PREVIOUS LITERATURE

One strand of research includes Ho’s (1962) seminal work on Ming-Qing social mobility, which examined the biographies of successful candidates in China’s civil service examinations; the study was seen as showing higher mobility than expected among elites. Other authors have extended this work, based on high-quality source material, including Huang (Reference Huang2016) and Chang (Reference Chang2023); Jiang and Kung (2020), in particular, emphasize the importance of “cultural capital” in the sense of a high-level ancestor, versus resources for success at the highest-level examinations during the long nineteenth century (1796–1905). By focusing on high-level graduates such as juren and jinshi (provincial and national graduates, respectively), this line of research provides insights into the pattern of mobility in the top 5 percent of society.Footnote ⁸ While this research has produced interesting insights, the mobility patterns of China’s top 5 percent are not the same as the mobility patterns of China’s population overall.Footnote ⁹

A second line of research has studied intergenerational processes using household registers in Northern China’s Liaoning province for the period of 1749–1909 (Lee and Campbell Reference Lee and Campbell1997; Campbell and Lee Reference Campbell and Lee2003; Mare and Song Reference Mare and Song2014), while Campbell and Lee (Reference Campbell and Lee2011) combine the data with retrospective survey data from the twentieth century. This work stresses the role of earlier generations and broader kin for mobility, as opposed to parents alone (see also Solon 2014; Braun and Stuhler Reference Braun and Stuhler2018; Keller and Shiue Reference Keller and Shiue2023). The Liaoning data has the advantage that it is more complete than the typical Chinese family genealogy known today. A disadvantage is that the Liaoning data is not representative because about 75 percent of the sample men were hereditary peasants, while the occupational choice of the remainder (war captives, exiled nobles, and special-duty peasants) was even more restricted.Footnote ¹⁰ Furthermore, the Liaoning data only starts in the mid-eighteenth century, too late to pick up turning points and increases in mobility that have been traced to the erosion of occupational restrictions of the late Ming (Watson and Ebrey 1991) and the broader reach of the civil service examinations in the Ming-Qing transition (Ho Reference Ho1962). In contrast, the present sample is broadly representative of China’s occupational restrictions at the time and spans more than two or three centuries. Moreover, the kind of information in family genealogies is essential for studying the questions at hand.

Third, there has been rising interest in understanding how genealogies may be useful to study long-run processes involving multigenerational data, with some work shedding new light on Malthusian responses, human capital coping strategies for big shocks, environmental-induced diseases, and migration constraints (Hu Reference Hu2023; Shiue and Keller 2023; Che Reference Che2023; Hess Reference Hess2023). Genealogical data has recently been employed to improve automated census linking methods in the study of U.S. intergenerational mobility in the nineteenth and twentieth centuries (Price et al. Reference Price, Buckles, Van Leeuwen and Riley2021), and self-reported, retrospective family data has been employed to obtain improved estimates of intergenerational mobility (Jácome, Kuziemko, and Naidu Reference Jácome, Kuziemko and Naidu2022).

Finally, the present paper documents drastic changes in social mobility over the course of several centuries while controlling for the most important groups at the time, namely, the clan. Existing research on mobility in China or elsewhere typically does not address the issue of group effects, given the shorter sample periods that are available; or it holds that mobility does not change over time based on pseudo-intergenerational links using surnames (Hao and Clark Reference Hao and Clark2012; Clark Reference Clark2014).Footnote ¹¹ It is well-known, however, that social mobility between groups—for example, black and white U.S. Americans—is relatively low. A concern with the surname approach is that the relatively low estimated mobility reflects, to some extent, group-level mobility rather than individual mobility (Chetty et al. Reference Chetty, Hendren, Kline and Saez2014). By controlling for clan effects, I effectively take out group differences, and the results show that doing so increases the mobility estimate. The results in this paper also show, however, that while clans were a force of social persistence, clan effects do not drive the mobility trends over time since mobility increased over time despite continued clan influence.

CENTRAL FEATURES OF CHINA’S ECONOMY, 1300–1900

This study covers the period from the late thirteenth to the late nineteenth centuries. Three imperial dynasties are covered in the sample period: part of the Yuan (1279–1368), all of the Ming (1368–1644), and the major part of the Qing Dynasty (1644–1911). Total population grew from very roughly 100 million in the late thirteenth century to 400 million by 1900 (Cao 2000, 2001). While the governing structure varied, especially from the Yuan to the late imperial Ming-Qing period, the effective power of government was organized around an autocratic central authority and lower administrative regions. The state taxed lightly in international comparisons with other states. Moreover, the scope of markets for allocating scarce resources was likely more limited by technology (e.g., transport technology, financial instruments) than by government regulation, in part because effective enforcement would have required more state resources than were in fact allocated.

In this structure of governance led by bureaucratic-scholar officials, education was the gateway for entry into higher-income classes. Consistent with low central taxation, the capacity of the state was limited. The provision of public goods was instead delegated to local governments and the leaders of local clans.Footnote ¹² While local elites exercised paternal authority over their extended families, the participation of local elites in the political decision-making body of the state was legitimized through the state-run civil service examination system.

