Some new techniques for applying the housing unit method of local population estimation

The housing unit method of population estimation is often characterized as being imprecise and having an upward bias. We believe that the method itself cannot properly be characterized by a particular level of precision or direction of bias. Only specific techniques of applying the method can have such characteristics. In this paper we discuss several new techniques we have developed for estimating households and the average number of persons per household. Estimates produced by these techniques are compared to estimates produced by several other techniques. Special census results from Florida provide preliminary evidence that the new techniques produce more precise, less biased estimates than the other techniques.     

A regression approach to estimating the average number of persons per household

In the housing unit method, population is calculated as the number of households times the average number of persons per household (PPH), plus the population residing in group quarters facilities. Estimates of households and the group quarters population can be derived directly from concurrent data series, but estimates of PPH have traditionally been based on previous values or estimates for larger areas. In our study, we developed several regression models in which PPH estimates were based on symptomatic indicators of PPH change. We tested these estimates using county-level data in four states and found them to be more precise and less biased than estimates based on more commonly used methods.     

An Evaluation of Persons per Household (PPH) Estimates Generated by the American Community Survey: A Demographic Perspective

The American Community Survey (ACS) is a U.S. Census Bureau product designed to provide accurate and timely demographic and economic indicators on an annual basis for both large and small geographic areas within the United States. Operational plans call for ACS to serve not only as a substitute for the decennial census long-form, but as a means of providing annual data at the national, state, county, and subcounty levels. In addition to being highly ambitious, this approach represents a major change in how data are collected and interpreted. Two of the major questions facing the ACS are its functionality and usability. This paper explores the latter of these two questions by examining “persons per household (PPH),” a variable of high interest to demographers and others preparing regular post-censal population estimates. The data used in this exploration are taken from 18 of the counties that formed the set of 1999 ACS test sites. The examination proceeds by first comparing 1-year ACS PPH estimates to Census 2010 PPH values along with extrapolated estimates generated using a geometric model based on PPH change between the 1990 and 2000 census counts. Both sets of estimates are then compared to annual 2001–2009 PPH interpolated estimates generated by a geometric model based on PPH from the 2000 census to the 2010 census. The ACS PPH estimates represent what could be called the “statistical perspective” because variations in the estimates of specific variables over time and space are viewed largely by statisticians with an eye toward sample error. The model-based PPH estimates represent a “demographic perspective” because PPH estimates are largely viewed by demographers as varying systematically and changing relatively slowly over time, an orientation stemming from theory and empirical evidence that PPH estimates respond to demographic and related determinants. The comparisons suggest that the ACS PPH estimates exhibit too much “noisy” variation for a given area over time to be usable by demographers and others preparing post-censal population estimates. These findings should be confirmed through further analysis and suggestions are provided for the directions this research could take. We conclude by noting that the statistical and demographic perspectives are not incompatible and that one of the aims of our paper is to encourage the U.S. Census Bureau to consider ways to improve the usability of the 1-year ACS PPH estimates.     

American fertility in transition: New estimates of birth rates in the United States, 1900–1910

This article presents new estimates of age-specific overall and marital fertility rates for the entire United States for the period 1900-1910. The estimation techniques are the two-census parity increment method and the own-children method. The data sources are the 1900 census public use sample and tabulations of 1910 census fertility data published with the 1940 census. Estimates are made for the total population, whites, native-born whites, foreign-born whites, and blacks. Low age-specific marital fertility at younger ages is consistent with a view of a distinctive American fertility pattern at this time.     

Making the Housing Unit Method Work: An Evaluation of 2010 Population Estimates in Florida

The housing unit (HU) method—in which population estimates are derived from estimates of occupied HUs—is the most commonly used method for making small-area population estimates in the United States. It is widely used because it is conceptually simple, can utilize a wide variety of data sources, can be applied at virtually any level of geography, and often produces reliable estimates. Yet the HU method is more nearly a general approach to population estimation than it is a specific methodology. In this paper, we describe and evaluate several data sources and estimation techniques that can be used in applying the HU method. Using a set of county and subcounty estimates produced by the Bureau of Economic and Business Research (BEBR) at the University of Florida for April 1, 2010, we analyze errors by population size and growth rate, calculate errors for each of the three components of the HU method, and investigate the accuracy of estimates based on several different data sources and estimation techniques. We compare the accuracy of the 2010 estimates with previous BEBR estimates and estimates produced by the U.S. Census Bureau. We conclude that although some data sources and estimation techniques work better than others, the HU method can be tailored to produce reliable population estimates for a wide variety of geographic areas.     

