Celebrating legacy: The intergenerational transmission of reproduction and human capital in Ming–Qing Chinese families

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This paper uses the genealogical records of 36,456 males to investigate the nexus—the intergenerational transmission of reproduction and human capital—within six Chinese lineages from 1350 to 1920. By examining the relationship between reproduction and long-run reproductive success, the empirical results reveal that the optimal level of reproduction exceeded the sample median. This finding suggests that greater reproduction in each generation was conducive to long-run reproductive success. In exploring the mechanisms through which reproduction affected long-run reproductive success, I investigate the relationship between child quantity and quality. The results indicate an absence of quantity-quality trade-off of children in the six lineages. This paper concludes that, in Ming–Qing (1368–1911) China, opting for larger families conferred definite advantages upon high-status men, enabling them to produce a greater number of high-quality male descendants across successive generations. JEL Classification I25, J13, N35 , O15 Reproduction Long-run reproductive success Child quantity-quality trade-off Ming–Qing China Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1 Introduction To explain the long-run economic growth, the “population-idea nexus” is always of the essence (Doepke, 2004; Mokyr and Voth, 2010). Technology, a key element of economic development, does not “just happen” but depends on the population, particularly the accumulation of human capital within it (Kremer, 1993). In many newly proposed unified growth models that seek to explain both the Malthusian stagnation and economic take-off, the relationship between reproduction and technology in the long run is carefully traced (Galor and Weil, 2000; Galor and Moav, 2002; Galor, 2011; Galor, 2022). Therefore, two crucial elements come into play: population size and population composition (Galor, 2022). In the era of Malthusian stagnation, higher living standards resulted in larger family sizes, leading to a gradual increase over time in the proportion of descendants from families with higher living standards within the total population. Over the long run, these two “wheels of change” operated under the influence of natural selection, ultimately increasing the representation of growth-promoting traits in the total population (Galor and Klemp, 2019; Galor, 2022). This dynamic, in turn, promoted investment in human capital and facilitated the demographic transition and transition from stagnation to sustained growth (Galor and Moav, 2002). Specifically, Galor and Klemp (2019) explore natural selection forces by using the genealogical data of half a million residents over four generations in pre-industrial Quebec and find a hump-shaped relationship between fecundity and long-run reproductive success. They conclude that moderate fecundity, coupled with a higher level of education, was more conducive to the continuity of the lines of descent; the negative effects on survival of larger family sizes also suggest the presence of child quantity-quality trade-offs (Galor and Klemp, 2019). Building on the work of Galor and Klemp (2019), I examine the evolution of the two wheels in a pre-transition context. I use a new genealogical dataset containing 36,456 males to exploit multigenerational associations in reproduction across six lineages in Southeast China from 1350 to 1920. This period covers the two last imperial dynasties, the Ming (1368–1644) and Qing (1644–1911) dynasties. My intention is to show the reproductive success of Chinese males in a multigenerational model by analyzing the pattern and mechanisms of fertility transmission. I focus on exploring two types of trade-offs: a Darwinian trade-off between reproduction and the long-run reproductive success and a Beckerian trade-off between the quantity and quality of children. I aim to illustrate how reproduction affected the long-run reproductive success of a patriline through the accumulation of human capital. 1 I first test for the presence of the Darwinian trade-off by examining the optimal level of reproduction for long-run reproductive success in the six lineages. I estimate the relationship between the number of sons and the number of patrilineal male descendants in the three subsequent generations in which a male had to test whether high reproduction in the first generation could translate into high reproduction in the three that would ensue. The estimation results show that there was no significant trade-off between reproduction and long-run reproductive success. A man who had seven sons would have more great-great-grandsons than a man who had more than seven sons. However, this optimal level of reproduction was much greater than both the sample median and mean reproduction levels, which were about two sons. I then analyze the possible mechanisms through which parental reproduction could affect next generation reproduction. The positive effect of reproduction on long-run reproductive success suggests a positive relationship between child quantity and quality, or in other words, the absence of a Beckerian trade-off. The family size of the first generation could affect the quality of the second generation and thus affect the likelihood of the second generation producing male descendants in subsequent generations. I use the number of sons a father had, that is, the number of brothers that a male had (including himself), to measure final family size. I use two indicators to measure child quality. The first measure is Married , which measures whether the male could have at least one marriage before he died. The logistic regression results reflect a positive correlation between the number of brothers possessed by a male and the likelihood of his getting married. Sons from larger families enjoyed a higher probability of entering into marriage, which was a prerequisite for leaving male descendants in traditional China. Following Shiue’s (2017) variable construction, the second indicator concerns a son’s formal education, Degree . Based on the education-related information recorded in the genealogies, 1,506 males (4.13 per cent) in the sample obtained academic degrees. The logistic regression analysis indicates that although fathers’ and grandfathers’ social status had the strongest effects on son quality, the number of brothers a male had was also positively correlated with his quality. Nevertheless, because of potential endogeneity issues arising from unobservable parental preferences and household characteristics affecting both family size and son quality, establishing a causal relationship becomes challenging, and correlations may be biased. Therefore, I instrument the number of sons a father had with his age at the birth of his first son. The instrument is valid because it was conditionally exogenous. With the father’s age being younger at the birth of his first son, the father’s reproductive span for bearing sons would be longer. After conditioning on cultural and socio-economic factors, the onset of son-bearing was largely random and not related to the father’s own preferences for child quality. Additionally, it could not directly affect a son’s likelihood of marriage or academic achievement. The instrumental variable results, similar to the baseline results, indicate significant positive effects of family size on the “quality” of a son. The number of brothers continued to significantly impact their chances of marrying or obtaining an academic degree. Large families exhibited positive aspects in the six lineages. In particular, degree- and office-holders could have larger families, and their sons were also more likely to marry and obtain academic degrees. The social gradient in human capital formation remained strong. In general, the logistic and IV results both suggest that a significant Beckerian trade-off was absent in the six lineages from 1350 to 1920. This paper contributes to the previous literature in two ways. On the one hand, this paper offers some of the first quantitative evidence on the narrative of reproductive success in a multigenerational model for pre-modern China. Biologists studying the trade-off between fertility and various biological traits find that high fertility does not always lead to high rates of survival (Lack, 1954; Williams, 1966; Stearns, 1989). Social scientists have then examined different types of Darwinian trade-offs within the human species and suggested different relationships between female fertility and offspring survivorship, parental fertility and next generation fertility, and the optimal level of fertility and long-run reproductive success in different societies (Kaplan et al., 1995; Hill and Hurtado, 1996; Kaplan, 1996; Borgerhoff Mulder, 2000; Strassmann and Gillespie, 2002; Galor and Klemp, 2019). To ensure greater continuity in bloodlines, high survival in only one generation is not enough; most importantly, reproductive success in one generation must be transmitted across generations. Song et al. (2015) employ two data samples from northern China during the Qing dynasty and discover that patrilineages with high social origins increased their representation in the overall population by minimizing the risk of extinction, rather than maximizing the number of male descendants in each generation. This paper, however, identifies a slightly different pattern for Southeast China. Productive ancestors were able to transmit their reproductive advantages for at least four generations. On the other hand, this paper extends the empirical literature on the trade-off between the quantity and quality of children in the pre-transitional era. In pre-modern societies, one of the mechanisms through which parental reproduction affected next-generation reproduction is that parents would make a trade-off between reproduction and investment in offspring quality, thus affecting offspring reproduction. Economists have studied this type of child quantity-quality trade-off since Becker (1960; Becker and Lewis, 1973; Becker, Murphy, and Tamura, 1990) first inserted fertility decisions into the economic analysis and argued that parents would sacrifice the number of children they could have for higher quality in the children they had. A considerable amount of empirical literature also tries to support or challenge this Beckerian argument in both historical and modern times (see the examples of Northern Europe: Baudin and De la Croix, 2023; of India: Rosenzweig and Wolpin, 1980; of Thailand: Knodel, Havanon, and Sittitrai, 1990; of Norway: Black, Devereux, and Salvanes, 2005; of Brazil: Ponczek and Souza, 2012; of the USA: Tan, 2019; of Korea: Lee and Park, 2019; of England: Clark and Cummins, 2016; Klemp and Weisdorf, 2019; of China: Qian, 2005; Rosenzweig and Zhang, 2006; Li, Zhang, and Zhu, 2008; Liu, 2014; Shiue, 2017; Bai, Li, and Lam, 2023). 2 Shiue (2017) examines genealogical data from Tongcheng County and finds a negative relationship between family size and sons’ education during the seventeenth and eighteenth centuries, which disappeared afterwards. Meanwhile, Bai et al. (2023) observe a similar trade-off in North China, but only after 1800. In addition, Song et al. (2015) speculate that in the Qing period, high-status founders may have strategically employed the child quantity-quality trade-off to ensure continuity in their bloodlines. Like Shiue (2017), this paper also conducts an analysis covering the entire Ming–Qing period from 1350 to 1920. Unlike in previous research, the geographical focus shifts to the core lower Yangtze region, which has been the most developed area in China for centuries and a central point in several significant debates over the past two decades in the economic history of China (Shiue, 2016). An examination of the relationships between reproduction and marriage, as well as between reproduction and education in an intergenerational model, demonstrates that family size affected child quality to varying extents. The results of the two trade-offs also shed light on the absence of a fertility transition in nineteenth-century China. The rest of the paper is structured as follows. Section 2 describes the genealogical data, and Section 3 introduces the empirical strategies. Section 4 reports the results for long-run reproductive success and the child quantity-quality trade-offs. Section 5 is a discussion of the results, and Section 6 concludes. 2 Data and main variables 2.1 The lineage sample In Ming–Qing China, lineages were the most widespread and long-lasting forms of social organizations (Feng and Chang, 2001; Zelin, 2009). In a society that attached great importance to the maintenance and expansion of the patrilines, keeping genealogical records became a standard practice for most of the lineages to remind the offspring of their family history (Zhao, 2001; Feng, 2009). The primary data used in this paper come from the genealogical books of six lineages in Southeast China; the sample includes 36,456 males born between 1350 and 1920. Online Appendix Figure A1 shows the two provinces and four prefectures where the six lineages are located. Genealogies of a lineage always include an introduction to the history of the family, the rules of compilation, the rules and regulations that family members had to follow, a family tree that includes all the male members recorded in the book, and finally a series of detailed entries for each male descendant in the family (see Figure A2 for an example of a male individual’s entry in the book). The family tree and sons’ names recorded under the fathers’ entries enable us to link male family members easily across generations. Although genealogical data are very useful for examining reproduction and survival, they are not free from selection bias. Hu (2023a) has a detailed discussion of selection biases in this six-lineage sample. The main bias that would affect the empirical estimation in this paper is the lack of information about daughters in the genealogies. Due to the strong preference for sons in imperial China, daughters are highly under-reported. The sample included 41,145 sons in total but only 9,636 daughters. Given that the number of sons who survived infancy is completely recorded for every male’s entry, I use this number in the present paper to measure reproduction and family size. Moreover, because of the patrilineal structure in the Chinese families, the “descendants” in this paper represent only the patrilineal male descendants who inherited the surname of the lineage. 2.2 Dependent and independent variables In the main analysis of the optimal level of reproduction, the dependent variable is the recorded number of patrilineal grandsons, great-grandsons, and great-great-grandsons of each male in the sample. The independent variable in this analysis is the number of a male’s sons who survived infancy. In the analysis that examines the child quantity-quality relationship, which is the mechanism through which parental reproduction affected next-generation reproduction, the dependent variables are two dummy variables that measure two indicatiors of quality in males: their marital status ( Married ) and their formal education ( Degree ). The independent variable is the number of brothers who survived infancy that a male had, in other words, the number of sons who survived infancy, both biological and adoptive, that the male’s father had. Therefore, the number measures the final family size in terms of male births. Since long-run reproductive success is measured in this paper by the number of male descendants a male could have, the two variables indicate a male’s quality in terms of his capability of leaving male descendants. Both quality measures are also closely related to the male’s parents’ investment in him. First, Married is considered a valid measure in this context because entering into marriage is the prerequisite for males to have male descendants. The shortage of women in Ming–Qing China, caused mainly by female infanticide and polygamy, made the marriage market seriously unbalanced (Lee and Wang, 1999). Marriage served as an especially “sensitive measure of privilege” because the ability to marry was contingent on having access to resources (Lee and Campbell, 1997; Lee and Wang, 1999). A substantial proportion of males, especially males from impoverished families and low-social-status males, failed to ever marry. 3 Thus, the “quality” of the male largely determined whether he could marry or not. Second, Degree is a commonly used measure of human capital in pre-modern China (Shiue, 2017). Moreover, it mattered because academic degrees determined the social status of men in Ming–Qing society, which, in turn, significantly influenced the number of sons they could leave behind (Hu, 2023a). Based on the social status records in the genealogies, I divide all the males in the sample into 14 levels of social status and construct the variable Degree based on their social status to measure their human capital (see Table 1). In the Ming–Qing period, education was closely related to social status and wealth, for education could bring people high social status and considerable wealth because of keju , the national civil examination system. 4 The exam mainly tested candidates’ knowledge of the Confucian classics. All male commoners, including peasants, artisans, and merchants, could attend civil examinations, and academic degrees on three levels — shengyuan , juren , and jinshi — would reward those who could pass the corresponding county-level, provincial-level, and national-level exams (Chen, Kung, and Ma, 2020). Candidates who failed exams could also repeatedly retake them (Miyazaki, 1981). Some of the more successful degree holders would later hold office. The keju degree holders and office holders would thus be coded 1 for Degree . Table 1 Degree and social status classification Status Class Degree Count Percent Description 1 0 0 34,555 94.79% No status 2 1 0 108 0.30% Lineage chief; donor to the lineage and the county 3 1 0 80 0.22% Literate and educated but with no academic degree (teacher of the village or editor of genealogical books) 4 1 0 64 0.18% Awarded official titles by the emperor, with no academic degree 5 1 1 487 1.34% Lower degree holder (normal shengyuan and civil shengyuan ) 6 1 1 524 1.44% Students at the Imperial Academy (lower degree) 7 1 1 35 0.10% Intermediate/high degree holder ( juren , gongsheng , jinshi ), but with no official position 8 1 0 52 0.14% Prospective officials ( houbu ), with no academic degree 9 1 1 67 0.18% Prospective officials ( houbu ), with academic degree 10 1 0 91 0.25% Clerks ( wei’ruliu ); the lowest-ranking official ( zong jiupin ), with no academic degree 11 1 1 106 0.29% Low-/medium-ranking local official and low-ranking court official, with normal and civil shengyuan degree 12 1 1 128 0.35% Low-/medium-ranking local official and low-ranking court official, with a degree of studentship at the Imperial Academy 13 1 1 82 0.22% Low-/medium-ranking local official and low-ranking court official, with an intermediate/ high degree 14 1 1 77 0.21% High-ranking local official and medium/high-ranking court official Source: Ho 1962, Chapter 1; Telford 1995, Appendix 3A; Shiue 2017, Table 1. 3 Empirical strategy 3.1 The Darwinian trade-off: the relationship between reproduction and long-run reproductive success 3.1.1 The model To test the presence of the optimal level of reproduction for long-run reproductive success, I apply a multigenerational model, following the methods in Kaplan et al. ( 1995 ) and Galor and Klemp ( 2019 ). The sample used in this analysis consists of 9,336 “ancestors” who had at least one son. Males with incomplete records of male descendants in the subsequent four generations are excluded. I first test whether the relationships between the number of sons and the log-transformed number of male descendants in the next three generations are monotonic. I run a non-parametric analysis by using the LOWESS method. As Fig. 1 presents, the relationships are not strictly linear. The man in the sample with the most sons and grandsons is Zhuang Chaosheng from the Zhuang lineage. He married 10 times and had 12 sons and 50 patrilineal grandsons in total. However, he is not the one with the most patrilineal great-grandsons and great-great-grandsons, while his father, Zhuang Yinghui, who had 5 sons, is the one with the most patrilineal great-grandsons, 88. Que Qixin from the Que lineage had only 4 sons, but his male descendants produced 194 patrilineal great-great-grandsons for him, which is the greatest number of great-great-grandsons in the sample. Because the number of grandsons (mean = 2.95, variance = 8.86), the number of great-grandsons (mean = 3.64, variance = 26.81), and the number of great-great-grandsons (mean = 3.90, variance = 61.22) are all count variables and are over-dispersed, I employ negative binomial regression to test the relationship between the number of sons and the number of male descendants in the following three generations based on the following equation: $${Descendants}_{i}=\alpha +{\beta }_{1}{Sons}_{i}+{\beta }_{2}{Sons}_{i}^{2}+{\delta P}_{i}+{\epsilon }_{i},$$ 1 where Descendants is the number of male offspring that a male (Generation 1) had in the three generations after his sons’ generation (Generations 3–5, i.e. grandsons, great-grandsons, and great-great-grandsons); i denotes male individuals. Sons is the number of sons that a male had. Given the non-monotonic relationships shown in Fig. 1 , I also control for the squared term of Sons. P is a set of control variables that would also affect the number of male descendants in generations 3–5. \(\epsilon\) is the error term. If the optimal level of reproduction did exist, men with a moderate level of reproduction would be expected to have the most grandsons, great-grandsons, and great-great-grandsons. Having more sons than the optimal number would lead to fewer male descendants in the following generations. 3.1.2 The control variables I condition on a set of control variables in the model to establish the causal relationship between reproduction and long-run reproductive success. Class and Marriages. In pre-modern China, education, wealth, and social status were closely related. The number of marriages that a male had was also positively associated with his social status and wealth. Thus, Class and Marriages are controlled for the effects of the male’s socio-economic characteristics on his long-run reproductive success. Class indicates whether the man belonged to a status group higher than status 1, referred to as the privileged group, as described in Table 1 . Marriages denotes the number of times that the man married during his life. Hao . I use Hao (pen name) to control for the effects of basic literacy training on reproduction. Even though the costs of attaining basic literacy in Ming–Qing China were modest, being literate was still a privilege (Shiue, 2017 ). This could be measured by whether a male gave himself a pen name or not and could also be considered a proxy for household wealth. Firstborn . In traditional Chinese culture, the firstborn son had a “demographic advantage” being tasked with the primary responsibility for leaving male descendants, which was expected to correlate positively with long-run reproductive success (Lee and Campbell, 1997 ; Li and Zhen, 2015 ). Survival to adulthood . Lifespan is closely related to reproduction and human capital formation. Only about one third of the males in the genealogies had complete vital records, but males who died before adulthood were also marked in the genealogies. I use the dummy Survival to distinguish males who failed to reach adulthood from the other males to control for its negative effects on reproduction. Out-migration . If a male migrated to another village, it was difficult for the compilers of the genealogy to update the information on him. I include Out-migration to control for the negative effect that this move could have on the number of male descendants recorded in the genealogy. Birth cohort , Lineage and Branch . The birth cohort, lineage, and branch to which the male belonged would affect his reproduction and long-run reproductive success. Of the 36,456 males in the sample, only 23,098 had birth years recorded. With these birth year records, I impute an approximate birth cohort for the relatives of these males whose birth years were not recorded. I classify 31,197 males into twelve birth cohorts, starting with a “pre-1400” interval (1350–1400), ending with a “post-1900” interval (1900–1920), and with ten half-century-long cohorts in between. 