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DATA SOURCES CHAPTER 2 SOURCES AND QUALITY OF DATA The People's Republic of China had an enumerated total population in 1982 of more than 1 billion persons. The population has experienced dramatic recent reductions in birth and death rates, apparently surpassing the changes in any other very large less-developed country. These general features of the Chinese population had until recently been revealed in scattered information, such as travelers' reports, short news dispatches, and occasional sketchy official releases. Since the late 1970s, however, information on the population of China has been enriched by the sudden availability of a treasure of detailed demographic data--data relating both to the recent past and to the early years of the People's Republic. Census and Fertility Survey Data The 1982 Census and the 1982 Fertility Survey. The major sources of detailed information are two large data collection efforts that took place in 1982. The first of these was the 1982 census of population in which a field staff of 5.1 million enumerators counted a total of 1.008 billion people. The second effort was a sample survey conducted by the State Family Planning Commission, also in 1982. This survey obtained information about the complete childbearing and marriage histories of a sample of women aged 15-67. The households included in the survey had a population totalling more than 1 million. The survey included data on contraceptive practice, education, occupation, ethnicity, recent abortions, and possession of a one-child certificate. 12

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13 The results were published (in Chinese) in a 176-page special issue of the journal Population and Economics. Data from the 1953 and 1964 Censuses. The first modern census of China was conducted in 1953. Very limited results, such as the total population, were revealed in 1954, although fundamental details, such as numbers of persons classified by age and sex, remained unavailable outside of China. A second census took place in 1964; the mere fact that it occurred was not generally known until some years later, and again no details were released. Within the past two years, however, the most essential demographic information--the nu~nJoer of persons of each sex classified by single years of age--from these two censuses has been published. The Ministry of Statistics has also recently published the Statistical Yearbook for 1983 with hundreds of tables, including annual birth and death rates since 1950. It is now possible to piece together from the newly available information the history of the population of the People's Republic of China from 1950 to 1982 with much more accuracy and more detail than has been possible until now. Indeed, as the following pages show, the accuracy and fineness of detail of the information about the Chinese population now exceed the accuracy and detail of what is known about almost every other less-developed country in the world. Independence of the Data Sources The various quantitative comparisons presented in the following pages convey a very surprising degree of consistency among numbers derived from the censuses of less, 1964, and 1982 and from the large-scale fertility survey. Some demographers and statisticians have suggested that the consistency of the data results from a lack of independence of the sources and is not convincing evidence of accuracy of the data. This possibility arises because China has a nationwide, comprehensive registration system. Each community maintains a register of the population in which there is a listing of the de jure population, to which an addition is made for each birth and legal in-migrant and a deletion is made for each death and legal out-migrant. The registration system also includes the maintenance of a household book

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14 containing a listing of the de jure members of each household. The 1982 census involved a preliminary nationwide updating of the registers in each community, and the registers and the household books played a part in the census itself. The fertility survey, which was conducted about 2 months after the census, used the census as the frame for its 1/1,000 sample and checked the roster of each household included in the sample against the census listing. The hypothesis that con- sistency may not imply accuracy derives from the possibility that the censuses (and perhaps the survey) were simply readings of the registers. If so, the mechanics of maintaining a register would guarantee that persons listed in 1964 and still alive in 1982 have a consistent age and that, on a national level (with inconsequential international migration), the change in the number listed in a cohort must be consistent with the deletions made as a result of recorded deaths. If the number of children born to a given woman is copied from the register, the number recorded in the 1982 census and the number listed in the sample survey might be the same without being correct. There are two reasons for rejecting the hypothesis that consistency may not imply accuracy. The first is that the procedures followed in the 1982 census and survey, as published, involved much more than checking the registers. For the census, there was extensive preparation, pretesting, and postenumerative checking along with the actual census. It is also of note that the census was conducted with substantial technical and financial assistance from the United Nations. The census was closely tied to the registers, but only after extensive updating and verification; individual data were verified by the person in question. For the 1/1,000- sample fertility survey, the published descriptions of the procedures specified face-to-face interviews for the detailed marriage and fertility histories. The second reason for rejecting the hypothesis is that the annual numbers of births derived from a combination of census-based estimates of numbers of women each year and survey-based retrospective data on fertility rates are quite different from official records of the annual number of births. In other words, the fertility histories are in wide disagreement with official data on births and so cannot have been derived from the registers.

