FIGURING AGE AT MARRIAGE FROM CHINESE GENEALOGIES
A THOUGHT PAPER


Age at marriage is one of the most important terms in the overall equation that determines a demographic regime (Chris Wilson). Particularly in societies like traditional China, where arranged marriage and customs of sexual separation made premarital sex and thus premarital pregnancy quite rare (but see Wolf and Huang 1980), age at marriage, along with mortality in the fertile years, is one of the most important determinants of total fertility, and thus of rates of population growth.

A BRIEF BUT CULTURALLY-TUNED LOOK AT THE CHINESE DEMOGRAPHIC REGIME

The Chinese demographic regime, as is well-known by now (Wolf 1985, Zhao 1992, Lavely and Wong 1998, Lee and Campbell 1997, Harrell 1996) is usually characterized by a set of factors such as early and universal marriage, moderate age specific marital fertility, and moderate to high mortality at all ages, such that the net result over long spans of time was gradual increase of less than .5 percent for year. There has been considerable debate about the nature and causes of the low marital fertility--some state that it was lower than others (see Wolf 1985 and Coale 1985; also Lee and Campbell 1997). Considerably less attention has been paid to the fact and or the nature of the purported phenomenon of "early and universal marriage."
Analysis of marriage rates and marriage ages is very important for understanding the Chinese demographic regime, for two reasons. First, we are of course interested in the aggregate growth rates of the Chinese population, which though gradual by 20th century standards, nevertheless resulted in a tripling of the population during the Qing period. If we pursue the conventional strategies of demography and historical demography, all we need to know to understand the mechanisms of fertility rates, and their spatial and temporal variation, is to look at the ages at which women married, the ages at which they terminated childbearing, and the age-specific fertility rates in between.
There is, however, another way of looking at the Chinese demographic regime, from the standpoint of the investigation of a patrilineal, patrilocal society. Patrilocal marriage means not only that women move across the kinship system, from their natal families to their husbands' families, but also that they move geographically, from their natal villages to their husbands' villages. If we thus want to look at variations in population growth from one social group to another, the relevant social groups pass on their membership in the male line. These include lineages, villages, and to an extent social classes and occupational groups, which usually marry in a mildly hypergamous manner. So in order to look at spatial, kinship, and class variations in demographic behavior, we need to consider an unconventional, male-centered approach to demography. What, we might ask, is the growth rate of patrilocal families, and how do behaviors such as rates of marriage and ages at marriage affect the growth of patrilocal families and through them of the local, kin, and class communities to which they belong?
Thus both for conventional demographic understanding of aggregate population dynamics, and for more socially- and culturally-tuned understanding of the rates of growth of families and communities, the study of age at marriage is extremely important.

THE IMPORTANCE OF FEMALE AND MALE AGE AT MARRIAGE
Female age at marriage has a great effect on total fertility, whether we take a conventional or a patrilocal, family-centered approach. Especially since age-specific fertility rates tend to decline in the second half of the fertile period from age 30 on (though biological fecundability does not seem to change much until the 40s), a delay in marital age means taking away an important chunk of the most fertile years of a woman's life. Assuming, for example, a total fertility rate of 10, delay of marriage by three years probably cuts at least one child out of the TFR. So a maximally pronatal family strategy in a patrilocal, patrilineal family system will mean bringing in a daughter-in-law as soon as she has passed puberty; this will also, of course, have maximal fertility affects on the aggregate demographic regime.
Male age at marriage also affects total fertility, especially in a system like the Chinese one where widow remarriage is discouraged (even though it certainly happened). If widows do not remarry, then male mortality of their husbands will leave them celibate, and thus cut down their total fertility. Since male age-specific mortality tends to rise with age, the older the husband, the more likely he will die and cut off the wife's fertility before its natural span.
Even if widows remarry, the contribution of their union with their second husband to the increase of the family is problematic. Since most areas of China (with the exception of the Southwest) prohibited leviratic marriage, the second marriage of a young widow would either have to be out of her first husband's family into a third family, in which case her subsequent children would belong to her new husband's patriline, or an uxorilocal union with a man from another line (if the first husband's lineage even permits such unions), in which case the filiation of any children will have to be determined by negotiation (Harrell, Pasternak, Wolf and Huang).
Age at marriage is also important for refining our understanding of that aspect of the Chinese demographic regime usually characterized as "early and universal marriage." It now seems that this characterization, first made in order to draw an explicit contrast with the Western European regime (Hajnal), in which marriage was late-and non universal, is a misleading one. In fact, marriage was early and universal (and thus by implication universally early) only among females. Three kinds of evidence support this revision: ethnographic and social survey information from the early 20th century, anecdotal but overwhelming qualitative reports from throughout the late imperial period, and such indirect quantitative evidence as we can deduce from genealogies and other late imperial sources. According to all these kinds of evidence, almost all women married quite early, within a few years of puberty, while male age at marriage varied by class, with certain elites marrying their sons while they were still boys, a more common practice of most people marrying their sons at ages two or three years older than their brides, and a significant rise in male age at marriage with declining position in the social class system, so that the poorest men of all never married but became the fabled "bare sticks" or ¼’¼— who seemed to play such a large role in rebellions and other anti-dynastic activity.
Evidence about sex ratios also supports, albeit indirectly, the assertion of class variable marriage ages for men, especially if we believe that there was such a thing as a marriage market. Since the sex-ratio at birth can be assumed to be about 105 or 106, and since we know empirically that female infanticide was widespread, and also that female mortality seems to have been higher than male mortality up to age 40 or later in many populations (Lee and Campbell), market-like competition for available brides would favor those who could both pay high bride-prices and offer better living conditions for the daughters they took from their natal families, meaning that wealthy people had the advantage in the marriage market. The medium-poor had to wait a long time to accumulate the resources necessary to find brides for their sons, while the very poor never made it and died without descendants.
The central importance of age at marriage means that those of us who are trying to understand China's historical population dynamics need to use every source and every creative methodology possible to try to determine what marriage ages were and how they varied by community and class. This means that those of us engaged in genealogical demography should also pursue this question, difficult as it may be with the sources available to us.

