# Lesson 5: Estimating Population Size

### Introduction

Course Objective

Develop skills to estimate the population size of a given locale

Expected Outcome

Skills to estimate population size for two periods in time, the current year and a year between census periods.

This lesson focuses on ways to estimate and project the population size of a locale. It discusses the difference between estimating, projecting, and forecasting the population and provides guidelines for performing accurate estimations and projections. It demonstrates how to calculate both the current population size of a locale and the midyear population size between census periods. The latter is necessary to calculate vital rates such as the general fertility rate and age-specific fertility rates for different time periods. The lesson concludes with the application of two estimation tools: an inter-census technique for estimating the midyear population and a post-census estimation using the housing unit method.

### 5.1 Estimates, Projections, and Forecasts

What Is the Difference between an Estimate, a Projection, and a Forecast?

A population estimate is a calculation of the size of a population for a year between census periods or for the current year. There are two types of estimation techniques: inter-census and post-census.

1. An inter-census estimation is for a date between two census takings and usually takes the results of the two censuses into account.
2. post-census estimate is typically conducted for the current year.

Estimates involve the use of data that are based on the following information:

• Components of population change, including migration, fertility, and mortality
• Census results
• Information that reflects change in population size such as the number of housing units, postal or mailing addresses, registered voters, school enrollment, and users of metered water and other utilities.

A projection is a calculation of the size of the population for a future date in time. Population information for past, present, and future conditions can be used to make a projection about the population. While estimations tend to calculate the total population size of a locale, projections calculate the total population size as well as the size of various segments of the population. For example, the population cohort projection method can be used to calculate the population size of males and females by 5-year age groups. The accuracy of estimation and projection tools is based on the rules and assumptions that are embodied in the method used.

A forecast is a projection that includes judgment statements concerning the future. Forecasting requires knowledge about past and present social, economic, and demographic trends. Planners who choose to forecast may modify the data employed in a projection to reflect their judgment of future trends. For example, if planners expect births to decline in the future, they can modify the age-specific fertility rates when projecting population by age and sex. The tools covered in Lessons 5-8 do not include population forecasting. Population estimations and projections are based on the assumptions of the tools rather than judgments of future trends. In this case, it is much easier to explain the assumptions than it is to justify personal judgments about future conditions.

Estimates and projections can be for de jure (usual resident) or de facto (physically present) populations. In most cases, they are based on de facto populations. This data can be divided into two categories:

Direct
information comes from census data and information on births, deaths, and migration.

### 5.2 Estimation and Projection Guidelines

Estimation and Projection Guidelines

The quality of information and data for a given locale, as well as the ability of the data to meet the basic assumptions of the analytic method are key to performing accurate estimates or projections. Shryock and Siegel (1973) and Morrison (1971) developed the following guidelines for performing population estimations and projections:

1. More accurate estimates can generally be made for an entire country than for geographic sub-divisions of a country. It is easier to obtain migration information at the national level since international migration is usually recorded when individuals and families enter a country. This is not the case, however, for cities, towns, and districts, where migration information is collected as part of a census every 10 years.
2. More accurate estimates and projections can generally be made for the total population of an area than for the demographic characteristics of the population. The census is the only data source available to project population by select attributes such as age, sex, and occupation. More information sources are available to estimate or project the size of the total population. When projecting or estimating total population size, it is possible to use several tools that are based on different information sources and compare the results.
3. Direct data are preferred to indirect data. Population information that is based on the components of population change such as births, deaths, and migration, and methods that parallel demographic processes, may produce more accurate estimations and projections.
4. An estimate or projection should always be checked by comparing it with another estimate or projection that employs an equally accurate or more accurate method.
5. The poorer the data quality and the longer the projection period, the less reliable are the results. 20-year projections are not as reliable as those of 5–10 years. In addition, economic activities can influence in- or out-migration and lead to the rapid growth or decline of a locale. The environment also influences population change. For example, droughts and floods can lead to major reductions in population size.
6. The most accurate projection is usually based on a combination of methods. For example, use two methods whose assumptions support available information sources, and take an average of the two.
7. Never take for granted that a data series is correct, regardless of the agency providing it. As discussed in Lesson 4, always review a series of data and information over time to be sure that it is consistent.
8. If a series of census information changes drastically over time, determine the cause. In some cases, census boundaries or data collection methods may have changed, rather than the actual size of the population.

