**IV. POPULATION ESTIMATES AND PROJECTIONS**

Standards of service provide important assessments of existing public facilities and programs in light of desired objectives and the population/client groups to be served.

Estimates of future population, including demographic and geographic distribution, are required to translate these standards into future capital improvement needs.

__Demographic Techniques__

Until very recently demographic projections (frequently known as "conditional forecasts") have had no predictive pretensions.

Demographers often apply a *range of projections* in lieu of more
definitive estimates of future population characteristics. Such parameters
usually are extrapolated from current data with insufficient detail to
be of much utility to the capital facilities planner.

The *basic demographic equation* is **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.

*Population estimates* are used to update population data gathered
from the last census to approximate the current situation.

*Population projections* refer to future population levels and
indicate what changes might occur, given assumptions inherent in the projection
method and data. Analysts typically develop more than one set of projections,
each set embodying different assumptions.

A *population forecast* is the set of projections deemed most likely
to occur. Projections do not necessarily lead to forecasts.

o Sets of projections often are prepared, ranging from slow growth to rapid growth, so that users may select the forecast that most closely approximate their needs.

o Alternative projections may be based on the same method, differing only in their designated growth rates, birth rates, population densities, and so forth.

Population change involves three separate components: *births*,
*deaths*, and *migration*.

o *Component models* consider the separate effects of each of these
factors.

o *Noncomponent models* use the net effects of the three components.

Noncomponent models may be based on past patterns of net population growth or may relate net growth to some indicator, such as changes in housing or the economic base of the community.

*Symptomatic data* are used to determine a correlation between
population size and various other events, such as tax returns, voter registration,
school enrollments, utility connections, telephone installations, occupancy
permits issued, and motor vehicle licenses.

Noncomponent models lack detailed age-sex breakdowns which are useful in planning for schools, community services, and different housing types.

Most models that project population below the state scale are usually of the noncomponent variety because of data limitations (and demographic skills).

Births and deaths are referred to as *vital statistics*, usually
available on an annual basis.

*o Natural increase* (or decrease) is numerical difference between
births and deaths.

o A *crude death rate* is a gross statistic which indicates the
number of deaths per 1,000 of population; it provides no age-sex detail.

o A *crude birth rate* indicates births per 1,000 population, but
provides no age-sex information.

o* General fertility rate *is the ratio of births to women of child-bearing
age (15 to 44 years of age).

o *Age specific fertility rate *provides a greater level of specification
by calculating fertility rates for each 5-year age cohort of women.

o Birth rates and fertility rates change fairly slowly, and are subject to regional, racial, and ethnic differences.

o Birth rates used in population projections often are determined empirically for the area under analysis.

*Migration* is subject to relatively rapid fluctuations and is
influenced by the location, size, shape, 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.

The* intercensal component method* of estimating migration makes
use of the population balancing equation which rewrites the basic population
equation as follows: I - O = P2 - P1 - B + D

The *reverse survival rate method* may be used to produce net migration
estimates by age, race, and sex groups.

o 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 members in that cohort who should have survived to the current census.

o 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.

__Types of Population Models __

In choosing a population model, it is important to consider its relative accuracy, the type of data available, the quality of available data, the scale of the analysis, the length of the projection period, the purpose of the projections, and the budget and time frame implications of the study.

*Trend extrapolatio*n is involved, to some extent, in nearly all
projection methods.

o This model uses historical growth patterns to project the future pattern, dealing with the net effects of births, deaths, and migration rather than with individual components.

o The primary disadvantage is the lack of detail regarding the components of population.

*Comparative forecasting* examines the locality's past growth pattern
in conjunction with growth patterns of older, larger, civil divisions,
the assumption being that the locality's pattern will match that of communities
more advanced in their stage of growth.

*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 and that population projections at the larger scale represent
degrees of reliability and component detail that are not possible to achieve
at the smaller scale of analysis.

