Local Government Finance: Capital Facilities Planning and Debt Administration by Alan Walter Steiss

POPULATION ESTIMATES AND PROJECTIONS

Establishing goals and objectives for public service programs and determining standards of service for carrying out these programs are essential elements in capital facilities planning. Standards of service often are delimited in measurable, quantitative terms. For example, standards for public open space can be expressed in terms of acres per given unit of population and/or in terms of optimum times or distances required for residents to travel to enjoy various forms of recreational experiences. Health care standards often can be expressed in terms of medical personnel and/or hospital beds per thousand population; educa-tional facilities in terms of classroom-pupil ratios; library facilities in terms of client capacity and time-distance factors; and so forth. While some standards are more difficult to quantify, those that can be measured provide important means of assessing existing public facilities and programs in light of desired objectives and population/client groups to be served.

To translate standards of service into future capital needs, it is necessary to have well-founded estimates of future population, including demographic and geographic distribution. Projective computations were introduced in the field of demography only a few decades ago, and as Roland Pressat, the noted French demographer, has observed, until very recently these projects (frequently known as "conditional forecasts") have had no predictive pretensions.

. . . they simply illustrate the effect on a population (on its total or its age and sex composition) of the operation of certain fertility and mortality conditions, chosen for specific purposes--whether they be hypotheses whose realization is doubtful or hypotheses singled out because they represent extreme situations between which the real situations seem certain to take place. [1]

In short, demographers (and planners using the techniques of demo-graphy) have applied the concept of a range of projections in lieu of more definitive estimates of future population characteristics for a given study area. Unfortunately, such future population parameters often are extra-polated from current data with insufficient detail to be of much utility to the capital facilities planner. The statement that the population of city X in 1995 will be between 150,000 and 175,000 does not provide an adequate basis for the development of capital facilities commitments.

Overview of Population Projection Techniques

For purposes of capital facilities planning, it is necessary to develop fairly detailed estimates and projections of population by age-cohorts. Such detail is particularly applicable to the identification of capital facility needs associated with certain age groups (such as school facilities, health care facilities, housing for the elderly, recreational needs, etc.).

Definitions

The concepts of population estimates and population projections often are confused even though the distinction between the two is relatively simple and straightforward. Both concepts involve the generation of a number that is intended to indicate the size of the population of a given geographic area at a specific point in time. Both techniques make use of the basic demographic equation:

P2 = P1 + B - D + I - O

which indicates that the population at any given point in time (P2) is a function of the population at a previous point in time (P1) plus the amount of natural increase (births minus deaths) and the net migration (in-migration minus out-migration) during the interim.

A population estimate refers to size of the current population in the area. Estimates are calculated in lieu of an actual census count and are used to update population data gathered by the last census. Population estimates generally are based on direct components of population change, such as the actual number of births and deaths occurring between the date of the previous population count and the date of the estimate. In the absence of direct data, a population estimate may be based on symptomatic indicators of the components of population change, such as changes in school enrollments or the number of motor vehicles being registered.

A population projection refers to size of the population at some point in the future. Population projections indicate what changes might occur, given assumptions inherent in the projection method and data. Since projections refer to the size of the population at some point in the future, they cannot be based on actual data comprising the components of population change. Rather, they must be based on an extension of either current or expected population trends into the future. Analysts typically develop more than one set of projections, each set embodying different assumptions. Projections may represent minimum, maximum, and midpoint growth rates, but all projections should be plausible.

The application of expected population trends to a base population generally is regarded as a population forecast. In the case of a population forecast, there is an implied expectation that the forecasted population will closely approximate the value of the population at some future date. A population forecast is judgmental; it is the set of projections deemed most likely to occur.

Projections do not necessarily lead to forecasts. Agencies often prepare sets of projections ranging from slow growth to rapid growth so that users may select the forecasts that most closely approximate their needs. Using projections which are on the high or low side can provide a margin of safety in projecting future municipal services or revenues.

