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.     

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.     

The Vital Statistics Method of Estimating Net Migration By Age Cohorts

The focus of this paper is the development and testing of a method of estimating deaths which occur during a decade to aging birth and death cohorts, so that it may be possible to estimate net migration by the vital statistics (VS) method for age cohorts. Until now the VS method has been used only in making estimates of total net migration.The results obtained by using the VS method for age cohorts show that (1) the average census survival rate (CSR) method generally yields algebraically lower estimates of net migration than does the VS method; but (2) there are some striking exceptions which are apparently associated with errors in census enumeration by age, sex, and color. Comparisons between the average CSR and the VS methods are shown, by age, for both the North Carolina and the coterminous United States populations.A cursory examination of these comparisons suggests that the exclusive use of the VS method in estimating net migration for age cohorts may lead to substantial error. Finally, the magnitude of these errors in estimating net migration, as well as in census enumeration, can be roughly approximated if it is assumed that the use of the CSR method yields reasonably accurate estimates of net migration.     

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.     

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.     

Migration between India and Pakistan, 1951–61

A critical evaluation of the available data on migration between India and Pakistan in the 1951-61 decade leads to the conclusion that there was a substantial net migration of Pakistan-born persons into India, but only a negligible net migration of India-born persons into Pakistan. Annual administrative statistics published by the Indian Government suggest an immigration from Pakistan of the order of 1.16 to 1.32 million. More importantly, birthplace data from the Indian censuses indicate a net intercensal immigration of Pakistan-born persons amounting to 1.19 to 1.34 million, depending on the assumed level of mortality. The Pakistani census data on the India-born show no net influx from India during 1951-61. Intercensal growth rates for the populations of different religious faiths in Pakistan are consistent with the estimates of net immigration into India. The migrants and the survivors of their progeny are estimated to represent a net gain of about 1.68 million by India and to account for no more than 2.2 per cent of the total population growth in India during 1951-61.     

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 probability model for census adjustment

The census can be adjusted using capture‐recapture techniques: capture in the census, recapture in a special Post Enumeration Survey (PES) done after the census. The population is estimated using the Dual System Estimator (DSE). Estimates are made separately for demographic groups called post strata; adjustment factors are then applied to these demographic groups within small geographic areas. We offer a probability model for this process, in which several sources of error can be distinguished. In this model, correlation bias arises from behavioral differences between persons counted in the census and persons missed by the census. The first group may on the whole be more likely to respond to the PES: if so, the DSE will be systematically too low, and that is an example of correlation bias. Correlation bias is distinguished from heterogeneity, which occurs if the census has a higher capture rate in some geographic areas than others. Finally, ratio estimator bias and variance are considered. The objective is to clarify the probabilistic foundations of the DSE, and the definitions of certain terms widely used in discussing that estimator.     

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.     

Annual fertility rates from census data on own children: Comparisons with vital statistics data for the United States

This paper begins by describing the procedure and data requirements for calculating annual fertility rates from census data on own children. Then, using data from the United States Censuses of 1960 and 1970, fully adjusted estimates are presented and compared with recorded vital statistics rates. Total fertility estimates derived from own children data for whites average less than two percent lower than the recorded rates- a difference that can be attributed partially to the fact that the estimates are adjusted for net census undercount but the recorded rates are not. Even without adjustments for mortality, children not living with their mothers, and net census undercount, the own children data estimates accurately replicate recorded trends (even though the levels are misspecified). The utility of own children data for the study of differential fertility is discussed.     

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.     

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...     

Inferring Directional Migration Propensities from the Migration Propensities of Infants in the United States

Beginning with the 2010 decennial census, the U.S. Census Bureau plans to drop its long-form questionnaire and to replace it with the American Community Survey (ACS). The resulting absence of the larger sample provided by the census count will complicate the measurement and analysis of internal migration flows. In addition, the strategy of averaging accumulated samples over time will mix changing migration patterns. The migration question will refer to a one-year time interval instead of the five-year interval used in the censuses between 1960 and 2000, complicating historical comparisons and the production of multiregional projections based on five-year age groups. Consequently, students of territorial mobility increasingly will find it necessary to complement or augment possibly inadequate data collected on migration with estimates obtained by means of “indirect estimation.” A method is presented that allows one to infer age-specific directional migration propensities at the regional level from birthplace-specific infant population data, which approximates infant migration propensities, and from these infers the migration propensities of all other ages. The method is applied to at the nine-division spatial scale.     

Some New Techniques for Applying the Housing Unit Method of Local Population Estimation: Further Evidence

The housing unit method of population estimation is often characterized as being imprecise and having an upward bias. In an earlier paper we argued that the method itself cannot be properly characterized by a particular level of precision or direction of bias. Only specific techniques of applying the method can have such characteristics. In that paper we presented several new techniques for estimating the number of households and average number of persons per household (PPH). However, the testing of these new techniques was limited by the lack of census results against which the estimates could be compared. Complete census data on population, households, and PPH are now available and can be used to test alternate estimation techniques. In this paper we replicate the tests reported in our earlier paper using 1980 census data for Florida’s 67 counties. These tests provide further evidence that the new techniques produce more precise, less biased estimates than previously used techniques.     

Estimators for the Horvitz-Thompson Statistic Based on Some Posterior Distributions

The knowledge of first-order inclusion probabilities characterizing a sampling scheme is essential in design-based estimation of finite population totals. Sometimes the scheme is so complex that these probabilities cannot be computed exactly. Instead, both inclusion probabilities and corresponding sampling weights are simulated. One empirical Horvitz-Thompson estimator for a population total using simulation-based range-preserving estimates of sampling weights is obtained by applying the restricted maximum likelihood principle directly to each inclusion probability. The assumption of a prior distribution and the assessment of resulting posterior for a weight lead to two other estimators. One of them is the posterior mean estimator of the Horvitz-Thompson statistic. In a simulation involving Polish agricultural census data and a sequential fixed-cost sampling scheme, this estimator has attractive properties also from a frequentist point of view.     

The hidden component in census-derived migration data: Assessing its size and distribution

Comparison of Norwegian "linked" decennial census data with statistics compiled from 10 years' migration registrations showed that the amount of movement omitted by census data was considerable. This hidden movement was of a similar order at every administrative level, but only when total movement was considered. There was wide variation between regions, migration directions, and streams. In some cases census data misrepresented the direction of net movement. Available evidence suggests that these patterns are not confined to Norway, raising the possibility that research findings based on census-derived migration data may merely be artifacts of the data.     

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.     

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.     

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.     

Estimating the Effect of the One-Child Policy on the Sex Ratio Imbalance in China: Identification Based on the Difference-in-Differences

In China, the male-biased sex ratio has increased significantly. Because the one-child policy applies only to the Han Chinese but not to minorities, this unique affirmative policy allows us to identify the causal effect of the one-child policy on the increase in sex ratios by using a difference-in-differences (DD) estimator. Using the 1990 census, we find that the strict enforcement of the one-child policy led to 4.4 extra boys per 100 girls in the 1980s, accounting for about 94% of the total increase in sex ratios during this period. The robust tests indicate that the estimated policy effect is not likely confounded by other omitted policy shocks or socioeconomic changes. Moreover, we conduct the DD estimation using both the 2000 census and the 2005 mini-census. Our estimates suggest that the one-child policy resulted in about 7.0 extra boys per 100 girls for the 1991–2005 birth cohorts. The effect of the one-child policy accounts for about 57% and 54% of the total increases in sex ratios for the 1991–2000 and 2001–2005 birth cohorts, respectively.