q q, technical paper Guide for Local Area Population Projections ^^N AUG 11977 | eared, and small ones (often former teachers' leges) have grown. At present, enrollment has 9led off at the national level, but many individual ools continue to change rapidly. As with the itary population, if such changes occur in a base iod which serves to establish a projected trend, projections may be very unrealistic. A problem :uliar to the college population is that enrollment inge may or may not mean a migratory move- nt of students. For example, the current large rease in adult enrollment can create a false pression of population change if the statistics are t carefully monitored. Institutions such as mental hospitals, sanatoriums, i detention facilities are somewhat less prone to tid change in size, and the age range is not always restrictive as with the college and military Dulation. Similar problems arise, however, and >uld not be overlooked. In dealing with special populations in projection >dels, it is best to distinguish clearly between the ;cial population and the general population for all evant statistics, and to project the two groups lependently. If the trend of some historical period involved, either for demographic or economic tistics, then the effect of the special population ist be removed. This is not always possible and independent jjections of the special population may not be isible. Some simpler technique is then indicated, :h as adjusting the projected total population in :ord with the expected future divergence of the 11 Richard B. Halley and Morton Paglin. "Population recast, State of Oregon and Economic Areas: 1960-1985." tland, Oregon: Oregon State Board of Census, Portland te College, p. 11, 1964. trend of the special population from the trend of the past. 2.34 Postcensal estimates. During the past 15 years the quality and volume of postcensal popu- lation estimates have increased significantly. In addition to estimates for States, there are annual published estimates for counties through the Fed- eral-State Cooperative Program for Local Population Estimates. 12 The Census Bureau has developed a new series of estimates for 38,000 administrative jurisdictions for use in the Federal General Revenue Sharing program. Estimates for 1973 have been published, and a set for 1975 will be completed early in 1977. The postcensal estimate can be used to monitor the projections by regularly comparing the estimate with the projected trend. This becomes progressively more important as the length of time since the last census increases. If the estimate deviates sub- stantially from the projected trend, the projections should be adjusted. There are two basic approaches in making this adjustment. One is to establish a new benchmark population figure by age and sex on the postcensal date and begin the first projection cycle from that date. Another is to "pass through" the population estimate, retaining the original projection dates, but adjusting the trend of the projection to account for the difference observed at the postcensal estimate date. This is the approach illustrated in the step- by-step procedure in Appendix H. The degree to which the difference between the postcensal esti- mate and the projected trend is allowed to influence the trend of future projections can be varied according to the analyst's confidence in the accuracy of the postcensal estimates, and the ex- pected permanence of the new trend. Operationally, the adjustment required by the postcensal estimate is most conveniently made by changing the migration component, although if projected birth and death data do not match with subsequent experience, they too can be adjusted. 2.35 Time Unit. Projections are usually pre- pared by 5- or 10-year units of time, repeating the projection cycle as many times as needed to reach the target date. If the projections are by age, the size of the age groups used is a limiting factor to the choice of the time unit, since this unit must either 1 2 See Exhibit 4-C, p. 40, for a list of the agencies cooper- ating in the program. 8 match exactly the size of the age group, or be an even multiple thereof. For example, if 5-year age groups are being used, the time unit can be 5 years or 10 years, etc. Projections are sometime carried out for single years of time by single years of age. If a comparison between decennial census data is involved, there is some advantage in using a 10-year projection time unit, as the intercensal change of the variables included in the model need not be sub- divided. For example, a serious error is involved in estimating net migration by the residual method for 5-year units of time and age from census data ten years apart, as described below in Section 3.234 under Adjacent cohort technique . The problem does not materialize when census data on gross migration for 5-year periods of time are used. The choice of time unit depends on the character of available data, the total time span covered by the projections, the intermediate dates for which pro- jections are desired, and the amount of data required by the project. Note that interpolation is an alternative for obtaining figures for dates within the projected time span. 2.36 Census undercount. The desire to adjust local population statistics for census undercount is often expressed. Estimates of net census undercount at the national level show sharp differentials by age, race, and sex, with high rates for some groups, notably young adult Black males. However, there are no reliable estimates of undercount below the national level, and it is reasonable to suppose that there is much variation in rates from one locality to another. The use of nationally derived rates to adjust local area statistics, therefore, does not necessarily improve the accuracy of the data. Futhermore, the national estimates are available only by age, sex, and race. For any other characteristic which might enter into a project, such as income and family status, there are no. estimates of any kind, although these factors may influence rates of net census undercount. It therefore may be just as accurate, and is certainly a great deal simpler, to carry out all computations using unadjusted census level statistics. It is possible in local projections, however, to take limited account of undercount in the estimates and projections of net migration by age through the use of national census survival rates (NCSR) in place of life table survival rates (LTSR). 13 Tables of NCSR's suitable for use in cohort-component projections are presented in Appendix B of this guide. Projections using census survival rates are still at "census level"; their use only adjusts for the difference in undercount (at the national level) of an age cohort in two successive censuses, carried out separately for each race-sex group if desired. 14 2.37 Administrative decisions and government policy. There are many ways that actions by governmental units influence population change. The decisions regarding military installations, colleges, afTd institutions are only one type of such actions, although they perhaps have the most direct impact on population change. There are many other governmental actions, some very broad and general in impact, others very specific as to locality, which influence the pattern and extent of local population change. As to general influences, the impact of govern- ment programs for highway construction and hous- ing is not always recognized. These programs have supported the pattern of suburban development since World War II. The huge sums spent on highway construction made it easier for tens of millions of Americans to live ever further from the central city. Another large subsidy to suburbanization is the complex of government programs supporting the financing of housing construction. Both of these programs are still in force, but in some communities, other forces influencing the extent of suburban development have increased in relative importance. In many of the larger metropolitan areas, the increasing costs of land, construction, financing, and transportation have driven up the cost of suburban living, resulting in more construction of townhouses and apartments, in some cases moving towards the city center from the periphery of suburban develop- ment. The complex interaction of these changing values will affect local population growth in the future. 13 For a discussion of the use of NCSR's in projections, see Section 3.233 under National census survival rates. 14 Note, however, that local differences in net census undercount by age, race, and sex are implicitly taken into account if residual estimates of past net migration rates are assumed to continue into the future, whether these estimates were derived using LTSR's or NCSR's. This assumption is illustrated in the projection shown step by step in Appendix H. For a detailed discussion of this factor, see Richard Irwin, "National Census Survival Rates in Population Projections for Local Areas." Paper presented at the 1976 Annual Meeting of the Population Association of America, Montreal, Canada. In a much more specific sense, State and local government policy can decisively influence popu- lation change. By regulating residential construction through zoning restrictions, issuance of building permits, and construction for water and sewage, population growth can be encouraged, or if desired, practically stopped. While zoning restrictions have often been overthrown by the forces favoring residential development, in recent years restrictive policies in the granting of building permits and sewer construction have had decisive effects in limiting population growth in some cases. In one large suburban county a building permit moratorium was an important factor in the reduction of the previous high rate of net migration to zero within a few years. 1 s In one middle-sized city an ordinance was passed in 1972 establishing a population growth policy which links population growth to the expansion of facili- ties for education, water supply, and sewage disposal. This ordinance places an annual limit on the number of new housing units having five or more units in a subdivision or in a structure. 16 1S Prince Georges County, Md. The capacity of existing sewage treatment facilities necessitated a moratorium on building beginning about May 1970. In some parts of the county, residential construction almost stopped, and in others was greatly reduced. 16 Petaluma city, Calif. An annual limit of 500 housing units in multi-unit structures is enforced with a maximum of 100 units for any one parcel of land. Construction with four units or less in the structure, or on single lots, is not affected by the ordinance. There was a challenge in the courts, and the appellate decision which supported the ordinance will stand, as the Supreme Court refused to review it. In a neighboring county, a population policy is being established with the intent of providing for orderly population growth by linking growth to the expansion of water and other needed facilities. 1 7 The actions by these three jurisdictions are symptomatic of a somewhat new attitude toward controlling population growth on the part of some local jurisdictions. Other manifestations of this attitude are zoning regulations imposing a very low population density, and policies restricting the establishment of new industries if they pose a threat to the physical or social environment. This new indifference to economic growth is exemplified by the recent refusal of the State of Colorado to pursue the promised economic benefits of the 1976 Winter Olympics. These attitudes seem to be spreading, and the future population of many local areas will be influenced by the outcome of conflicts between the proponents of population growth and Lhose wanting to restrict it. 17 Marin County, Calif. Beginning in 1972 the electorate had twice turned down bills relating to expanded water supply capacity. In 1973 a county-wide plan was adopted for implementing a growth policy. 3. PROJECTION METHODOLOGY CURRENTLY IN USE 3.1 Introduction The most striking feature of the current scene in local area projections is the sheer volume of activi- ty. State agencies, city and metropolitan planners, health planners, federal agencies, universities, private corporations— all are producing projections for various classifications of local areas, using a wide variety of methods. In a systematic survey taken in North Carolina, 1 it was found that five organi- zations had produced complete sets of projections for the counties of that State. One set was prepared by a private company, one by a university-related organization, two by different State agencies, and a fifth by a research institute. Add to this the projections for metropolitan areas by two federal agencies (Bureau of Economic Analysis and Bureau of the Census) and the miscellaneous projections by local planners for their own areas, and the collection becomes large, indeed. Although there are an un- usually large number of projections available for areas in North Carolina, in other States two or three alternative sets of projections are typically available for metropolitan areas and their constituent coun- ties. These projections are produced by a variety of new methods and modifications of old ones. It is not surprising that the respondents in the North Carolina survey indicated a strong concensus on the need for "uniform, single source estimates and projections, "2 The variety of methods now in use is greater than it was a few years ago, and there is increased use of the more sophisticated methods. In 1969 the Bureau of the Census prepared a bibliography of population projections for States and local areas. Of the 246 publications reviewed, only 34 used the cohort- component technique to develop age detail. The Bureau has begun updating this bibliography, and initial results indicate much greater use of this method as well as greater variation in its application, especially for the migration component. The geographic detail given in population pro- jections has also increased. Twenty years ago there was little attention given to projecting the popu- lation of census tracts. One analyst wrote, "I shall consider a 'small area' a specific geo- graphic subdivision of the country such as a region, State, subregion, metropolitan area or district, county, or city." 3 Today one often hears of projections for census tracts or even smaller areas. The quality of available projections varies a great deal. Much published work is well thought out and shows an awareness of basic problems. For example, adjustments for shifts in college and military popu- lations are not unusual, and adjustments for a postcensal estimate are also done. It is hoped that in the future some concensus and standardization of methodology will emerge from the present extensive experimentation. 3.2 Methodology for Projections of the Population of Local Areas There are five broad categories into which most projections can be placed: (1) mathematical extra- polation, (2) ratio, (3) cohort-component, (4) economic base, and (5) land use. These might better be termed procedures than methods, because there is much variation in the manner in which they are applied. We will stay with the traditional nomen- clature which refers to these categories as methods, even though current applications frequently use more than one and might be called "methods" in their own right. A linking of economic-based projections with the cohort-component technique is one of these cases. 1 Harry M. Rosenberg, "North Carolina Demographic Data Needs and Capabilities: Survey Results." Proceedings of the North Carolina Demographic Data Workshop, Chapel Hill, North Carolina: Carolina Population Center, University of North Carolina, pp. 26-38, 1974 2 Ibid., p. 35. In spite of this interaction between categories, it will still be useful to consider each in turn. 3 Jacob S. Siegel, "Forecasting the Population of Small Areas," Land Economics, Vol. 10, No. 1, pp. 72-87, Feb. 1953. 11 12 3.21 Mathematical extrapolation. The simplest and quickest way to obtain a projected population figure is to extrapolate along some kind of mathe- matical curve. This method is not generally held in very high regard, but if only a rough approximation is required, without detail by age and sex, a mathematical extrapolation may be useful. Straight lines and geometric and logistic curves are used to extend a population trend of the past into the future. Sometimes a least-squares line is passed through the known data points of the past. 4 Intuitively, the logistic curve is best suited to population growth, yet few actual uses are on record. In one test, the use of the Gompertz curve, similar to the logistic curve, did not produce satisfactory results on New Jersey counties. 5 The most common form of mathematical extra- polation is the extension of an historical rate of growth for the total population into the future. A simple illustration of such an extrapolation is shown in figure 1 for "Exurban County, USA". 6 The total population of the county on July 1, 1960 was 24,580 and in 1970 was 32,499. On the simple assumption that the amount of change for 1960-70 will be repeated in 1970-80, the 1980 population is projected to be 40,418. This is shown in figure 1 as the "arithmetic projection." It can also be assumed that the 1960-70 rate of population change will be repeated in the succeeding decade. This assumption gives a projection of 42,969 which is shown in figure 1 as the "geometric projection." 7 Obviously, some base period other than 1960-70 could be selected, and the projected numbers might be very different. A postcensal estimate can be consulted in order to evaluate the projections. On July 1, 1974 such an estimate for this county was 41,700, which is 4 Research Triangle Regional Planning Commission. "Population and Urban Land Use Projections, Research Triangle Region of North Carolina." Research Triangle Park: North Carolina, 1969. 5 Bruce E. Newling, "Population Projections for New Jersey to 2000." New York: The City College of New York, p.1, 1968. 6 "Exurban County, USA" is a fictitious name for an actual United States county used in Appendix H to illustrate projection techniques. For a discussion of the characteristics of the county see Appendix H, Section 5.1. 7 The preliminary projection by the cohort-component procedure illustrated in Appendix H gives a 1980 population of 45,105 as shown in table H-10. considerably higher than any of the projected trends. The estimate is shown in figure 1 by an "*." In the light of this estimate, the preliminary 1980 projections should be re-evaluated. A large scale application of mathematical extra- polation can become quite complex, like those offered by a team at Rutgers University for doing large sets of projections for minor civil divisions. 8 Three models are given, which in essence project rates of population growth, setting maximum and minimum allowable limits. After calculating pro- jections for all parts of the whole, the results are adjusted pro-rata to a previously determined control total. The Rutgers group offers another technique originally proposed by Newling. 9 It could be called a mathematical extrapolation, but since it intro- duces a population density function, it will be discussed later in Section 3.25, Land use methods. In general, mathematical extrapolations can lead to unreasonable population projections, especially if carried far into the future. In any group of subareas, some grow faster than others. The common assump- tion that a rate of growth will continue in the future results in the fast-growing areas receiving larger and larger population gains, becoming unrealistic in terms of the implied migration that is necessary to effect the population shift. There are many uses of mathematical extra- polation in projection models other than just pro- jecting the total population of an area. Subsets of the model, such as survival rates, the number of persons per household, or labor force participation rates, may need to be projected into the future. Extrapolation is a standard technique. For example, in projecting labor force participation rates, the trend of the past might be noted and this trend extrapolated into the future. Regression technique, as used in population projection models, can be thought of as a sophisti- cated means of extrapolating a trend; the expected 8 Michael R. Greenberg, Donald A. Krueckeberg, and Richard Mautner. "Long Range Population Projections for Minor Civil Divisions: Computer Programs and User's Man- ual." New Brunswick, New Jersey: Center for Urban Policy Research, Rutgers University, 1973. 9 Newling, op. cit. 13 future behavior of variables known to be related to population change is mathematically integrated into a single expression. The associations established during the base period are assumed to continue into the future. This very useful technique is often used for projecting some subset of a model, such as migration, but the dependent variable may also be population. It is not classified here as a "method," but a number of examples of its use are discussed in Section 3.24, Economic-based methods. Figure 1. Estimated and Projected Population, "Exurban County, USA": July 1, 1960 to July 1, 1980 ["Exurban County, USA" is a fictitious name for an actual county in the United States. See Appendix H Section 5.1, for a description of its characteristics] Population in Thousands 50 r— 45 40 35 30 25 20 15 10 • •• Geometric Projection — «• Arithmetic Projection * 1974 Postcensal Estimate 1960 1970 Year (July 1) 1980 14 3.22 Ratio method. In this method the data are expressed as shares or ratios of a larger, or "parent," population for which a projection already exists. The historical trend of the ratios is then determined, projected into the future, and multiplied by the projection for the parent population. The trend may be established by fitting a least-squares line to the historical data or by some other mathematical technique, or the projection may simply be drawn freehand on a graph. To cite a specific example, the share each county had of the total population of "Tri-county Area, USA", as shown by the decennial censuses from 1930 to 1970, is illustrated in figure 2. 10 The share 1 °"Tri-county Area, USA" is a fictitious name for an actual metropolitan area in the United States used in Appendix H to illustrate projection techniques. "Central County, USA" is one of the three counties making up the area. For a description of these counties, see Appendix H, Section 5.1. for "Central County, USA" increased from 1930 to 1960. The remaining counties of the area both had decreasing shares. The situation reversed from 1960 to 1970. If these county shares (ratios) are projected to 1980 they can be multiplied by an independent projection of the total population of the area to obtain projections for each county. Observation of figure 2 suggests that the county ratios projected for 1980 will vary according to the length of the base period upon which the projection is based. If the trend from 1930 to 1960 is included in some way in the projection, the 1980 projected share for "Central County, USA" will be higher than if only the trend from 1960 to 1970 serves as the base period for projecting ratio change. The projection of the ratios into the future is critical, and care must be taken to prevent small declining ratios from decreasing too rapidly and increasing ratios from becoming too large. One way Figure 2. County Share of Area Population, "Tri-county Area, USA": 1930 to 1970 (April 1) ["Tri-county Area, USA" is a fictitious name for an actual SMSA in the United States. See Appendix H, Section 5.1 , for a description of the characteristics of the area's countiesj Census Year 1930 1940 1950 1960 1970 "Central County" "Suburban County" "Exurban County" 10 20 1^ 30 T- 40 50 60 - r - 70 80 90 100 Percent of "Tri-county, USA" of handling this is to assume that the ratios will reach stability at a determined future date, and systematically diminish the projected amount of change. 