Effect of census errors on the measurement of net migration

This paper traces the history of the use of vital statistics, survival rates, and ratios in the estimation of net migration from one decade to another. Net migration studies by Hart (1921); Baker (1933) ; Hamilton (1934); Thornthwaite (1934); Lively and Taeuber (1939) ; Henderson (1943); Hamilton and Henderson (1943); Hamilton (1951); Siegel and Hamilton (1952); Lee and Bowles (1954); Price (1955); Lee, Miller, and others (1957); Hamilton (1959); Zachariah (1962); Tarver (1962); Shryock (1964); Eldridge (1965); Hamilton (1965); and the United States Census Bureau are cited as the principal users of various residual methods of estimating net migration. All these demographers have either implicitly or explicitly recognized that errors in census enumeration and in the registration of births and deaths have been reflected in errors of estimated net migration.The underlying characteristic of all the methods used by these demographers has been the estimation of net migration as a residual obtained by subtracting natural increase in an area during a decade from the population change during the same decade. This method has been most generally stated in the classic formula {fx394-1} This formula has been used both with total populations and with aging cohorts. The principal variations of the basic formula have involved the use of life table and census survival ratios as a means of measuring natural increase (B - D), or of estimating "expected" populations assuming no migration. The main points of controversy have involved life table v. censm survival ratios, assumptions regarding the similarity in national and state census enumeration errors, and ways and means of estimating the errors involved in estimates of migration and of migration rates by the various methods.Daniel O. Price (1955) and Zachariah (1962) made important mathematical contributions and attempted to evaluate the errors involved in the me of census survival rates. Eldridge (1965) discovered that, in the United States between 1950 and 1960, the use of the census survival rate method usually gave much lower estimates of net migration than did the classic vital statistic method. Hamilton (1965), using some suggestions by Hope T. Eldridge, developed a mathematical theory or explanation of not only why the CSR estimates were usually lower than the VS estimates but also why the CSR estimates would usually give closer estimates on the true net migration than would the EVS method, which itself is subject to errors of census enumeration and of underregistration of births and deaths. The author also discusses the effect of improvement in census enumeration between 1950 and 1960 on estimates of net migration and derives a generalized formula which takes the timing of migration into consideration.The author acknowledges with sincere appreciation important constructive suggestions made by Dr. Hope T. Eldridge, Population Studies Center, University of Pennsylvania, and the authors of the many papers used as original material. This paper is a revision of a paper read before the annual meeting ot the Population Association of America, Hotel Roosevelt, New York, New York, April 29-30, 1966. Contribution from the Departments of Sociology and Experimental Statistics, North Carolina Agricultural Experiment Station, North Carolina State University. Published with the approval of the Director of Research as Paper No. 2227 of the Journal series.     

The completeness of enumeration in the 1973 census of the population of Colombia

The effort is made to determine the true size and distribution by age and sex of the population of the Republic of Colombia in October 1973. After initially arriving at estimates of the levels of fertility and mortality during the intercensal period and then correcting the 1964 census population for age misreporting and selective undernumeration of males, a hypothetical populaiton corresponding to October 1973 is constructed. Comparing the constructed population with the population observed in the census yelds an estimate of completeness of enumeration in 1973 that is relative to the enumeration of females in 1964. This estimate is obtained under the assumption that net international migration during the period was of negligible importance. As there is reason to believe that this is not a valid assumption and upon examining the limited amount of evidence available, speculaitons are made concerning the amount of net out-migration to have occurred during the 1964-1973 period and the size of the coresponding modificaiton in the estimate of completeness of enumeration. After adjusting for underenumeration of males in 1964 and neglecting the impact of international migration, a theoretical 1973 census population of 23,201,000 was estimated. Apart from the total number of people enumerated, the information that was analyzed from the advance sample appears to be of good quality, at least in relation to prior censuses. The estimates of fertility and mortality reveal an important decline in Colombian fertility. By coming up with separate estimates of infant and childhood and adult mortality, it has been possible to shed new light on the shape and the level of mortality in Colombia. The new Brass method for estimating adult mortality provides reliable results even when mortality has been declining, and there are recognizable distortions in the distribution of the population by age.     

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.     

Estimating census and death registration completeness

This article presents a new method for estimating the relative completeness of 2 census enumerations and of intercensal registered deaths. The Growth Balance Equation was developed by Brass (1975) to estimate the completeness of death registration relative to the completeness of census enumeration. The method presented here can be seen either as an extension of Martin's formulation to allow explicitly for changes in census coverage or as a modification of Brass's method to use deaths by age group rather than deaths by cohort, preferable on the grounds that age group comparisons will be less distorted by age misreporting than cohort comparisons if the patterns of age misreporting are similar for 2 successive censuses. This simple method estimates simultaneously the relative coverage of the 2 censuses and the completeness of registration of intercensal deaths. The key assumptions of the method are that the population is closed to migration and that all the coverage factors involved are invariant with age, at least for the age range studied. Analysis of the sensitivity of the estimates to the assumptions and further work on extending the method to open populations would be useful.     

