Marital Bargaining and Assortative Mating on Fertility Preference : Evidence based on Cross-sectional Data in China

Fertility decisions

Family decisions involve several resource allocation problems, from how to divide income between consumption and saving, to how to allocate time between work and leisure, and from whether and whom to marry, to whether and when to have children.

There are three strands of theoretical household decision-making models. The first model is the unitary model, which assumes a single and unified household utility, where, typically, the male (husband or father) makes all major decisions (Becker, 1960, 1973). The second model is the cooperative model, which allows for heterogeneous utility functions and preferences among spouses. This model has two frameworks: the explicit bargaining model, which incorporates the negotiation process based on each spouse’s outside options, as proposed by Manser and Brown (1980) and McElroy and Horney (1981); and the collective model, which internalizes the negotiation process, as introduced by Chiappori (1988, 1992). The third model is the non-cooperative model, which relaxes the assumption of Pareto efficient equilibria, and the threat point is non-cooperation within the marriage rather than divorce (Lundberg and Pollak, 1993, 1994). Commitment plays a crucial role in the latter two strands². The empirical research on fertility decisions follows three strands corresponding to the three types of theoretical models.

Within the unitary model framework, the quantity–quality theory often uses twins as a natural experiment, showing that an increase in family size decreases the children’s educational attainment (Rosenzweig and Wolpin, 1980; Rosenzweig and Zhang, 2009). Additionally, extensive literature explores fertility from women’s perspectives, showing that the relationship between income, education, and fertility has shifted from negative to positive (Butz and Ward, 1979; Ahn and Mira, 2002; Baudin et al., 2015)³.

Although it is difficult to incorporate cooperation into an empirical model, examining marriage outcomes, such as divorce or specialization within marriage, and partners’ interactions can help infer how fertility is determined. Rasul (2008) finds that Malay couples’ fertility preferences equally and positively influence outcomes, indicating cooperative bargaining, supported by high divorce rates for Malay couples, which serve as threat points in bargaining models. Bankole (1995) shows that Nigerian couples generally cooperate on fertility decisions, with both spouses’ preferences equally influencing outcomes. However, the husband’s preferences dominate early (fewer than four children), while the wife’s dominate later, suggesting that cooperation shifts over the marriage span and is not always consistent.

Regarding non-cooperative empirical studies, Ashraf et al. (2014) and Ashraf et al. (2020) use Zambian field experiments to show that asymmetric information between spouses leads to non-cooperative fertility decisions. Concealing contraceptive use reduces fertility but lowers women’s well-being (2014), while asymmetric maternal health knowledge affects communication and spousal transfers, highlighting inefficiencies in fertility choices (2020). Field (2003) links Peru’s property rights reform to reduced fertility, as women’s economic independence reduced the reliance on children for old-age support, aligning with the non-cooperative model by enhancing women’s control over fertility decisions⁴.

Assortative mating

Lafortune (2013) studies how the male-biased sex ratio, driven by the influx of same-ethnic immigrants, affects the marriage patterns of second-generation Americans, who tend toward endogamy. Addressing concerns that influx locations might be related to labor market opportunities, which could also affect second-generation Americans, the study uses historical immigrant networks as an instrument. It finds that higher sex ratios lead to increased male education and exogamy, while females remain more endogamous. Persson (2020) studies a 1989 Swedish insurance reform that reduced marital benefits for women, leading to an increase in skill-based assortative mating. Before the reform, the insurance system subsidized skill-mismatched marriages, providing financial incentives for lower-skilled women to pair with higher-skilled husbands. After the reform, couples prioritized maximizing marital surplus, resulting in more skill-similar pairings. Abramitzky et al. (2011) use World War I as a natural experiment in France, showing that a decline in the male population increased male bargaining power, enabling them to “marry up” into higher social classes categorized by occupation. Considering the potential reverse causality that marriage outcomes could also affect the sex ratio, they instrument the sex ratio with the regional military mortality rate, which provides geographic variation in the sex ratio. Fisman et al. (2006) use a dating field experiment to show the asymmetric preferences between males and females, while Banerjee et al. (2013) show the persistence of caste in the Indian marriage market using matrimonial advertisement data, attributing it to a frictionless marriage market. Recent work by Goñi (2022) uses a natural experiment that introduced search costs to overcome the limitations of survey data. The interruption of the London Season (an occasion where aristocrats met) during 1861–1863 made search and mating with partners with similar socioeconomic traits more difficult. The study finds that increased search costs discourage assortative mating by social class.

Applications to the Chinese case

In China—one of the most populous countries facing a decline in fertility—quantitative research on marital bargaining remains scarce⁵. Peng (2020) qualitatively highlights the role of negotiations in fertility through interviews with 53 urban couples. However, the empowerment of Chinese women in recent decades has likely influenced household decisions in this representative developing country.