Throughout the Ming-Qing period, participation in the tournament-style civil service exams provided the most direct path to status and income. Passing the exam and obtaining a government office held substantial rewards and social status. These returns were so attractive that non-scholarly families who obtained wealth also invested in their sons’ education.Footnote ¹³ On the one hand, local leadership by elites who passed the civil service exam strengthened and ensured the legitimacy of the central state. On the other hand, local elites who supported the state by participating in the civil service earned high financial rewards. There thus arose, in effect, a partnership between the central state and local elites, to mutual advantage. The result was a kind of equilibrium based on distinctively Chinese characteristics and different from, for example, European forms of social organization (Greif and Tabellini Reference Greif and Tabellini2017). While there is little controversy that local clans were an important part of the social infrastructure, little is known at present about the economic impact of clans.Footnote ¹⁴

Overall, the return to human capital investments in the sample period is closely aligned with the civil service examination system. In this paper, I use one of the main sources of information produced by clans, the genealogy. Genealogies allow for a more expanded definition of status as status information mirrors the ranking of exam degrees and official titles used by the state; in addition, genealogies record non-official types of wealth that clearly mattered. In the next section, I discuss this data source.

DATA

Sample Data: Coverage, Selection, and Representativeness

The data are from genealogies of clans that resided in Tongcheng County of Anhui Province (Shiue 2025). In the year 1790, Tongcheng County had about 1.3 million inhabitants (Beattie Reference Beattie1979). The county was relatively developed and densely settled, one of the many thriving regions located near the lower Yangzi River Basin. Tongcheng was about 150 miles away from Nanjing, the early Ming Dynasty capital; Beijing, the later Ming and Qing capital, was about 650 miles away. The region was mainly a rice-producing area where the wealthiest families were typically landowners. Over the Ming and Qing Dynasties, the region gained some fame for having produced a number of the highest officials of the empire.

Genealogies exist for numerous clans in Tongcheng, with one historical account relying on more than 60 genealogies (Beattie Reference Beattie1979) and another study utilizing 39 genealogies (Telford Reference Telford1992). The sample I use is developed from data collection by Ted Telford in the 1980s. Although individual titles were privately sponsored during the Ming and Qing Dynasties, genealogies became not only commonplace, but the conventions of compilation became more standardized. According to genealogical principles of compilation, lineage membership is determined by patrilineal descent—that is, being an adult male—not wealth or status (Telford Reference Telford1992). While not every genealogy adheres to this principle, those that do will have created a document that contains hundreds or thousands of individuals dispersed over many villages and towns that captures a cross-section of society from commoners to elites. The presence of high-status individuals in these genealogies ought to be rare.

Because employing all known genealogies from Tongcheng would lead to the oversampling of elites, a targeted approach is used to choose the genealogies included in this study, with the goal of obtaining a broadly representative sample in the raw data. Given the focus on social mobility, an important part of the approach is to target the fact that most of the population in the genealogy had no social status (“commoner”) while top-status holders may have been around 2 percent, depending on the exact definition (Chang Reference Chang1955; Telford Reference Telford1992). For any genealogy chosen, all individuals in the data are included. These criteria led to the utilization of genealogies from seven clans—the Chen, Ma, Wang, Ye, Yin, Zhao, and Zhou—a total of about 40,000 individuals, including men, women, and children.

An important question is the representativeness of genealogical information relative to the overall population, which is affected by the completeness of genealogical records. Harrell (Reference Harrell1987) conducted one of the earliest studies comparing genealogical figures with official data. For the early twentieth century, his study found that genealogies consistently recorded over 80 percent of the population under study in Taiwan, as benchmarked against the highly reliable Japanese household registers. For present purposes, ideally, one would obtain accurate data on Tongcheng’s population, but official Chinese household registration figures, at least for some periods between 1300 and 1900, are patchy.Footnote ¹⁷

Figure 1 plots the official registered population for Tongcheng County as a whole together with the population of the seven sample clans. Notice that between 1400 and 1825, the officially registered population is observed infrequently and unevenly, about 20 times over a stretch of 425 years. Furthermore, the official population data exhibits virtually zero population growth between the late fifteenth and the early seventeenth centuries, which is at odds with what is known about demographic processes in China’s history.Footnote ¹⁸ In contrast, the information on the genealogical sample population changes relatively smoothly because observations are available at an annual frequency.Footnote ¹⁹ That official data is imperfect and only infrequently available during this period is not surprising, but it means that no benchmark population data exists that can be used to assess the representativeness of the sample underlying this study.

Figure 1 SAMPLE POPULATION AND TONGCHENG TOTAL HOUSEHOLDS, 1400–1825

Sources: Registered household population from Beattie (Reference Beattie1979, table 3); sample population is number of head-of-household males, author’s computations.

Completeness, meaning full population counts, is only one factor affecting whether genealogies give a representative sample and yield valid research results. Indeed, when the research objective is not focused on determining population totals, which is the case in the present study, then genealogies are suitable for obtaining within-sample comparisons over time (Harrell Reference Harrell1987). To gauge the sample’s representativeness from this perspective, one can compare within-sample characteristics of the genealogical data to that obtained from other research, keeping in mind that the latter are partially estimated as well. Fei (Reference Fei1946), for example, holds that the leisure class accounts for the top 20 percent of the distribution. In my analysis, groups 2 to 22 in Online Appendix Table A.4, with a 20.2 percent share of the total, come quite close to Fei’s estimate; these include, for example, people who might have attempted the civil service exam but failed, were village chiefs, had multiple wives and concubines, or purchased degrees.

