Office of Planning, Environment, & Realty (HEP)

# Population Forecasting Methods: A Report on Forecasting and Estimating Methods

## Part II: Current Techniques of Forecasting

Several general methods for making population projections for areas and communities are in common use. Under each of these general methods, a variety of procedures and techniques has been developed. Those most followed in practice will be briefly reviewed. The general methods are:

• Graphical or mathematical projections of the curve of past population growth (trend based methods).
• Projections based on relationships of population growth in an area to that in other areas (ratio methods).
• Projections of net migration and of natural increase (component methods).
• Forecasts based on specific estimates of future employment and other occasionally used methods.

It must be emphasized that in practice few studies will use one method in the manner described in this report. Often a particular area will have conditions which will best be met by adopting a unique method. Often, the background of the staff may lead them to change methods to achieve what they believe are better results. For example, the projections presented in the St. Paul, Minnesota, Community Plan Report No. 12 are based on empirical data from other studies. The Army engineers, faced with a need for forecasts to the year 2020 in the San Francisco Bay Area, adopted a ratio technique combined with considerable judgment and modifications.

### Method I - Graphical or Mathematical Projection of the Curve of Past Population Growth (Trend Based Methods)

The trend based methods assume that population growth follows natural laws and, therefore, can be expressed in mathematical or graphical form. Basically, population is forecast by examining and projecting past trends into the future. Various types of expressions have been used such as linear, geometric, exponential, logarithmic, etc., to explain past historical growth and predict future growth. Usually, no analysis is made of factors that cause population changes, e.g., births, deaths, and migration.

#### Trend Based Projections by Graphic Techniques

Graphic projections are most commonly made using arithmetic, semilog, or probability paper. The data used in the plotting are historic data from decennial census reports and from available local or State census reports from intermediate years. The historic data are often plotted on all three types of graph paper, and the plot which comes closest to a straight line indicates the mathematical form to be used for the projection. In using the plotted information for projection purposes, the analyst assumes that the condition implied by the straight line will continue into the future.

(1) Constant arithmetic population increase

Historic data which plot as a straight line on arithmetic graph paper imply constant arithmetic change in population each year. This growth pattern implies that the population has changed by the same number of people each year. The data from Table 1 would appear as a straight line when plotted on arithmetic paper as shown in Figure 1. Since the base population each year has increased (or decreased) by a constant amount, the rate of change is different each year.

(2) Constant rate of population increase

A different historic growth pattern for a city might show a constant rate of change. When the data shown in Table 2 are plotted on arithmetic graph paper, such a pattern of growth forms a curve as shown in Figure 2. When the same data are plotted on semilog paper (with population on the log scale and time on the arithmetic scale), a straight line plot results as shown in Figure 3. In this situation, the numerical increase each year is greater than the year before, although the rate of increase is constant.

(3) Variable rate of population change

Arithmetic plots for some cities have shown that at first the population increased at a low rate, then accelerated for a period of time, and later, as the city matures, the rate of growth decreased. When the data in Table 3 are plotted on arithmetic paper, such a condition results in the characteristic "S" shade curve shown in Figure 4. These same data may be plotted on probability paper resulting in a straight line as shown in Figure 5. This curve is known as the logistic curve.

The logistic curve is based on a "law of growth in a limited area" propounded and mathematically developed by P. F. Verhulst in 1838. It is shaped like an elongated and flattened letter "S." The curve was rediscovered independently many years later by Messrs. Raymond Pearl and Lowell J. Reed from observation of the growth of fruit flies contained in glass jars and subjected to controlled conditions of food consumption.

It was found that in the early stages the increase in the number of fruit flies per unit of time accelerated to a maximum, after which it decreased at a continuously decelerating rate per unit of time, inverse to the previous growth. Some population analysts believe that what happens to the growth of fruit flies in a jar would apply to the human population of a completely self-contained area.

In fact, several population forecasts made a few decades ago indicated an upper limit to the population of the United States would be reached before 1990. The validity of this "law" for areas subject to net immigration that might accelerate for a time is questionable.