Regarding assortative mating, Chinese studies on educational assortative mating show that its effect is significant and steadily increasing (Dong and Xie, 2023), while it is less likely to occur in remarriages (Hu and Qian, 2019). Sun and Zhang (2020) find a positive effect of housing prices on the father-in-law’s years of schooling.

Chinese studies also emphasize the role of the hukou status, which categorizes residents into urban and rural groups. When local hukou is restricted, assortative mating based on hukou increases (Qian and Qian, 2017). Conversely, when it is unrestricted, intermarriage becomes more common, reducing assortative mating (Han et al., 2015; Hu, 2024), which, in turn, exacerbates inequality (Wang and Schwartz, 2018). However, no study, either in China or globally, has examined assortative mating based on fertility preferences.

This study addresses these research gaps by providing novel insights into how fertility outcomes are associated with the fertility preferences of both spouses, and how preferences regarding a second child are aligned between men and women, using the Chinese case as an example.

Data set

The primary dataset utilized in this study is the China Family Panel Studies (CFPS)—a nationally representative longitudinal sample of Chinese communities, families, and individuals (Xie and Hu, 2014). The survey includes information on economic activities, educational outcomes, family relationships, migration, and health. Initiated by the Institute of Social Science Survey (ISSS) at Peking University, the baseline survey was conducted in 2010, with follow-up full-sample surveys conducted biennially in 2012, 2014, 2016, 2018, and 2020. Our analysis uses the cross-sectional data from the 2018 CFPS, which includes approximately 44,000 individuals in 15,000 households from more than 900 counties and cities within 31 provinces, municipalities, and autonomous regions.

The CFPS employs a multi-stage probability sampling strategy to ensure a representative sample of the Chinese population. In the first and second stages, it stratifies and selects provinces and counties using official administrative divisions. Recognizing the geographic disparities inherent in China’s economic development, the design emphasizes geographic representation. In the third stage, households within the chosen counties are selected based on a systematic sampling method, targeting 25 households per county to fulfill the study’s requirements.

Since we seek to understand how fertility outcomes are associated with both spouses’ fertility preferences, we initially restricted the sample to individuals who responded to questions regarding their ideal number of children. In the 2018 CFPS dataset, 16,268 out of 18,802 females and 16,214 out of 18,552 males provided their responses. Considering both the husband’s and the wife’s preferences, we further constructed a household-level sample that includes information on both spouses. We limited the sample to couples where both spouses responded to the question about the “ideal number of children,” as this measures their fertility preference for a second child. We also restricted the age range for women to be equal to or less than 37, corresponding to the possible reproductive age. The distribution of female ages in the sample is illustrated in Figure 2. Ultimately, the sample comprises 2,351 household observations with detailed information on both husbands and wives. We obtained the permission to use this data set on August 9, 2021.

Figure 2. Distribution of Female Age in the Sample, N=2,351.

The main outcome variable in this study is whether the household has two or more children. This variable is derived from the number of children in the family. Since the CFPS does not directly provide complete information on family size, we generated this variable using information available for each child. If both spouses reported their ideal number of children but the actual number of children is missing, we replaced the missing values with 0. In the sample, 49.43% of households have more than two children. The key explanatory variables are the fertility preferences of both spouses for the second child, derived from their reported ideal number of children. In the sample, 79.41% of wives and 80.82% of husbands prefer more than two children. In the second part, the outcome variables are individual fertility preferences, measured by their ideal number of children. On average, both females and males desire fewer than two children. Control variables include both spouses’ employment status (employed or unemployed, without distinguishing between being out of the labor force or unemployed), years of education, age, hukou type (rural or urban), and family income. We assigned the income to be zero if the individuals are currently unemployed. Family income in logarithmic form is calculated by summing the incomes of both spouses and adding one, to avoid issues with missing values when both spouses have no income.

The previous literature has shown, both empirically and theoretically, that a skewed sex ratio increases women’s bargaining power in the marriage market (Angrist, 2002; Chiappori et al., 2002; Bulte et al., 2015). As this study focuses on the marital bargaining process regarding family fertility outcomes, we use the provincial-level sex ratio as a proxy for bargaining power. We collected data on the number of males and females aged 20-39 from the China Population Census Yearbooks for 2000, 2010, and 2020. The age range of 20-39 captures the potential population in the marriage market. There is no information available for 2018, as the census is conducted every ten years. We calculated the sex ratio as a percentage by dividing the number of males by the total number of males and females. Given that the statistics are similar across these three census waves, we report only the results using the 2020 sex ratios in this paper. In 2020, the average sex ratio for the population aged 20-39 across 31 provinces was 51.89%, implying there are more males than females in the marriage market. The detailed summary statistics for all variables are presented in Table 1.

