Note on the population size at age 0 in Taiwan
The problem: increasing population size for each cohort?
The population and vital statistics of Taiwan in the postwar period, which are
based on the household registration and censuses, have usually been considered to be
quite good (Speare, et al., 1975).
One problem, however, is with the population size at age 0.1 Table 1 shows the
population size of various cohorts increases, rather than decreases due to deaths, over
time. For most cohorts born after 1950, the differences in size between age 0 and age
1 are particularly noteworthy.
Table 1 Population of different cohort at age 0-9, Taiwan Area, 1950-2000
age
b.1950
b.1960
b.1970
b.1980
b.1990
b.2000
0
146,401
190,968
172,981
181,047
154,594
139,256
1
148,596
193,161
183,217
195,673
160,414
145,895
2
145,313
192,804
184,665
196,719
160,921
145,838
3
144,326
192,236
185,450
197,229
162,330
145,797
4
144,273
192,367
185,297
196,766
160,687
145,767
5
144,195
192,516
185,276
197,362
159,440
145,743
6
143,268
192,249
186,026
196,052
158,953
145,723
7
143,176
192,426
185,941
196,115
159,234
145,705
8
143,245
192,973
185,228
195,905
159,377
145,689
9
143,444
193,048
185,267
196,155
159,339
145,675
Figures in boldface: an increase from the previous age
Source: Ministry of Interior
The causes
Delay in registration is the main reason. Migration could account for very little
of the strange phenomenon. Although there are no figures of migration by age, net
international migration is between –52,055 to +36,978 in 1991-2004 for all ages,
1
After reviewing previous studies, Speare et al. (1975, p.72) concluded that “the birth and death
registration are excellent with the exception of infants who die soon after birth.”
which is only –0.5%-0.34% of total population.2 Net domestic migration from the
two offshore islands belonging to Fukien, i.e., Kinmen and Matsu, to the so-called
“Taiwan area” that include the Taiwan island and offshore islets belong to the Taiwan
province, is also negligible. The number ranges from –2,215 to +4,808 persons per
year in 1991-2004.
Other factors also affect the accuracy of cohort size, which include delayed
registration, under-reporting or errors in registration of births and deaths. The
registration of deaths is relatively more prompt and more accurate than the
registration of other vital events, because it involves insurance, pension, and other
rights to the family. In addition, death registration is required before burial, cremation
or the use of a funeral home. Nevertheless, neonatal deaths which occurred before
birth registration are often under-registered (TPS, 1973, p.10). A study of selective
areas in Taiwan indicated that unregistered neonatal deaths were about 20% as much
as registered neonatal deaths in 1962-1963, though the impact on death rate by age 0
is less than one percentage point (TPS, 1970).3
Besides the under-reporting of neonatal births and deaths, a more important
explaining factor is the delay in birth registration. Due to the working of the
household registration system, registered births in the current year include the births
of delayed registration. More clearly, the registered births consist of not only babies
zero year old, but also children 1, 2 or several years of age. In the year-end population
statistics, such registered population is tabulated in the appropriate age groups so that
the size of a cohort as shown at age 1, 2 and 3 in successive years keeps increasing.
Table 2 shows a comparison of birth registration and birth by occurrence, with the
former figure collected by the Ministry of Interior (or its predecessor) and the latter by
health departments. Table 3 further shows the degree of delay.
The cause of late birth registration is complicated4 and will be left for future
studies. Before 1998, the grace period for birth registration was 15 days, and was
lengthened to one month in 1998. There is a penalty for late birth registration in
2
3
4
The difference between the numbers of people leaving and entering the national border for age 0~14
is 700-4000 per year in the recent decade.
Sullivan (1971) also found that substantial discrepancies in infant mortality rates due to
under-registration and misclassification by to age 1 due to the use of date of registration of death
rather than date of occurrence.
Reasons may include illegal births (e.g., extramarital births), the long waiting searching period for
good names that would improve the fortune of children and so on.
