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OCR for page 12
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
OCR for page 13
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
OCR for page 14
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.
OCR for page 15
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):
OCR for page 16
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
OCR for page 17
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
OCR for page 18
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
~ . ~ ~ . _ _
OCR for page 19
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
OCR for page 20
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
OCR for page 21
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
OCR for page 22
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
OCR for page 28
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)
OCR for page 29
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
OCR for page 30
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
OCR for page 31
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
OCR for page 32
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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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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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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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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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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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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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.
Representative terms from entire chapter:
fertility rates
