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

Abstract

This article quantifies the frequency of infanticide and abortion in one region of Japan by comparing observed fertility in a sample of 4.9 million person-years (1660–1872) with a Monte Carlo simulation of how many conceptions and births that population should have experienced. The simulation uses empirical values for the determinants of fertility from Eastern Japan itself as well as the best available studies of comparable populations. This procedure reveals that in several decades of the eighteenth century, at least 40 % of pregnancies must have ended in either an induced abortion or an infanticide. In addition, the simulation results imply a rapid decline in the incidence of infanticide and abortion during the nineteenth century, when in a reverse fertility transition, this premodern family-planning regime gave way to a new age of large families.

Introduction

From qualitative sources, it is well known that many historical societies practiced infanticide and abortion as a regular form of family limitation. Apart from small-n ethnographic observations and analyses of sex ratio distortions, however, no rigorous estimates exist for the frequency of infanticides. The frequency of abortions has been altogether impossible to establish for premodern populations, giving rise to radically divergent interpretations, for example, for the inhabitants of the Qing Empire.¹ This article employs a fine-grained simulation method to establish minimum estimates for the extent of post-conception family limitation in one particularly well-documented historical society: the villagers of eastern Tokugawa Japan.

In their village studies, historical demographers of Tokugawa Japan (1600–1868) have long found some of the lowest recorded fertility in the premodern world. Although five to seven children per woman were common in central Japan, in Japan’s Northeast, even total marital fertility rates could fall below three children per woman.² Contemporary observers often noted this phenomenon and were in little doubt about its fundamental cause: villagers, or so dozens of reports asserted, would raise only two, three, or four children and kill all others, either in the womb or at the moment of birth (Drixler 2013:313n86–87). When historical demographers first rediscovered the low fertility of parts of Tokugawa Japan, they gave frequent infanticides and abortions a prominent place in their analyses (Eng and Smith 1976; Hanley 1972, 1974; Hayami 1973). More recently, however, many economists, sociologists, and historians have accorded them only a minor role; instead, these researchers have credited labor migration that separated spouses, pathological sterility, chronic malnutrition, or excessive female workloads with keeping fertility levels low (Cornell 1996; Kinoshita 2002:83–91; Kitō 2007:100–101; Mosk 1978; Saitō 1992; Tomobe 2002, 2008). Other historical demographers (Narimatsu 1985, 1992; Takahashi 2005; Tsuya and Kurosu 2010) see infanticide as an important factor but have made no attempt to quantify its frequency.

The demography of Tokugawa Japan was notably diverse. Late marriage and labor migration, either to other villages or to some of the largest cities in the early modern world, were common in some regions but rare in others (Hayami 2001; Hayami and Kurosu 2001; Hayami and Ochiai 2001). Attitudes regarding infanticide, too, varied between different parts of the archipelago (Drixler 2013:25–46; Ōta 1997:9–11). This article, therefore, quantifies the role of infanticides and abortions in just one region, albeit the largest contiguous area that was infamous for these practices and whose local populations failed to reproduce themselves in the eighteenth century. This is Japan’s Deep East, a region that I have elsewhere (Drixler 2013) dubbed “Eastern Japan.” The Deep East stretched from the environs of the shogun’s capital of Edo (modern Tokyo) all the way into the northeast of Honshu. Its population reached about 5 million around 1700, and then contracted continually for about a hundred years before rebounding in the early nineteenth century.

Data

My sample of the Deep East’s population comprises 2,600 population registers from 800 villages (Fig. 1; for a list and sources, see Drixler 2013:261–275). Drawing on a Japanese name for the region, I call it the “Tōgoku data set.” From these snapshots of age structure and household composition (745,500 individual observations), I estimate fertility rates with the own-children method using mortality assumptions that derive from the life tables of 22 villages in the region and 248 time series of deaths from necrologies (see Drixler 2008:455–469; Drixler 2013:6–9, 245–260).³ The resulting data set comprises 4.9 million person-years. Although the own-children method is an indirect estimation technique, its results have been shown to be potentially more accurate than full birth histories (Avery et al. 2013) and not very sensitive to errors in mortality assumptions (Breschi et al. 1999; Kurosu 2003:59–61).⁴

The victims of infanticide cannot be recovered by this method and are counted just as aborted children would be: if we take the perspective of infanticidal parents, who typically saw little distinction between abortions and destroying the child at birth, we may call the resulting measure “fertility.” Readers who object to this unconventional definition may prefer the phrase “total rearing rate.”⁵ The total rearing rate hovered around 3.5 children per woman during the eighteenth century and gradually increased to near 5 children per woman by 1850 (Fig. 2).

To assess to what extent the observable fertility of Japan’s Deep East can be explained without resort to infanticide and abortion, I run a Monte Carlo simulation model that combines information from the Tōgoku data set itself with empirical values that physicians, anthropologists, and demographers have established for the processes that determine whether a woman conceives and delivers a child. The simulation then makes different assumptions about the frequency of infanticide and abortion for each age group and determines which level is most consistent with the fertility observed.

The Simulation Model and Its Empirical Basis

Reproductive models have an illustrious history (reviewed in Wood and Weinstein (1988)) but have recently become one of the quieter areas of demographic research. Most such models were intended to assess the sensitivity of fertility outcomes to changes in their proximate determinants. Many were linear models rather than simulations. My model draws on these antecedents (especially Ridley and Sheps (1966), and Wood and Weinstein (1988)) but serves a different goal: to make visible the extent of family limitation in a historical population without reliable survey data on this topic. It does so by calculating (1) a minimum number of live births that women in my sample population should have experienced, given everything that we know about them; and (2) the number of infanticides and abortions necessary to explain the gap between that minimum number and the fertility actually observed.