Taiwan, but the low fee (NT 300 in the recent decade, which is less than USD $10)
does not make a formidable punishment.
Table 2. Registered Births by Year of Occurrence, Taiwan Area, 1970-1973
Year of Occurrence for the Registered Births
Year of
Registration
1966
and
before
Total
1973
1972
1971
1970
1969
1968
1967
Number of Births
1970
394,015
―
―
―
361,841
25,892
2,819
1,384
2,079
1971
380,424
―
―
349,724
24,471
2,690
1,383
*2,156
―
1972
365,749
―
335,060
24,217
2,633
1,361
**2,478
―
―
1973
366,942
334,307
26,226
2,433
1,366
***2,610
―
―
―
0.7
0.4
0.5
Percentage Distribution
1970
100.0
―
―
―
91.8
6.6
1971
100.0
1972
100.0
―
―
91.9
6.4
0.7
0.4
*0.6
―
―
91.6
6.6
0.7
0.4
**0.7
―
―
1973
100.0
91.1
7.1
0.7
0.4
***0.7
―
―
―
Note: *includes 1967 and before. **includes 1968 and before. ***includes 1969 and before.
Source: Table 4 in Taiwan Population Statistics, 1973, p.9
Table 3. Cumulative Percentage of Birth Registration by Time Differential
between Dates of Occurrence and Registration
Cumulative Percentage
Year
Registered
Births
Within
15 days
Within
1 mo.
Within
2 mo.
Within
3 mo.
Within
4 mo.
Within
5 mo.
Within
6 mo.
6 mo.+
1965
406,593
79.6
89.1
94.2
95.8
96.6
97.2
97.5
100.0
1967
*71,109
70.1
82.2
90.4
93.2
94.8
95.7
96.3
100.0
1969
*38,510
70.3
83.3
91.9
94.6
96.1
97.0
97.5
100.0
1971
*37,369
66.0
81.0
90.7
93.8
95.3
96.2
96.8
100.0
1972
*50,656
61.5
77.8
89.2
92.8
94.6
95.6
96.2
100.0
Source: Table 4 in Taiwan Population Statistics, 1973, p.10
How serious is the problem of late registration?
Table 2 above shows that in the early 1970s, about 92% of all births of the
current year were registered in the same year. By age 3, about 99.5% of all births are
registered. These estimates may be overly optimistic, as the sizes of the 1965 and
1966 cohorts, for example, reached the peak at age 11 and 10, respectively. In other
words, birth registrations can be delayed until age 10 or later.
Evidence about whether the delay gets better or worse over time is mixed. Table
3 shows that the degree of delay seems to increase between 1965 and 1972. In 2003,
the number of failures to register was10,648 cases, or 4% of 263,094 birth
registrations that year, which compares favorably with the 1970s as presented in Table
2.5 In any case, it is reasonable to assume that the delays may be minimal after age 7
as all children have to be registered before going to schools. And for convenience
sake, we may use age 4 or age 9 to begin the revision of population size at young ages
in order to match the format of existing data.
Extrapolation
To correct for the overstatement of survival rate at young ages, we incorporate
the information of mortality to reconstruct the cohort size. We shall use the mortality
rate at a certain age, say age 4 or age 9, to calculate backwards the end-of-year
population size of younger ages and the number of births. These are termed method (1)
and method (2) respectively.
6
For comparison, the population of age 0 at year end is
also calculated using the difference between registered births and registered death of
babies born in the same year.7 The latter is termed method (3). We did not use the
actual number of deaths because the single-age data is less complete than the
mortality rates.
Method (1) and Method (2) follow the same steps. For method (2), we begin the
calculation at age 4. The estimation of the cohort size at age 0-3 is as follows:
5
6
7
p*(3)-1
= p(4)
+ p*(3)-1
p*(a)-1
= p*(a+1)
+
x
m(4)
p*(a)-1 x
m(a+1),
for a=0~2
But there were 54,506 cases of late registration in year 1994, which is 16.91% of the number of
registered births of 322,263. The higher ratio is due mainly to the lengthening of the grace period of
registration from 15 to 30 days in 1998.