3.2 The Beckerian trade-off: mechanisms through which reproduction affected long-run reproductive success 3.2.1 Baseline model I first run logistic regressions based on the following equation: $${P(Quality}_{i}=1)={\Phi }(\alpha +\beta {Brothers}_{i}+\delta {Z}_{i}+\gamma {W}_{i}+{\epsilon }_{i}),$$ 2 where Quality denotes the male individual’s quality, and i denotes male individuals. I use two indicators to measure quality, Married and Degree . Married equals one if the male was married at least once, and Degree equals one if the male was a keju degree holder. \(\alpha\) is the constant. As the number of daughters is incomplete in the genealogies, I use Brothers to measure the quantity of children. It equals the number of brothers (including himself) in a male’s generation of his family of origin, in other words, the number of sons who survived infancy that his father had. Z denotes a set of control variables, most of which are also used in Eq. ( 1 ), including Firstborn , Survival to adulthood , Out-migration , Lineage and Birth cohort . W includes a set of factors linked to the male’s father and grandfather that could affect his marital status and education. \(\epsilon\) is the error term. If a trade-off existed, a negative \(\beta\) would be expected since it represents parents choosing between the quantity and quality of their sons. The additional control variables I condition on include whether the male was adopted, his father’s social status and number of marriages, as well as his grandfather’s social status and number of sons. Adoptee. In a society that highly values filial piety, having a male heir to continue the bloodline is a priority for every male. However, not every male could fulfill this task, leading to the widespread practice of adoption. 5 As an adoptee, the sole heir in the new adoptive family, he would face additional pressure to excel and perform well (Waltner, 1990; Wolf and Huang, 1980). Therefore, I control for whether the male was an adoptee or not. 6 Father’s class and Father’s marriages . For each male individual I control for his father’s social status and the number of times his father married to reflect the socio-economic characteristics of his family of origin. Father’s class equals 1 if one’s father had a status higher than 1; otherwise, Father’s class equals 0. Grandfather’s class and Number of uncles . Moreover, I include the effects of the grandfather in the model to address the endogeneity issue. The major difficulty in establishing the causal relationship between family size and child quality is omitted variable bias. The effects of unobserved household features and parental preference on child quantity and quality would obscure the existence or absence of a trade-off between child quantity and quality. In a male-dominant society that values filial piety, the couple’s preference would be influenced by the husband’s parents’ decisions. Moreover, in natural populations with minimal social gradients in fertility, an intergenerational correlation in reproductive fitness was also evident (Pluzhnikov et al., 2007 ). Therefore, I control for the social status of the grandfather of every male individual and the number of uncles that he had, in other words, the number of sons his grandfather produced, to partly address endogeneity. Table A1 in the Online Appendix reports the summary statistics of the sample. 3.2.2 Instrumental variable model As mentioned before, the unobservable parental preference and household features that would affect both quality and quantity of children would bias the effects of family size on child quality. To address the concern of omitted variable bias, I construct an instrumental variable, the father’s age at the birth of his first surviving son. The onset of son-bearing and consequently the duration of one’s reproductive period are directly correlated with family size and are also conditionally exogenous. 7 To investigate the trade-off between fertility and offspring quality, Galor and Klemp ( 2019 ) employ the concept of the “protogenesic interval” (PI), which represents the duration between the date of marriage and the birth of the first child, as a measure of fertility. Since the genealogical records do not include specific marriage dates or the birth dates of the first child but only the birth dates of the first surviving son, I modify this PI measure to another variable, namely, the father’s age at the birth of his first surviving son. There was an old saying in traditional Confucian ideology: “There are three things which are unfilial, and to have no posterity is the greatest of them.” In a society that values filial piety highly, having male heirs to continue the bloodline is the priority for every male. Ming–Qing China primarily adhered to a “natural fertility regime”, where deliberate fertility controls—late starting, longer spacing, and early stopping—were largely absent (Hu, 2023b ). Hence, if a male had a surviving son at an earlier age, this suggests that he could have a longer reproductive span, resulting in more surviving sons throughout his lifetime. As depicted in Fig. 2 , most fathers had their first surviving sons in their 20s. To be a valid instrument, the timing of a father’s first male birth needs to be conditionally exogenous. However, time is affected not only by random events that affect the process of conception but also by cultural and socio-economic factors (Galor and Klemp, 2019 ). In particular, men from wealthy families or those with higher social status could hypothetically marry earlier and have their first son earlier than those without. To account for potential socio-economic confounding factors affecting child quality, I directly control for a series of family-related characteristics to isolate the effect of random variations in the father’s age at the birth of his first son. This includes the grandfather’s social status, as well as the father’s social status, both of which could affect the timing of the father’s marriage. Hence, I then instrument the number of brothers that a male had by the conditionally exogenous variation induced by his father’s age at first son’s birth. I use an OLS regression and a probit regression to estimate Equations ( 3 ) and ( 4 ), respectively, $${Brothers}_{i}={\alpha }_{2}+{\beta }_{2}{FatherAge}_{i}+{\delta }_{2}{Z}_{i}+{\gamma }_{2}{W}_{i}+{\epsilon }_{i}$$ 3 , $${P(Quality}_{i}=1)={\Phi }({\alpha }_{3}+{\beta }_{3}{\widehat{Brothers}}_{i}+{\delta }_{3}{Z}_{i}+{\gamma }_{3}{W}_{i}+{\epsilon }_{i})$$ 4 , in which the variable FatherAge equals father’s age at the birth of his first surviving son. Brothers still denotes the final family size. The other notations are the same as in Eq. ( 2 ). 4 Results 4.1 The absence of an optimal level of reproduction for long-run reproductive success 4.1.1 Baseline results Table 2 reports the results of regressions based on Equation (1). As expected, the number of descendants in generation 2, Sons , had a strong positive effect on the number of patrilineal male descendants in generations 3–5. The square term of Sons maintains its negative and statistically significant effects on reproduction of the subsequent three generations in all columns in all three specifications. This suggests the possible presence of an optimal level of net reproduction for long-run reproductive success. The fitness for long-run reproductive success could diminish beyond a certain level of reproduction. Table 2 The effects of Sons on the number of male descendants for males born between 1350 and 1920, negative binomial regression Dependent Variable: Number of male descendants in Gen.3 Gen.4 Gen.5 Gen.3 Gen.4 Gen.5 Gen.3 Gen.4 Gen.5 (1) (2) (3) (4) (5) (6) (7) (8) (9) Sons 1.834*** (0.067) 1.854*** (0.071) 1.876*** (0.080) 1.776*** (0.069) 1.784*** (0.072) 1.778*** (0.080) 1.786*** (0.049) 1.802*** (0.057) 1.788*** (0.069) Sons 2 0.965*** (0.006) 0.964*** (0.006) 0.962*** (0.006) 0.967*** (0.006) 0.967*** (0.006) 0.964*** (0.006) 0.963*** (0.004) 0.960*** (0.004) 0.958*** (0.005) Class 1.172*** (0.039) 1.308*** (0.070) 1.369*** (0.104) Hao 1.127*** (0.040) 1.547*** (0.077) 1.645*** (0.117) Marriages 1.101*** (0.022) 1.153*** (0.031) 1.228*** (0.042) Controls Firstborn N N N Y Y Y Y Y Y Out-migration N N N Y Y Y Y Y Y Survival N N N Y Y Y Y Y Y Birth cohort FE N N N Y Y Y Y Y Y Lineage & Branch FE N N N Y Y Y Y Y Y N 9,336 9,336 9,336 6,992 6,992 6,992 6,992 6,992 6,992 Pseudo R 2 0.093 0.040 0.023 0.106 0.058 0.055 0.112 0.064 0.060 Notes: 1. Coefficients are incidence rate ratios (IRR) for the negative binomial regression, and robust standard errors are in parentheses, clustered on fathers. 2. *p<0.1; **p<0.05; ***p<0.01. After conditioning on all factors, hump-shaped patterns persist between the number of sons and the number of patrilineal male descendants in the next three generations in the six lineages. As shown in Figure 3, based on the results from columns 7 to 9, the predicted numbers of patrilineal grandsons, great-grandsons, and great-great-grandsons all reach their peaks when the number of sons equals seven. This finding suggests that the optimal level of reproduction for long-run reproductive success in the six lineages was about seven sons. The statistically significant coefficients on Class , Hao , and Marriages in columns 7 to 9 also indicate that high-status and literate males could leave more male descendants than their low-status and illiterate counterparts in subsequent generations. A male’s social status and wealth not only affect his own reproduction but also affect the reproductive success of at least the next three generations. Figure 4 shows the social gradient in the long-run reproductive success; males who had a status higher than 1 could have more patrilineal grandsons, great-grandsons, and great-great-grandsons than males with status 1. The persistent effect of social status shown in the six lineages also validates what Song et al. (2015) find in North China from 1725 to 1875 and Lee and Park (2019) find in pre-modern Korea. However, as Figure 5 demonstrates, only 165 males (1.77%) from the “ancestor” sample had more than 5 sons. The sample mean and median of 2 sons are both below the potential optimal level of reproduction, 7 sons. The results for the six Chinese lineages suggest a difference between pre-transitional Southeast China and Quebec, as observed in Galor and Klemp (2019). In Quebec during the sixteenth to the eighteenth centuries, the optimal level of reproduction was below the population median (Galor and Klemp, 2019). In the six lineages, the potential optimal level of reproduction for having the greatest number of patrilineal grandsons, great-grandsons, and great-great-grandsons was significantly greater than the reproduction observed for the majority. For nearly all men in the sample, having more sons could directly translate into reproductive success in the long run. In contrast to the situation in Quebec, where a significant Darwinian trade-off gradually evolved into a demographic transition and subsequent economic transition, the findings in this paper indicate the absence of a significant Darwinian trade-off in the six Chinese lineages. 4.1.2 Robustness This section tests the robustness of the previous results of the Darwinian trade-off to (1) an alternative estimation model, (2) converting the number of sons into a categorical variable and (3) controlling for lifespan. A hump-shaped relationship between the number of sons and long-run reproductive success is established using a negative binomial regression model. Table B1 in the Online Appendix demonstrates that this hump-shaped relationship is robust to the use of an OLS regression model. 8 Although the analysis includes males with at least four generations of male descendants, their lifespan might significantly affect their own reproduction and thus long-run reproductive success. To address this concern, I further condition the analysis on males with complete birth and death records, controlling for lifespan. The results are reported in Online Appendix Table B2. Lifespan had a positive effect on the number of male descendants a male could have in generations 3–5. When lifespan is included as a control, the coefficients of Sons and Sons 2 are highly comparable to the results in columns 7–9 of Table 2, indicating that the baseline results are robust. The coefficients on Sons 2 in Table 2, Table B1, and Table B2 consistently suggest a hump-shaped relationship between reproduction and long-run reproductive success. To validate the non-monotonic nature of the relationship, I also conduct an additional regression using the same estimation equation. In this regression, I convert the number of sons from a continuous variable to a categorical variable, excluding the square term of the number of sons. 9 The results in Table B3 and Figure B1 in the Online Appendix affirm the persistence of the hump-shaped pattern, particularly in the relationship between the number of sons and the number of great-great-grandsons. The optimal level of reproduction remains at seven sons, underscoring the robustness of the baseline results. 4.2 Mechanisms through which reproduction affected long-run reproductive success Galor and Klemp (2019) report that moderate fecundity could enhance child quality by increasing the probability of marrying and becoming educated, which would thus enable children to leave more descendants. Therefore, in this section, I examine the two types of Beckerian child quantity-quality trade-off in the six lineages: the effects of family size on the probability of sons marrying and achieving a keju degree. 4.2.1 Logistic estimation results Tables 3 and 4 report the logistic regression results based on Equation (2). 10 In Table 3, where quality is measured by marital status, the key independent variable Brothers consistently retains positive coefficients across all six specifications. If a male had more brothers, he was more likely to marry. Moreover, being the firstborn son or an adopted son in a family would offer a “demographic advantage”, increasing the likelihood of marriage (columns 3 and 4). Columns 5 and 6 affirm that the positive correlation between child quantity and quality remains even when controlling for the effects of the father and grandfather. Table 3 Relationship between family size and marital status, logistic regression Dependent Variable: Married (1) (2) (3) (4) (5) (6) Brothers 1.013 (0.012) 1.069*** (0.016) 1.120*** (0.018) 1.135*** (0.019) 1.097*** (0.019) 1.096*** (0.019) Firstborn 1.381*** (0.040) 1.409*** (0.042) 1.404*** (0.042) 1.404*** (0.042) Adoptee 1.344*** (0.086) 1.429*** (0.093) 1.431*** (0.094) Father’s class 1.948*** (0.116) 1.916*** (0.127) Father’s marriages 1.269*** (0.054) 1.270*** (0.054) Grandfather’s class 1.036 (0.062) Uncles 0.998 (0.013) Out-migration N Y Y Y Y Y Survival N Y Y Y Y Y Birth cohort FE N Y Y Y Y Y Lineage FE N Y Y Y Y Y N 36,360 31,106 31,106 31,106 31,106 31,080 Pseudo-R 2 0.0001 0.232 0.235 0.235 0.244 0.244 Notes: 1. If the individual is an adoptee, then “Father’s class” and “Grandfather’s class” denote the stepfather’s and step-grandfather’s social status, respectively. 2. Coefficients are the odds ratios for the logistic regression, and robust standard errors are in parentheses, clustered on fathers. 3. *p<0.1; **p<0.05; ***p<0.01. Table 4 Relationship between family size and degree, logistic regression Dependent Variable: Degree (1) (2) (3) (4) (5) (6) Brothers 1.235*** (0.032) 1.210*** (0.028) 1.252*** (0.030) 1.266*** (0.031) 1.050* (0.028) 1.025 (0.027) Firstborn 1.348*** (0.075) 1.368*** (0.076) 1.403*** (0.088) 1.401*** (0.090) Adoptee 1.398*** (0.176) 1.482*** (0.200) 1.451*** (0.199) Father’s class 13.770*** (1.311) 9.448*** (1.017) Father’s marriages 1.265*** (0.062) 1.273*** (0.062) Grandfather’s class 2.485*** (0.248) Uncles 0.980 (0.020) Out-migration N Y Y Y Y Y Survival N Y Y Y Y Y Birth cohort FE N Y Y Y Y Y Lineage FE N Y Y Y Y Y N 36,360 30,190 30,190 30,190 30,190 30,164 Pseudo-R 2 0.014 0.161 0.163 0.164 0.316 0.332 Notes: 1. If the individual is an adoptee, then “Father’s class” and “Grandfather’s class” denote his stepfather’s and step-grandfather’s social status, respectively. 2. Coefficients are the odds ratios for the logistic regression, and robust standard errors are in parentheses, clustered on fathers. 3. *p<0.1; **p<0.05; ***p<0.01. Table 4 suggests that family size played a similar role. Before including the father’s and grandfather’s effects, columns 1–4 suggest that for a one-unit increase in Brothers , the odds of a male achieving an academic degree versus not achieving one would increase by a factor of about 1.3. However, after including the effects of fathers and grandfathers in columns 5–6, the coefficients on Brothers remain positive but lose statistical significance. Nevertheless, the results still demonstrate that having a larger number of brothers was not negatively associated with the likelihood of a male attaining a keju degree. As expected, fathers’ social status had the most substantial effect on sons’ quality. Figure 6 demonstrates the predicted probability of being married and holding a keju degree for families of different sizes, conditioned on fathers’ social status. The figure shows that the considerable difference in the quality of sons arises from the difference in fathers’ social status. For a male who was raised in a family of two sons, the predicted probability of marriage was about 75.5 per cent if he had a high-status father, while that for a male who had a low-status father was about 66.2 per cent. The convergence of these two percentages becomes more pronounced as family size increases. The differences are wider for the probabilities of achieving academic degrees. The predicted probability of holding degrees for males with high-status fathers in a two-son family was 11.7 per cent, and that for males with low-status fathers was only 1.6 per cent. The results clearly show that the Beckerian trade-off, measured by the probability of marriage and attainment of keju degrees, was absent in the six lineages. A larger family size would not diminish the quality of sons; instead, it would enhance the likelihood of marriage while exhibiting a positive albeit weak effect on the probability of achieving a keju degree. 4.2.2 Robustness This section presents the robustness of the previous results of the Beckerian trade-off to (1) subperiods, (2) controlling for lifespan, and (3) alternative human capital indicators. I first divide the sample into three sub-samples that refer to three distinct cohorts and report the results in Table B4. For males born between 1400 and 1600, the number of brothers they had and their quality measures were not significantly correlated. However, after 1600, the number of brothers a male had displayed a positive correlation with the probability of his marriage. When measuring quality based on education, ­the coefficients on Brothers are not statistically significant across all three periods. Overall, similar to the baseline results in Tables 3 and 4, family size exhibited a stronger correlation with the likelihood of marriage, while a weak correlation emerged with the likelihood of attaining a keju degree. I then further condition on lifespan in the model. Similar to previous reasoning, one’s lifespan would affect one’s probability of marrying and holding a keju degree. Therefore, I include the male’s age at death, and the results are shown in Table B5. Father’s class and marriages remain positively correlated with one’s human capital, but the coefficients on Brothers lost statistical significance in both models, which suggests that family size did not strongly contribute to sons’ human capital formation. The results still show that a Beckerian trade-off was absent in the six lineages, which confirms the baseline results. Finally, I use whether a man had a Zi (courtesy name) or Hao (pen name) as two alternative measures for human capital. As Degree measures the most “upper-tail” human capital in traditional China, I use Zi and Hao to measure rudimentary literacy. Zi , courtesy name, is a name given to a male by his father or his teacher when he reached adulthood, and hao , as mentioned earlier, is a pen name that a literate male would give himself. Having a Zi or Hao means that the male was capable of reading at least a rudimentary literacy. These two measures are much similar to signature-based literacy, the conventional indicator for human capital (Schofield, 1968; Ogilvie, Edwards, and Küpker, 2022). Therefore, I change the outcome of interest from Degree to Zi and Hao , and Table B6 reports the results. As shown in columns 1 and 3, before conditioning on fathers’ and grandfathers’ social status, the number of brothers a male had was positively correlated with his probability of having Zi and Hao . However, after conditioning on father’s and grandfather’s class, and father’s marriages, both coefficients on Brothers in columns 2 and 4 lose significance. The results are comparable to those in Table 4, which suggests that the baseline results are robust. The results of the three indicators of child quality, marital status ( Married ), upper-tail human capital ( Degree ), and rudimentary literacy ( Zi and Hao ), all demonstrate the absence of a Beckerian trade-off of children in the six lineages in Ming­–Qing China. 