For the past two decades, scholars and policymakers have examined the phenomenon of China’s missing females and corresponding numbers of involuntary bachelors to better understand the causes and consequences of the state’s demographic plight. China has both a heavily skewed male to female sex ratio and faces a drastically shrinking population in coming years.

We have made the case in our research, outlined in Bare Branches and other publications, that there are harmful links between abnormal sex ratios and antisocial behavior, including crime. Two recent articles challenge this research.

The first, by Ryan Schacht, Douglas Tharp, and Ken R. Smith in Human Nature, suggests that crime is not elevated in the context of high sex ratios. See addendum for a full discussion of our problems with this work, but suffice it to say that there are major methodological issues, some of which are outlined by Ben Raffield, Neil Price, and Mark Collard in Evolution and Human Behavior. Crucial information is missing, samples are oddly chosen, apples are compared to oranges.

The second, an article by Yaojiang Shi and John James Kennedy in the Cambridge journal, China Quarterly, claims that three quarters of China’s “missing girls” were simply never registered and thus are not missing at all.

Both results run against the grain of almost 15 years of published research by scholars in several disciplines. An explanation for what may be going on in Shi and Kennedy’s result requires a longer explanation and reveals the challenges of doing demographic research.

Tracking the Unreported

For decades, surveys in China have recorded a significant female deficit in the population. According to the National Bureau of Statistics, at the end of 2015, men outnumbered women by 33.7 million. Scholars have estimated that between 15 percent and 20 percent of men in China will remain single throughout the mid- to late-21^st century, and journalists have reported on “bachelor villages” in rural areas.

There have been many attempts to explain this disparity. As the birth sex ratio began to rise steadily in the 1990s (from 114.7 boys per 100 girls in 1990 to 122.7 in 1999), scholars pointed to the widespread practice of prenatal sex selection as the dominant explanation. Shi and Kennedy’s assertion that unreported births and late registration account for some of the missing girls has also been studied.

Underreporting of births can be attributed to the substantial penalties inflicted on parents who have violated the fertility restrictions imposed by China’s fertility policy, the so-called “One-Child Policy.” In 2003, Yong Cai and William Lavely compared child cohorts across the 1990 and 2000 censuses and concluded that 6.2 percent of boys and 7.5 percent of girls age 0-4 were under-counted in the 1990 census. Daniel Goodkind and Yong Cai also recently argued that the high sex ratios recorded in censuses from 1990 to 2010 were due to underreporting and the “stopping rule” – stopping fertility after giving birth to sons.

These two studies and Shi and Kennedy’s work differ in the extent to which they believe daughters are underreported. Comparing the 2000 and 2010 censuses, Goodkind claims that 30 percent of the elevated sex ratio in 2000 is attributable to under-reporting of daughters. Cai finds that an average of 13 percent of female births and 8 percent of male births in 2000 are underreported. Shi and Kennedy claim that an incredible 73 percent of the missing girls from 1990 to 2010 are unreported but present in the population.

Behind the Numbers

How do Shi and Kennedy arrive at such a large percentage compared to earlier work? Comparing the infant population in 1990 with the population aged 20 in 2010, they find that while the cohort age 0 in 1990 had a sex ratio of 112, two decades later, this same cohort has a sex ratio of 103, and the number of females had increased by 2.9 million, whereas the number of males had only increased by 1.9 million. Overall, this suggests 4.8 million under-counted births, with 900,000 more female under-counted births than males. The authors state that similar numbers of under-counts are found when comparing higher age cohorts across the 1990-2010 censuses, with under-counts for each year ranging from 550,000 to 950,000. Multiplying the lower estimate of 550,000 for 20 years of births from 1990 to 2010, the authors conclude that 11 million of the 13.7 missing females from these birth populations may be under-counted.

If we examine the assumptions made in their calculations, however, it becomes difficult to accept these findings. Shi and Kennedy have used the sex ratios of the adult population aged 20 and above from the 2010 census to estimate the number of underreported births in the previous two decades. Yet the sex ratios for the adult population between 20 and 29 are unrealistically low (ranging between 99 and 102), suggesting a problem with the 2010 census data for this age group.

Looking at Table 1, we can see how the birth population from 1990 has increased in size by 2010, which in the absence of large-scale migration suggests a combination of under-counting in 1990 and 2000, or over-counting in 2000 and 2010.

In 2000 we observe an increase in both male and female numbers, and the male-female differential has actually increased over 1990. The possibility of over-counting is not raised by the authors, who do not question the validity of the 2010 census. However, the sex ratio of 102.7 for this cohort, we would argue, is unrealistic. As Cai points out in his 2013 study, even if the sex ratio in 1990 had been a “normal” ratio of 105, the sex ratio for the adult population 20 years later should be no lower than 104.

Changes to the census enumeration in 2010 may explain why over-counting is likely, particularly for the 20-year-old age group. In 2010, Chinese citizens were required to register for the census from their current place of residence but also their normal place of household registration if this differed from their current residence. As a result, 221 million people were classified as migrants living away from their normal household residence. The 20-29 age group comprised a significant proportion of this migrant or floating population, and many may have been double-counted.