A FEW BITS OF DIRECT EVIDENCE
As is probably well known to people at this conference, it is not easy to determine ages at marriage for Chinese populations before the 1950s, when the Communist Party, for the first time in history, established effective lower limits on marriage ages and required marriages to be registered. Ebrey (1996) has adduced some evidence from epitaphs written in the Song period, when the date or age of marriage was customarily inscribed on the tombstones of both males and females. She found, in fact, explicit marriage ages for 65 of the 189 couples for which epitaphs were available, and her findings demonstrate that the ages in the Song followed the same pattern outlined above for the Ming-Qing period: women had a much narrower range of marriage ages, 89% marrying between the ages of 14 and 21, and 54% between 15 and 18; the mean and median age were both 18. Men, on the other hand, had a slightly later median (20) and mean (20.8) age, and the difference between the median and the mean shows that they had a much wider range: to encompass 90% of the marriage ages, we need to expand the range to 14 to 29, and we should remember that we are dealing only with members of the high elite here.
Lee and Campbell (1997) and Lee and Wang (1999) are also able to use direct evidence, in this case for a late-imperial population, the banner households of Daoyi in Liaoning. They find, in fact, the same kind of pattern, where 90% of women were married by age 23 (and over half by 18), while the corresponding percentages for men were 54% and 20%, respectively (1997: 85). Their sample, unlike Ebrey's, is quite large, and they are working in the same period that concerns us here. The challenge, however (and I might add that I think this is the major challenge facing the study of Chinese historical demography in general) is to determined to what extent the findings of Lee and Campbell apply to the rest of the country, to non-banner populations, and to a variety of rural and urban social groups. Unfortunately for demographers, household registers were kept only for banner populations. For the rest of the country we need to rely on sources such as genealogies.

PROBLEMS WITH GENEALOGIES
As most of you know already, Chinese genealogies, documents written to determine the ritual and property rights and obligations of male members of large patrilineages, pay less attention to females than they do to males (Harrell 1987, Telford 1990). The degree of sex-bias varies from one genealogy and from one regional tradition to another (Telford, Thatcher, and Yang 1983), but no genealogies record age at marriage. The best of them, for our purposes, contain fairly complete records on the birth and death dates of male lineage members and their wives, but even the best still contain more complete information for males than they do for wives, and I know of none that record vital dates for daughters, though some of them give detailed information on where and to whom the daughters married. Thus if we are going to deduce anything about ages at marriage from genealogies, we have to do so indirectly. In the remainder of this short paper I will record some of the approaches that have been taken by various authors, and I would hope that the conference discussion will concern itself with the adequacy or inadequacy of these methods, along with suggestions for improving on what we have done so far.

ATTEMPTS TO ESTIMATE AGE AND MARRIAGE FROM GENEALOGIES

Liu Ts'ui-jung 1985

The first attempts to determine age at marriage that I know of were made by Liu Ts'ui-jung. In order to facilitate discussion, I quote her description of her methods in full:

The most appropriate procedure for men is to estimate the proportions single at given ages and then to apply John Hajnal's methods of calculating what he terms the "singulate mean age at marriage." The problem is to decide what assumptions to apply in estimating the proportion of single men in the critical age categories 15-19 and 20-24. One possibility is to assume that all men who did not have sons were single. Another is to assume that the only single men were those who died single. Since the two sets of assumptions produce very different results, I have calculated two sets of figures, one under the high age-at-marriage assumption and the other under the low age-at-marriage assumption. Our best estimate of men's age at marriage is probably an average of these two sets of figures.