4.2.3 Causal identification: Using father’s age at the first son’s birth as an instrument This section turns to the instrumented evidence on the trade-off between child quantity and quality. The logistic regression results in the previous section could be biased because of the unobserved parental preference and household features, although controlling for the grandfather’s social status and the number of uncles could partially capture the unobserved features. The IV estimation results based on Equations (3) and (4) are shown in Tables 5 and 6. Table 5 details the results of the full sample, comprising all males born between 1350 and 1920 who had records of their fathers’ age at the birth of their fathers’ first sons across the six lineages. Before I report the 2SLS results, I report those of the reduced-form estimates in columns 1 and 2 of Table 5. The OLS results for the first stage are reported in column 3, and the average marginal effects of the probit regressions for the second stage are reported in columns 4 and 5, where the dependent variables are Married and Degree , respectively. Table 6 reports the results for three sub-cohorts, 1400 to 1600, 1600 to 1800, and 1800 to 1900. Columns 1, 4, and 7 report the first-stage results, and the remaining columns report the second stage results. The F -statistic on the instrument remains higher than the Stock and Yogo (2005) critical value in Table 5 and in the specifications of periods after 1600 in Table 6, ruling out the weak instrument concern. The instrumented results in Table 5 show a largely comparable pattern with those in Tables 3 and 4. Family size continued to be a positive factor contributing to the quality of sons. Father’s age at first son’s birth had both statistically and quantitatively significant average marginal effects on the probability that a male would be married and achieve a keju degree (columns 1–2 and 4–5). As shown in columns 4 and 5, an increase of one son in family size is associated with a 9-percentage-point increase in the likelihood of marriage and a 2-percentage-point increase in the likelihood of obtaining an academic degree for males in the six lineages. Additionally, male individuals with high-status fathers exhibit a 9.2-percentage-point and 9.4-percentage-point increase in the probability of marriage and degree attainment, respectively. Table 5 Impact of the quantity of children on the quality of children: Instrumented results Reduced-form 2SLS Married Degree Brothers Married Degree (1) (2) (3) (4) (5) Father’s age at first son’s birth 0.979*** (0.002) 0.984*** (0.006) -0.038*** (0.002) Brothers 0.091*** (0.013) 0.019*** (0.007) Firstborn 1.525*** (0.056) 1.630*** (0.113) -1.224*** (0.021) 0.181*** (0.018) 0.045*** (0.009) Adoptee 1.334*** (0.142) 1.235 (0.252) -0.440*** (0.034) 0.081*** (0.019) 0.019*** (0.010) Father’s class 2.070*** (0.158) 11.199*** (1.421) 0.273*** (0.051) 0.092*** (0.013) 0.094*** (0.005) Father’s marriages 1.382*** (0.071) 1.341*** (0.068) 0.431*** (0.083) 0.013*** (0.011) 0.006*** (0.004) Grandfather’s class 0.989 (0.072) 2.543*** (0.305) 0.081* (0.045) -0.008 (0.012) 0.039*** (0.005) Observations 18,521 18,521 18,521 18,521 18,521 Number of clusters 9,518 9,518 9,518 9,518 9,518 Pseudo R 2 0.226 0.345 F -statistic on instrument 262.65 Notes: 1. Robust standard errors clustered by fathers in parentheses. 2. All specifications shown include uncles, out-migration, survival to adulthood, birth cohort FE, and lineage FE. 3. Columns 1–2 are subjected to logistic regression. Coefficients are the odds ratios for the logistic regression. 4. Columns 3–5 present the results of the Ivprobit estimation: the first stage being OLS, and the second stage involves probit regression on the predicted values from the first stage. The two models in columns 4 and 5 have the same first stage. The coefficients in columns 4–5 are average marginal effects. The F -statistic on the instrument is derived from a 2SLS estimate, which has the same first stage. 5. *p<0.1; **p<0.05; ***p<0.01. Table 6 Two-stage regression with father’s age at first son’s birth by period, measured by marriage and degree Born in 1400–1600 Born in 1600–1800 Born in 1800–1900 1 st Stage 2 nd Stage 1 st Stage 2 nd Stage 1 st Stage 2 nd Stage Brothers Married Degree Brothers Married Degree Brothers Married Degree (1) (2) (3) (4) (5) (6) (7) (8) (9) Father’s age at first son’s birth -0.036*** (0.245) -0.037*** (0.004) -0.038*** (0.003) Brothers -0.018 (0.069) 0.002 (0.067) 0.085*** (0.018) 0.018 (0.011) 0.089*** (0.019) 0.017* (0.009) Firstborn -0.868*** (0.080) -0.004 (0.059) 0.157** (0.065) -1.209*** (0.033) 0.177*** (0.025) 0.051*** (0.015) -1.248*** (0.029) 0.177*** (0.026) 0.029** (0.011) Adoptee -0.959*** (0.358) -0.137 (0.112) -0.021 (0.164) -0.661*** (0.054) 0.067** (0.032) 0.026 (0.018) -0.303*** (0.041) 0.074*** (0.024) 0.010 (0.010) Father’s class 0.388*** (0.162) -0.004 (0.050) 0.233*** (0.062) 0.219*** (0.070) 0.094*** (0.016) 0.131*** (0.008) 0.246*** (0.074) 0.088*** (0.019) 0.060*** (0.007) Father’s marriages 0.403*** (0.132) 0.080 (0.054) 0.029 (0.030) 0.498*** (0.123) 0.018 (0.016) 0.012* (0.007) 0.371*** (0.059) 0.011 (0.015) 0.003 (0.005) Grandfather’s class -0.148 (0.187) -0.024 (0.042) 0.084* (0.050) 0.085 (0.061) -0.033** (0.015) 0.062*** (0.008) 0.058 (0.068) 0.004 (0.017) 0.013** (0.006) Observations 452 441 445 8,604 8,604 8,604 8,716 8,716 8,439 Number of clusters 226 216 224 4,425 4,425 4,425 4,810 4,810 4,695 F -statistic on instrument 11.52 112.80 167.75 Notes: 1. Robust standard errors clustered by fathers in parentheses. 2. All specifications shown include uncles, out-migration, survival to adulthood, and lineage FE. 3. Ivprobit estimation: the first stage being OLS, the second stage probit, regressed on the predicted values from the first stage. The two models have the same first stage. 4. The coefficients in columns 2, 3, 5, 6, 8, and 9 are average marginal effects. The F -statistic on the instrument is derived from a 2SLS estimate, which has the same first stage. 5. *p<0.1; **p<0.05; ***p<0.01. Table 6 reveals that the relationships varied across different cohorts. When using marital status as the indicator of “quality”, family size exhibited a positive effect during the cohorts 1600–1800 and 1800–1900: having one more brother could increase the likelihood of a male’s marriage by approximately 9 percentage points. However, for males born in any of these periods, the number of brothers a male had only had a positive albeit weak effect on the probability of him attaining a degree: there was an approximately 2-percentage-point increase for the 1800–1900 cohort; in the previous two cohorts, family size did not significantly impact a son’s formal education. 11 Moreover, the results also suggest that a father’s social status could account for a son’s human capital to a great extent. For instance, as indicated in columns 3 and 6 of Table 6, for the 1400–1600 cohort, having a father with high social status would increase the probability of attaining a degree by 23.3 percentage points, and for the cohort 1600–1800 cohort, this increase would be 13.1 percentage points. For all men in the six lineages who had high-status fathers, despite being raised in larger families, they were still more likely to achieve academic degrees than those with fathers of low social status. In summary, both the baseline and instrumented results suggest that family size did not have a negative impact on a son’s quality and may have even had a positive effect. Moreover, the father’s social status played a more crucial role. A substantial Beckerian trade-off was absent in the six lineages from 1350 to 1920. 5 Discussion: Why were the two trade-offs absent in Ming–Qing China? Section 4 demonstrates the absence of the two trade-offs within the six lineages. The findings of the two trade-offs collectively illustrate a distinct relationship between reproduction and human capital in a multigenerational model. High-status males in the six lineages could produce more patrilineal male descendants for at least four consecutive generations. This phenomenon stemmed from the inheritance of privileges by their sons, grandsons, and great-grandsons, subsequently amplifying their probability of getting married and educated. It constituted a winner-take-all scenario: a greater number of sons translated to an elongated bloodline through an augmented likelihood of raising accomplished male offspring, without detriments arising from increased family sizes. For both prosperous and impoverished families, the absence of any trade-offs is not surprising. High-status fathers, including degree- and office-holders, possessed sufficient resources to support a large number of sons and assure their education. Leveraging their own social capital and providing “cultural capital” to their sons, it was unsurprising that their sons more easily attained keju degrees (Ho, 1962; Jiang and Kung, 2021). 12 For these fathers, having more sons was akin to buying more lottery tickets for success in the keju competition. The budget constraints of these households were sufficiently high that they did not face trade-offs between reproduction and long-run reproductive success or between child quantity and quality; instead, they could afford both. In contrast, impoverished fathers faced constraints on family size, and the smaller size of their families was not a deliberate choice to limit family size and invest in their sons’ human capital. Rudimentary literacy was easy to acquire, but full literacy was not. 13 Although the rise in social status created strong motivations for low-status men to pursue keju degrees, the high opportunity costs and intense competition prevented most of them from devoting persistent effort to repeated exam attempts (Ebrey, 1993; Shiue, 2017). Elman (2000, 240) highlights that classical literacy “required substantial investments of time, effort, and training”, and always exacted “financial and labor sacrifices”. Due to the extremely low chances and high costs associated with winning the keju prize, these families lacked the incentives to participate in the lottery game in the first place. This paper thus also reveals the consanguineous nature of Chinese society. As mentioned in Fei (1992, 120), traditional China “maintains structural stability by using the biological process underlying reproduction as the medium to establish social continuity…An aristocrat’s son becomes an aristocrat; such succession in identity is consanguineous. A rich man’s son becomes rich; such succession in wealth is consanguineous.” For those privileged men, the men who attained higher social status in the lineages, their male descendants also inherit these privileges, at least for the subsequent four generations. The lack of these two trade-offs also sheds light on the absence of a fertility transition in nineteenth-century China. Coale (1974, 352–353) points out that a crucial condition for a society to experience a secular decline in fertility is that “perceived social and economic circumstances must make reduced fertility seem an advantage to individual couples”. 14 While most Western European societies fulfilled this condition in the nineteenth century, with affluent families leading in limiting family size compared to poorer ones (see, for example, Clark and Cummins, 2015), nineteenth-century China did not. The Malthusian mechanism continued to function throughout this period. The empirical investigation in this paper directly responds to this condition, implying that reduced fertility was not advantageous to parents, especially those of high status, as having more sons equalled having more high-status sons. Without a secular fertility decline, the absence of a modern economic take-off is unsurprising (Galor and Weil, 2000). 6 Conclusion The transition from Malthusian stagnation to sustained economic growth necessitates a transitioned demographic pattern. This paper uses a new genealogical dataset to illustrate the demographic dynamics of patrilines across six Chinese lineages from 1350 to 1920. The empirical investigation reveals the absence of both a Darwinian trade-off and a Beckerian trade-off in the six lineages throughout the period. Greater reproduction could result in long-run reproductive success. A close analysis of the mechanisms demonstrates the positive effect of a father’s reproductive behavior on two aspects of offspring quality, measured by marital status and education. Instrumenting family size with the variation induced by the father’s age at the birth of his first son confirms the absence of a trade-off between child quantity and quality in the six lineages. The results indicate a highly unequal Chinese society. A high-status man’s household budget constraint in the six lineages was so high that he did not need to choose between child quantity and quality, but could have them both. High-status men could leave a greater number of patrilineal male descendants for at least four generations; additionally, their sons, grandsons, and great-grandsons were more likely to be married and to hold keju degrees. This winner-takes-all scenario could also explain the absence of a demographic transition in nineteenth-century China, consequently contributing to the missed opportunity for experiencing an economic take-off from stagnation to growth to some extent. Declarations Funding: The author also acknowledges the financial support of the National Natural Science Foundation of China (No.72203224). Conflicts of interest/Competing interests : Financial interests: The author has no financial interests to declare that are relevant to the content of this article. Non-financial interests: The author received PhD supervision from Neil Cummins and Debin Ma. James Kai-sing Kung and Noam Yuchtman were the examiners of the author’s PhD thesis. Availability of data and material : The data used in this paper were hand-collected by the author. Acknowledgment I am grateful to Shuji Cao and Qin Jiang at Shanghai Jiaotong University for kindly sharing the original digitalized genealogies of the Zhou, Que, and Huang lineages with me and Familyserach.org for providing researchers with digital images of the genealogical records of the Gu, Zha, and Zhuang lineages. I acknowledge Rongyu Jian for her research assistance. I am especially grateful to Neil Cummins, Debin Ma, Eric Schneider, James Kai-sing Kung, Noam Yuchtman, Oded Galor. I also wish to thank Gregory Clark, Jan Kok, Zhiwu Chen, Nan Li, Qin Jiang, Zhan Lin, Yu Hao, Ming Lei, Qun Che, and Qing Wang for their extensive feedback and also participants in the LSE Asia Economic History Seminar, LSE Graduate Economic History Seminar, EHS Annual Conference 2021, RES Annual Conference 2021, European Social Science History Conference 2021, Eighth International Symposium on Quantitative History, 2022 World Economic History Congress, and Economic History Workshop at Peking University for their comments. I acknowledge the financial support of the National Natural Science Foundation of China (No.72203224). Any errors are my own. Author Contribution S.H. wrote the entire manuscript. 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Correlation of Intergenerational Family Sizes Suggests a Genetic Component of Reproductive Fitness. The American Journal of Human Genetics , 81 (1), 165–169. https://doi.org/10.1086/518446 Ponczek, V., & Souza, A. P. (2012). New Evidence of the Causal Effect of Family Size on Child Quality in a Developing Country. Journal of Human Resources , 47 (1), 64–106. https://doi.org/10.1353/jhr.2012.0006 Qian, N. (2005). Quantity-Quality: The Positive Effect of Family Size on School Enrolment in China. Working paper, Department of Economics, Brown University. Rawski, E. (1979). Education and Popular Literacy in Ch’ing China. Ann Arbor, MI: The University of Michigan Press. Rosenzweig, M.R., & Wolpin, K.I. (1980). Testing the Quantity-Quality Fertility Model: The Use of Twins as a Natural Experiment. Econometrica , 48 (1), 227–240. https://doi.org/10.2307/1912026 Rosenzweig, M.R., & Zhang, J. (2006). Do Population Control Policies Induce More Human Capital Investment? Twins, Birthweight, and China’s “One Child” Policy. IZA Discussion Paper No. 2082 . Institute for the Study of Labor, Bonn, Germany. Schofield, R. S. (1968). The Measurement of Literacy in Pre-industrial England. In J. Goody (Ed.), Literacy in Traditional Societies . Cambridge, UK: Cambridge University Press. Shiue, C.H. (2016). A culture of kinship: Chinese genealogies as a source for research in demographic economics. Journal of Demographic Economics , 82 (4), 459–482. https://doi.org/10.1017/dem.2016.24 Shiue, C.H. (2017). Human capital and fertility in Chinese clans before modern growth. Journal of Economic Growth , 22 (4 ), 351–396. https://doi.org/10.1007/s10887-017-9148-9 Song, X., Campbell, C.D., & Lee, J.Z. (2015). Ancestry matters: Patrilineage growth and extinction. American Sociological Review , 80 (3), 574–602. https://doi.org/10.1177/0003122415576516 Stearns, S. C. (1989). Trade-offs in Life-history Evolution. Functional Ecology , 3 (3), 259–268. https://doi.org/10.2307/2389364 Stock, J., & Yogo, M. (2005). Asymptotic Distributions of Instrumental Variables Statistics with Many Instruments. In D. W. K. Andrews, & J. H. Stock (Eds.), Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg (pp. 109–120). Strassmann, B. I., & Gillespie, B. (2002). Life–history Theory, Fertility and Reproductive Success in Humans. Proceedings of the Royal Society of London. Series B: Biological Sciences , 269 (1491), 553–562. https://doi.org/10.1098/rspb.2001.1912 Tan, H.R. (2019). More is Less? The Impact of Family Size on Education Outcomes in the United States, 1850–1940 . Journal of Human Resources , 54 (4), 1154–1181. https://doi.org/10.3368/jhr.54.4.0517.8768R1 Telford, T.A. (1995). Fertility and Population Growth in the Lineages of Tongcheng County, 1520–1661. In S. Harrell (Ed.), Chinese Historical Microdemography (pp. 48–93). Berkeley, CA: University of California Press. Waltner, A. (1990). Getting an Heir: Adoption and the Construction of Kinship in Late Imperial China . Honolulu, HI: University of Hawaii Press. Williams, G. C. (1966). Adaptation and Natural Selection. Princeton, NJ: Princeton University Press. Wolf, A. P., & Huang, C. (1980). Marriage and Adoption in China, 1845 – 1945 . Stanford, CA: Stanford University Press. Zelin, M. (2009). The Firm in Early Modern China. Journal of Economic Behavior and Organization , 71(3), 623–637. https://doi.org/10.1016/j.jebo.2009.03.002 Zhao, Z. (2001). Chinese Genealogies as a Source for Demographic Research: A Further Assessment of Their Reliability and Biases. Population Studies , 55 (2), 181–193. https://doi.org/10.1080/00324720127690 Footnotes Given that only patrilineal male descents are officially recorded in the genealogical books, this paper focuses on all the male descents within the six lineages. Moreover, in pre-modern China, a typical patriarchal society, only patrilineal male descendants mattered (Freedman, 1966 ; Harrell, 1985 ; Song, Campbell, and Lee, 2015 ). The evidence from contemporary China is conflicting. Qian ( 2005 ) and Li et al. ( 2008 ) both exploit the 1990 population census, but find a contradictory relationship between family size and children’s educational attainment. Liu ( 2014 ) finds a strong negative relationship between family size and children’s height. In the sample, 8.8 per cent men failed to survive to adulthood, and 23.8 per cent of men who survived to adulthood were unmarried throughout the lifetime. Keju was initiated in 600 AD and abolished in 1905. Its presence changed imperial China into a meritocracy. In the tenth century, Emperor Zhenzong of the Song dynasty (960–1276) once wrote “There is no need to buy farmland, for books will get you a position with a high salary;/There is no need to build a house, for books will bring you a luxurious residence with golden walls.” Typically, a man without a male heir would adopt his nephew from his brothers and male cousins (Lee and Wang, 1999 ; Waltner, 1990 ; Wolf and Huang, 1980 ). In my sample, 18,927 males have biological sons, and 2,056 of them surrendered one or more sons. After transferring sons between families, 20,342 males have sons in total, and 2,188 of them adopted one or more sons. Of the 41,145 sons, 2,280 in total are adoptees. Of the 8,975 fathers with complete birth and death date records, their average lifespan was 53.47 years old. To better fit the OLS regression model, I log-transform Descendants , and, to keep all the zero observations, make the outcome variable used in the OLS model is ln (Descendants i +1) . As only one man in the sample, Zhuang Chaosheng, had more than 10 sons, I combine him with the men who had 10 sons, forming a group of males with more than 10 (including 10) sons. Online Appendix Tables A2 and A3 also report the OLS regression results based on Eq. ( 2 ). The result in column 9 of Table 6 confirms to a certain degree what Shiue ( 2017 ) reveals. Shiue ( 2017 ) finds that in Tongcheng, a county in Southeast China, a trade-off of children, measured also by their attainment of academic degrees, disappeared after 1800. However, in the Qing dynasty before 1800, Shiue finds the presence of a quantity-quality trade-off of children in Tongcheng. The somewhat contrasting results in this paper may suggest regional variations in pre-modern China. In Ming–Qing China, large lineages each maintained their own lineage schools (Zelin, 2009 ). The existence of these schools led to a relatively low marginal cost for rearing additional sons. In terms of rudimentary literacy, Rawski ( 1979 , 23) estimates that in nineteenth century China, the literacy rates of the male population ranged from 30 to 45 per cent. The other two conditions that Coale ( 1974 , 352–353) mentioned are “fertility must be within the calculus of conscious choice” and “effective techniques of fertility reduction must be available.” Additional Declarations No competing interests reported. Supplementary Files JEGOnlineSupplementaryAppendices.docx Cite Share Download PDF Status: Published Journal Publication published 26 Apr, 2025 Read the published version in Journal of Economic Growth → Version 1 posted Editorial decision: Revision requested 07 May, 2024 Reviews received at journal 07 May, 2024 Reviews received at journal 24 Apr, 2024 Reviewers agreed at journal 11 Mar, 2024 Reviewers agreed at journal 08 Mar, 2024 Reviewers agreed at journal 06 Mar, 2024 Reviewers invited by journal 06 Mar, 2024 Submission checks completed at journal 06 Mar, 2024 Editor assigned by journal 06 Mar, 2024 First submitted to journal 03 Mar, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4009995","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":276915796,"identity":"2633aa73-89bd-498b-8c18-313504fc9848","order_by":0,"name":"Sijie Hu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYDACZoaEA4wNDHIQHhsJWoxJ0AICQC2JDURrkW9neHjg447D6dtnJD9g+FB2mIF/dgN+LQaHGRIOzjxzOHfOjTQDxhnnDjNI3DlAQAvQL4d52w7nzpDIYWAGMhgMJBIIOKwZqOVv2+F0CZCWv8RoYQA67DBj2+EEsBZGYrSA/dLblm44g+eZwcGec+k8EjcIOaz/TPKHn23W8hLsyQ8f/CizluOfQchhDDwIFQdAXELqgYD9ABGKRsEoGAWjYEQDALdxRAFs3NdVAAAAAElFTkSuQmCC","orcid":"","institution":"Renmin University of China","correspondingAuthor":true,"prefix":"","firstName":"Sijie","middleName":"","lastName":"Hu","suffix":""}],"badges":[],"createdAt":"2024-03-04 00:59:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4009995/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4009995/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10887-025-09255-5","type":"published","date":"2025-04-26T15:58:23+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":52305847,"identity":"00bb9e93-0954-4926-b289-7a610e300a5a","added_by":"auto","created_at":"2024-03-08 19:26:17","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":9359,"visible":true,"origin":"","legend":"\u003cp\u003eThe qualitative pattern between reproduction and long-run reproductive success, the LOWESS method.\u003c/p\u003e\n\u003cp\u003eNotes: 1. The outcome of interest used in the analysis is log-transformed number of male descendants in the following three generations. I also add 1 to the origin number to keep all the zero observations. 2. The shaded area represents the 95% confidence interval for the LOWESS smooth curve.\u003c/p\u003e","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4009995/v1/20a1f29276a48fe4bc36f56d.png"},{"id":52305848,"identity":"cd15daad-595d-499b-a24c-2142bde06796","added_by":"auto","created_at":"2024-03-08 19:26:17","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":5404,"visible":true,"origin":"","legend":"\u003cp\u003eThe distribution of fathers’ age at first male birth.\u003c/p\u003e\n\u003cp\u003eSource: The lineage sample.\u003c/p\u003e","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4009995/v1/be45a1841e816274abc1955b.png"},{"id":52306160,"identity":"2c9dce2e-1685-4db9-87cb-4f96c0497474","added_by":"auto","created_at":"2024-03-08 19:34:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":78961,"visible":true,"origin":"","legend":"\u003cp\u003ePredicted number of patrilineal male descendants in the three generations at each level of reproduction\u003c/p\u003e\n\u003cp\u003eNotes: 1. The predicted values are calculated from the results in columns 7–9 of Table 2. 