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.     

A note on the measurement of accuracy for subnational demographic estimates

Mean absolute percentage error (MAPE), the measure most often used for evaluating subnational demographic estimates, is not always valid. We describe guidelines for determining when MAPE is valid. Applying them to case study data, we find that MAPE understates accuracy because it is unduly influenced by outliers. To overcome this problem, we calculate a transformed MAPE (MAPE-T) using a modified Box-Cox method. Because MAPE-T is not in the same scale as the untransformed absolute percentage errors, we provide a procedure for calculating MAPE-R, a measure in the same scale as the original observations. We argue that MAPE-R is a more appropriate summary measure of average absolute percentage error when the guidelines indicate that MAPE is not valid.     

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.     

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.     

The impact of incomplete geocoding on small area population estimates

Small-area population estimates are often made using geocoded address data in conjunction with the housing-unit method. Previous research, however, suggests that these data are subject to systematic incompleteness that biases estimates of race, ethnicity, and other important demographic characteristics. This incompleteness is driven largely by an inability to complete georeference address-based datasets. Given these challenges, small-area demographers need further, and to date largely unavailable, information on the amount of error typically introduced by using incompletely geocoded data to estimate population. More specifically, we argue that applied demographers should like to know if these errors are statistically significant, spatially patterned, or systematically related to specific population characteristics. This paper evaluates the impact of incomplete geocoding on accuracy in small-area population estimates, using a Vintage 2000 set of block-group estimates of the household population for the Albuquerque, NM metro area. Precise estimates of the impact of incomplete geocoding on the accuracy of estimates are made, associations with specific demographic characteristics are considered, and a simple potential remediation based on Horvitz-Thompson theory is presented. The implications of these results for the practice of applied demography are reviewed.     

MAPE-R: a rescaled measure of accuracy for cross-sectional subnational population forecasts

Accurately measuring a population and its attributes at past, present, and future points in time has been of great interest to demographers. Within discussions of forecast accuracy, demographers have often been criticized for their inaccurate prognostications of the future. Discussions of methods and data are usually at the centre of these criticisms, along with suggestions for providing an idea of forecast uncertainty. The measures used to evaluate the accuracy of forecasts also have received attention and while accuracy is not the only criterion advocated for evaluating demographic forecasts, it is generally acknowledged to be the most important. In this paper, we continue the discussion of measures of forecast accuracy by concentrating on a rescaled version of a measure that is arguably the one used most often in evaluating cross-sectional, subnational forecasts, Mean Absolute Percent Error (MAPE). The rescaled version, MAPE-R, has not had the benefit of a major empirical test, which is the central focus of this paper. We do this by comparing 10-year population forecasts for U.S. counties to 2000 census counts. We find that the MAPE-R offers a significantly more meaningful representation of average error than MAPE in the presence of substantial outlying errors, and we provide guidelines for its implementation.     

A Comparative Evaluation of Error and Bias in Census Tract-Level Age/Sex-Specific Population Estimates: Component I (Net-Migration) vs Component III (Hamilton–Perry)

While the housing-unit method continues to be the preferred method nationwide for producing small-area population estimates, this procedures lacks a method for making age/sex-specific estimates. This paper reports evaluation research on implementation of component-based methods for estimating census tract populations with age/sex detail. Two alternatives are explored: (1) the Component I method relying upon estimates of births, deaths, and net-migration and (2) the Component III method relying solely upon 1990 and 2000 Census counts. From an April 1, 2000 base, each method is used to make estimates moving forward to an April 1, 2010 estimate that is compared to the results of the 2010 Census. The two methods are compared in terms of accuracy and bias using both absolute and algebraic mean and median percentage errors. Results are reviewed and discussed in light of their implications for applied demographers tasked with making small-area demographic estimates.     

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.     

Assessing post-census state poverty estimates

While the decennial census provides poverty figures for states and other subnational geographic units every ten years, their utility declines over the course of a decade. Consequently, there is growing interest in producing post-census estimates for a variety of indicators. This study extends recent efforts to estimate post-census poverty figures for states by producing such estimates using a multiple regression approach. The accuracy of the multiple regression estimates along with recently produced estimates from the Current Population Survey (CPS) are evaluated relative to the decennial census. The mean absolute percentage point error (MAPPE) using the ratio-correlation technique (1.56 percentage points) was somewhat higher than the MAPPE of 1989 CPS (1.37 percentage points) and an average of 1988–1990 CPS data (1.15 percentage points). However, a simple regression technique using data from 1979 to estimate poverty in 1989 produced a set of estimates where the MAPPE (1.37 percentage points) is nearly as accurate as the single-year CPS estimates. Estimates which average regression estimates and CPS-based estimates are more accurate than either regression or CPS estimates used alone. Several suggestions are offered for improving regression estimates.This article is a revised version of a paper presented at the annual meeting of the Population Association of America, 1–4 April 1993, Cincinnati, OH, USA.     