*Density ceiling models* use capacity constraints by assuming that
when a given density is reached, population will either stabilize or decline.

o The density model may utilize linear, exponential, or logistic curves to express population density growth rates.

o Maximum population levels typically determined via zoning and land use development patterns that affect population density.

The* ratio correlation method* is similar to the ratio trend method
except that population is treated as a function of some other independent
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.

The *housing unit method* establishes a relationship between the
number of dwelling units and population via a family-size multiplier.

o Net changes in dwelling units presumed to indicate net changes in population.

o Dwelling units can be estimated by utility or telephone connections, building permit data, land use surveys, vacancy rates, home interviews, and other local records.

*Market force methods* include: deterministic regression models,
holding capacity, multiplier studies, and mathematical programming.

o 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.

o Employment forecasts made by shift and share, economic base, and input-output techniques may be converted by the use of multipliers to population forecasts.

o The future population distributions may be modeled to represent improved conditions in which a specific objective is sought--such as minimizing travel time to work--subject to equations representing constraints on supply and demand for developable land, avail-ability of services, and other factors.

The *Greenberg-Kruckeberg-Mautner (GKM)* model combines historical
extrapolation, ratio trend, and density ceiling alternatives at the local
scale, constrained by federal-state-county projections developed by component
and market force techniques, and provides the option of five separate submodels
to project local population.

The* residual method*--through an examination of the records of
births and deaths, the known population (based on the last census) is 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.

The *vital rates method* is a ratio technique that relates total
population to births and deaths.

o Ratios between state and local births and deaths are derived from the historical records and are then used to develop estimated populations based on births and deaths.

o Estimates based on the ratio are averaged to reduce errors involved in each of the projections.

o Rapid migration, which affects the age structure, will impact the vital statistics, resulting in inaccurate estimates.

*Cohort-survival models *project future population based on growth
due to natural increase.

o The population is disaggregated into male and female age five-year cohorts, and age-specific death rates (or survival rates) are developed and applied to each cohort.

o Age-specific fertility rates are applied to female cohorts between the ages of 15 and 44.

o 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.

o Births are added to the bottom of the pyramid and aged forward accordingly.

Various *cohort-component methods* have been developed by the Bureau
of the Census.

o 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.

o Method II 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.

The *composite model* applies various techniques to different segments
of the total population.

o Instead of analyzing the components of change, the population is projected for different age groups using different methods and then summed for a total population figure.

o It takes advantage of the fact that different methods are better focused for estimating population of different groups.

The choice of the methods employed to develop population estimates or projections usually involves a trade-off of some sort with the level of accuracy required, the availability of data, and the composition of the final product as the chief determining factors.

**Exhibit 1. Comparison of Population Estimation & Projection Methods**

Type of Model |
Estimation or Projection |
Historic Counts |
Vital Statistics |
Other Indices |
Period |
Scale |
Complexity |

NONCOMPONENT |
|||||||

Trend Extrapolation | Both | X | X | Short | Local | Moderate | |

Comparative Forecast | Projection | X | Short | Local | Simple | ||

Ratio Trend | Both | X | Short-Middle
-Long |
Local-State | Simple | ||

Density Ceiling | Projection | X | Middle-Long | Local | Complex | ||

Ratio Correlation | Estimation | X | X | Short | Local | Complex | |

Housing Unit | Both | X | X | Short-Middle | Local | Complex | |

Market Force | Projection | X | X | X | Short-Middle
-Long |
Local-State
-National |
Complex |

GKM | Projection | X | X | X | Short-Middle
-Long |
Local-State | Complex |

COMPONENT |
|||||||

Residual | Estimation | X | Short | Local-State
-National |
Simple | ||

Vital Rates | Both | X | Short | Local-State | Moderate | ||

Cohort-Survival | Both | X | Short-Middle
-Long |
Local-State
-National |
Complex | ||

Cohort-Component | Both | X | Short-Middle
-Long |
Local-State
-National |
Complex | ||

Composite | Both | X | X | X | Short-Middle
-Long |
Local-State | Complex |