Furthermore, I compare the within-sample share of elites in the current genealogical sample with historical accounts. Chang (Reference Chang1955) takes the more restricted definition that sheng-yuan holders and above were in the upper class and estimates that they accounted for the top 2 percent of the total population in the later half of the Qing period. In my sample, the part of the population corresponding to Chang’s (1955) definition accounts for 3.4 percent.Footnote ²⁰ This figure falls to 1.9 percent if I include only those men who obtained an official degree through the civil service exam. These comparisons indicate that the sample is comparable to what is generally believed to be true about the share of higher-status individuals in China during this time. Furthermore, more than 70 percent of men in the sample are commoners in the sense that they do not have any signs of elevated status. Since most of the Tongcheng men during this period must have lived close to subsistence, the sample broadly captures the distribution of status at the lower end as well.

I also compare the sample status distribution with the “China Multigenerational Dataset” for Liaoning province (Campbell and Lee Reference Campbell and Lee2003). For this data, which starts in the mid-eighteenth century, 2 percent were “Officials,” while in the present sample, about 1.4 percent had an official position.Footnote ²¹ The somewhat lower fraction of officials in the present sample compared to the Liaoning data may be related to the fact that men in the Liaoning data had closer ties to the Qing government than members of the typical Chinese population (see Mare and Song Reference Mare and Song2014).

Finally, the number of jinshi individuals (19 in the sample) lines up with official lists from the Chinese state for Tongcheng, increasing the credibility of the lineage records. Overall, given some differences in terms of samples and definitions, the sample under analysis is broadly comparable to the distribution of status in existing studies. The following section examines selection further by using cross-clan analysis.

EVIDENCE ON SELECTION FROM CROSS-CLAN ANALYSIS

The sample used for the mobility analysis consists of all male members of seven clans that reached adulthood and married at least once.Footnote ²² The largest of the clans, the Wang clan, accounts for close to half of the sample, while the smallest, the Chen clan, accounts for 3 percent. Clans are typically observed by the fourteenth century.Footnote ²³

First, I examine wealth bias. Much of the wealth bias may have already been eliminated because of the targeted approach of building the sample, but if there remains positive selection into the genealogical sample due to wealth bias, it would likely show up as a positive relationship between clan size and status. Figure 2 indicates that there is no such positive relationship. Thus, there is little evidence that clan size simply reflects a clan’s resources or that high-status clans systematically report more members than lower-status clans.Footnote ²⁴ Figure 2 also considers other indicators of resources. I include marriage as a measure of wealth since wealthier men could afford multiple wives and maintain larger families (Harrell Reference Harrell, Susan and Arthur1985). The figure shows the relationship between clan size and the number of wives is essentially flat. Furthermore, the figure shows fertility as measured by the number of male children is not strongly related to clan size either.

Figure 2 CLAN SIZE VERSUS STATUS, SONS, AND FEMALE PARTNERS

Notes: Figure shows three relationships, between average (i) number of sons, (ii) status, and (iii) number of females per man, each with the number of clan members across seven clans.

Source: Author’s calculation as described in text.

Other concerns one might have about selection and representativeness derive from recall bias and the retrospective nature of how genealogies are compiled. One way this bias could manifest is if, after a clan member attains a particularly high level of status, the clan reports a surge in new members. This could happen because the clan uses its resources to emphasize the significance of an individual’s achievements or because, ex-post, people who were not originally part of the clan might try to establish an ancestral relationship with the high-status individual. Online Appendix Table A.3 evaluates such hypotheses of recall bias using regression analysis and finds little evidence for it.

Table 3 Intergenerational Transitions between Status Levels

Notes: Transition probabilities between six levels in percent.

Sources: Author’s calculations based on status levels as defined Chang (Reference Chang1955, Reference Chang1962), Eberhard (Reference Eberhard1962), Ho (Reference Ho1962), and Telford (Reference Telford1986, Reference Telford1992).

A related concern is survivorship bias: over time, this type of bias could result in a disproportionately higher fraction of high-achieving individuals compared to low-achieving individuals. One implication is that toward the end of the sample period, the distribution becomes skewed toward relatively high-achieving clans. As Figure 3 shows, however, there is little evidence for this. For the interested reader, additional results on aspects of sample selection can be found in the Online Appendix sections A.2 and A.3. In sum, the analysis provides evidence that the level of representativeness of the sample is relatively high while the degree of selection is relatively limited.

Figure 3 EVIDENCE ON SURVIVOR BIAS

Notes: Figure shows number of clan men born in periods 1800–1825 and post-1825, both versus average clan status.

Source: Author’s calculation as described in text.

Measurement of Status

A challenge in contemporary studies of intergenerational mobility is that income is measured with error due to life-cycle and transitory income fluctuations, and thus, biases on both parent and child income can be large and difficult to eliminate (Nybom and Stuhler Reference Nybom and Stuhler2016). Although there is no income information, one advantage of genealogical data is that it records the highest lifetime achievements in biographical sections that resemble obituaries. In the genealogies collected for this sample, there is uniformity in the types of status indicators that are mentioned across different lineages, likely due to shared social perspectives across lineages.

In line with other research that uses sectoral or occupational categories when individual-level data is not available, I employ six different classifications, as shown in Table 1. Information on official titles and degrees awarded by the state is useful because it is consistently recorded and can be ranked. The main sources include Chang (Reference Chang1955, Reference Chang1962), Ho (Reference Ho1962), and Telford (Reference Telford1986, Reference Telford1992).Footnote ²⁵ Further details on the status classifications, as well as the relationship between status and income, are given in section A.4 of the Online Appendix.

Table 1 Income Distribution

Notes: Sample is all married males linked over three generations (son, father, and grandfather); N = 8,893.

Sources: Information is based on Chang (Reference Chang1955, Reference Chang1962), Eberhard (Reference Eberhard1962), Ho (Reference Ho1962), and Telford (Reference Telford1986, Reference Telford1992). See Online Appendix for more information.