Alternative projections may be based on the same method, differing only in their designated growth rates, birth rates, population densities, and so forth. Or they may be the result of different methods. All projec-tion methods have weaknesses and strengths. Some analysts attempt to mitigate the weak points by averaging together projections obtained by two or more different methods to produce a set of most likely projections.

Component and Noncomponent Models

Population change involves three separate components: births, deaths, and migration. Component models consider the separate effects of each of these factor and require more comprehensive and detailed data than usually are available to local planners. Models that use the net effects of the three components are called noncomponent models. Most models that project population below the state scale are usually of the noncomponent variety because of data limit-ations (and demographic skills).

Noncomponent models may be based on past patterns of net popula-tion growth, or they may relate net growth to some indicator information, such as changes in housing or the economic base of the community. Symptomatic data often are useful in these models because there is a correlation between population size and various other events, such as tax returns, voter registration, school enrollments, telephone installations, utility meter connections, occupancy permits issued, and motor vehicle licenses. Non-component models lack detailed age-sex breakdowns which are useful in planning for schools, community services, and different housing types. Overall, it is desirable, although not always possible, to consider the three components of population change separately and combine, not average, their effects. This is particularly true for mid- and long-range projection periods because the forces driving births, deaths, and migration may not be correlated.

Births and deaths are referred to as vital statistics. The numerical difference between births and deaths is called natural increase (or decrease). Death rates in urban industrial nations at peace tend to be fairly stable over time and space. Therefore, age-specific mortality rates for the nation as a whole often are applied to local area population projections.

A crude death rate is a gross statistic which indicates the number of deaths per year for each 1,000 people in a given geographic area; it provides no age-sex detail. The crude death rate is based on vital statistics which usually are readily available on an annual basis and is easy to calculate. The formula for the crude death rate is as follows:

CDR = number of deaths in theyear (divided by) midyear population x 1000

Thus, if the total population in a given area is 625,000 and the number of death annually is 6,000, then the crude death rate would be 6000/625000 x 1000 = 9.6. Similar calculations could be made for males and females in the population or for whites and nonwhites.

A crude birth rate indicates the number of births each year per 1,000 population, but provides no age-sex information. As with the crude death rate, the numerator (number of births) is based on data gathered from vital registration information, while the denominator consists of a midyear population estimate.

The general fertility rate is the ratio of births to women of child-bearing age (defined as 15 to 44 years of age). The general fertility rate overcomes one of the disadvantages associated with the crude birth rate by taking into account the sex structure of the population. Unlike the crude birth rate, the general fertility rate is calculated using the population that is most likely to give birth.

The age specific fertility rate is an extension of the general fertility rate which provides an even greater level of specification by calculating fertility rates for each 5-year age cohort of women, beginning with the 15 to 19 age group through the 40 to 44 age group. By using a more narrowly defined age group in its calculations, the age specific fertility rate provides better controls over the bias that may be introduced by the variations in fertility levels over the reproductive span.

Birth rates and fertility rates change fairly slowly, and are subject to regional, racial, and ethnic differences. Birth rates used in population projections often are determined empirically for the area under analysis. It is important, however, to allocate births to the mother's city of residence. Otherwise, the "births" assigned to the city's hospitals will not materialize as school children, and this will lead to erroneous conclusions, suggesting out migration.

Migration is the most difficult component to estimate or project at the local level. Migration is subject to relatively rapid fluctuations and is influences by the size, shape, location, and economic base of the locality. A large county or city will have a lower proportion of migrants than will a small one, since many moves cover a relatively short distance. A narrow geographic entity will experience more migration across its boundaries than will a wide one. A city located close to state boundaries may be impacted by migration more than one that is centrally located, particularly if there is a twin city on the other side of the state line. Morrison divides the population of a region into "stayers" and "chronic immigrants". An example of this latter group is middle management executives. The second group accounts for about half of the moves in any given economic area and these moves appear to be relatively insensitive to local employment conditions. On the other hand, the location of a major new economic activity may have a most significant impact on the current and future population of an area.

