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

## Appendix I: Methods Used in Current Population Estimation

An important part of the population forecasting process is the estimation of actual population at the time the study is undertaken (the base year). If the study is undertaken at the same time as a census or within one or two years of such a census, most areas will find it satisfactory to use the census counts with only gross adjustments. Since the United States census is made only at 10-year intervals and few States make intermediate census enumerations, it is usually necessary to prepare or obtain current population estimates as the first stage in preparing a population forecast. These current estimates will become the base year population which will be used in making the population forecast.

Many private and governmental agencies have needs for current population counts and prepare them for their own use. The first step should therefore be to determine whether such figures have already been prepared for all or part of the study area. Since transportation study area boundaries do not ordinarily correspond with the boundaries used by other agencies, it is usually necessary to make adjustments to get estimates for the study area. Often, use can be made of estimates for those areas pre-pared by other agencies, leaving to the transportation study the job of preparing only the remaining estimates.

If current population estimates are not available, the forecaster will have to prepare them. Several methods can be used including any of the forecasting methods previously discussed. If such procedures are used, the population is forecast forward from the last census year to the current year.

Other estimating procedures make use of "symptoms" of population change which are supposed to reflect changes in population. Symptoms are usually items which are readily counted or measured. Procedures using symptoms as indicators are normally better than forecasting methods since forecasting methods use historic population trends projected forward while the "symptomatic" methods attempt to determine the population by measuring the actual changes in the symptomatic factors.

An example of a symptom which is commonly used is elementary school enrollment figures. Assuming the size and other characteristics of families constant, changes in the number of children in elementary school would indicate changes in the total number of families and, therefore, changes in total population. Special adjustments are made to account for persons not having school age children (i.e., older persons, single people, etc.).

Considerable care must be exercised in the choice of symptoms to be used. At the time of the 1960 census several cities were surprised to find that their actual population had not increased as much as was indicated by the precensus estimates that they had prepared. Several reasons for these differences have been given, but one of the most common cause was the use of symptoms of changes in the standard of living of the community. For example, the ownership of automobiles and telephones usually increases as income increases. Thus, an overall increase in disposable income in an area might cause an increase in automobiles and telephones even if no additional people move into the area. Care must be taken to see that symptomatic data actually reflect population changes.

Any estimating method has certain inherent disadvantages and tends to more accurately estimate one segment of the population than other segments. It is usually desirable, therefore, to prepare local area estimates by utilizing more than one method and averaging the results. The exact methods to use and the desirability of weighing the estimates before averaging must be determined by studying local population characteristics.(11)

### Estimates prepared by the U.S. Bureau of the Census

The U.S. Bureau of the Census prepares and distributes regularly current population estimates for the United States and less frequently for each State.(12) These estimates take into account immigration and emigration, natural increase, and for the State estimates, interstate migration. Natural increase is estimated by using birth and death data corrected for under reporting. Migration is estimated by comparing actual school enrollment with estimated school enrollment due to natural increase alone. These census estimates are useful as indicators of national and State changes and may be used directly in a ratio type of local estimate or as a control on the reliability of the local estimate.

Census Method I estimates net migration based on the difference between the percentage change in the school age population for the State and the corresponding change for the whole United States. This method has not performed well on tests, and is no longer used. Census Method II estimates net migration based on the difference between the actual population of elementary school age as reflected by school enrollment figures compared with the population of elementary school age which would exist if only natural increases occurred.(13)

### Elementary School Enrollment Methods

There are many variations of the use of school data in estimating population. The following is an illustration of one of these methods. In this illustration the population on April 1, 1963, will be estimated using a procedure similar to Census Method II. The basic data are assumed available for the study area from the following sources; 1960 U.S. Census of Population and Housing, local area birth and death records and school records. Since these data would come from several sources, it is assumed that they have been corrected to represent the same geographic area as well as the same time period.

 Total population, April 1, 1960, census count 100,000 Children, 7 through 14 years of age, April 1, 1960 20,000 School enrollment, grades 2 through 8, April 1, 1960 19,000 Net migration to study area, April 1, 1955, to April 1, 1960 (five years of age and over) 10,000 Net migration, children under five years of age April 1, 1955, to April 1, 1960 (obtained from State records) 2,000 Net number of children age 7 through 14 years who were migrants to the study area, April 1, 1955 to April 1, 1960 2,000 Number of children age 4 through 11, April 1, 1960 (these are the children who will be 7 through 14 on April 1, 1963) 21,000 Ratio, total population to children age 7 through 14 years of age 5.00 Ratio, children grades 2 through 3 to children 7 through 14 years of age, April 1, 1960 0.95 Ratio, net migration to study area April 1, 1955, to April 1, 1960, to children 7 through 14 years of age who were migrants to the study area, April 1, 1955, to April 1, 1960 6.00

The above figures and ratios are all for April 1, 1960.

The next step will be to list the necessary data for April 1, 1963:

 Number of children grades 2 through 6, April 1, 1963 24,000 Number of births to study area residents, April 1, 1960, to April 1, 1963 7,000 Number of deaths of study area residents, April 1, 1960, to April 1, 1963 4,000 Number of deaths of study area residents who would have been 7 through 14 years of age on April 1, 1963, which occurred between April 1, 1960, to April 1, 1963 100

The first calculation would be the number of residents in the study area allowing for births and deaths but no migration.