More than 70 percent of men in the sample are in the lowest category of the distribution because they do not have anything in their biographies indicating uncommon levels of income, wealth, or status (Table 1). To account for variation in group size—see Column (3)—I convert each man’s status into the percentile status rank, as in Dahl and DeLeire (Reference Dahl and DeLeire2008) and Chetty et al. (Reference Chetty, Hendren, Kline and Saez2014). Each individual is coded with the midpoint of his category’s status ranking. An individual belonging to the lowest category, for example, has a percentile rank of 0.356, which is equal to 71.1 percent divided by two.

Summary Statistics

Sample information on status and demographic characteristics for N = 8,893 father-son pairs are given in Table 2. Panel A provides information on fathers, mothers, and sons. With status levels ranging from 0 to 5 (Table 1), the average for fathers is 0.58, which confirms that the majority of men are in the lowest status category. The average birth year of fathers in the sample is 1732. The birth year of the first father that appears in the data set is 1298. When using genealogies to study intergenerational mobility, one sample restriction is that the sample consists of men who had married and had descendants. In this period, almost all women married, but not all men were able to marry during their lifetime; the fraction of unmarried men in this sample is similar to Telford’s (1992) estimate of 22.1 percent for Tongcheng clans between 1520 and 1661.Footnote ²⁶ Another restriction is that the intergenerational analysis is confined to people who lived within the county or migrated within the county. However, only a small percentage migrated over long distances.Footnote ²⁷

Table 2 Summary Statistics

Notes: Status levels 0 to 5, as shown in Table 1. “Early” is birth year of son before 1780, “Late” is son’s birth year after 1780 (which is roughly half of the sample). Panel B. shows information on sons.

Source: Author’s calculation as described in text.

Turning to information on the women who were the wives and mothers of the male members, the average birth year is 1736, similar to that of their husbands, as one would expect.Footnote ²⁸ The earliest-recorded mother in the dataset was born in the year 1300, only two years later than the earliest-born father. Almost all marriages are between husbands and wives of different clans (endogamy is very rare). The average birth years of fathers and sons imply a generational interval of approximately 30 years.

Panel B shows size and status statistics separately for each of the seven clans by time period (before and after 1780). The largest clan is the Wang, followed by the Ye, while the highest average status is obtained by the Ma clan. It is also interesting to see that the Ma clan’s average status increased while the number of its clan members decreased over time. The finding confirms the analysis noted previously that there is no evidence that wealth is an important reason for sample inclusion in these data.

INTERGENERATIONAL MOBILITY IN TONGCHENG, 1300–1900

Transition matrices for the six status categories reveal the nature of intergenerational mobility for the sons of elites and non-elites. In low-income families where the father was at level 0, nearly 9 out of 10 sons remained in the lowest income level; see Table 3. In contrast, sons from the elite jinshi families (level 5) have a 7 percent chance of retaining jinshi status. This relatively low percentage can be explained by the fact that educational degrees were awarded to individuals and could not be transferred from one generation to the next. Nevertheless, the rate is about 35 times the population share of jinshi. Even if few sons of the jinshi reached the same high status as their father, at least one in three sons stayed within the top 2 percent of the population, with approximately 36 percent of the sons staying in levels 4 and 5. Thus, at the top of the distribution, there is substantial intergenerational persistence.

Moreover, the probability that a son rises in status to a given level is increasing in the status of his father. For example, the chance of a son reaching status level 4 is 0.07 percent for a son of a level-0 father, and 1.17 percent, 4.05 percent, and 5.83 percent for a son of a level-1, level-2, and level-3 father, respectively.

Conversely, the chance of dropping to the bottom of the distribution is decreasing in father income. For example, the chance of falling to level 1 is about 11 percent for a son of a level-5 father, but 28 percent, 61 percent, and 66 percent for a son of a level-4, level-3, and level-2 father, respectively.

The regression approach for estimating intergenerational mobility is an OLS relationship relating son to father status:

(1) $${R_S}\left( i \right) = \alpha + {\beta _c}{R_F}\left( i \right) + \varepsilon \left( i \right).$$

In Equation (1), R _S (i) and R _F (i) are the percentile ranks of the son and the father, respectively, in pair i, i = 1,…, 8,893.Footnote ²⁹ For all father-son pairs, I compute percentile ranks of father and son separately for their respective birth cohorts, defined as a 25-year time window. For example, percentile ranks for the fathers from 1575 to 1600 are computed by ranking the status levels of all fathers born during this period.Footnote ³⁰ The mean-zero error term ε(i) captures all other influences affecting pair i.

A coefficient β _c close to one in Equation (1) indicates low mobility because the son’s rank in the income distribution is strongly determined by his father’s rank, while there is relatively high mobility when β is close to zero. Table 4, Column (1) shows the estimated β _c = 0.528, suggesting that a father with a 10 percentage point rank advantage over another father can expect that his son has about a 5 percentage point rank advantage. Put differently, any advantage in the father’s generation is approximately cut in half in one generation.

Table 4 also reports separate measures of upward and downward mobility. A relatively low-status father, with a percentile rank of 0.25, can expect that his son will have a rank of 0.42 in the next generation’s distribution. In contrast, a high-status father, at rank 0.80, can expect that his son will be at rank 0.65. The direction of these moves confirms that there is regression to the mean, while their magnitude provides new information on the speed of intergenerational mobility.Footnote ³¹

Table 4 Intergenerational Mobility for the Full Sample Period

Notes: Estimation of β _c (Equation (1)) by OLS; E[R _S(i) |R _F(i) = 0.25] is the expectation of percentile rank of sons with fathers at percentile rank <0.5; E[R _S(i) |R _F(i) = 0.80] is the expectation of percentile rank of sons with fathers at percentile rank > 0.6; N = 8,893 in Columns (1) and (2); and N = 8,892 in Column (3).

