Conjuring the Ghosts of Missing Children: A Monte Carlo Simulation of Reproductive Restraint in Tokugawa Japan

See Sommer’s (2010) revision of Bray (1997) and Lee and Wang (1999).

The following studies have detected TFRs or TMFRs below 3: Hayami and Okada (2005:206); Ishihara (1988:115); Kitō (1986); Ritsumeikan Daigaku Takagi Zemi (1985, 1986, 1988); Takahashi (2005:121); Tsuya (2001:232). For surveys of fertility results from longitudinal village studies throughout Tokugawa Japan, see Tomobe (1991:41) and Drixler (2013:35–36). These figures do not include children who were born and died in the same interval between two annual registers, but such early deaths cannot often have exceeded one-fifth of the registered children. Several types of sources allow us to study the infant mortality rate at the time, including the records of pregnancy surveillance and child welfare systems. All agree that infant mortality from sickness and accidents rarely averaged more than 20 % over long time spans. For partial summaries and a discussion of methodological issues, see Drixler (2008:467–469; 2013:107–108, 250–252) and Kitō (1976).

The life tables derive from surveillance documents expressly designed to track the fate of children from pregnancy to about 1 year of age, as well as from longitudinal analyses of population registers. Because the latter often did not register children in their first months of life, I adjusted them for known regularities in the distribution of infant deaths over the first months of life in breast-feeding populations (Drixler 2008:467–469; Drixler 2013:250–251). This reconstruction distinguishes between normal years and two levels of mortality crises. Weighted by person-years of the reconstruction, life expectancy at birth (excluding the victims of infanticide) averaged 37 years.

Although the mortality assumptions for this reconstruction have a broad empirical foundation, it may be reassuring that even if we raise by one-half the probabilities of dying at all ages (thereby reducing life expectancy at birth from 36.9 years to an implausibly low 26 years), the estimates for eighteenth-century TFRs rise by less than 0.7 children (see Drixler 2013:251).

I thank Jordan Hamzawi for helping me coin this term.

I did not back-project patterns of marriage and labor migration. Instead, I calculated for the present moment of each population register and then averaged them for each decade.

None of the numerous longitudinal village studies in Japan’s Deep East has demonstrated such a change. Given that IMRs in eighteenth century village studies are often somewhat lower than in the late nineteenth-century vital statistics for the same areas, any large improvement in survival beyond the abatement of infanticide is not likely. Future research may give us better information about the trends in infant mortality; for the time being, it seems likely that the level and patterns remained stable, fluctuating only between normal and crisis years.

I derive this range and the observations of the factors influencing the age at menarche from the following studies and review articles: Backman (1948:326–327); Bojlén and Bentzon (1968); Eveleth and Tanner (1976:213–219); Malik and Hauspie (1986:546); Pawson (1976:94–95); Satwanti et al. (1983); Thomas et al. (2001:274–276); Tomobe (2007:60–64); Wood (1994:418–419); Wyshak and Frisch (1982:1033); Zhongguo Xuesheng Tizhi Jiankang Yanjiuzu (1987:1691).

The Chimbu, Bundi, Lumi, and Gainj people in Papua New Guinea; Rwandans; and the Sherpas of Nepal. Even some populations living at high altitudes have mean ages at menarche between 14 and 17 years. See Malik and Hauspie (1986:546). The sole example of a lowland population in this high range appears to be an 1882 small-n German study, cited in Backman (1948:431), whose methodology may not have been consistent with the modern studies.

Some of the early studies of the age of menarche suffer from serious methodological issues, all of which lead to overestimates of the age at menarche (Bojlén and Bentzon 1968:74). After adding one-half year to correct for one of these, the conflation of completed years and nth year, Backman (1948) reported mean ages above 17 for some nineteenth-century Scandinavian studies, but this procedure may actually exaggerate rather than mitigate the error.

By the 1980s, Japan’s mean age at menarche was around 12.5 years (Tomobe 2007:60).

In addition to sexually transmitted diseases, smallpox has been cited as a cause of male infertility, but this was not borne out by a study of Dutch smallpox survivors (Rutten 1993).

If one-half of women attempted to raise two children, and the other one-half raised three children, 40 % infant and child mortality would produce a rate of childlessness of about 11 % among women at the end of their childbearing years.

Estimating sterility is beset with methodological problems. See Larsen (1994).

Coital frequencies typically decline with the woman’s age and the duration of marriage, but the effects vary greatly between different populations. This simulation folds the duration effect into the age pattern of coital frequency. This is because the Tōgoku data set does not permit confident estimates for the frequency of divorce and remarriage, supplying only the proportions married at each age. Because much of the duration effect is parallel to the effect of the wife’s age, any error arising from this simplification is minor compared with the general uncertainty surrounding coital frequencies.

See upcoming Figs. 5 and 9 for a comparison of how different coital frequency assumptions affect the simulation results.

In each gestational month, I calculated how many extra fetal losses the 1930 stillbirth figures for Miyagi and Yamagata prefectures imply at each age. I then distributed these extra fetal deaths across the days of the pregnancy based on their 1930 gestational distribution.

On methodological problems with many other studies, see Ford and Kim (1987) and Potter and Kobrin (1981:86).

The simulation model, specified in Python, takes about 0.24 seconds to simulate one life on an Intel Core i7-2860QM CPU @ 2.50GHz. At 201,000,000 realizations, the results reported in this article would have taken about 560 days to generate on one CPU.

Wrigley et al. (1997:478–479) analyzed the effect of infant deaths on birth intervals, which implied that women in their parishes breast-fed their children extensively.

In 1901, rural Kanagawa still had an implausibly high legitimate stillbirth rate of 9 %, suggesting that a large percentage of pregnancies ended in a late-term abortion or infanticide.

Because Shimizu and Miyai (1968) reported no distributions within age groups, this estimate assumes the same distribution as in Taiwan 1986 (Sun et al. 2002), but with the daily probabilities multiplied by 1.68, the average ratio of Taiwanese and Northeastern Japanese coital frequencies in each age group.

For sources, see Drixler (2013:17, 120-123).