Estimates of net internal migration for Korea, 1985-90

The authors "estimate the volume and rate of net internal migration in [South] Korea for each five-year age group for the period between 1985 and 1990, adopting the forward census survival ratio method.... Two sets of [estimates] are made: (1) net internal migration for administratively defined provinces and equivalent districts with urban-rural distinction and (2) net internal migration for each of 73 cities in 1990." Extensive tables contain the estimates.     

Missing Minorities? The Phases of IRCA Legislation and Relative Net Undercounts of the 1990 vis-à-vis 2000 Decennial Census for Foreign-born Cohorts

The quality of the decennial census of the United States is compromised by population undercount, which often misses immigrants and racial/ethnic minorities, thereby diminishing federal resources allocated to such groups. Using a modified version of demographic analysis and informed by the latest contributions of emigration scholarship, this research estimates net undercount for the 1990 census relative to the 2000 census by age, sex, year-of-entry, and place-of-birth cohorts. Ordinary least squares estimates suggest that males, recent arrivals, and cohorts aged 15–44 had higher relative net undercount for 1990 compared with 2000. Much higher relative net undercount was found for cohorts from Africa, Latin America, and the Caribbean (excluding Cuba and Puerto Rico) who were ineligible for amnesty under the Immigration Reform and Control Act of 1986 (i.e., those fitting the profile of an undocumented immigrant). Larger implications of these findings suggest that the political climate in which a person is embedded—particularly for persons who may feel threatened or marginalized by the government and/or the public—affects that person’s willingness to respond to the census.     

Consistent correction of data for aboriginal populations

A consistent correction procedure is used to determine improved, consistent estimates by sex of census age distributions, intercensal births, intercensal deaths and net migration by age for the Aboriginal populations of the Northern Territory, South Australia and Western Australia during the period 1986–91. Undercount estimates and life tables show the Aboriginal populations to have lower coverage in statistical collections and much higher death risks than the total Australian population. Inter-regional net migration estimates show that component of change can no longer be ignored.     

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.     

Reconstructing the size of the African American population by age and sex, 1930–1990

We estimate the size of the African American population in five-year age groups at census dates from 1930 to 1990 using a three-part strategy. For cohorts born after 1935, we follow the U.S. Census Bureau in using classical demographic analysis. To estimate the size of cohorts born before 1895, we use extinct-generation estimates. For remaining cohorts, we implement an age/period/cohort model of census counts. All approaches are applied to a data set in which the age distribution of deaths has been corrected for age misreporting. Results provide strong confirmation of the basic validity of Census Bureau estimates of census undercounts for African Americans while extending estimates to new cohorts and periods. Our estimates are less consistent with an historical series prepared by Coale and Rives (1973).     

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.     

Differential Privacy and the Accuracy of County-Level Net Migration Estimates

Population Research and Policy Review - Each decade since the 1950s, demographers have generated high-quality net migration estimates by age, sex, and race for US counties using decennial census...     

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.     

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.     

Estimating the completeness of death registration

Summary Death registration statistics, even when incomplete, can provide valuable information about mortality. In particular, the age structure of deaths can be used to estimate the completeness of registration, provided that this completeness does not vary substantially with age. Two methods of estimating the completeness of death registration from the distribution of deaths by age are described. The first is derived from stable population theory and requires an estimate of the rate of natural increase of the population, as well as assuming stability. However, the technique can also be used to generate simultaneously estimates of the rate of natural increase and of death registration completeness. The second method which requires two census age distributions and intercensal deaths by age, estimates the relative enumeration completeness of the two censuses as well as the completeness of death registration and requires only that the population be closed. Results are sensitive to overstatement of age. The methods are illustrated by being applied to figures from Thailand for the period 1960-70 and are found to work satisfactorily.     

A reply to Kim's comment

This reply criticizes Kim's note as incorrectly characterizing the essential feature of the method proposed for life table construction. The method suggested for estimating N(a), the number attaining age 2 during the intercensal period, is to make a separate estimate of the contribution to N (a) made by each single-year cohort that attains 'a' during the period between censuses. Each cohort estimate is constructed by interpolation, utilizing as data the recorded number in the relevant single-year cohorts in the 2 censuses. 2 methods of interpolation were proposed. 1 is an iterative procedure that constructs a preliminary life table by linear interpolation for each cohort and then derives more refined interpolation factors from this preliminary life table. The other procedure derives interpolation factors on the assumption that the proportionate distribution of deaths by age as each cohort moves from the earlier to the later census date is the same as the proportionate distribution of deaths by age over the same age range in a model life table. The advantage of the proposed procedure is that it supplies better estimates of N (a) than do alternative methods. The author concedes that a life table calculated from accurately recorded deaths and an accurately enumerated population would ordinarily be superior. However, he also notes that in the absence of registered deaths data, there is no precise enough conventional method to yield accurate values of average intercensal single-year age-specific mortality rates from nothing more than 2 accurate censuses 11 years apart. A common procedure for calculating life expectation at a very advanced age is to calculate the reciprocal of the death rate among persons over the age in question.     