ŠUnder the high age-at-marriage assumption the average age at marriage for these fifteen cohorts was 25.02 years; under the lowŠassumption it was 17.58 years; ont he average it is 21.3 years, which is strikingly close to the Princeton group's estimate of 21.39 years for South China in the 1930s.
Liu then goes on to calculate the wives' age at marriage from the differences between their and their husbands' ages, using the average figure for males and the mean age difference between husbands and wives to obtain a figure of 16.1 years for women.

This can be characterized as a valiant and creative attempt to solve the age at marriage problem using genealogies, but I think its assumptions are so unreliable as to render it fairly useless. The problems are as follows:

1. If, as we well know, the range of variation for men's ages at marriage was quite wide, just solving the problem of percentages unmarried at ages 15-24 does not address the problem of much later marriages among poorer men, who from anecdotal evidence can be seen marrying for the first time in their late 20s or even 30s.

2. Averaging the figures for age at marriage obtained under two opposing and admittedly ridiculous assumptions--either that all sonless men were single, or conversely that all married men had sons; or that the only men who were single at ages 15-24 were never to marry, or conversely that every man who married did so by age 24--seems to assume that truth can be obtained by averaging the results of two opposing fictions. The way Liu works this out, she seems to be making an implicit assumption that half of the men without sons were unmarried at a particular age, an assumption that has no demographic grounding that I know of, and comes close to begging the question of the relationship between marriage and having sons.

3. Trying to determine marital status on the basis of having sons or not runs into another problem that most genealogies do not record sons who died young. Depending on the rates of infant and early childhood mortality (which at any rate could not have been low for such a population), a large number of the men who appeared not to have sons would in fact have sons who died before they grew to the age at which they were included in the genealogy.

4. It seems very strange that the female age at marriage should average as low as 16, knowing what we know about menarche in traditional agricultural societies. This would seem to indicate that the average age for men is too low, probably by one or two years.

5. Finally, the mean says little about the standard deviation, and we know from those cases for which we have direct evidence that the standard deviation was much wider for men than for women. We should thus be talking about median ages rather than, or at least along with, mean ages, and we should examine the variation as well as the average.

The primary overall problem with Liu's procedure is that there is no good way for determining the relationship between marriage and the production of a son who lives to genealogically relevant age.

Telford 1992

Methods that project backwards from the birth of the first son recorded in the genealogy seem more promising than those that depend on percentages married at various ages. Ted Telford has explained his method as follows, in his article entitled "Covariates of Men's Age at First Marriage: The Historical Demography of Chinese Lineages," published in Population Studies:

Assume an hypothetical situation in which ten women all marry at age 17 and immediately begin having male and female children (M, F) with a sex ratio at birth of 105, until each has had a first son. Next, assume infant mortality for boys (I) at approximately 200 per 1000 live births (William Lavely, 'The rural Chinese fertility transition: A report from Shifang Xian, Sichuan', Population Studies, 38, 3 (1984), pp. 365-384); a first birth interval of 3.5 years and uniform average birth intervals of 2.5 years thereafter (Lavely, loc. cit.). Finally, account for underrecording of surviving sons (U) by arbitrarily setting them at ten per cent of all recorded sons. Infant mortality and/or infanticide of girls does not significantly alter the outcome based on birth of sons only, and are ignored for this simulation. Using this set of assumptions, recorded sons will be born as follows:

Mother's age at each birth

Case 20.5 22.0 24.5 27.0 29.5 32.0

1 M
2 M(I) M
3 M
4 M
5 M(U) M
6 F M(I) M
7 F M
8 F F M(I) M
9 F F F F M
10 F F F F F M


Total observed surviving (3) (3) (1) (1) (1) (1)
sons' births

Median age of mothers at birth of first surviving son = 22.00.
Mean age of mothers at birth of first surviving son = 24.05.
Actual mean age of mothers at first marriage = 17.00.
Actual median age of mothers at first marriage = 17.00.
Adjustment factor (difference between mean and actual) = 7.05. Adjustment factor (difference between median and actual) = 5.00.


While these ten women would have to give birth to 14 sons and 13 daughters in order to record a total of ten surviving sons, it is possible for a woman married at age 17 who does not produce a surviving son until she is age 32 (as in case 10), to have had five or more previous births, all of which were girls, or sons who died as infants, or were otherwise lost to the records. Altering the simulated timing of events lowers the mean age of mothers at birth of first son in some scenarios and increases it in others, but the adjustment never goes below six or above eight years.