#### Trend Based Projections by Mathematical Techniques

The mathematical technique for projecting population also utilizes historic data and produces results similar to those obtained through the graphical techniques. In their simplest form, mathematical techniques are nothing more than the equations that will reproduce a straight or curved line. The basic theory for this is that any smooth line which can be plotted can be expressed (or at least approximated) by an equation.

A somewhat more advanced method is to derive the equation for the line which best fits the historic points and use this equation to estimate future population. Normally, the method of least squares would be used to obtain the equation of this line. Occasionally multivariate equations or equations using terms expressed to a power are utilized. Some of the factors included in these equations have been economic changes, land available, historic inter- and intra area population movements, etc. There is no standard group of variables employed in these equations, however, and in most cases the mathematical and graphic techniques have been used for very specific small area projections of only certain sectors of the population such as the number of home owners, or children in school.

#### Modified Projections

Forecasters often modify or alter projections arrived at by the previously described mathematical and graphic techniques according to their ideas about how the projected curve should look. In fact, given the same data of past growth, a dozen forecasters probably would come out with somewhat different graphic or mathematical projections. It is often difficult to determine by eye the graphic projection that would exactly fit the curve. Likewise, in computing the mathematical equation for projecting the curve, there might be differences in the number of points that would be considered or differences in the starting points.

In addition, forecasters often raise or lower their projections they have a hunch that the future population will be larger or smaller than the projected figure. Such subjective modifications are usually hazardous , and they are not recommended. Modifications should be made after a thorough study of influences end conditions affecting rate of population change in the area.

It is suggested, however, that projections obtained by other methods described later be plotted along with the curve of past growth. If the Projections thus plotted appear to differ sharply from the previous curve, careful review of the analysis should be made to catch any error in the evaluations or computations.

#### Critique

The advantage of graphic or mathematical projections is that they are the easiest to make. They generally are better suited to areas which have had relatively constant changes per decade in the size of their populations and for which no marked changes from past trends appear likely, than for areas subject to rapid or erratic fluctuations in population. Obviously, they should be more dependable for short-term projections of 5 to 10 years, than for longer projections.

The weakness of such projections is that they are founded on the assumption that the factors and conditions which produced population growth or decline in the area in the past will continue unchanged and will have the same effects in the future, or that they are derived from an assumed curve of population growth. In view of the changes that have taken place during the past two decades in fertility, mortality, and migration trends, projections of this kind are becoming less reliable. Graphic and mathematical projections are useful, however, as rough checks on those obtained by other methods.

### Method II - Projections Based on Relationships of Population Growth in an Area to Growth in Other Areas (Ratio Methods)

The factors and influences that accelerate or retard natural population increase are pervasive and tend to speed it up or slow it down concurrently throughout the Nation. Moreover, as mentioned before, economic and social conditions that cause birth rates to rise, or decline, also tend to accelerate or decelerate internal migration. Because of this, the rate of population growth in most areas and communities is related to some extent to the growth rate of the national population.

Population growth in an area or community is usually closely related to, or affected by., economic and population changes in the economic region or State in which it lies. Future population changes in those larger areas may have an important influence on growth or decline in the smaller area. Hence, past relationships between population growth in an area or community and that of its economic region or State are valuable guides for projection of the local population. If logically founded population projections for the Nation, State, or economic region are available, projections for the area or community can be derived directly therefrom. National projections are available in the Current Population Reports, Series P-25 published by the Bureau of the Census (see Appendix II, Data Sources).

#### Statistical Projections Based on Relative Rates of Past Growth

The population growth of a study area can be projected into the future by relating its growth to a larger area of which it is a part, such as the State, the region,, or the Nation. The basic procedure is to compute the ratio between the population of the study area and some larger area at the time of past censuses. This ratio may simply be between the study area and a larger area, or a series of interrelated ratios may be calculated between pairs of successively smaller geographical areas. Such a series, known as step-down ratios, might be between the study area and the State economic area, the State economic area and the whole State, the State and the region and, finally, the region and the Nation. The availability of a reliable forecast for a larger area and comparable historic data for the subareas to be used should be examined before this method is selected.