1 J Another way is to select some value for the terminal date of the projections and obtain projections for intermediate years by interpolation. Note that if a complete set of subareas is projected, the ratios must be adjusted so as to sum to 1. However, the ratio technique need not necessarily take into account all the subareas of the parent area. A large scale application of this method has been carried out by calculating ratios of regions to the Nation, then of urban zones to regions, and finally of the metropolitan areas to urban zones, using decennial census data from 1920 to I960. 12 Pro- jected change in the ratios was obtained by first computing the change in each ratio for the decennial periods between censuses. These changes were assigned shifting weights according to an established plan in calculating the projected changes in ratios after 1960. A special adjustment prevented small decreasing ratios from becoming negative, while a similar adjustment automatically limits population gain for rapidly increasing ratios. A similar method is now being applied to the areas served by the Appalachian Regional Commission. This type of across the board use of the ratio method is not the rule, however. More typically, ratios are used at some point in a projection utilizing in part a different method. Projections were prepared for the State of Nebraska using the cohort-component method, but this projected population was then allocated to counties by a ratio technique. 13 The population of places (incorporated and unincorporated) was calculated as ratios of the counties. In projecting the ratios, consideration was given to such factors as the 15 pace of rural out-migration, past growth rates, availability of residential land, and available trans- portation facilities. A county planning commission in Iowa also used ratios to arrive at a county population projection. 14 The ratio concept has a broader aspect than simply projecting the total population of local areas. Ratios may be introduced in one part of a model, as by the Bureau of the Census in projections of births for States and metropolitan areas. 1 5 Although these projections use the cohort-component technique, age-specific birth rates are not projected for each State. Rather, the ratio of the general fertility rate for the State to the Nation is calculated with the most recent historical data. The projected national general fertility rate is then multiplied by this ratio to approximate the projected rate for the State. The ratio is made to gradually approach 1, thus assuming convergence toward the national average. The ratio method can also be used to project age distributions. In this case the all-ages population becomes the parent population, and the age groups are computed as shares of the total. The ratio method is flexible and can be applied in a large variety of situations. When used to project total population, it has the advantage of relating the projections of individual areas to a projection for a larger area, which is presumably more reliable than individual projections for the smaller areas would be. However, like mathematical extrapolation, it can produce unreasonable results, especially if projected far into the future. 3.23 Cohort-component method. 16 The cohort-component method is usually considered to be complex and sophisticated, but actually may be n This technique was used by Margaret J. Hagood and Jacob S. Siegel, in "Projections of the Regional Distribution of the Population of the United States to 1975." Agricultural Economic Research, Vol. 3, No. 2, pp.41 -52, April 1951. 2 Jerome P. Pickard, "Appendixes to Dimensions of Metropolitanism," Research Monograph 14A. Washington, D.C.: Urban Land Institute, 1967. 13 University of Nebraska. "Nebraska Population Pro- jections: State, County, Region and Town: 1975-2020," Nebraska Economic and Business Report No. 6. Omaha: Bureau of Business Research and Center for Applied Urban Research, 1973. 14 David H. Hammond. "Linn County Population and Employment: An Analysis of Trends with Projections to 1995." Cedar Rapids, Iowa: Linn County Regional Planning Commission, 1973. 15 U.S. Bureau of the Census. Current Population Reports, Series P-25, Nos. 375 and 415. See Section 5, Selected References , for a complete citation. 16 This method is used in the step-by-step illustration in Appendix H; for this reason the discussion which follows is relatively comprehensive, especially as it relates to births and deaths, cohort change, and net migration. These subsections provide a general theoretical background for the method illustrated. 16 quite simply applied. The method is sometimes called cohort-survival, but the two basic concepts underlying the method are better illustrated by the words cohort-component. It should be understood that the method is not restricted to purely "demo- graphic" applications. Cohort-component is a broad concept, and many economic-based projections (see Section 3.24) use the procedure. The word "cohort" indicates that the compu- tation is done by age, retaining the identity of each age group as it is carried forward through time. For example, the cohort aged 5-9 years in 1970 is projected to 1975 by appropriate adjustments for deaths and migration, at which time the cohort is 10-14 years of age. The computation is usually done by sex, and sometimes by race as well. Five-year age groups are the most commonly used with a time unit of either 5 or 10 years. Note that this unit must be in multiples of the size of the age group, in order to retain the identity of the cohort. The notion of a cohort may be added to mathematical extrapolation and ratio techniques as a fundamental resource in making projections. It cuts across the usual method of tracing an historical series, by taking as its point of reference the successive experiences of a group of people as they age through time. In addition to the projection of population by age, as described here, the cohort technique has been used to project school enroll- ment, fertility, household formation, labor force activity, and other characteristics (see Section 3.3). To consider next the "component" concept, population change is taken to result from the interaction of three components, as shown in the expression: P! = P + B- D + NM (3.1 Where P is the population of an area at the beginning of some period, Pj is the population at the end of the period, B and D are births and deaths, and NM is net migration, that is, the difference between the number of persons who move into the area (in-migrants) and the number who move out (out-migrants). As will be discussed further on, separate computations for in- and out-migrants are sometimes made, and international migration may be treated separately. The cohort-component method has been criti- cized as being mechanical and unrealistic, but in fact these criticisms are applicable to the manner in which it is applied, not to the method itself. The projection of the various components into the future need not be a simple extension of past trends. There are different techniques for projecting each component, and once specific techniques are selected, assumptions are made about the expected future behavior of each component. If these assump- tions turn out to be correct, and there is no error in the basic historical data (population, births, deaths, and migration), or in the calculations, the future population will be exactly as predicted. In this sense the method is strictly logical. The problem, of course, is to make correct assumptions, and the task of the user is to evaluate them. Forecasting the future behavior of the com- ponents has not proved easy, and there are problems with the basic data used as input. Before discussing the limitations to the use of the cohort-component method suggested by these problems, and its advantages (Section 3.235), it will be useful to discuss the technical aspect in more detail. 3.231 Projections of fertility. Special pro- cedures are always required in cohort-component projections to take account of the population born after the beginning date of the projections. The number of births need not necessarily be projected; in making a projection to 1980 from a base date of 1970, the population under 10 years of age in 1980 can be estimated by means of a child-woman ratio. 1 7 However, in the United States, detailed birth data are available for counties and sometimes for other small areas as well, and the usual procedure is to project age-specific birth rates or the general fertility rate. The use of the more sophisticated cohort fertility method is sometimes carried out at the State level. 1 8 Cohort fertility projections require so much detail that they rarely appear in local pro- jections. The national population projections de- veloped by the U.S. Bureau of the Census use this method, and a description of the technique and 17 Henry S. Shryock, Jacob S. Siegel, and Associates. "The Methods and Materials of Demography." Washington, D.C.: U.S. Bureau of the Census, U.S. Government Printing Office, p. 797, 1971. 18 California Department of Finance. "Population Pro- jections for California Counties, 1975-2020." Sacramento, California, p. 3, 1974. 17 other related information will be found in the most recent published projections. 19 A common approach in projecting births for States or counties is to work with age-specific fertility rates by age of mother in 5-year groups. These are calculated for dates in the past and projected into the future either on t he-basis of past trends or some more refined procedure, or by reference to an already prepared projection for a larger area— the State or the Nation— using a ratio technique. The latter procedure is recommended as being simpler, since in projections for local areas, there is more advantage in focusing on the analysis of migration. Although it is common to use age-specific rates for counties, it may be more accurate to use the general fertility rate, because an error in projecting the age detail for the migration of young adults can have a very large impact on the birth projections. Unless there is confidence in the 5-year age detail, the general fertility rate is to be preferred. The projection model illustrated in Appendix H uses the latter. With respect to accuracy, the projection of births for small areas is subject to all the hazards of 1 9 U.S. Bureau of the Census, Current Population Reports, Series P-25, No. 601. "Projections of the Population of the projections at the national level, plus the local variation which might result from inaccurate basic data, or change in the socioeconomic character of the local area during the projection period, relative to the nation. For these reasons, alternative pro- jections of births are often included in population projections for local areas. An example of such alternative projections is given in Appendix H in the step-by-step illustration of the cohort-component method. See Effect of alternative fertility assump- tions in Appendix H, Section 3.22. 3.232 Cohort change. Once the procedure for projecting births is decided, there are a number of options in the treatment of the other two com- ponents. The simplest is the "cohort change" method. The basic notion is the extension 10 years into the future of the rate of change observed for the population of each cohort between the two most recent decennial censuses, in accord with the following expression: ,80 JO >70 x-10 ,60 x-10 (3.2) United States, 1975 to 2050." Washington, D.C. Government Printing Office, 1975. U.S. where P is population; 60, 70, and 80 represent decennial census dates; x denotes an age group; and x-10 is the same age group 10 years younger. This idea is shown graphically below for the cohort 5 to 9 in 1960 becoming 15 to 19 in 1970: Age 1960 5 10 15 20 Births Births 65+ 1970 1980 (R) 75+ (3.3) 18 where the ratio R, representing the right side of equation (3.2), is assumed to continue for the succeeding decade. The formula can be applied to any local area with constant geographic boundaries during the time frame specified. The first widely known application of this formula for small area forecasting was made by Hamilton and Perry. 20 Special procedures are required for the cohorts born during the projection period in order to obtain the population under 10 years of age in 1980. For the cohorts already born on the base date, the change in cohort size is caused by deaths and net migration; the projection assumption is that the rate of change resulting from these two components will be re- peated in the future. Census errors in either census will also affect the relationship, and the projection assumes that the impact of these errors will be the same. The method has the advantage of simplicity, but in spite of being widely recognized, has not been used often in projections which reach published form. The combination of mortality and migration in one expression makes it difficult to introduce assumptions of future change in either of the components. Nonetheless, the relationships involved in the cohort change concept underlie many of the more detailed procedures. 3.233 Projections of mortality. The most common approach in projecting the mortality com- ponent is to compute age-specific survival rates from an appropriate life table and project these "life table survival rates" (LTSR) into the future. Locally oriented technicians, such as planners for metro- politan areas, often use a State life table. If a table is available for the exact area being considered, it of course can be used. An illustration of the compu- tation of survival rates from a life table is presented in Appendix C. National LTSR'S for the decades 1960-70, 1970-80, and 1980-90 are given in Ap- pendix A. If State or local LTSR's are used, they may be projected on the basis of past trends or by reference to national projections. The U.S. Bureau of the Census customarily includes a table of projected survival rates by age and sex in its reports presenting population projections for the Nation. 2 ' Rather than use survival rates specific to the local area, the technician may choose to use national rates, since death rates specific by age, race, and sex are somewhat similar throughout the United States. In fact, there are differences between regions and by socioeconomic status, but any error in projecting deaths may be completely overshadowed by possible errors in the migration component. 22 National census survival rates. The other important resource in allowing for mortality is the use of national census survival rates (NCSR). Operationally, these rates can be used in place of LTSR's and tables are presented in Appendix B for optional use in the illustrative projections shown step by step in Appendix H. As the name implies, NCSR's are calculated for the Nation as a whole from two successive censuses. The later census is adjusted by removing the effects of net immigration from abroad during the inter- censal period. The ratio of these results to the population enumerated in the first census is calcu- lated for each cohort to obtain the "national census survival rate." The U.S. Bureau of the Census publishes a set of rates following each decennial census period. 2 3 The NCSR's as calculated above implicitly include a partial correction factor for net census under- count, since errors in the National census counts due to underenumeration and misstatement of age are reflected in the survival rates. When these rates are used to calculate survivors of the population of a subarea of the Nation, the assumption is that the 20 Horace C. Hamilton and Josef Perry. "A Short Method for Projecting Population by Age from One Decennial Census to Another." Social Forces, Vol. 41, No. 22, pp.163-70, December 1962. 2 'U.S. Bureau of the Census. Current Population Reports, Series P-25, No. 601 , op. cit., p. 1 30. 22 In addition, an error in the mortality component tends to be counterbalanced by a shift in the estimate of net migration, in projections using estimated net migration calculated by the forward survival rate method. This is discussed in Irwin, op. cit. 23 U.S. Bureau of the Census. Current Population Reports, Series P-23, No. 41, "Preliminary National Census Survival Rates, by Race and Sex, for 1960 to 1970." Washington, D.C.: U.S. Government Printing Office, 1972. For a more complete discussion of the derivation of these rates, see Shryock, Siegel, and Associates, op. cit., p. 632. 19 impact of mortality and net census undercount on the subarea is the same as for the Nation. On the average, this assumption is justified, but for any individual area the actual rate of undercount may be very different from the national average. With respect to mortality it is possible to bring the NCSR's closer to a State-specific concept by adjust- ing them with the ratios of State to national LTSR's, by age, race, and sex. Census survival rates have not been widely used in population projection models, 24 but there has been much study of their use in estimating net migra- tion. 25 Estimates of net migration by age, race, and sex for all U.S. counties for the decade 1960-70, using a modification of the census survival rate method, have recently been published. 26 Estimates for the period 1950-60 were prepared by a similar method. 27 Demographers have had their greatest success in projecting the mortality component. Until 1960, even a large error in the migration component did not cause a proportionate error in the projection of deaths, because migrants are predominantly in the young ages for which mortality rates are low. Since 1960 this has changed dramatically in many retire- ment areas, where an increase in the in-migration of elderly persons in a lightly populated area results in a substantial error in the projection of deaths. Such areas could be called special cases but nonetheless are a new problem to be faced in small area population projections. 3.234 Migration. The component posing the greatest problem in local population projections is migration. The Current Population Survey consis- tently has shown that about 6 to 7 percent of the population lived in a different county 1 year before. (The migration question related to a 1-year refer- ence period until 1972.) The most recent survey reflects a 5-year period, from 1970 to 1975, and indicated that 17 percent of the population lived in a different county in 1975. 28 These migration rates are for the total population; for young adults the rates are much higher. Furthermore, the United States has traditionally experienced great net migration flows. One thinks of the Westward migration, the rural to urban move- ment, and the migration from South to North of the Black population. In response to the problems and questions raised by these flows, and of population mobility in general, demographers have developed a wide variety of migration statistics. Two types stand out for projection purposes: (1) residual net migra- tion calculated for intercensal periods, and (2) gross migration statistics obtained from a question in a census or survey on prior residence, as used in the decennial censuses since 1940. Residual net migration. The amount of net migration for an area during an intercensal period can be estimated by rearranging equation (3.1) as follows: NM = P, -P - B + D (3.4) 24 For a detailed discussion of their use in population projections, see Irwin, op. cit. Tables of projected NCSR's are given in Appendix B of this guide. 2S A good review is given by Horace Hamilton, "Effect of Census Errors on the Measurement of Net Migration." Demography, Vol. 3, No. 2, pp.393-415, 1966. 26 Gladys Bowles, Calvin L. Beale, and Everett S. Lee. "Net Migration of the Population, 1960-70, by Age, Sex, and Color, United States, Regions, Divisions, States, and Counties." Population-Migration Report 1960-70, parts 1-6. Athens, Georgia: Economic Research Service, U.S. Depart- ment of Agriculture; The Institute for Behavioral Research, University of Georgia; and Research Applied to National Needs, National Science Foundation, cooperating, 1975. 27 Gladys Bowles and James D. Tarver. "Net Migration of the Population, 1950-60, by Age, Sex, and Color." Popu- Ition-Migration Report, Vol. I. Economic Research Service, U.S. Department of Agriculture, Washington, D.C.: U.S. Government Printing Office, 1965. where NM is net migration, and the remaining symbols are the same as in equation (3.1). This estimate of net migration is called "residual" be- cause it represents that part of the change between Pj and P not explained by births and deaths. As such, it is an indirect measure, and the estimate of migration is affected by all errors in the counts of population, births, and deaths. In cohort-component computations the mortality component in (3.4) is estimated by the use of U.S. Bureau of the Census. Current Population Re- ports, Series P-20, No. 285. "Mobility of the Population of the United States: March 1970 to March 1975." Washington, D.C.: U.S. Government Printing Office, 1975. 