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15 Characteristics of the 1982 Census and Fertility Survey Procedures of the 1982 Census. Li Chengrui, the - director of the State Statistical Bureau and head of the National Population Census Office, has described the procedures of the 1982 census in detail (Li 1983a and 1983b). The procedures included pretests of the census in successive stages, beginning with a pretest conducted by the central government and extending to pretests in each of China's 2,741 counties, covering a total of more than 25 million people. In addition, the register of the population was updated before the census. Li summarizes these procedures (1983a:337): First, from the beginning of 1981 through March 1982, household registration was updated. In a sense, this amounted to a precensus check. During this period, more than 5.7 million household registration personnel, statistical personnel, and other basic-level cadres were mobilized to update household registration throughout the country. They conducted a systematic investigation through household interviews and found and corrected errors: 6.1 double registrations per thousand and 5.4 omissions per thousand. Second, prior to the formal enumeration on 1 July 1982, the enumerators arrived at their census districts and conducted a further investigation. They checked household by household for the "five types of persons" identified in the "Census statutes manual. During this procedure, further errors were found and corrected. Based on the information from a subset of areas, double registrations were found to amount to 3 per thousand population and omissions to 2.5 per thousand. Third, after the conclusion of the census enumeration, 10-20 days were spent rechecking household by household and person by person all the census questionnaires. Some errors were again found and corrected. Based on the information from a subset of areas, during the recheck, double courting s of 0.1 per thousand and omissions of 0.2 per thousand were found and corrected. Following these precensus and census procedures, there was a post-enumeration survey (Li, 1983a:338):

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16 . . . the population census offices of the provinces, municipalities, and autonomous regions first selected, by multistage random sampling, 972 production teams and resident groups (a total of 187,362 persons according to the census) as the survey units. The provincial, prefectural, and county-level offices then selected persons who were of higher educational level and were conscientious and responsible in their work to undergo special training to become sample enumerators. They conducted the postenumeration survey in the selected sample units household by household and then compared the figures obtained with the figures of the original census enumeration. When errors were found, a second check was made before the data were corrected. Based on the stipulations, the census personnel who originally carried out the census enumeration in these production teams and resident groups were not selected as sample survey enumerators . The sample check mentioned above shows a net overcount of 0.1S per thousand. On the specific issue of the dependence of the census on the register, Li writes that the census included (1983a:339-340): 1. De jure population: 990,658,313 2. Persons who lived in the local area for more than one year but whose residence is registered elsewhere: 6,364,518 Persons who have lived less than one year in the locality but have left their place of registered residence for more than one year: 210,322 4. Persons who are living in the locality but whose residence registration is still pending: 4,754,602 Persons who originally lived in the locality but are working or studying abroad and have no residence registration: 56,930

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17 The population of types 2 through 5 totals 11,386,372. These are persons who are not included in the local household registration books. The 4.75 million persons whose household registration is still pending have not been omitted from the census enumeration. They are listed as the fourth type and are included in the census population total. The figures given above are sufficient evidence that the population census is absolutely not a repetition of the household registration. Features of the 1982 Fertility Survey. The large- scale survey of fertility conducted by the State Family Planning Commission in September 1982 (described in Xiao, 1983), had a reference date of July 1, the same date as the census. The sample frame was the census listing itself. It was a stratified self-weighting cluster sample, covering all households in 815 areas: 732 rural production brigades and 83 urban residents' committees. The total population in the survey was a little more than 1 million, involving a sampling fraction of about 1/1,000. The choice of such a very large sample size was based on the calculated number of respondents required to yield 95 percent confidence limits for the peak single-year age- specific fertility rates that would differ by only 5 percent from the rate calculated from the sample, after allowance for the greater variance in a cluster sample than in a simple random sample.1 Because the sample was so large, estimates of age-specific fertility rates and rates of first marriage by single years of age extending back into the 1950s have remarkably low sampling variabil- ity. The estimated annual total number of births in China (and the associated crude birth rates and total fertility rates) are derived from the reported numbers of births in the sample, which range from about 15,000 for each year in the 1950s to more than 20,000 for 1981. The sampling standard deviation of such large numbers is no more than about 1 percent. The survey had two parts, the survey of the de jure population to establish the composition of the households included in the sample and the detailed survey encom- passing a variety of information about "qualified women~-- all women aged 15-67. Data on the de jure population was copied from the results of the census, with verification of changes that might have taken place since July 1 using sources in the local areas (presumably the registers plus