My model also departs from earlier efforts in some details of its methodology. First, it takes into account a greater range of physiological factors—such as anovulatory cycles and different cycle lengths—than the earlier models, whose goal was typically to simplify rather than to simulate nature. Second, its time increments are single days so that it can calculate events such as fetal loss or lactational amenorrhea according to their empirical distributions.

To give birth, a woman needs to meet a series of conditions. To conceive, she must have experienced menarche but not yet menopause, and she cannot suffer from pathological sterility. She must be going through menstrual cycles, which is unlikely as long as she nurses an infant. Her menstrual cycle must be ovulatory, and sexual intercourse must take place at the right time relative to ovulation. Many conceptuses miscarry, most of them so early that their mother may not even notice that she was pregnant. If the child is born and lives, it influences the mother’s subsequent reproduction by inducing lactational amenorrhea through frequent breast-feeding. The model simulates this process by creating an artificial woman and tracking 23 variables that define her reproductive state. These variables change as the result of 25 types of events (see Table 1).

To run a realistic simulation of the reproductive process, we need to stock this model with empirical probabilities (see Table 2). These probabilities derive from three types of sources. The population whose reproduction the model simulates—that is, women whose lives are captured in the Tōgoku data set—provides some of the necessary information: how many women of a given age were married and how many were separated from their husbands because of labor migration.⁶ Mortality figures for children and mothers come from necrologies and longitudinal village studies in the same region. For other inputs, Tokugawa Japan has left us only qualitative data. In such cases, the model draws on populations from other parts of the nineteenth and twentieth century world, chosen for their apparent similarity with the Tōgoku population.

Finally, with physiological processes that have been measured only in a narrow range of populations (such as embryonic losses and cycle length), the numbers derive from medical studies in Europe, North America, Hawaii, and India. When multiple studies were available, I chose those that the wider literature (especially Wood 1994) considers the most methodologically sound, or have combined the results of several studies of high quality.

For many events, a range of values is plausible. In these cases, I have chosen a value that biases the fertility rate downward in order to reduce any positive gap between expected and observed fertility that has to be explained by abortion or infanticide. Hence, the model embeds a worst-case scenario against my hypothesis that this population exhibited a high frequency of abortion and infanticide.

Many of these probabilities vary with the age of the woman. Ages are determined according to the Western count (age at birth = 0 years) or the old Japanese count (age at birth = 1 sai, age on first New Year’s Day thereafter = 2 sai, and so on).

Sensitivity Analysis

In a sensitivity analysis of this model, I removed each event in turn while leaving all others in the standard configuration. For example, I ran the simulation with the assumption that intercourse takes place every day, or that all cycles are ovulatory, or that all women experience menarche by age 10. The results are reported in the right-most column of Table 2. Six types of events changed the simulated total fertility rate by more than one child: if we remove celibacy, pathological sterility, lactational amenorrhea, failed pregnancies, days without sexual intercourse, or unsuccessful inseminations on susceptible days from the model, the TFR rises from 4.50 (standard model configuration) to between 5.54 and 7.15. All other effects are quite small.

Of the six events with large effects on simulated TFR, one is known from the study population (celibacy), and four are set near the fertility-reducing extreme of their known empirical distributions (pathological sterility, lactational amenorrhea, failed pregnancies, and coital frequency). The probability of the sixth event—conception after intercourse on susceptible days—presumably may vary somewhat between populations (it may be lower in modern populations with low sperm counts, for example), but because the model uses this distribution for nonsterile couples only, any large variation is covered by the pathological sterility variable.

There are many interaction effects. For example, the model is not very sensitive to upward changes in the age at menopause in large part because rates of sterility and rates of fetal loss rise sharply toward the end of the childbearing years; conversely, lowering the age at menarche would have a greater effect if more perimenarcheal girls were already married, and so on.

These effects would be a cause for concern if the model were used to compute a best guess. In this article, however, the model simulates the plausible minimum value for conceptions and live births, and then—by extension—for infanticides and abortions.

Individual Variables

Marriage

The age at which a majority of women in Japan’s Deep East married changed relatively little across the two centuries of our simulation, ranging from 18 to 23 sai, with an average of 20.2 sai and all the lowest average ages recorded in the eighteenth century. Because divorce was frequent and bore little social stigma, many women entered matrimony several times over their lifespan (Fuess 2004; Kurosu 2011). Figure 3 charts the changing proportions married, averaged across the 213 years of this study. The model translates the proportions married into daily risks of marrying and ending a union. Late marriage and celibacy were a major restraint on fertility in Japan’s Deep East. According to the simulation, reproductive years spent unmarried reduced fertility by an average of about 30 % (see upcoming Fig. 6).

Spousal Separation Due to Labor Migration

Many population registers of Tokugawa Japan noted whenever a villager entered an employment contract, often outside the village. In the late seventeenth century, contracts often had long durations in Japan’s Deep East, with 10-year indentures no rarity. In the early eighteenth century, one or two years became typical instead (Hayami 1968:165; Ramseyer 1996). In contrast to central Honshu, where a large proportion of men and women spent at least one year working outside their native village, labor migration was relatively rare in the Deep East. Especially after about 1700, many of its children grew up with only one or two siblings and could expect to either inherit the farm or marry the heir to another. As such, they had fewer reasons to become hired laborers elsewhere.