 Total population, April 1, 1960 100,000 Births to study area residents, April 1, 1960 to April 1, 1963 7,000 Subtotal 107,000 Deaths to study area residents, April 1, 1960 to April 1, 1963 4,000 Resident population, April 1, 1963 103,000

Next the number of children who would have been in grades 2 through 6 if no migration occurred will be determined. (This assumes that the ratio of children 7 through 14 years old to children in grades 2 through 8 does not change). First, survivors in the 7 through 14 year range as of April 1, 1963, are determined. These are the children who were 4 through 11 years old on April 1, 196), less those who died.

 Children age 4 through 11, April 1, 1960 21,000 Deaths to these children occurring between April 1, 1960, and April 1, 1963 100 Survivors who are children 7 through 14 years of age, April 1, 1963 20,900

The number of these children in elementary grades will be estimated by applying 1960 ratio of children in these grades to children in this age group.

 Survivors Who Are Children 7 through 14 Years of Age Ratio, Children Grades 2 through 8 to Children 7 through 14 Years of Age Estimated Resident Children in Grades 2 through 8 April 1, 1963 20,900 X 0.95 = 19,855

School enrollment showed that there were actually 24,000 children in these grades. Assuming no changes in enrollment procedures which would introduce inconsistencies in the data, the difference between those who would be in school if no migration occurred and the actual school enrollment would be the children of migrants who moved into the area.

 Number of children, grades 2 through 8, April 1, 1963 24,000 Estimated resident children, grades 2 through 8, April 1, 1963 19,655 Estimated children of migrants, grades 2 through c3, April 1, 1963 4,145

Assuming that the ratio of children in grades 2 through 8 to children age 3 through 14 is valid for migrants as well as residents, an estimate of the number of children of migrants aged 7 through 14 on April 1, 1963, can be made. The procedure is to multiply the inverse of the ratio times the estimated children in grades 2 through S.

 Estimated Children of Migrants Grades 2 through 8 April 1, 1963 Inverse of Ratio of Children in Grades 2 through 8 to those 7 through 14 Years of age Estimated Children 7 through 14 Years of Age Who Moved to Study Area, April 1, 1960 to April 1, 1963 4,145 X 1 = 4,363 0.95

To get the estimated total number of migrants, the ratio of the number of people who moved to the study area, April 1, 1955, to April 1, 1960, to children aged 7 through 14 who moved to the study area in the same period will be used.

 Estimated Children 7 through 14 Years of Age April 1, 1963 Who Moved to Study Area April 1, 1960 to April 1, 1963 Ratio, Net Migration to Study Area April 1, 1955, to Children April 1, 1960, to Children 7 through 14 Years of Age Who were Migrants to the Study Area, April 1, 1960 Estimated Migrants April 1, 1960 to April 1, 1963 4,363 X 6.00 = 26,178

Adding this to the net population derived from adjusting the 1960 resident population for births and deaths the total April 1, 1963, population is estimated.

 Estimated resident population, April 1, 1963 103,000 Estimated migrants, April 1, 1960,. to April 1, 1963 26,178 Estimated population, study area, April 1, 1963 129,178

Obviously many simplifications have been made in the example just described. For instance, a more accurate estimate might have been-obtained by using ages 7½ to 14½ or 7¾ to 14¾ and making adjustments for differences in school enrollment in April and other months. Also, most analysts will not be fortunate enough to have all their data for the same time period and so will have to adjust it to the estimate and census dates.(14)

### Composite method of estimating population

A more complex method of estimating current population is the composite method. As described by Donald Bogue(15) the current population estimate is prepared by making separate estimates for persons in different age groups using the "symptoms" that most accurately reflect the number of persons in each age group. The graph in Figure 7 illustrates how certain events are more common at certain ages than at others. The total estimate is then prepared by summing up the number of persons estimated in each group.

The method may be briefly described in six steps:

1. Estimate the current population aged 45 years and over utilizing death rates and number of actual deaths recorded for residents of the study area.
2. Estimate the current number of females aged 15-44 years based upon birth rates and the number of births recorded for residents of the study area.
3. Estimate the current number of males aged 15-44 years based on historic ratios of males to females in this age range. (This estimate must also allow for males in the armed forces.)
4. Estimate the current population aged 5-14 years using current school enrollment figures and the ratio of children in this age range to children actually enrolled in school.
5. Estimate the current population under 5 years of age using the number of children in this age range per 1,000 women aged 20-34 and the estimated number of women in this age range.
6. Sum the components derived in steps 1-5 to obtain the total current estimate of population.

### Endnotes

11. A report presenting several methods of preparing population estimates is: U.S. Bureau of the Census, Current Population Reports, Population Estimates, Series P-25, No. 282, April 14, 1964.

12. These estimates are available in the publication Current Population Reports, Population Estimates, Series P-25, which is published monthly and is available by subscription from the U.S. Bureau of the Census.

13. For a more detailed explanation of Census Methods see: U.S. Bureau of the Census, Current Population Reports, Population Estimates, Series P-25, No. 20, May 6, l949, No. 133, March 16, 1956, No. 1 5, Nov. 4, 1957.

14. For a description of a slightly different method of using school enrollment data to obtain current estimates see: Brown, Hugh H., "A Technique for Estimating the Population of Counties", Journal of the American Statistical Association, Vol. 50, No. 270, June 1955, PP- 323-343.

15. Bogue, Donald J. "A Composite Method for Estimating Postcensul Population of Small Areas by Age, Sex, and Color, Vital Statistics Special Reports, U.S. Dept. of Health, Education, and Welfare, Public Health Service, Vol. 47, No. 6, Aug. 24, 1959, PP. 167-185.

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