In the absence of official data on migration, it is necessary to examine other types of data that might serve as an indicator of migration. These are called symptomatic indicators since they may be symptoms of migration just as certain physical conditions may be symptomatic of a particular disease. The major source of symptomatic data on migration come from those things that one might do when first moving to a new location. For example, most states require new residents to obtain a valid driver's license within 30 to 90 days after moving into the state. Many jurisdictions require new residents to obtain a local automobile registration after moving into the area. The issuance of new telephone numbers to residential customers is another indicator. Property tax data may also serve as a means of tracking migration. None of these indicators provide a perfect data source for migration. They are all subject to intervening variables which must be taken into account.

The intercensal component method of estimating migration makes use of what demographers refer to as the population balancing equation. This equation represent the difference in population at two points in time as a function of birth minus deaths plus in-migration minus out-migration. The intercensal component method rewrites the basic population equation as follows:

I - O = P2 - P1 - B + D

Assume that the population of a given area in 1980 was 65,257 and the population of the area in 1990 was 72,486, an increase of 7,229. If the number of births recorded in the ten year period was 10,115 and the number of death recorded in this decade was 5,810, then the net migration can be determined, as follows:

Net Migration = 72,486 - 65,257 - 10,115 + 5,810 = 2,924

It may be desirable to calculate a migration ratio based on the resulting estimate of net migration. The migration ratio would be determined by dividing net migration by birth - deaths and multiply the results by 1000. Using the previous assumptions, the migration ratio would be:

2,924 divided by (10,115 - 5,810) x 1000 = 679.2.

The reverse survival rate method is a more flexible approach to estimating migration in that it may be used to produce net migration estimates by age, race, and sex groups as contrasted to the total net migration estimate resulting from the intercensal component method. Estimates of net migration are produced by applying 10-year survival rates to the number of individuals recorded in a particular cohort in the earlier census in order to predict the number of members in that cohort who should have survived to the census. Survival rates are derived from actuarial tables (or "life tables"). The difference between the actual number of individuals in the cohort that has been "aged" by 10 years and the estimated number based on the survival rate is assumed to be the estimated migration. For example, if in 1980, there were 14,000 individuals in the 20-24 age cohort for which the 10-year survival rate was 0.983073, in 1990, the expectation would be that approximately 98.3% of these individuals (or 13,763) would have survived to be in the 30-34 age cohort. If the census count for the 30-34 cohort shows 14,300 people, then the difference of 537 is assumed to be the result of in-migration over out-migration. The application of this information to making population projections will be discussed in greater detail in the case study.

Types of Models

The general methodologies for producing population projections fall into four general categories: (1) ratio allocation methods; (2) mathematical extrapolation methods; (3) econometric methods; and (4) cohort component methods. Ratio allocation methods are used to allocate an existing population projection for a state or region among the subareas that comprise the larger area. Mathematical extrapolation methods involve the application of a selected growth rate into the future. Econometric methods project population as part of an overall forecast of the economy in an area and usually generate a population projection by linking future population levels to expected future employment. Cohort component methods project population by examining separately for each cohort (or age group) the three major components of population change: births, deaths, and net migration. Cohort component methods generally result in projections with the highest level of detail by age, race, and sex of any projection method.

The choice of a projection methodology is best made by considering its relative accuracy, the type of data available, the quality of available data, the scale of the analysis, the geographic level of the projection, the length of the projection period, the purpose of the projections, and the budget and time frame implications of the projection study. The simpler methods have a wider range of application and may be used to produce population projections at almost any geographic level. Econometric and cohort component models have more extensive data demands and may be less appropriate for smaller geographic areas.