Because not all registers recorded labor migration, the Tōgoku data set allows us to establish only a range: a minimum, which assumes that villages with no recorded labor migrants really had none; and a maximum, which assumes that all such villages did not record labor migrants on principle and therefore must be removed from the denominator. Given that other scholars have given great weight to the demographic impact of labor migration (albeit in other regions and without quantifying that impact), I use the maximum end of this range for the simulation. Even this maximum estimate suggests that most reproductive lives were little affected by labor migration (Fig. 3 and upcoming Fig. 6). Among women in their late 20s, an average of only 1.4 % lived apart from their spouse because of labor migration in any given year, with a peak value of just 6.9 % in the 1690s.

Life Tables for Women and Children

Japan’s Deep East had moderately high life expectancies for the preindustrial world. Across 30 longitudinal village studies (Drixler 2008:463–465), they average 37 years for women in years without mortality crises. These figures incorporate my correction for undercounted unintended infant deaths by assuming that the regularities in the timing of neonatal and infant deaths observed in other breast-feeding populations also apply to Japan’s Deep East. Life expectancies were much shorter during periodic crisis years (Drixler 2008:466–469). Smallpox was a common disease of childhood, measles struck about once per generation (Jannetta 1987; Kawaguchi 2010), and in the northern reaches of the Deep East, famine mortality could be devastating. The simulation model determines the frequency of mortality crises based on the proportion of the Tōgoku population that lived in an affected area, and calculates mortality rates for children and women accordingly. The effect of mortality crises on the simulation results, however, is quite small (see Table 2 and upcoming Fig. 6).

For children whom parents attempted to raise, infant mortality rates (IMRs) appear to have been strikingly low in Japan’s Deep East. In the records of pregnancy surveillance systems, which tracked the fate of each child from about the fifth month of gestation to the age of about 12 months, IMRs averaged 187 across 14 locations (n = 3,548 births). Because pregnancy surveillance created incentives to misstate infanticides as deaths from illness, these rates may be too high. In longitudinal population registers from Japan’s Deep East, IMRs average just 146, including deaths during mortality crises and a correction for underreported neonatal deaths.

Some readers may suspect that the rising observed fertility (or rearing rate) in Fig. 2 reflects an improved disease environment for young children. There is currently no clear indication that IMRs in Japan’s Deep East improved over the course of the nineteenth century.⁷ Even if natural infant survival should have improved in the early nineteenth century, it can hardly account for any significant rise in fertility. After all, even a massive hypothetical fall in IMR from 170 to 120 would raise the resulting TFR estimate by only 5 %, far less than the increase observed here.

Menarche

The villages of Tokugawa Japan have left little direct evidence on the mean age at menarche (MAM). In 277 Japanese samples between the 1880s and the 1950s, recently collected by the economic historian Tomobe Ken’ichi, the MAM averaged between 14.5 and 15 years in every decade. The lowest mean age among these studies was 13.3, and the highest, 16.5 (Tomobe 2007:60–64). In deciding whether these findings can be extended backward into the Tokugawa period, the wider global context is useful to consider. Hundreds of studies have established the MAM for a variety of populations: from eighteenth-century Germans to nineteenth-century Calcuttans, from Inuit hunters to farmers of the Rwandan highlands. Within these studies, the MAM ranges from about 12 to a maximum 18.6 years.⁸ Virtually all mean ages above 17.5 years have been found in populations living at high altitudes in East Africa, the Himalayas, and especially Papua New Guinea.⁹ Averages above 16 years have also been reported for samples from northern Europe in the nineteenth century as well as for a small number of twentieth-century samples from Japan and nomadic hunter and gatherer groups in the Philippines and Botswana.¹⁰ In Europe, there has been a secular trend toward earlier maturation since the nineteenth century, and a similar development is evident in Japan since about 1960. In nineteenth-century Europe, girls tended to menstruate earlier in the South and later in the North, but in the twentieth century, ages at menarche were similar for Inuit hunters and those of many populations in the tropics. Within a population, girls with high socioeconomic status tend to experience menarche earlier than their poorer compatriots, but athletes menstruate later than their less-active classmates. These patterns imply that genetics, altitude, climate, net nutrition, protein intake, and physical exertion are all likely influences on the age at menarche.

Based on this information, we can triangulate the MAM for the women of the Tōgoku data set as follows. In genetic terms, Japanese women do not seem to have a predisposition to particularly late menarche.¹¹ Given that the women of the Tōgoku data set lived at low altitudes, we can therefore assume with some confidence that their MAM was below 17.5, and probably below 17. Compared with most twentieth-century populations, their diets were low in protein and calories, while heavy physical workloads, thin clothes, and drafty houses made high energy demands on their bodies. In Japan, these conditions improved only gradually before the mid-twentieth century. The MAM in Japan’s Deep East during the Tokugawa period should, therefore, have been similar to that of the twentieth-century Japanese studies or somewhat higher. Thus, the plausible range for the MAM for the women of the Tōgoku data set is 14.5 to 17 years.

The simulation uses the age distribution at menarche for two groups of Japanese schoolgirls surveyed in 1919, whose MAM was 16.1 years (see Fig. 3). A somewhat higher MAM would make no great difference to the results of the simulation because the singulate mean age at marriage in the Tōgoku data set was 20.2 sai and the model assumes that no intercourse took place outside marriage. For famine years, the model sets the probability of menarche at 0.

Menopause

Globally, reported mean ages at menopause over the past 160 years have ranged from 42 to 52.6 (Backman 1948:453–460; Pavelka and Fedigan 1991:28–29; Sievert 2006:82–87; Singh and Ahuja 1980:298–299; Thomas et al. 2001:274–276; Wood 1994:82–87). A good part of this variation probably derives from different methods of determining the age at menopause (Sievert 2006:94–103). Within populations, genetic predisposition is a strong predictor (Sievert 2006:84–88); the same is likely to be true between different populations. The effect of nutrition on the age at menopause is disputed and likely to be small at best; low birth weight and low body weight at age 7 are not consistently linked to early menopause (Sievert 2006:102–104). Even with outright starvation, the effect is modest (less than three months) unless children are exposed to severe famine conditions, in which case the reduction can approach two years (Elias et al. 2003). Although a number of studies in Europe and the United States have reported secular increases in the age at menopause, this finding has long been controversial (Danubio and Sanna 2008:101–103; Pavelka and Fedigan 1991:28–29).