2. The shaded area represents the 95% confidence interval for the predicted curve.\u003c/p\u003e","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4009995/v1/1584b2ae43a6c93a6034287c.png"},{"id":52305849,"identity":"a536da54-f142-4e0f-b91f-0f052e808411","added_by":"auto","created_at":"2024-03-08 19:26:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":14689,"visible":true,"origin":"","legend":"\u003cp\u003ePredicted number of male descendants in the three generations at each level of reproduction by social status\u003c/p\u003e\n\u003cp\u003eNotes: 1. The predicted values are calculated from the results in columns 7–9 of Table 2. 2. The shaded area represents the 95% confidence interval for the predicted curve.\u003c/p\u003e","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4009995/v1/f2e6d7eab776d8622001dcde.png"},{"id":52305851,"identity":"257dc0fc-fcab-4259-83eb-de734eee960a","added_by":"auto","created_at":"2024-03-08 19:26:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":4749,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of the number of sons\u003c/p\u003e\n\u003cp\u003eSource: The lineage sample.\u003c/p\u003e","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4009995/v1/325579ffe9981a01d4a9211d.png"},{"id":52306161,"identity":"51deb084-a7aa-4796-ab92-f0cb61e69d08","added_by":"auto","created_at":"2024-03-08 19:34:18","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":7156,"visible":true,"origin":"","legend":"\u003cp\u003ePredicted probability of being married and earning a degree for families of different sizes, with a low-status and a high-status father.\u003c/p\u003e\n\u003cp\u003eNotes: 1. The predicted values are calculated from the results of column 6 of Table 3 and column 6 of Table 4. 2. The shaded area represents the 95% confidence interval for the predicted curve.\u003c/p\u003e","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4009995/v1/097ea06d17b5c5fd31971032.png"},{"id":81569794,"identity":"73ad6c92-a7df-4acf-b595-4a93ccabe7d5","added_by":"auto","created_at":"2025-04-28 16:11:17","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1665089,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4009995/v1/c0fcf2c6-b05c-426c-b9db-68933bf982bf.pdf"},{"id":52305853,"identity":"31da1d57-46d5-48ae-94f3-6aea0c9b1ca5","added_by":"auto","created_at":"2024-03-08 19:26:18","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":4788790,"visible":true,"origin":"","legend":"","description":"","filename":"JEGOnlineSupplementaryAppendices.docx","url":"https://assets-eu.researchsquare.com/files/rs-4009995/v1/7d6618201d8598b0f352a7dd.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Celebrating legacy: The intergenerational transmission of reproduction and human capital in Ming–Qing Chinese families","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eTo explain the long-run economic growth, the \u0026ldquo;population-idea nexus\u0026rdquo; is always of the essence (Doepke, 2004; Mokyr and Voth, 2010). Technology, a key element of economic development, does not \u0026ldquo;just happen\u0026rdquo; but depends on the population, particularly the accumulation of human capital within it (Kremer, 1993). In many newly proposed unified growth models that seek to explain both the Malthusian stagnation and economic take-off, the relationship between reproduction and technology in the long run is carefully traced (Galor and Weil, 2000; Galor and Moav, 2002; Galor, 2011; Galor, 2022).\u003c/p\u003e\n\u003cp\u003eTherefore, two crucial elements come into play: population size and population composition (Galor, 2022). In the era of Malthusian stagnation, higher living standards resulted in larger family sizes, leading to a gradual increase over time in the proportion of descendants from families with higher living standards within the total population. Over the long run, these two \u0026ldquo;wheels of change\u0026rdquo; operated under the influence of natural selection, ultimately increasing the representation of growth-promoting traits in the total population (Galor and Klemp, 2019; Galor, 2022). This dynamic, in turn, promoted investment in human capital and facilitated the demographic transition and transition from stagnation to sustained growth (Galor and Moav, 2002).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSpecifically, Galor and Klemp (2019) explore natural selection forces by using the genealogical data of half a million residents over four generations in pre-industrial Quebec and find a hump-shaped relationship between fecundity and long-run reproductive success. They conclude that moderate fecundity, coupled with a higher level of education, was more conducive to the continuity of the lines of descent; the negative effects on survival of larger family sizes also suggest the presence of child quantity-quality trade-offs (Galor and Klemp, 2019).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBuilding on the work of Galor and Klemp (2019), I examine the evolution of the two wheels in a pre-transition context. I use a new genealogical dataset containing 36,456 males to exploit multigenerational associations in reproduction across six lineages in Southeast China from 1350 to 1920. This period covers the two last imperial dynasties, the Ming (1368\u0026ndash;1644) and Qing (1644\u0026ndash;1911) dynasties. My intention is to show the reproductive success of Chinese males in a multigenerational model by analyzing the pattern and mechanisms of fertility transmission. I focus on exploring two\u0026nbsp;types of trade-offs: a Darwinian trade-off between reproduction and the long-run reproductive success and a Beckerian trade-off between the quantity and quality of children. I aim to illustrate\u0026nbsp;how reproduction affected the long-run reproductive success of a patriline through the accumulation of human capital.\u003ca href=\"#_ftn1\" name=\"_ftnref1\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e1\u003c/sup\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eI first test for the presence of the Darwinian trade-off by examining the optimal level of reproduction for long-run reproductive success in the six lineages. I estimate the relationship between the number of sons and the number of patrilineal male descendants in the three subsequent generations in which a male had to test whether high reproduction in the first generation could translate into high reproduction in the three that would ensue. The estimation results show that there was no significant trade-off between reproduction and long-run reproductive success. A man who had seven sons would have more great-great-grandsons than a man who had more than seven sons. However, this optimal level of reproduction was much greater than both the sample median and mean reproduction levels, which were about two sons.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eI then analyze the possible mechanisms through which parental reproduction could affect next generation reproduction. The positive effect of reproduction on long-run reproductive success suggests a positive relationship between child quantity and quality, or in other words, the absence of a Beckerian trade-off. The family size of the first generation could affect the quality of the second generation and thus affect the likelihood of the second generation producing male descendants in subsequent generations.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eI use the number of sons a father had, that is, the number of brothers that a male had (including himself), to measure final family size. I use two indicators to measure child quality. The first measure is \u003cem\u003eMarried\u003c/em\u003e, which measures whether the male could have at least one marriage before he died. The logistic regression results reflect a positive correlation between the number of brothers possessed by a male and the likelihood of his getting married. Sons from larger families enjoyed a higher probability of entering into marriage, which was a prerequisite for leaving male descendants in traditional China. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFollowing Shiue\u0026rsquo;s (2017) variable construction, the second indicator concerns a son\u0026rsquo;s formal education, \u003cem\u003eDegree\u003c/em\u003e. Based on the education-related information recorded in the genealogies, 1,506 males (4.13 per cent) in the sample obtained academic degrees. The logistic regression analysis indicates that although fathers\u0026rsquo; and grandfathers\u0026rsquo; social status had the strongest effects on son quality, the number of brothers a male had was also positively correlated with his quality.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNevertheless, because of potential endogeneity issues arising from unobservable parental preferences and household characteristics affecting both family size and son quality, establishing a causal relationship becomes challenging, and correlations may be biased. Therefore, I instrument the number of sons a father had with his age at the birth of his first son. The instrument is valid because it was conditionally exogenous. With the father\u0026rsquo;s age being younger at the birth of his first son, the father\u0026rsquo;s reproductive span for bearing sons would be longer. After conditioning on cultural and socio-economic factors, the onset of son-bearing was largely random and not related to the father\u0026rsquo;s own preferences for child quality. Additionally, it could not directly affect a son\u0026rsquo;s likelihood of marriage or academic achievement.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe instrumental variable results, similar to the baseline results, indicate significant positive effects of family size on the \u0026ldquo;quality\u0026rdquo; of a son. The number of brothers continued to significantly impact their chances of marrying or obtaining an academic degree. Large families exhibited positive aspects in the six lineages. In particular, degree- and office-holders could have larger families, and their sons were also more likely to marry and obtain academic degrees. The social gradient in human capital formation remained strong. In general, the logistic and IV results both suggest that a significant Beckerian trade-off was absent in the six lineages from 1350 to 1920.\u003c/p\u003e\n\u003cp\u003eThis paper contributes to the previous literature in two ways. On the one hand, this paper offers some of the first quantitative evidence on the narrative of reproductive success in a multigenerational model for pre-modern China.\u0026nbsp;Biologists studying the trade-off between fertility and various biological traits find that high fertility does not always lead to high rates of survival (Lack, 1954; Williams, 1966; Stearns, 1989). Social scientists have then examined different types of Darwinian trade-offs within the human species and suggested different relationships between female fertility and offspring survivorship, parental fertility and next generation fertility, and the optimal level of fertility and long-run reproductive success in different societies (Kaplan et al., 1995; Hill and Hurtado, 1996; Kaplan, 1996; Borgerhoff Mulder, 2000; Strassmann and Gillespie, 2002; Galor and Klemp, 2019).\u0026nbsp;To ensure greater continuity in bloodlines, high survival in only one generation is not enough; most importantly, reproductive success in one generation must be transmitted across generations. Song et al. (2015) employ two data samples from northern China during the Qing dynasty and discover that patrilineages with high social origins increased their representation in the overall population by minimizing the risk of extinction, rather than maximizing the number of male descendants in each generation. This paper, however, identifies a slightly different pattern for Southeast China. Productive ancestors were able to transmit their reproductive advantages for at least four generations.\u003c/p\u003e\n\u003cp\u003eOn the other hand, this paper extends the empirical literature on the trade-off between the quantity and quality of children in the pre-transitional era.\u0026nbsp;In pre-modern societies, one of the mechanisms through which parental reproduction affected next-generation reproduction is that parents would make a trade-off between reproduction and investment in offspring quality, thus affecting offspring reproduction.\u0026nbsp;Economists have studied this type of child quantity-quality trade-off since Becker (1960; Becker and Lewis, 1973; Becker, Murphy, and Tamura, 1990) first inserted fertility decisions into the economic analysis and argued that parents would sacrifice the number of children they could have for higher quality in the children they had. A considerable amount of empirical literature also tries to support or challenge this Beckerian argument in both historical and modern times (see the examples of Northern Europe: Baudin and De la Croix, 2023; of India: Rosenzweig and Wolpin, 1980; of Thailand: Knodel, Havanon, and Sittitrai, 1990; of Norway: Black, Devereux, and Salvanes, 2005; of Brazil: Ponczek and Souza, 2012; of the USA: Tan, 2019; of Korea: Lee and Park, 2019; of England: Clark and Cummins, 2016; Klemp and Weisdorf, 2019; of China: Qian, 2005; Rosenzweig and Zhang, 2006; Li, Zhang, and Zhu, 2008; Liu, 2014; Shiue, 2017; Bai, Li, and Lam, 2023).\u003ca href=\"#_ftn2\" name=\"_ftnref2\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003eShiue (2017) examines genealogical data from Tongcheng County and finds a negative relationship between family size and sons\u0026rsquo; education during the seventeenth and eighteenth centuries, which disappeared afterwards. Meanwhile, Bai et al. (2023) observe a similar trade-off in North China, but only after 1800. In addition, Song et al. (2015) speculate that in the Qing period, high-status founders may have strategically employed the child quantity-quality trade-off to ensure continuity in their bloodlines. Like Shiue (2017), this paper also conducts an analysis covering the entire Ming\u0026ndash;Qing period from 1350 to 1920. Unlike in previous research, the geographical focus shifts to the core lower Yangtze region, which has been the most developed area in China for centuries and a central point in several significant debates over the past two decades in the economic history of China (Shiue, 2016). An examination of the relationships between reproduction and marriage, as well as between reproduction and education in an intergenerational model, demonstrates that family size affected child quality to varying extents. The results of the two trade-offs also shed light on the absence of a fertility transition in nineteenth-century China.\u003c/p\u003e\n\u003cp\u003eThe rest of the paper is structured as follows. Section 2 describes the genealogical data, and Section 3 introduces the empirical strategies. Section 4 reports the results for long-run reproductive success and the child quantity-quality trade-offs. Section 5 is a discussion of the results, and Section 6 concludes.\u003c/p\u003e\n\u003cdiv id=\"ftn2\"\u003e\u003cbr\u003e\u003c/div\u003e"},{"header":"2 Data and main variables","content":"\u003cp\u003e\u003cstrong\u003e2.1 The lineage sample\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn Ming\u0026ndash;Qing China, lineages were the most widespread and long-lasting forms of social organizations (Feng and Chang, 2001; Zelin, 2009). In a society that attached great importance to the maintenance and expansion of the patrilines, keeping genealogical records became a standard practice for most of the lineages to remind the offspring of their family history (Zhao, 2001; Feng, 2009). The primary data used in this paper come from the genealogical books of six lineages in Southeast China; the sample includes 36,456 males born between 1350 and 1920. Online Appendix Figure A1 shows the two provinces and four prefectures where the six lineages are located.\u003c/p\u003e\n\u003cp\u003eGenealogies of a lineage always include an introduction to the history of the family, the rules of compilation, the rules and regulations that family members had to follow, a family tree that includes all the male members recorded in the book, and finally a series of detailed entries for each male descendant in the family (see Figure A2 for an example of a male individual\u0026rsquo;s entry in the book). The family tree and sons\u0026rsquo; names recorded under the fathers\u0026rsquo; entries enable us to link male family members easily across generations.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAlthough genealogical data are very useful for examining reproduction and survival, they are not free from selection bias. Hu (2023a) has a detailed discussion of selection biases in this six-lineage sample. The main bias that would affect the empirical estimation in this paper is the lack of information about daughters in the genealogies. Due to the strong preference for sons in imperial China, daughters are highly under-reported. The sample included 41,145 sons in total but only 9,636 daughters. Given that the number of sons who survived infancy is completely recorded for every male\u0026rsquo;s entry, I use this number in the present paper to measure reproduction and family size. Moreover, because of the patrilineal structure in the Chinese families, the \u0026ldquo;descendants\u0026rdquo; in this paper represent only the patrilineal male descendants who inherited the surname of the lineage. \u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.2 Dependent and independent variables\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn the main analysis of the optimal level of reproduction, the dependent variable is the recorded number of patrilineal grandsons, great-grandsons, and great-great-grandsons of each male in the sample. The independent variable in this analysis is the number of a male\u0026rsquo;s sons who survived infancy.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn the analysis that examines the child quantity-quality relationship, which is the mechanism through which parental reproduction affected next-generation reproduction, the dependent variables are two dummy variables that measure two indicatiors of quality in males: their marital status (\u003cem\u003eMarried\u003c/em\u003e) and their formal education (\u003cem\u003eDegree\u003c/em\u003e). The independent variable is the number of brothers who survived infancy that a male had, in other words, the number of sons who survived infancy, both biological\u0026nbsp;and adoptive,\u0026nbsp;that the male\u0026rsquo;s father had. Therefore, the number measures the final family size in terms of male births.\u003c/p\u003e\n\u003cp\u003eSince long-run reproductive success is measured in this paper by the number of male descendants a male could have, the two variables indicate a male\u0026rsquo;s quality in terms of his capability of leaving male descendants. Both quality measures are also closely related to the male\u0026rsquo;s parents\u0026rsquo; investment in him. First, \u003cem\u003eMarried\u003c/em\u003e is considered a valid measure in this context because entering into marriage is the prerequisite for males to have male descendants. The shortage of women in Ming\u0026ndash;Qing China, caused mainly by female infanticide and polygamy, made the marriage market seriously unbalanced (Lee and Wang, 1999). Marriage served as an especially \u0026ldquo;sensitive measure of privilege\u0026rdquo; because the ability to marry was contingent on having access to resources (Lee and Campbell, 1997; Lee and Wang, 1999). A substantial proportion of males, especially males from impoverished families and low-social-status males, failed to ever marry.\u003ca href=\"#_ftn1\" name=\"_ftnref1\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e3\u003c/sup\u003e Thus, the \u0026ldquo;quality\u0026rdquo; of the male largely determined whether he could marry or not. Second, \u003cem\u003eDegree\u003c/em\u003e is a commonly used measure of human capital in pre-modern China (Shiue, 2017). Moreover, it mattered because academic degrees determined the social status of men in Ming\u0026ndash;Qing society, which, in turn, significantly influenced the number of sons they could leave behind (Hu, 2023a).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBased on the social status records in the genealogies, I divide all the males in the sample into 14 levels of social status and construct the variable \u003cem\u003eDegree\u003c/em\u003e based on their social status to measure their human capital (see Table 1). In the Ming\u0026ndash;Qing period, education was closely related to social status and wealth, for education could bring people high social status and considerable wealth because of \u003cem\u003ekeju\u003c/em\u003e, the national civil examination system.\u003ca href=\"#_ftn2\" name=\"_ftnref2\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e4\u003c/sup\u003e The exam mainly tested candidates\u0026rsquo; knowledge of the Confucian classics. All male commoners, including peasants, artisans, and merchants, could attend civil examinations, and academic degrees on three levels \u0026mdash; \u003cem\u003eshengyuan\u003c/em\u003e, \u003cem\u003ejuren\u003c/em\u003e, and \u003cem\u003ejinshi\u003c/em\u003e \u0026mdash; would reward those who could pass the corresponding county-level, provincial-level, and national-level exams (Chen, Kung, and Ma, 2020). Candidates who failed exams could also repeatedly retake them (Miyazaki, 1981). Some of the more successful degree holders would later hold office. The \u003cem\u003ekeju\u003c/em\u003e degree holders and office holders would thus be coded 1 for \u003cem\u003eDegree\u003c/em\u003e. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1\u003c/strong\u003e Degree and social status classification\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"699\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003eStatus\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003eClass\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003eDegree\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003eCount\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003ePercent\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eDescription\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e34,555\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e94.79%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eNo status\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e108\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0.30%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eLineage chief; donor to the lineage and the county\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0.22%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eLiterate and educated but with no academic degree (teacher of the village or editor of genealogical books)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0.18%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eAwarded official titles by the emperor, with no academic degree\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e487\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1.34%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eLower degree holder (normal \u003cem\u003eshengyuan\u0026nbsp;\u003c/em\u003eand civil \u003cem\u003eshengyuan\u003c/em\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e524\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1.44%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eStudents at the Imperial Academy (lower degree)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0.10%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eIntermediate/high degree holder (\u003cem\u003ejuren\u003c/em\u003e, \u003cem\u003egongsheng\u003c/em\u003e, \u003cem\u003ejinshi\u003c/em\u003e), but with no official position\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0.14%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eProspective officials (\u003cem\u003ehoubu\u003c/em\u003e), with no academic degree\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0.18%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eProspective officials (\u003cem\u003ehoubu\u003c/em\u003e), with academic degree\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0.25%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eClerks (\u003cem\u003ewei\u0026rsquo;ruliu\u003c/em\u003e); the lowest-ranking official (\u003cem\u003ezong jiupin\u003c/em\u003e), with no academic degree\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0.29%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eLow-/medium-ranking local official and low-ranking court official, with normal and civil \u003cem\u003eshengyuan\u0026nbsp;\u003c/em\u003edegree\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e128\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0.35%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eLow-/medium-ranking local official and low-ranking court official, with a degree of studentship at the Imperial Academy\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0.22%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eLow-/medium-ranking local official and low-ranking court official, with an intermediate/ high degree\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.895265423242467%\"\u003e\n \u003cp\u003e0.21%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"55.52367288378766%\"\u003e\n \u003cp\u003eHigh-ranking local official and medium/high-ranking court official\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eSource: Ho 1962, Chapter 1; Telford 1995, Appendix 3A; Shiue 2017, Table 1.