Sources: Author’s calculations based on status levels as defined Chang (Reference Chang1955, Reference Chang1962), Eberhard (Reference Eberhard1962), Ho (Reference Ho1962), and Telford (Reference Telford1986, Reference Telford1992). See Table 1 and Online Appendix Table A.4.

The remaining two columns in Table 4 present results for two alternative specifications. Column (2) employs six discrete categories valued at 0 to 5, yielding a β _c estimate of 0.552, similar to the baseline estimate in Column (1). Column (3) in Table 4 reports results based on percentile ranks with more disaggregated 23 status categories; the estimated β _c (= 0.570) implies somewhat more intergenerational persistence than the baseline (Column (1)), but the result is similar.Footnote ³²

Overall, these estimates fall within a relatively narrow range, with the intergenerational regression coefficient for the entire sample period estimated to be somewhat above 0.5.

CHANGES IN INTERGENERATIONAL MOBILITY

Evidence from Transition Matrices

To examine overall changes over time in intergenerational mobility based on transition matrices, I repeat the analysis for two sub-periods: before 1780 versus after 1780, which splits the sample in half based on the number of observations.

Table 5 shows that in the earlier period, more than 91 percent of sons from lowest-income families stayed in the bottom group of the distribution. Also, 18 percent of top-level jinshi families (group 5; top 0.2 percent of the distribution) stayed in that group from one generation to the next.

Table 5 Transition Matrix for First Half of Sample Period

Notes: Transition probabilities (percent) between six status levels before the year 1780.

Sources: Author’s calculations based on status levels as defined by Chang (Reference Chang1955, Reference Chang1962), Eberhard (Reference Eberhard1962), Ho (Reference Ho1962), and Telford (Reference Telford1986, Reference Telford1992).

Table 6 shows results for the latter half of the sample. Notice that the corresponding probabilities fall to 82 percent and 0 percent, respectively. Fewer sons from poor families stay poor, and fewer sons from very rich families stay very rich—upward and downward mobility has increased. Importantly, this result is not driven by a change in the share of these groups in the population. As the last columns in Tables 5 and 6 indicate, the population shares of the poor (group 0) and the very rich (income group 5) are approximately 71 percent and 0.2 percent, similar in the earlier and later periods.

Table 6 Transition Matrix for Later Half of Sample

Notes: Transition probabilities (percent) between six status levels in the year 1780 and after.

Sources: Author’s calculations based on status levels as defined by Chang (Reference Chang1955, Reference Chang1962), Eberhard (Reference Eberhard1962), Ho (Reference Ho1962), and Telford (Reference Telford1986, Reference Telford1992).

Shorrocks (1978) proposes a measure of the mobility of a transition matrix based on its trace, defined as, where P is the square transition matrix and n is its dimension. The higher the trace, the lower the mobility. In the present case, M for the earlier period is 0.83, while M for the later period is 0.87. Thus, evidence from transition matrices indicates that mobility has increased in China over the sample period.

Relative Mobility over Time

In addition to transition matrices, it is useful to examine mobility by comparing relative mobility estimates that vary by cohort, β _c. Figure 4 shows the evolution of β _c for birth cohorts of 25 years each (such as years 1575 to 1600).Footnote ³³ Mobility was low through the seventeenth century (high β _c), then increased in the eighteenth century, reaching values of β _c close to 0.4 by the nineteenth century.Footnote ³⁴ Furthermore, if instead of 12 different birth cohorts, only two are allowed—namely, birth years before 1700 and birth years after—the point estimates are β _<1700 = 0.69 and β _>1700 = 0.49. The two estimates are significantly different (p-value 0.00). This confirms that relative mobility increased over time.

Figure 4 INTERGENERATIONAL MOBILITY OVER TIME

Notes: Shown are β_c coefficients from OLS regressions of percentile rank son on percentile rank father (Equation (1)). Ten 25-year birth cohorts (1575 to 1825), plus birth cohorts before 1575 and after 1825. Each cohort coefficient is given equal weight in the construction of the confidence intervals (90 percent). Median birth year of son in cohort is given on horizontal axis. Earliest son birth year in sample is 1330, latest son birth year is 1885.

Source: Author’s calculation as described in text.

The Online Appendix provides additional estimates showing not only did relative mobility—as measured by β in Equation (1)—increase over time, but both upward and downward mobility also rose from the early to the later centuries of the sample period (see Online Appendix Figures A.6 and A.5, respectively). For example, a son whose father was at the 25th percentile rank could expect to rise by 13 percentage points around the year 1550, but by the beginning of the nineteenth century, a son with a father at the same rank could expect to rise 20 percentage points, reaching the 45th percentile rank instead of the 38th.

MEASUREMENT OF STATUS

Table 7 considers four alternative specifications to examine the robustness of the finding that mobility increased over time. Since the focus is on the change in mobility over time, to limit the number of reported results, I show only the correlation across birth cohorts with the baseline relative mobility finding shown in Figure 4; see Columns (1), (2), (3), and (4) of Table 7.

Table 7 Correlation of Baseline Results with Alternative Specifications

Sources: Table gives correlation between the mobility measure of the baseline specification with four alternative specifications, as described in the text; 12 birth cohorts.