A method for combining sample survey data and symptomatic indicators to obtain population estimates for local areas

Past efforts of statistical demographers to compute postcensal population estimates for local units have been hampered by the fact that they have had to rely completely on symptomatic information. In this paper, a new method of postcensal estimation is presented in which the symptomatic information is combined with sample data by means of a regression format. Combining symptomatic information on births, deaths, and school enrollment with sample data from the Current Population Survey, county estimates of population growth were computed by means of the new method for the postcensal period after 1960. These estimates were tested for accuracy by comparison with a set of special censuses which were conducted between 1964 and 1967 in 75 counties. The results of this test are promising, but not conclusive. A more conclusive test is currently underway using 1970 data. While the method has been tested as a means for estimating population growth, it is to be emphasized that it can be used to compute postcensal estimates for any variable for which the necessary symptomatic information and sample data are available.     

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.     

How Far Has Fertility in China Really Declined?

According to births in the last year as reported in China's 2000 census, the total fertility rate (TFR) in the year 2000 in China was 1.22 children per woman. This estimate is widely considered to be too low, primarily because some women who had out‐of‐quota births according to China's one‐child family policy did not report those births to the census enumerator. Analysis of fertility trends derived by applying the own‐children method of fertility estimation to China's 1990 and 2000 censuses indicates that the true level of the TFR in 2000 was probably between 1.5 and 1.6 children per woman. A decomposition analysis of change in the TFR between 1990 and 2000, based on our best estimate of 1.59 for the TFR in 2000, indicates that about two‐fifths of the decline in the conventional TFR between 1990 and 2000 is accounted for by later marriage and less marriage, and three‐fifths by declining fertility within marriage. The analysis also applies the birth history reconstruction method of fertility estimation to the two censuses, yielding an alternative set of fertility estimates that are compared with the set derived by the own‐children method. The analysis also includes estimates of trends in fertility by urban/rural residence, education, ethnicity, and migration status. Over time, fertility has declined sharply within all categories of these characteristics, indicating that the one‐child policy has had large across‐the‐board effects.     

Coverage of the population in Census 2000: Results from Demographic Analysis

Since the 1960 Census, Demographic Analysis (DA) has been used by the Census Bureau to evaluate the coverage of the population. Administrative statistics on births, deaths, immigration and Medicare enrollments as well as estimates of legal emigration and net undocumented immigration are used to produce demographic analysis estimates of the population for the census date. These estimates are compared to the Census 2000 data to evaluate coverage in the census. The results are also compared to measures of undercount obtained from dual system estimation. The DA measures substantial reduction in net undercount in Census 2000 compared to 1990. The reductions occur among all demographic categories: all broad age groups, males and females, Blacks and Non-Blacks.     

Note on the accuracy of local population estimates

Mr. Silcock's article will be of interest to all concerned with local population data. It may be useful to supplement it by a brief account of the fuller examination of the local population estimates made in 1951 by the General Register Office, since this covered all 1472 administrative areas in England and Wales and could be made in more detail than was possible for a private investigator.

Any census, of course, provides information not available, at least in such detail, at other times or from other sources, and also serves as a base from which estimates for succeeding years can be derived. In addition, however, the General Register Office takes the opportunity of a census to try and assess the accuracy of the various types of current population estimates made by the Department. In the case of local administrative areas the comparison of actual and expected populations made after the 1931 Census is discussed in the Text Volume of the Registrar General's Statistical Review for 1930 (pages 100-102).     

Precision in population estimates

Summary

Given the Registrar General's estimate of the home population of a local government administrative area in England and Wales, is it possible to construct a 95 per cent. confidence interval for the true value? The author has attempted to provide an approximate answer to this question by considering estimates made before and after the 1951 census, together with such data as are available to improve the comparability of the estimates. The analysis suggests that urban and rural areas must be separately considered, and that the margin of error is of the order of five per cent, for the former and eight per cent. for the latter.     

On the validity of MAPE as a measure of population forecast accuracy

The mean absolute percent error (MAPE) is the summary measure most often used for evaluating the accuracy of population forecasts. While MAPE has many desirable criteria, we argue from both normative and relative standpoints that the widespread practice of exclusively using it for evaluating population forecasts should be changed. Normatively, we argue that MAPE does not meet the criterion of validity because as a summary measure it overstates the error found in a population forecast. We base this argument on logical grounds and support it empirically, using a sample of population forecasts for counties. From a relative standpoint, we examine two alternatives to MAPE, both sharing with it, the important conceptual feature of using most of the information about error. These alternatives are symmetrical MAPE (SMAPE) and a class of measures known as M-estimators. The empirical evaluation suggests M-estimators do not overstate forecast error as much as either MAPE or SMAPE and are, therefore, more valid measures of accuracy. We consequently recommend incorporating M-estimators into the evaluation toolkit. Because M-estimators do not meet the desired criterion of interpretative ease as well as MAPE, we also suggest another approach that focuses on nonlinear transformations of the error distribution.     