\u003c/p\u003e\n\u003cdiv id=\"ftn2\"\u003e\u003cbr\u003e\u003c/div\u003e"},{"header":"3 Empirical strategy","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 The Darwinian trade-off: the relationship between reproduction and long-run reproductive success\u003c/h2\u003e\n \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\n \u003ch2\u003e3.1.1 The model\u003c/h2\u003e\n \u003cp\u003eTo test the presence of the optimal level of reproduction for long-run reproductive success, I apply a multigenerational model, following the methods in Kaplan et al. (\u003cspan class=\"CitationRef\"\u003e1995\u003c/span\u003e) and Galor and Klemp (\u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). The sample used in this analysis consists of 9,336 \u0026ldquo;ancestors\u0026rdquo; who had at least one son. Males with incomplete records of male descendants in the subsequent four generations are excluded.\u003c/p\u003e\n \u003cp\u003eI first test whether the relationships between the number of sons and the log-transformed number of male descendants in the next three generations are monotonic. I run a non-parametric analysis by using the LOWESS method. As Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e presents, the relationships are not strictly linear. The man in the sample with the most sons and grandsons is Zhuang Chaosheng from the Zhuang lineage. He married 10 times and had 12 sons and 50 patrilineal grandsons in total. However, he is not the one with the most patrilineal great-grandsons and great-great-grandsons, while his father, Zhuang Yinghui, who had 5 sons, is the one with the most patrilineal great-grandsons, 88. Que Qixin from the Que lineage had only 4 sons, but his male descendants produced 194 patrilineal great-great-grandsons for him, which is the greatest number of great-great-grandsons in the sample.\u003c/p\u003e\n \u003cp\u003eBecause the number of grandsons (mean\u0026thinsp;=\u0026thinsp;2.95, variance\u0026thinsp;=\u0026thinsp;8.86), the number of great-grandsons (mean\u0026thinsp;=\u0026thinsp;3.64, variance\u0026thinsp;=\u0026thinsp;26.81), and the number of great-great-grandsons (mean\u0026thinsp;=\u0026thinsp;3.90, variance\u0026thinsp;=\u0026thinsp;61.22) are all count variables and are over-dispersed, I employ negative binomial regression to test the relationship between the number of sons and the number of male descendants in the following three generations based on the following equation:\u003c/p\u003e\n \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$${Descendants}_{i}=\\alpha +{\\beta }_{1}{Sons}_{i}+{\\beta }_{2}{Sons}_{i}^{2}+{\\delta P}_{i}+{\\epsilon }_{i},$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere \u003cem\u003eDescendants\u003c/em\u003e is the number of male offspring that a male (Generation 1) had in the three generations after his sons\u0026rsquo; generation (Generations 3\u0026ndash;5, i.e. grandsons, great-grandsons, and great-great-grandsons); \u003cem\u003ei\u003c/em\u003e denotes male individuals. \u003cem\u003eSons\u003c/em\u003e is the number of sons that a male had. Given the non-monotonic relationships shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, I also control for the squared term of \u003cem\u003eSons.\u003c/em\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eP\u003c/em\u003e is a set of control variables that would also affect the number of male descendants in generations 3\u0026ndash;5. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\epsilon\\)\u003c/span\u003e\u003c/span\u003e is the error term. If the optimal level of reproduction did exist, men with a moderate level of reproduction would be expected to have the most grandsons, great-grandsons, and great-great-grandsons. Having more sons than the optimal number would lead to fewer male descendants in the following generations.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\n \u003ch2\u003e3.1.2 The control variables\u003c/h2\u003e\n \u003cp\u003eI condition on a set of control variables in the model to establish the causal relationship between reproduction and long-run reproductive success.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eClass\u003c/em\u003e and \u003cem\u003eMarriages.\u003c/em\u003e In pre-modern China, education, wealth, and social status were closely related. The number of marriages that a male had was also positively associated with his social status and wealth. Thus, \u003cem\u003eClass\u003c/em\u003e and \u003cem\u003eMarriages\u003c/em\u003e are controlled for the effects of the male\u0026rsquo;s socio-economic characteristics on his long-run reproductive success. \u003cem\u003eClass\u003c/em\u003e indicates whether the man belonged to a status group higher than status 1, referred to as the privileged group, as described in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. \u003cem\u003eMarriages\u003c/em\u003e denotes the number of times that the man married during his life.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eHao\u003c/em\u003e. I use \u003cem\u003eHao\u003c/em\u003e (pen name) to control for the effects of basic literacy training on reproduction. Even though the costs of attaining basic literacy in Ming\u0026ndash;Qing China were modest, being literate was still a privilege (Shiue, \u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e). This could be measured by whether a male gave himself a pen name or not and could also be considered a proxy for household wealth.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eFirstborn\u003c/em\u003e. In traditional Chinese culture, the firstborn son had a \u0026ldquo;demographic advantage\u0026rdquo; being tasked with the primary responsibility for leaving male descendants, which was expected to correlate positively with long-run reproductive success (Lee and Campbell, \u003cspan class=\"CitationRef\"\u003e1997\u003c/span\u003e; Li and Zhen, \u003cspan class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eSurvival to adulthood\u003c/em\u003e. Lifespan is closely related to reproduction and human capital formation. Only about one third of the males in the genealogies had complete vital records, but males who died before adulthood were also marked in the genealogies. I use the dummy \u003cem\u003eSurvival\u003c/em\u003e to distinguish males who failed to reach adulthood from the other males to control for its negative effects on reproduction.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eOut-migration\u003c/em\u003e. If a male migrated to another village, it was difficult for the compilers of the genealogy to update the information on him. I include \u003cem\u003eOut-migration\u003c/em\u003e to control for the negative effect that this move could have on the number of male descendants recorded in the genealogy.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eBirth cohort\u003c/em\u003e, \u003cem\u003eLineage\u003c/em\u003e and \u003cem\u003eBranch\u003c/em\u003e. The birth cohort, lineage, and branch to which the male belonged would affect his reproduction and long-run reproductive success. Of the 36,456 males in the sample, only 23,098 had birth years recorded. With these birth year records, I impute an approximate birth cohort for the relatives of these males whose birth years were not recorded. I classify 31,197 males into twelve birth cohorts, starting with a \u0026ldquo;pre-1400\u0026rdquo; interval (1350\u0026ndash;1400), ending with a \u0026ldquo;post-1900\u0026rdquo; interval (1900\u0026ndash;1920), and with ten half-century-long cohorts in between.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 The Beckerian trade-off: mechanisms through which reproduction affected long-run reproductive success\u003c/h2\u003e\n \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\n \u003ch2\u003e3.2.1 Baseline model\u003c/h2\u003e\n \u003cp\u003eI first run logistic regressions based on the following equation:\u003c/p\u003e\n \u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e$${P(Quality}_{i}=1)={\\Phi }(\\alpha +\\beta {Brothers}_{i}+\\delta {Z}_{i}+\\gamma {W}_{i}+{\\epsilon }_{i}),$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere \u003cem\u003eQuality\u003c/em\u003e denotes the male individual\u0026rsquo;s quality, and \u003cem\u003ei\u003c/em\u003e denotes male individuals. I use two indicators to measure quality, \u003cem\u003eMarried\u003c/em\u003e and \u003cem\u003eDegree\u003c/em\u003e. \u003cem\u003eMarried\u003c/em\u003e equals one if the male was married at least once, and \u003cem\u003eDegree\u003c/em\u003e equals one if the male was a \u003cem\u003ekeju\u003c/em\u003e degree holder. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha\\)\u003c/span\u003e\u003c/span\u003eis the constant. As the number of daughters is incomplete in the genealogies, I use \u003cem\u003eBrothers\u003c/em\u003e to measure the quantity of children. It equals the number of brothers (including himself) in a male\u0026rsquo;s generation of his family of origin, in other words, the number of sons who survived infancy that his father had.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eZ\u003c/em\u003e denotes a set of control variables, most of which are also used in Eq. (\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e), including \u003cem\u003eFirstborn\u003c/em\u003e, \u003cem\u003eSurvival to adulthood\u003c/em\u003e, \u003cem\u003eOut-migration\u003c/em\u003e, \u003cem\u003eLineage\u003c/em\u003e and \u003cem\u003eBirth cohort\u003c/em\u003e. \u003cem\u003eW\u003c/em\u003e includes a set of factors linked to the male\u0026rsquo;s father and grandfather that could affect his marital status and education. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\epsilon\\)\u003c/span\u003e\u003c/span\u003e is the error term. If a trade-off existed, a negative \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\beta\\)\u003c/span\u003e\u003c/span\u003e would be expected since it represents parents choosing between the quantity and quality of their sons.\u003c/p\u003e\n \u003cp\u003eThe additional control variables I condition on include whether the male was adopted, his father\u0026rsquo;s social status and number of marriages, as well as his grandfather\u0026rsquo;s social status and number of sons.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eAdoptee.\u0026nbsp;\u003c/em\u003eIn a society that highly values filial piety, having a male heir to continue the bloodline is a priority for every male. However, not every male could fulfill this task, leading to the widespread practice of adoption.\u003ca href=\"#_ftn1\" name=\"_ftnref1\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e5\u003c/sup\u003e As an adoptee, the sole heir in the new adoptive family, he would face additional pressure to excel and perform well (Waltner, 1990; Wolf and Huang, 1980). Therefore, I control for whether the male was an adoptee or not.\u003ca href=\"#_ftn2\" name=\"_ftnref2\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e\n \u003cp\u003e\u003ca class=\"FNLink\" href=\"#Fn6\" id=\"#FNLinkFn6\"\u003e\u003c/a\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eFather\u0026rsquo;s class\u003c/em\u003e and \u003cem\u003eFather\u0026rsquo;s marriages\u003c/em\u003e. For each male individual I control for his father\u0026rsquo;s social status and the number of times his father married to reflect the socio-economic characteristics of his family of origin. \u003cem\u003eFather\u0026rsquo;s class\u003c/em\u003e equals 1 if one\u0026rsquo;s father had a status higher than 1; otherwise, \u003cem\u003eFather\u0026rsquo;s class\u003c/em\u003e equals 0.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eGrandfather\u0026rsquo;s class\u003c/em\u003e and \u003cem\u003eNumber of uncles\u003c/em\u003e. Moreover, I include the effects of the grandfather in the model to address the endogeneity issue. The major difficulty in establishing the causal relationship between family size and child quality is omitted variable bias. The effects of unobserved household features and parental preference on child quantity and quality would obscure the existence or absence of a trade-off between child quantity and quality. In a male-dominant society that values filial piety, the couple\u0026rsquo;s preference would be influenced by the husband\u0026rsquo;s parents\u0026rsquo; decisions. Moreover, in natural populations with minimal social gradients in fertility, an intergenerational correlation in reproductive fitness was also evident (Pluzhnikov et al., \u003cspan class=\"CitationRef\"\u003e2007\u003c/span\u003e). Therefore, I control for the social status of the grandfather of every male individual and the number of uncles that he had, in other words, the number of sons his grandfather produced, to partly address endogeneity. Table A1 in the Online Appendix reports the summary statistics of the sample.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e\n \u003ch2\u003e3.2.2 Instrumental variable model\u003c/h2\u003e\n \u003cp\u003eAs mentioned before, the unobservable parental preference and household features that would affect both quality and quantity of children would bias the effects of family size on child quality. To address the concern of omitted variable bias, I construct an instrumental variable, the father\u0026rsquo;s age at the birth of his first surviving son. The onset of son-bearing and consequently the duration of one\u0026rsquo;s reproductive period are directly correlated with family size and are also conditionally exogenous.\u003ca href=\"#_ftn1\" name=\"_ftnref1\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e\n \u003cp\u003e\u003ca class=\"FNLink\" href=\"#Fn7\" id=\"#FNLinkFn7\"\u003e\u003c/a\u003e\u003c/p\u003e\n \u003cp\u003eTo investigate the trade-off between fertility and offspring quality, Galor and Klemp (\u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e) employ the concept of the \u0026ldquo;protogenesic interval\u0026rdquo; (PI), which represents the duration between the date of marriage and the birth of the first child, as a measure of fertility. Since the genealogical records do not include specific marriage dates or the birth dates of the first child but only the birth dates of the first surviving son, I modify this PI measure to another variable, namely, the father\u0026rsquo;s age at the birth of his first surviving son.\u003c/p\u003e\n \u003cp\u003eThere was an old saying in traditional Confucian ideology: \u0026ldquo;There are three things which are unfilial, and to have no posterity is the greatest of them.\u0026rdquo; In a society that values filial piety highly, having male heirs to continue the bloodline is the priority for every male. Ming\u0026ndash;Qing China primarily adhered to a \u0026ldquo;natural fertility regime\u0026rdquo;, where deliberate fertility controls\u0026mdash;late starting, longer spacing, and early stopping\u0026mdash;were largely absent (Hu, \u003cspan class=\"CitationRef\"\u003e2023b\u003c/span\u003e). Hence, if a male had a surviving son at an earlier age, this suggests that he could have a longer reproductive span, resulting in more surviving sons throughout his lifetime. As depicted in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, most fathers had their first surviving sons in their 20s.\u003c/p\u003e\n \u003cp\u003eTo be a valid instrument, the timing of a father\u0026rsquo;s first male birth needs to be conditionally exogenous. However, time is affected not only by random events that affect the process of conception but also by cultural and socio-economic factors (Galor and Klemp, \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). In particular, men from wealthy families or those with higher social status could hypothetically marry earlier and have their first son earlier than those without. To account for potential socio-economic confounding factors affecting child quality, I directly control for a series of family-related characteristics to isolate the effect of random variations in the father\u0026rsquo;s age at the birth of his first son. This includes the grandfather\u0026rsquo;s social status, as well as the father\u0026rsquo;s social status, both of which could affect the timing of the father\u0026rsquo;s marriage.\u003c/p\u003e\n \u003cp\u003eHence, I then instrument the number of brothers that a male had by the conditionally exogenous variation induced by his father\u0026rsquo;s age at first son\u0026rsquo;s birth. I use an OLS regression and a probit regression to estimate Equations (\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e) and (\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e), respectively,\u003c/p\u003e\n \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e$${Brothers}_{i}={\\alpha }_{2}+{\\beta }_{2}{FatherAge}_{i}+{\\delta }_{2}{Z}_{i}+{\\gamma }_{2}{W}_{i}+{\\epsilon }_{i}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\n \u003c/div\u003e,\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e$${P(Quality}_{i}=1)={\\Phi }({\\alpha }_{3}+{\\beta }_{3}{\\widehat{Brothers}}_{i}+{\\delta }_{3}{Z}_{i}+{\\gamma }_{3}{W}_{i}+{\\epsilon }_{i})$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\n \u003c/div\u003e,\u003cp\u003ein which the variable \u003cem\u003eFatherAge\u003c/em\u003e equals father\u0026rsquo;s age at the birth of his first surviving son. \u003cem\u003eBrothers\u003c/em\u003e still denotes the final family size. The other notations are the same as in Eq. (\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"4 Results","content":"\u003cp\u003e\u003cstrong\u003e4.1 The absence of an optimal level of reproduction for long-run reproductive success\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.1.1 Baseline results\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTable 2 reports the results of regressions based on Equation (1). As expected, the number of descendants in generation 2, \u003cem\u003eSons\u003c/em\u003e, had a strong positive effect on the number of patrilineal male descendants in generations 3\u0026ndash;5. The square term of \u003cem\u003eSons\u003c/em\u003e maintains its negative and statistically significant effects on reproduction of the subsequent three generations in all columns in all three specifications. This suggests the possible presence of an optimal level of net reproduction for long-run reproductive success. The fitness for long-run reproductive success could diminish beyond a certain level of reproduction.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2\u003c/strong\u003e The effects of \u003cem\u003eSons\u003c/em\u003e on the number of male descendants for males born between 1350 and 1920, negative binomial regression\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"832\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.548076923076923%\" valign=\"bottom\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"82.45192307692308%\" colspan=\"9\" valign=\"bottom\"\u003e\n \u003cp\u003e\u003cem\u003eDependent Variable:\u0026nbsp;\u003c/em\u003eNumber of male descendants in\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eGen.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eGen.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eGen.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eGen.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eGen.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eGen.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eGen.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eGen.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003eGen.