What does this global context imply for the women of the Tōgoku data set? Some were exposed to severe hunger as children, arguing for a reduction in the age of menopause compared with their modern descendants. In addition, to bias the model against frequent conceptions, it seems advisable to account for the possibility that the age at menopause has risen in Japan since the nineteenth century. The simulation model, therefore, subtracts four years from the age distribution at menopause of a study conducted on Japanese women in the late 1980s (Tamada and Iwasaki 1995), resulting in a mean of 45.5 years.

As with menarche, the age at menopause has a relatively modest influence on the simulation results. Menstrual cycles past age 45 are often anovulatory (15 % of the time in this model) as well as of irregular length, and the rate of pregnancy loss rises sharply with the age of the mother (30 % at age 30, 45 % at age 40, and 72 % at age 50). In addition, the model assumes extremely high rates of pathological sterility among older women (see Fig. 3).

Pathological Sterility

Syphilis, chlamydia, and gonorrhea appear to have been common among urban prostitutes in Tokugawa Japan, and these infections may have afflicted a substantial portion of the rural population as well.¹² One indication is that in the Tōgoku data set, 16 % of women around age 40 were recorded without coresident children, with decadal averages between 11 % and 20 %. Many of these women may have had children who died young or married into other households and therefore no longer appeared in the registers; some childless women were only recently married, and others were remarried divorcees who left behind children in other households. Such considerations can easily explain 11 % apparent childlessness, but 20 % leaves room for elevated rates of pathological sterility.¹³

A cohort study of a large rural town in the region (Takahashi 2005:123) is broadly consistent with these results. In Kōriyama Kamimachi, 20 % of women born between about 1705 and 1825 recorded no children over their reproductive lives. Some infant deaths from sickness or accidents are missing from that number. However, not all apparent childlessness needs to have been the result of sterility. The lowest rate in the Tōgoku data set, 11 %, was recorded in the 1860s; in Kōriyama, only 13 % of the last cohort (women born around 1820) recorded no children, compared with 23 % among women born around 1800. I am aware of no other evidence that sexually transmitted diseases declined in the mid-nineteenth century. Conversely, much evidence suggests that people raised more children as their attitudes to infanticide and abortion changed.

Nevertheless, in the spirit of biasing the results against frequent conceptions, the model derives its sterility assumptions from the region in which demographers have observed its highest prevalence: the “infertility belt” of central Africa, where in the 1980s, typically about every other couple had acquired pathological sterility by the age of 40 (see Fig. 3).¹⁴

Coital Frequencies and Contraception

Coital frequencies pose a particular challenge. At low frequencies, the model is quite sensitive to this parameter, but as with other historical populations, no quantitative evidence for the frequency of marital sex has as yet been discovered for the women of Japan’s Deep East. As with other parameters, one solution lies in establishing an empirical range across populations and then situating the women of Japan’s Deep East at the low end of that range.

Among the studies of Asian, African, and Western populations collected by William Lavely (2007), mean monthly frequencies ranged from 3.4 (Thailand, 1987) to 10.3 (Belgium, 1975). The oldest large-scale study of rural Japan known to me found an average of 7.4 sexual encounters per month (Shimizu and Miyai 1968). It is not clear that the ancestors of the study participants had sex less frequently. In Japan, rural society may actually have been more sexually permissive in prior centuries (Smith 1983:77–78), and the long, dimly lit nights would have provided fewer alternative forms of recreation.

As important as the mean coital frequency is the distribution of coital frequencies across the population. A mean monthly frequency of 3 could equally describe a population in which each woman had sex once every 10 days and a population in which one-tenth of women had sex every day and nine-tenths abstained completely. The implications of the two patterns for the number of resulting pregnancies are, of course, starkly different. Few studies of rural populations in East Asia publish such distributions by age group; one notable exception is the KAP IV survey conducted in rural Taiwan in 1986 (Sun et al. 2002). Among its respondents, 5.5 % of 30-year-old women had no intercourse all month, which is five times the rate if the daily likelihood of sex were evenly distributed across all couples of the same age.

Although rural Taiwan in 1986 seems far removed from Tokugawa Japan, for our purposes, the KAP IV survey has the virtue of reporting the lowest coital frequency (4.1 times per month) among all such studies of rural Chinese populations listed in Lavely (2007). Chinese populations may be a good model for a conservative estimate of reproduction in Tokugawa Japan because they address one possible challenge to explaining low observed fertility with infanticide and abortions: that traditional Chinese medicine recommended abstinence to men because it considered every ejaculation an expenditure of vital energy. To what extent this understanding was current in rural Tokugawa Japan is an open question. The fact that it was common for villages to hold communal wakes on every 60th night to avoid conceptions under its unlucky zodiac sign suggests that abstinence was not otherwise widespread nor thought to be easily achieved without the supervision of the community. Given these considerations, Taiwan’s KAP IV survey is unlikely to show coital frequencies that are lower than those of the women of the Tōgoku data set. Because coital frequencies in one month are likely to be a good predictor for those in the next, the simulation resets the monthly frequencies for each woman once per year.¹⁵

These low assumptions can probably accommodate a moderate level of contraception, although it is far from clear that contraception played a significant role in conjugal relations. Effective contraceptive practices, including paper pessaries, were widely used by Tokugawa-period prostitutes; there is little evidence, however, that these became common among married women in the countryside, and there are a number of strong indications to the contrary (Drixler 2013:117–118).

