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

## Part I: Problems of Population Analysis

Population forecasting is essentially a matter of judgment. Judgment is required in selecting the kind of forecast to present, in determining the procedures for making it, and in appraising effects of the factors that induce population changes. Obviously, this should be an informed judgment, backed up by the most complete and thorough analysis of the particular problem that the forecaster is able to make.

The problem, of course, is much simpler for areas which have shown marked stability in the size of their populations for several decades, and for which no great change in the economic and social conditions of the locality seems likely. On the other hand 1 it may be extremely difficult and complex for areas which have had sharp fluctuations in the direction or rate of population change in the past, and which may continue to have them.

The crux of the solution lies in the thoroughness with which the probable effects of the factors influencing population growth, or decline, in the particular areas are evaluated and the skill with which the evaluations are translated into numerical figures.

Numerous aids to judgment in making population projections are pointed out in this report. Even the most thorough study will not assure that the forecast will come true. Well-founded projections are the best obtainable guides, but they are not infallible. Those who use population projections should always keep in mind the possibility that they may prove off the mark.

### How Logically Founded Projections May Be Developed

The number of people residing in an area can be changed in only three ways: (1) By births, (2) by deaths, and (3) by movement in or out, the net result of which is called net migration, whether inward or outward.

The factors and conditions that cause the people to have children, to die, and to move from one place to another., are, of course., almost infinite in their variety. A comparative few, however, usually have greater influence than the others in changing the number of residents in an area. For example, establishment of a large new industry generally has greater and more direct effects on the size of a city's population than improvement of its parks and playgrounds. Analysis of the causes, nature, and rates of past changes in the area's population, together with a careful appraisal of the probable effects of the more influential factors, can provide valuable clues to the size of the future population.

Rational population projections can be made by two operations:

• Tabulating, plotting, and analyzing data showing the trends and rates of changes in the area population in the past.
• Determining, as far as possible, the extent and nature of probable deviations from past trends likely to be caused by changes in factors affecting the volume of births, deaths, and net migration in the particular area.

Stated another way, the forecaster must try to answer the following questions for the period covered by his forecast:

• Will the population of the area increase or will it decrease?
• Is the increase, or decrease, expected to be in the same amount or at the same rate as in similar periods during the past, or will it probably be different?
• If so, why and by how much is it expected to be different?

The forecaster should give some idea about how large the population of the area or community will be on the forecast date, and why he expects it to be that size. He should support his Projections with sufficient data and analysis to show clearly the assumptions and methodology on which they are based so that the user can judge their validity for himself. If it is desired to provide a range rather than a single figure for the forecast, such a range can be provided by preparing alternative series of forecasts. For example, a high alternative series might be provided utilizing assumptions of high birth rates and/or in-migration while a low series might be based upon assumptions of low birth and/or in-migration rates.

### Basic Assumptions Implicit in All Forecasts

Every population projection, except a pure guess, is based on some assumptions. These may be explicitly set forth in the projection, but, if not, they are implicit in the method that is used. By definition, a population projection assumes that the factors affecting births, deaths, and migration will interact in a manner that will produce the projected figure. In practice, the analysis should set forth the specific assumptions on which the forecasts for the particular area are based.

In addition to such special assumptions, several basic assumptions are implicit. It is usually assumed that during the period of the forecast:

The form of government and the Political, economic, and social organization and institutions of the United States will remain substantially unchanged.

• No all-out war, internal revolution, nationwide devastation, epidemic, or other disaster will occur.
• No large-scale epidemic, destruction by military action, fire, earthquake, or other disaster will occur in the area or within the geographical or economic region to which the area is closely related.

Any of these events might have completely unpredictable effects on the population. These basic assumptions, therefore, are either explicitly stated or are implied in nearly every population projection.

### Knowledge of Population Data Essential

A variety of population figures are now reported differing according to the kind of population they represent. Therefore, the forecaster should have a good working knowledge of the population data reported by the Bureau of the Census, of birth and death statistics, and of the limitations and uses of these data.