Indeed, if we take a closer look at the change in sex ratio and the relative sizes of the male and female populations in the three censuses from 1990 to 2010, we can see evidence of data problems, as shown in Table 2.

The first thing we can detect as we follow the results for the population aged 0-9 from the 1990 to 2000 censuses is that the sex ratio declines somewhat for this cohort, dropping from 109 to 107, and there is an additional 12.6 million people (5.5 million males and 7.1 million females). This suggests a possible under-counting of both males and females for the 0-9 cohort in the 1990 census. If we look at this cohort again in the 2010 census (red cell), we can clearly see a problem because there is a loss of 3.4 million males compared to 2000 – a figure too large to be explained by mortality – but an additional count of 3.4 million females. Shi and Kennedy do not address this significant drop in the male population, nor do they comment on the abnormally low sex ratio in this age group in 2010.

Despite what appears to be a data error in the 2010 census, Shi and Kennedy use the female under-count from this age group to argue that females are not really missing in China’s population – a charge many unfortunate bachelors would argue. The abnormally low sex ratio of 101 and the loss of males in this cohort points to a serious data problem in the census and calls into question the use of this cohort to create a formula for calculating missing females.

What can we learn about the missing females from the census data? If we assume that the age 20-29 cohort is problematic because of the large numbers of migrants present in that age group, and the 0-9 age group is problematic due to prior under-counting, can we assume that the 10-19 is a more accurate reflection of the male-female population? In Table 2 we can see that there are significant differences in the overall counts of the 0-9 populations and the 10-19 populations from 1990 to 2000 and from 2000 to 2010, with 12.6 million people possibly under-counted in 1990 and 15.7 million under-counted in 2000. In both the 1990 and 2000 censuses, female children may have been under-counted to a greater extent than male children, but the high sex ratios observed for the population aged 10-19 suggests that only a small portion of the “missing females” have been recovered. The sex ratios of primary school enrolment in China offers further support to the argument that girls are genuinely missing from the population: from 2003 to 2010, the sex ratios of primary school students age 9-10 rose from 112 to 116.

There is likely to be some under-counting even in the population aged 10-19, because as Shi and Kennedy point out, some girls in particular may not be registered until they attend secondary school, or even until the point of marrying in their early twenties. A survey of the numerous Chinese studies on the accuracy of the Chinese census reveals a consensus view that the 0-9 population suffers from severe under-counting, but there is disagreement regarding the exact age at which additional over- or under-counting appears in the adult population. Some suggest that the 15-24 year old population has been over-counted; others argue that the 20-45 year old population suffers from both over- and under-counting.

Given the acknowledged and severe problems with the data for the 0-9 and the 20-29 census cohorts, we feel it is best to assume that the sex ratios of the 10-19 cohort, though still not perfect, is a more accurate reflection of the imbalance between males and females in the youth population.

Using a reverse survival method as employed by Cai and Lavely, which uses age and sex-specific mortality rates to predict population figures at an earlier age, we can calculate what the 0-9 population might have looked like in 2000. In this case we are calculating what the 10-19 male and female populations might have looked like at ages 0-9 in 2000.

In 2000, we find that instead of the observed sex ratio of 117.5 for the 0-9 population, the sex ratio may have been 111.3. The 2000 census for the 0-9 cohort recorded 85.95 million males and 73.18 million females (see Table 2 above). If the birth sex ratio had been the global average of 105, then in the absence of differential mortality, there would have been 81.86 million females, suggesting that 8.7 million were missing from that population (81.86 expected minus the actual figure of 73.18). If the 2010 census is more accurate for the 10-19 cohort, our calculations suggest that instead of 8.7 million missing for that 10-year age group, there are in fact 5.1 million missing females, which means that under-reporting could account for 41 percent of the missing females.

Using the 10-year cohort, we estimate the percentage of missing girls accounted for by underreporting ranges from 22 percent (as determined by the 10-14 cohort in 2010) to 63 percent (as found in the 15-19 cohort). Shi and Kennedy’s claim that 73 percent of missing females are actually cases of underreporting therefore ranges from slightly overly optimistic to drastically so. Furthermore, the use of the mobile 20-29 age cohort means that their estimates are subject to considerable reporting errors.

Our calculations support the claims by Goodkind and Cai which suggest that under-counting/under-reporting explains a portion of the missing females, but not the majority.

The results of Shi and Kennedy, and Schacht et al.’s work (see addendum for our analysis of Schacht et al.’s research) matter because abnormal sex ratios are becoming more prevalent. In 1990, 5 nations had abnormal sex ratios; now there are 19. A foundational question faces our world: Is the practice of culling girls from a population harmful or harmless? Offspring sex selection is ultimately the result of a devaluing of women on multiple levels – as heirs, as property owners, as someone worth educating, as equal human beings – and it is a matter, literally, of life and death. It is important that we get this right.