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18 local informants). But great emphasis was put on the requirement that the survey of qualified women should be conducted by face-to-face interviews. The instructions on obtaining information in these interviews were explicit and detailed. They included specifications that all ages shall be entered in completed years and all dates in the solar calendar. An explanation of the relations among animal symbols, Chinese ages, solar ages in completed years, and solar and lunar calendars was included. QUALITY OF DATA Data By Single Years of Age Consistency of the Census Age Distributions. Figure 4 shows the proportion of women surviving from one census to the next classified by single years of age at the earlier census: the survival ratios are for 1953 to 1964 and 1964 to 1982. Also shown in Figure 4 are survival ratios extracted from a life table expressing the propor- tion that would survive from birth to each age in a hypothetical cohort subject to the average mortality rate at each age for the intercensal interval.2 The sur- prising feature of the single-year survival ratios calculated directly from the censuses is that there is so little irregularity. In most censuses the reported age distribution is distorted by what demographers call age-heaping, a tendency for too many persons to be reported at ages that respondents favor (usually ages ending in 0 or 5). However, because most intercensal intervals are either 5 or 10 years, the effect of age- heaping on survival ratios is usually dampened because preferred ages (e.g., 30 and 40) are in both numerator and denominator of the ratios. In China the intercensal intervals are 11 years and 18 years, but the survival ratios show almost no effect of age-heaping: from 1953 to 1964 the survival ratios for women aged 30, 3S, 40, 45, 50, and 60 in 1953 are slightly too low (a favored age is in the denominator) and ratios at 29, 39, and 49 are slightly too high (a favored age is in the numerator), but the effect is very small. The high survival ratio from age 0 in 1953 to age 11 in 1964 is almost certainly the result of an undercount of infants under age 1 in l9S3, possibly caused by age misstatement that inflates the number at age 1, leading to too low a survival ratio for this cohort. Other defects in the data are indicated ~ . ~ ~ . _ _

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19 1.1 1 .0 0.9 Z 0.8 0.7 ~ 0.6 0 0.5 ~ 0.4 o O 03 CC cat 0.2 0.1 o 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 o 0 10 20 30 Censuses of 1953 and 1964 - at, \ 40 50 60 70 80 85 AGE Censuses of 1964 and 1982 1 _ 1 1 1 1 1 ~1 , 40 50 60 70 80 85 0 1 0 20 30 AGE FIGURE 4 Proportion of Females Surviving Between Successive Censuses for Each Age (solid line is proportion derived from intercensal life table, dotted line is ratio taken directly from the census enumerations): China

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20 by survival ratios above 1.0 at ages 2 and 4 in 1964-82 and at age 15 in 1953-64. The limited fluctuations in the survival ratios indicate highly uniform completeness of coverage by age and extremely limited age misreporting. That very accurate information about age can be obtained from a Chinese population is well known. The reason is a cultural one. People of East Asian culture (Chinese, Japanese, Korean, etc.) almost universally know their date of birth, even when illiterate, usually in terms of the animal year of birth (in a cycle of 12 animals and S different qualities for each animal, a complete cycle that repeats every 60 years) and the lunar month. Because of this knowledge, if age is determined through a question asking the date of birth, followed by use of a formula that converts the animal year and lunar month to a Western date, age can be determined with precision. Evidently, such a procedure was used in all three censuses. Consistency of Census and Fertility Survey Data. The data collected and tabulated from the large-scale fer- tility survey conducted by the Ministry of Family Planning in 1982 are even more remarkable than the census data in their internal consistency. The published tables include rates of childbearing by single years of age and single calendar years for women aged 15-49 for the years from l9SO to 1981. Analogous rates of first marriage by age are also included in the publication. These rates are derived directly from the births and marriages reported in the survey; because the dates of events are accurately reported, the age of each woman at the time of marriage and of each birth is readily determined. The listing of birth rates by age of woman makes it possible to construct an annual series of the total number of births in China for each calendar year from 1950 to 1981. In order to construct that series, the number of women by single years of age from 15 to 50 in each calendar year is calculated by interpolating between the number in each cohort recorded in two censuses. That is, one can determine with good precision (on the assumption that the censuses are accurate) the number of persons at age 15 in 1954 by subtracting from the number 14 in 1953 one-eleventh of the decrease in this cohort between its enumeration in 1953 at age 11 and its enumeration in 1964 at age 25.3 The number of births that occurred in each year is then calculated by