20 survival rates of the types discussed above. For the period 1960 to 1970, net migration would be calculated by cohort as follows: NM = P 70 x x (pf 10 )SR (3.5) where SR is the survival rate (either a national census survival rate or one calculated from a life table ), NM is net migration, and the other symbols are the same as in equation (3.2). The value after the minus sign is often called the "expected" popu- lation. For the cohorts under 10 years of age in 1970, the number of births for the appropriate intercensal period are substituted for P 60 x-10. This is the "forward survival" technique and is the one most easily adapted to population pro- jections. For this purpose, net migration is usually expressed as a rate by dividing by the expected population— the initial population can also be used— as follows: RNM = P 70 - (P 60 ln )SR x x-10 ,60 x-10 )SR (3.6) persistent. However, the longer into the future these trends are projected, the weaker becomes the rationality of the procedure. If projections are prepared for a set of subareas, for example all counties of a State, the assumption of a continued rate of net migration creates a difficulty of a mathematical nature. The rapidly growing areas with a net in-migration grow more and more rapidly as the projection period is extended, demanding more and more net migrants. The areas with lower rates of net in-migration or with net out-migration are not growing as rapidly or are losing population. The total net migration computed as the sum of the individual area calculations tends to exceed the value calculated by the same tech- nique for the area as a whole. The greater is the variation in growth rates among the subareas, the greater the imbalance, and as the projection period is extended, the imbalance becomes progressively more severe. Various means have been developed to adjust the parts to sum to the control total for the whole, but the problem is difficult, especially when some of the areas have net out-migration. One of the techniques used in this situation is the plus-minus adjustment. An illustration of its use is given in the illustrative population projection in Appendix H. 29 where RNM is the rate of net migration. The most common projection procedure is to assume that rates calculated in this way for the historical base period will continue in the future. This procedure is closely related to the "cohort change" technique, because if the survival rate as well as the net migration rate is held constant, it can be shown that the projected population is exactly the same as would be obtained by the use of formula (3.2) rearranged as follows: ,80 ,70 ,60 , x-10 ,70 x-10 (3.7) Formula (3.7) is the "projection of past trends" which is cited by critics of the method as being mechanical and unrealistic. To a degree they are correct, although the assumption is not altogether unrealistic because net migration trends tend to be There are, however, alternatives to the assump- tion of a continuation of rates into the future. The in-migration areas can be restricted in the growth rate allowed, thus diminishing the size of the adjustment to the subarea totals. A simple restric- tion would be that the projected number of net migrants is not allowed to exceed the number estimated for the base period, or could exceed it only by a certain proportion, based for example on the anticipated growth in the size of the gross migrant pool for the Nation. (See below for a discussion of this concept.) This restriction could be specific by age, if desired. Such measures would diminish the degree of imbalance and the adjust- ment required. In fact, any control total for net migration obtained by independent analysis can be imposed on the cohort-component projections, for example, the 29 The plus-minus technique is shown in table H-1 1, foot- note 3. 21 output of a regression analysis, and migration totals and age distributions can be adjusted to the new controls. 30 If the particular age distribution has both positive and negative values, as is not unusual for counties, the adjustment can become a serious problem. The plus-minus technique can be used, but a new technique has been suggested to make such adjustments, whereby standard age patterns are established which can be applied according to the type of area involved. 3 i If these adjustments can be made more logical as a result of this technique, or by some other means, it would be a tremendous service to this approach to population projections, because net migration is easy to calculate and can be prepared for any size area, for any intercensal period. The "adjacent cohort" technique. An addi- tional consideration in all cohort-component^ pro- jections is the time unit used. All of the illustrations regarding net migration given thus far assumed 10-year projection periods, matching the length of the historical base period. The illustrative pro- jections in Appendix H also use this time period. If the projections are to be carried out for 5-year periods, a problem arises in adapting the 10-year intercensal migration data to the 5-year time inter- val. To consider one cohort as an example, a net migration rate is needed for the cohort aged 10-14 at the beginning of a 5-year period, becoming 15-19 at the end. During the intercensal period from 1960 to 1970, two cohorts pass through this range, as shown by the following diagram: 1960 1965 1970 Age u 5 10 15 20 65+ u 5 10 15 20 75+ The cohort aged 5-9 becoming 15-19 has the experience in the second half of the decade, while the next older cohort has it in the first, as indicated by the shaded areas. A common practice has been to divide the 10-year rate for each cohort by two and average these rates for adjacent cohorts, obtaining an estimate for a 5-year period. There are other procedures that are somewhat more sophisticated, but all have the same basic premise. This practice has been referred to as the "adjacent cohort" technique. 32 It works fairly well if the net migration rates do not vary too much from one age group to the other. If, however, there are large differences in rates between adjacent cohorts, the procedure results in a deviation from the original cohort migration values, producing serious errors in the projected population after 5 years, and after 10 years as well. Large variations in net migration rates from age to age are common for counties which represent only a part of a metropolitan area. A growing suburban county in the 1960's typically experienced net in-migration of Whites at about ages 25 to 40 and under 15 years. These, of course, are the large families who migrated to the suburbs during the period. But in the same county there is often an out-migration or a much lower in-migration at ages 15 to 24, as the older children reach the age to attend college, take a job, and marry. These persons gravitate to the central city where they are closer to their employment and find smaller housing units at a rental they can afford. The central city thus tends to have opposite flows from those of the suburban county, and typically at a high rate. In these situations the adjacent cohort practice can lead to errors in the order of 10 percent or over where moderately heavy migration flows are in- volved. This has been demonstrated with gross migration data from the 1970 census. 33 Migration statistics for a 5-year time period for a suburban (3.8) In the step-by-step illustration given in Appendix H, the precise use of such an independently derived projection of net migration in table H-4 is described at Step 7 of Section 3.3. 3 'Donald B. Pittenger, "A Typology of Age-Specific Net Migration Rate Distributions." Journal of the American Institute of Planners, Vol. 40, No. 3, pp. 278-83, 1974. 32 Richard Irwin, "Use of the Cohort-Component Method in Population Projections for Small Areas." Paper prepared for the Conference on Population Forecasting for Small Areas. Oak Ridge, Tennessee: Oak Ridge Associated Uni- versities, 1975. 3 3 Ibid., pp.14-17. 22 county were manipulated so as to show the effect of the adjacent cohort averaging technique. After combining the 5-year data to form rates for 10-year periods, the 5-year data were "recreated" using the averaging technique. The results of these compu- tations are as follows: Age Original "Recreated" Difference ("recreated " Beginning End of rates rates minus of period period original ) 5-9 10-14 8.5 9.4 0.9 10-14 15-19 4.4 6.2 1.8 15-19 20-24 7.4 13.4 6.0 20-24 25-29 36.0 25.6 -10.4 25-29 30-34 24.8 24.8 0.0 30-34 35-39 13.8 15.8 2.0 The deviations of the "recreated" net migration rates from the original values are substantial for the two age groups with initial ages 15-19 and 20-24 years. Faced with this degree of distortion, the use of the adjacent cohort technique is not recommended if the distribution of net migration rates by age shows substantial deviations between adjacent co- horts. A better procedure is to project for a 10-year period, and obtain population data for intermediate years by interpolation, age by age. This is the procedure followed in the step-by-step illustration of the cohort-component method in Appendix H. Gross migration. However, there are more fundamental problems in the use of net migration in population projections. 34 Migration is in reality a two-way phenomenon, consisting of out-migrants and in-migrants. "Net migration" is in a way a statistical artifact; there is no person who can be termed a net migrant. This theoretical objection contributes to the mathematical difficulty in ad- justing net migration projections discussed above after formula (3.7). For these and other reasons, interest has been growing in the analysis and use of gross migration data, whereby for a given area, out-migration and in-migration are shown sepa- rately. One way of obtaining gross migration statistics is through questions in censuses and surveys, asking the residence of the respondent at some prior date. Such questions have been included in the decennial censuses since 1940 and are asked annu- ally in the Current Population Survey. From these data a wide variety of migration statistics can be obtained, such as place-to-place migration streams, gross in-and out-migration for each place, and net migration. All of these can be used as basic data for population projection models. In its population projections for States and metropolitan areas, the U.S. Bureau of the Census has used the gross migration data provided by the 5-year retrospective question on migration in the decennial census. 35 These "demographic" pro- jections use conventional techniques for birth and death projections but make separate computations for in- and out-migration. For each area, out- migration by age, race, and sex is projected first using rates observed during the base period. The out-migrants from all areas are summed to form a national migration pool. This pool of migrants is allocated back to the subareas on the basis of the proportions observed in the base period census data. This procedure has the effect of causing the net migration projected for the various areas to converge toward a central value as the projection period is extended. Gross migration data are closer to the real process of migration than are net figures, and their use in projections avoids some of the problems which appear in net migration models. For example, the sum of all out-migrants automatically equals the 14 Additional material can be found by consulting works included in Section 5, Selected References. 35 U.S. Bureau of the Census, Current Population Reports, Series P-25, Nos. 375 and 415. See Section 5, Selected References , for complete citations. 23 sum of all in-migrants in the gross migration procedure outlined in the preceding paragraph. In projections using rates of net migration, as mentioned earlier, the sum of net in-migrants always tends to exceed the sum of net out-migrants, and a special adjustment must be carried out. The migration process is even more closely represented by place-to-place statistics. Data of this type have figured in analytical studies from time to time, but have not been incorporated in the prepa- ration of published population projections for local areas.- Net immigration from abroad. Since net civilian immigration has been about 25 percent of total U.S. population growth in recent years, it should be either explicitly or implicitly taken into account in preparing population projections for local areas affected by international migration. Intercensal estimates of net migration for local areas by the residual method implicitly include net movement of all persons from abroad (including members of the Armed Forces if no special adjust- ment is made for the military population). If it is assumed in a projection model that past net migration trends will continue, the implicit assump- tion is that the international portion will also continue. Users and producers of population pro- jections should be aware of this aspect of a net migration assumption, even if no special adjustment is required. By contrast, gross migration statistics obtained from census questions about prior residence cannot include net international movement, because the question is only put to persons residing inside the country and to American citizens abroad. These statistics show all internal in- and out-migration, but typically reflect only the total movement into the country from abroad. If gross migration statistics are used in a projection model, net immigration from abroad must be explicitly introduced if it is to be taken into account. The 1970 census provides information which can be of assistance in quantify- ing this component (tables 1 19, 144, and 145 of the State volumes, et al). 3.235 Advantages and limitations of the co- hort-component method. Whether or not to use the cohort-component method in preparing a set of population projections is one of the most basic decisions to be made. It is therefore important to be familiar with the advantages and limitations of the method. These can be considered under two cate- gories: (1) level of detail, and (2) geographic unit of reference. Level of detail. A cohort-component pro- jection involves a good deal of detail, even for a simple model. Other things being equal, a more sophisticated method should give better results. There are, however, both positive and negative aspects to the relatively large amount of detail. On the positive side, the detail by age— and by sex and race if desired— is useful for many planning functions. Medical facilities and services are often aimed at a certain age range, for example, pediatrics, cardiology, and geriatrics; or may be specific by sex, e.g., prenatal care. Housing needs are also specific to the age of the user. Interest has been growing in the aged population, since providing services for retired persons has become an important part of the national economy. Planning for all these functions requires accurate projections by age and justifies the time to produce them. Another advantage of the component approach is that the data produced on births, deaths, and migration are useful for planning in themselves. In addition, the analyst has the option of using greater detail on the component most fundamentally re- lated to the problem at hand. By contrast, the high level of detail also requires more data as basic input, and more calculation. The latter can be done by computer, but if only a few areas are involved, use of the computer may not be justified. The input data on population and vital statistics have to be prepared by hand in any case. If corrections are needed for a special population, additional time is required to collect the data if available, or estimate it, if not. All in all, a set of projections by this method is a major under- taking. 36 Geographical reference unit. The cohort- component method produces the best results when working with a labor market area as a unit, for example, an SMSA. Logically the method is per- fectly applicable to any area, no matter how small, whose geographic boundaries are fixed and for which the basic data can be obtained. Practically, however, as the area becomes smaller, both in land area and population size, the difficulty of using the method increases. Migration between SMSA's is a fundamental alteration of a person's social and economic ties, usually involving a change of employ- ment. Migration rates are low, relative to smaller 36 See Section 2.32, Complexity of method , for a general discussion of the advantages and disadvantages of the more complex methods. 24 areas, and the age distribution of migrants is closer to the national mobility pattern, making the pro- jected age detail more reliable. Within an SMSA there is much migratory movement to obtain suit- able housing and various services, as family com- position changes through time. This results in very high net migration rates for small areas and sharp variation from one age group to the next. 37 The smaller the area, the higher the migration rate across its boundaries. At the county level, the cohort-component method is still manageable. Most counties are fairly large in land area and encompass persons of hetero- geneous social and economic characteristics, so that no single event will completely change the popu- lation picture. For a census tract or smaller area, a single large new apartment house will be translated into very high rates of net in-migration. It is difficult to adjust these rates for expected future develop- ment of the area. For such small areas, some other method based on housing change and population density is indicated. In using the cohort-component method on local areas, the geographic size of the area has an important influence on the selection of the type of migration data to be used, gross or net. For large areas like SMSA's, either gross or net migration techniques can be used, but gross migration is preferred because of the closer relationship to the real migration process, with the possibility of separate determination of the factors affecting in- and out-migration. However, net migration is simpler and easier to calculate, and may be pre- ferable if a single local area is under consideration. At the county level, and for areas of small population size in general, gross migration data have not been readily available; and data from the decennial census, if tabulated, may have too large a sampling variation to recommend their use. Correc- tions for special populations require more detailed computations, which in turn are dependent on the form of tabulation of the census data on gross migration. Estimates and projections of net migra- tion are independent of this restriction, and adjust- ments for special populations can be designed to fit the specific local situation. Errors of measurement in basic data. Each component has its own special problems. Although birth registration was shown to be nearly complete by a recent nationwide study, 38 there are problems in the proper allocation of births to the place of residence of the mother. In general this is believed to be accurate at the county level, although there are indications that births to Black residents of some suburban counties in the South are not attributed to the proper county. As to the mortality component, the number of deaths estimated by life table survival rates may differ from registered deaths for a given small area for several reasons. (1) There are real differences in mortality between regions and between socioeco- nomic classes. A life table which relates strictly to the population of each local area is not always available. (2) There are random fluctuations in the number of deaths for a small area. (3) There is the allocation of deaths in institutions to place of former residence. This is the recommended practice, but it is not always logical, since the deceased may have been institutionalized for a long period of time. There may also be errors in the allocation process. In any case, a cohort-component computation will automatically assign these deaths to the institutional location. Finally, a technical problem in projecting deaths is the failure of the forward survival method— the most convenient to use in net migration pro- jections—to take deaths of migrants into account. In the case of net in-migration, the tendency is to underestimate deaths, with the reverse tendency for out-migration. In general, migrants are young people, for whom death rates are low, and the error is not large; but for retirement communities, this factor must be kept in mind. If the projection model uses residual net migra- tion, errors in the birth and death components are compensated by the migration component, and the projected population remains essentially the same as would be obtained by the cohort change procedure of formula (3.2). A calculation using gross migration data will not have this element of compensation; errors will be reflected in the final population projection. For example, if the survival rates yield too many deaths, the projected population will be lower than intended. The gross migration data are obtained in a census and reflect net census underenumeration, and misre- See Section 3.234, Adjacent cohort technique , for comment on the age distribution of net migrants. 38 U.S. Bureau of the Census, Census of Population: 1970. Evaluation and Research Program, PHC(E)-2, "Test of Birth Registration Completeness, 1964 to 1968." Washington, D.C.: U.S. Government Printing Office, 1973. 25 porting of age and other information. In addition, it is believed that migrants are less completely enu- merated than the general population. Once enu- merated, the accuracy of the data depends on the ability of respondents to give accurately their resi- dence exactly 5 years earlier; if they were in the Armed Forces or in college, they were expected to give residence there, not at the home of their parents. There is also the problem of nonresponse. The migration statistics from the 1970 census show that 11.1 percent of the persons who reported that they had moved between 1965 and 1970 did not indicate their place of residence in 1965. 39 For the Black population the figure was 17.2 percent. These persons were not included in the gross in- and out-migration statistics since the origin of their move is not known, and they were not assigned anywhere as an out-migrant. A special tabulation of the 1970 census gross migration data has been prepared at the Census Bureau, in which non- response on this item was allocated on the basis of other information. 40 These data will be suitable for use in population projection models. With all these problems, special interest attaches to the use of administrative records to obtain migration statistics. The Bureau of the Census has been working with records of the Internal Revenue Service (IRS) to estimate migration. Net migration calculated from this source was used in preparing population estimates for small areas under the Federal General Revenue Sharing program, but it is also possible to obtain gross migration data for States and counties. Potentially, the method could produce place-to-place flow data. There are limita- tions due to coverage and reporting of residence, however, as well as the purely mechanical concerns of access to files, the expenses involved in processing large computer files, and related issues. The Con- tinuous Work History Sample (CWHS) of the Social Security Administration is another set of adminis- trative data that has been used to obtain migration statistics. See Section 4.4 in the section on data sources for comment on the CWHS, and for a refer- ence to material evaluating the use of IRS and CWHS data in generating migration estimates. Use of the cohort-component method is in- creasing, and problems in its use are being resolved. The method provides a flexible instrument which can be fitted to the particular needs of a project. For example, the method serves as a basic frame- work for many economic-based population pro- jections. If projections by age are desired, the cohort-component technique will usually find a place somewhere in the projection model. 3.24 Economic-based methods. In the interest of making better forecasts of population, there has been growing interest in basing the projection of population, or of migration, on projected economic data. This interest was stimulated by a study by Lowry 41 examining the relation of migration streams to unemployment rates, wages, labor force size, and distance of move. Lowry found that unemployment and wage rates at the point of destination significantly influenced in-migration. In another model presented in the same study, he found a very high correlation between the volume of net migration and change in employment. Lowry concluded, however, that his results did not indicate a causal relationship of employment to migration, but that there was a "series of feedbacks or mutual adjustments between migration and the demand for labor." 42 Many economists nonetheless believed that migra- tion should be made a function of projected employment in population projections. Prior to the appearance of Lowry's study, projections had been prepared for labor market areas in Oregon whereby the size of the migration component was determined by an employment projection. 