the beginning of a five-year projection period is: (1) and (2)

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--> for the last, open-ended age interval, where x+ is the population age x to the end of life, and each equation is separate for males and females. We calculate the total births during the five-year interval as: (3) where P is for the female population only. Then the population aged 0 to 4 years at t+5 is: (4) and would use the sex ratio at birth to calculate the number of male and female births. P and S are also separate by sex, and indicates the survival from birth to age 0-4 for the appropriate sex during the period t to t+5. Model With International Migration. The basic population projection model can be modified to include the effects of international migration. Define as in-migrants age x during the period t to t+5 and as out-migrants age x during the period t to t+5, each separate by sex. Then the net migrants age x during the period t to t+5 is The impact of international migration on the population alive at the beginning of a five-year projection period is: (5) and

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--> (6) for the open-ended age category. Equation 3 for total births is affected by migration and reflects births to the resident population plus births to the net immigrants during the period: (7) where births to net immigrants is: (8) ¬ The population aged 0 to 4 years is also altered by international migration: (9) where P, S, and N are separate by sex and the sex ratio at birth is needed to calculate the number of male and female births. Model With Population by Generations. The population described above is distinguished by an age and time index (and is assumed to be separate by sex). Consider now a population indexed by k generations, where k=1, 2, 3, and 4: k=l indicates the first generation, k=2 indicates the second, k=3 represents the third, and k=4 indicates the fourth and later generations. For the survival of the population alive at the beginning of the projection period equation 5 becomes: (10) and equation 6 becomes: (11) for the open-ended age category, where

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--> represents the survival values for the kth generation and indicates the number of net migrants for the kth generation. In general, the number of immigrants by generation is non-zero for the first generation (k = 1) and zero for the second and later generations (k = 2,3,4). Immigrants are generally not native-born persons. On the other hand, this model makes apparent that emigrants by generation may have non-zero values for all generations. Hence, observed values of net migrants by generation are usually positive for the first generation (representing net immigration of the foreign-born) and typically negative for the second and later generations (indicating some emigration and negligible immigration of the native-born). In a female-dominant model,48 a mother in the kth generation would produce an offspring in the k+1 generation. The population aged 0 to 4 for the first generation would derive solely from immigration (it is logically impossible for a mother to give birth to a foreign-born child in the United States): (12) separate for each sex. The population aged 0 to 4 years for the second and third generations results from births to mothers in the first and second generations, respectively, plus the effect of net migration: (13) 48   We use female dominance here to mean the model derives the generational characteristics of children from the mother. This is to say that the generational characteristics of the father have no relevance for the offspring in the female dominant perspective.

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--> for k=2,3 and for each sex separately, where the sex ratio at birth is needed to calculate the number of male and female births and where: (14) We would ordinarily assume that births to net immigrants during the period would be non-zero only for the second generation. The population aged 0 to 4 years in the fourth and later generations results from births to third-generation mothers plus fourth- and later-generation mothers along with the effects of net migration: (15) for each sex separately, where total births during the period are obtained using equation 14. However, the female-dominant model does not correspond to the classifications used in U.S. censuses or surveys for most recent immigrant ancestor. A kth-generation female might marry a male of a different immigrant generation, and their offspring would not necessarily be the k+1 generation. If a third-generation woman produces an offspring in union with a first-generation man, the child would report ancestry relative to the father (the most recent immigrant generation of the parents) and indicate second-generation ancestry. Because some females marry males with a lower-order immigrant generation than themselves, the observed generational composition of births (and the resulting population aged to 4 years) is always a lower order than implied by a female-dominant model. To make the model correspond to data collection methods, consider a matrix which indicates the proportion of births in the mth (m= 1,2,3,4) generation born to women in the kth generation, subject to the condition for k= 1,2,3, and 4. In the female-dominant model

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--> and all other cells in the G matrix are zero. A model incorporating the G matrix, where mothers of the kth generation produce births in the mth generation is: (16) for m = 1,2,3,4 and separate by sex. The empirical challenge, in this case, is to estimate the intergenerational birth matrix The population projection model requires information about the probability that a kth generation mother gives birth to a mth generation child. The fertility assumptions for the model determine the overall chances of having a child; the intergenerational birth matrix therefore affects the generational distribution of births, and not the fertility process itself. Data are lacking on childbearing by parental generation, for both parents, for racial/ethnic groups in the United States. We used data from the 1989 Current Population Survey (CPS) to make estimates of this matrix, examining births to parents for the first, second, and third-plus generation for the Asian, black, Hispanic, and white non-Hispanic populations. We then adopted an iterative procedure to develop estimates that fit both the CPS data and the known overall number of births (U.S. Bureau of the Census, 1989). This procedure produces approximate estimates for the intergenerational birth matrix. We estimate, for example, that births to third-generation Hispanic mothers are distributed roughly as 30 percent in the second generation, 20 percent in the third generation, and 50 percent in the fourth-plus generation. Our current analysis of intergenerational births is preliminary. However, analysis of the 1989 CPS data suggests that the intergenerational birth matrix is affected by the generational distribution of males and females. In a population with a high proportion of immigrants, the chances are greater that a native-born person will marry a foreign-born person and produce a child with a more recent immigrant generation. Populations with few immigrants, in contrast, would have an intergenerational birth matrix that more closely resembles the female dominant perspective. For the population projections presented here, we assume that each racial/ ethnic group has an intergenerational birth matrix in 1990 that is estimated from 1989 CPS data, for the particular racial/ethnic group. Over time, we assume that the matrix changes, depending on the generational distribution of males and females in the population at the beginning of the projection period.