Immigration data and national population estimates for the United States

The immigration component in national population estimates is comparatively small, but it is not insignificant and may indeed be an important source of error. Therefore, it warrants the considera-tion of those concerned with population estimates. The paper considers alternative methods for deriving estimates of immigration from the raw data and presents estimates of net immigration from 1950 to 1965. They are developed from estimates previously published by the Bureau of the Census, but they differ at some points where new data have become available or where a review of the data has led to a change in judgment on how best to use them. The paper also presents suggestions on how immigration statistics might be altered for purposes of improving the estimates.Census data may be used to estimate net immigration by three different methods, but upon analysis each method proves to be inadequate. Hence, data based on visas surrendered at the port of entry must be the principal source of immigration estimates. These data have their limitations because (1) they do not cover net arrivals of citizens from abroad and from Puerto Rico, (2) they do not report departures of aliens, and (3) they do not allocate all immigrants to year of entry. Alien registration and passenger data offer possible alternative estimates.The paper attempts to measure unrecorded immigration, discusses how net arrivals of citizens from abroad and from Puerto Rico may be estimated, and how the age, sex, and race of immigrants may be treated.     

Cohort parity analysis: Statistical estimates of the extent of fertility control

Cohort parity analysis (CPA) is a method for indirect measurement of the extent and timing of the adoption of fertility control within marriage. It uses information on the parity distribution of a cohort of women of specified marriage ages and durations. A multinomial model of parity provides a convenient framework for the computation of distributional parameters describing the extent to which marital fertility control has been accepted and characterizing the way control has been used within specific durations of marriage. This leads to a pair of easily implemented formulas for upper- and lower-bound estimates of the expected proportion of the population ever controlling and the distribution of controllers by parity. The power of CPA is illustrated, using census data for currently married couples in Dublin, Belfast, and other county boroughs of Ireland in 1911.     

Evaluating the relative accuracy and significance of net migration estimates

This paper presents the elements of a theory for evaluating the quality of a set of net migration estimates. The total error in a net migration estimate is decomposed into total bias and total variation. The bias is further decomposed into three bias elements-selection bias, estimator bias, and measurement bias. Tables of bounds for measurement and estimator biases in the vital statistics and the forward survival ratio estimates of net intercensal migration are presented. Both net migration levels and net migration ratios are treated, and provision is made for both life table and census survival ratio estimates. Some of the statistical tables are applied illustratively to net migration data for Canadian counties or census divisions during the 1951-61 decade. Tests of significance and confidence intervals are indicated for net migration estimates, and the basic technical notes are presented in appendices.     

Estimates of coverage of the population by sex,race, and age in the 1970 census

Several estimates of total net underenumeration and of net census errors by sex, race (white, Negro-and-other-races, Negro), and age (five-year groups) in the 1960 and 1970 Censuses, for the total population of the United States, derived by the methods of demographic analysis, are presented. The different data, procedures, and assumptions employed in developing the various estimates are described briefly, and the findings are then discussed in terms of a”preferred” set of estimates. The preferred set of estimates of corrected population for 1970 combines estimates for persons under age 35 based directly on birth, death, and migration statistics, estimates for females aged 35 to 64 based on the Coale-Zelnik estimates (white) for 1950 or the Coale-Rives estimates (Negro) for 1960, estimates for males aged 35 to 64 based on the use of expected sex ratios, and estimates for the population 65 and over based on”Medicare” enrollments and expected sex ratios. These estimates indicate an overall net underenumeration of 5.3 million persons or 2.5 percent in 1970, as compared with 5.1 million or 2.7 percent in 1960, and a net underenumeration of 1.9 percent for whites and of 7.7 percent for Negroes in 1970, as compared with 2.0 percent and 8.0 percent, respectively, in 1960. As in 1960, undercoverage in 1970 was greatest for Negro males (9.9 percent); net error rates exceeded 12 percent in each age group 20 to 49 and reached 17 to 19 percent at ages 25 to 44. All sex-race groups showed marked increases between 1960 and 1970 for children under ten and marked declines at ages ten to 24. Equally reliable estimates of population coverage cannot be prepared for states and smaller geographic units or for the population of Spanish ancestry.