To allow for different opinions about the frequency of marital sex, the extent of deliberate abstinence, and the use of contraception, I run the simulation with two levels of coital frequency. One reduces this parameter to two-thirds of the Taiwanese sample; at 2.7 encounters per month, the resulting monthly average is lower than in any rural survey known to me. Another variant of the simulation brings coital frequencies up to those of the Northeastern Japanese sample in Shimizu and Miyai (1968), with an average of 7.4 per month.¹⁶

Conception Probabilities and Pregnancy Loss

The majority of unsuccessful pregnancies occur very early, especially in the days preceding the implantation of the embryo. Research that detects pregnancies clinically (that is, well after implantation) rather than chemically will return a lower frequency of conception but also a lower frequency of pregnancy loss. The simulation model derives its conception probabilities from a British study in the 1960s (Barrett and Marshall 1969), which does not mention hormonal assays and therefore can be assumed to have diagnosed pregnancies clinically. In consequence, it treats early pregnancy losses as children never conceived. For the risk of pregnancy loss, the model uses estimates in Wood and Weinstein (1988) (see Fig. 3) that correct empirical figures upward for an undercount of early pregnancies and early losses. The combination of these two inputs is therefore likely to underestimate the number of successful pregnancies. Again, this follows my guiding principle of biasing the model against the conclusion that the fertility rates of the Tōgoku data set should have been higher than their observed level.

Because Wood and Weinstein’s estimates derive from the mid-twentieth century, I have adjusted these figures for the generally higher rate of stillbirths in earlier periods. In populations innocent of modern medicine, rates of 3 % to 4 % are typical. By 1930, Japan published stillbirths by month of gestation as well as by the age of the mother, allowing me to make this adjustment both to the overall risk of pregnancy loss and its distribution over different ages.¹⁷ In 1930, vestiges of a once-common practice of reporting the victims of infanticide as stillborn still existed in some regions. I therefore chose the only two prefectures in eastern Japan with stillbirth rates under 5 % as the empirical basis for the stillbirth adjustment.

Lactational Amenorrhea

The women of Tokugawa Japan typically breast-fed their children, and often only weaned them after several years (Drixler 2013:106–108; Kitō 1995). The simulation assumes long breast-feeding with short intervals between bouts of nursing throughout the day and night, which produces the longest periods of postpartum amenorrhea.

The simulation bases the daily risks of returning to menstrual cycles on a group of Javanese women in Ngalik, subjects of one of the methodologically best (prospective) studies of lactational amenorrhea in a poor, heavily nursing population (Jones 1989:94).¹⁸ These women nursed six times per day for more than six minutes each. One-half had returned to menses 20 months after the birth of their child. This is one of the longest durations of lactational amenorrhea in the literature; in studies of African, Indian, East Asian, Central American, and highland Papua New Guinea populations with an average duration of breast-feeding between 12 and 36 months, the average duration of amenorrhea has ranged from 6.8 to 24 months (Buchanan 1975; Corsini 1979:198; Dada et al. 2002; Ford and Kim 1987; Lesthaeghe and Page 1980; Peng et al. 1998; Wood et al. 1985).

Simulation Method

The empirically based parameters discussed earlier allow us to simulate the reproductive life of a woman. The model starts with a set of 1 million hypothetical 10-year-old premenarcheal girls, each with a randomly assigned birthday between 1610 and 1870. For each girl, the computer looks up in the empirical tables on every new day whether any of 25 possible events occur that cause changes in the 23 variables (listed in Table 1) that together define her reproductive state. Each event has an empirically defined probability x. To see whether it occurs, the computer generates a random number between 0 and 1: if that number is lower than x, the event occurs. With three exceptions that are established on each New Year’s Day only, all events are calculated daily (see Table 2).¹⁹

On each new day, the simulation calculates whether the girl experiences menarche. When she does, her first menstrual cycle begins. On the first day of each cycle, the computer establishes its length and whether it is ovulatory. In a simplification designed to bias the results against frequent pregnancies, the model assumes that sexual intercourse occurs only when the woman is married and cohabits with her husband. If these conditions are met, the computer looks up the likelihood of sexual intercourse each day. A child is conceived if sexual intercourse coincides with the susceptible days of the menstrual cycle, the cycle is ovulatory, and the woman is postmenarcheal, premenopausal, and not sterile. The computer now determines whether the pregnancy will ultimately fail. If so, each new day the randomly generated number is compared with the probability that the conceptus dies at that precise gestational age. Induced abortions are treated in the same manner, with the chief difference that the likelihood of a pregnancy ultimately ending in an induced abortion is assumed for different versions of the model rather than derived from empirical studies. Successful pregnancies all result in a birth on the 281st day of gestation.

Each day, the computer also looks up in a life table whether the woman dies. On days on which she gives birth or has a miscarriage, a stillbirth, or an induced abortion, she suffers an additional risk of 0.8 % of dying on that day. With her children, too, the computer looks up daily in a life table (specific to the child’s age in days) whether the child dies.

Menstrual cycles can be suspended for four reasons. During famine years, all women in the affected region are—again, in the spirit of reaching an absolute minimum estimate for the number of children conceived—assumed to suffer from famine amenorrhea. When pregnancies fail or are terminated, they are followed by postpartum amenorrhea; the average length of postpartum amenorrhea is shorter for pregnancies that fail before the 140th day than in those that fail thereafter. If the woman gives birth to a living child, she acquires lactational amenorrhea while nursing it. On each day, the computer calculates whether lactational amenorrhea ends. When the child dies, amenorrhea ends as soon as the computer generates a number smaller than either the probability of lactational amenorrhea ending on the current day since delivery or the probability of postpartum amenorrhea ending on the current day since the child’s death.