### 5.3 Estimation Tools

Estimation Tools

This section demonstrates how to calculate two types of population estimations: the population size of a locale between census periods and the current population of a locale. You may use Equation 5-1 to estimate the midyear population between census periods, as well as the current population, provided that reliable information is available on the number of births, deaths, in-migrants, and out-migrants.

Equation 5-1
Components of Demographic Change

This equation will provide the most accurate population estimate. However, data on all three components of demographic change are rarely available. Therefore, it is necessary to use other estimation methods. The methods presented in this lesson assume that reliable information is not available on the components of demographic change, but that planners will have access to census data and indirect information that reflects population change. Suggestions for other estimation methods are included at the end of the lesson.

Inter-Census Estimation: Midyear Population

The following estimation method is used primarily to estimate the midyear total population, or a subset of the population of a given locale.

Indirect
data include information that reflect changes in population size, such as school enrollment, housing units, gas and electric meters, employment statistics, tax information, voter registration, and postal addresses.
Assumptions
This method assumes that yearly changes in the population size are equal. It also assumes that population change between the two census periods is linear. Plotting several census periods with time on the horizontal line (X-axis) and population size on the vertical line (Y-axis) results in a straight line between the points.
When to Use this Tool?
This estimation tool is primarily used to calculate the midyear population for vital rates such as the crude birth or death rate, age-specific fertility or death rates, and the general fertility rate.

Equation 5-2 can be used to estimate the population size of a subset of the population, or the total size of a population between census periods.

Equation 5-2
Estimating the population size between two census periods

Equation 5-3
Crude Birth Rate

For example, in order to calculate the crude birth rate for Durham County, North Carolina for the year 1999, it is necessary to estimate the midyear population for 1999. Equation 5-3 provides the calculation for the crude birth rate.

The date of the census taking for both periods is April 1. The date of the midyear population is July 1. Note that the midyear month is different from the census month. These differences are taken into account when calculatingn. The following example demonstrates Equation 5-2 in estimating the midyear population and the calculation of the crude birth rate.

Example of Equation 5-3

Exercise 5-1

Calculate the crude birth rate for Durham County in 1998, where the number of births is 3,288. Discuss the limitations of this estimation tool.

Post-Census Estimation: Housing Unit Method

The housing unit method uses information on housing to estimate the total population size for a locale.

Assumptions
The housing unit method assumes that a change in the number of occupied housing units reflects a change in the population size.
When to Use this Tool?
Use this tool to perform an estimate for an area with little or limited demographic information. This method can be used for districts or counties, cities, and towns. It can also be used for rural areas provided that the necessary information on housing units and average household size can be collected for the locale. In addition, it can be used to estimate the current population size as well as population size between census periods, provided that information can be obtained for the estimation year.
Information Needs
A census of population and housing is required. Census information is needed for the total number of residential housing units, number of vacant residential units, number living in group housing, and average household size. This information can also be obtained from surveys. In addition, data are needed on new building permits, demolitions activity, certificates of occupancy, and building conversions. Obtain this information from those agencies that are responsible for building inspections and housing.

The next section presents the summary equation for the Housing Unit Method tool, as shown in Equation 5-4. In addition, an explanation and calculation of the various components in Equation 5-4 are provided.

Equation 5-4
Housing Unit Method Summary Equation

Stages in the Housing Unit Method

1. Population living in group housing

Residents of group housing include individuals residing in institutional housing such as dormitories, military barracks, prisons, and patients living in long-term care facilities such as mental hospitals and nursing homes. It also includes individuals and families living in non-institutional facilities such as boarding houses. In some countries, this information is collected as part of the census. The accuracy of this estimate can be improved by contacting institutions and boarding homes to collect information on the number of residents living in group housing. Ensure that the institutions contacted are within the geographic boundaries of the estimation area.