Family fertility outcome

The OLS results are reported in Table 2. Column (1) includes only explanatory variables and their interaction term; column (2) adds demographic characteristics; column (3) further controls for provincial fixed effects. All regression results show a statistically significant positive relationship between the second-child preferences of either spouse and the fertility outcome regarding a second birth.

We consider the situation with provincial fixed effects as the benchmark, as detailed in column (3). Our results show that when the couple has the same preference for having the second child, it is associated with an increase in the likelihood of having a second child by 45.39% (0.150+0.0929+0.211). When only the wife prefers having two or more children, the likelihood of the couple having a second child increases by 15 percentage points, holding other factors constant; similarly, when only the husband prefers having a second child, the likelihood increases by approximately 9.3 percentage points. The interaction term indicates the complementary effect between the wife’s and husband’s preferences. When a husband (wife) desires a second child, the association between their own preference and the actual fertility outcome becomes more pronounced if their partner also expresses a desire for a second child. For example, when the husband prefers a second child, the wife’s marginal effect on the likelihood of having two or more children increases from 0.15 to 0.36 (0.15+0.21). Similarly, when the wife strongly prefers a second child, the husband’s marginal effect increases from 0.093 to 0.30 (0.093+0.21). All estimates are significant at the 1% level and are robust across different specifications. These findings imply that when both spouses prefer to have a second child, reduced negotiation and bargaining enhance the marginal effect of one spouse’s preference on the actual outcome of having a second child, thus highlighting the importance of assortative mating.

Moreover, the propensity for non-random marriage matching reinforces these findings, as individuals are more likely to pair with partners who share the same preference regarding having a second child. Table 3 illustrates this non-random distribution of marriage matching by fertility preference for the second child. For both men and women, the ratios of those preferring to have a second child to those who do not are approximately 4:1. If marriage matching were random, based on the sample size, we would expect to find 1,509 pairs of men and women both agreeing to have a second child, and 93 pairs agreeing not to have one. However, the actual numbers are higher: there are 1,670 and 254 households, respectively, that share the same fertility preference. Similarly, the households where couples share different fertility preferences are fewer than expected under the assumption of random matching. This discrepancy supports the idea that couples match non-randomly based on fertility preferences.

Building on these observations, we are now interested in whether, and how, one spouse’s fertility preference associates with their partner’s.

Individual fertility preference

In this section, we examine how—and to what extent—one partner’s fertility preference is associated with the other’s. The OLS results for husbands and wives are reported in Tables 4 and 5, respectively. In each table, the explanatory variables include one partner’s fertility preferences and the interaction term between fertility preference and the sex ratio, which serves as a proxy for female bargaining power. Since we control for province fixed effects, provincial-level sex ratio estimates are automatically omitted. Control variables are added incrementally: column (1) includes age, column (2) adds hukou status, column (3) incorporates years of schooling, and column (4) introduces employment status and income (in logarithmic form).

We use the scenario that includes all demographic characteristics as the benchmark, as shown in column (4) of both tables. The findings reveal that both husbands and wives exhibit a positive association between their own preferences for more children and those of their partners. All estimates are highly significant at the 1% level. Specifically, husbands whose ideal number of children exceeds the average male preference by one tend to have wives whose preferences are 0.32 higher than the average female preference. Similarly, wives whose ideal number exceeds the average female preference by one are associated with husbands whose preferences are 0.49 higher than the male average.

Males’ and females’ correlation to their spouse’s preference exhibit asymmetry when considering the provincial-level sex ratio. We use the sex ratio for those aged 20-39 in a province to capture the potential population in the marriage market. A larger sex ratio, indicating more males than females, serves as a proxy for women’s higher bargaining power. This is because a higher sex ratio intensifies competition among males for potential female partners, thereby enhancing women’s bargaining position in the marriage market and in family outcomes. In provinces where the sex ratio is one percentage point higher than the national average, the husband’s preference is much more strongly associated with the wife’s preference. More specifically, wives who prefer one more child than the average female ideal number tend to have husbands who prefer 0.53 (0.491 + 0.0436) more children than the average male ideal number. Conversely, the husband’s fertility preference is associated with his wife’s preference, but this association does not significantly vary with the sex ratio in their province of residence. This suggests that greater bargaining power—driven by women’s smaller numbers in the marriage market—enables them to pair with partners whose fertility preferences align more closely with theirs.