Estimating historic population data for small geographies using census housing information

Historical population data for small geographies (e.g. blocks, block-groups, and census tracts) are not available for periods earlier than 1980. In this research note, we propose a geographically-constrained housing unit method (GHUM) to estimate historic population for small geographies using housing age data available in the 1980–2000 censuses. The GHUM is a two-stage method. The first stage follows a traditional housing unit method and provides initial household and group quarter population estimates for small geographies. The second stage takes advantage of the availability of historic data for larger geographies (e.g. counties, states) to adjust the first stage estimates and to provide final estimates. The GHUM is used to estimate 1940–1990 county population and census tract population in Kentucky. The quality of the population estimates is assessed. A two-sample Kolmogorov–Smirnov test indicates that these estimates are statistically reliable at the 10 % significance level.     

Emigration Rates From Sample Surveys: An Application to Senegal

What is the emigration rate of a country, and how reliable is that figure? Answering these questions is not at all straightforward. Most data on international migration are census data on foreign-born population. These migrant stock data describe the immigrant population in destination countries but offer limited information on the rate at which people leave their country of origin. The emigration rate depends on the number leaving in a given period and the population at risk of leaving, weighted by the duration at risk. Emigration surveys provide a useful data source for estimating emigration rates, provided that the estimation method accounts for sample design. In this study, emigration rates and confidence intervals are estimated from a sample survey of households in the Dakar region in Senegal, which was part of the Migration between Africa and Europe survey. The sample was a stratified two-stage sample with oversampling of households with members abroad or return migrants. A combination of methods of survival analysis (time-to-event data) and replication variance estimation (bootstrapping) yields emigration rates and design-consistent confidence intervals that are representative for the study population.     

New techniques in small area population estimates by demographic characteristics

The increasing demand for small area population estimates calls for both innovative ways of using existing data and new techniques suitable for small area estimates. This paper explores the methods for population estimates by age, sex, race, and Hispanic origin at the census tract level for Multnomah County, Oregon. New techniques include employing building permits to indirectly estimate migration and examining the changes in age/sex structure using the American Community Survey (ACS). A practical method for bridging the race categories is also developed. Finally, the paper discusses some reflections on small area estimates and the potentials of using ACS to track the changes of the demographic characteristics for the sub-county level.     

Comparing the U.S. Decennial Census Coverage Estimates for Children from Demographic Analysis and Coverage Measurement Surveys

Following every U.S. decennial census since 1960, the U.S. Census Bureau has evaluated the completeness of coverage using two different methods. Demographic analysis (DA) compares the census counts to a set of independent population estimates to infer coverage differences by age, sex, and race. The survey-based approach (also called dual system estimation or DSE) provides coverage estimates based on matching data from a post-enumeration survey to census records. This paper reviews the fundamentals of the two methodological approaches and then initially examines the results of these two methods for the 2010 decennial census in terms of consistency and inconsistency for age groups. The authors find that the two methods produce relatively consistent results for all age groups, except for young children. Consequently, the paper focuses on the results for children. Results of the 1990, 2000, and 2010 decennial censuses are shown for the overall population in this age group and by demographic detail (age, race, and Hispanic origin). Among children, the DA and DSE results are most inconsistent for the population aged 0–4 and most consistent for ages 10–17. Results also show that DA and DSE are more consistent for Black than non-Black populations. The authors discuss possible explanations for the differences in the two methods for young children and conclude that the DSE approach may underestimate the net undercount of young children due to correlation bias.     

Fertility and replacement: Some alternative stochastic models and results for Brazil

The observed joint distribution of births and child deaths for a cohort of women at a given point in time depends on the number of children that would have been born had the family experienced no deaths, the number of child deaths experienced, and the proportion of these deaths that are replaced by a subsequent birth. In this paper we estimate the parameters of the assumed distributions of these three events using a minimum distance estimation model and data from the 1970 Brazilian census. The parameter estimates are shown to be similar to those obtained previously using a maximum likelihood estimation model. When the data are subdivided according to women's years of schooling, estimates of probability of a child death and mean and variance of children born if no deaths decrease while estimates of probability of replacement of a dead child increase as years of schooling increase.     