43 More recently the State of Pennsylvania has prepared a comprehensive set of projections with a similar basic premise. 44 A cohort-component projection assuming zero net migration was made for each subarea to produce a "closed population," and labor force participation rates were projected by age and sex. The closed population multiplied by the participation rates yielded the labor supply in the absence of migration. After allowing for unemployment, the difference between this supply and the employment projected U.S. Bureau of the Census, Census of Population: 1970. Subject Reports, PC(2)-2B. "Mobility for States and the Nation." Washington, D.C.: U.S. Government Printing Office, p. 1, 1973. 40 For further information, see Section 4.4. 41 Ira S. Lowry, "Migration and Metropolitan Growth: Two Analytical Models." San Francisco, California: Chandler Publishing Company, 1966. 42 Ibid., p.44. 43 Richard B. Halley and Morton Paglin. "Population Forecast, State of Oregon and Economic Areas: 1960-1985." Portland, Oregon: Oregon State Board of Census, Portland State College, 1964. 44 Pennsylvania Governor's Office of State Planning and Development. "Population and Labor Force, by Age and Sex— to 1990." Pennsylvania Projection Series, Report No. 73, Harrisburg: Commonwealth of Pennsylvania, 1973. 26 by an economic model determined total migration for the labor force. The age and sex distribution of the migrants needed to provide the employemnt differential was obtained by adjusting residual net migration estimates for the 1960-70 decade. In broad outline, this is the approach used by the National Planning Association (NPA) in preparing population projections for subnational areas. The NPA pioneered in the establishment of the method; their most recent projections for States were pub- lished in 1972. 45 A projection model for development districts in Tennessee 46 utilized similar elements to obtain detail by age and sex, and the model provides for interaction among various subsystems. The key projection of total net migration, however, is determined by a regression equation in which the independent variables relate to college enrollment, income, employment, rate of unemployment, and labor supply. A problem common to all regression formats is the necessity to project the independent variables before the regression equation can produce the projected dependent variables. One study used some unusual independent variables in a regression equa- tion for determining net migration in developing cohort-component projections for counties. 47 The independent variables are: (1) number of super- highways, (2) number of colleges by type, (3) previous migration rate, (4) number of cities over 10,000 population within 30 miles, (5) number of cities over 20,000 lying 30 to 80 miles away, and (6) distance from a large out-of-State metropolitan area (30 to 80 miles). The externally prepared pro- jections needed for these independent variables are subject to relatively small error. The U.S. Bureau of Economic Analysis has prepared population projections for the 173 eco- nomic areas they have delineated. 48 They projected 45 Joe W. Lee and William B. D. Hong. "Regional Demographic Projections: 1960-1985." 1972 Regional Economic Projections Series, Report No. 72-R-1. Washington, D.C.: National Planning Association, 1972. 46 Richard A. Engels and Annie A. Moore, "Tennessee Migration, Population, Families, Income, and Manpower Demand Projections to 1990, for Development Districts and Counties." Nashville, Tennessee: Tennessee State Planning Office, 1974. 47 Kentucky Program Development Office. "Kentucky Population Projections, 1975-2020, Vol. I." Frankfort: Commonwealth of Kentucky, 1972. 48 U.S. Bureau of Economic Analysis, Department of Commerce. "Area Economic Projections 1990." Washington, D.C.: Government Printing Office, 1974. total employment for each area from a procedure initiated by a projection of labor earnings, industry by industry, in "export" industries, augmented by "residentiary" employment. The projections of population were then obtained as a function of changes in area employment. However, in order to reflect properly changes in population which are not related directly to economic opportunity, the 1970 population in each economic area was grouped into three age categories and each was projected indepen- dently. The three groups were: (1) the labor pool (ages 14-64), (2) the pre-labor pool (aqes0-13), and (3) the post-labor pool (ages 65 and over.) The population in the labor pool was projected as a function of area employment. The pre-labor pool was projected as a function of the labor pool, but the post-labor pool was projected independently. Although the population and employment projec- tions are initially prepared for the 173 economic areas, the data are subdivided and reaggregated to provide data for States and SMSA's. The use of the BEA economic areas is an important advance in linking economic data to population dynamics. The areas are drawn to delineate labor markets. As such, the patterns of interarea migration should be more susceptible to economic-demographic analysis, because a job shift from one area to another almost surely means a matching migration of the job holder. Within labor market areas there is heavy migration from one jurisdiction to another with no change in site of employment by any member of the family. Un- fortunately, census data on gross migration for BEA economic areas have never been available, but are included in a special tabulation for the Deriod 1965-70. (See Section 4.4) None of the published economic-based popu- lation projections reviewed here used gross migra- tion data. However, as an outgrowth of Lowry's work 49 a series of theoretical studies have investi- gated the separate characteristics of in-migration and out-migration. Working with gross migration data for State economic areas, Olsen developed a model for projecting in-migration and out-migration rates by age. 50 He used a single-equation model, with the dependent variable being either in-migration or Lowry, op. cit. s0 Richard J. Olsen. "Population Migration: State Economic Areas in the Interior Southeast," Regional Envi- ronmental Systems Analysis Report No. 74-13. Oak Ridge, Tennessee: The Oak Ridge National Research Laboratory, 1974. 27 out- migration rates by age. The independent vari- ables relate to unemployment, population density, presence of college and military population, occu- pation, race, and labor force participation. A key characteristic is that migration is analyzed not only in terms of economic data for the area but also in terms of the characteristics of persons, such as educational attainment. An important feature of Olsen's work is the use of "pooled cross-sectional" data. This technique is described as a pseudo time-series analysis whereby the change in the relationship between the variables between two points in time is the critical factor. In his analysis of gross migration rates, both the 1955-60 and the 1965-70 data are incorporated in the regression format. A more recent study by Kleiner extends the investigation by using different variables in the equations for in- and out-migration and by including separate data by race. 5 1 Kleiner used data for States and tested his model on 15 States by preparing "projections" to 1970 and comparing them with a projection using demographic data only. These and other studies are producing new insights into the interrelationships between the migration process and the economic and social characteristics of places and persons. The key assumptions as to future migration flows in popu- lation projections can be more closely related to the real process of population redistribution. However, research up to now has usually been directed toward showing that migration is caused by the various factors used as independent variables in a regression format. This causal relationship has not been satisfactorily demonstrated, and the inter- action of migration with the economy, "the series of feedbacks or mutual adjustments" in Lowry's words, 52 still remains to be discovered. Nonetheless, the linking of demographic and economic projec- tions is desirable, in that mutually consistent pro- jections of the two disciplines are useful as planning tools. It is not necessary to establish the causal effect of one on the other, and future research can profitably explore the relationship without assigning either as the prime mover. The user of either the economic or demographic projections from such an integrated set should keep in mind, however, that there may be a circularity in the influence of demographic and economic factors in the construc- tion of the system, which may lead to an unjustified confidence in the reliability of the projections. 3.25 Land use methods. A final category of population projections centers on the spatial aspect of population growth. One approach often used by city planners is the "saturation" method. Given a certain pattern of land use, as specified by zoning ordinances, how many housing units by type can be accommodated, assuming full utilization? The addition of an assumption as to average number of persons per housing unit produces a population projection. The city planner frequently has accurate data on housing for very small areas on a current basis. Of course zoning ordinances can be changed, and an error can also be introduced by unexpected change in average household size. The method is, however, well suited to small areas like census tracts. A different approach to projections for census tracts was taken by a group in Oregon for a four-county health planning area. 53 Briefly, a re- gression analysis suggested that 1970-73 changes in housing were related to changes from 1960 to 1970, and to housing density levels. The analysis was carried out by type of structure, that is, single family, multi-family, and trailers. Changes in hous- ing by type were projected from 1970 to 1980 with these relationships. The model was iterated to extend the projections, with increasing housing density acting as a constraint. The population implied by these projections was controlled at each decennial date to a previously prepared demographic population projection for the entire area. The change in housing stock by type also determined change in the distribution of population by broad age groups. Another method with a new approach was demonstrated on New Jersey minor civil divisions and elaborated by the Rutgers group. 54 For lack of a better category, it is discussed here under land use because popuation density is the critical factor, measured in two ways: (1) change over time, and (2) level. A relationship between the rate of change in population density and the level of density is 5 Morris M. Kleiner. "An Analysis of Interregional Migration for Manpower Planning." Urbana, Illinois: Center for Advanced Computation, University of Illinois, 1974. 52 Lowry, op.cit., p.44. 53 Portland State University, Center for Population Re- search and Census. "Population Projections to the Year 2000: Oregon Administrative District 2." Portland, Oregon: Comprehensive Health Planning Association for the Metro- politan Portland Area, 1975. 54 Newling, op. cit., and Greenberg, Krueckeberg, and Mautner, op. cit. 28 established by regression, and is incorporated in a mathematical expression which sets a limit to the increase in density as the projection is extended. Since the area is fixed, the limit on density is a limit on population. This model is dependent on the mathematical resolution of the dynamic factors in the equations, which in turn are determined by the pattern and pace of the changing geographic distri- bution of the population in the 1950's and 1960's. It is unlikely that these patterns will be maintained in the future, due to changing relationships between personal income and the cost of land, construction, and transportation. In addition, the model assumes that the relation between different geographic areas at a single point in time is valid as a guideline for future growth of a single geographic area during the passage of time. 3.26 Trends in methodological development. It is interesting to note that density was used as an independent variable by Kleiner and appears in the Portland State model. When dealing with small land parcels with high population density, or the poten- tial to attain it, density must not be overlooked. But a simple density ceiling is of doubtful value. Chang- ing costs of house construction and commuting, and in the price of land, have the force to crumple existing patterns of land use. Still, the developments in projecting by land use methods are among the most interesting in the field, especially for very small areas. Other significant trends are the increased use of the cohort-component technique, and the incorporation of economic factors in pro- jections of migration. 3.3 Methodology for Projections of Miscellaneous Population Characteristics Mention has already been made of the wide application of ratio and cohort techniques in pro- jecting various population characteristics (Sections 3.22 and 3.23). This section will outline the principal techniques and considerations involved in the projections of such characteristics as school enrollment, labor force participation, numbers of households, health-related characteristics, income, urban-rural residence, and others. A thorough discussion of each of these subjects is beyond the scope of this guide, but some general information will help the local analyst to recognize their func- tion, if included in a population projection pro- ject. 55 55 For a detailed discussion of this subject, see "Appendix A, Methodology of Projections of Urban and Rural Popu- lation and Other Socioeconomic Characteristics of the Population," in Shryock, Siegel and Associates, op. cit., pp. 841-63. Projected characteristics can help in evaluating the population projections. Current annual data are available for some characteristics and can be used to monitor the projections. For example, school enroll- ment is almost invariably available annually in considerable detail and can be used to check on the projections of the youthful segment of the popu- lation. Employment is another such series, and building permits may be compared with projected change in the number of households. Of course, such projections are primarily prepared to obtain a projection of the characteristic itself, but the evaluation function should not be overlooked. A simple example to illustrate the use of labor force participation rates for this purpose is presented in Appendix G of this guide. 3.31 Cohort techniques. A general review of current methodology for the projection of popu- lation characteristics can best be approached under two headings: (1) cohort-related techniques, and (2) the participation rate method. The latter is related to the ratio method (Section 3.22). The cohort approach is very simply illustrated by the use of grade progression ratios to project school enrollment. Enrollment by grade for successive years is assembled, and the ratio of the enrollment in grade x in one school year to that in grade x minus 1 in the preceding year is computed for all grades. A time series of such ratios is calculated, and the observed trend projected into the future. Some way of obtaining first entries into the system at the beginning grade must be included, usually involving the projection of births. Note that the progression ratio implicitly includes migration, mortality, and drop-out rates in one factor, somewhat in the style of the "cohort change" technique (Section 3.232). The projection of enrollment by cohort can be carried out in more detail by taking separate account of entries and departures, with the whole population in the model, including those not en- rolled. The application of cohort analysis to fertility has been the subject of much work and study by demographers during the past 15 years. A whole new body of statistics was created by assembling historical birth data by cohort, and the Bureau of the Census uses this technique in projecting fertility in the national population projections. This method is analytically superior but involves detailed input data and complicated statistical techniques not appropriate at the local level. There has been continued interest in projecting families by the cohort method, although rather complex models are needed. Creation of new families, and dissolution of existing ones, can be 29 carried out by cohort in varying degrees of detail. Marriages, divorces, and deaths all must be con- sidered relative to their assumed impact on family formation and dissolution. All statistics must be by age and be systematically arranged by cohort. If different types of families and family size are included, the model quickly becomes complex. Projections of the labor force by cohort present somewhat similar problems. The above discussions of cohort applications imply what might be termed an "aggregate" approach. The actual population being projected is carried forward by age, subdivided into various categories, and the categories adjusted by accessions and diminutions. Simulation models take a very different approach. Here one hypothetical person at a time is processed through a series of probabilities (by computer necessarily) which approximate a life cycle. 56 In projections of marriages and families, for example, the first "person" processed may never marry, since there is a chance at every age of remaining single. The next "person" run through the schedule proba- bly will marry, since the probabilities of marrying, to which each individual is subjected at each age, are high in the young adult years. After the required number of individuals are processed, based on the needed sampling confidence limits, a population takes form at each point in time, classified by all the characteristics which were included in the model. This distribution is then superimposed on the actual population to obtain the final projections. Simulation models have not been extensively used in published population projections for local areas. The models are complicated, being patterned after real life choices, and computer costs are high. However, simulation techniques are very useful for studying the interaction between changes in various factors affecting the life cycle. 3.32 Participation rates. Projections of popu- lation characteristics based on participation rates are much more commonly encountered than the cohort applications described above. This method presumes an already prepared population projection by age and projects the proportion of each age group which takes part in a given activity. Many activities are highly specific as to age. School enrollment is a good example; almost all children from 6 to 15 years of age are enrolled, with a decreasing proportion beyond that age. Labor force is another, with participation beginning at age 14 or 16 (depending on statistical policy), increasing to a very high proportion for adult males, and decreasing at the advanced ages. The labor force consists of the employed plus the unemployed, and a labor force participation rate is simply the labor force divided by the population, specific by age and sex. Some of the important sources of basic labor force data needed as input are the decennial census, the monthly labor force survey conducted by the Bureau of the Census for the Bureau of Labor Statistics (BLS), 57 and the various State employment security programs. Many States have a section in their employment security office that makes labor force projections for their State, and BLS published a four-volume report which serves as a guide for developing State and local manpower projections. 5 8 Labor force participation rates are fairly stable but do change in response to fundamental changes in the life style and occupation of the population; for a local area especially, rates may change due to a shift in employment opportunity, or because of a turnover in population through migration. All of these aspects can be analyzed, and the projection of the rates into the future is a legitimate undertaking, though with its own problems. 59 The Bureau of Labor Statistics prepares and publishes projections of labor force participation rates for the Nation, and from time to time for States. These projections can be used as a reference point in projecting rates for a local area. A simple example of such use is illus- trated in Appendix G. Households and families can also be projected by "participation" rates, in this case called headship rates. The ratio of household heads to an appro- priately defined population, specific by age and sex, is calculated from actual data. These rates are projected forward and multiplied by the projected population, obtaining the number of future heads, and therefore, the number of households. The relationship of persons to a household or family is a fundamental characteristic but also is subject to The term "micro-simulation" is sometimes used to describe this technique. 57 Data from this survey are published monthly by the Bureau of Labor Statistics in Employment and Earnings. 58 U.S. Bureau of Labor Statistics, Department of Labor. BLS Bulletin 1606, "Tomorrow's Manpower Needs." Wash- ington, D.C.: U.S. Government Printing Office, 1969. 59 See Sol Swerdloff, "How Good Were Manpower Projections for the 1960's?" Monthly Labor Review, pp. 17-22, November 1969. 30 change as life style changes. For young adults at the present time, for example, the proportion of house- holds headed by young unmarried persons of both sexes is increasing, thus raising headship rates at these ages. Increasing divorce may also tend to increase headship rates, as two households may appear where one existed before. The Current Population Survey conducted by the Bureau of the Census provides current data on households and families, and the Bureau projects "households and families for the Nation from time to time by this method. 60 60 U.S. Bureau of the Census. Current Population Reports, Series P-25, No. 607. "Projections of the Number of Households and Families: 1975 to 1990." Washington, D.C.: U.S. Government Printing Office, August 1975. In projecting such characteristics as labor force status, household membership, and school enroll- ment by participation rates, there are almost as many variants in methodology employed as there are sets of projections. Many other characteristics have been projected by this method, such as income and educational attainment; and others could be, for example for health care, number of visits to a doctor, and food requirements, to name a few. In fact, any characteristic which varies systematically by age (and by sex and race if applicable) can be approximated by this method, though with varying degrees of accuracy depending on the stability and predictability of the particular participation rate. A reasonably accurate projection of the age distribution of the population is of course a prere- quisite, and effort spent to improve the age detail is justified in part by improvement in the projections of characteristics. 