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21 multiplying the number of women at each age (determined through cohort interpolation of census data) by the age-specific rate of childbearing taken from the fertility survey and summing these births for all women aged 15-49. (The number of women classified by single years of age from 15-49 in each year appears in Table A-1. Tables that contain primarily raw data or large sets of calculated data are included in the appendix.) The numbers of births so calculated from 1951 to 1981 permit a sensitive test of the consistency of the fertility rates from the survey with the data on age distribution in the censuses of 1964 and 1982. For example, the number of persons at age 5 (i.e., between exact age 5.0 and exact age 6.0) in 1964 must equal the number born between July 1, 1958, and July 1, 1959, multiplied by the proportion who survived from birth to age 5.4 The number of persons aged 23 in 1982 must equal the number at 5 in 1964 in this cohort multiplied by the proportion who survived from 1964 to 1982. Appropriate survival rates have been extracted from intercensal life tables derived from the censuses and the estimated numbers of births. In short, there are two sets of numbers for the population classified by single years of age from 0 to 11 in 1964 and from 0 to 29 in 1982. One set is taken from the census and the other from estimated births and survival rates from the survey--the births calculated from retrospective fertility rates combined with interpolated numbers of women and the survival rates from intercensal life tables. In Figure 5 the two sets of numbers are compared. The agreement is extraordinary, especially since the reallocation of births from calendar year to fiscal year is necessarily only approximate and would be so even if the number of calendar-year births were exact. Abnormal Ratios of Men to Women in Census and Survey Data Omission of Males from the Census Age Distributions. A systematic deficiency in the reported age and sex distributions in the Chinese censuses becomes evident when the ratio of men to women at each age is plotted. Such plots are shown in Figures 6 and 7. In each census it is apparent that the number of males in the young adult span--from 16 to 40 in 1953, from 16 to 24 in 1964, and from 16 to 23 in 1982--is too low, because of the

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22 30 25 20 a o ~ 15 cam o cam 10 5 To t 1 964 t 0 5 10 1 1 1 1 1 15 20 25 30 AGE FIGURE 5 Number of Persons Under Age 30 in 1982 and Number of Persons Under Age 11 in 1964 (in millions) by Single Years of Age, as Projected (solid line) and as Enumerated in the Census (dotted line): China omission of males, mostly those who are in the army. The 1982 census lists the number of males and females in the army, although without giving their ages. The number in the army is 4.2 million, of whom 109,000 are female. In 1953 the news release that reported the conduct of the census gave a population of 574.2 million who were "directly enumerated," and an additional 8.4 million who were indirectly enumerated. The recently released single-year age distribution for 1953 totals only 567.4 million. The 6.8 million difference between the total for which an age distribution is released and the total that was directly enumerated may be taken as the number of persons in military service. Ostensibly the 1964 census included the army, but it is evident from the ratio of males to females in the ages of principal military service that a large number of males at these ages were omitted. In less and 1982 an adjusted age distribution was constructed by allocating the known or estimated number of persons in the armed services age by age, using a rough estimate of the ratio of males to females at each age based on the ratio at ages prior to the range of military service and the ratio at ages above

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28 TABLE 1 Annual Number of Births (in millions) from Official Figures and as Calculated from Fertility Rates in Survey and Interpolated Populations, and Estimated Completeness of Reporting, 1953-82: China Number of Births . Completeness Year Official Calculated of Reporting 1953 21.51 24.54 .877 1954 22.45 25.76 .877 1955 19.79 25.94 .763 1956 19.76 29.45 .808 1957 21.67 27.13 .799 1958 19.0S 24.16 .788 1959 16.47 18.48 .892 1960 13.89 17.38 .799 1961 11.88 14.52 .818 1962 24.60 26.78 .918 1963 29.54 33.53 .881 1964 27.29 28.01 .974 1965 27.09 27.94 .968 1966 25.77 29.28 .880 1967 25.63 25.35 1.011 1968 27.57 31.48 .878 1969 27.15 28.68 .947 1970 27.36 29.98 .913 1971 25.67 29.07 .883 1972 25.66 27.49 .933 1973 24.63 26.14 .942 1974 22.35 25.26 .885 1975 21.04 22.70 .927 1976 18.54 21.64 .857 1977 17.87 19.97 .894 1978 17.45 19.96 .873 1979 17.27 20.95 .824 1980 17.99 17.74 .844 1981 17.46 21.05 .830 1982 (21.26) (21.56)