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Trend Extrapolation. Nearly all projection methods, to some extent, extrapolate past or present trends into the future. A trend extrapolation model refers specifically to a fairly simplistic model that uses the historical growth pattern to project the future growth pattern. Such a model deals with the net effects of births, deaths, and migration rather than with the individual components. After graphing past population growth (either the actual numbers or the rates of growth), one fits a curve to that growth and extends it into the future. Past growth may show a linear, exponential, or logistic curve over the historic period. Linear and nonlinear regression formulas also can be used. The prime disadvantage of trend extrapolation methods is the lack of component detail. The future growth rates also become dependent upon the depth of the historical period analyzed. If the past twenty-five years are examined, for example, the projections may be influenced by a rapid period of growth in the 1950's, but if only the past ten years are used in the analysis, projections may be considerably different.

Comparative Forecasting. A locality's past growth pattern can be examined in conjunction with growth patterns of older, larger, civil divisions. The assumption behind this method is that the locality's growth pattern will match that of communities more advanced in their stage of growth. Comparative forecasting is useful for short-term projections, but is not used as an estimating method. There may be no reason to assume that factors currently affecting the components of population will produce patterns of net growth exhibited by the older minor civil divisions.

Ratio Trend or Step-Down Techniques assume that the relationship of a locality to some larger geographic entity--county or state--will prevail in the future. For example, if the city accounted for 25 percent of the county's population in 1980, it is assumed that it will account for 25 percent of the county's projected population in 1990 and 2000. Or, if the city's share of the county's population has been growing over the years, its share will continue to increase according to the same pattern in the future. This method assumes that population projections at the larger scale represent degrees of reliability and component detail that are not possible to achieve at the small scale of analysis. As with the two pre-vious techniques, this method is flawed in that historic trends may not hold in the future, and the length of the historical period used for determining the ratios will influence future growth rates. Sometimes there is no simple historic relationship between, for example, a city and its surrounding county or region.

Density Ceiling models employ capacity constraints. Such a model assumes that when a given density is reached, population will either stabilize or decline. The density model may utilize linear, exponential, or logistic curves to express population density growth rates. Maximum population levels are typically determined via zoning and land use development patterns that affect population density. The advantages of density ceiling models are that they provide practical means of con- straining the levels of population projection, and they provide empirical detail regarding probable distribution and concentrations of population. They also provide a basis for experimentation with zoning changes. The obvious disadvantage of the density model is the accurate selection of maximum densities. These methods are subject to the same flaws as methods that extrapolate net population growth.

The Ratio Correlation Method is an estimating technique rather than a projection technique. It is similar to the ratio trend method except that population is treated as a function of some other variables--employment, housing units, motor vehicles registered, or other symptomatic data. Multiple regression may be used to determine the population's historic relationship to the independent variables. Current shares or logarithms of past shares may also express the relationship among the variables. The advantage of this method is that it uses indicators of actual population to determine growth rates. It also can provide good detail on spatial or occupational distribution of the population.

Housing Unit Method can be used for both projection and estimation purposes. It establishes a relationship between the number of dwelling units and population via a family-size multiplier. Dwelling units can be estimated by utility or telephone connections, building permit data, land use surveys, vacancy rates, construction data, home interviews, and other local records. Net changes in dwelling units are presumed to indicate net changes in population.

Market Force Methods include the following techniques: holding capacity, deterministic regression models, multiplier studies, and mathematical programming. Market force methods are generally more complex causal models. Linear regression may be used to formulate equations that will relate population distribution to such factors as vacant land, the presence of minority group populations, accessibility to work, land values, and other important variables. Employment forecasts made by shift and share, economic base, and input-output techniques may be converted by the use of multipliers to population forecasts. Finally, the future distribution of population may be treated by a procedure to improve conditions in which an objective such as minimizing travel time to work is sought, subject to equations representing constraints on supply and demand for developable land, availability of services, and other factors. These models are more applicable at the state and regional scales than at the scale of local government because more information about causal relationships is available.