4. SOURCES OF DATA (The references in parentheses in the text refer to Exhibit 4-A, Selected List of Data Sources, at the conclusion of this section) The great variety of methods used to develop local area population projections and the diversity in the geographic units for which projections are made (States, counties, cities, minor civil divisions, census tracts), bring into play a large and varied reservoir of potential data sources. A complete bibliography is beyond the scope of this review; instead an outline will be presented covering the most important categories. These relate to demo- graphic data only; for information relating to economic variables, other sources must be con- sulted. Some of the economic-based studies mentioned in Section 3.24 contain references and comment on basic data. 1 4.1 Births and Deaths The historical vital statistics needed in developing subnational population projections are provided by the national registration system. The U.S. National Center for Health Statistics (NCHS) processes the data collected by the States, and issues definitive tabulations yearly. The most recent publications at this writing are for deaths in 1973 and births in 1972 (U.S. NCHS, 1975b and 1975c). 2 More up-to-date final tabulations are available on special request. NCHS also publishes provisional data and prepares analytical studies (U.S. NCHS, 1952). The various State offices responsible for vital statistics also publish their own reports. Many States provide preliminary data with a very short time lag, typically providing totals by county. NCHS periodi- cally prepares a directory of the offices which produce these reports. A list of these offices is given in Exhibit 4-B at the end of this section. The professional literature and various govern- mental publications provide a large amount of detailed data and analysis on fertility and mortality, especially the former. Of general interest are the national population projections of the U.S. Bureau 1 See previously cited works by Lowry, Olsen, and Kleiner, cited in Section 5. Selected References . 2 See headnote to this section regarding the references in parentheses. of the Census (1975b), emphasizing fertility trends; and of the U.S. Social Security Administration (1974), with emphasis on mortality. 4.2 Population Censuses and Surveys The enormously varied population data provided by the U.S. Bureau of the Census from the decennial censuses, the Current Population Survey, and other sources are listed in their Catalog of Publications. The current version of the basic volume covers publications from 1790 to 1972 (U.S. Bureau of the Census, 1974). New publications are compiled and presented quarterly, with monthly supplements. These are accumulated to annual volumes, the most recent of which is for 1974. The Catalog covers all types of data produced by the Bureau, including population estimates and projections, which are discussed below in Section 4.5, Miscellaneous Data Sources. Of the standard population data produced by the Census Bureau, the regular decennial census vol- umes, one for each State, are of universal interest for preparing population projections (U.S. Bureau of the Census, 1972a). In addition, a series of publi- cations are presented for census tracts (U.S. Bureau of the Census, 1972c). Data are also provided on computer tape in standard packages, and special tabulations can be obtained. The Data User Services Division was created to assist the public in obtaining information. Not as widely known is the availability of a tabulation of the population of counties on April 1, 1970, by age, race and sex, with adjust- ments to the basic census data (U.S. Bureau of the Census, 1975a). Private organizations also provide basic and special tabulations of census data. Finally, special censuses of local jurisdictions conducted at their request by the Census Bureau and by some of the States provide a resource for evaluation of pro- jections and the creation of new benchmarks. 4.3 Net Migration The most important source of recent historical net migration for small areas is the data for counties by age, race, and sex developed by Bowles, Beale, and Lee (1975). These estimates were prepared by a 31 32 modified census survival rate method. A similar technique was used in preparing estimates for the decade 1950-60 (Bowles and Tarver, 1965). For earlier decades (1870 to 1950), net migration statistics have been developed for States (Lee, Miller, Easterlin, and Brainerd, 1957). The U.S. Bureau of the Census prepares inter- censal estimates of births, deaths and net migration for counties (not by age). For the decade 1960-70, detail by race is shown for counties with a substantial Black and other races population (U.S. Bureau of the Census, 1971). 4.4 Gross Migration A resource of growing interest to population projections is the data obtained by means of census questions on former residence. In 1950, the question related to residence 1 year prior to the census date, and in 1940, 1960, and 1970, the reference period was 5 years. These questions provide statistics on place-to-place migration streams, and on gross out- and in-migration for the various jurisdictions shown. Net migration is, of course, also obtained, being the difference between these two flows. The State economic area is the smallest unit for which tabulations are presented in the 1970 census (U.S. Bureau of the Census, 1972b). Sampling variation is a problem with small areas; in 1970 a 15 percent sample formed the basis for the detailed tabulations shown in the subject reports for migration. Detailed statistics for regions, States, and metropolitan areas are cross- tabulated with various special charac- teristics of migrants (U.S. Bureau of the Census, 1973a, 1973b). There was a high rate of nonresponse to the question on residence 5 years earlier in the 1970 census, and a special file is now being processed at the Census Bureau in which the place of former residence will be allocated for persons who moved, but did not specify former residence. Tabulations by age, race, and sex and certain special characteristics are planned, and summary data will be published for States and counties. Special tabulations can be obtained at a cost by writing to the Data User Services Division, making reference to the 1970 Census Gross Migrant file. The migration reports generated by the Census Bureau's Current Population Survey (CPS) should be mentioned, even though no data are presented below the geographic level of the four census regions. The CPS has included a question on previous residence every year since the first survey in 1947. Until 1973, the question related to resi- dence 1 year prior to the survey date. From 1973 to 1975, the reference year was the previous decennial census date, that is, 1970. The most recent report is for 1975 (U.S. Bureau of the Census, 1975c). These reports provide information on the socio- economic characteristics of migrants, and are very important for monitoring national migration trends on an annual basis. Migration is only one of a number of subjects for which tabulations from the CPS are prepared (U.S. Bureau of the Census, 1947a, 1948). A relatively new resource is the Continuous Work History Sample of the Social Security file. It has recently been increased from a 1 percent to a 10 percent sample, which will greatly increase the amount of usable detail. There are serious problems, however, in the use of these data for obtaining migration statistics. The file does not regularly contain place of residence of the wage earner, only place of work; and basic coverage is a problem. There has been considerable experimentation in the use of the file to develop migration data, and the Bureau of the Census has evaluated the CWHS, as well as records of the Internal Revenue Service, as sources of migration data. 3 4.5 Miscellaneous Data Sources The population estimates and projections pub- lished by the Census Bureau provide material of direct application to local area projections (U.S. Bureau of the Census, 1947b, 1969). Current estimates are typically published annually, while projections for the Nation, for States, and for metropolitan areas are prepared on an occasional basis. The national projections especially have been widely used as reference points for projections of local fertility and mortality rates. To a lesser extent, the Bureau's projections for States have served as a starting point for locally prepared small area pro- jections. As to estimates, the practice of using a postcensal estimate as the starting point for projections is increasing. The Bureau annually publishes estimates 3 Meyer Zitter and David Word, "Use of Administrative Records for Small Area Population Estimates." Paper pre- sented at the 1974 Annual Meeting of the Population Association of America, New Orleans, Louisiana. See also U.S. Bureau of the Census, Current Population Reports, Series P-23, No. 31, "Use of Social Security's Continuous Work History Sample for Population Estimation." Wash- ington, D.C.: U.S. Government Printing Office, 1970. 33 for States, SMSA's and counties. Some age detail is provided for States. County estimates of the total population are produced by the Federal-State Cooperative Program for Local Population Esti- mates. The estimates are prepared using metho- dology developed and tested jointly by the Census Bureau and the States, and are published annually (U.S. Bureau of the Census, 1969). A list of the addresses of the State and territory offices preparing population estimates can be found in Exhibit 5-C at the conclusion of this section. These offices may be able to provide references to local projections prepared for their States; some prepare projections themselves. In 1974 a new series of estimates of population and per capita income for local areas were Drepared by the Census Bureau for use in the Federal Revenue Sharing program. Estimates for 1973 were developed for about 38,000 local jurisdictions from the administrative records of the Internal Revenue Service and the Social Security Administration, and census data. Estimates for 1975 will be published early in 1977. See Section 3.235 under Errors of measurement in basic data for further comment. The projections published by the U.S. Bureau of Economic Analysis (1974) and by the National Planning Association (Lee, et al, 1976) should also be cited as data sources, since they offer complete national sets of data for States and metropolitan areas. As discussed in the text, these projections are economic-based and serve as im- portant reference points for other work. State and local governmental organizations also provide an important source of new methodology and reference data. A number of States prepare population projections for the State total and for sub-areas such as counties or planning districts. Local jurisdictions develop useful basic data and methodoloqy in working with smaller areas. A survey of this activity was carried out in 1969 and is currently being updated and extended by the Census Bureau. New methodology and sets of projections are also developed by research centers and by consulting firms, sometimes with financial support from State or Federal agencies. Along with the work by State and local planners, these form an important addition to the data available for use in the preparation of population projections and for reference. 34 Exhibit 4-A. Selected List of Data Sources Bowles, Gladys, and James D. Tarver. 1965. "Net Migration of the Population, 1950-60, by Age, Sex, and Color." Economic Research Service, U.S. Department of Agriculture, Washington, D.C.: U.S. Government Printing Office. Bowles, Gladys, Calvin L Beale, and Everett S. Lee. 1975. "Net Migration of the Population, 1960-70, by Age, Sex, and Color. United States, Regions, Divisions, States, and Counties." Population-Migration Report 1960-70 Parts 1-6. Athens, Georgia: Economic Research Service, U.S. Department of Agriculture; The Institute for Behavioral Research, University of Georgia; Research Applied to National Needs, National Science Foundation, in cooperation. Lee, Everett S., Ann R. Miller, Richard A. Easterlin, and Carol P. Brainerd. 1957. "Population Redistribution and Economic Growth, United States 1870-1950. Vol. I, Methodological Considerations and Reference Tables." Philadelphia, Pennsylvania: American Philosophical Society. Lee, Joe W., Timothy B. Sivia, and David W. Fay. 1976 Regional Economic Projections Series Report 76-R-1 (by subscription only) "States and Large Metropolitan Areas." Washington, D.C.: National Planning Associ- ation, 1976. U.S. Bureau of the Census. 1947a to present. Current Population Reports, Series P-20, "Population Characteristics." Washington, D.C.: U.S. Government Printing Office. . 1947b to present. Current Population Reports, Series P-25, "Population Estimates and Projec- tions." Washington, D.C.: U.S. Government Printing Office. . 1948 to present. Current Population Reports, Series P-60, "Consumer Income." Washington, D.C.: U.S. Government Printing Office. 1964. Census of Population: 1960. Vol. I, Characteristics of the Population. Washington, D.C.: U.S. Government Printing Office. . 1969 to present. Current Population Reports, Series P-26, "Federal-State Cooperative Program for Population Estimates." Washington, D.C.: U.S. Government Printing Office. . 1971. Current Population Reports, Series P-25, No. 461. "Components of Population Change by County: 1960 to 1970." Washington, D.C.: U.S. Government Printing Office. . 1972a. Census of Population: 1970. Vol. I, Characteristics of the Population. Washington, D.C.: U.S. Government Printing Office. . 1972b. Census of Population: 1970. Subject Reports, PC(2)-2E, "Migration between State Economic Areas." Washington, D.C.: U.S. Government Printing Office. . 1972c. Census of Population and Housing: 1970. Census Tracts. Series PHC (1). Washington, D.C.: U.S. Government Printing Office. . 1973a. Census of Population: 1970. Subject Reports, PC(2)-2C, "Mobility for Metropolitan Areas." Washington, D.C.: U.S. Government Printing Office. . 1973b. Census of Population: 1970. Subject Reports, PC(2)-2B. "Mobility for States and the Nation." Washington, D.C.: U.S. Government Printing Office. . 1974. Bureau of the Census Catalog of Publications: 1790-1972. Washington, D.C.: U.S. Government Printing Office. . 1975a. "Adjusted 1970 Population by Race, Sex, and Age for States and Counties." These adjustments (1) compensate for errors in the census tabulations of centenarians and of nonspecified races, and (2) provide estimated age-race-sex distributions for corrections that change the county total. Serial No. P: D40, Data User Services Division, U.S. Bureau of the Census, Washington, D.C. 20233. 35 Exhibit 4-A. Selected List of Data Sources— Continued . 1975b. Current Population Reports, Series P-25, No 601. "Projections of the Population of the United States: 1975 to 2050." Washington, D.C.: U.S. Government Printing Office. . 1975c. Current Population Reports, Series P-20, No. 285. "Mobility of the Population of the United States: March 1970 to March 1975." Washington, D.C.: U.S. Government Printing Office. . 1975d. Historical Statistics of the United States. Colonial Times to 1970. Bicentennial Edition. Washington, D.C.: U.S. Government Printing Office. U.S. Bureau of Economic Analysis, Department of Commerce. 1974. "Area Economic Projections 1990." Washington, D.C.: U.S. Government Printing Office. U.S. National Center for Health Statistics. 1952 to present. Monthly Vital Statistics Report. Washington, D.C.: U.S. Department of Health, Education and Welfare. . 1975a. "1975 Directory, Registration Areas, United States and Canada— Health Officers, Registrars, Principal Statisticians and Research Directors." Washington, D.C.: U.S. Government Printing Office. . 1975b. Vital Statistics of the United States, 1973. Vol. II, Part B, "Mortality." Washington, D.C.: U.S. Government Printing Office. . 1975c. Vital Statistics of the United States, 1972. Vol. I, "Natality." Washington, D.C.: U.S. Government Printing Office. . 1976. Vital Statistics of the United States, 1972. Vol. II, Part A, "Mortality." Washington, D.C.: U.S. Government Printing Office. U.S. Social Security Administration. 1974. Actuarial Study No. 72, Report No. 75-11518, "United States Population Projections for OASDHI Cost Estimates." Washington, D.C.,: U.S. Department of Health, Educa- tion and Welfare. 36 Exhibit 4-B. List of State and Territory Offices Responsible for Vital Statistics Tabulations (Taken from the 1975 Directory of Registration Areas, United States and Canada, National Center for Health Statistics. Updated November 1975 by telephone survey) State Registrar and Director Bureau of Vital Statistics State Department of Public Health State Office Building Montgomery, Alabama 36104 State Registrar of Vital Statistics Department of Health and Social Services Pouch "H 02G" Juneau, Alaska 99811 Registrar Vital Statistics Section Department of Medical Services LBJ Tropical Medical Center Pago Pago, American Samoa 96799 Manager, Vital Records Section Arizona Department of Health Services 1740 West Adams Street Phoenix, Arizona 85007 Director, Division of Health Statistics Arkansas State Department of Health 481 5 West Mark ham Street Little Rock, Arkansas 72201 Chief, Center for Health Statistics Department of Health 744 P Street Sacramento, California 95814 Vital Statistics Clerk Office of the Health Director Canal Zone Government Box M Balboa Heights, Canal Zone Chief, Records and Statistics Section State Department of Health 4210 East 11th Avenue Denver, Colorado 80220 Chief, Public Health Statistics Section State Department of Health 79 Elm Street Hartford, Connecticut 061 15 Director, Bureau of Vital Statistics Department of Health and Social Services Division of Public Health Jesse S. Cooper Memorial Building Federal and Wm. Penn Streets Dover, Delaware 19901 Chief, Research and Statistics Division Department of Human Resources 614 H Street, N.W. Washington, D.C. 20001 Chief, Public Health Statistics Section Department-of Health and Rehabilitative Services Division of Health Post Office Box 210 Jacksonville, Florida 32201 Director, Health Services Research and Statistics Section Division of Physical Health Department of Human Resources 47 Trinity Avenue, S.W. Atlanta, Georgia 30334 Territorial Registrar Office of Vital Statistics Department of Public Health and Social Services Government of Guam Post Office Box 2816 Agana, Guam 96910 State Registrar Research and Statistics Office Hawaii Department of Health Post Office Box 3378 Honolulu, Hawaii 96801 Chief, Bureau of Vital Statistics Department of Health and Welfare Statehouse Boise, Idaho 83720 37 Director, State Center for Health Statistics Illinois Department of Public Healt k 535 West Jefferson Street Springfield, Illinois 62761 Director, Public Health Statistics State Board of Health 1330 West Michigan Street Indianapolis, Indiana 46206 Director, Statistical Services Division of Records and Statistics Iowa State Department of Health Robert Lucas Building Des Moines, Iowa 50319 Chief, Research and Analysis Branch Bureau of Registration and Health Statistics State Department of Health and Environment 6700 South Topeka Avenue Topeka, Kansas 66620 Supervisor, Health Reports Section Bureau for Administration and Operations Department for Human Resources 275 East Main Street Frankfort, Kentucky 40601 Head, Public Health Statistics Health and Human Resources Administration Division of Health Post Office Box 60630 New Orleans, Louisiana 70160 Director, Division of Research and Vital Records Department of Health and Welfare State House Augusta, Maine 04333 Chief Statistician Office of Vital Statistics Maryland Center for Health Statistics State Department of Health and Mental Hygiene 201 West Preston Street Baltimore, Maryland 21201 Director, Office of Health Planning and Statistics Massachusetts Department of Public Health 80 Boylston Street Boston, Massachusetts 021 16 Chief, Statistical Services Section Office of Planning and Evaluation Michigan Department of Public Health 3500 North Logan Street Lansing, Michigan 48914 State Demographer Minnesota State Planning Agency 101 Capitol Square Building 550 Cedar Street St. Paul, Minnesota 55101 Supervisor, Statistical Services Department Vital Records Division State Board of Health Post Office Box 1 700 Jackson, Mississippi 39205 Director, State Center for Health Statistics Division of Health Missouri Department of Social Services Broadway State Office Building Jefferson City, Missouri 65101 State Registrar Bureau of Records and Statistics State Department of Health Helena, Montana 59601 Director, Division of Health Data and Statistical Research State Department of Health Lincoln Building 1003 Street Lincoln, Nebraska 68508 Chief Biostatistician Section of Vital Statistics Nevada Division of Health Department of Human Resources Capitol Complex Carson City, Nevada 89710 State Registrar Bureau of Vital Statistics Division of Public Health 61 South Spring Street Concord, New Hampshire 03301 Principal Statistician Public Health Statistics Program Division of Laboratories and Epidemiology State Department of Health Post Office Box 1 540 Trenton, New Jersey 08625 38 Director, State Health Agency Health and Social Services Department State of New Mexico Post Office Box 2348 Santa Fe, New Mexico 87501 Director of Health Statistics New York State Department of Health Empire State Plaza Tower Building Albany, New York 12237 Head, Public Health Statistics Branch Division of Health Services State Department of Human Resources Post Office Box 2091 Raleigh, North Carolina 27602 Director, Division of Health Statistics State Department of Health State Capitol Building Bismarck, North Dakota 58505 Chief Statistician Data Services Unit Division of Vital Statistics Ohio Department of Health 266 North Fourth Street Columbus, Ohio 43215 Director, Public Health Statistics State Department of Health N.E. 10th and Stonewall Post Office Box 53551 Oklahoma City, Oklahoma 73105 Chief Analyst Vital Statistics Department Oregon State Health Division Post Office Box 231 Portland, Oregon 97207 Director, Data Processing Division Division of Vital Statistics Pennsylvania Department of Health 700 Health and Welfare Building Harrisburg, Pennsylvania 17121 Director, Division of Demographic Registry and Vital Statistics Puerto Rico Department of Health Post Office Box 9342 Santurce, Puerto Rico 00908 Chief, Division of Vital Statistics Rhode Island Department of Health Health Building 75 Davis Street Providence, Rhode Island 02908 Assistant State Registrar Office of Vital Records South Carolina Department of Health and Environmental Control Sims Building 2600 Bull St. Columbia, South Carolina 29201 Director, Office of Public Health Statistics State Department of Health Foss Building Pierre, South Dakota 57501 Director, Statistical Services Tennessee Department of Public Health Room C2-237 Cordell Hull Building Nashville, Tennessee 37219 Chief, Records and Statistics Section State Department of Health Resources 410 East Fifth Street Austin, Texas 78701 Director, Bureau of Statistical Services Utah State Division of Health 554 South Third East Salt Lake City, Utah 84111 Chief, Division of Public Health Statistics Vermont Department of Health 1 15 Colchester Avenue Burlington, Vermont 05401 State Registrar Virginia Health Data Center James Madison Building Post Office Box 1000 Richmond, Virginia 23208 Director, Research and Statistical Services Virgin Islands Department of Health Charlotte Amalie St. Thomas, Virgin Islands 00801 39 Chief Research Analyst Vital Records Section Health Services Division Department of Social and Health Services Post Office