First, Column (1) gives estimates that come from employing 23 status categories instead of just six categories.Footnote ³⁵ Table 7 shows the estimated regression coefficients β _c from the disaggregated approach with 23 categories correlated with the corresponding baseline β _c with 6 categories. The correlation is 0.996. This suggests the aggregation level of lifetime income does not play an important role in the result showing that mobility has increased over time.

Column (2) recodes the status of the sons and grandsons of relatively high-status men. In the baseline, these men are assigned some status, even if they did not earn any degrees or titles themselves. Within the historical context of Ming-Qing society, individuals from such families would typically have received some education and, even without formally earning a degree, would not be considered commoners. However, their exact status remains somewhat ambiguous. I explore how the results change if, instead, these individuals are placed in the lowest status level.Footnote ³⁶ Results indicate that recoding status in this way does not greatly change the main finding of an increase in mobility over time (correlation of 0.82 with results from the baseline, Column (2) of Table 7).

Column (3) of Table 7 explores how the results would change if the status of certain categories changed over time. In particular, some accounts indicate that the status of lower-ranked officials declined in the later part of the sample period. Thus, I recode the status of men whose fathers received a lower-level degree (sheng-yuan) to level 0 (instead of level 1 in the benchmark) after the year 1786, and men who were sheng-yuan themselves are demoted to level 1 (from level 2 or 3) after 1786. We see that accounting for the potentially lower status of lower-ranked official degree holders in the later part of the sample leads to similar results on mobility over time (correlation of 0.966 with the baseline results, see Column (3), Table 7).

Also, I explore the role of measurement error in the definition of status. In particular, classical measurement error in the independent variable would lead to attenuation bias and an underestimate of the β _c coefficients (overestimating mobility). To investigate whether this type of measurement error might play a role in the finding that mobility increased over time, I introduce additional measurement error in father income. Results are shown in Column (4) of Table 7. The introduction of measurement error with mean zero and a standard deviation of 0.5 does not change the key finding that mobility was increasing over time (correlation with baseline measures of mobility over time of 0.950, see Column (4) of Table 7).

Overall, these checks suggest that the increase in mobility over time documented earlier is a robust finding.

CHANGING IMPORTANCE OF OTHER FACTORS THAT AFFECT STATUS

The analysis noted earlier showed that mobility increased over time. In this section, I examine a range of alternative explanations that could have influenced these mobility patterns. Since the variables used in this section are often associated with wealth—wealthier men tend to purchase degrees, marry multiple times, and have more sons—this section allows us to check whether alternative definitions of income, which rely less on education and official titles, produce the same trends in mobility over time.

I extend Equation (1), estimated cohort by cohort, to include a characteristic of cohort c and father-son pair i, denoted by Z ^c(i):

(2) $$R_S^c(i) = \alpha + {\beta _c}R_F^c(i) + {\theta _c}{Z^c}(i) + {\varepsilon ^c}(i),\forall c,i.$$

The estimates described earlier demonstrated that when factor Z ^c(i) is not included, estimates of β _c are higher in earlier cohorts than in later cohorts (i.e., mobility is increasing). It could be, however, that increases in mobility simply reflected omitted demographic factors, such as changing numbers of sons, family size, or gender ratios that could impact marriage patterns. In addition, it is possible that events such as wars or famine, which disrupted the health or longevity of parents in the later part of the sample, played a role in changing mobility patterns over time. Also, some degrees could be purchased, especially in times when state revenues fell short, and these could have offered a new avenue for the persistence of status between fathers and sons. Further, since participation in the civil service examination was only open to males, variation in the ratio of daughters to sons could influence the fraction of children in a given cohort that earned degrees, potentially influencing mobility measures.

The first specification in this section includes the number of sons in cohort c as variable Z ^c(i) on the right-hand side of Equation (2) in order to proxy for fertility. If there is selection on fertility over time in a way that is correlated with mobility, the estimates of β _c will be different, depending on whether fertility appears on the right-hand side. A sufficiently strong effect could eliminate the finding that mobility increased over time.

Figure 5 on the upper left shows estimates of β _c that include fertility as variable Z ^c(i) in Equation (2) using “×” as the symbol, and it also shows the trend line of these estimates over time. In addition, the panel shows hollow squares for estimates of β _c that do not include a variable Z ^c(i). The difference between the two sets of β _c estimates indicates whether time-varying fertility trends play an important role in the finding that mobility has increased over time.

Figure 5 SELECTION ON OTHER TIME-VARYING FACTORS

Sources: Results from estimating Equation (1) and Equation (2), respectively; line is lowess smoother of the particular robustness check.

Similarly, the remaining five subpanels of Figure 5 show results for five alternative factors Z ^c(i). This includes the number of wives per married man (“Multiple Women”), and an indicator that a man was the first-born male of his parents (“Son first-born”). The number of wives variable captures changes in marriage behavior and sex ratios, while differences in the shares of first-born males may be associated with changes in mobility because parental investments into first-borns tend to be higher than for other children. If the cross (×) and square symbols are closely overlapping for a given birth cohort, the factor under consideration is relatively unimportant in affecting intergenerational mobility. Results in the lower part are for the (i) prevalence of “Purchased Degrees,” the (ii) “Share of Daughters” among the children, and (iii) “Lifespan” (death year minus birth year) of males.