The historic ratios developed must then be plotted in a time series and projected forward. Their projection is not a simple mechanical procedure, but involves taking into account all the factors discussed in part of this report. Local conditions must be examined and the probable factors which will influence the future ratios fully understood. Simply because a ratio has had a particular trend in the past is no assurance that it will continue to have that relationship in the future. For example, during the early decades of this century., coal mining towns in the Appalachian area grew at a faster rate than their State as a whole. However, during the past few decades, this trend has been reversed.(6)

#### Example of the Ratio Method

To illustrate the procedure used in the ratio method, a sample projection for the years 1970 and 1980 will be made of the population of a hypothetical study area by projecting the historic ratio with the State.

The first step is to list the historic population data for the study area and the State in order to derive the necessary historic rates. The type of information required, as shown in Table 4, may be obtained from census data.

In developing the ratios, care must be taken to see that the geographic boundaries of the area used in each census year are the same as for each of the other years. Thus, if a four-city area is the study area in 1960, the same geographic area of the four cities must be used in the time series.

The next step is to obtain State population forecasts for the years 1970 and 1980. These could be obtained by stepping down from the national forecasts prepared by the U.S. Bureau of the Census or some other agency. In this example, it will be assumed that a State agency has prepared population forecasts. The forecasted figures are 2,500,000 persons in 1970 and 3,200,000 in 1980.

In addition to obtaining the population forecast for the State, it is necessary to prepare ratios of the study area population to State population for the years 1970 and 1980. The preparation of these ratios is the most important part of this forecasting technique. All of the factors which influence population change as discussed in part I must be considered and analyzer as to their probable future effect on the study area's share of the future State population. In this example the study area share in the total State copulation has been increasing. Assuming that a study of births, deaths, migration, employment, and economic trends indicate a continuation of an increasing ratio, although at a declining rate, then the forecast ratios of 0.124 for 1970 and 0.126 in 1980 can be considered reasonable. With this information, the study area population can be forecast for 1970 and 1980 as shown in Table 5.

#### Critique

Purely statistical projections made by ratio methods should be used with caution. Former relationships between population growth in the area under consideration and that in other areas may suddenly change. Moreover, the economic and social forces that cause births and migration to increase, or decline, nationally exert differing effects at different times on particular areas. Some areas have shown fairly consistent trends between their population growth and that of their region, State, or the Nation. Others have shown divergent or erratic relationships to population changes in the larger areas. For these this method appears less valid than for areas exhibiting more consistent trends.

The ratio method, based upon a forecast for a large area, is subject to all the errors, incorrect assumptions, and inaccuracies inherent in that forecast.

Very often local forecasters are not aware of all the assumptions made in preparing the larger base area figures. Moreover, there is no assurance that the assumptions made would have the same effect on the study area as they would have on the larger base area. It is quite possible that the growth in the economy which is assumed in a national forecast would imply a change in technology. This change might force the basic economic activities in the study area to make radical reductions in employment or move to new areas. (Examples of such situations are the Appalachian coal mining companies and the New England textile mills.) Even on the State level., a forecast of continued population growth in a particular State does not necessarily imply an even distribution of growth within the State. It might also mean a large growth in one or two urban areas with little or no growth (or even out-migration) in other urban areas within the State.

On the other hand, these procedures have several advantages over trend methods. The factors affecting population growth in the area or community may be more clearly visualized and appraised with a knowledge of its past relationships to growth in its economic region, State, and the Nation than if these relationships have not been studied. It may be easier to foresee and evaluate the effects of new conditions that may change past relationships than it would be to appraise the prospects for future growth in tile area irrespective of the rate of growth in other areas. Population projections for the Nation and for States have generally been closer to the mark than those for smaller areas or communities. By tying in their projection with those for the larger area, the range for error may be lessened.

Several recent transportation studies have used ratio techniques; among them Niagara Frontier, Billings, Montana, and Champaign-Urbana, Illinois. In the Puget Sound area, both the Regional Planning Council and the regional transportation study have used ratio techniques in preparing population forecasts.

### Method III - Projections of Net Migration and Natural Increase (Component Methods)

Component analysis methods study separately several factors, such as births, deaths, and migration which affect the future size of population. The theory behind component analysis is that more accurate estimates can be made using the rates of change of the individual components of population than can be made using the rates of change for the population as a whole. For example, it is reasonable to assume that birth, death, and migration rates for 80-year old people are different than those for 20 year old people and that, based on historic experience, one can forecast the rates for such groups with reasonable accuracy. This discussion will concentrate on the two most common component methods: First, the natural increase and net migration methods, and then cohort survival and net migration methods. Because migration is common to both methods, and forecasts of net migration are usually made before those for the natural increase, migration projections will be discussed first.