Box 1788, M.S. 50-2 Olympia, Washington 98504 Director, Division of Vital Statistics State Department of Health 1800 Washington Street Charleston, West Virginia 25305 Chief, Statistical Services Section Bureau of Health Statistics Wisconsin Department of Health and Social Services Post Office Box 309 Madison, Wisconsin 53701 Deputy State Registrar Vital Records Services Division of Health and Medical Services Department of Health and Social Services State Office Building West Cheyenne, Wyoming 82002 40 Exhibit 4-C. List of State and Territory Offices Participating in the Fed era I -State Cooperative Program for Local Population Estimates (September 1976) Center for Business and Economic Research Graduate School of Business University of Alabama Box AK University, Alabama 35486 Research and Analysis Section Alaska Department of Labor Box 3-7000 Juneau, Alaska 99801 Department of Economic Security Bureau of Planning Post Office Box 61 23 Phoenix, Arizona 85005 Industrial Research and Extension Center University of Arkansas Post Office Box 3017 Little Rock, Arkansas 72203 Population Research Unit State Department of Finance 1025 P Street Sacramento, California 95814 Colorado Division of Planning 520 Centennial Building 1313 Sherman Street Denver, Colorado 80203 Vital Statistics Section State Health Department 79 Elm Street Hartford, Connecticut 061 15 State Planning Office Thomas Collins Building 530 South Dupont Highway Dover, Delaware 19901 Statistical Systems Division Office of Planning and Management Room 644 - Munsey Building 1329 E Street, N.W. Washington, D.C. 20004 Division of Population Studies Bureau of Economic and Business Research College of Business Administration University of Florida Gainesville, Florida 3261 1 Office of Planning and Budget 270 Washington Street, S.W. Atlanta, Georgia 30334 State Department of Health Post Office Box 3378 Honolulu, Hawaii 96801 Department of Planning and Economic Development Post Office Box 2359 Honolulu, Hawaii 96804 Bureau of Vital Statistics Idaho Department of Health and Welfare Statehouse Boise, Idaho 83720 Illinois Department of Public Health 535 West Jefferson Street Springfield, Illinois 62761 Indiana State Board of Health 1330 West Michigan Street Indianapolis, Indiana 46206 Planning Support Unit Office of Planning and Programming 523 East 1 2th Street Des Moines, Iowa 50319 Population Research Laboratory Kansas State University Manhattan, Kansas 66506 Urban Studies Center University of Lousiville Gardencourt Campus Alta Vista Road Louisville, Kentucky 40205 41 Research Division College of Administration and Business Louisiana Tech University Ruston, Louisiana 71270 Research and Vital Records State Department of Health and Welfare Augusta, Maine 04330 Maryland Center for Health Statistics State Department of Health and Mental Hygiene O'Connor Building 201 West Preston Street Baltimore, Maryland 21201 Information Systems Section Office of the Budget Michigan Department of Management and Budget Lewis Cass Building Post Office Box 30026 Lansing, Michigan 48909 Minnesota State Planning Agency 101 Capitol Square Building 550 Cedar Street St. Paul, Minnesota 55101 Department of Sociology Mississippi State University Post Office Drawer C State College, Mississippi 39762 Missouri Division of Budget and Planning State Capitol Post Office Box 809 Jefferson City, Missouri 65101 Bureau of Business and Economic Research University of Montana Missoula, Montana 59801 Bureau of Business Research The University of Nebraska Lincoln, Nebraska 68508 Bureau of Business and Economic Research University of Nevada Reno, Nevada 89507 Office of Comprehensive Planning Executive Department State House Annex Concord, New Hampshire 03301 Office of Business Economics Room 1007 Division of Planning and Research Department of Labor and Industry Post Office Box 845 Trenton, New Jersey 08625 Bureau of Business and Economic Research The University of New Mexico Albuquerque, New Mexico 87131 New York State Economic Development Board AESOB- 17th Floor Post Office Box 7027 Albany, New York 12225 Office of State Planning North Carolina Department of Administration 1 16 West Jones Street Raleigh, North Carolina 27603 Division of Health Statistics Department of Health 17th Floor Capitol Building Bismarck, North Dakota 58505 Office of Research Department of Economic and Community Development State Office Tower 30 East Broad Street Columbus, Ohio 43215 Research and Planning Division Oklahoma Employment Security Commission 310 Will Rogers Building Oklahoma City, Oklahoma 73105 Center for Population Research and Census Portland State University Box 751 Portland, Oregon 97207 Office of State Planning and Development Post Office Box 1 323 Harrisburg, Pennsylvania 17120 42 Puerto Rico Planning Board Minillas Government Center North Building, De Diego Avenue Post Office Box 9447 Santurce, Puerto Rico 00908 Statewide Planning Program Room 201 265 Melrose Street Providence, Rhode Island 02907 Division of Research and Statistical Services South Carolina Budget and Control Board 1026 Sumter Street Columbia, South Carolina 29201 Public Health Statistics State Department of Health Pierre, South Dakota 57501 Tennessee State Planning Office Division of State Planning 660 Capitol Hill Building 301 Seventh Avenue, North Nashville, Tennessee 37219 Utah Department of Employment Security 174 Social Hall Avenue Salt Lake City, Utah 841 1 1 Division of Public Health Statistics State Department of Health 115 Colchester Avenue Burlington, Vermont 05401 Tayloe Murphy Institute Graduate School of Business Administration University of Virginia Post Office Box 6550 Charlottesville, Virginia 22906 Population Studies Division Office of Program Planning and Fiscal Management House Office Building Olympia, Washington 98504 Office of Research and Development Center for Extension and Continuing Education West Virginia University Morgantown, West Virginia 26505 Bureau of Health Statistics State Division of Health Post Office Box 309 Madison, Wisconsin 53701 Division of Business and Economic Research College of Commerce and Industry University of Wyoming University Station - Box 3925 Laramie, Wyoming 82071 5. SELECTED REFERENCES Bogue, Donald J. and Louise Rehling. "Techniques for Making Population Projections: How to Make Age-Sex Projections by Electronic Computer." Family Planning Research and Evaluation Manual No. 12. Chicago, Illinois: Family Study Center, University of Chicago, 1974. Greenberg, Michael R., Donald A.Krueckeberg, and Richard Mautner. "Long Range Population Projections for Minor Civil Divisions: Computer Programs and User's Manual." New Brunswick, New Jersey: Center for Urban Policy Research, Rutgers University, 1973. Hagood, Margaret J., and Jacob S. Siegel. "Projections of the Regional Distribution of the Population of the United States to 1975." Agricultural Economic Research, Vol. 3, No. 2, pp. 41-52. April 1951. Hamilton, C. Horace, and Josef Perry. "A Short Method for Projecting Population by Age from One Decennial Census to Another." Social Forces, Vol. 41, No. 2, pp. 163-170. December 1962. ^____. "Effect of Census Errors on the Measurement of Net Migration." Demography, Vol. 3, No. 2, pp. 393-415,1966. Keyfitz, Nathan. "On Future Population." Journal of the American Statistical Association, Vol. 67, No. 338, pp. 347-363. June 1972. Kleiner, Morris M. "An Analysis of Interregional Migration for Manpower Planning." Urbana, Illinois: Center for Advanced Computation, University of Illinois, 1974. Lee, Joe W., Timothy B. Sivia, and David W. Fay. 1976 Regional Economic Projections Series Report 76-R-1 (by subscription only), "States and Large Metropolitan Areas." Washington, D.C.: National Planning Associ- ation, 1976. Lowry, Ira S. "Migration and Metropolitan Growth: Two Analytical Models." San Francisco, California: Chandler Publishing Company, 1966. Morrison, Peter A. "Demographic Information for Cities: A Manual for Estimating and Projecting Local Population Characteristics." Santa Monica, California: Rand Corporation, 1971. Newling, Bruce E. "Population Projections for New Jersey to 2000." New York: The City College of New York, 1968. Olsen, Richard J. Regional Environmental Systems Analysis Report No. 74-13, "Population Migration: State Economic Areas in the Interior Southeast." Oak Ridge, Tennessee: The Oak Ridge National Research Laboratory, 1974. Pickard, Jerome P. Research Monograph 14A, "Appendixes to Dimensions of Metropolitanism." Washington, D.C.: Urban Land Institute, 1967. Pittenger, Donald B. "Projecting State and Local Populations." Cambridge, Massachusetts: Ballinger Publishing Company, 1976. Shryock, Henry S., Jacob S. Siegel, and Associates. "The Methods and Materials of Demography." Washington, D.C.: U.S. Bureau of the Census, U.S. Government Printing Office, 1971. 43 44 Siegel, Jacob S. "Forecasting the Population of Small Areas." Land Economics, Vol. 10, No. 1, pp. 72-87. February 1953. Tarver, James D. "Evaluation of Census Survival Rates in Estimating Intercensal State Net Migration." Journal of the American Statistical Association, Vol. 57, No. 300, pp. 841-62. December 1962. , and Therel R. Black. "Making County Population Projections— A Detailed Explanation of a Three-Component Method, Illustrated by Reference to Utah Counties." Bulletin (Technical) 459. Logan: Utah Agricultural Experiment Station, 1966. U.S. Bureau of the Census. Current Population Reports, Series P-25, No. 375. "Revised Projections of the Population of States: 1970 to 1985." Washington, D.C.: U.S. Government Printing Office, 1967. . Current Population Reports, Series P-25, No. 415. "Projections of the Population of Metropolitan Areas: 1975." Washington, D.C.: U.S. Government Printing Office, 1969. . Current Population Reports, Series P-25, No. 601. "Projections of the Population of the United States: 1975 to 2050." Washington, D.C.: U.S. Government Printing Office, 1975. U.S. Bureau of Economic Analysis, Department of Commerce. "Area Economic Projections 1990." Washington, D.C.: U.S. Government Printing Office, 1974. . "1972 OBERS Projections, Regional Economic Activity in the U.S., Series E Population," (7 Volumes). With the Economic Research Service, Department of Agriculture, for the U.S. Water Resources Council. Washington, D.C.: U.S. Government Printing Office, 1974. APPENDIXES 45 46 APPENDIX A Table A-l. Life Table Survival Rates by Age, Race, and Sex, for the United States: 1960 to 1970 (Derived from the official life table for 1965 prepared by the National Center for Health Statistics) Age of cohort All races White Black Line No. Age in 1960 Age in 1970 Male (1) Female (2) Male (3) Female (4) Male (5) Female (6) 1 2 3 4 Born April 1, 1965-70... Born April 1, 1960-65... All ages, total. to 4 years. . . . 5 to 9 years. . . . 10 to 14 years. . 15 to 19 years. . 20 to 24 years. . 25 to 29 years. . 30 to 34 years. . 35 to 39 years. . 40 to 44 years. . 45 to 49 years. . 50 to 54 years. . 55 to 59 years. . 60 to 64 years. . 65 to 69 years. . 70 to 74 years. . (X) .9713 .9673 .9936 .9932 .9873 .9826 .9812 .9779 .9691 .9528 .9250 .8826 .8249 .7474 .6505 .3760 (X) .9776 .9744 .9952 .9964 .9948 .9930 .9909 .9871 .9810 .9716 .95 76 .9380 .9097 .8649 .7969 .4513 (X) .9747 .9711 .9942 .9935 .9879 .9840 .9837 .9814 .9734 .9578 .9307 .8888 .8315 .7550 .6584 .3738 (X) .9807 .9779 .9957 .9967 .9952 .9938 .9925 .9896 .9844 .9758 .9626 .9444 .9183 .8760 .8078 .4505 (X) .9541 .9478 .9903 .9914 .9830 .9718 .9620 .9510 .9333 .9086 .8738 .8247 .7631 .6720 .5679 .4062 (X) .9625 .95 70 .9922 5 6 7 .9950 .9921 .9871 8 20 to 24 years .9801 9 10 .9698 .9557 11 12 .9383 .9152 13 14 15 16 17 .8805 .8285 .7531 .6788 .4715 X Not applicable, Table A-2. Projected Life Table Survival Rates by Age, Race, and Sex, for the United States: 1970 to 1980 (Consistent with national projections in Current Population Reports, Series P-25 , No, 601) Age of cohort All races White Black Line No. Age in 1970 Age in 1980 Male (1) Female (2) Male (3) Female (4) Male (5) Female (6) 1 2 3 4 5 Born April 1, 1975-80. .. Born April 1, 1970-75. .. All ages, total. to 4 years. . . . 5 to 9 years. . . . 10 to 14 years. . 15 to 19 years. . 20 to 24 years. . 25 to 29 years. . 30 to 34 years. . 35 to 39 years. . 40 to 44 years. . 45 to 49 years, . 50 to 54 years. . 55 to 59 years. . 60 to 64 years. . 65 to 69 years. . 70 to 74 years. . (X) .9782 .9732 .9937 .9930 .9858 .9805 .9800 .9782 .9 704 .9546 .9279 .8878 .8328 .7592 .6622 .3940 (X) .9830 .9796 .9956 .9963 .9946 .9929 .9914 .9884 .9828 .9737 .9600 .9410 .9140 .8767 .8183 .4909 (X) .9804 .9765 .9947 .9934 .9866 .9823 .9827 .9816 .9747 .9599 .9340 ,8944 .8398 .7662 .6686 .3917 (X) .9850 .9820 .9960 .9966 .9950 .9938 .9927 .9901 .9854 .9771 .9644 .9464 .9210 .8851 .8262 .4901 (X) .9666 .9578 .9889 .9912 .9784 ,9687 .9604 .9511 .9357 .9127 .8797 .8303 .7689 .6891 .5948 .4189 (X) .9728 .9671 .9935 .9950 6 10 to 14 years 9917 7 15 to 19 years 9875 8 9829 9 25 to 29 years .9758 10 30 to 34 years .9648 11 35 to 39 years .9492 12 .9270 13 45 to 49 years 8948 14 .8511 15 55 to 59 years . 7949 16 60 to 64 years. 7319 17 65 and over .49 74 X Not applicable. 47 Table A-3. Projected Life Table Survival Rates by Age, Race, and Sex, for the United States: 1980 to 1990 (Consistent with national projections in Current Population Reports, Series P-25 , No. 601) Age of cohort All races White Black Line No. Age in 1980 Age in 1990 Male (1) • Female (2) Male (3) Female (4) Male (5) Female (6) 1 2 3 4 Born April 1, 1985-90... Born April 1, 1980-85. . . All ages, total. to 4 years. . . . 5 to 9 years. . . . 10 to 14 years. . 15 to 19 years. . 20 to 24 years. . 25 to 29 years. . 30 to 34 years. . 35 to 39 years. . 40 to 44 years. . 45 to 49 years. . 50 to 54 years. . 55 to 59 years. . 60 to 64 years. . 65 to 69 years. . 70 to 74 years. . (X) .9823 .9776 .9941 .9930 .9853 .9800 .9800 .9787 .9720 .9571 .9317 .8922 .8391 .7673 .6719 .4096 (X) .9862 .9828 .9958 .9964 .9946 .9932 .9919 .9892 .9842 .9756 .9625 .9437 .9180 .8846 .8325 .5134 (X) .9837 .9798 .9949 .9933 .9862 .9816 .9824 .9817 .9755 .9614 .9369 .8984 .8456 .7736 .6770 .4076 (X) .9874 .9845 .9962 .9966 .9951 .9939 .9929 .9905 .9860 .9780 .9660 .9482 .9237 .8914 .8384 .5125 (X) .9740 .9656 .9897 .9915 .9808 .9696 .9631 .9555 .9426 .9219 .8906 .8427 .7829 .7058 .6157 .4298 (X) .9793 .9738 9943 5 9953 6 9922 7 15 to 19 years 9888 8 20 to 24 years 9855 9 25 to 29 years. ......... .9800 10 30 to 34 years 9717 11 35 to 39 years 9584 12 9381 13 9089 14 50 to 54 years 8710 15 8228 16 60 to 64 years 7647 17 5139 X Not applicable. 48 APPENDIX B Table B-l. National Census Survival Rates by Age, Race, and Sex, for the United States: 1960 to 1970 (Based on the total resident population, plus Armed Forces overseas, adjusted to exclude net civilian immigration during the decade) Age of cohort All races White Black Line No. Age in 1960 Age in 1970 Male (1) Female (2) Male (3) Female (4) Male (5) Female (6) 1 2 3 4 5 6 Born April 1, 1965-70... Born April 1, 1960-65... All ages, total. to 4 years 1 . . . 5 to 9 years 1 . . . 10 to 14 years. . 15 to 19 years. . 20 to 24 years. . 25 to 29 years. . 30 to 34 years. . 35 to 39 years. . 40 to 44 years. . 45 to 49 years. . 50 to 54 years. . 55 to 59 years. . 60 to 64 years. . 65 to 69 years. . 70 to 74 years. . (X) .9463 .9439 1.0053 1.0061 .9841 .9688 .9860 .9790 .9697 .9437 .9290 .8806 .8439 .7527 .6776 .3899 (X) .9568 .9534 1.0006 1.0083 .9979 .9929 1.0026 .9957 .9872 .9632 .9602 .9338 .9336 .8943 .8358 .5075 (X) .9605 .9522 1.0020 1.0052 .9889 .9732 .9847 .9801 .9718 .9483 .9326 .8852 .8455 .7505 .6747 .3893 (X) .9 701 .9610 .9970 1.0069 .9979 .9886 .9963 .9938 .9889 .9678 .9644 .9394 .9356 .8914 .8367 .5094 (X) .8755 .8996 1.0251 1.0119 .9500 .9366 .9962 .9705 .9515 .9045 .8961 .8389 .8286 .7740 .7093 .3962 (X) .8922 .9141 1.0211 1.0170 .9982 7 1.0234 8 9 10 1.0455 1 . 0082 .9748 11 12 35 to 39 years.......... .9258 .9244 13 14 .8846 .9141 15 .9222 16 .8255 17 .4833 X Not applicable. ^Based on registered births. Table B-2. Projected National Census Survival Rates by Age, Race, and Sex, for the United States: 1970 to 1980 (Based on the total resident population, plus Armed Forces overseas. Consistent with national projections in Current Population Reports, Series P-25 , No. 601) Age of cohort All races White Black Line No. Age in 1970 Age in 1980 Male (1) Female (2) Male (3) Female (4) Male (5) Female (6) 1 2 3 4 Born April 1, 1975-80... Born April 1, 19 70-75... All ages, total. to 4 years 1 . . . 5 to 9 years 1 . . . 10 to 14 years. . 15 to 19 years. . 20 to 24 years. . 25 to 29 years. . 30 to 34 years. . 35 to 39 years. . 40 to 44 years. . 45 to 49 years. . 50 to 54 years. . 55 to 59 years. . 60 to 64 years. . 65 to 69 years. . 70 to 74 years. . (X) .9531 .9487 1.0157 1.0105 .9681 .9330 .9561 .9773 .9755 .9683 .9509 .9047 .8362 .7826 .6803 .4189 (X) .9620 .9575 1.0166 1.0180 .9912 .9661 .9822 1.0067 .9993 .9759 .9649 .9335 .8917 .9210 .8444 .5495 (X) .9662 .9571 1.0067 1.0053 .9731 .9463 .9652 .9852 .9818 .9659 .9489 .9081 .8383 .7851 .6866 .4111 (X) .9744 .9647 1.0061 1.0135 .9923 .9898 .9826 1.0089 1.0036 .9791 .9693 .9398 .8961 .9091 .8505 .5469 (X) .8869 .9041 1.0631 1.0375 .9288 .8429 .8985 .9260 .9204 .9719 .9594 .8748 .8182 .8578 .6836 .4208 (X) .9017 .9186 1.0699 5 1.0419 6 .9820 7 .9409 8 .9806 9 .9933 10 .9678 11 35 to 39 years. ......... .9464 12 .9276 13 45 to 49 years .8803 14 15 .8563 .9794 16 .7706 17 .5154 X Not applicable. 1 Based on births not adjusted for underregistration. 49 Table B-3. Projected National Census Survival Rates by Age, Race, and Sex, for the United States: 1980 to 1990 (Based on the total resident population, plus Armed Forces oversea;-. . Consistent with national projections in Current Population Reports, Series P-25 , No. 601) Age of cohort All races White Black Line No. Age in 1980 Age in 1990 Male (*D Female (2) Male (3) Female (4) Male (5) Female (6) 1 2 3 4 Born April 1, 1985-90. .. Born April 1, 1980-85. .. to 4 years All ages, total. to 4 years 1 . . . 5 to 9 years 1 . . . 10 to 14 years. . 15 to 19 years. . 20 to 24 years. . 25 to 29 years. . 30 to 34 years. . 35 to 39 years. . 40 to 44 years. . 45 to 49 years. . 50 to 54 years. . 55 to 59 years. . 60 to 64 years. . 65 to 69 years. . 70 to 74 years. . (X) .9570 .9529 1.0161 1.0105 .9677 .9325 .9561 .9778 .9771 .9 709 .9547 .9093 .8426 .7910 .6902 .4356 (X) .9651 .9607 1.0168 1.0181 .9913 .9664 .9827 1.0075 1.0007 .9778 .9674 .9362 .8956 .9293 .8591 .5747 (X) .9694 .9603 1.0069 1.0053 .9726 .945 7 .9650 .9854 .9826 .9675 .9518 .9122 .8441 .7927 .6952 .4278 (X) .9768 .9671 1.0063 1.0135 .9923 .9899 .9828 1.0093 1.0042 .9801 .9709 .9416 .8987 .9155 .8631 .5719 (X) .8937 .9115 1.0640 1.0378 .9311 .8437 .9011 .9303 .9271 .9817 .9713 .8878 .8332 .8787 .7077 .4318 (X) .9077 .9250 1.0707 5 1.0422 6 .9825 7 15 to 19 years .9421 8 .9832 9 .9975 10 .9748 11 .9556 12 40 to 44 years .9386 13 .8941 14 .8764 15 1.0139 16 .8051 17 .5326 X Not applicable. 1 Based on births not adjusted for underregistration. 50 APPENDIX C DERIVATION OF SURVIVAL RATES FROM A LIFE TABLE This section describes techniques for calculating survival rates from an abridged life table. Such a table for the United States, representing the year 1965, is shown in table C-1. This table was developed by the National Center for Health Sta- tistics, Department of Health, Education and Wel- fare, and was published in the Mortality volume, Part A, for that year. Table C-1. Abridged Life Table for White Females for the United States: 1965 Age interval Proportion dying Of 100,000 born alive Stationary population Average remaining lifetime Period of life between two exact ages stated in years (1) Proportion of persons alive at beginning of age interval dying during interval (2) Number living at beginning of age interval (3) Number dying during age interval (4) In the age interval (5) In this and all subsequent age intervals (6) Average number of years of life remaining at beginning of age interval (7) x to x + n n^x e x n x n L x T x e °x WHITE FEMALE to 1 0.0183 .0029 .0017 .0014 .0025 .0032 .0035 .0051 .0075 .0117 .0185 .0277 .0407 .0607 .0988 .1540 .2464 .3888 1.0000 100,000 98,166 97,879 97,715 97,578 97,334 97,026 96,683 96,193 95,468 94,351 92,606 90,045 86,384 81,139 73,124 61,861 46,620 28,496 1,834 287 164 137 244 308 343 490 725 1,117 1,745 2,561 3,661 5,245 8,015 11,263 15,241 18,124 28,496 98,378 391,978 488,948 488,250 487,313 485,918 484,305 482,260 479,278 474,750 467,690 456,988 441,671 419,666 386,885 339,016 272,734 187,629 134,678 7,468,335 7,369,957 6,977,979 6,489,031 6,000,781 5,513,468 5,027,550 4,543,245 4,060,985 3,581,707 3,106,957 2,639,267 2,182,279 1,740,608 1,320,942 934,057 595,041 322,307 134,678 74.7 1 to 5 75.1 5 to 10 71.3 10 to 15 66.4 15 to 20 61.5 20 to 25 56.6 25 to 30 51.8 30 to 35 47.0 35 to 40 42.2 40 to 45 37.5 45 to 50 32 9 50 to 55 28 5 55 to 60 24.2 20.1 16.3 12.8 9.6 6.9 4.7 60 to 65 65 to 70 70 to 75 75 to 80 80 to 85 Source: U.S. National Center for Health Statistics, Vital Statistics of the United States . 1965 . Vol. II, Part A, Mortality. 51 A life table is based on actual death statistics and can be used to calculate a survival rate suitable for use in a cohort component population computation. Some life tables give figures for each single year of age. The abridged life table shown in table C-1 shows 5-year age groups, the same as are used in the projections illustrated in Appendix H. All but three of the needed survival rates are obtained from the column of the life table labeled L^. This column (with T x ) is often called the "Stationary Population" and may be thought of as the actual population that would evolve in a closed geographic area where 100,000 persons are born each year, these persons being subject to a fixed mortality schedule throughout their life span. In an abridged life table the subscript x in n l_ x is a variable delimiting the lower limit of an age group and the subscript n indicates the number of years of age in the group. Thus, 5L-J5 represents the sta- tionary population from age 15 to, but not in- cluding 20 years of age. Ten years later the survivors of this group would be labeled 5L25 It follows that the survival rate for this 5-year cohort for 10 years of time is simply 5L25 divided by 5L-15 or .993827 in this life table. A survival rate for the same cohort for a 5-year time period would be 5 1_20 divided by 5 L 15 or .997137. The youngest and oldest age groups require special procedures. To begin with the youngest group, the life table assumes 100,000 births per year (the value labeled l ; some tables show 10,000), and^for 5 successive years of time this will sum to 500,000 written as 5'o. The table shows that of these births, 490,356 still survive at the end of the 5-year period, written as 5^-0. (It is customary to show a single year of age for the youngest group labeled L Q , followed by a 4-year group, labeled 4L-1 Adding these two figures gives 5^.) Dividing 490,356 by 500,000 gives .980712, which is the required survival rate for a 5-year period. A special case arises if the time unit of the projections is 10 years as with the illustrative method shown in Appendix H. In this case a survival rate is needed for the population aged 5 to 9 years at the end of the period, being the cohort which was born during the first 5 years of the decade. To calculate this rate, divide 5L5 by d . In table C-1, this will be 488,948^500,000, or .977896. The survival rate for the births occurring in the second half of the decade is .980712, as calculated above. The survival rate for the terminal age group (the oldest group, which includes all persons of a certain specified age and over) is calculated from the column labeled T x . The values in this column represent the total number of persons of age x and above (the T x value is calculated as the sum of all l_ x values for age x and above). The survival rate for the age group 65 years and over becoming 75 years and over 10 years later is therefore T75 -j- Tgg or .450467. 