No population census is 100 percent accurate in every respect. Obviously a few persons will be missed, while an even smaller number will be counted twice. The number of persons in the older-age group, 55 years and over, are often under-reported in some age brackets and over-reported in others. The number of births and deaths reported for an area is seldom complete.(1) Since these limitations in the data may affect the forecast, depending on the characteristics of the local area and the forecasting techniques to be used, they should be examined and understood.

The forecaster also should understand the principal factors and conditions affecting the number of births, deaths., and the direction and volume of net migration in an area. A brief discussion of these factors follows.

### Principal Factors Affecting Births, Deaths, and Net Migration

#### Births

The number of births per thousand population during a year is called the "crude birth rate." It is obtained simply by dividing the number of births during the year by the total population and multiplying the result by 1,000. Such a figure does not take into account unique characteristics of an area. For example a frontier town where few women live would have a very low crude birth rate even though these women might be having a large number of children.

Amore meaningful figure would be the "fertility ratio." This is the number of children under age five per thousand women of child-bearing age. (Child-bearing age is usually defined as women aged 15 to 45.) Another term used in demography is the "fertility rate," which is the number of births in a given year per 1,000 women of child-bearing age. For more detailed analysis, an age-specific birth rate is sometimes used. This rate is composed of the number of births per 1,000 women of a specified age or age group.

Fertility rates are now widely used in making projections for areas in which natural increase or decrease (the excess or deficiency of births compared to deaths) is expected to be the predominant source of population change.

Fertility rates and age-specific birth rates seldom remain constant, but rise or decline from year to year depending on various factors and conditions. Chief among these are the rise or decline of economic activity and employment, and changes in the racial composition, religious affiliation of the population, and the attitudes of married couples toward having children. From 1910 to 1936, fertility rates in the United States showed a steady downward trend. World War II and the years that followed saw a sharp reversal of this trend while the late 1950's and early 1960's have seen a leveling off and slight decline in fertility rates.

Fertility rates differ widely among areas and communities as well as for different ages within the child-bearing age range. The trends in these rates, however, usually follow and move toward the national average. Thus, in preparing local trend forecasts, it is advisable to study historic and projected national trends.

#### Deaths

The number of deaths in an area is determined chiefly by the size and age distribution of its population. The greater the proportion of elderly persons, the higher generally is the crude death rate, or number of deaths per thousand population. Approximately 60 percent of all deaths are of persons age 65 and over.(2) A large number of births also tends to cause a temporary rise in the average death rate because of the high mortality of infants in their first year.

In areas where natural increase predominates, it is often desirable to use age-specific mortality rates instead of crude death rates. Age-specific mortality rates are the number of deaths during the year per thousand persons in specific age groups. Changes in these rates are usually slow and gradual.

The long-term trend in age-specific mortality rates is downward because of the continual improvement in living conditions, and increasing control of disease and prolongation of life by the advancement of medical science. Future mortality rates will probably show some improvement, but it will be very slight and, in fact, many age-specific rates may remain constant. Other important factors affecting these rates are the racial composition of the population and the climatic and occupational characteristics of the locality. Some climates and some types of work are obviously more healthful than others.

Mortality rates differ among various areas of the nation, but the differences are generally smaller than for fertility rates.

#### Net Migration

Net migration is the difference between the number of people who move into an area and the number who move out during a specific period of time. The day-to-day and week-to-week movements can usually be ignored. What the forecaster needs to know is whether the net migration over a period of years has usually been inward or outward; the size of the net migration; the sex, age, racial, and occupational composition of those who have been adding to or subtracting from the area population; and the principal causes of their movement.

An approximate measure of net migration in past decades can be obtained by subtracting the crude natural increase (reported excess of births over deaths) in the area during the decade from the total numerical population change shown by the decennial census reports.

Approximate measures of the age, sex., and racial distribution of the net migration can also be obtained by comparing the changes by five-year age groups by sex, and by race, shown in the census reports. Rough approximations of interstate movements by decades also can be derived from the State-of-birth and State-of-residence data in the census volumes.

Causes of migration are many and varied. Chief among them are:

• The desire for better economic opportunities. Interstate migration is largely a movement from areas with relatively low planes of living to areas with higher income levels.
• The attraction of milder or more suitable climates in other areas.
• Desire for better living or housing conditions. This applies particularly to short distance migration within the same general locality.
• Movement for reasons of health, education., or retirement.
• Wives, young children, and close relatives usually follow the movement of their breadwinners, or family heads.