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e(1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e(2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e(3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e(4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e(5)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e(6)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e(7)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e(8)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003e(9)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003eSons\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.834***\u003c/p\u003e\n \u003cp\u003e(0.067)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.854***\u003c/p\u003e\n \u003cp\u003e(0.071)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.876***\u003c/p\u003e\n \u003cp\u003e(0.080)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.776***\u003c/p\u003e\n \u003cp\u003e(0.069)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.784***\u003c/p\u003e\n \u003cp\u003e(0.072)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.778***\u003c/p\u003e\n \u003cp\u003e(0.080)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.786***\u003c/p\u003e\n \u003cp\u003e(0.049)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.802***\u003c/p\u003e\n \u003cp\u003e(0.057)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003e1.788***\u003c/p\u003e\n \u003cp\u003e(0.069)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003eSons\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.965***\u003c/p\u003e\n \u003cp\u003e(0.006)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.964***\u003c/p\u003e\n \u003cp\u003e(0.006)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.962***\u003c/p\u003e\n \u003cp\u003e(0.006)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.967***\u003c/p\u003e\n \u003cp\u003e(0.006)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.967***\u003c/p\u003e\n \u003cp\u003e(0.006)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.964***\u003c/p\u003e\n \u003cp\u003e(0.006)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.963***\u003c/p\u003e\n \u003cp\u003e(0.004)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.960***\u003c/p\u003e\n \u003cp\u003e(0.004)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003e0.958***\u003c/p\u003e\n \u003cp\u003e(0.005)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003eClass\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.172***\u003c/p\u003e\n \u003cp\u003e(0.039)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.308***\u003c/p\u003e\n \u003cp\u003e(0.070)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003e1.369***\u003c/p\u003e\n \u003cp\u003e(0.104)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eHao\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.127***\u003c/p\u003e\n \u003cp\u003e(0.040)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.547***\u003c/p\u003e\n \u003cp\u003e(0.077)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003e1.645***\u003c/p\u003e\n \u003cp\u003e(0.117)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003eMarriages\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.101***\u003c/p\u003e\n \u003cp\u003e(0.022)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e1.153***\u003c/p\u003e\n \u003cp\u003e(0.031)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003e1.228***\u003c/p\u003e\n \u003cp\u003e(0.042)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eControls\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003eFirstborn\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003eOut-migration\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003eSurvival\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003eBirth cohort FE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003eLineage \u0026amp; Branch FE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e9,336\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e9,336\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e9,336\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e6,992\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e6,992\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e6,992\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e6,992\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e6,992\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003e6,992\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"17.56919374247894%\" valign=\"top\"\u003e\n \u003cp\u003ePseudo R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.093\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.040\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.023\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.058\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.055\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.112\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.14560770156438%\" valign=\"top\"\u003e\n \u003cp\u003e0.064\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"9.265944645006018%\" valign=\"top\"\u003e\n \u003cp\u003e0.060\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eNotes: 1. Coefficients are incidence rate ratios (IRR) for the negative binomial regression, and robust standard errors are in parentheses, clustered on fathers. 2. *p\u0026lt;0.1; **p\u0026lt;0.05; ***p\u0026lt;0.01.\u003c/p\u003e\n\u003cp\u003eAfter conditioning on all factors, hump-shaped patterns persist between the number of sons and the number of patrilineal male descendants in the next three generations in the six lineages. As shown in Figure 3, based on the results from columns 7 to 9, the predicted numbers of patrilineal grandsons, great-grandsons, and great-great-grandsons all reach their peaks when the number of sons equals seven. This finding suggests that the optimal level of reproduction for long-run reproductive success in the six lineages was about seven sons.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe statistically significant coefficients on \u003cem\u003eClass\u003c/em\u003e, \u003cem\u003eHao\u003c/em\u003e, and \u003cem\u003eMarriages\u003c/em\u003e in columns 7 to 9 also indicate that high-status and literate males could leave more male descendants than their low-status and illiterate counterparts in subsequent generations. A male\u0026rsquo;s social status and wealth not only affect his own reproduction but also affect the reproductive success of at least the next three generations. Figure 4 shows the social gradient in the long-run reproductive success; males who had a status higher than 1 could have more patrilineal grandsons, great-grandsons, and great-great-grandsons than males with status 1. The persistent effect of social status shown in the six lineages also validates what Song et al. (2015) find in North China from 1725 to 1875 and Lee and Park (2019) find in pre-modern Korea.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eHowever, as Figure 5 demonstrates, only 165 males (1.77%) from the \u0026ldquo;ancestor\u0026rdquo; sample had more than 5 sons. The sample mean and median of 2 sons are both below the potential optimal level of reproduction, 7 sons. The results for the six Chinese lineages suggest a difference between pre-transitional Southeast China and Quebec, as observed in Galor and Klemp (2019). In Quebec during the sixteenth to the eighteenth centuries, the optimal level of reproduction was below the population median (Galor and Klemp, 2019). In the six lineages, the potential optimal level of reproduction for having the greatest number of patrilineal grandsons, great-grandsons, and great-great-grandsons was significantly greater than the reproduction observed for the majority. For nearly all men in the sample, having more sons could directly translate into reproductive success in the long run. In contrast to the situation in Quebec, where a significant Darwinian trade-off gradually evolved into a demographic transition and subsequent economic transition, the findings in this paper indicate the absence of a significant Darwinian trade-off in the six Chinese lineages.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.1.2 Robustness\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis section tests the robustness of the previous results of the Darwinian trade-off to (1) an alternative estimation model, (2) converting the number of sons into a categorical variable and (3) controlling for lifespan.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eA hump-shaped relationship between the number of sons and long-run reproductive success is established using a negative binomial regression model. Table B1 in the Online Appendix demonstrates that this hump-shaped relationship is robust to the use of an OLS regression model.\u003ca href=\"#_ftn1\" name=\"_ftnref1\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e8\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003eAlthough the analysis includes males with at least four generations of male descendants, their lifespan might significantly affect their own reproduction and thus long-run reproductive success. To address this concern, I further condition the analysis on males with complete birth and death records, controlling for lifespan. The results are reported in Online Appendix Table B2. Lifespan had a positive effect on the number of male descendants a male could have in generations 3\u0026ndash;5. When lifespan is included as a control, the coefficients of \u003cem\u003eSons\u003c/em\u003e and \u003cem\u003eSons\u003csup\u003e2\u003c/sup\u003e\u003c/em\u003e are highly comparable to the results in columns 7\u0026ndash;9 of Table 2, indicating that the baseline results are robust.\u003c/p\u003e\n\u003cp\u003eThe coefficients on \u003cem\u003eSons\u003csup\u003e2\u003c/sup\u003e\u003c/em\u003e in Table 2, Table B1, and Table B2 consistently suggest a hump-shaped relationship between reproduction and long-run reproductive success. To validate the non-monotonic nature of the relationship, I also conduct an additional regression using the same estimation equation. In this regression, I convert the number of sons from a continuous variable to a categorical variable, excluding the square term of the number of sons.\u003ca href=\"#_ftn2\" name=\"_ftnref2\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003eThe results in Table B3 and Figure B1 in the Online Appendix affirm the persistence of the hump-shaped pattern, particularly in the relationship between the number of sons and the number of great-great-grandsons. The optimal level of reproduction remains at seven sons, underscoring the robustness of the baseline results.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2 Mechanisms through which reproduction affected long-run reproductive success\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eGalor and Klemp (2019) report that moderate fecundity could enhance child quality by increasing the probability of marrying and becoming educated, which would thus enable children to leave more descendants. Therefore, in this section, I examine the two types of Beckerian child quantity-quality trade-off in the six lineages: the effects of family size on the probability of sons marrying and achieving a \u003cem\u003ekeju\u003c/em\u003e degree. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2.1 Logistic estimation results\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTables 3 and 4 report the logistic regression results based on Equation (2).\u003ca href=\"#_ftn3\" name=\"_ftnref3\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e10\u003c/sup\u003e In Table 3, where quality is measured by marital status, the key independent variable \u003cem\u003eBrothers\u003c/em\u003e consistently retains positive coefficients across all six specifications. If a male had more brothers, he was more likely to marry. Moreover, being the firstborn son or an adopted son in a family would offer a \u0026ldquo;demographic advantage\u0026rdquo;, increasing the likelihood of marriage (columns 3 and 4). Columns 5 and 6 affirm that the positive correlation between child quantity and quality remains even when controlling for the effects of the father and grandfather. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3\u003c/strong\u003e Relationship between family size and marital status, logistic regression\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"587\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.12436115843271%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"78.8756388415673%\" colspan=\"6\"\u003e\n \u003cp\u003e\u003cem\u003eDependent Variable:\u0026nbsp;\u003c/em\u003eMarried\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e(1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e(2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e(3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e(4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e(5)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\" valign=\"top\"\u003e\n \u003cp\u003e(6)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eBrothers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.013\u003c/p\u003e\n \u003cp\u003e(0.012)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.069***\u003c/p\u003e\n \u003cp\u003e(0.016)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.120***\u003c/p\u003e\n \u003cp\u003e(0.018)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.135***\u003c/p\u003e\n \u003cp\u003e(0.019)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\" valign=\"top\"\u003e\n \u003cp\u003e1.097***\u003c/p\u003e\n \u003cp\u003e(0.019)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\" valign=\"top\"\u003e\n \u003cp\u003e1.096***\u003c/p\u003e\n \u003cp\u003e(0.019)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eFirstborn\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.381***\u003c/p\u003e\n \u003cp\u003e(0.040)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.409***\u003c/p\u003e\n \u003cp\u003e(0.042)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\" valign=\"top\"\u003e\n \u003cp\u003e1.404***\u003c/p\u003e\n \u003cp\u003e(0.042)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\" valign=\"top\"\u003e\n \u003cp\u003e1.404***\u003c/p\u003e\n \u003cp\u003e(0.042)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eAdoptee\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.344***\u003c/p\u003e\n \u003cp\u003e(0.086)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\" valign=\"top\"\u003e\n \u003cp\u003e1.429***\u003c/p\u003e\n \u003cp\u003e(0.093)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\" valign=\"top\"\u003e\n \u003cp\u003e1.431***\u003c/p\u003e\n \u003cp\u003e(0.094)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eFather\u0026rsquo;s class\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.948***\u003c/p\u003e\n \u003cp\u003e(0.116)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\" valign=\"top\"\u003e\n \u003cp\u003e1.916***\u003c/p\u003e\n \u003cp\u003e(0.127)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eFather\u0026rsquo;s marriages\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.269***\u003c/p\u003e\n \u003cp\u003e(0.054)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\" valign=\"top\"\u003e\n \u003cp\u003e1.270***\u003c/p\u003e\n \u003cp\u003e(0.054)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eGrandfather\u0026rsquo;s class\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\" valign=\"top\"\u003e\n \u003cp\u003e1.036\u003c/p\u003e\n \u003cp\u003e(0.062)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eUncles\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\" valign=\"top\"\u003e\n \u003cp\u003e0.998\u003c/p\u003e\n \u003cp\u003e(0.013)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003eOut-migration\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003eSurvival\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003eBirth cohort FE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003eLineage FE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e36,360\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e31,106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e31,106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e31,106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e31,106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e31,080\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003ePseudo-R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.0001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.232\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.235\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.235\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.244\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.244\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eNotes: 1. If the individual is an adoptee, then \u0026ldquo;Father\u0026rsquo;s class\u0026rdquo; and \u0026ldquo;Grandfather\u0026rsquo;s class\u0026rdquo; denote the stepfather\u0026rsquo;s and step-grandfather\u0026rsquo;s social status, respectively.\u0026nbsp;2. Coefficients are the odds ratios for the logistic regression, and robust standard errors are in parentheses, clustered on fathers. 3. *p\u0026lt;0.1; **p\u0026lt;0.05; ***p\u0026lt;0.01.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 4\u003c/strong\u003e Relationship between family size and degree, logistic regression\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"584\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.232876712328768%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"78.76712328767124%\" colspan=\"6\"\u003e\n \u003cp\u003e\u003cem\u003eDependent Variable:\u0026nbsp;\u003c/em\u003eDegree\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e(1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e(2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e(3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e(4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e(5)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e(6)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eBrothers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.235***\u003c/p\u003e\n \u003cp\u003e(0.032)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.210***\u003c/p\u003e\n \u003cp\u003e(0.028)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.252***\u003c/p\u003e\n \u003cp\u003e(0.030)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.266***\u003c/p\u003e\n \u003cp\u003e(0.031)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.050*\u003c/p\u003e\n \u003cp\u003e(0.028)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.025\u003c/p\u003e\n \u003cp\u003e(0.027)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eFirstborn\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.348***\u003c/p\u003e\n \u003cp\u003e(0.075)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.368***\u003c/p\u003e\n \u003cp\u003e(0.076)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.403***\u003c/p\u003e\n \u003cp\u003e(0.088)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.401***\u003c/p\u003e\n \u003cp\u003e(0.090)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eAdoptee\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.398***\u003c/p\u003e\n \u003cp\u003e(0.176)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.482***\u003c/p\u003e\n \u003cp\u003e(0.200)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.451***\u003c/p\u003e\n \u003cp\u003e(0.199)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eFather\u0026rsquo;s class\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e13.770***\u003c/p\u003e\n \u003cp\u003e(1.311)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e9.448***\u003c/p\u003e\n \u003cp\u003e(1.017)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eFather\u0026rsquo;s marriages\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.265***\u003c/p\u003e\n \u003cp\u003e(0.062)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e1.273***\u003c/p\u003e\n \u003cp\u003e(0.062)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eGrandfather\u0026rsquo;s class\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e2.485***\u003c/p\u003e\n \u003cp\u003e(0.248)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\"\u003e\n \u003cp\u003eUncles\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.980\u003c/p\u003e\n \u003cp\u003e(0.020)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003eOut-migration\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003eSurvival\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003eBirth cohort FE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003eLineage FE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003eY\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e36,360\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e30,190\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e30,190\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e30,190\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e30,190\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e30,164\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.160409556313994%\" valign=\"top\"\u003e\n \u003cp\u003ePseudo-R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.014\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.161\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.163\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.164\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.316\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.139931740614335%\"\u003e\n \u003cp\u003e0.332\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eNotes: 1. If the individual is an adoptee, then \u0026ldquo;Father\u0026rsquo;s class\u0026rdquo; and \u0026ldquo;Grandfather\u0026rsquo;s class\u0026rdquo; denote his stepfather\u0026rsquo;s and step-grandfather\u0026rsquo;s social status, respectively. 2. Coefficients are the odds ratios for the logistic regression, and robust standard errors are in parentheses, clustered on fathers. 3. *p\u0026lt;0.1; **p\u0026lt;0.05; ***p\u0026lt;0.01.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTable 4 suggests that family size played a similar role. Before including the father\u0026rsquo;s and grandfather\u0026rsquo;s effects, columns 1\u0026ndash;4 suggest that for a one-unit increase in \u003cem\u003eBrothers\u003c/em\u003e, the odds of a male achieving an academic degree versus not achieving one would increase by a factor of about 1.3. However, after including the effects of fathers and grandfathers in columns 5\u0026ndash;6, the coefficients on \u003cem\u003eBrothers\u003c/em\u003e remain positive but lose statistical significance. Nevertheless, the results still demonstrate that having a larger number of brothers was not negatively associated with the likelihood of a male attaining a \u003cem\u003ekeju\u003c/em\u003e degree.\u003c/p\u003e\n\u003cp\u003eAs expected, fathers\u0026rsquo; social status had the most substantial effect on sons\u0026rsquo; quality. Figure 6 demonstrates the predicted probability of being married and holding a \u003cem\u003ekeju\u003c/em\u003e degree for families of different sizes, conditioned on fathers\u0026rsquo; social status. The figure shows that the considerable difference in the quality of sons arises from the difference in fathers\u0026rsquo; social status. For a male who was raised in a family of two sons, the predicted probability of marriage was about 75.5 per cent if he had a high-status father, while that for a male who had a low-status father was about 66.2 per cent. The convergence of these two percentages becomes more pronounced as family size increases. The differences are wider for the probabilities of achieving academic degrees. The predicted probability of holding degrees for males with high-status fathers in a two-son family was 11.7 per cent, and that for males with low-status fathers was only 1.6 per cent.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe results clearly show that the Beckerian trade-off, measured by the probability of marriage and attainment of \u003cem\u003ekeju\u003c/em\u003e degrees, was absent in the six lineages. A larger family size would not diminish the quality of sons; instead, it would enhance the likelihood of marriage while exhibiting a positive albeit weak effect on the probability of achieving a \u003cem\u003ekeju\u003c/em\u003e degree.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2.2 Robustness\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis section presents the robustness of the previous results of the Beckerian trade-off to (1) subperiods, (2) controlling for lifespan, and (3) alternative human capital indicators.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eI first divide the sample into three sub-samples that refer to three distinct cohorts and report the results in Table B4. For males born between 1400 and 1600, the number of brothers they had and their quality measures were not significantly correlated. However, after 1600, the number of brothers a male had displayed a positive correlation with the probability of his marriage. When measuring quality based on education, \u0026shy;the coefficients on \u003cem\u003eBrothers\u003c/em\u003e are not statistically significant across all three periods. Overall, similar to the baseline results in Tables 3 and 4, family size exhibited a stronger correlation with the likelihood of marriage, while a weak correlation emerged with the likelihood of attaining a \u003cem\u003ekeju\u003c/em\u003e degree.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eI then further condition on lifespan in the model. Similar to previous reasoning, one\u0026rsquo;s lifespan would affect one\u0026rsquo;s probability of marrying and holding a \u003cem\u003ekeju\u003c/em\u003e degree. Therefore, I include the male\u0026rsquo;s age at death, and the results are shown in Table B5. Father\u0026rsquo;s class and marriages remain positively correlated with one\u0026rsquo;s human capital, but the coefficients on \u003cem\u003eBrothers\u003c/em\u003e lost statistical significance in both models, which suggests that family size did not strongly contribute to sons\u0026rsquo; human capital formation. The results still show that a Beckerian trade-off was absent in the six lineages, which confirms the baseline results.