Model Validation

How does the model perform in populations in which high rates of infanticide, abortion, or contraception are unlikely? The ideal test population would live in premodern conditions, breast-feed its children extensively, and have longitudinal data of high quality. Among the most carefully analyzed large populations that meet these criteria are the people of 26 parishes in England, whose families the Cambridge Group has painstakingly reconstituted for 1583 to 1837.²⁰ The published age-specific marital fertility rates (ASMFR) of women who married between the ages of 15 and 19 will serve as the benchmark for the simulation (Wrigley et al. 1997:399). To take into account the differences between Japan’s Deep East and this particular English sample, the simulation is modified in the following ways: (1) all women marry on their 18th birthday and remain married to the same husband throughout their reproductive lives; (2) they never physically separate from their husbands and suffer no famine amenorrhea; and (3) the mortality of their children follows the empirical distribution for the same 26 parishes (Wrigley et al. 1997:226, 251). Because all women in the English sample were alive throughout their reproductive years, I omit the entire lifespan of simulated women who die during childbirth or of other causes.

Since our model is biased toward generating few conceptions and live births, it should produce age-specific fertility rates (ASFRs) that are lower than those of the English women. The results suggest that the simulation model is indeed conservative (Fig. 4). Before their late 40s, where the two curves converge at a very low level, the English women had higher fertility at every age than the model produces, with an observed fertility rate (TMFR_20–44) of 7.0 as opposed to the simulated TMFR_20–44 of 5.7. That the simulation understates the fertility of the English parishes is particularly notable given that in early modern England, contraceptive practices and abortion were far from unknown (McLaren 1984).

Quite how conservative the model is becomes clear in a second validation with modern Japanese census data. At a national level, the whole complement of necessary data—proportions married by age, the female population by age, births by legitimacy and mother’s age, and infant mortality rates by age in months—is available only from 1925. For Kanagawa, a prefecture of about a million inhabitants just south of Tokyo, however, such data exist as early as 1901 (Kanagawa-ken 1903; Kojima 2004; Naikaku Tōkeikyoku 1905; Yokohama-shi 1903). By 1901, the physical conditions of life in the countryside still maintained important continuities to the Tokugawa period. Unintended infant mortality, for example, was at least as high as that observed in Tokugawa-period village studies, and adult heights remained very short, with everything that this implies for net nutrition. It is likely that many of the probability distributions in the model—lactational amenorrhea, the age at menarche, pathological sterility—remained very similar to those prevailing in the Tokugawa period. Nevertheless, when run with the proportions married and child deaths from the rural districts of Kanagawa (and assuming no spousal separation due to labor migration), the simulation returns a TFR_16–45 (legitimate children only) of only 3.2, compared with a reported figure of 5.3 (Fig. 5).²¹ Given this comfortable margin, the risk seems slight that the simulation overstates fertility for the women of the Tōgoku data set and therefore imputes spurious infanticides.

This remains true even when we raise the model variable with the greatest uncertainty—coital frequency—to the levels observed among Northeastern Japanese villagers in the 1960s (Shimizu and Miyai 1968).²² Even if married women in their early 20s had sex on 8.3 days per month rather than the 3.4 assumed in the standard configuration of the model, the legitimate TFR_16–45 for Kanagawa rises to only 3.9 (Fig. 5).

Results

When this model (in its low coital-frequency standard configuration) runs without any infanticides or abortions for the women of the Tōgoku data set, it returns TRFs of between 3.9 and 5.4 children in each decade of the simulation (Fig. 6). With three exceptions (the 1650s, 1660s, and 1850s), this was higher than the values actually observed. When the ASFRs are compared, several age groups in every decade fell short of their simulated fertility level.

The simulation also makes it possible to assess the relative contribution of celibacy, labor migration, variation in mortality patterns, and famine conditions in this population. Postmarital labor migration was only a minor restraint on fertility, especially after 1750. By contrast, life years during which women could have been married but remained single reduced fertility by an average of 2 children per woman (Fig. 6).

Several hypothetical explanations exist for the discrepancy between the simulated and observed TFRs. First, the model may still overestimate the reproductive vigor of Eastern Japan’s women. But given the very pessimistic assumptions for such factors as coital frequency and sterility, and the results of the model validations, this is unlikely. Second, some readers may suspect that the Tōgoku data set underrecorded births. After the correction through the own-children method, this explanation is not likely, either. Third, married couples in Eastern Japan may have employed effective contraception in large numbers. Although this possibility merits further research, there is at present little evidence to this effect. The many Tokugawa-period commentators who worried about declining populations never mentioned contraception as a factor (Drixler 2013:118–119). By the early twentieth century, folklorists collected a colorful variety of contraceptive traditions in the region; most of these consisted of talismans and other magical beliefs that can have done little to avert pregnancies (Onshi Zaidan Boshi Aiikukai 1975). In elite discourse of the early twentieth century, meanwhile, contraception was sufficiently novel to inspire lively debates (Ogino 2008). The issue is far from settled, but it seems unlikely that effective contraception was widely employed in the eighteenth century only to be largely forgotten by the early 1900s.