The direction and volume of net migration also vary widely from time to time. The levels and fluctuations of national economic activity have marked effects on internal population movements. People are more willing to take a chance on a new location when business is on the upgrade than when payrolls are shrinking and times are getting hard. Also it is easier to pull up stakes by selling property or liquidating other fixed assets when times are good.

The level of national economic activity also affects the direction of migration. When employment is high or rising, the movement is generally from rural areas and small towns to the medium-size and larger cities, because of the relatively larger dollar wages and economic opportunities in urban areas. But during periods of economic depression, the net movement in the past has usually been from the cities to the rural areas., generated largely by the hope of achieving a subsistence through living on the land. The extent to which old age pension payments, unemployment compensation insurance, and other governmental programs will affect such movements in the future is difficult to appraise, but they should tend to lessen back-to-the-land migration during periods of low economic activity. Newer generations, however, do not have ties to the farm and/or the skills and knowledge required to subsist in an agricultural environment. In addition social and economic ties developed in urban areas by these newer generations would inhibit any movement back to the farm in the future.

The relative income level and the expansion or decline of economic opportunities in an area obviously have an important influence on the direction and volume of its net migration.

Other factors are the size of the pool from which potential migrants might be drawn (i.e., the population of the nation outside the area), the size of the local population., and the rates of economic expansion and population growth in the area relative to those in other areas.

### Employment Levels - The Dominant Influence on Area Population Growth

As indicated before, substantial changes in the size of the population of most areas are closely related to changes in the area's employment level. Principal exceptions are "dormitory" suburbs and educational communities, and those with large institutional populations, or other special features.

By enlarging the number of individuals to be provided with goods and services, natural increase in population of an area itself tends to expand economic opportunities and employment in that locality. But if employment opportunities in the area expand, or appear capable of expansion, at a rate faster than the natural increase in the population of employable age, people will move in from other areas. On the other hand, if the population of working age increases more rapidly than employment opportunities, unemployment will rise and out-migration may ensue. Because of its effects on migration, the upward or downward trend of employment in an area or community has a greater influence on local population growth than the national level of employment has on the growth of the national population.

The national level of employment.. however, affects both the birth rate and the rate of economic development in most localities. Birth rates are generally higher throughout the Nation when national employment is high or rising, than when it is low or declining. In areas having potentialities for greater development., the expansion of agriculture, industry, and business is at a faster rate when national employment is high than when it is relatively low.

Population projections for areas and communities (with exceptions noted before) therefore involve assumptions concerning future levels of both national and local economic activity and employment. Such assumptions will be derived from intensive study of expected employment levels., which should be prepared as a part of the economic study phase of the transportation planning process.

### Demographic Upheaval of the 1940s and 1950s and Its Future Effects

During the 1940s and 1950s, drastic and unexpected changes occurred in the population trends of the United States. These shifts were so radical and widespread that they virtually amounted to a demographic upheaval. Their effects on the future populations of areas and communities everywhere will be far reaching, and should be taken into account in making forecasts. These significant shifts were:

• A remarkable upsurge in the rate of population growth
• An extraordinary increase in migration from rural areas and small towns to metropolitan areas and large urban communities.

#### Upsurge in Rate of Population Growth

During the 1930s, most demographers became convinced that the population of the United States would reach its peak about 1960 and would then become stationary., or gradually decline. This conviction was based on a long decline in fertility rates and the restrictions placed on immigration from foreign countries in the 1920s. The increase in birth rates during and following the second world war soon made demographers aware that the national population would not decline or even remain stationary.

From 1950 to 1960 the population of the United States increased almost 28 million, the largest gain of any decade. More children were born than in any previous 10-year period and mortality rates declined. Together, these factors assure that the national population will continue to grow to the year 2000 at least, and probably for some time thereafter unless some unpredictable disaster should occur.

Not only was the downtrend in fertility and birth rates reversed, but the reversals were greatest where the declines had been relatively most severe, namely in urban areas and among families in the middle and upper income brackets.