For men, the estimation results indicate that men cannot show a stronger association with their partner’s preference, even in provinces with a smaller ratio of men, because there are more men than women in the Chinese marriage market to begin with.

Heterogeneity analysis

To further explore how these relationships vary across different demographic groups, we conduct a heterogeneity analysis based on educational level and hukou type. We define individuals with education above high school as highly-educated, and otherwise as less-educated. Hukou type is divided into either rural or urban.

First, we observe the results on the relationship between both spouses’ fertility preferences and the realization of the second-child fertility outcome. Tables A4 and A5 present the heterogeneity analysis by educational levels and hukou types, respectively, where the unit of observation is the household, and the sample is divided based on both spouses’ characteristics.

Among couples in which the wife is highly educated (regardless of the husband’s education level), the second-child fertility outcome is associated with both spouses expressing a preference for a second child, whereas individual preferences alone do not show significant associations. Among couples in which the wife is less educated (regardless of the husband’s education level), the insignificant interaction terms imply a lack of evidence for complementarity. These results suggest that complementary effects are more pronounced among highly-educated women. The weighted (weighted by subgroup sample sizes) average treatment effect of the interaction term is 0.190, indicating that when one spouse prefers a second child, the marginal association between the other spouse’s preference and the realization of a second birth increases by 0.19.

Among urban–urban, rural–rural, and urban-husband/rural-wife couples, complementary fertility preferences are positively associated with fertility outcomes. In contrast, for urban-wife and rural-husband couples, the wife’s preference appears to play a dominant role in determining the fertility outcome. This suggests that when the wife holds a more advantageous social status (i.e., urban hukou) than the husband, her fertility preference alone is more likely to determine the fertility outcome. Averaging different effects in different subgroup, the weighted average treatment effect of the interaction term across those different groups is 0.196, indicating that when one spouse prefers a second child, the marginal association between the other spouse’s preference and the realization of a second birth increases by 0.196.

Next, we observe that the results vary across subgroups defined by educational level and hukou type. Tables A6 and A7 present the heterogeneity analysis on the association between a husband’s (or wife’s) fertility preference and that of his (or her) spouse. The sample is divided based on individuals’ educational level and hukou status.

Among men, husbands who are either highly-educated urban, highly-educated rural, or less-educated rural exhibit a stronger association with their wives’ fertility preferences. In contrast, for all subgroups of women, a consistently strong association is observed between their preferences and those of their husbands. Averaging those effects in different subgroups, the weighted average treatment effect across subgroups is 0.333 (0.470), indicating that a one-child increase in husband’s (wife’s) preference corresponds to 0.33 (0.47) more in wife’s (husband’s) preference.

Heterogeneity analysis provides more detailed information. Consistent with the baseline results, variation is only observed in how husbands’ fertility preferences are associated with their wives’ preferences, but not in the opposite direction. In addition, the effect differs across subgroups.

For less-educated urban women, a higher sex ratio is associated with a weaker alignment between their preferences and those of their husbands; while for less-educated rural women, it is associated with a stronger alignment. This suggests that in rural areas, when there are fewer females than males, couples tend to have similar fertility preferences. The weighted average effect of the interaction term is 0.0458, indicating that in provinces where the sex ratio is one percentage point higher, wives who prefer one more child than the female average tend to have husbands whose preferences are approximately 0.52 (0.4696 + 0.04578) children higher than the male average.

Underlying data

We are not allowed to distribute the original data since the data was collected by Peking University and the agreement with Peking University does not allows us to distribute the data. However, we provide the link to obtain the data from Pekin University and we provide the code to replicate our results. The original dataset used in this study is available from the following URL: https://opendata.pku.edu.cn/dataverse/CFPS?language=en.

Extended data

Supplementary files are available at Open Science Framework (OSF) (Zhuang and Naito, 2024): https://doi.org/10.17605/OSF.IO/F5DPZ.

Zhuang and Naito (2024) on OSF contains the following data:

The above data are available under the terms of the Creative Commons Zero “No rights reserved” data waiver (CC0 1.0 Public domain dedication).

Reporting guideline

Repository: STROBE checklist for ‘Marital Bargaining and Assortative Matching on Fertility Preference: Evidence based on Cross-sectional Data in China’ is available at https://doi.org/10.17605/OSF.IO/2Z8HY.

Ethics and consent: we obtained the approval to use this data on August 9, 2021 from Peking University. Since this data is in the public domain and it is widely used, the review thorough the ethical committee at the University of Tsukuba was not needed. The original data collection project by Peking University was approved by the Biomedical Ethics Committee of Peking University, Beijing, China. The ethical approval number is IRB00001052-14010. We obtained the permission to publish this research on June 2 ^nd 2024 from Peking University.