Figure 5 shows that these six factors vary in their importance for social mobility. Most of the time-varying factors are relatively unimportant, except for purchased degrees and the number of wives per married man, where the difference between the cross and square symbols is larger. Furthermore, some factors have the same qualitative influence on mobility across all cohorts, while for others the influence is changing over time. For example, controlling for multiple women in the household always increases mobility (lower β _c, upper center) for every temporal interval, while controlling for lifespan can both increase and decrease estimated mobility (lower right panel).Footnote ³⁷

While there are interesting differences among the various factors, the six panels of Figure 5 indicate that the finding of increasing mobility over time is robust. The difference between the highest estimate of β _c around the year 1630 and the lowest estimate of β _c around the year 1830 is larger than 0.2 and typically about 0.3, no matter which other time-varying factors are controlled for. Overall, Figure 5 indicates that accounting for possible selection on other time-varying factors does not alter the finding that intergenerational mobility in Tongcheng County increased over time.Footnote ³⁸

THE ROLE OF THE CLAN FOR THE INCREASE IN MOBILITY OVER TIME

A high-ranking descendant of the clan would presumably benefit the clan as a whole. Thus, even if the father did not have official titles or degrees, it might be that other members of the lineage did. For example, if a person had an uncle who was an official, and if we allowed the uncle to proxy for the role of the father, we might find a higher correlation across generations than if we just used fathers and sons. In the case of lineage-based societies where clan members would often act as a cooperative unit (in contrast to individual nuclear family units), it might be useful to adopt a broader conception of the notion of mobility in order to account for the contribution of the lineage to the mobility between father and son.

I examine the evolution of social mobility over time based on estimates with and without clan fixed effects, along the lines of Equation (1). Notice that the inclusion of clan fixed effects tends to reduce the estimates of the intergenerational coefficients (Figure 6). The relatively greater social mobility estimated within clans means that between-clan differences contribute to intergenerational persistence. This could be due to variation across clans in terms of resources, genetic endowments, or cultural traits. The result tends to confirm the a priori notion that status beyond the immediate household had an influence. At the same time, Figure 6 demonstrates that the increase in mobility between 1600 and 1850 remains robust even with clan fixed effects included in the specification. In other words, clan effects remain relatively consistent throughout the entire time period. Neither the intergenerational persistence observed in the earlier period nor the increase in mobility that emerged in the later period can be explained by changes in the impact of the clan. Furthermore, the finding of an increase in mobility over time is also obtained when (subclan) segment fixed effects are added; see the lower series in Figure 6. This indicates that potential differences in data characteristics at the subclan level do not drive the result.Footnote ³⁹

Figure 6 MOBILITY OVER TIME AND CLAN EFFECTS

Notes: Shown are β _c (Equation (1)) with and without clan fixed effects in the regression, as well as with clan and segment fixed effects. Smoothed β _c based on 12 birth cohorts (lowess running mean smoother). Horizontal axis shows median birth year in cohort; earliest birth year of son is 1330, latest is 1885.

Source: Author’s calculation as described in text.

EXPLAINING THE INCREASE IN INTERGENERATIONAL MOBILITY

This section highlights a number of important changes related to compulsory occupational registration as well as the institution of the civil service examination, which, taken together, plausibly affected mobility over time. To recap, the empirical pattern found so far shows that until the year 1700, mobility was relatively low, before increasing toward the end of the sample period (see Figure 4 and Online Appendix Figures A.5 and A.6). Furthermore, there is some evidence that mobility was lowest around the year 1650.

These empirical patterns are consistent with the timing of trends described in the historical literature. First, before the seventeenth century, there were formal barriers to occupational mobility. For example, occupational mobility was limited during the Yuan Dynasty (1279–1368) due to the way the state extracted labor services from the civilian population. To enforce these obligations, the state required households to be registered in segregated occupational groups—commoner, artisan, soldier, salt producer, miner, scholar, astrologer, and other categories. These occupational groups were hereditary and largely determined the position of an individual. The practice of compulsory occupational registration was carried over from the Yuan to the Ming (1368–1644) Dynasty. By the latter half of the Ming, however, the hereditary nature of the categories had started to break down. The biographies of exam candidates of the Ming period show that the family backgrounds of some jinshi degree holders included occupational status designations—soldiers, army officers, horse breeders, medical officials, and official cooks—that were not previously allowed to participate in the civil service examinations (Ho Reference Ho1962; see cite to Li 1746).

Second, as argued in Naquin and Rawski (1987), fewer institutionalized and legal barriers to mobility were consistent with the increasing commercialization of the eighteenth century compared to earlier centuries. The hiring of workers for a wage had likely become a more efficient way to find workers compared to the old system of compulsory labor service. While aspects of the older practice of hereditary occupations were still present, occupational mobility increased as the Ming state could afford to be lax in enforcing labor obligations. For example, the Ming state resorted more frequently to paying wages for desired services rather than extracting labor. The Qing state discontinued the practice of family occupational registration altogether, by which time there were no effective legal barriers to mobility due to any pre-designated occupational status of the family (Ho Reference Ho1962). As Mann (Reference Mann, Rubie and Patricia1991, p. 206) remarks: “Surely the most striking development with respect to mobility in the mid-Qing era was the series of imperial edicts eradicating the final remaining hereditary class barrier in Chinese society.”

Third, the pool of men eligible for the civil service examinations expanded as the national civil service examinations became more routine in nature, and over time, regional quotas for the various academic degrees became less discretionary. While sumptuary laws had previously restricted commoners from taking the civil examinations, these laws were eliminated in the later part of the Ming Dynasty (1368–1644). The effect of lifting occupational restrictions and hereditary privileges is the basis for Ho’s (1962) argument that entry into higher-status groups was newly possible.