Many influences contributed to this reversal. Among these were postponement of child-bearing during the depression of the 1930s, the war and war-hastened marriages, high levels of employment and earnings, enhanced desires of married couples to have children., and the younger age at which people have been getting married.

This tremendous growth has injected a new and potent force into the economic and social life of the nation and its cities. Even though birth rates may decline from their current high levels., the millions of children born during the two decades are almost certain to create another upsurge of births in the 1960's and 1970's and probably a third wave in the 1980's and 1990's. Persons age 65 and over will be more numerous than previously estimated; however, they will constitute a smaller proportion of the whole population.

From 1850 to 1900, the population of the United States more than tripled from 23 million to 76 million. From 1900 to 1950 it doubled from 76 million to 151 million. If it were to increase only 50 percent during the second half of the century, it would exceed 225 million in 2000 A.D. By 1960 the actual population was almost 180 million and recent projections of population indicate a range between 233 million and 252 million by 1980.(3)

The full economic and social effects of the recent tidal wave of babies, of course, will not be felt until the children grow up. Then they will show up in many ways - in larger employment, production, and incomes; in greater demands for goods, services, and facilities of all kinds, including transportation facilities.

The population forecaster must appraise the short- and long-term effects on his particular area of the recent rise in fertility rates and birth rates. He must evaluate as far as he can (1) the probable levels of fertility rates (or birth rates by age of mother) during the next decade or two, and (2) the probable increase in number of women of 15 to 45 years., when the oncoming wave of girl babies reaches the child-bearing ages.

The forecaster should also recognize the continuing decline in age-specific mortality rates. While this decline will gradually level off, the number of survivors per thousand population in each age bracket should be greater in the future than in the past.

#### Increase in Population Migration to Urban Areas

Analysis of decennial census information indicates that more than 75 million Americans changed their home addresses between 1955 and 1960.(4) Of these, almost 28 million moved to another county and more than 14 million of these moved to another State.

This movement was predominantly from rural areas and small towns to larger urban places. According to the Bureau of the Census, the population increase within urban areas from 1950 to 1960 was larger than the national population increase during that period.(5) Nearly all large cities received a share of the migrants.

Continuing the trend of previous decades, most of the population growth in the metropolitan areas occurred outside the central cities. From 1950 to 1960, the population of the central cities as a whole increased 20 percent, while that of the outlying sections increased 81 percent or four times as fast.

Part of this increased migration can be attributed to the great expansion of employment in the heavily industrialized urban areas during World War II, and to the construction during that period of new manufacturing facilities and military establishments in certain localities. Another cause was the doubling up of families during the depression of the 1930's and the lack of desirable housing during the war years. This brought after the war an enormous increase in residential construction and in movement of families to new locations. Still another cause was the attraction of millions of new jobs created in the larger urban areas by high levels of postwar business and incomes.

The increase of migration to urban areas is further compounded by movements within the urban areas. While the areas themselves were growing, certain sections within the areas such as the central cities were remaining almost constant or even declining. Thus the simple figures of net growth do not tell the full story of change in a study area.

Moreover, wage scales in similar occupations are now more nearly the same throughout the country than they were before the war and will probably continue to become more uniform in the future. With high level employment and more nearly equal wage scales throughout the Nation, migration will probably be influenced to a greater degree than in the past by climatic attractions and other factors.

### Ranges in a Population Forecast

Population forecasts may be developed and presented as a single figure; as two figures, one high and one low, showing the expected range for the future population; or in three or more figures based on different assumptions.

Most of the forecasts that have been made for areas and communities in the United States have been single-figure projections. However, Census Bureau projections of the national population consist of four series, each based on a different set of assumptions.

The assumptions introduced into a forecasting technique will determine the magnitude of the forecast population. Thus, if assumptions which imply a low rate of growth are used, the forecast population will be smaller than if the assumptions imply a rapid rate of growth. The preparation of two forecasts, one using the high rate assumptions and one using the low rate assumptions, will give the user an indication of the likely range within which the future population will actually occur. On the other hand, the use of a single, most likely, set of assumptions will give a single figure forecast indicating the most likely size of future population.