#### Migration Projections

Logically founded projections of net migration can be developed from study of net migration in the area in the past and the conditions causing people to move into or out of it.

The direction and approximate volume and composition of net migration into or out of the area during recent decades are first determined. The influences that have induced the population movements., especially economic factors, are next investigated. The economic factors themselves are part of the economic study phase of the transportation planning process and the population forecaster should work closely with the economists in understanding these relationships. Analysis of the physical and economic resources and characteristics of the area, the trends and rate of its development, and other factors will usually reveal the principal causes. Factors affecting migration have been briefly reviewed in part I. Past relationships between net migration in an area and population growth in its economic region, State., and the Nation provide further guides for the projections.

Changes that occurred, or appear likely to occur, in the conditions and relationships affecting migration in the area are then considered. Finally, the probable effects of such changes on net migration during the forecast period are reviewed and appraised.

With these analyses and appraisals, it is usually possible to develop reasonable high and low projections for net migration. At least, they provide some indication whether net migration during the next decade may be expected to be about the same as, or larger or smaller than) that of the preceding decade.

Estimates of future net migration in substate areas also have been made by analyzing the trends of geographical distribution of net migration into the State in recent decades and projecting these trends.(7)

#### Natural Increase Projections

In the natural increase methods., the population is treated as a whole or as a few major groups and appropriate growth rates which reflect the net effects of births and deaths are applied to each group. For areas having substantial portions of nonwhite residents, historic trends should be analyzed and projections made separately. If natural increase is expected to be the principal source of growth, then this component of population change assumes greater importance and should be examined in greater depth. The natural increase rates to be used for projection are derived by study and analysis of the factors which influence births and deaths as discussed in part I of this report. The projected rates are then applied to the base period population to arrive at the population growth due to natural increase.

#### Migration and Natural Increase Methods

As an illustration of the natural increase and net migration method, another hypothetical city having the characteristics shown in Tables 6 and 7 and 8 will be used.

#### Cohort-Survival and Net Migration Methods

The other component method which will be discussed here is the cohort-survival and net migration method. A cohort in a population analysis is defined as a group of people with a common set of characteristics who were born during the same tire period. An example of a cohort would be all males born in January 1, 1915, through December 31, 1944, (this group would have been 15-44 year old male group in 1960), or all females, white born from January 1, 1940., through December 31. 1944.

Note that any specific age grouping (say 20-24 years of age) refers to any particular cohort at only one period in time. At the next period all the living members of the cohort will be in the next higher age group (in this case the group 25-29 years of age), but they will still be members of the same cohort (i.e., those born during the same time period).

There are no set of rules for defining the detailed breakdown of cohorts but a commonly used procedure in planning studies is to divide the population into five-year cohorts with two five-year intervals corresponding to one 10-year U. S. Census period. The five-year cohorts are then usually subdivided into male and female and where nonwhite population is of significant size, the age-sex groupings are further subdivided into white and nonwhite.

The future population is forecast by taking each of these age-sex groups and aging them through one of the forecast intervals. Assuming this period to be five years in length, this means that each cohort will move to the age group five years older. During this period some members of each cohort can be expected to die. Deaths are forecast by using annual death rates for each age-sex group multiplied by the forecast interval to obtain total forecast deaths for the interval. The survivors, who will become the new age group five years later, are forecast by subtracting anticipated deaths from the size of the cohort at the start of the forecast period.

The total net migration projected for the area to the forecast date is then distributed by sex and by age, and added to, or subtracted from, the figures for the surviving residents in the corresponding age groups. It should be noted that the sex and age characteristics of the migrant population are usually quite different from those of the resident populations of the areas from which they move or in which they settle. The sex and age distribution of net migrations into or out of the particular area or its State during recent decades, therefore, should be carefully analyzed and used as guides in estimating the sex and age distribution of the projected net migration.

