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Average age ratio method and age heaping in Chinese censuses

of age reporting is also affected by census enumerators and the household registration management and archiving, these
errors are often systematical biases and thus may not generate “age heaping” in practice.
1.1. Common Methods for Checking Age Heaping
Some common methods to examine the data quality of age reporting in census include the Whipple’s Index (Whipple,
1919), the Myers’ Blended Index (Myers, 1940), the Bachi’s Index (Bachi, 1954), the Carrer’s Index (Carrier, 1959),
the Ramchandran’s Index (Ramachandran, 1965; Shryock and Siege, 1973), and the UN Age-sex Accuracy Index
(United Nations, 1952). The Whipple’s and Myers’ Blended indexes are among the most commonly used methods to
check digit preferences or age heaping (Spoorenberg, 2007). The conventional Whipple’s Index checks digit preferences
for ages ending with digits of 0 and 5, and the modified Whipple’s Index could check digit preferences for ages ending
digits other than 0 and 5 (Spoorenberg, 2007). The Myers’ Blended Index also can be used to check digit preferences.
The UN age-sex Accuracy Index is designed to assess the overall quality check of age reporting, not particularly for
checking age heaping (United Nations, 1983). The details of these methods and their applications can be found in common
demographic textbooks and above literature, and thus, they are not repeated herein.
In the existing literature, the age ratio method is only used in checking a segment of age ranges such as the adjacent
five ages, instead of the whole age range at adulthood ages, such as the Whipple’s Index, and thus it has not commonly
been used to check digit preferences in age-reporting. In this study, we argue that age ratio method may be a good
alternative for checking the digit preference or age heaping in age reporting from population censuses, vital registration,
and/or sample surveys with large-scale and high representativeness.
1.2. Literature on Age Heaping Studies in China
Age heaping in China’s censuses has been frequently considered as one major research theme among Chinese demographers, with
a vast majority of studies using the Whipple’s Index (Guo and Che, 2008; Li, 2012; Ma, 1984; Qiao, 1993; Qiao and Li, 1993;
Li, Qiang and Yang, 1993; Wang, 2012; Wu and Gan, 2013; Yang, 1988; Zha and Qiao, 1993; Zhai, 1987). Most of these studies
revealed that the overall age heaping was minor in Chinese censuses, with a few exceptions in the ethnic minorities. Enlighten
by Keyfitz’s “demographic discontinuity” theory (Keyfitz, 1987), Huang (1993, 2009), and Huang and Xiao (2009) investigated
the digit preference through calculating the frequency of distribution of signs (+/-) on each digit based on the age-specific first- or
second-order difference in its proportional share of population. The first-order difference in the population proportion for age x
is the difference in population between age x and age x+1. One limitation of this method is that a negative sign of a given age x
can be due to underreports at age x, or due to overreports at age x+1, or due to both. The second-order difference is the difference
between age x, age x+1, and age x+2, which also suffers from the limitation above. Nevertheless, all these previous studies have
contributed to our understanding of age heaping and the accuracy of aging reporting in censuses of China.
Except for the Huang’s method of differential signs, all methods assume that the changes of the study population
are in a stable and smooth manner. For example, both the conventional and modified Whipple’s Indexes assume that the
population change linearly (Spoorenberg, 2007). If the population changes were not smooth, both the conventional and
modified Whipple’s Indexes would produce somewhat biased results. However, affected by natural disasters, extreme
weathers, and birth planning policies since the 1950s, the population of China witnessed irregular changes in annual
births and deaths. Such irregular population changes will bring forward errors in the application of the routine methods
and undermine the research validity in demographic analyses. Another limitation of these methods is the lack of validation
across multiple censuses. A more effective method is thus needed to investigate digit preferences for populations with
irregular changes, and for age heaping in general as well as at some specific ages. This paper proposes an extended age
ratio method to fill this gap and uses the census data of China for an empirical illustration and validation.

2. Data and Method

We used an extended age ratio method, consisting of the average period age ratio (APAR) and the average cohort age ratio
(ACAR), to examine age heaping for Chinese censuses in the years of 1953, 1964, 1982, 1990, 2000, and 2010. The data of single
year of age by sex in these six censuses were obtained from the National Statistical Bureau of China (1983, 1992, 2002, 2012).

2.1. Average Period Age Ratio (APAR)
• Step 1: Calculate the period age ratio
For a given census, we calculate age ratio for a certain age based on the five consecutive single years of age (three,
seven, or nine ages are also applicable):

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