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--> Appendix 3.B Population Projection Assumptions This appendix presents detailed tables for the population projection assumptions. The tables that follow provide the assumptions used in the projections for fertility, mortality, immigration and emigration, exogamy, and ethnic attribution for multiple-ancestry persons. These appendix tables do not show assumptions made for American Indians, Eskimos, and Aleuts; the text and the tables do not present results for these population groups because they are relatively small and not affected by variations in immigration. Tables, graphs, and information for the U.S. total population, however, includes estimates for American Indians, Eskimos, and Aleuts. TABLE 3.B1 Mortality Assumptions for Life Expectancy at Birth for U.S. National Population Projections by Race and Hispanic Origin, 1995 and 2050   1995 2050 Race/Ethnicity Low Medium High Low Medium High White Male 73.6 73.6 73.6 72.6 81.9 87.5 Female 80.0 80.0 80.0 79.8 85.3 92.9 Asian Male 79.6 79.6 79.6 78.6 83.9 87.5 Female 80.2 80.2 80.2 79.8 85.0 89.3 Black Male 64.5 64.5 64.5 62.2 69.5 80.8 Female 74.3 74.3 74.3 73.4 78.8 89.8 Hispanic Male 74.9 74.9 74.9 73.1 84.4 85.5 Female 82.2 82.2 82.2 81.7 89.6 91.4   Source: Mortality assumptions made in national population projections of the U.S. Bureau of the Census (1996a).

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--> TABLE 3.B2 Intermarriage Rates by Race/Ethnicity and Nativity, 1980, and by Race/Ethnicity, Nativity, and Racial/Ethnic Ancestry, 1990, Aged 20 to 29 Years     1990 Race/Ethnicity 1980 Overall Single Multiple White Foreign-Born 1.9 2.1 1.8 5.5 Native-Born 1.7 2.0 1.8 4.3 Total 1.7 2.0 1.8 4.4 Asian Foreign-Born — 48.0 38.3 91.7 Native-Born — 79.7 71.6 90.9 Total 48.6 63.7 54.0 91.5 Black Foreign-Born — 9.1 7.3 17.1 Native-Born — 5.4 5.6 6.3 Total 3.1 5.4 5.4 6.8 Hispanic Foreign-Born — 18.9 18.3 33.5 Native-Born — 50.8 45.7 56.0 Total 29.2 37.0 36.2 48.1 Note: rates are shown as the percentage of persons in marital unions who are married to a person of a different race or Hispanic status.—= estimate not made. Source: U.S. Bureau of the Census microdata files, 1980 and 1990. TABLE 3.B3 Exogamy Estimates for Ethnic Groups by Immigrant Generation   Immigrant Generation Race/Ethnicity First Second Third Fourth+ White .10 .09 .08 .08 Asian .13 .34 .54 .54 Black .14 .12 .10 .10 Hispanic .08 .32 .57 .57   Source: Panel estimates using 1990 census microdata and 1994 birth data from the National Center for Health Statistics.

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--> TABLE 3.B4 Racial and Ethnic Attribution Rates for Multiple-Ancestry Persons for Racial and Ethnic Groups   Level of Ethnic Attribution Race/Ethnicity Very Low Low Half Medium High Very High White .00 .22 .50 .42 .62 1.00 Asian .00 .19 .50 .39 .59 1.00 Black .00 .41 .50 .61 .81 1.00 Hispanic .00 .44 .50 .64 .84 1.00   Source: Panel estimates from 1990 census microdata. Appendix 3.C Sensitivity of Population Projection Results Different assumptions for each component of population change lead to shifts in population size. Using alternative assumptions for immigration, fertility, and mortality—each projected under low and high assumptions—we obtain changes in the projected population size. These variations can be compared with the medium-level projections, assuming medium levels for immigration, fertility, and mortality. Table 3.C1 shows results for these projections. In the intermediate 10 to 15 year period, different assumptions about immigration and fertility could increase or decrease the population size by 2 to 3 percent (see Table 3.C2). In the long run, by 2050, different mortality assumptions will result in population size differences of 6 to 7 percent. In contrast, the cumulative effects of immigration and fertility are greater. Different immigration assumptions, ranging from low to high, will result in population size differences of 10 percent. Different fertility assumptions will account for differences of 12 to 14 percent. These results are consistent with other studies (Long, 1991) concluding that variability in fertility and immigration outpaces the contribution to long-term population size from mortality, in the U.S. context.

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--> TABLE 3.C1 U.S. Population Size Under Alternative Immigration, Fertility, and Mortality Assumptions, 1995-2050     Immigration Fertility Mortality Year Medium Low High Low High High Low 1995 263 263 263 263 263 263 263 2000 277 275 279 271 274 277 277 2010 302 295 310 296 308 299 305 2020 327 313 341 314 340 320 334 2030 351 330 373 330 372 337 362 2040 370 341 400 337 407 352 385 2050 387 349 426 341 441 360 410 TABLE 3.C2 U.S. Population Size Relative to Medium-Level Assumptions Under Alternative Immigration, Fertility, and Mortality Assumptions, 1995-2050     Immigration Fertility Mortality Year Medium Low High Low High High Low 1995 100 100 100 100 100 100 100 2000 100 99 101 99 100 100 100 2010 100 97 103 98 102 99 101 2020 100 96 104 96 104 98 102 2030 100 94 106 94 106 96 103 2040 100 92 108 91 110 95 104 2050 100 90 110 88 114 93 106