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29 1.10 1 .05 _ _ 1.00 in in LL ~ 0.95 LL 0.90 0.85 0.80 _ 0.75 1950 1955 1 960 1965 1 970 1975 1 980 1 985 ~~ o o TV YEAR FIGURE 8 Completeness of Recording of Births (dotted line is 3-year moving average), 1953-81: China Note: Circles designate years with 13 lunar months. The moving average of completeness rises from about 80 percent in the mid-1950s to above 90 percent from 1963 to 1974; there is a decrease in completeness to less than 85 percent for years in the late 1970s. The official pres- sure for restriction of the number of births probably led to incomplete recording in those later years, both by parents fearful of penalties and by officials eager to meet targets. Official Records of Death Rates. The completeness of death registration for each intercensal period as a whole can be estimated on the basis of the total population recorded in each census and the total number of births found to occur in each intercensal period. The differ- ence between the total number of births between two censuses and the intercensal growth in population is the total number of deaths in that interval. The figure used for 1953 in these calculations includes the 8.4 million officially reported as indirectly enumerated; the 1964 figure includes an estimated 2.35 million young males omitted from the census, an estimate obtained by cor- recting understated ratios of males to females from age

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30 16 to age 24; and the 1982 figure includes the official number in the armed service, whose ages were not reported. The number of deaths calculated in this way can be compared with the number implied by official figures for the population each year and with the annual death rate (State Statistical Bureau, 1983b). The calculations are as follows: Period 1953-64 1964-82 Calculated Births (millions) 265.4 Intercensal Increase in Population (millions) 114.3 Calculated Deaths (millions) 151.1 Official Number of Deaths (millions) Completion of Recording of Deaths (percent) 448.6 311.3 137.3 93.7 0.620 115.8 0.843 The aggregate completeness of recording of deaths is 62.0 percent for 1953-64, and 84.3 percent for 1964-82. The degree of understatement, especially in the earlier period, is surprising, but it is hard to see how the omission of deaths could in fact have been much less. The consistency between the calculated annual births and the census enumerations by age was noted earlier; besides, it seems unlikely that respondents in the fertility survey overstated the number of births that had occurred to them. This possibility is especially remote because of the extraordinary agreement (mostly within 1 percent) between the number of children ever born by five-year age intervals constructed from the survey and the number reported by women in the same intervals in the 1982 census. The annual number of births estimated for the intercensal years incorporates the census populations as the source of the estimated number of women at each childbearing age, so that the birth estimates are

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31 necessarily consistent with the increasing population from one census to the next (if the fertility rates are correct). The other possible source of an overestimate of the omission of deaths in the official data is under- statement of the intercensal increase in population--an understatement that would imply that the earlier census was a more complete count than the later one, which is unlikely. Comparison of the total number of registered births with the estimated total for the same intercensal periods leads to an estimate of average completeness of birth registration of 84.2 percent in 1953-64 and 91.2 percent in 1964-82. If a large fraction of the omitted births were births soon followed by an infant death that also went unrecorded, much of the estimated underrecording of deaths would be accounted for. The estimated number of unrecorded births in 1953-64 is 41.9 million, and the estimated number of unrecorded deaths is 57.4 million; the corresponding numbers for 1963-82 are 40.4 million unrecorded births, and 21.5 million unrecorded deaths. These calculations are sensitive to the relative completeness of enumeration in the census. For example, if the 1964 census was undercounted by 2 percent more than the other two censuses, the calculated intercensal births would be increased by about 1 percent, the 1953-64 increase in population would be augmented by 13.9 million, and the 1964-82 increase would be diminished by the same amount. The estimated completeness of death recording would then be 67 percent for 1953-64 and 74 percent for 1964-82. In the analysis of mortality in Chapter S. three other sources of data are used for comparative purposes. One is an epidemiological survey conducted throughout China in 1973-7S in which deaths by age and sex and an age distribution of the population were recorded; the second is another large-scale survey in 1978 covering a sample population of over 100 million, reported in System Engineering and Science Management (Beijing) February, 1980, and the third is a life table constructed from the deaths in 1981 recorded in the 1982 census. Data on Children and Marriage Consistency of Survey and Census Data on Number of Children Ever Born. In addition to the consistency test described above (nConsistency of Census and Fertility