Birth rates by age of mother during the forecast period are then projected or assumed. The expected number of births is then obtained by multiplying the assumed age-specific birth rates by the average number of women in each five-year age group within the child-bearing ages during the forecast period. This average figure is usually obtained by adding the number of women at the beginning and end of the forecast period in each five-year age group, and dividing by two. The survivors of those births on the forecast date are then computed by using death rates of young children. As the number of male births usually exceeds the number of female births in the ratio of about 105 or 106 to l00, this should be taken into account in precise calculations.(8)

The cohort-survival procedure does not directly measure natural increase itself. Instead, the population projection is obtained by-adding the survivors of the resident population., the expected net migration., and the survivors of babies born to residents and to newcomers during the period. If the net migration is outward, the estimate of births is reduced because of the smaller average number of women in the child-bearing ages. Since most of the adult migrants are between ages 20-45 years,. when they move, net out-migration tends to reduce the crude birth rate also. Further refinements, such as allowances for births to in-migrant women who the during the period, are sometimes included in the calculations.

As an illustration of the cohort-survival technique, a population forecast will be made for one cohort in a hypothetical city. The cohort will be all those women born during the period January 1, 1935, through December 31, 1939. These are the women who were 20 through 24 years of age on January 1, 1960. It will be assumed that in the 1960 Census of Population., there were exactly 2,000 women in this age group.

The cohort-survival method requires as input the expected number of migrants in each age-sex group for each forecast period. This forecast is usually prepared by first forecasting the total migrants and then distributing them to the age-sex groups. The distribution into age-sex groups must recognize the different characteristics of migrants and residents. Often the historic ratios between the age-sex groups of migrants are used directly for this purpose.

To illustrate this method of distributing migrants into age-sex groups,, the anticipated number of women migrants for this cohort in 1965 and 1970 will be calculated. Historic ratios are calculated based on migration information obtained from the 1960 census which contains information on 1955 to 1960 migration. Table 9 shows ratios derived from census data for the study area.

It will be assumed that for this example the forecast net migration into the study area is 4,000 for the period January 1, 1960, to January 1, 1965., and 5,000 for the period January, 1, 1965, to January 1, 1970. The migrants will be added in as a group at the beginning of each five-year time period.

The allocation of these migrants to age-sex groupings now becomes a simple process of using the historic ratios (or changing them if a study indicates that a change is to be expected) in conjunction with the total migration figure. In the following illustration it will be assumed that the ratios are satisfactory so they will be used unchanged. The allocations to the sample cohort of women will be:

 Total net immigration 1960-1964 Ratio immigrants who are women age 25-29 Number of women migrants age 25-29 January 1, 1965 4,000 X 0.049 = 196 Total net immigration 1965-1969 Ratio immigrants who are women age 30-34 Number of women migrants age 30-34 January 1, 1970 5,000 X 0.045 = 225

The natural increase part of the cohort-survival method consists of estimating deaths occurring among members of each cohort during each iteration period and subtracting these deaths from the membership of each cohort. Death rates can be obtained from one of the sources described in the section on sources of data. The death rate in the study area for women age 20 through 24 will be assumed to be 2.4 deaths per year per 1,000 women. Thus, in the case of this cohort the following calculations would be made:

 No. of Members in cohort women age 20-24 Annual death rate per 1,000 women age 20-24 No. of years in interation period Anticipated deaths per five-year interation period 2,000 X 2.4 X 5 =24 1000

These deaths are subtracted from the members in the cohort at the beginning of the iteration period to determine survivors at the end of the period. (2000 - 24=1976).

These survivors are now members of the 25 through 29 year age cohort in 1965. The full cohort in 1965 will consist of these survivors plus or minus migrants. In this example we have already calculated 196 women immigrants in this age group during this time period. Thus, the total membership of the cohort women born January 1, 1935, through December 31., 1939., is estimated to be: (1976 + 196=2172).

This total cohort is now in the 25-29 year age group in 1965, and may now be moved forward another five years by the same procedure. For example, assume that the projected death rate for women 25 through 29 years of age is 2.8 deaths per year per 1,000 women. The estimated deaths would then be calculated by multiplying the rates by the number of years in the iteration period.

 2.8 (2172 X l000 x 5=30)

The forecast number of women immigrants in this cohort during this five-year period was calculated as 225. Thus, on January 1, 1970, the forecasted population of women age 30 through 34 is: (2172 - 30 + 225=2367).