52 APPENDIX D Table D-l. State Factors for Estimating County Population on July 1, 1970 by Extrapolation from Census Data (See text for expl anation of method) Extrapolation factors State Extrapolation factors State 1970 census 1960 census 1970 census 1960 census factor (f^) factor (f2) factor (f]^) factor (f2) 1.025636 .025016 1.028977 .025097 1.025758 1.029629 1.027733 1.022348 .025018 .025113 .025067 .024935 1.026950 1.023850 1.026422 1.024671 .025048 New Hampshire .024972 .025035 .024992 1.027137 1.023871 1.024820 .025052 .024972 .024996 1.030809 1.024464 1.025640 .025142 .024987 .025016 Dist. of Columbia..... 1.024921 1.026871 1.025381 .024998 .025046 .025009 1.028689 1.023847 1.025940 .025090 .024972 .025023 Hawaii ...... ........ . . 1.026207 .025029 1.025646 .025016 Idaho. . 1.030199 .025127 1.025603 .025015 1.023959 1.024111 .024975 .024978 1.023896 1.025673 .024973 South Carolina. ...... .025016 Iowa. ................. 1.026964 1.024300 .025048 .024983 1.027712 1.026089 .025066 Tennessee. . .025027 1.027206 .025054 1.024923 .024998 1.024780 1.027528 .024995 .025062 Utah. 1.027627 1.025659 .025064 Maine. ................ .025016 1.023636 .024967 1.023484 .024963 Massachusetts. ........ 1.025569 .025014 1.022098 .024929 Michigan. ............. 1.023704 .024968 1.030681 .025139 Minnesota. ............ 1.025056 .025001 Wisconsin. ........... 1.024783 .024995 1.026157 .025028 Wyoming .............. 1.029162 .025102 Missouri .............. 1.025340 .025008 APPENDIX E 53 Table E-l. Estimated and Projected General Fertility Rates by Race, for the United States: 1970 to 1990 (Annual births per 1,000 women aged 15-44 years) Year or period All races White Black 1 ESTIMATES 1970 (c PROJECTIONS Series I 87.5 83.5 113.8 July 1, 1970-75 74.8 70.7 100.8 July 1, 1975-80 83.5 80.3 102.1 July 1, 1980-85 92.7 91.3 100.4 July 1, 1985-90 93.9 93.6 95.5 Series II July 1, 1970-75 73.9 70.0 99.1 July 1, 1975-80 72.2 68.8 92.3 July 1, 1980-85 76.5 74.5 87.5 July 1, 1985-90 Series III 74.4 73.2 80.2 July 1, 1970-75 73.4 69.3 99.1 July 1, 1975-80 62.8 59.6 82.0 July 1, 1980-85 63.9 61.9 74.8 July 1, 1985-90 60.6 59.3 67.1 1 Includes, in addition to the Black population, all races other than White. 2 Differs from the rates published by the U.S. National Center for Health Statistics that the July 1, 1970 population is the base for computation, rather than the April 1, sus population used by the NCHS. (NCHS) in 1970 cen- Source: U.S. Bureau of the Census, Current Population Reports , Series P-25 , No. 601. "Pro- jections of the Population of the United States: 1975 to 2050." In some cases, the 5-year general fertility rates (GFR's) shown here differ slightly from the 5-year GFR ' s in Series P-25, No. 601, table A-8, which represent averages of GFR's for single years. 54 APPENDIX F Table F-l. Cohort-Size Adjustment Factors for Interpolation to July 1, 1975, from Population for July 1, 1970 and 1980 (Calculated from national population estimates and projections, U.S. Bureau of the Census, Cur ^ rent Population Reports , Series P-25 , No. 601; by formula, f = P x 1975 -5-l/2 (P x 1970 + P x 1980 ) where f is the adjustment factor, P is population, and x is any 5-year age group) All races White Black Age Male Female Male Female Male Female .9327 .9656 1.0606 1.0563 1.0139 1.0429 .9785 .9252 .9539 1.0205 1.0489 .9900 1.0059 .9996 .9313 .9676 1.0600 1.0575 1.0142 1 . 0442 .9803 .9316 .9459 1.0206 1.0566 .9907 1.0041 1.0036 .9237 .9652 1.0599 1.0555 1.0127 1.0502 .9782 .9225 .9477 1.0204 1.0511 .9930 1.0049 .9988 .9219 .9666 1.0601 1.0567 1.0112 1.0489 .9801 .9289 .9395 1.0199 1.0600 .9929 1.0028 1.0036 .9764 .9678 1.0645 1.0612 1.0215 .9963 .9804 .9434 .9971 1.0215 1.0313 .9644 1.0152 1.0083 .9753 .9722 10 to 14 years 1.0593 1.0620 1.0323 1.0156 30 to 34 years .9812 .9487 .9882 1.0257 1.0294 .9722 1.0159 1.0026 Table F-2. Cohort-Size Adjustment Factors for Interpolation to July 1, 1985, from Population for July 1, 1980 and 1990 (Calculated from national population estimates and projections, U.S. Bureau of the Census. Cur- rent Population Reports, Series P-25, No. 601; by formula, f = P 1985 -H/2 (P 1980 + P i99 °) where f is the adjustment factor, P is population, and x is any 5-year age group) All races White Black Age Male Female Male Female Male Female 1.0591 .9667 .9293 .9619 1.0564 1.0523 1.0095 1.0374 .9746 .9225 .9516 1.0187 1.0471 .9973 1.0590 .9663 .9282 .9636 1.0558 1.0524 1.0077 1.0381 .9762 .9283 .9428 1.0182 1.0547 .9985 1.0654 .9585 .9215 .9622 1.0563 1.0521 1.0093 1.0459 .9756 .9209 .9461 1.0188 1.0496 .9982 1.0654 .9584 .9195 .9634 1.0566 1.0530 1.0070 1 . 0448 .9775 .9266 .9370 1.0179 1.0586 .9991 1.0285 1.0064 .9666 .9604 1.0567 1.0536 1.0111 .9817 .9673 .9337 .9910 1.0173 1.0259 .9889 1.0286 1.0034 15 to 19 years. .9682 .9648 20 to 24 years 1.0518 1.0489 30 to 34 years 1.0122 .9972 .9679 .9394 .9822 55 to 59 years 1.0203 1.0230 .9921 55 APPENDIX G LABOR FORCE EVALUATION Having obtained population projections by age, race, and sex, an evaluation by means of the labor force implied by the data helps to determine the reasonableness of the projections. This evaluation can be carried out by using labor force participation rates to calculate a projected labor force consistent with the population projections. This labor force is then compared with current employment statistics. This section describes in general terms the prepara- tion of the data and presents the results of the analysis in table G-1. The procedure in this evaluation was to (1) note the labor force participation rates by age, race, and sex for "Tri-county Area, USA" in the 1970 census, (2) project these rates to 1980 by comparison with projections for the Nation, and (3) project a labor force for 1980 by multiplying these rates by the population projections for the area. The population projections (not shown) were obtained in the manner described in the final three paragraphs of Appendix H. Since the labor force projections are by age, race, and sex, the computation auto- matically allows for changes in the 1970 and 1980 Table G-1. Estimated and Projected Population and Labor Force by Sex, "Tri-county Area, USA' and the United States: July 1, 1970, 1974 and 1980 (Population and labor force in thous ands) Average annual Line Area, labor force status and sex 1970 1974 1980 percent change No. 1970-74 1970-80 "TRI-COUNTY AREA, USA" All Classes 1 337.8 362.0 398.1 1.7 1.7 2 133.1 151.6 179.6 3.3 3.0 3 101.4 116.1 (NA) 3.4 (NA) Males 4 171.2 89.7 184.4 101.8 204.1 119.5 1.9 3.2 1.8 5 2.9 Females 6 166.6 177.6 194.0 1.6 1.5 7 43.4 49.8 60.1 3.5 3.3 UNITED STATES 8 204,878 211,894 224,132 0.8 0.9 9 85,903 93,241 101,809 2.1 1.7 NA Not available. x Total population including the Armed Forces overseas. 2 Based on the total noninstitutional population. Sources: Lines ] Line 8. Line 9, to 7. See text. (1970 and 1974) U.S. Bureau of the Census, Current Population Reports, Series P-25 , No. 614, November 1975. (1980) U.S. Bureau of the Census, Current Population Reports, Series P-25, No. 493, December 1972. (1970 and 1974) U.S. Bureau of Labor Statistics. Employment and Earnings, Vol. 17, No. 7. January 1971, and Vol. 21, No. 7, January, 1975. (1980) Denis F. Johnston. "The U.S. Labor Force: Projections to 1990," Monthly Labor Review , July 1973, or Special Labor Force Report, No. 156, U.S. Statistics, 1973. Bureau of Labor 56 age-race-sex population structure and differences between the United States structure and that of the local area. The projection of labor force participa- tion rates was very simplistic, however, making the assumption that the ratio of the "Tri-county Area, USA" rates to national rates will be the same in 1980 as it was in 1970. Projections of national rates are subject to error, and the ratio of local area to national rates may change. After calculating the labor force for 1980, the rate of change from 1970 to 1980 for the total was noted. These data are in table G-1 and show an average annual increase of 3.0 percent for the total labor force, 2.9 percent for males, and 3.3 percent for females. Note that the population is projected to increase much more slowly. This is due to the decrease in growth rates for the population below labor force age and to increased labor force partici- pation rates for young workers, at a time when this group is growing in numbers as a result of the "baby boom" of the 1950's. As a means of verifying this projected trend, current employment statistics published by the State employment security offices were consulted. The most recent available data were for 1974. Accordingly, the population by age was calculated for 1974 by interpolation between data for 1970 and 1980 (as adjusted in Appendix H for the 1974 postcensal estimate), and labor force participation rates were developed, also by interpolation. Multi- plying the two elements gave the labor force for 1974, shown in table G-1. The labor force (both sexes) is projected to grow 3.3 percent per year from 1970 to 1974 (line 2). Current employment is generally not available by age or sex for local areas, and in this case only an all classes figure was provided by the State employment security office. Employment is entered in table G-1 on line 3. The average annual change in employment during the period 1970-74 was 3.4 percent, which is close to the projected figure of 3.3 percent for the labor force (line 2). We conclude that this evaluation supports the projected population trend, because of the similarity between the estimated and projected percent of change. 1 The absolute level of employ- ment shown is affected by multiple jobholding and by the fact that place of work, not place of residence, is the basis for compiling employment statistics. The correspondence between the estimates and projections will not always materialize, and if the difference is great, a reappraisal is in order. The employment data can be examined in the light of the above-mentioned problems, and the projected labor force participation rates reconsidered. The postcensal population estimate, which enters into the comparison, is subject to some error, and the input and assumptions of the projections can be checked. Finally, change in the population of retirement age might have little or no effect on employment. For comparison, data on population and labor force for the United States are shown on lines 8 and 9 of table G-1. The labor force is shown as growing more rapidly than the population, as was the case for "Tri-county Area, USA", but the growth rates for both population and labor force of the local area are higher than those for the Nation. The projected net in-migration for the area is consistent with this relationship. Several technical difficulties will be encountered in the preparation of data for labor force evaluation. In "Tri-county Area, USA", one of the counties was officially added to the SMSA after 1970. For this county, the statistics from the 1970 census are in very much less detail. Finer subdivisions of age had to be estimated, requiring considerable staff time. Another problem involves the classification by race. The population projections are for (1) White, and (2) Black and other races. This dichotomy is useful for local areas, and also was dictated by the type of county data by race and age available in the 1960 census. In the 1970 census volumes however, county labor force data by age are available only for (1) Black, and (2) all other. For the evaluation shown in this section, the 1970 census data were converted to the classification used in the projec- tions by a tedious estimation process. 'See column 2. 'The rates of change in reported employment and estimated labor force shown in table G-1 are not strictly comparable because the labor force includes members of the Armed Forces and the unemployed. However, the strength of the military bases in the area did not change materially during the 1970-74 period. APPENDIX H STEP-BY-STEP ILLUSTRATION OF THE COHORT-COMPONENT PROCEDURE FOR POPULATION PROJECTIONS OF LOCAL AREAS (The term "Black" as used in this section refers to the population of Black and other races) 1. Introduction This section provides a detailed explanation of one of the standard methods used in making popula- tion projections for local areas, the cohort-com- ponent method. Tables H- to H-9 demonstrate the use of the method by projecting the White female population of "Central County, USA" to 1980. This is a fictitious name for a United States county which in fact is the central county of a three-county SMSA. The actual name of the county is not given because the method illustrated here is designed for general use in the United States. The basic method is shown for "Central County" only, but Section 5 in this appendix illustrates the technique of adjusting the projections for the three individual counties to a control projection for the total area (tables H-10 toH-14). The projection method shown serves two func- tions. On the one hand, the procedure has been kept as simple as possible, and the inexperienced tech- nician will find all the materials needed to make standard "demographic" projections which rely on the assumption that past trends of net migration will continue. The computations can be carried out on a simple desk calculator. On the other hand, the basic procedure is methodologically sound, within the general limitations of net migration models. If a more sophisticated determination of projected migration trends is available, for example by means of an economic-demographic model, and if correc- tions for extreme migration rates and special popula- tions are introduced, as mentioned in the text, the method can serve as the demographic framework for a more complex model involving sets of subareas, controlled to an area total. The cohort -component method illustrated here is especially appropriate for making projections by age, and by sex and race if desired. It is, however, not suitable for very small areas such as census tracts, functioning best when used for metropolitan areas (or other similar grouping of counties) and counties. For subcounty projections, other methods should be employed. See Section 3 (pp. 11-30) for a review of existing methodology, and Section 2.31 for further discussion of the county as a unit for projections. It should also be understood that the method shown here in a step-by-step format does not specif- ically take account of the economic prospects of the area. Projections currently being developed by State and local technicians sometimes introduce projec- tions of employment and other economic data. It has not been established that such projections are superior to purely demographic projections in pre- dicting the future total population of a local area. However, it is clearly useful for planning purposes to produce a set of mutually consistent demographic and economic projections. To achieve such consistency, special adjustments to the demographic projections would be required. One of the important features of the step-by-step method that follows is the method shown for adjust- ing the preliminary population projections to 1980 to take into account a postcensal population esti- mate. If economic projections were involved, these same techniques would form a substantial part of an adjustment to make demographic projections con- sistent with an externally prepared projection of economic data. The adjustments would lead to a final population projection by age, sex, and race perfectly consistent with the externally derived data. The further adjustment of the individual county projections to agree with a multi-county total is shown in Section 5 of this appendix, which de- scribes the more complex statistical techniques needed to bring into balance the demographic pro- jections by age for the various counties. 2. General Procedure The basic procedure in the main body of the cohort-component method given below is to project independently the three components of population change (births, deaths, and migration) from 1970 to 57 58 1980. l Projections for the year 1975 are obtained by a modified interpolation technique (table H-8). The computation is by cohort and provides for detail by age, race, and sex. Complete calculations are shown only for White females, but the results of similar computations for the other three race-sex groups are introduced in some steps as necessary. Births are projected using the general fertility rate, deaths are taken into account by using survival rates calculated from a life table (See Appendix C), and migration is projected by first calculating re- sidual net migration for the period 1960-70 by the forward survival method, then assuming that the migration rate observed will continue from 1970 to 1980. Important modifications of the migration rate are introduced to take the 1974 postcensal estimate into account; it is the method used to make these modifications which would be used to adjust to an externally derived projection of migration. Finally, the 1975 population (and any other intercensal year) is obtained by interpolation between the 1970 and the 1980 populations. 1 A fundamental feature of the method presented here is that the projection from 1970 to 1980 is made in one 10-year calculation, not in two 5-year periods. The potential error introduced in the migration component by the latter procedure is discussed in Section 3.234, under Adjacent cohort technique. Note that this guide provides the background data needed to project the population either by race or not, at the option of the user, by providing data first for all races, then separately for the White and Black populations. The illustration shown below does exercise the option to obtain race detail, recognizing the importance of this factor in analyzing popula- tion change in local areas. 3. Step-by -step Instructions 3.1 Computation of net migration by age, 1960-70 (table H-1). Before entering any numbers in column 1, read all the instructions relating to the column. Column 1. On lines 4 to 17, enter the White female population from the April 1, 1960 census in 5-year age groups. (See Exhibit 4-A, "Selected List of Data Sources", for a complete reference to the 1960 census.) Note that the computation is by cohort, and each line (2 to 17) of the table repre- sents the demographic experience of a cohort from 1960 to 1970. Enter the population 0-4 years of age on line 4 in accord with the labeling of the column "Age in 1960." On line 17, the population 65 and over is entered as the terminal age group, and on line 1, the all ages population is entered. Table H-1. Computation of Net Migration by Age for White Females by the Forward Survival Method for "Central County, USA": April 1, 1960 to 1970 Age of cohort Population April 1, 1960 and births 1960-70 (1) Life table survival rates (2) Expected population 1970 (3)=(l)x(2) Population April 1, 1970 (4) Net migration Line No. Age in 1960 Age in 1970 Amount (5)=(4)-(3) Percent (6)=|d00 1 2 3 4 Born April 1, 1965-70. Born April 1, 1960-65. x 66,674 2 (8, 945) 2 (10,099) 8,626 7,178 6,073 5,120 5,450 4,981 5,009 5,231 4,160 3,610 2,982 2,385 1,760 4,109 (X) .9807 .9779 .9957 .9967 .9952 .9938 .9925 .9896 .9844 .9758 .9626 .9444 .9183 .8760 .8078 .4505 81,409 8,772 9,876 8,589 7,154 6,044 5,088 5,409 4,929 4,931 5,104 4,004 3,409 2,738 2,089 1,422 1,851 79,340 6,992 7,699 7,781 7,143 8,719 6,221 4,851 4,726 4,696 4,831 3,939 3,282 2,733 2,046 1,508 2,173 -2,069 -1,780 -2,177 -808 -11 2,675 1,133 -558 -203 -235 -273 -65 -127 -5 -43 86 322 -2.54 -20.29 -22.04 -9.41 5 -0.15 6 7 8 9 10 11 12 13 14 15 16 17 44.26 22.27 -10.32 -4.12 -4.77 -5.35 -1.62 -3.73 -0.18 -2.06 6.05 17.40 X Not applicable. Excluding births. Total including births is 85,718. Registered births, shown in parentheses to distinguish from population covints. 59 On line 2, enter births for the period April 1, 1965 to April 1, 1970 to begin the calculation for the cohort 0-4 years of age in 1970. Enter births for the period April 1, 1960 to April 1, 1965 on line 3. Registered births by year for counties, needed to complete lines 2 and 3, are available from each State Health registrar (see Exhibit 4-B). The usual pro- cedure for obtaining these values is to subdivide annual data as needed by straight line interpolation. Thus line 2 can be obtained by adding three-fourths of 1965 births to data for 1966 to 1969, plus one- fourth of 1970 births. Line 3 can be obtained by a similar computation for the period April 1, 1960 to April 1, 1965. It would be preferable to use monthly data, if available. In footnote 1, enter the total population plus all births for the decade for later use in computing the number of deaths, and to provide a control total for all of the entries in the column. It is recommended that lines 2 and 3 be shown in parentheses as a reminder that these represent births, not popula- tion alive in 1960. Column 2. Enter life table survival rates (LTSR's) for the period 1960 to 1970. Rates for the Nation, derived from a table prepared by the National Center for Health Statistics (NCHS), are given in table A-1 and are used here. These can be used for all U.S. counties, although it would be preferable to use survival rates derived from an appropriate State life table, which are also prepared by NCHS for decennial census years. Sometimes a life table is available for a specific multi-county area. The method of computing survival rates from a life table is illustrated in Appendix C. The national rates are provided for use in case more appropriate rates are not available. 2 An important alternative to LTSR's is the use of national census survival rates (NCSR). NCSR's calcu- lated for the periods 1960-70 and 1970-80 are given in Appendix B. See Section 3.233 for a discussion of the issues involved in their use as opposed to LTSR's. The technician may substitute these rates for the LTSR's, but whichever type is selected must be used in both periods, 1960-70 and 1970-80. If NCSR's are used, the computation for 1960-70 in table H-1 will yield very similar estimates of net migration to those prepared for all counties by Bowles, Beale, and Lee except that their estimates are adjusted to agree with vital statistics totals. 