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32 Survey Datan), a second test of the consistency of the age-specific fertility rates derived from the fertility survey and the 1982 census provides further evidence of very precise data. The age-specific fertility rates presented in the report of the survey for calendar years of time are converted into estimated fertility rates for _ fiscal years (July 1 to June 30) by a simple arithmetic average of the rates in two consecutive years. The rate of childbearing for women aged 15 in 1977-78, plus the rate of those aged 16 in 1978-79, plus the rate of those aged 17 in 1979-80, plus the rate of those aged 18 in 1980-81, plus the rate of those aged 19 in 1981-82 equals the average number of children ever born to women reaching exact age 20 in the middle of 1982.6 By an analogous summation the estimated number of children ever her n Pm women of each exact ace from 16 to 65 can be ascertained. Then the average number of lifetime births of women at conventional single-year age intervals (15-16, 16-17, etc.) can be obtained by averaging (but using the geometric mean for the number born to women below age 20, to allow for the nonlinearity of the increasing number of children ever born at the youngest ages). Finally, the average number of children ever born to women at age 15 can be multiplied by the number of 15-year-olds in the 1982 census; the sum of such products for ages 15 through 19 yields the total number of chil- dren ever born to women aged lS-l9. In Table 2 the total number of children ever born to women by five-year age intervals from ages 15-19 to 55-59 as constructed by this procedure is compared with the total number of children ever born reported by women in these age intervals in the 1982 census. The degree of consistency is remarkable: at 15-19 and 20-24 the constructed number of children ever born is within 2 percent of the census number; above age 25 for every age interval the agreement is within 1 percent. Consistency Between Survival Rates of Cohorts and l Proportion of Children Ever Born Reported as Surviving. - William Brass was the originator of a widely used system for estimating child mortality from the fraction of children reported as surviving among the children ever born to women at different ages (Brass, 1968; United Nations 1983). One estimates the fraction of births that occurred to women in each time interval before a census or survey and selects a mortality schedule (e.g., from model life tables) that would yield the reported

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33 TABLE 2 Total Number of Children Ever Born to Women Classified in Five-Year Age Intervals, 1982: China Number of Children Ever Born (millions) From 10 Percent Constructed from Sample Tabulation Age-Specif ic Fertility Ratio: Age of Women of Census Rates in Survey Survey/Censu s 15-19 0.873 .859 .984 20-24 15.29 15.08 .986 25-29 71.27 71.51 1.003 30-34 96.68 96.66 1.000 3 5-39 97.36 96.92 .996 40-44 104.67 104.00 .994 4 5-49 119.54 118.62 .992 50-54 109.42 109.03 .996 5 5-59 90 .79 90 .81 1.000 proportion surviving, given the time distribution of the births. If c(a) is the proportion of the children ever born to women aged 25-29 who were born "a" years before the census or survey and p(a) is the fraction of these children surviving from birth to the census or survey date, then the overall proportion surviving, P. neces- sarily equals i0 c(a)p(a)da, when ~ is the time between the earliest birth and the census date. Brass' technique is to estimate c(a) from information about the fertility history of the women in question, and by trial and error (or the logical equivalent) to select a survival function, p(a), that is consistent with the reported proportion surviving among the children ever born to these women. In the 10 percent sample tabulation of the 1982 census there are tables listing the number of children ever born alive, and the number of children surviving, for women classified in five-year age intervals from 15-19 to 55-59. For each age group of women the fraction of the children they have borne that were born in each year prior to the census can be determined from the age- specific fertility rates recorded in the fertility survey (which had the same effective date as the census). Consider women at exact age 20 in mid-1982: The births