The data on this cohort may be arranged as shown in Table 10.

Note that the group illustrated is one cohort. That is, they were all born during the same time period and have common characteristics as they were previously defined. During each time period some of the original members are lost through deaths and new individuals migrate into the area and are added to the cohort. (The migration could be negative in which case the cohort would lose members.) The survivors and migrants are then moved to the next older age group. Note also that an identical table format would be prepared for males in the study area.

Births are handled as a separate set of calculations in cohort survival analysis. The local birth rates for each age group of women are obtained from vital statistics and these rates are then applied to the number of women in each age group. Since most children are born to women in the 15-44 year age range, the rates are usually prepared and applied only to these groups.

As an illustration., it will be assumed that the birth rates in the study area are found to be 239.6 births per year per 1,000 women in the 20 through 24 year age range. Applying the proper rate to women in the 20-24 year age range, the following calculations are made:

 Av. No. women age 20-24 alive during 5-year period Ann. birth rate women age 20-24 (per 1,000 women) No. of years in iteration period No. of births to women age 20-24 during iteration period 2,000 1,976 X 239.6 X 5 =2,380 2 1,000

Similarly the number of births occurring in the study area to women who move into the area may be calculated by assuming that they live here one half of the time. (Such an assumption would assume an equal number of migrants would arrive each year during the five-year period.) Thus, the formerly assumed rate of 4,000 migrants from 1960-65 implies that 800 arrive each year. As noted earlier, 204 of the 4,000 migrants have been assumed to be in the 20-24 year age group. The following calculations are made:

 No. of female migrants age 20-24 during 5-year period Ann. birth rate women age 20-24 (per 1,000 women) One-half No. years in iteration period No. of births to migrant women age 20-24 during iteration period occurring in study area 204 X 239.6 X 2.5 =122 1,000

The estimated births to women in this age group are added to the births estimated for women in other age groups in the child-bearing range to determine the children born in the study area to be assigned to the 0-4 year age group in the next iterative period. Breakdowns by sex are obtained by studying past ratios of males to females among local births. To these children must be added children of migrants who were born elsewhere during this time period and brought into the study area by their parents (or who left with their parents if the local area is undergoing out-migration).

#### Critique

The component method is being relied on more and more for population projections. For most areas and cities, it should yield better forecasts than trend and ratio methods, particularly for projections not exceeding two decades.

Component methods take into account the size of the area's population at the beginning of the forecast period, and the effects of a population of that size on future births, deaths, and migration. Trend and ratio methods do not provide as accurate measures of the effects of changes in the size of the population from decade to decade.

Moreover, this method requires the forecaster to appraise the effects of various influences on each of the three sources of population change instead of making a less discriminate evaluation of their effects on population growth as a whole. Certain influences, such as rapid economic development, may accelerate migration into an area but have relatively little effect on its birth and death rates. This method also measures the reaction of migration on natural increase instead of blanketing this quantitative effect in with a host of qualitative considerations.

The range of future birth and death rates usually can be determined with a smaller margin of error than that of future migration. Component methods are therefore especially useful for projections in which natural increase is expected to be the principal source of population growth. Hence, it is almost invariably used for projections of the national population.

If the population information is needed for a special purpose for example, anticipated school enrollment or licensed drivers - the cohort-survival method will provide this information without the need for additional calculations. In addition, the method is highly recommended for areas which have a population distribution which differs radically from that in the rest of the region (e.g., an area which has a large number of elderly residents).

Approximate projections of natural increase) assuming no migration in the area, can be made easily and quickly. These will give a good indication of minimum growth to the forecast date, unless there is a net out-movement, and are valuable checks on projections made by other methods.

It is also easy, once the initial data have been gathered, to prepare more than one forecast based upon different assumptions as to births, deaths, and migration. Such alternative series are especially of value in understanding the implications of some change which will affect one of these components (as for example, a road system which would encourage growth of economic activities which would attract heavy immigration).

Component methods have been used by several studies; among them the Penn-Jersey Transportation Study, the Portland, Oregon, Metropolitan Planning Commission, the Salt Lake Area Transportation Study, and the Dade County Planning Department. The Luzerne County, Pennsylvania, (Wikles - Barre - Hazleton area) Planning Commission used this method for the forecast and then used a ratio method as a check on the reasonableness of the projected figures.

