Page 28 - IJPS-5-1

Average age ratio method and age heaping in Chinese censuses

household registration systems, the age heaping phenomenon in China will eventually diminish. Second, there existed
a preference for specific ages in certain periods of time, which was mainly related to the implementation of some
age-related policies such as regulation on the minimal legal ages of marriage, childbearing, and retirement. People
likely intentionally misreported, typically over-reported, their ages to meet the age thresholds of these policies. Last,
we found that, although the preference for ending digit of age declined after 1990, inconsistencies of age reporting
across censuses had indeed increased. This suggests that the overall data quality of age reporting in the 2000 and 2010
censuses likely decreased, which may be due to the increased domestic migrations that made it difficult to enumerate
accurately in censuses after 1990. More research is clearly warranted for more insights on this theme.
Using data from Japan and Sweden, two countries with the best quality of demographic data, we show that the APAR
method has similar properties as the modified Whipple’s Index (Noumbissi, 1992; Spoorenberg, 2007). However, we
also acknowledged the limitation of both the Whipple’s Index and the APAR method. When population changes are
not smooth (due to significant differences in births, deaths, and migration), it may not accurately reflect age heaping if
the direct calculation of the ratio or the index is used (Barrett, 2019). That means, when applying these two methods to
identify the age preference/avoidance, it is necessary to consider the historical background of the specific birth cohort
or time period in the study population, to clarify whether the observed age heaping is due to misreporting or is due to
particular historical events such as wars that caused the major cohort differences. As a result, we suggest taking the birth
cohort size into the calculation as an adjusting factor if such data are available and relatively reliable.
However, cautions are needed for a few issues on applying the APAR and ACAR methods. First, the calculation of
ACAR must be based on two or more censuses, to capture the degree of the age preference/avoidance or age reporting
consistency. Since the general preference/avoidance for ending digits of age is mainly driven by the cultural tradition
and custom, which are difficult to change, the age preference/avoidance at the same age or same digit is generally
comparable between adjacent censuses when the censual interval is relatively short. (e.g., less than 20 years). Second,
when the censual interval is exactly 10 years, unless ACAR is adjusted by the size of the birth cohort, the utility of
this method could be weakened. However, in this case, the method is yet helpful to examine the consistency of age
registration and reporting in multiple censuses. Third, when using the cohort age ratios to identify the preference/
avoidance of the ending digits of age, it is ideal to combine with the period age ratios, and if possible, it is also good
to adjust the cohort age ratios by the number of births of the cohort if such data are available and relatively reliable
(Equation 1a). Otherwise, it may be difficult to clarify whether there really exists digit preferences or digit avoidances
in age-reporting. Fourth, the criterion used for assessing the levels of a preference/avoidance in the present study is
quite arbitrarily. We suggest using a combination of criteria of different age ratio methods to determine the level of
age heaping in the study population(s). A systematic examination using various data sources with the known quality
(e.g., data from human mortality database) is also warranted to shed light on this issue. Fifth, the average age ratio
is not reliable, especially after age 90, when population numbers vary greatly across ages. Other methods are thus
needed for analyzing and detecting age heaping in age-reporting among older and very older people. Sixth, as the
preference/avoidance of a certain age may be a response to certain policies and the preference for a certain ending
digit of age may mainly come from customs, it is recommended to pay attention to both situations when investigating
age heaping. Seventh, the large scale of international migration in some countries may produce a bias in detecting the
digit preference in age-reporting in censuses if such migration is not evenly distributed across ages. This makes up
a challenge to assess the age heaping in such countries. This is also the case for examining the age heaping in sub-
national populations when domestic migration is relatively large.
Our approach presented in this study uses age ratios calculated from five adjacent ages. To test its statistical sensitivity,
we also examined the situations of three, seven, and nine adjacent ages. The tests produced similar outcomes and
supported the effectiveness and robustness of age ratios based on five adjacent ages. Furthermore, besides the census data
as illustrated in the current study, the method can also be applied to data obtained from vital registration or even surveys
if its coverage and representativeness are adequate.
In sum, APAR and ACAR are likely good alternative methods for the traditional or the modified Whipple’s Index to
study the digit preference/avoidance in age reporting. Both the APAR and ACAR methods can be applied to ages beyond
adulthood ages used by the Whipple’s Index as long as the population changes are smooth. If APAR is adjusted by the
size of birth cohorts, it would better reflect ending digit preference in age-reporting. ACAR could also be used to test the
consistency of age registration/reporting across multiple censuses if the birth registration data quality is reasonably good.
However, the limitations of this method abovementioned still suggest a need for new and better methods for examining
the age heaping.

22 International Journal of Population Studies | 2019, Volume 5, Issue 1