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34 they had at age 19 occurred in 1981-82, those they had at age 18 in 1980-81, at 17 in 1979-80, at 16 in 1978-79, and at 15 in 1977-78. From age-specific fertility rates, one can calculate the fraction of births to those women that occurred at specified single-year periods in the past. A similar calculation can be made for women at exact age 18 in 1982; an average of the fraction in each period for those aged exactly 18 and those aged exactly 19 is a robust estimate of the fraction born in each period to women who were 18-19. Combining such calcula- tions for women aged 15-16, 16-17, 17-18, 18-19, and 19-20, one obtains an estimate of the fraction of the children born alive by women 15-19 whose birth occurred in 1981-82, the fraction whose birth occurred in 1980-81, etc. The proportional distribution of births by fiscal year before the censuses, calculated in this manner, is shown for each group of women from 15-19 to 50-54 in Table A-3. The distributions in Table A-3 are single-year interval tabulations of the function c(a) that is combined with the proportion surviving, p(a), in the Brass equation: proportion surviving = i0 c(a)p(a)da. It would be possible to try different cohort survival functions and choose which among a set of possible p(a) functions is consistent with the proportion surviving reported in the census. Instead, a value of p(a) for each birth cohort is taken from Table 3, in which the survival ratio from birth in a given year to enumeration in 1982 has been calculated as the ratio of (lNa)82/B(82-a), where (lNa)82 is the number enumerated at age a to a + 1 in 1982, and B(82-a) is the number of fiscal-year births a years before mid-1982. The fiscal-year births are based, in turn, on interpolated populations of women of childbearing age and age-specific fertility rates for each year in the past from the fertility survey. In other words, instead of using the Brass equation to chose a p(a) function from some arbitrary set of such functions, the equation is used to calculate the proportion of children surviving among the children ever born to women in each f ive-vear ace interval. ~ _ ~ _ The determination of proportion surviving uses a c(a) for each age group of women derived from their fertility histories and a p(a) for each cohort derived from the census enumeration and estimated births. The result is a set of constructed proportions surviving (based primarily on the fertility histories from the survey) that can be compared with the proportions reported in the census. The comparison is shown in Table 4.

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35 TABLE 3 Estimated Fiscal Year Births, 1951-52 to 1981-82, Number Recorded in Corresponding Cohort in 1982, and Proportion Surviving: China Fiscal Year Number in Age in Year of Births Census Proportion 1982 Birth (millions) (millions) Surviving 0-1 1981-82 21.71 20.81 .959 1-2 1980-81 18.93 17.38 .918 2-3 1979-80 19.06 18.27 .959 3-4 1978-79 20.87 19.62 .940 4-5 1977-78 19.63 18.63 .949 5-6 1976-77 20.67 ~ 19.42 .939 6-7 1975-76 22.07 20.42 .926 7-8 1974-75 24.00 21.78 .907 8-9 1973-74 25.86 24.03 .929 9-10 1972-73 26.73 25.09 .938 10-11 1971-72 28.33 25.22 .891 11-12 1970-71 29.88 27.33 .915 12-13 1969-70 29.09 26.50 .911 13-14 1968-69 30.68 28.24 .920 14-15 1967-68 28.28 24.52 .867 15-16 1966-67 26.72 22.74 .851 16-17 1965-66 28.10 25.97 .892 17-18 1964-65 27.11 24.78 .915 18-19 1963-64 31.61 25.78 .815 19-20 1962-63 32.38 28.59 .883 20-21 1961-62 19.46 16.59 .852 21-22 1960-61 14.28 11.20 .784 22-23 1959-60 17.57 14.51 .826 23-24 1958-59 21.08 14.29 .678 24-25 1957-58 26.69 19.45 .729 25-26 1956-57 25.97 18.89 .727 26-27 1955-56 24.88 17.92 .720 27-28 1954-55 26.20 19.67 .751 28-29 1953-54 25.00 18.62 .747 29-30 1952-53 25.52 17.49 .685 30-31 1951-52 24.44 17.36 .711 The agreement between constructed and reported proportions surviving is remarkably close for women aged 25-29 to 40-44. The deviation at the youngest age intervals (under age 25) is explained by the fact that survival of children is not independent of age of mother. The construction for women aged 15-19, for example, uses the estimated survival ratio for all births in 1981-82, 1980-81, and 1979-80; but in fact the infant