By the start of the Qing in 1644, the only types of hereditary privileges and automatic status that remained belonged to the imperial dynasty, where the throne was passed from the emperor to one of his sons, and the leading families of the Eight-Banner system. Despite the fact that some members of the elite and high-ranking officials of the state had long been selected on the basis of examinations (already in the Song Dynasty, 960 AD), candidates had been selected in a discretionary fashion, which in turn restricted access to high-level degrees. With the start of the Qing Dynasty in 1644, the state relied more heavily on the civil service examinations to test a candidate’s knowledge. The shift to a more rules-based system reduced uncertainty regarding the returns to human capital investments by making them more predictable.

The empirical results in this paper demonstrate that the trend toward higher intergenerational mobility in Tongcheng starts around the year 1700, and by the 1800s, the β-coefficient has fallen by about 20 percentage points to around 0.45. Ultimately, however, since the Chinese state was the largest employer of the recipients of higher degrees, the decline in the return to higher levels of human capital was driven in part by a decline in state fiscal capacity (see Online Appendix Figure A.7). Furthermore, there was a crowding-out effect because despite the substantial increase in population, the number of high-ranking official positions did not proportionally increase. All else equal, an increase in the number of competitors in the state exam reduces the ex-ante return to human capital investments. With more competitors, an individual would need to invest more to keep the same expected probability of achieving a particular degree or position, thereby reducing the net return.

Although there is no systematic evidence that the nominal return from holding a certain rank or position fell over time, the change in the officials’ lifestyle and spending patterns, based on information from biographies, clan genealogies, and gazetteers, is consistent with a decline in the expected return from human capital investments. Anecdotal evidence points to how the generous allowances official students during the Ming Dynasty received in the form of food (two bushels of rice), cotton and silk cloth, embroidered silk cloth, sets of clothing, headgear, and boots, as well as travel money to go home to visit family, had fallen away by the Qing Dynasty, when students received only a minimal grain stipend and tax exemptions from the state (Ho Reference Ho1962).Footnote ⁴⁰ Moreover, income derived from teaching fell over time. Men who passed the lower-level exams but repeatedly failed to pass the intermediate or higher exams could not obtain an official position, with the result that many of these individuals resorted to a livelihood as schoolteachers. Toward the end of the Qing, the income from teaching was so low that in some cases teachers could not sustain themselves on teaching alone, forcing them to take up other tasks (Chang Reference Chang1962; Ho Reference Ho1962). Teachers’ real wages were lower in the nineteenth century compared to the earlier Qing period (Rawski Reference Rawski1979, figure 1).

Thus, various types of descriptive evidence all point to a decline in the return that could be expected from human capital investments in the later period of the Qing. This history is consistent with the trends toward greater mobility. Next, I show that the higher level of mobility over time was accompanied by lower levels of inequality across households. This provides additional evidence that mobility increased due to a decline in the return to education.

Does the “Great Gatsby” Curve (Krueger Reference Krueger2012) Exist over Time?

Additional evidence on the importance of changes in mobility comes from asking if there is a relationship between mobility and inequality. Historical accounts describe such trade-offs at the clan level. For example, Brook (Reference Brook, Joseph and Rankin1990) describes elite families as essentially facing the choice between harboring the resources of the family in order to channel them toward investments for their own sons in the next generation, or alternatively, sharing those resources in the current period with their poorer fellow kin.Footnote ⁴¹ In the workhorse model of intergenerational investments due to Becker and Tomes (Reference Becker and Tomes1979, Reference Becker and Tomes1986), a decline in the return to education will, in fact, lead to a decline in inequality. This is because when human capital returns are low (high), parents have more incentives to channel resources away from (toward) child investments, which in turn results in increased (decreased) intergenerational mobility and less (more) inequality over time.

To investigate if increases in mobility occurred with decreases in inequality, consider the Theil (Reference Theil1967) index, a well-known measure of inequality. Lower values of the Theil indicate less inequality, or equivalently, more equality.Footnote ⁴² It is defined as

(3) $${T_c} = {1 \over N}\sum\limits_{i = 1}^{{N_c}} {{{{R_F}(i)} \over {{\mu _c}}}ln} \left( {{{{R_F}(i)} \over {{\mu _c}}}} \right),$$

where R _F (i) is the percentile rank status of the father in father-son pair i belonging to cohort c, µ _c is the average percentile father rank in cohort c, and N _c is the number of fathers in cohort c, c = 1, …, 12. The circles (fitted with a solid line) in Figure 7 show the intergenerational mobility of sons in the different cohorts; for each of these cohorts, the figure also shows a triangle (fitted with a dash-dot line) that gives the cross-sectional income inequality observed in the father’s generation.

Figure 7 MOBILITY AND INEQUALITY: GREAT GATSBY IN THE TIME SERIES

Notes: Shown are β _c and the Theil index (Equation (3)) of status in the father generation for 12 birth cohorts. Earliest son’s birth year is 1330.

Source: Author’s calculation as described in text.

Figure 7 shows that times of relatively high inequality are times of high β _c (low mobility). Intergenerational coefficients of 0.6 and above before the year 1700 are found when the Theil index is equal to 0.12 and higher. By the year 1850, when β _c has fallen to 0.45, the Theil index is lower as well. The correlation between the intergenerational coefficient β _c and T _c is 0.77.

In sum, the evidence suggests that the estimated increase in social mobility is due to a decline in the return to human capital. This evidence is further strengthened by the simultaneous decline in inequality, which, in economic models of intergenerational investments, is a key implication of a lower return to human capital.