Rounding errors should not be serious, as there are five digits after the decimal in the reported
mortality rate in the abridged life table. For example, in 1970, the death rate of female at age 0 is
0.01452. As there were 172981 of newborn baby girls in 1970, the error due to rounding should be
very small.
But not including the deaths of babies at age 0 who were born in the previous year.
p*(B)-1
= p*(0) +
p*(0)-1 x
m(0),
for total births
where p(i) is the year-end population size of age i of a certain year, with p* denoting
the estimated population size, m the mortality rate, and subscript -1 the previous year.
All estimations are calculated backwards from age 4 for 1950-2002.
The single-age mortality rate in the abridged life table for 1970-2003 is provided
by the Ministry of Interior; and the single-age mortality rate for 1950-1969 is
interpolated from the abridged life table at 5-year age groups, using the ratios of 1970.
To match the geographical region covered in the Survey of Family Income and
Expenditure, we use the abridged life table for the Taiwan area.
There is plenty of room for refinement in the estimation. First, the single-age
mortality rates for 1950-1969 are just interpolated figures. No trend is fitted. Second,
we use the end-of-year population due to data availability while the model life tables
are based on mid-year population. The estimates, though rough, result in an upward
adjustment for most years. Table 4 compares the size of registered population and the
estimates of Method (1). The last column summarizes the average adjustment ratio in
1950-2002. It is clear that most of the adjustment takes place at age 0. The case for
male children is similar but not listed.
Table 4 Adjustment of Population Size in Selective Years for Females
AGE
1960
1980
1950-2002
avg diff
2000
registered
estimated
registered
estimated
registered
estimated
0
190,968
197,534
181,047
197,637
139,256
146,100
6.77%
1
193,585
194,300
197,478
202,266
134,565
134,847
0.83%
2
189,352
189,207
193,870
196,720
127,957
127,996
0.33%
3
180,472
179,702
187,504
188,543
154,528
154,582
0.12%
4
185,707
185,707
202,212
202,212
154,386
154,386
--
Female
Table 5 shows the adjustment using the mortality rate and extrapolating from age
4. A comparison of the estimated and registered population is listed in Table 4. The
results from method (1) and method (2) are rather close, and the adjustment ratios are
higher for 1970 and 1980.
Table 5 Population Size of Age 0 and Various Estimates for Females
Method
1950
1960
1970
1980
1990
2000
(0) Basic statistics: by
registration
146,401
190,968
172,981
181,047
154,594
139,256
(1) calculated from age 4,
using mortality rate
155,182
197,534
187,077
197,637
161,093
146,100
(6.00%)
(3.44%)
(8.15%)
(9.16%)
(4.20%)
(4.91%)
155,354
198,843
187,415
197,324
159,928
146,100
(6.12%)
(4.12%)
(8.34%)
(8.99%)
(3.45%)
(4.91%)
153,641
198,777
188,814
198,838
158,663
144,495
(4.95%)
(4.09%)
(9.15%)
(9.83%)
(2.63%)
(3.76%)
Female
(2) calculated from age 9,
using mortality rate
(3) calculated from
registered births
As the adjustments for age 5 and over are small, and sometimes negative using
method (2), it may be reasonable to choose method (1) for the principle of frugality.
Therefore the population of age 0-4 in 1950-2003 is revised following method (1),
while the population of year 2004 is not yet modified. Once the mortality rate of year
2004 is published, many of the figures for age 0-4 in 2001-2004 will be revised
accordingly.
References
1. Speare, Aiden Jr., Paul K. C. Liu, Kuo-shu Hwang, Ching-lung Tsay and Mary C.
Speare 1975, “A Measurement of the Accuracy of Data in the Taiwan Household
Register”, Academia Economic Papers vol. 3, no.2, pp. 35-74.
Author: An-Chi Tung
Last Revised: September 22, 2005