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36 TABLE 4 Proportion of Children Surviving Among Children Ever Born Alive to Women Aged 15-19 to 50-54, 1982: China Age of Constructed from Reported Woman Fertility Survey in Census 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 .920 .938 .936 .925 .903 .877 .843 .801 mortality rate among first births and among children born to very young women is higher than the general infant mortality rate. The deviation at ages 45-49 and 50-54 may be caused either by a slight overstatement of pro- portion surviving in the census reports by older women or by a slight overestimate of births in the early 1950s (for which the fertility rates of older women are not based on retrospective data because of the age limit of 67 years in the survey). Another possibility is that at higher ages differential mortality among mothers may have left respondents with relatively favorable mortality experience and with children who also had higher than average survival rates. The basic agreement between reported and constructed proportions attests to the probable validity of the cohort survival ratios--not to the validity of individual ratios, but to the average survival of groups of cohorts. Individual survival ratios can be in error because the estimation of fiscal-year births involves an arbitrary element and because of slight deviations of the reported time of birth caused by incomplete adjustment from the lunar to the solar calendar. Consistency of First-Marriage Rates and Marital Status Data. When the single-year rates of first marriage are cumulated for persons aged 15 in year t, 16 in t + 1, and 17 in t + 2, the resultant sum is the proportion of ever-married women at exact age 18 at the end (December

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37 31) of year t + 2. By such cumulations the proportions of ever-married women at age a and a + 1 at the beginning and end of each year can be determined; the average of these four numbers is an estimate of the proportion of ever-married women in the middle of the year of those between ages a and a ~ 1. The proportion of ever-married women aged 15-35 from 1950 to 1981 calculated in this way is shown in Table A-4, which also lists the proportion of ever-married women in 1982 as ascertained in the de jure listing of households. The series of constructed proportions in 1980 and 1981 are very similar through age 19 to the reported proportion in 1982; above age 20 the increase in proportion married from 1980 to 1981 and from 1981 to 1982 reflects the rise in first-marriage rates. The proportion of ever-married women by age are tabulated at 15-19 and by single year of age from 20 to 29 in the 10 percent tabulation of the 1982 census. For women aged 22 to 29 the proportion ever-married in the survey differs by at most 0.005 from the proportion in the census, but for women aged 15-19 the proportion is 2 percent greater in the survey (.062 compared with .042), and at 20 and 21 the proportion ever married in the survey exceeds the proportion ever married in the census by 1.2 percent and 0.9 percent, respectively. In the survey the enumerators were instructed to include as married those for whom no marriage certificate had been issued but who were recognized as being married by the family and the society (Xiao, 1983). This explainable difference is further evidence that data for the census and survey were not simply copied from the same register. Quality of Data: Summary A number of results have emerged from this examination of the quality of Chinese population data. The most important is the good but not perfect accuracy of the fertility and marriage information collected in the large-scale fertility survey. The retrospective fertility data provide the basis for constructing an annual series of births and birth rates, which is an addition to the published total fertility rates. The number of births in this series exceeds the number of births listed in official sources by a substantial margin; the fertility data could not have been copied from registers. In fact, the synchronism of low points in the ratio (of the number of officially reported births

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38 to the number of calculated births) with years containing 13 lunar months is evidence that the fertility histories were obtained from respondents. In addition, there is a slight systematic bias in the time sequence of total fertility rates--which are too high in years with 13 lunar months. Further evidence of the independence of the survey from the register (and the census) is found in the higher proportion of ever-married women in the survey than in the census at young ages, a natural result of instructions in the survey to include married persons whose marriages had not been registered. The consistency of cumulative fertility in the survey with the number of children ever born in the census is so close that independence is hard to believe. Nevertheless, there is no doubt, given the explicit nature of the instructions, the overreporting of births in 13-month years, and the excess of births reported in the survey in comparison with the official reports, that the detailed fertility history was in fact obtained by interviews with the qualified respondents. The interviewers might have had access to the total number of children ever born that the respondent listed on the census and might have probed for an omitted birth when the total number reported was less than the census response. But if the detailed fertility history yielded one more birth than the census, the interviewer would have been unlikely to scratch one birth from the survey form and it would not have been impossible to add one to the census. Moreover, the latter would have an inconsequential effect on the census results since the survey was a 1/1,000 sample. The congruence of the proportions dead among children ever born constructed from the calculated birth sequence and the proportions dead reported in the census is powerful evidence of the validity of the birth sequence. It supports, indeed, the approximately equal coverage of the 1964 and 1982 censuses since the constructed survival rates for children born to women aged 40-44 are heavily weighted by the births estimated around 1964. If the 1964 census had been undercounted relative to 1982, the number of births around 1964 would have been under- estimated, the survival rates to 1982 would be too high, and the constructed proportion surviving for women aged 40-44 would exceed the reported proportion. With some minor exceptions, then, the fertility and nuptiality information taken from the census and survey can be accepted as of high quality; as such, they provide the basis for a valid history of recent trends in China.