### Census Bureau Classifications of Population

Before World War II, only one population figure was in general use in the United States, namely the total number of people residing in an area at a particular date. Because persons in the military services were then relatively few and widely scattered throughout the Nation, no distinction was made between the civilian and military population. They were lumped together in the Census figures.

The 1950 and 1960 decennial censuses of population enumerated each person as an inhabitant of his usual place of residence, which was generally construed to mean the place where he lives and sleeps most of the time. Visitors and transients in other areas when the Census was taken were allocated to their home communities.

Persons in the armed forces quartered on military installations were counted as residents of the States, counties,, and minor civil divisions in which their installations were located. Members of their families, however, were reported where they actually resided.

Several definitional changes have also occurred between recent censuses. In the 1950 and 1960 censuses, college students living away from home were considered residents of the communities in which they were residing while attending college. In the 1940 census they were allocated to their home areas. Crews of vessels in the American merchant marine were credited in 1940 to the home port from which the vessel operated., but in 1950 and 1960 were credited to the port where the vessel was berthed on April 1.

Persons confined to prisons, houses of correction, State hospitals, asylums, and other public or private institutions are reported as "institutional population" by the Census Bureau. The size of the institutional population usually remains about the same over long periods. Increases or decreases are brought about chiefly by the construction of new institutions or the abandonment of old ones,, rather than by the influences that normally induce changes in the size of the noninstitutional population.

The forecaster therefore should determine the size of the institutional population in the area he is studying. If it constitutes about 10 percent or more of the total figure, he should make separate studies of past growth and separate projections for the institutional and the noninstitutional populations.

It is important that the forecaster clearly define the kind of population his projections represent. If the population reported by the 1960 census is used as a starting figure, the projections presumably would represent the same kind of population unless they were otherwise defined and developed.

Because of large variations in the size of military forces quartered in several areas in the United States, it may be desirable to prepare projections for a more predictable type of population for the area. This might consist of resident civilians plus residents serving in the armed forces irrespective of their locations. The projections may be made by any of the methods discussed later in this report. Military personnel stationed in the area on the projected date therefore would be excluded, unless they had been residents at the time of their induction into the military service. Any projection of this group will involve an evaluation of the most likely future activities of the military establishment.

Thus, by preparing separate figures for civilian residents, military personnel residing in the area and residents serving in the armed forces, more meaningful studies and analyses can be made than if only one figure were presented.

### Endnotes

1. The evaluation and adjustment of census figures and birth and death registrations are described in detail in the Handbook of Statistical Methods for Demographers (Preliminary Edition) by A. J. Jaffe, published by the Bureau of the Census in 1951. This handbook also describes procedures for measuring net migration, the use of life tables, and other statistical techniques helpful in making population projections. The third printing of this reference (published in 1960) is available from the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402, for \$1.75.

Since the Jaffe book was prepared for use with 1950 census data, some of the technical procedures are incorrect when applied to 1960 data. Some recent publications dealing with 1960 census data are:

U.S. Bureau of the Census, 1960 Census of Population, Volume 1, Characteristics of the Population, Part 1, United States Summary, pages XXXIX and XL.
Taeuber, Conrad, and Hansen, Morris H., "A Preliminary Evaluation of the 1960 Census of Population," Demography Volume 1, No. 1, 1964.

2. U.S. Department of Health, Education, and Welfare, Vital Statistics of the United States, 1962, volume II - Mortality, Part B, table 9-4, page 9-87. U.S. Government Printing Office, Washington, D.C., 20402.

3. U. S. Bureau of the Census. Current Population Reports, "Population Estimates" Series P-25, No. 279, February 4, 1964, table 2.

4. U.S. Bureau of the Census, U.S. Census of Population 1960, Detailed Characteristics, United States Summary, Final Report PC (1) - ID, U.S. Government Printing Office, Washington, D.C., 20402, 1963. Table 164, page 1-367.

5. U.S. Bureau of the Census, U.S. Census of Population, 1960, Number of Inhabitants, United States Summary,. Final Report PC (1) - IA, table 4, page 1-5, U.S. Government Printing Office, Washington, D.C., 20402, 1961.

Updated: 3/25/2014
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