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFinally, I use whether a man had a \u003cem\u003eZi\u003c/em\u003e (courtesy name) or \u003cem\u003eHao\u003c/em\u003e (pen name) as two alternative measures for human capital. As \u003cem\u003eDegree\u003c/em\u003e measures the most \u0026ldquo;upper-tail\u0026rdquo; human capital in traditional China, I use \u003cem\u003eZi\u003c/em\u003e and \u003cem\u003eHao\u003c/em\u003e to measure rudimentary literacy. \u003cem\u003eZi\u003c/em\u003e, courtesy name, is a name given to a male by his father or his teacher when he reached adulthood, and \u003cem\u003ehao\u003c/em\u003e, as mentioned earlier, is a pen name that a literate male would give himself. Having a \u003cem\u003eZi\u003c/em\u003e or \u003cem\u003eHao\u003c/em\u003e means that the male was capable of reading at least a rudimentary literacy. These two measures are much similar to signature-based literacy, the conventional indicator for human capital (Schofield, 1968; Ogilvie, Edwards, and K\u0026uuml;pker, 2022). Therefore, I change the outcome of interest from \u003cem\u003eDegree\u003c/em\u003e to \u003cem\u003eZi\u003c/em\u003e and \u003cem\u003eHao\u003c/em\u003e, and Table B6 reports the results.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAs shown in columns 1 and 3, before conditioning on fathers\u0026rsquo; and grandfathers\u0026rsquo; social status, the number of brothers a male had was positively correlated with his probability of having \u003cem\u003eZi\u003c/em\u003e and \u003cem\u003eHao\u003c/em\u003e. However, after conditioning on father\u0026rsquo;s and grandfather\u0026rsquo;s class, and father\u0026rsquo;s marriages, both coefficients on \u003cem\u003eBrothers\u003c/em\u003e in columns 2 and 4 lose significance. The results are comparable to those in Table 4, which suggests that the baseline results are robust. The results of the three indicators of child quality, marital status (\u003cem\u003eMarried\u003c/em\u003e), upper-tail human capital (\u003cem\u003eDegree\u003c/em\u003e), and rudimentary literacy (\u003cem\u003eZi\u003c/em\u003e and \u003cem\u003eHao\u003c/em\u003e), all demonstrate the absence of a Beckerian trade-off of children in the six lineages in Ming\u0026shy;\u0026ndash;Qing China.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2.3 Causal identification: Using father\u0026rsquo;s age at the first son\u0026rsquo;s birth as an instrument\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis section turns to the instrumented evidence on the trade-off between child quantity and quality. The logistic regression results in the previous section could be biased because of the unobserved parental preference and household features, although controlling for the grandfather\u0026rsquo;s social status and the number of uncles could partially capture the unobserved features.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe IV estimation results based on Equations (3) and (4) are shown in Tables 5 and 6. Table 5 details the results of the full sample, comprising all males born between 1350 and 1920 who had records of their fathers\u0026rsquo; age at the birth of their fathers\u0026rsquo; first sons across the six lineages. Before I report the 2SLS results, I report those of the reduced-form estimates in columns 1 and 2 of Table 5. The OLS results for the first stage are reported in column 3, and the average marginal effects of the probit regressions for the second stage are reported in columns 4 and 5, where the dependent variables are \u003cem\u003eMarried\u003c/em\u003e and \u003cem\u003eDegree\u003c/em\u003e, respectively. Table 6 reports the results for three sub-cohorts, 1400 to 1600, 1600 to 1800, and 1800 to 1900. Columns 1, 4, and 7 report the first-stage results, and the remaining columns report the second stage results.\u003c/p\u003e\n\u003cp\u003eThe \u003cem\u003eF\u003c/em\u003e-statistic on the instrument remains higher than the Stock and Yogo (2005) critical value in Table 5 and in the specifications of periods after 1600 in Table 6, ruling out the weak instrument concern.\u003c/p\u003e\n\u003cp\u003eThe instrumented results in Table 5 show a largely comparable pattern with those in Tables 3 and 4. Family size continued to be a positive factor contributing to the quality of sons. Father\u0026rsquo;s age at first son\u0026rsquo;s birth had both statistically and quantitatively significant average marginal effects on the probability that a male would be married and achieve a \u003cem\u003ekeju\u003c/em\u003e degree (columns 1\u0026ndash;2 and 4\u0026ndash;5). As shown in columns 4 and 5, an increase of one son in family size is associated with a 9-percentage-point increase in the likelihood of marriage and a 2-percentage-point increase in the likelihood of obtaining an academic degree for males in the six lineages. Additionally, male individuals with high-status fathers exhibit a 9.2-percentage-point and 9.4-percentage-point increase in the probability of marriage and degree attainment, respectively.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 5\u003c/strong\u003e Impact of the quantity of children on the quality of children: Instrumented results\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.34228187919463%\" valign=\"top\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"26.006711409395972%\" colspan=\"2\" valign=\"top\" style=\"width: 20.1424%;\"\u003e\n \u003cp\u003eReduced-form\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.74496644295302%\" valign=\"top\" style=\"width: 9.127%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.926174496644295%\" colspan=\"2\" valign=\"top\" style=\"width: 10.8055%;\"\u003e\n \u003cp\u003e2SLS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.79194630872483%\" colspan=\"2\" valign=\"top\" style=\"width: 14.5822%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003eMarried\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003eDegree\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003eBrothers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003eMarried\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003eDegree\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e(1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e(2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e(3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e(4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e(5)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003eFather\u0026rsquo;s age at first son\u0026rsquo;s birth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e0.979***\u003c/p\u003e\n \u003cp\u003e(0.002)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e0.984***\u003c/p\u003e\n \u003cp\u003e(0.006)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e-0.038***\u003c/p\u003e\n \u003cp\u003e(0.002)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003eBrothers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.091***\u003c/p\u003e\n \u003cp\u003e(0.013)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.019***\u003c/p\u003e\n \u003cp\u003e(0.007)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003eFirstborn\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e1.525***\u003c/p\u003e\n \u003cp\u003e(0.056)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e1.630***\u003c/p\u003e\n \u003cp\u003e(0.113)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e-1.224***\u003c/p\u003e\n \u003cp\u003e(0.021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.181***\u003c/p\u003e\n \u003cp\u003e(0.018)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.045***\u003c/p\u003e\n \u003cp\u003e(0.009)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003eAdoptee\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e1.334***\u003c/p\u003e\n \u003cp\u003e(0.142)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e1.235\u003c/p\u003e\n \u003cp\u003e(0.252)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e-0.440***\u003c/p\u003e\n \u003cp\u003e(0.034)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.081***\u003c/p\u003e\n \u003cp\u003e(0.019)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.019***\u003c/p\u003e\n \u003cp\u003e(0.010)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003eFather\u0026rsquo;s class\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e2.070***\u003c/p\u003e\n \u003cp\u003e(0.158)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e11.199***\u003c/p\u003e\n \u003cp\u003e(1.421)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.273***\u003c/p\u003e\n \u003cp\u003e(0.051)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.092***\u003c/p\u003e\n \u003cp\u003e(0.013)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.094***\u003c/p\u003e\n \u003cp\u003e(0.005)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003eFather\u0026rsquo;s marriages\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e1.382***\u003c/p\u003e\n \u003cp\u003e(0.071)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e1.341***\u003c/p\u003e\n \u003cp\u003e(0.068)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.431***\u003c/p\u003e\n \u003cp\u003e(0.083)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.013***\u003c/p\u003e\n \u003cp\u003e(0.011)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.006***\u003c/p\u003e\n \u003cp\u003e(0.004)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003eGrandfather\u0026rsquo;s class\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e0.989\u003c/p\u003e\n \u003cp\u003e(0.072)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e2.543***\u003c/p\u003e\n \u003cp\u003e(0.305)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.081*\u003c/p\u003e\n \u003cp\u003e(0.045)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e-0.008\u003c/p\u003e\n \u003cp\u003e(0.012)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e0.039***\u003c/p\u003e\n \u003cp\u003e(0.005)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" valign=\"top\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003eObservations\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" valign=\"top\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e18,521\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" valign=\"top\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e18,521\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" valign=\"top\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e18,521\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" valign=\"top\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e18,521\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" valign=\"top\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e18,521\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" valign=\"top\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003eNumber of clusters\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" valign=\"top\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e9,518\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" valign=\"top\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e9,518\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" valign=\"top\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e9,518\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" valign=\"top\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e9,518\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" valign=\"top\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e9,518\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003ePseudo R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" valign=\"top\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e0.226\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" valign=\"top\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e0.345\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" valign=\"top\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.430976430976433%\" style=\"width: 20.562%;\"\u003e\n \u003cp\u003e\u003cem\u003eF\u003c/em\u003e-statistic on instrument\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" valign=\"top\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.962962962962964%\" valign=\"top\" style=\"width: 10.0712%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e262.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" colspan=\"2\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.814814814814815%\" valign=\"top\" style=\"width: 11.5399%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eNotes: 1. Robust standard errors clustered by fathers in parentheses. 2. All specifications shown include uncles, out-migration, survival to adulthood, birth cohort FE, and lineage FE. 3. Columns 1\u0026ndash;2 are subjected to logistic regression. Coefficients are the odds ratios for the logistic regression. 4. Columns 3\u0026ndash;5 present the results of the Ivprobit estimation: the first stage being OLS, and the second stage involves probit regression on the predicted values from the first stage. The two models in columns 4 and 5 have the same first stage. The coefficients in columns 4\u0026ndash;5 are average marginal effects. The \u003cem\u003eF\u003c/em\u003e-statistic on the instrument is derived from a 2SLS estimate, which has the same first stage. 5. *p\u0026lt;0.1; **p\u0026lt;0.05; ***p\u0026lt;0.01.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 6\u003c/strong\u003e Two-stage regression with father\u0026rsquo;s age at first son\u0026rsquo;s birth by period, measured by marriage and degree\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"854\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.608187134502923%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"26.549707602339183%\" colspan=\"3\" valign=\"top\" style=\"width: 23.8936%;\"\u003e\n \u003cp\u003eBorn in 1400\u0026ndash;1600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"26.549707602339183%\" colspan=\"3\" valign=\"top\" style=\"width: 23.8936%;\"\u003e\n \u003cp\u003eBorn in 1600\u0026ndash;1800\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"26.549707602339183%\" colspan=\"3\" valign=\"top\" style=\"width: 23.7902%;\"\u003e\n \u003cp\u003eBorn in 1800\u0026ndash;1900\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.608187134502923%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.88888888888889%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e1\u003csup\u003est\u003c/sup\u003e Stage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.660818713450293%\" colspan=\"2\" valign=\"top\" style=\"width: 15.9291%;\"\u003e\n \u003cp\u003e2\u003csup\u003end\u003c/sup\u003e Stage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.88888888888889%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e1\u003csup\u003est\u003c/sup\u003e Stage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.660818713450293%\" colspan=\"2\" valign=\"top\" style=\"width: 15.9291%;\"\u003e\n \u003cp\u003e2\u003csup\u003end\u003c/sup\u003e Stage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.88888888888889%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e1\u003csup\u003est\u003c/sup\u003e Stage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.660818713450293%\" colspan=\"2\" valign=\"top\" style=\"width: 15.7222%;\"\u003e\n \u003cp\u003e2\u003csup\u003end\u003c/sup\u003e Stage\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003eBrothers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003eMarried\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003eDegree\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003eBrothers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003eMarried\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003eDegree\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003eBrothers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003eMarried\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003eDegree\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e(1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e(2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e(3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e(4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e(5)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e(6)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e(7)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e(8)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003e(9)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003eFather\u0026rsquo;s age at first son\u0026rsquo;s birth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.036***\u003c/p\u003e\n \u003cp\u003e(0.245)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.037***\u003c/p\u003e\n \u003cp\u003e(0.004)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.038***\u003c/p\u003e\n \u003cp\u003e(0.003)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003eBrothers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.018\u003c/p\u003e\n \u003cp\u003e(0.069)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.002\u003c/p\u003e\n \u003cp\u003e(0.067)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.085***\u003c/p\u003e\n \u003cp\u003e(0.018)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.018\u003c/p\u003e\n \u003cp\u003e(0.011)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.089***\u003c/p\u003e\n \u003cp\u003e(0.019)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003e0.017*\u003c/p\u003e\n \u003cp\u003e(0.009)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003eFirstborn\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.868***\u003c/p\u003e\n \u003cp\u003e(0.080)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.004\u003c/p\u003e\n \u003cp\u003e(0.059)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.157**\u003c/p\u003e\n \u003cp\u003e(0.065)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-1.209***\u003c/p\u003e\n \u003cp\u003e(0.033)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.177***\u003c/p\u003e\n \u003cp\u003e(0.025)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.051***\u003c/p\u003e\n \u003cp\u003e(0.015)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-1.248***\u003c/p\u003e\n \u003cp\u003e(0.029)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.177***\u003c/p\u003e\n \u003cp\u003e(0.026)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003e0.029**\u003c/p\u003e\n \u003cp\u003e(0.011)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003eAdoptee\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.959***\u003c/p\u003e\n \u003cp\u003e(0.358)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.137\u003c/p\u003e\n \u003cp\u003e(0.112)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.021\u003c/p\u003e\n \u003cp\u003e(0.164)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.661***\u003c/p\u003e\n \u003cp\u003e(0.054)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.067**\u003c/p\u003e\n \u003cp\u003e(0.032)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.026\u003c/p\u003e\n \u003cp\u003e(0.018)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.303***\u003c/p\u003e\n \u003cp\u003e(0.041)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.074***\u003c/p\u003e\n \u003cp\u003e(0.024)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003e0.010\u003c/p\u003e\n \u003cp\u003e(0.010)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003eFather\u0026rsquo;s class\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.388***\u003c/p\u003e\n \u003cp\u003e(0.162)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.004\u003c/p\u003e\n \u003cp\u003e(0.050)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.233***\u003c/p\u003e\n \u003cp\u003e(0.062)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.219***\u003c/p\u003e\n \u003cp\u003e(0.070)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.094***\u003c/p\u003e\n \u003cp\u003e(0.016)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.131***\u003c/p\u003e\n \u003cp\u003e(0.008)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.246***\u003c/p\u003e\n \u003cp\u003e(0.074)\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.088***\u003c/p\u003e\n \u003cp\u003e(0.019)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003e0.060***\u003c/p\u003e\n \u003cp\u003e(0.007)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003eFather\u0026rsquo;s marriages\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.403***\u003c/p\u003e\n \u003cp\u003e(0.132)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.080\u003c/p\u003e\n \u003cp\u003e(0.054)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.029\u003c/p\u003e\n \u003cp\u003e(0.030)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.498***\u003c/p\u003e\n \u003cp\u003e(0.123)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.018\u003c/p\u003e\n \u003cp\u003e(0.016)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.012*\u003c/p\u003e\n \u003cp\u003e(0.007)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.371***\u003c/p\u003e\n \u003cp\u003e(0.059)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.011\u003c/p\u003e\n \u003cp\u003e(0.015)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003e0.003\u003c/p\u003e\n \u003cp\u003e(0.005)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003eGrandfather\u0026rsquo;s class\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.148\u003c/p\u003e\n \u003cp\u003e(0.187)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.024\u003c/p\u003e\n \u003cp\u003e(0.042)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.084*\u003c/p\u003e\n \u003cp\u003e(0.050)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.085\u003c/p\u003e\n \u003cp\u003e(0.061)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e-0.033**\u003c/p\u003e\n \u003cp\u003e(0.015)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.062***\u003c/p\u003e\n \u003cp\u003e(0.008)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.058\u003c/p\u003e\n \u003cp\u003e(0.068)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e0.004\u003c/p\u003e\n \u003cp\u003e(0.017)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003e0.013**\u003c/p\u003e\n \u003cp\u003e(0.006)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" valign=\"top\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003eObservations\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e452\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e441\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e445\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e8,604\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e8,604\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e8,604\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e8,716\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e8,716\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003e8,439\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003eNumber of clusters\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e226\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e216\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e224\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e4,425\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e4,425\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e4,425\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e4,810\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e4,810\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003e4,695\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"16.55011655011655%\" style=\"width: 14.8947%;\"\u003e\n \u003cp\u003e\u003cem\u003eF\u003c/em\u003e-statistic on instrument\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e11.