### Method IV - Forecasts Derived Directly from Specific Estimates of Employment and Other Occasionally Used Methods

The three methods already discussed; trend based, ratio, and component, are the most prevalent methods of forecasting population. Several other methods have also been used enough to warrant a brief discussion of them. Three of these methods will be discussed here; first, forecasts based on economic projections; second, comparative or analogy methods; and third, the holding capacity method. The last two methods are not considered satisfactory for large area forecasts and would best be avoided for transportation study purposes.

#### Population forecasts based on future labor force estimates

The ability of any area to grow in population depends to a great extent upon its ability to support this population with jobs. Thus, a forecast of the labor force(9) available from an economic study as a part of the urban transportation planning-process can form the basis for a population forecast. When so developed, this population forecast can be used to check the population forecast arrived at by demographic methods (i.e., using mathematical, graphical, or other type of projections of past relationships in which the effects of economic factors on population change are implied but not expressly stated or studied in detail).

The translation of a labor force forecast into a population forecast is accomplished by using the projected labor force-to-population ratio. (This is called the "labor force participation rate.")(10) Before undertaking to project it into the future a study should be made of past trends to gain an understanding of the factors that have influenced this rate in the past and which may affect it in the future; for example, the delayed entrance into the labor market of young people continuing their education and the increasing participation in the labor force of married women after their children are grown. Additionally, the early retirement of older workers may be an important element affecting this rate in a particular area, depending upon the characteristics of the population and the hiring practices of the firms in that area.

The population forecast is prepared by applying the projected labor force participation rate to the labor force forecast and making adjustments as necessary to account for the military and/or the institutionalized population. To illustrate, the following tabulation shows historical data on the total civilian population, the civilian labor force, and the labor force participation rates for an assumed study area.

Year Total Civilian Population Civilian Labor Force Labor Force Participation Rate (Col. 3/col. 2)
1930100,00039,70039.7%
1940120,00048,20040.2%
1950145,00062,20042.9%
1960185,00075,90041.0%

Using the forecast of the total civilian labor force prepared by the economic study and applying the forecasted labor force participation rates (i.e., dividing the labor force by the rate and multiplying by 100), the civilian population can be computed as shown in the following tabulation.

Year Forecast Civilian Labor Force Forecast Labor Force Participation Rate Labor Force Civilian Population
196531,60040.8%200,000
197087,10040.5%215,100
197594,50040.2%235,300
1980102,00040.0%255,000

If the labor force figures are broken down by types Of jobs and characteristics of workers, it is possible to prepare more detailed estimates of population by age, sex, and race.

#### Critique

This method assumes that the volume of employment in an area on a future date can be forecast from consideration of certain economic factors alone, without taking into account the probable size of the future population. It implies that the volume of future employment can be forecast with greater accuracy without reference to the size of the future population than the size of the population can be forecast without having a specific forecast of the future employment level.

The relationship between economic expansion and population growth in an area, however, is somewhat like that of the chicken and the egg. Development of extractive or commodity producing industries, a new irrigation project or a large -new factory, normally will create new jobs. But people also move into an area for a variety of other reasons (e.g., health or retirement) and such in-migration itself tends to expand employment.

In most areas, the future employment level will not be determined solely by the rate of expansion or decline of the so-called "basic" industries. It will also be affected by the rate of population growth in the area, and by changes in transportation, trade, and service activities, and government employment,. Which may be unrelated to local production of tangible goods. Moreover, the rates of expansion in local agriculture, manufacturing, and construction themselves may be influenced by such changes. This is particularly true of areas receiving continuous immigration, such as those on the Pacific Coast.

Furthermore, the proportion of the population in the employable ages and the ratio of labor force to population may also differ over time from the assumed ratios. It would therefore seem unwise to rely solely on population forecasts made by this method.

On the other hand, the analyses and evaluations of prospects for increase or decline of economic activities provide valuable information which is useful in making projections of net migration and natural increase by component methods. They can especially aid the forecaster in determining net migration during the forecast period would likely be in the same direction. and in higher or lower amount, than in the preceding decade.