2. Occupied Housing Units

The calculation for occupied housing units is shown in Equation 5-5.

Equation 5-5
Occupied Housing Units

A census of population and housing, however, will include data on the number of housing units. It is also possible to obtain this information from housing surveys. Note that a housing unit is not the same as a building. A housing unit is the place of residence for an individual, family, or a group of unrelated adults and children. For small locales, such as a town or village, it may be possible to actually count the number of housing units.

If census information is available, update the information on the number of occupied housing units. This is a two-step process. Available housing is constantly changing as new units are built and old ones are destroyed or converted to other uses. The first step is to record changes in the number of housing units from the time of the census taking to the estimation year as shown in Equation 5-6.

Equation 5-6
Changes in the Number of Housing Units Between Two Census Periods

Net conversions are included because a building's use can change several times during its existence. Households may decide to turn a home into a business and find a new place to live. Conversely, buildings that were created for commercial or industrial use can be converted into apartment units.

The second step, once information is obtained on the number of housing units, is to determine the number of housing units occupied by people, as shown in Equation 5-7. For this calculation, multiply the number of housing units by the occupancy rate. To do this calculation, it is necessary to determine the occupancy rate.

Finding the occupancy rate:

Equation 5-7
Occupancy Rate

In some countries, the vacancy rate can be obtained from census reports, as shown in Equation 5-8.

Equation 5-8
Vacancy Rate Using Census Data

These are alternative ways to obtain vacancy rates. In cities, towns, and rural areas where a high percentage of the population legally use utilities such as electricity and water, information should be available from a utility company or government office to determine active and inactive use of a given utility. Make sure this information matches the geographic locale for the estimation area.

Equation 5-9
Calculating a Vacancy Rate from Utility Accounts

3. Average Household Size

The number of occupied houses is multiplied by the average household size. The results provide an estimated population size of those living in residential units. The average household size can be obtained from census information or household surveys.

Problems with the Housing Unit Method:
First, it is difficult to obtain reliable information because some countries do not require building permits. Second, not all residential building permits are for housing units. In some countries, residential permits are required to add a garage, a storage shed, or another room to existing housing. Also, the fact that a permit is issued in a particular year does not mean that a unit will be built in that year. To increase the accuracy of data based on building permits, use certificates of occupancy as an added check; many countries require these before a tenant moves into a residential unit.
Problems in collecting demolition data:
Inspectors may not indicate the number of units within a structure that is being torn down. The identity of the person/group who demolished the structure must be determined in order to calculate how many units were used for residential housing. Problems may also exist with conversion data. Not all households report conversions or changes in how a home is being used. In some locales, families can find other places to live and use an entire house for a small business.
The bottom line for all estimation and projection tools:
Determine if it is possible to collect the required information and the feasibility of working within with the basic assumptions of the method.

### 5.4 Summary Equations

The following steps demonstrate how to use the housing unit estimation tool. This example uses data from Table 5-1 to estimate the population size of an urban district for year 2000.

 Table 5-1:Sources of Informationfor Using the Housing Method toEstimate the Population Size of anUrban District for the Year 2000 Source of Information Data Census Information Occupied housing units, 1990 Vacant housing units, 1990 Average household size, 1990 Population in group housing, 1990 58,360 2,237 2.42 7,825 Building Inspector's Office Building Permits, 1990–2000 18, 247 Demolitions Private demolition companies, 1990–2000 315 Building Conversions From industrial to apartment units, 1990–2000 From housing to commercial use, 1990–2000 2010
Step 1:
Use the actual census count for 1990 on group housing and the Housing Unit Method Summary Equation as presented in Equation 5-4 to estimate the population size. The population living in group housing = 7,825. When possible, identify the types of institutions used by the census, contact each institution to determine if it still exists, and obtain the number of residents for each type of facility for the estimation year.
Step 2:

Use Equation 5-10 to calculate the number of housing units. Data for this example can be found in Table 5-1.

Equation 5-10
Housing Units

Step 3:

Next, obtain an occupancy rate as presented in Equations 5-7 and 5-8 to determine how many of the housing units are occupied. Census information from Table 5-1 is used to calculate the vacancy rate that is presented in Equation 5-11.