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e112.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e167.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" valign=\"top\" style=\"width: 7.9645%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"8.857808857808857%\" style=\"width: 7.7577%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eNotes: 1. Robust standard errors clustered by fathers in parentheses. 2. All specifications shown include uncles, out-migration, survival to adulthood, and lineage FE. 3. Ivprobit estimation: the first stage being OLS, the second stage probit, regressed on the predicted values from the first stage. The two models have the same first stage. 4. The coefficients in columns 2, 3, 5, 6, 8, and 9 are average marginal effects. The \u003cem\u003eF\u003c/em\u003e-statistic on the instrument is derived from a 2SLS estimate, which has the same first stage. 5. *p\u0026lt;0.1; **p\u0026lt;0.05; ***p\u0026lt;0.01.\u003c/p\u003e\n\u003cp\u003eTable 6 reveals that the relationships varied across different cohorts. When using marital status as the indicator of \u0026ldquo;quality\u0026rdquo;, family size exhibited a positive effect during the cohorts 1600\u0026ndash;1800 and 1800\u0026ndash;1900: having one more brother could increase the likelihood of a male\u0026rsquo;s marriage by approximately 9 percentage points. However, for males born in any of these periods, the number of brothers a male had only had a positive albeit weak effect on the probability of him attaining a degree: there was an approximately 2-percentage-point increase for the 1800\u0026ndash;1900 cohort; in the previous two cohorts, family size did not significantly impact a son\u0026rsquo;s formal education.\u003ca href=\"#_ftn4\" name=\"_ftnref4\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003eMoreover, the results also suggest that a father\u0026rsquo;s social status could account for a son\u0026rsquo;s human capital to a great extent. For instance, as indicated in columns 3 and 6 of Table 6, for the 1400\u0026ndash;1600 cohort, having a father with high social status would increase the probability of attaining a degree by 23.3 percentage points, and for the cohort 1600\u0026ndash;1800 cohort, this increase would be 13.1 percentage points. For all men in the six lineages who had high-status fathers, despite being raised in larger families, they were still more likely to achieve academic degrees than those with fathers of low social status.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn summary, both the baseline and instrumented results suggest that family size did not have a negative impact on a son\u0026rsquo;s quality and may have even had a positive effect. Moreover, the father\u0026rsquo;s social status played a more crucial role. A substantial Beckerian trade-off was absent in the six lineages from 1350 to 1920. \u0026nbsp;\u003c/p\u003e"},{"header":"5 Discussion: Why were the two trade-offs absent in Ming–Qing China?","content":"\u003cp\u003eSection 4 demonstrates the absence of the two trade-offs within the six lineages. The findings of the two trade-offs collectively illustrate a distinct relationship between reproduction and human capital in a multigenerational model. High-status males in the six lineages could produce more patrilineal male descendants for at least four consecutive generations. This phenomenon stemmed from the inheritance of privileges by their sons, grandsons, and great-grandsons, subsequently amplifying their probability of getting married and educated. It constituted a winner-take-all scenario: a greater number of sons translated to an elongated bloodline through an augmented likelihood of raising accomplished male offspring, without detriments arising from increased family sizes.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFor both prosperous and impoverished families, the absence of any trade-offs is not surprising. High-status fathers, including degree- and office-holders, possessed sufficient resources to support a large number of sons and assure their education. Leveraging their own social capital and providing \u0026ldquo;cultural capital\u0026rdquo; to their sons, it was unsurprising that their sons more easily attained \u003cem\u003ekeju\u003c/em\u003e degrees (Ho, 1962; Jiang and Kung, 2021). \u003ca href=\"#_ftn5\" name=\"_ftnref5\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e12\u0026nbsp;\u003c/sup\u003eFor these fathers, having more sons was akin to buying more lottery tickets for success in the \u003cem\u003ekeju\u003c/em\u003e competition. The budget constraints of these households were sufficiently high that they did not face trade-offs between reproduction and long-run reproductive success or between child quantity and quality; instead, they could afford both.\u003c/p\u003e\n\u003cp\u003eIn contrast, impoverished fathers faced constraints on family size, and the smaller size of their families was not a deliberate choice to limit family size and invest in their sons\u0026rsquo; human capital. Rudimentary literacy was easy to acquire, but\u0026nbsp;full literacy was not.\u003ca href=\"#_ftn6\" name=\"_ftnref6\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e13\u0026nbsp;\u003c/sup\u003eAlthough the rise in social status created strong motivations for low-status men to pursue \u003cem\u003ekeju\u003c/em\u003e degrees, the high opportunity costs and intense competition prevented most of them from devoting persistent effort to repeated exam attempts (Ebrey, 1993; Shiue, 2017). Elman (2000, 240) highlights that classical literacy \u0026ldquo;required substantial investments of time, effort, and training\u0026rdquo;, and always exacted \u0026ldquo;financial and labor sacrifices\u0026rdquo;. Due to the extremely low chances and high costs associated with winning the \u003cem\u003ekeju\u003c/em\u003e prize, these families lacked the incentives to participate in the lottery game in the first place.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis paper thus also reveals the consanguineous nature of Chinese society. As mentioned in Fei (1992, 120), traditional China \u0026ldquo;maintains structural stability by using the biological process underlying reproduction as the medium to establish social continuity\u0026hellip;An aristocrat\u0026rsquo;s son becomes an aristocrat; such succession in identity is consanguineous. A rich man\u0026rsquo;s son becomes rich; such succession in wealth is consanguineous.\u0026rdquo; For those privileged men, the men who attained higher social status in the lineages, their male descendants also inherit these privileges, at least for the subsequent four generations.\u003c/p\u003e\n\u003cp\u003eThe lack of these two trade-offs also sheds light on the absence of a fertility transition in nineteenth-century China. Coale (1974, 352\u0026ndash;353) points out that a crucial condition for a society to experience a secular decline in fertility is that \u0026ldquo;perceived social and economic circumstances must make reduced fertility seem an advantage to individual couples\u0026rdquo;.\u003ca href=\"#_ftn7\" name=\"_ftnref7\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e14\u0026nbsp;\u003c/sup\u003eWhile most Western European societies fulfilled this condition in the nineteenth century, with affluent families leading in limiting family size compared to poorer ones (see, for example, Clark and Cummins, 2015), nineteenth-century China did not. The Malthusian mechanism continued to function throughout this period. The empirical investigation in this paper directly responds to this condition, implying that reduced fertility was not advantageous to parents, especially those of high status, as having more sons equalled having more high-status sons. Without a secular fertility decline, the absence of a modern economic take-off is unsurprising (Galor and Weil, 2000).\u0026nbsp;\u003c/p\u003e\n\u003cdiv id=\"ftn7\"\u003e\u003cbr\u003e\u003c/div\u003e"},{"header":"6 Conclusion","content":"\u003cp\u003eThe transition from Malthusian stagnation to sustained economic growth necessitates a transitioned demographic pattern. This paper uses a new genealogical dataset to illustrate the demographic dynamics of patrilines across six Chinese lineages from 1350 to 1920. The empirical investigation reveals the absence of both a Darwinian trade-off and a Beckerian trade-off in the six lineages throughout the period. Greater reproduction could result in long-run reproductive success. A close analysis of the mechanisms demonstrates the positive effect of a father\u0026rsquo;s reproductive behavior on two aspects of offspring quality, measured by marital status and education. Instrumenting family size with the variation induced by the father\u0026rsquo;s age at the birth of his first son confirms the absence of a trade-off between child quantity and quality in the six lineages.\u003c/p\u003e \u003cp\u003eThe results indicate a highly unequal Chinese society. A high-status man\u0026rsquo;s household budget constraint in the six lineages was so high that he did not need to choose between child quantity and quality, but could have them both. High-status men could leave a greater number of patrilineal male descendants for at least four generations; additionally, their sons, grandsons, and great-grandsons were more likely to be married and to hold \u003cem\u003ekeju\u003c/em\u003e degrees. This winner-takes-all scenario could also explain the absence of a demographic transition in nineteenth-century China, consequently contributing to the missed opportunity for experiencing an economic take-off from stagnation to growth to some extent.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding:\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author also acknowledges the financial support of the National Natural Science Foundation of China (No.72203224).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest/Competing interests\u003c/strong\u003e:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFinancial interests: The author has no financial interests to declare that are relevant to the content of this article.\u003c/p\u003e\n\u003cp\u003eNon-financial interests: The author received PhD supervision from Neil Cummins and Debin Ma. James Kai-sing Kung and Noam Yuchtman were the examiners of the author\u0026rsquo;s PhD thesis.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and material\u003c/strong\u003e: The data used in this paper were hand-collected by the author.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eI am grateful to Shuji Cao and Qin Jiang at Shanghai Jiaotong University for kindly sharing the original digitalized genealogies of the Zhou, Que, and Huang lineages with me and Familyserach.org for providing researchers with digital images of the genealogical records of the Gu, Zha, and Zhuang lineages. I acknowledge Rongyu Jian for her research assistance.\u003c/p\u003e\n\u003cp\u003eI am especially grateful to Neil Cummins, Debin Ma, Eric Schneider, James Kai-sing Kung, Noam Yuchtman, Oded Galor. I also wish to thank Gregory Clark, Jan Kok, Zhiwu Chen, Nan Li, Qin Jiang, Zhan Lin, Yu Hao, Ming Lei, Qun Che, and Qing Wang for their extensive feedback and also participants in the LSE Asia Economic History Seminar, LSE Graduate Economic History Seminar, EHS Annual Conference 2021, RES Annual Conference 2021, European Social Science History Conference 2021, Eighth International Symposium on Quantitative History, 2022 World Economic History Congress, and Economic History Workshop at Peking University for their comments. I acknowledge the financial support of the National Natural Science Foundation of China (No.72203224). Any errors are my own.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eS.H. wrote the entire manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgment\u003c/h2\u003e \u003cp\u003eI am grateful to Shuji Cao and Qin Jiang at Shanghai Jiaotong University for kindly sharing the original digitalized genealogies of the Zhou, Que, and Huang lineages with me and Familyserach.org for providing researchers with digital images of the genealogical records of the Gu, Zha, and Zhuang lineages. I acknowledge Rongyu Jian for her research assistance.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBai, Y., Li, Y., \u0026amp; Lam, P.H. (2023). Quantity-quality trade-off in Northeast China during the Qing dynasty. \u003cem\u003eJournal of Population Economics\u003c/em\u003e, 36, 1657\u0026ndash;1694. https://doi.org/10.1007/s00148-022-00933-x\u003c/li\u003e\n\u003cli\u003eBaudin, T., \u0026amp; De la Croix, D. (2023). 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Series B: Biological Sciences\u003c/em\u003e, 269 (1491), 553\u0026ndash;562. https://doi.org/10.1098/rspb.2001.1912\u003c/li\u003e\n\u003cli\u003eTan, H.R. (2019). More is Less? The Impact of Family Size on Education Outcomes in the United States, 1850\u0026ndash;1940\u003cem\u003e. Journal of Human Resources\u003c/em\u003e, 54 (4), 1154\u0026ndash;1181. https://doi.org/10.3368/jhr.54.4.0517.8768R1\u003c/li\u003e\n\u003cli\u003eTelford, T.A. (1995). Fertility and Population Growth in the Lineages of Tongcheng County, 1520\u0026ndash;1661. In S. Harrell (Ed.), \u003cem\u003eChinese Historical Microdemography\u003c/em\u003e (pp. 48\u0026ndash;93). Berkeley, CA: University of California Press.\u003c/li\u003e\n\u003cli\u003eWaltner, A. (1990). \u003cem\u003eGetting an Heir: Adoption and the Construction of Kinship in Late Imperial China\u003c/em\u003e. Honolulu, HI: University of Hawaii Press.\u003c/li\u003e\n\u003cli\u003eWilliams, G. C. (1966). \u003cem\u003eAdaptation and Natural Selection.\u003c/em\u003e Princeton, NJ: Princeton University Press. \u003c/li\u003e\n\u003cli\u003eWolf, A. P., \u0026amp; Huang, C. (1980). \u003cem\u003eMarriage and Adoption in China, 1845\u003c/em\u003e\u003cem\u003e\u0026ndash;\u003c/em\u003e\u003cem\u003e1945\u003c/em\u003e. Stanford, CA: Stanford University Press.\u003c/li\u003e\n\u003cli\u003eZelin, M. (2009). The Firm in Early Modern China. \u003cem\u003eJournal of Economic Behavior and Organization\u003c/em\u003e, 71(3), 623\u0026ndash;637. https://doi.org/10.1016/j.jebo.2009.03.002 \u003c/li\u003e\n\u003cli\u003eZhao, Z. (2001). Chinese Genealogies as a Source for Demographic Research: A Further Assessment of Their Reliability and Biases. \u003cem\u003ePopulation Studies\u003c/em\u003e, 55 (2), 181\u0026ndash;193. https://doi.org/10.1080/00324720127690\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Footnotes","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e Given that only patrilineal male descents are officially recorded in the genealogical books, this paper focuses on all the male descents within the six lineages. Moreover, in pre-modern China, a typical patriarchal society, only patrilineal male descendants mattered (Freedman, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1966\u003c/span\u003e; Harrell, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1985\u003c/span\u003e; Song, Campbell, and Lee, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e The evidence from contemporary China is conflicting. Qian (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) and Li et al. (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) both exploit the 1990 population census, but find a contradictory relationship between family size and children\u0026rsquo;s educational attainment. Liu (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) finds a strong negative relationship between family size and children\u0026rsquo;s height.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e In the sample, 8.8 per cent men failed to survive to adulthood, and 23.8 per cent of men who survived to adulthood were unmarried throughout the lifetime.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e \u003cem\u003eKeju\u003c/em\u003e was initiated in 600 AD and abolished in 1905. Its presence changed imperial China into a meritocracy. In the tenth century, Emperor Zhenzong of the Song dynasty (960\u0026ndash;1276) once wrote \u0026ldquo;There is no need to buy farmland, for books will get you a position with a high salary;/There is no need to build a house, for books will bring you a luxurious residence with golden walls.\u0026rdquo;\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Typically, a man without a male heir would adopt his nephew from his brothers and male cousins (Lee and Wang, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Waltner, \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e1990\u003c/span\u003e; Wolf and Huang, \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e1980\u003c/span\u003e).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e In my sample, 18,927 males have biological sons, and 2,056 of them surrendered one or more sons. After transferring sons between families, 20,342 males have sons in total, and 2,188 of them adopted one or more sons. Of the 41,145 sons, 2,280 in total are adoptees.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Of the 8,975 fathers with complete birth and death date records, their average lifespan was 53.47 years old.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e To better fit the OLS regression model, I log-transform \u003cem\u003eDescendants\u003c/em\u003e, and, to keep all the zero observations, make the outcome variable used in the OLS model is \u003cem\u003eln (Descendants\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e+1)\u003c/em\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e As only one man in the sample, Zhuang Chaosheng, had more than 10 sons, I combine him with the men who had 10 sons, forming a group of males with more than 10 (including 10) sons.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Online Appendix Tables A2 and A3 also report the OLS regression results based on Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e The result in column 9 of Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e confirms to a certain degree what Shiue (\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) reveals. Shiue (\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) finds that in Tongcheng, a county in Southeast China, a trade-off of children, measured also by their attainment of academic degrees, disappeared after 1800. However, in the Qing dynasty before 1800, Shiue finds the presence of a quantity-quality trade-off of children in Tongcheng. The somewhat contrasting results in this paper may suggest regional variations in pre-modern China.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e In Ming\u0026ndash;Qing China, large lineages each maintained their own lineage schools (Zelin, \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). The existence of these schools led to a relatively low marginal cost for rearing additional sons.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e In terms of rudimentary literacy, Rawski (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e1979\u003c/span\u003e, 23) estimates that in nineteenth century China, the literacy rates of the male population ranged from 30 to 45 per cent.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e The other two conditions that Coale (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1974\u003c/span\u003e, 352\u0026ndash;353) mentioned are \u0026ldquo;fertility must be within the calculus of conscious choice\u0026rdquo; and \u0026ldquo;effective techniques of fertility reduction must be available.\u0026rdquo;\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-economic-growth","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"joeg","sideBox":"Learn more about [Journal of Economic Growth](http://link.springer.com/journal/10887)","snPcode":"10887","submissionUrl":"https://submission.nature.com/new-submission/10887/3","title":"Journal of Economic Growth","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Reproduction, Long-run reproductive success, Child quantity-quality trade-off, Ming–Qing China","lastPublishedDoi":"10.21203/rs.3.rs-4009995/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4009995/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn unified growth models, a key to achieving sustained economic growth is the evolving nexus between population dynamics and technological change. This paper uses the genealogical records of 36,456 males to investigate the nexus—the intergenerational transmission of reproduction and human capital—within six Chinese lineages from 1350 to 1920. By examining the relationship between reproduction and long-run reproductive success, the empirical results reveal that the optimal level of reproduction exceeded the sample median. This finding suggests that greater reproduction in each generation was conducive to long-run reproductive success. In exploring the mechanisms through which reproduction affected long-run reproductive success, I investigate the relationship between child quantity and quality. The results indicate an absence of quantity-quality trade-off of children in the six lineages. This paper concludes that, in Ming–Qing (1368–1911) China, opting for larger families conferred definite advantages upon high-status men, enabling them to produce a greater number of high-quality male descendants across successive generations.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eJEL Classification \u003c/strong\u003eI25, J13, N35\u003cstrong\u003e, \u003c/strong\u003eO15\u003c/p\u003e","manuscriptTitle":"Celebrating legacy: The intergenerational transmission of reproduction and human capital in Ming–Qing Chinese families","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-08 19:26:13","doi":"10.21203/rs.3.rs-4009995/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-05-07T14:18:08+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-05-07T10:23:14+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-24T16:36:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"8966c0ef-1831-4e91-8024-1bd5e342ebc1","date":"2024-03-11T10:01:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"44a842fb-87d4-499f-a0d8-0b6fa1533dfb","date":"2024-03-09T00:34:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"152050f9-e112-4c59-8397-49556e878acd","date":"2024-03-06T23:16:19+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-03-06T23:04:10+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-03-06T07:08:43+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-03-06T07:08:43+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Economic Growth","date":"2024-03-04T00:50:10+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-economic-growth","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"joeg","sideBox":"Learn more about [Journal of Economic Growth](http://link.springer.com/journal/10887)","snPcode":"10887","submissionUrl":"https://submission.nature.com/new-submission/10887/3","title":"Journal of Economic Growth","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"6f122075-033c-41b5-b9fd-807ad5c37ad5","owner":[],"postedDate":"March 8th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-04-28T16:04:05+00:00","versionOfRecord":{"articleIdentity":"rs-4009995","link":"https://doi.org/10.1007/s10887-025-09255-5","journal":{"identity":"journal-of-economic-growth","isVorOnly":false,"title":"Journal of Economic Growth"},"publishedOn":"2025-04-26 15:58:23","publishedOnDateReadable":"April 26th, 2025"},"versionCreatedAt":"2024-03-08 19:26:13","video":"","vorDoi":"10.1007/s10887-025-09255-5","vorDoiUrl":"https://doi.org/10.1007/s10887-025-09255-5","workflowStages":[]},"version":"v1","identity":"rs-4009995","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4009995","identity":"rs-4009995","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}