#### Comparative or analogy method (not recommended)

This method assumes that if two areas have similar characteristics such as geography, climate, economic potential, culture, natural resources, etc., their growth patterns will be similar. In practice the forecaster chooses a city which has these similar characteristics and is already further developed than his study area. He then projects the future growth of his study area as similar to the past growth of the developed area.

The simplest projection method is to choose a developed area with similar characteristics whose early population, growth curve is similar to the past growth curve of the study area: that is, the population growth curve for the developed area from 1850 to 1900 might be parallel to the growth curve for the study area from 1940 to 1960. An assumption is then made that the part of the curve being projected beyond 1960 for the study area will parallel the historic curve for the developed area following 1900. Such a situation is shown in Figure 6. Note that the population size for the two areas is not necessarily equal nor need the time scales (the X axis) be identical.

A more complex method of making a comparative forecast is to study several developed areas, each of which has at least one or two similar characteristics in common with the study area. The differences and similarities between the study area and each of the developed areas are examined and an average population curve is developed from the several curves analyzed. This "cumulative" curve then becomes the population growth that is used in projecting the total population in the study area.

#### Critique

As a method of projecting population for a metropolitan area the comparative forecast analogy method has severe weaknesses. It is doubtful that there are two urban areas that are sufficiently alike to be able to say that the second will grow in a similar manner to the first. Moreover, even if one could assume that they were identical, it is still doubtful that two areas developing at different periods in history would follow the same patterns of growth.

The comparative or analogy method may still have same value in forecasting population for small areas. A good example would be in out-lying areas of a metropolitan community where urban development and population growth in a currently open area may be anticipated to follow that of a similar, but already developed area. When used in conjunction with such factors as zoning, holding capacity, accessibility, available utilities, etc., this procedure may give a reasonable indication of the small area patterns which might occur.

#### Holding capacity method (not recommended)

This procedure assumes that an upper population density limit can be established for an area, and therefore an upper limit to the number of people who live in that area can be established. The maximum. population capacity is derived through studies of zoning, land characteristics, available water, and other land use measures. The population is then -assumed to grow until it fills all or a certain percentage of this capacity.

#### Critique

Since the holding capacity of any metropolitan area is likely to be much larger than any realistic population size that will live in the area, the method requires the forecaster to assume some percentage of the capacity which will be filled. This in effect results in subjective decisions by the forecaster. Moreover, holding capacity is not a constant. Areas currently zoned for low density may be changed to density when the demand arises. For small area analysis within an urban area, the method may have more validity but it becomes less reliable When used for the total metropolitan study area.

An example of a study using this method is the Seattle, 98 Washington, City Planning Commission forecast by census tracts to 1985. It is important to note that this forecast is for a closed area, the city of Seattle, and not for the total area which would have to be included in the transportation study.

### Endnotes

6. For a discussion of a method of projecting ratios, see: U. S. Bureau of the Census, Current Population Reports, "Population Estimates," Series P -25, No. 110, February 20, 1955.

7. Considerable data on migration in local areas are available from the 1960 census of Population. A report of special interest is: U.S. Bureau of the Census, "Components of Population Change, 1950 to 1960,, for Counties, Standard Metropolitan Statistical Areas, State Economic Areas, and Economic Subregions," Current Population Reports, Series P-23,, No. 7., November 1962.

8. Many areas will find that a completely update forecast may be obtained by the simple use of birth rates for all women aged 15-44 and the number of women in this age group rather than perform the individual calculations for each five-year age group.

9. The U.S. Department of Labor defines the labor force as the noninstitutional population, 14 years of age and older, working or looking for work. Thus, those classified as employed plus those classified as unemployed constitute the labor, force. The total force includes the armed forces. The civilian labor force excludes the armed forces.

10. The labor force participation rate (or ratio) may be expressed in various ways. For example, the labor force figure may or may not include the military. The denominator of this ratio may also vary by including or excluding persons under 14 years of age. The national labor force participation rate relating the total labor force to total noninstitutionalized population varies around 41 percent (give or take 5 percent). But the rate for the nation that relates the total labor force to the population 14 years of age or older, varies around the 55 percent figure.

Updated: 3/25/2014
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