The Greenberg-Kruckeberg-Mautner (GKM) model seeks information at different scales of analysis; it combines historical extrapolation, ratio trend, and density ceiling alternatives at the local scale and constrains these with federal-state-county population projections developed by component and market force techniques. The model gives the user the option of five separate submodels to project local population. It is quite useful when state projections are to be distributed to various minor civil divisions within its boundaries.

Component Models

The Residual Method is used for estimation. It starts with a known population, usually based on the last census. Records of births and deaths are examined, and the population adjusted accordingly to produce an estimate of current population. The difference between this anticipated population and the actual population is assumed to be the result of net migration. This method is relatively simple and does not call for age-sex breakdowns of the population.

The Vital Rates method is a ratio technique that relates total population to births and deaths. Ratios are developed between state and local births and deaths from the historical record. Birth and death rates for the local unit are obtained for the estimated period by substituting the known state rates into the ratio and solving for the local rates. The rates are used to develop estimated populations based on births and deaths, Then the estimates based on the ratio are averaged to reduce errors involved in each of the projections. This is both an estimating and a projection technique. It assumes that a change in the rate of vital statistics signals a change in population size. The assumption that the relationship between the vital statistics and population remains constant and the difficulty of developing accurate ratios between population and births and deaths are drawbacks of this method. Another drawback is that rapid migration, which affects the age structure, will impact the vital statistics and produce inaccurate estimates.

Cohort-Survival Models are the most basic method for providing age-sex detail. While it is a component model, it does not account for the migration component. The cohort-survival model projects future population on the basis of growth due to natural increase. Population is disaggregated into male and female age cohorts. Each cohort spans five years. Age-specific death rates (or survival rates) are developed and applied to each cohort. Age-specific fertility rates are applied to female cohorts between the ages of 15 and 44. Each cohort group is then "aged forward" towards the final projection year, with mortality and fertility rates applied to the survivors at five year intervals. Births are added to the bottom of the pyramid and aged forward accordingly.

The advantage of this technique is the excellent detail provided in projecting future demand for age-specific needs, such as schools, jobs, or services for the elderly. It is a fairly accurate forecasting technique when migration is either known or negligible. Various methods of estimating and projecting migration can be added to the basic model; the result is known as a cohort-component method.

Various Cohort-Component Methods have been developed by the Bureau of the Census. Method I uses school enrollment data to estimate the migration component--net migration is assumed to be the difference between the growth rate of school-age cohorts at the national level and the growth rate of school-age population at the scale of analysis. Method It assumes that the migration component is the difference between the anticipated school-age population, based on natural increase, and the actual population of school age. A variation of Method II is the grade progression method that breaks down school enrollment by grades. Cohort component models are effective in creating alternative projection sets because of the simplicity of varying assumptions. For example, one may use high fertility with low migration, or vice versa.

The shortcoming of these census methods is the tendency to under estimate young married couples, elderly, and single migrants. Other migration estimates can be made by extrapolating migration trends from past decades (e.g., by using a residual method), or by a ratio-correlation method that relates migration to symptomatic data, such as dwelling units.

The Composite Model applies different techniques to different segments of the total population. Like the component method, it uses age-specific information on births and deaths. Instead of analyzing the three components of change, however, the composite method projects population for different age groups using different methods and then sums them for a total population figure. It takes advantage of the fact that different methods are better focused for estimating population of different groups.

The Final Choice of Methods

No population indicator can be considered the best measure in all situations. The choice for a particular application involves consideration of several factors, including the desired level of accuracy, ease of calculation, desired detail in estimates or projections, and the availability of data. In the final analysis, the choice of the methods employed will almost always involve a trade-off of some sort. The level of accuracy, data availability, and the composition of the final product usually will be the chief determining factors in the selection process. The requirements of capital facilities planning often dictate a level of detail that has greater specificity than the level of available data, resulting in the requirement for carefully constructed assumptions to bridge the data deficiencies.

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