3 The NCSR's produce census-level population projections, just as do the LTSR's, but the age detail is adjusted by correcting for age differentials in net census undercount at the national level. When NCSR's are used on a local area, the implicit assumption is that the effect of net census undercount on the estimates is the same for the local area as for the Nation. Column 3. Compute the population "expected" in 1970 in the absence of migration by multiplying column 1 by column 2. Line 1 of column 3 is obtained by addition. Column 4. Enter the April 1, 1970 census popula- tion on lines 2-17. Follow the labeling in the column "Age in 1970." Enter the population 0-4 on line 2 (note that the 5-year age detail extends to 75 and over on line 17). On this line in column 1, the 1960 population aged 65 and over has been entered, being the same cohort. Column 5. The difference between the census population and the expected population is assumed to be net migration (census minus expected). This is sometimes referred to as "residual" net migration, and in addition to migration, implicitly reflects the net result of errors in the census counts and in the estimates of births and survival rates used. 4 A minus sign indicates net out-migration, as the expected population is greater than the census count. These results show an estimated net out-migration (all ages) of 2,069; but for ages 20-24 in 1970, there is a substantial net in-migration and some in-migration for the age group 25 to 29. This type of opposite net flow is not unusual for a central city, and a substantial portion of the population of "Central County, USA" could be thus described. However, in this case a contributing factor is the presence of military population. It would be desirable to adjust for this factor and for colleges and institutions as well; there is also a small college in "Central County, USA." (See Section 2.33) As to the military base, there are no readily available data of any kind for dependents residing with a member of the military, so that the female population cannot be adjusted, short of a special count made at the military instal- lation. Methods of adjusting for military, college, 2 Although the estimated net migration 1960-70 is directly affected by the use of inappropriate survival rates, the popu- lation projected for 1980 using rates of migration based on these values is affected very little. See Section 3.234, formu- las 3.6 and 3.7. 3 Bowles, Beale, and Lee, op. cit. 4 If NCSR's are used, residual net migration includes the net effect of the variation of local net census undercount from the pattern for the Nation. 60 and institutional population have been developed, but they involve a good deal of data input and computation. 5 Column 6. Compute the rate of net migration by dividing the net migration (col. 5) by the expected population (col. 3). The initial population may also be used as the denominator, but the procedure recommended here is more commonly used. 3.21 Projections by age, 1970-80, for cohorts 10 years of age and over in 1980 (table H-2). The preliminary projection of the population in this table is carried out in two sections. The first section projects the 1980 population 10 years of age and over. This provides the projection of the female pop- ulation needed to calculate the number of births during the decade in table H-3. Once these births are obtained, table H-2 is completed by projecting the 1980 population under 10 years of age. 3.2 Preliminary population projections. This sec- tion develops preliminary projections to 1980. Two tables are involved, table H-2, which carries out a computation for 1970-80 similar to that in table H-1 for 1960-70, and table H-3, which projects births as input to table H-2. 5 Methods of adjusting for special populations are discussed in detail in Walter P. Hollmann and Isabel Ham- bright, "Population Projections as Affected by Special Popu- lations: Problems and Solutions." Paper presented at the 1974 meeting of the Population Association of America, Seattle, Washington. See also Richard Irwin and Warren Kalbach, "A Technique for Handling Military, College, and Institutional Populations in Cohort Survival Computations for Small Areas." Paper presented at the 1964 meeting of the Population Association of America, San Francisco, Cali- fornia. Column 1. The population on July 1, 1970 is ob- tained by extrapolation, age by age, of the April 1, 1960 and April 1, 1970 census counts given in table H-1 using the procedure described below. Popula- tion estimates and projections are usually prepared as of July 1 since they are often used as a denomi- nator in computing rates representing a calendar year. Making a small adjustment at this step avoids converting all projected data to July 1 at a later step. The extrapolation is carried out by the formula: P x 7/1/7 ° = (fi P x 4/1/70 ) (f 2 P v 4/1/60 ) where P x stands for the population of any age group x (not by cohort) on the dates indicated by the superscript, and fj and f 2 are State-specific factors given in table D-1. These factors, if applied to all counties of a State, will produce a population on Table H-2. Preliminary Population Projection by Age for White Females, for "Central County, USA": July 1, 1970 to 1980 Line No. Age of cohort Age in 1970 Age in 1980 Population July 1, 1970 and births 1970-80 (1) Life table survival rates ( projected) (2) Expected population July 1, 1980 (3)=(l)x(2) Net migration (4) = (A6)x(3) 100 Population July 1, 1980 (5)=(3)+(4) 2 3 4 5 6 7 8 9 10 11 12 13 14 15 li, 17 All ages, total. All ages, total. Born July 1, 19 75-80. Born July 1, 1970-75. to 4 years 5 to 9 years 10 to 14 years 15 to 19 years 20 to 24 years 25 to 29 years 30 to 34 years 35 to 39 years 40 to 44 years 45 to 49 years 50 to 54 years 55 to 59 years 60 to 64 years 65 and over to 4 years. . „ 5 to 9 years. . . 10 to 14 years. 15 to 19 years. 20 to 24 years. 25 to 29 years. 30 to 34 years. 35 to 39 years. 40 to 44 years. 45 to 49 years. 50 to 54 years. 55 to 59 years. 60 to 64 years. 65 to 69 years. 70 to 74 years. 75 and over. . . . 1 79 ,708 3 (8,591) 3 (7,792) 6,956 7,717 7,829 7,198 8,806 6,256 4,850 4,716 4,712 4,865 3,966 3,307 2,759 5,771 (X) .9850 .9820 .9960 .9966 .9950 .9938 .9927 .9901 .9854 .9771 .9644 .9464 .9210 .8851 .8262 .4901 90,834 8,462 7,652 6,928 7,691 7,790 7,153 8,742 6,194 4,779 4,608 4,544 4,604 3,653 2,927 2,279 2,828 2 -342 -1,717 -1,687 -652 -12 3,448 1,593 -902 -255 -228 -247 -74 -172 -7 -60 138 492 90,492 6,745 5,965 6,276 7,679 11,238 8,746 7,840 5,939 4,551 4,361 4,470 4,432 3,646 2,86 7 2,417 3,320 X Not applicable. Excluding births. Total including births is 96,091. 2 Sum of individual values. 3 Projected births, shown in parentheses to distinguish from estimated population. 61 July 1, 1970 consistent with the postcensal popula- tion estimate for the State on that date developed by the Bureau of the Census. This extrapolation pro- cedure is not a postcensal estimate in the ordinary sense, but any error introduced is small. If an inde- pendent estimate of the July 1, 1970 population is available, the age detail can be adjusted pro rata so as to sum to the estimate. The April 1, 1960 and 1970 population data are taken from table H-1 columns 1 and 4. Since table H-1 is arranged by cohort, in applying this formula to each age group one must take the 1960 popula- tion in column 1 from a line two spaces below the 1970 population in column 4. Thus on line 17 in column 1, the value for 1960 for the population 65 and over is shown, but in column 4 the last three values in lines 15, 16, and 17 must be summed to obtain the population aged 65 and over. The compu- tation may be checked by computing an all ages total which will differ from the sum of the indi- vidual computations only slightly, due to individual rounding. This extrapolation produces data in table H-2 for line 1 and lines 4 to 17 in column 1 . Lines 2 and 3 will be completed at a later step with prelimi- nary projections of births for the decade 1970-80. Column 2. Enter life table survival rates (LTSR's) projected for the 1970-80 decade (if LTSR's were used in table H-1). National rates will be found in table A-2. If national census survival rates were chosen in table H-1, they must also be used here. Projected NCSR's are given in Appendix B. If LTSR's specific to the locality or State are being used, they must be projected. It has not been un- common in recent years to assume no change for the 1970-80 decade from the 1960-70 rates, although this introduces a small error. Column 3. Compute the "expected" population in 1980 in the absence of net migration (except for the birth cohorts) by multiplying the 1970 popula- tion (col. 1) by the survival rates (col. 2). Column 4. Compute the projected net migration for the period 1970-80 (except for the birth co- horts) by multiplying the 1960-70 rates (col. 6) of table H-1 by the population expected in 1980 (col. 3). The all ages rate in table H-1 is not used; the total projected net migration is the sum of the age detail. In this illustration, net migration is projected as a rate, but some technicians prefer to use the absolute amount of net migration 1960-70. A compromise would be to first project net migration as a rate, but to control the calculation of net migrants for each cohort so as not to exceed the amount of net migra- tion for the cohort of the same age in 1960-70 by more than a specified ratio, say 20 percent. In the interest of simplicity, this option is not shown. The net in-migration projected in the illustration for ages 20 to 24 and 25 to 29 is larger than that estimated for 1960-70, because the population in these age groups increased in size in the decade 1970-80. To the extent that the net in-migration in 1960-70 for these age groups was due to the dependents of mili- tary personnel, this increase is illogical, since it de- pends in fact on the projected size of the military bases in the area, which size is not a function of the population residing in the area. If basic data are available, some adjustment method of the type mentioned in Section 2.33 can be used. See Section 3.31 below for a further discussion of the distribu- tion of projected net migration by age. Column 5. Compute the preliminary projected population in 1980 aged 10 years and over by adding net migration (col. 4) to the expected popu- lation (col. 3). At this point births must be projected in table H-3 for use in obtaining the population under 10 years of age in 1980. 3.22 Preliminary projections of births, 1970-80 (table H-3). This table illustrates the projection of births by race and sex for the periods July 1, 1970 to 1 975 and July 1 , 1 975 to 1 980 for use in project- ing the population under 10 years of age in 1980. Columns 1 to 3 provide the births needed for the preliminary projection of the 1980 population; columns 4 and 5 give a similar calculation made after the postcensal estimate adjustment (table H-4) which revises the 1980 projected population (table H-6) and therefore the number of births during the projection period. The birth projections utilize the general fertility rate (GFR) and relate the projection of the local GFR to projections for the Nation developed by the U.S. Bureau of the Census (shown in Appendix E). Age-specific fertility rates, rather than the relatively less precise GFR's, are often used in projections for 62 local areas, but the added accuracy obtained by the fineness of the detail may be overshadowed by distortions in the age detail of the projected female population, due to errors in projecting the age distri- bution of migrants. For use in table H-2, only White female births are needed, but for illustrative purposes, the preliminary projections shown in table H-3 simultaneously carry out separate projections for All races, White and Black. The sum of the race detail does not neces- sarily equal the separate calculation of All races. The GFR's for the Nation needed at steps 5a to 5c are taken from Appendix E. Another basic input is the proportion of births which are male at step 9b. The illustrative projections use: All races, .5133; White, .5144; and Black, .5081. These are computed from final birth registration data for the Nation in 1970. Table H-3. Preliminary and Revised Projections of Births by Race and Sex for "Central County, USA": July 1, 1970 to 1980 Procedural step Preliminary projections Revised projections All races White Black 1 White Black 1 (1) (2) (3) (4) (5) 1. Births (a) 1969. 5,570 5,628 5,563 5,587 3,625 3,615 3,545 3,595 1,945 2,013 2,018 1,992 (b) 1970 . (c) 1971 2. Average births 1969-71 [( 2)=(la+lb+lcK3]. . . . 3. Female population aged 15-44 years July 1, 1970 53,123 36,539 16,584 g z 4. County general fertility rate 1970 t(4)=(2)4(3) 1 .1052 .0984 .1201 5. U.S. general fertility rate (Series II) 2 > > (a) 1970 .0875 .0835 .1138 3 K (b) July 1, 1970-75 .0739 .0722 1.2023 .0700 .0688 1.1784 .0991 .0923 1.0554 o z O (c) July 1, 1975-80 6. Fertility ratio, 1970 [(6)=(4)r(5a) ] 7. County general fertility rate (a) July 1, 1970-75 C(7a)=(6)x(5b) 1 .0888 .0868 .0825 .0811 .1046 .0974 (b) July 1, 1975-80 [( 7b) = (6)x(5c) 1 8 , Female population aged 15-44 years (a) July 1, 1980 63, 194 55,641 45,993 38,902 17,201 16,738 46,934 39, 138 17, 788 (b) Jan. 1, 1973 C. 75(3)+. 25(8a) ] 16,885 (c) Jan. 1, 1978 t . 25 (3 ) +. 75 ( 8a) 3 60,676 43,630 17,047 44,335 17,487 9. Projection of births July 1, 1975-80 (a) Total births [(9a)=(7b)x(8c)x5 . 0] 26,333 17,692 8,302 17,978 8,516 .5133 13,517 12,816 .5144 9,101 8,591 .5081 4,218 4,084 .5144 9,248 8,730 .5081 (c) Male births [(9c)=(9a)*(9b) 1 4,327 4,189 10. Projections of births July 1, 19 70-75 24, 705 16,047 8,754 16,144 8,831 (b) Male births [(10b)-(10a) x (9b) ] 12,681 12,024 8,255 7,792 4,448 4,306 8,305 7,839 4,487 (c) Female births L( 10c)-(10a)-( 10b) 1 4,344 includes in addition to the Black population, all races other than White. Consistent with the Series II projections of fertility in "Projections of the Population of the United States: 1975-2050." U.S. Bureau of the Census, Current Population Reports , Series P-25, No. 601, October, 19 75. The general fertility rate is presented here per woman, rather than per 1,000 women, as is the custom for analytical tables. 63 The procedural steps in the calculation of the pre- liminary projections (cols. 1-3) are as follows: Step 1. Births, 1969-71. Enter the number of registered births for the years indicated at steps 1a to 1c, in columns 1-3. Step 2. Calculate the average number of births per year for the 3-year period as shown and enter here. Step 3. Enter the female population aged 15-44 years on July 1, 1970 after summing the data in table H-2, column 1, (lines 7-12) for the appropriate age groups. Step 4. The general fertility rate (GFR) for the county (or other local area) in calendar year 1970 is calculated as shown and entered here as a rate per woman. This rate is customarily shown per 1,000 women, as in Appendix E. Step 5. The GFR for the Nation 6 in calendar year 1970 and projected for the periods July 1, 1970 to 1975, and July 1, 1975 to 1980 from table E-1 is entered at the appropriate steps, 5a to 5c. (Entered as a rate per woman, not per 1,000 women.) Step 6. Calculate the ratio of the local GFR in 1970 to that of the Nation as shown, and enter here. Step 7. This ratio is assumed to continue to 1980, and projected GFR's for the county are obtained by multiplying this ratio by the GFR projected for the Nation for the two 5-year periods indicated, enter- ing the data at steps 7a and 7b. If desired, it can be assumed that the local GFR will converge to the national rate at some selected future date, and the ratio in step 6 can be adjusted by making it approach 1 . Step 8. Enter the projected female population aged 15-44 years on July 1, 1980 at step 8a after summing the data in table H-2, column 5 for the appropriate age groups (lines 5-10). The populations for the midpoints of the two 5-year time periods involved (January 1, 1973 and January 1, 1978) are obtained by straight-line interpolation between the July 1, 1970 and 1980 data, as indicated, and entered at steps 8b and 8c. Step 9. Compute the births for the 1975-80 period (who will become the population 0-4 years in 6 The rates used here are consistent with Series II of the national population projections of the U.S. Bureau of the Census. See further discussion under Effect of Alternate Fertility Assumptions in Section 3.22 regarding alternative series. 1980) by multiplying the appropriate GFR (7b) by the population at the midpoint of the period (8c). Since the GFR is for a 1-year period, the result must be multiplied by 5 to produce total births which in turn are multiplied by the proportion of births which are male (9b, taken from national data for 1970) to obtain male births, entered at step 9c. Female births for step 9d equal total births minus male births. Step 10. A similar computation is made for births from July 1, 1970 to 1975, as shown. The projec- tions indicate 8,591 White female births for July 1, 1975 to 1980; and 7,792 for July 1, 1970 to 1975. Effect of Alternative Fertility Assumptions. The procedure for projecting births described above makes the assumption that the general fertility rate for "Central County, USA" will maintain a constant ratio to the rate projected for the Nation under Series II of the most recent national population pro- jections prepared by the U.S. Bureau of the Census. 7 In the national projections the regular Series I, II, and III differ only with respect to the fertility assumptions. Series II, the middle Series, assumes an average of 2.1 children per woman at completion of childbearing, which is approximately the rate at which population change would be zero (in the absence of immigration) if it continued long enough. Series I assumes 2.7, and Series III, 1.7 children per woman. To illustrate the impact of these alternative series on the actual number of births projected, calcula- tions were carried out consistent with the Series I and Series III assumptions for the period 1975 to 1980. The projections of births were 10,021 and 7,436, respectively. These are 17 percent higher and 13 percent lower than the Series II projection of 8,591. The computation now returns to table H-2 to enter the Series II birth projections in column 1, lines 2 and 3, to complete the projection of the population under 10 years of age in 1980. 3.23 Projections by age, 1970-80, for cohorts under 10 years of age in 1980 (table H-2 cont.). Column 1. Enter the 8,591 White female births projected for the period July 1, 1975 to 1980 on line 2 of this column, and the 7,792 births for the period July 1 , 1 970 to 1 975 on line 3. 7 U.S. Bureau of the Census, Current Population Reports, Series P-25, No. 601, op. cit. 64 Column 2. The survival rates have already been entered. Column 3. Compute the "expected" population under 10 years of age in 1980 by multiplying column 1 by column 2. Column 4. Compute the net migrants by multi- plying the 1960-70 rates in table H-1, column 6, by the expected population (col. 3). Column 5. The preliminary population projection for the birth cohorts is the sum of the "expected" population (col. 3) and net migrants (col. 4). 3.3 Adjustment of preliminary projection of net migration, 1970-80, for postcensal estimate (table H-4). This table generates the revised net migration needed as a first step toward obtaining a revised population projection on July 1, 1980, adjusted to take account of a postcensal estimate, in this case for July 1, 1974. The general procedure is to begin with the estimated net migration for the period 1970-74 and add to it a projection of migration from 1974 to 1980 obtained by assigning weights to (1) the 1970-80 average annual rate of projected net migration, and (2) the 1970-74 average annual rate of net migration indicated by the 1974 postcensal estimate. In this example, equal weight is given to each trend, following the notion that although the 1970-80 rate is a reflection of the ten-year inter- censal period 1960-70, as compared to only a four- year period for the postcensal estimate, the more recent experience should be given relatively more weight. A simple resolution of these two opposing factors is to assign equal weight to each trend. However, the analyst developing the basic assumptions is free to assign weight as seems most reasonable, or simply insert a different projected net migration for the period 1974-80 as indicated by externally developed projections. These options are discussed in the material which follows. Presentation of basic data Step 1. Preliminary projected net migration. Here the all ages migration 1970 to 1980 of -342, calcu- lated for White females at line 1, column 4 of table H-2 is entered at step 1b, along with results of similar calculations (not shown) for the three re- maining race-sex groups at the appropriate steps. Enter the sum of the data at step 1e as the all classes total. Step 2. Enter the estimated population for the most recent postcensal date, in this case July 1, 1974. This estimate was prepared under the Federal-State Cooperative Program and published in Current Population Reports, Series P-26, U.S. Bureau of the Census. (See Exhibit 4-A for a com- plete reference.) Since race detail is not published, this example uses only data for all classes. Step 3. Enter the estimated net migration from April 1, 1970 to July 1, 1974 from the source just cited. Since the base date for the preliminary projec- tions is July 1, 1970, at step 3a a straight-line inter- polation takes 16/17, or .941176 of the original total, to adjust for the 3-month difference. Step 4. Calculate the total population on July 1, 1970 needed as a base for computing migration rates from the above data by entering at steps 4a to 4d the values by race and sex obtained in column 1, table H-2 for White females, and similar computa- tions not shown for other race-sex groups. Calculate the all classes population by summing these data and enter it in 4e. Adjustment of net migration (Ail classes) Step 5. Average annual rate of projected net migration, 1970-80. This is obtained by taking 1/10 of the rate of net migration for the 10-year period (the preliminary net migration total divided by the total population on July 1, 1970). A refinement would be to calculate the geometric rate instead of the arithmetic average calculated here, but for low rates of net migration, there is little difference. In the computer, or on a modern statistical calculator, the geometric rate is easily calculated, and in Sec- tion 5 of this appendix, this geometric calculation is explained while demonstrating the steps for adjust- ing projections for individual counties to agree with an area total. (Although most of the computations in this illustration are carried out to only four decimals, factors to be used in subsequent adjust- ments are carried out to six decimals, as in this in- stance.) Step 6. Average annual rate of estimated net migration, 1970-74. The computation is exactly as described above, except that the 1970-74 rate is divided by 4 to obtain the annual average. Step 7. Projected average annual rate of net migration, 1974-80. The procedure recommended here is to average the 10-year and the 4-year rates, to obtain a projected value to carry forward from 65 Table H-4. Revision of Preliminary Projection of Net Migration by Race and Sex for Postcensal Estimate, for "Central County, USA": July 1, 1970 to 1980 (All data are for population of all ages. See text for data sources and method of computation) Procedural step Data PRESENTATION OF BASIC DATA 1. Preliminary net migration, July 1, 1970 to July 1, 1980 (a) White males . „ (b) White females. (c) Black males 1 (d) Black females 1 (e) All classes, total (le) = I^(l) 2. Estimated population (all classes): July 1, 1974 3. Estimated net migration (all classes): April 1, 1970 to July 1, 1974, (a) Adjustment to period July 1, 1970 to July 1, 1974 (3a) = .941176x(3) 4. Population, July 1, 1970 (a) White males (b) White females (c) Black males 1 (d) Black females 1 (e) All classes, total ADJUSTMENT OF NET MIGRATION (ALL CLASSES) 2 5. Average annual rate of projected net migration: 1970-80 (5)=[