An analysis of net immigration in census coverage evaluation

National surveys monitored growth in the foreign-born population for the 1980s, especially net undocumented migration's continuing role, but the 1990 census portrayed an even larger foreign-born population than these surveys. Undercoverage in 1990 could have been higher than initially presented because preliminary studies may have insufficiently accounted for decadal net immigration. Assumptions intended to maintain a high undocumented undercount performed poorly when census counts of foreign-born residents became known. Any point estimate for net undocumented migration, calculated as a residual, is likely to be biased by assumptions and data gaps for components of calculating net legal immigration, especially in the direction of underestimation. A reasonable statement is that at least 2.1–2.4 million undocumented residents were enumerated in the 1990 census. The number of unenumerated undocumented residents may easily have ranged between 0.5 million and 3.0 million, and a narrower range of 1 million to 2 million is plausible. Despite the importance of undocumented migration measurement for census evaluation and policy purposes, differences among various undocumented estimates are more likely to stem from discrepancies in universe, reference dates, or individual judgment, rather than analytic refinement. Better measurement of the foreignborn population or its census coverage would aid in setting upper limits on net undocumented migration.     

Provisional evaluation of the 1970 census count of American Indians

Estimates of the American Indian population under 20 years of age on April I, 1970, based on birth and death statistics for a 20-year period, show a possible net undercount of 6.9 percent for this age group in the 1970 census. However, for some particular ages the estimates indicate net overcounts in the census. Likewise, the net increase of the entire American Indian population as measured by the difference between the 1960 and 1970 censuses is 67,000 greater than the natural increase for the decade. Detailed analysis of cohort data with respect to the possible causes of the differences between the estimates and the census figures indicate that a portion of the estimated net overcounts can be attributed to classification, as well as coverage, problems. The estimated net overcounts offer support for the hypothesis that many individuals who were registered as white at birth and who were counted as white in the 1960 census shifted their racial self-identification from white to American Indian during the 1960s.     

事后调查的理论和它在人口普查修正中的应用

人口普查不可避免地存在误差,如遗漏、重复。为发挥普查的作用,对其结果修正是必要的。一般采用事后调查法修正。事后调查在人口普查结束后进行,主要目的是为修正提供基础数据。普查局利用这些数据,使用捕获再捕获模型,修正人口普查数。     

Cohort Parity Analysis and Fertility Transition Dynamics: Reconstructing Historical Trends in Fertility Control from a Single Census

The Cohort Parity Analysis (CPA) method for the indirect measurement of the extent of marital fertility control makes use of parity distribution data of the kind reported, for specified marriage duration and marriage-age (or current age) groups of women, by a fertility census. Corresponding to every such distribution, CPA yields efficient upper and lower bounds on the proportion of controllers in the specified cohort, as well as bounds for the parity distribution of the controllers. As the women who belong to different marriage cohorts are observed at different durations of marriage in a census, it is possible to infer inter-cohort trends in the extent of fertility control (at some specified marriage duration(s)) if one knows the time pattern of the adoption of control among the members of each cohort. It is shown in this paper that robust estimates of the intracohort diffusion pattern can be obtained from the census cross-section itself, by supplementing the basic assumptions of the CPA framework with a plausible assumption about the behaviour of the ‘representative’ controller in a given cohort. The estimation technique is illustrated by applications to data for married women in urban Eire from the Census of Ireland in 1911, and to native white married women in the U.S. South from the U.S. Census of 1910.     

Changes in cohort wealth over a generation

Empirical computation of expected wealth is hampered by two problems: mortality risks vary in the population and over time; and observation of net estates for most cohorts is truncated, as some individuals in a cohort survive the calendar date on which observation is terminated. These two problems are solved in estimating cohort wealth for a sample of Wisconsin taxpayers. Hazard rate models of differential occupational mortality risks were estimated from the occupational information on the tax records. Values of net estate are simulated for individuals in each birth cohort who survived. Survivors have characteristics that imply greater wealth holdings than the deceased in every birth year covered by the study (1890-1924). Because of this, estimates of wealth-age relationships produced by the estate multiplier method for any given year will have a serious downward bias. Longitudinal data imply that dissaving does not occur after age 65.