Using Equations 5-7, 5-8, and 5-10

Step 4:
Obtain the average household size using 1990 census information as indicated in Table 5-1.
Putting it all together. The results are shown in summary equation 5-13.

Example of the Housing Unit Method Summary Equation (Equation 5-4)

Note that the actual population of the urban district in 2000 was 181,854.

Exercise 5-2
What can be done to improve this estimation and bring it closer to the census population?

• Review the process of calculating this estimation technique. Think about the data sources employed.
• Describe how to improve the estimate for the urban district.
• What type of information can be used?
• Where could the information be obtained?

### 5.5 Discussion

This lesson demonstrated the use of two estimation tools that require limited data. It provided guidelines for selecting and conducting population estimations and projections. These are not the only estimation tools that are available; additional projection tools will be provided in Lesson 6. An excellent web site demonstrating the use of a range of estimation techniques may be found at the United States Bureau of the Census. This site is particularly useful in explaining the housing unit estimation tool.

Population Estimate for 1998 = 152,785 + 99 / 120 (181,835 - 152,785)

Population Estimate for 1998 = 152,785 + (.825)(29,050)

Population Estimate for 1998 = 176,751

Crude Birth Rate for 1998 = (3,288 / 176,751) x 1,000 = 18.6

The tool assumes that the same number of people is added to the population each year and that growth is linear. In most cases, locales do not increase by the same number of residents each year.

Because the estimation for the urban district relied heavily on 9-year-old census data, it was necessary to identify other sources of information. For example, try to improve the data for group homes. This can be done by identifying institutions, boarding homes, and long-term hotels that provide housing for individuals and households and collecting information on the total number of residents in each type of group housing.

Census information was used to calculate the vacancy rate, but housing surveys could also provide information. Check with the housing division in the district planning office or with nearby university faculty in sociology, geographic, and planning departments to see whether studies are available. If a high percentage of the population uses electricity legally, utility information can be used to estimate the vacancy rate. If multiple information sources are available, use an average of the two best vacancy rates.

There are several ways to improve the information on building permits as well. Verify whether the permits issued during the estimation period were actually used, and make sure they were used for housing units versus other types of construction, such as adding a room or garage to an existing house. Substitute certificates of occupancy for building permits if available. These certificates are needed in order for new residents to move into a housing unit.

Information on demolished buildings is often available from private companies that demolish buildings. In the example, information was not available on the number of housing units destroyed for each structure. In this case, it is possible to improve the estimation, by identifying where buildings were destroyed and asking neighbors about the number of housing units that were in the buildings.

Information on average household size was taken from the census. Household survey data could have been obtained from different studies to observe changes in household size and then averaged.

It is also possible to assess the quality of available census information. How did the census count the homeless? Did it collect information on those living in slum and squatter settlements? Try to determine how many people live in makeshift or temporary housing in squatter settlements. In most cases, makeshift housing appears overnight. If these types of housing units are not destroyed by government on a regular basis, include them in the count. Also, check with institutions that provide services to the homeless to get an idea of how many to add to the estimation.

These results can be compared with other estimates to see if they are too low or high (see Lesson 6 for other tools that can be used to estimate the current population).

These are just a few examples of estimating. Experiment with different ideas to improve the accuracy of this tool in your locale.

### References

George W. Barclay, "Rates and Ratios," Techniques of Population Analysis (New York: John Wiley & Sons, 1958) 16–55.

Peter A. Morrison, Demographic Information for Cities: A Manual for Estimating and Projecting Local Population Characteristics (Santa Monica, CA: Rand, 1971).

Norfleet W. Rives and William J. Serow, Quantitative applications in the social sciences: Paper 39,Introduction to Applied Demography: Data Sources and Estimation Techniques, (Newbury Park: Sage Publications, 1984).

Henry S. Shryock and Jacob S. Siegel, "Population Estimates," The Methods and Materials of Demography, (Washington, D.C.: Bureau of the Census, 1973) 725–770.

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