The effect of undercount on the accuracy of small-area population estimates: Implications for the use of administrative data for improving population enumeration

The effects of underenumeration on the accuracy of alternative methods of population estimation have not been sufficiently analyzed. Although the US Bureau of the Census has decided not to adjust either the counts or its estimates for underenumeration in 1990, the extent to which local population estimates may account for underenumeration is of importance both for those who may wish to adjust existing estimates and in anticipation of future census adjustments. This paper examines the accuracy of small-area population estimation methods with and without adjustment. Mean Percent Errors, Mean Absolute Percent Errors, and Mean Percent Absolute Differences between local estimates for 1990 and 1990 adjusted and unadjusted census counts are computed. Population estimates for 1990 made using housing unit, ratio correlation, and component methods are compared for 451 counties and 2,633 places in the states of California, Florida, Texas, and Wisconsin. An analysis of the data for counties shows little indication that local estimates more accurately estimate the adjusted than the unadjusted population counts. The results for places show clear improvements in accuracy for places in Florida and Texas. Implications of the findings for issues related to undercount adjustment and local population estimates are discussed.     

Revising Infant Mortality Rates for the Early Twentieth Century United States

Accurate vital statistics are required to understand the evolution of racial disparities in infant health and the causes of rapid secular decline in infant mortality during the early twentieth century. Unfortunately, U.S. infant mortality rates prior to 1950 suffer from an upward bias stemming from a severe underregistration of births. At one extreme, African American births in southern states went unregistered at the rate of 15 % to 25 %. In this study, we construct improved estimates of births and infant mortality in the United States for 1915–1940 using recently released complete count decennial census microdata combined with the counts of infant deaths from published sources. We check the veracity of our estimates with a major birth registration study completed in conjunction with the 1940 decennial census and find that the largest adjustments occur in states with less-complete birth registration systems. An additional advantage of our census-based estimation method is the extension backward of the birth and infant mortality series for years prior to published estimates of registered births, enabling previously impossible comparisons and estimations. Finally, we show that underregistration can bias effect estimates even in a panel setting with specifications that include location fixed effects and place-specific linear time trends.     

Bayesian population reconstruction of female populations for less developed and more developed countries

We show that Bayesian population reconstruction, a recent method for estimating past populations by age, works for data of widely varying quality. Bayesian reconstruction simultaneously estimates age-specific population counts, fertility rates, mortality rates, and net international migration flows from fragmentary data, while formally accounting for measurement error. As inputs, Bayesian reconstruction uses initial bias-reduced estimates of standard demographic variables. We reconstruct the female populations of three countries: Laos, a country with little vital registration data where population estimation depends largely on surveys; Sri Lanka, a country with some vital registration data; and New Zealand, a country with a highly developed statistical system and good quality vital registration data. In addition, we extend the method to countries without censuses at regular intervals. We also use it to assess the consistency of results between model life tables and available census data, and hence to compare different model life table systems.     

An Evaluation of Population Estimates in Florida: April 1, 2000

The housing unit (HU) method is the most commonly used method for making small-area population estimates in the United States. These estimates are used for a wide variety of budgeting, planning, and analytical purposes. Given their importance, periodic evaluations of their accuracy are essential. In this article, we evaluate the accuracy of a set of HU population estimates for counties and subcounty areas in Florida, as of April 1, 2000. We investigate the influence of differences in population size and growth rate on estimation errors; compare the accuracy of several alternative techniques for estimating each of the major components of the HU method; compare the accuracy of 2000 estimates with that of estimates produced in 1980 and 1990; compare the accuracy of HU population estimates with that of estimates derived from other estimation methods; consider the role of professional judgment and the use of averaging in the construction of population estimates; and explore the impact of controlling one set of estimates to another. Our results confirm a number of findings that have been reported before and provide empirical evidence on several issues that have received little attention in the literature. We conclude with several observations regarding future directions in population estimation research.     

An overview of demographic analysis as a method for evaluating census coverage in the United States

"Since the 1950 U.S. census, demographic methods based on the fundamental balancing equation of demography have played an important role in the evaluation of the census net undercount. Application of this set of methods, called demographic analysis, results in national estimates of the net undercount for age-race-sex groups. Although results of demographic analysis are readily available in Bureau of the Census publications, the procedures used to estimate each of the components of population change are less well-known. In this paper we review the historical foundation of demographic analysis, beginning with Coale's 1950 census evaluation project and concluding with the recent evaluation of the 1990 census. We examine each of the components of the method, how their estimation has changed over time, and how they were estimated for the 1990 census."     