This leaves infanticides and abortions to account for the discrepancy. Descriptive sources state that both actions were common in Japan’s Deep East. Although none of the sources quantify the relative number of these two interventions with precision, most imply that at least during the eighteenth century, infanticides were much the more common of the two. Perceived as less dangerous and allowing parents to inspect a child before deciding whether to raise or reject it, infanticide had clear advantages as long as few drew clear distinctions between the moral status of fetuses and of newborns. Sex ratio distortions, which can be explained only by infanticides, were far greater in the eighteenth than in the nineteenth century, but persisted into the early twentieth century (Drixler 2013:91–96, 209–211). This trend may have reflected a growing preference for raising daughters, but it is also possible that more couples opted for abortions after the imposition of pregnancy surveillance over much of Japan’s Deep East (Sawayama 1998), especially because there was some ambiguity as to whether abortions before the fifth month of gestation were covered by the official bans.

This simulation cannot establish how many missing children died in the womb and how many died postpartum. It does, however, establish a range for the combined number of abortions and infanticides necessary to explain the fertility observed. Apportionment between the two is not simply a matter of dividing a constant sum of missing children. Mothers who have an abortion return faster to a susceptible state than those who carry the child to term. Hence, if the number of abortions is high, there will be more pregnancies, and the total number of missing children must be higher to match the fertility observed.

It follows that the minimum number of such interventions will occur if all are infanticides. To establish this lower bound, I ran the model assuming no contraception and no abortions. The simulation was repeated for 101 levels of infanticide, from 0 % of all live births to 100 %. For each decade and age group of women, I then selected the percentage of infanticides whose simulation came closest to the fertility (ASFR) actually observed. When the resulting numbers of infanticides for each age group are summed, in a procedure analogous to calculating a TFR from ASFRs, they reveal the levels and trends shown in Fig. 7.

According to this simulation, infanticides were already common in the 1660s, claiming about 4 % of newborn lives. By the mid-eighteenth century, that minimum proportion averaged nearly one-third, with two peaks above 40 %. In the nineteenth century—an age when throughout much of the Deep East, governments and philanthropists deployed childrearing subsidies, pregnancy surveillance, and moral suasion in an effort to protect newborn children—infanticides became rarer, falling to 4 % in the 1850s before a small rebound in the 1860s. These are minimum figures. If we relax just one variable of the simulation model by assuming that the coital frequencies of Tokugawa, Japan’s Deep East equaled those observed in Northeastern Japanese villages in the 1960s, the proportion of implied infanticides averaged fully 48 % in the eighteenth century.

When the simulation assumes that all unwanted pregnancies ended in an abortion rather than an infanticide, women return to a susceptible state sooner. The proportion of averted infancies is therefore higher by an average of about 7 %. Again, the implied abortion rates are even higher when the coital frequency of the Northeastern villagers is used (Fig. 8).

Based on the conservative standard configuration of the simulation, the proportion of otherwise successful pregnancies that ended in an abortion or an infanticide peaked somewhere between 44 % (all infanticides) and 53 % (all abortions), and averaged between 33 % and 41 % across the eighteenth century. Locally, the rate must have been far higher. The conservative assumptions of the simulation model (including extremely high rates of sterility, very long lactational amenorrhea, no sex outside marriage, and low coital frequencies within marriage) bias downward the number of abortions or infanticides required to explain the fertility observed. In addition, there was a good deal of variation in fertility rates within the Deep East (Drixler 2013:37–38, 276–280), so that in some areas, the combined rate of infanticide and abortion must have approached two-thirds.

Conclusion

Other Evidence on the Frequency of Infanticide and Abortion in Japan’s Deep East

The magnitude of these simulated rates of abortion and infanticide finds support in three other types of evidence. First, a number of Tokugawa-period observers stated how many children were raised and how many killed. For example, a scholar banished to a Northeastern village stated that parents brought up only two to four children instead of “afflicting six with hunger and cold” (Ashi 1754/1966), which would translate into a rate of infanticide between one-third and two-thirds. In a comparison of two family-planning strategies, a rural merchant in the North Kantō implied that in order to limit themselves to “two sons and a daughter,” a couple would have to abort about four fetuses (Suzuki ca. 1800/1936). Referring to the North Kantō, another observer noted that “those who give birth to many children but cannot raise them”—presumably, a subset of the population—killed two out of five children (Ōta ca. 1810:vol. 3, 310.). Yet another thought that in large swaths of the Deep East, farmers married so early that they gave birth to more than 10 children each, so that “many” were killed (Shiba 1811:478). If we combine this statement with the frequent assertion (found in dozens of contemporary accounts) that people in this area reared only two to four children, we are left with an implied rate of infanticide of at least 60 %.

Second, especially in the eighteenth century, the children of the Tōgoku data set had most peculiar sex ratios. For children with at least two elder sisters but no elder brothers, the sex ratio exceeded 350 in the 1760s; for children with at least two elder brothers but no elder sisters, it averaged 82 between1700 and 1790. When we tally the missing children whose traces survive in these distortions, they reach a similar order of magnitude as the simulation results in some decades (Fig. 9). Because no source describes infanticide in Japan as predominantly sex-selective, it comes as no surprise that for most decades far fewer missing children are evident in the sex ratios than in the simulation results.

Finally, stillbirth statistics in Japan’s Deep East routinely exceeded 10 %, and could top 45 % in individual districts. Reported stillbirth rates were impossibly high both under many local pregnancy surveillance systems of the Tokugawa period (to 1868) and the statistics of the modern state, collected nationally from 1886.²³ Given that stillbirth rates above 7 % are very rare even in the premodern world, a stillbirth rate of 45 % implies a rate of infanticides and late-term abortion of about 40 %. By the late nineteenth century, this was a local extreme rather than a regional average; but it confirms that the scale of infanticides and abortions suggested by the simulations was possible in a rural Japanese society (Fig. 9).