This analysis seems much more reliable than that of Liu. As Telford mentions, however, the adjustment factor can be off by as much as two years, ranging from six years to eight depending on the assumptions made about infant mortality rates and about birth intervals. These two factors are, of course, connected.
If infant deaths are not recorded, then the higher the rate of infant mortality, the higher the ratio of recorded birth interval to actual birth interval. In this particular analysis, Telford simply assumes both a birth interval and an infant mortality rate, taken from Lavely's estimates based on 20th-century data. It seems questionable, however, whether one can assume both, if the apparent or recorded birth interval is fixed by the empirical data at hand in the genealogy. Perhaps for this reason, Telford is more cautious than Liu, and does not use actual ages at marriage in his analysis, but instead simply uses age at the birth of the first recorded son as a proxy value for male age at marriage, and shows how this proxy varies with a series of socioeconomic measures that are assumed to be independent variables. If he were to calculate these ages, however, he would come up with female ages at marriage ranging from slightly under 15 for the gentry to almost 17 for the non-gentry (1992:29). These also seem low, but are in concert with what Liu found.

Harrell and Pullum 1996

In our article, we take a tack similar to Telford's, but not exactly the same. We explain our procedure as follows:

[We] work backward from age at the birth of the first [recorded] son, subtracting from this latter figure an amount equal to an estimate of the average time from the marriage until the first son's birth. This latter must be calculated semiempirically from the data contained in the genealogies. First, we find the mean birth interval. For the Xiaoshan lineages we have not intervals between births ut simply intervals between births of sons who survived to maturity and are thus included in the genealogies. The man interval between births of first and second surviving sons is 6.7 years i the Shi lineage and 7.1 years in the Wu lineage. If we assume, for simplicity's sake, that half the births are female and that females have the same mortality as males at young ages, then the mean birth interval for those who survived to adulthood is 4.6 years for the Shi and 4.7 for the Wu.

Footnote: This figure is counter-intuitive, but in fact the average interval between male births is not twice the interval between births. The relationship between the two figures is complex, depending on the average number of births per mother. But if each mother has five total children, the ration of male-male birth intervals to child-child birth intervals is 1.47; it increases as the number of children increases. We use 1.5 as an estimate.

Now we have to come up with a figure for the interval between marriage and birth of the first surviving child. There is no indication at all what figure we should use for this, but two years cannot be far off. Then approximately half the couples will have their first son at a mean of two years after their marriage. Another quarter of the couples will have first a daughter, then a son. Adding the 2 years from the marriage to the daughter's birth to the 4.6 years until the son's birth, we have 25% of the couples with a son born a mean of 6.6 years after the marriage. Similarly, 12.5% of the couples will have first two daughters, then a son, born at a mean of 11.2 years after the marriage. So on until we reach insignificant quantities of people who will have a lot of daughters and then a son. This procedure yields an average interval from marriage to birth of the first surviving son of 6.5 years for the Shi lineage and 6.7 years for the Wu lineage [1996:145-46].

Using these figures, we arrive with a mean age at marriage of 24.1 for men and 17.6 for women. This does not, however, agree with our finding that the mean age difference between husbands and wives was only 3.3 years. How could the mean age difference between husbands and wives be 3.3 years, when the difference between husbands' and wives' mean ages at marriage is 6.5 years? The answer is that some of the men did not have surviving sons by their first wives, but rather by second wives or concubines. So in fact the age of the wife is not the same as the age of the mother of the first surviving son, and not surprisingly the wives are older. In other words, figuring backward from mother's age at the birth of first son is a good method (despite the fact that we probably still don't know quite the best way to do it), because wives are ordinarily married only once. But figuring backward from husband's age to the age at the birth of the first son does not work so well, because some portion of marriages of husbands are second marriages or concubinages.

Many of the same criticisms can be levelled at the Harrell and Pullum method as at the Telford method. In the end, they both depend on completely arbitrary or analogous reasoning to come up with what is probably the average first-birth interval. After that, the H and P method perhaps has a slight advantage (am I prejudiced?) because we do not need to know the actual inter-birth intervals for all children, but work directly from the intervals for recorded children. This means that we do not need to estimate an infant-mortality rate, or the ratio of recorded children to total children, which amounts to close to the same thing.

It is interesting that whatever methods we use, we are not terribly far from each other. Discounting the very real possibility that we are dealing with different samples whose real mean and median values were different, we still find a mean female age at marriage ranging from 15 to 19, with most of the estimates clustering around 16 or 17, and a mean male age of 20 to 24, which seems to vary clearly with the sample. Any of these estimates put the mean ages of marriage in China below those found for the Western European demographic regime, and thus confirm half of the old adage that marriage was early and universal. It was early, in comparison to Western Europe, for both sexes, and universal for males.

Just how early Chinese marriage actually was still seems to me a legitimate subject for research. I hope the scholars at this conference will be able to suggest ways that we can improve upon the three still rather crude methods outlined here of estimating age at marriage from Chinese genealogical records.