Estimation of interprovincial migration for Canada from place of birth by residence data, 1951–1961

In Canada, unlike many other countries, birth-residence data by age and sex are available in each of the decennial censuses from 1931 to 1961 which permit the estimation of intercensal net migration for the provinces and regions. After a brief discussion of the basic measures of migration from birth-residence data the paper focusses on the problems and procedures in estimating interprovincial net migration, 1951–1961 for Canada using “the place of birth survival ratio method, ” and it evaluates the estimates thus obtained. The evaluation of the estimates, taking into consideration the inherent limitations of the method and its merits compared with period migration estimates by the census survival ratio method and life table survival ratio method, suggests that the net migration estimates for the Canadian born by the place of birth survival ratio method are probably more reliable than those by the other two methods. One striking finding was that the net migration curves by age obtained from the census survival ratio and place of birth survival ratio estimates were smoother than the curve obtained with the use of the more accurate life table survival ratios. Furthermore, whatever the relative accuracy of net migration may be, the birth-residence approach is capable of furnishing more details about the net migration of the native born than by the standard survival-ratio methods. For the population under age 10 intercensal estimates were directly derived from the place of birth and residence distributions by age.     

Drawing statistical inferences from historical census data, 1850–1950

Virtually all quantitative microdata used by social scientists derive from samples that incorporate clustering, strati cation, and weighting adjustments (Kish 1965, 1992). Such data can yield standard error estimates that differ dramatically from those derived from a simple random sample of the same size. Researchers using historical U.S. census microdata, however, usually apply methods designed for simple random samples. The resulting p values and confidence intervals could be inaccurate and could lead to erroneous research conclusions. Because U.S. census microdata samples are among the most widely used sources for social science and policy research, the need for reliable standard error estimation is critical. We evaluate the historical microdata samples of the Integrated Public Use Microdata Series (IPUMS) project from 1850 to 1950 in order to determine (1) the impact of sample design on standard error estimates, and (2) how to apply modern standard error estimation software to historical census samples. We exploit a unique new data source from the 1880 census to validate our methods for standard error estimation, and then we apply this approach to the 1850–1870 and 1900–1950 decennial censuses. We conclude that Taylor series estimation can be used effectively with the historical decennial census microdata samples and should be applied in research analyses that have the potential for substantial clustering effects.     

New Directions in the Development of Population Estimates in the United States?

The advent of a continuously updated Master Area File (MAF) following the 2000 census represents an information resource that can be tapped for purposes of developing timely, cost-effective, and precise population estimates for even the smallest of geographical units (e.g., census blocks). We argue that the MAF can be enhanced (EMAF) for these purposes. In support of our argument we describe a set of activities needed to develop EMAF, each of which is well within the current capabilities of the U.S. Census Bureau and discuss various costs and benefits of each. We also describe how EMAF would provide population estimates containing a wide range of demographic (e.g., age, race, and sex) and socio-economic characteristics (e.g., educational attainment, income, and employment). As such, it could largely negate and eliminate the need for many of the traditional demographic methods of population estimation and possibly reduce the number of sample surveys. We identify important challenges that must be surmounted in order to realize EMAF and make suggestions for doing so. We conclude by noting that the idea of the EMAF could be of interest to other countries with MAF files and strong administrative records systems that, like the United States, are facing the challenge of producing good population information in the face of increasing census costs.     

The Population of Centenarians in Brazil: Historical Estimates from 1900 to 2000

Since the nineteenth century, the census has provided the number of 100-year-olds in Brazil, one of the most populous countries worldwide. In 1900, 4,438 individuals reported themselves to be centenarians, a figure that increased about fivefold by the 2000 census. However, due to data quality issues, we are skeptical about the real size of the recorded population in the Brazilian census. We offer alternative estimates of the most likely number of centenarians during the twentieth century by combining variable-r relations with different mortality models. Our results indicate there was virtually no centenarian at the beginning of the twentieth century. The population has become larger than 1,000 individuals only in the 1990s, suggesting there has been an extensive, although diminishing, overenumeration of centenarians in the census records. Our results can help policymakers to plan the demands of a growing old age population in places that face stricter family and public budget constraints.