High Rates of Infanticide and Abortion in Other Populations

How exceptional are such rates of abortion and infanticide in a wider historical context? Very little firm quantitative information exists on the prevalence of abortion before its legalization in statistically advanced societies. Although effective abortion techniques could remain esoteric knowledge even in large, sophisticated populations (see, e.g., Sommer (2010) on early modern China), at least some premodern societies appear to have achieved very high rates (see, e.g., Shepherd (1995) on the Siraya of seventeenth-century Taiwan). In turn-of-the-century France, (possibly exaggerated) estimates for the number of abortions ran from about one to seven for every seven live births, with higher figures still for Paris and Lyon (McLaren 1978:478–480). Since 1920, when the Soviet Union wrote history by decriminalizing the termination of pregnancies, and when technological advances reduced the attendant physical pain and medical risks, induced abortions have, of course, outnumbered live births in many countries, including Japan in the 1950s.

A well-established school of thought sees infanticide as “a normal feature of social life” (Carr-Saunders 1922:216) in a majority of human societies, and as a practice with a compelling evolutionary logic (Hrdy 1999). Estimates of the rate of infanticide, however, are quite rare. Thus far, they have relied on ethnographic observations, interviews, or skewed sex ratios. While living as an ethnographer with the Eipo in the highlands of Irian Jaya, Wulf Schiefenhövel (1986:62–66) observed 49 births, 43 % of which were followed by an infanticide. An interview-based study of the Ayoreo of Bolivia limited its results to women known to have killed at least one newborn; it counted 54 such cases, or 38 % of all births to infanticidal women between the 1930s and 1980 (Bugos and McCarthy 1984:514). A similar (if less rigorous) study was conducted by a group of female American missionaries in nine Chinese cities between 1873 and 1883. It took the birth histories of 160 women above age 50, who between them admitted to having killed 29 % of their daughters and thus about 14 % of their children overall (Fielde 1887, discussed in King 2014:97). By reputation, far higher rates are on record. When another missionary asked the local Chinese to estimate the rate of female infanticide in their home towns in Fujian, some responses were as high as “70 or 80%” (Abeel 1843:540–542; discussed in King 2014:94–96). Also in the nineteenth century, certain Rajput clans in Gujarat were even said to destroy all daughters at birth (Clark 1983).

For historical demographers, however, sex ratio anomalies have been the main evidence for infanticide. Analyzing the genealogy of the Qing imperial lineage, Lee et al. (1994:410) estimated that imperial clansmen of the fourth rank “killed as many as one-quarter of their daughters.” In a village of demobilized Qing soldiers in Liaoning, Lee and Campbell estimated that one-fifth of daughters were destroyed (Lee and Campbell 1997:70n.25). In the Indian census of 1872, the sex ratios for children among many castes were so high as to suggest that they killed or mortally neglected about one-half of their daughters (Miller 1981:65).

The rates simulated for eighteenth-century Japan, therefore, coincide with the high range established by other methodologies for other societies. It is notable that among the Eipo and a subset of the Ayoreo—cultures of infanticide that, like Japan’s Deep East, did not hinge on sex selection—women also did away with about 40 % of their newborns to achieve the desired sequence and number of children.

Applications Beyond Abortion and Infanticide

Although the simulation model is designed for the specific context of Tokugawa-period infanticide and abortion, it could, mutatis mutandis, be applied to other historical settings to look for the traces of contraception, abstinence, or postconception forms of family planning. For example, researchers have argued that deliberate abstinence played an important part in limiting the fertility of Chinese couples during the Qing period (Lavely 2007; Lee and Wang 1999) as well as in the precocious fertility decline among Quakers (Vann and Eversley 2002:170). Adapting the model introduced here, it would be possible to simulate what levels and patterns of abstinence would be required to explain the observed fertility of Chinese or Quaker women.

The simulation model also offers a new approach to determining whether a population practiced deliberate fertility control. It is now well established that parity-specific control (Henry 1961; Coale and Trussell 1974, critiqued in Wilson et al. 1988) is not the only form of conscious family limitation. The methodological difficulties in detecting “spacing” rather than “stopping” behavior, however, are considerable (Van Bavel 2004a). One response to these difficulties has been to look for the effect of child survival (David and Mroz 1989; Reher and Sanz-Gimeno 2007; Van Bavel 2004b; Van Bavel and Kok 2004) or short-term economic fluctuations (Bengtsson and Dribe 2006; Dribe and Scalone 2010) on birth intervals. This approach, however, depends on high-quality longitudinal data, which are not available for many populations. In addition, even with the best data, this approach cannot determine whether the responses it detects are the full extent of deliberate fertility control or instead are like the waves on a deep lake. For the people of Japan’s Deep East, for example, the response to even dramatic short-term fluctuations in economic conditions was quite muted; any study that focused exclusively on short-term responses to economic stress would overlook that this was a culture that aborted or killed nearly as many children as it attempted to raise. It is worth asking what levels of abstinence, contraception, or abortion are required to explain the level of fertility observed in the European populations that have been so extensively studied through event-history analyses.

If the simulation method has potential for applications far afield, it also has important limitations. Because it must proceed from very conservative assumptions for some of the measures that are lacking for most or all historical populations (such as coital frequency and pathological sterility), it can detect only very large interventions in fertility. By itself, it also cannot settle what form family limitation took: abstinence, contraception, abortions, or infanticide. When put in conversation with other forms of evidence, however, it can do much to establish and narrow a range of plausible scenarios in societies past and present.

Acknowledgments

George Ehrhardt wrote the Python code for the simulation model. Robert Wyman improved the manuscript with his suggestions, as did three anonymous reviewers. This work was supported in part by the facilities and staff of the Yale University Faculty of Arts and Sciences High Performance Computing Center and by the National Science Foundation under Grant No. CNS 08-21132 that partially funded acquisition of the facilities.

Notes

References