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

Introduction

Chinese society and economy have undergone significant shifts over the past seven decades. Social issues have evolved from a vast population base with low human capital following the establishment of the People’s Republic of China, to a demographic characterized by an aging population and a labor force shortage in recent years. Correspondingly, fertility policy transitions can be divided into three periods: the first, following 1949, encouraged higher birth rates to support the burgeoning workforce demands; the second, beginning in the 1970s with the “Later, Longer, Fewer” campaign and later reinforced by the One–Child Policy, aimed to control the booming population; and the third, a response to declining fertility rates and an aging population, where a series of two-child policies emerged. In 2011, couples who were both only children were permitted to have a second child under the Double–Single Two–Child Policy; in 2013, the policy expanded to allow couples to have a second child if either spouse was an only child under the Selective Two-Child Policy; and in 2016, the Universal Two-Child Policy was implemented, allowing all couples to have two children.

However, the Chinese birth rate has continued to decline in recent years. While there was a temporary increase in birth and natural growth rates following 2016, these rates decreased to new lows in subsequent years, as illustrated in Figure 1. With the belief “more children, more blessings" and the strict enforcement of the One-Child Policy, couples generally do not disagree on having the first child. Disagreements occur over the second and subsequent children, especially when women are empowered by their market status. The Universal Two-Child Policy encourages families to consider a second child, potentially initiating a bargaining process between spouses when their preferences differ. Furthermore, with China’s rapid economic development and a continuously skewed sex ratio, women’s bargaining power within the family has increased (Bulte et al., 2015). These factors underscore the importance of understanding fertility decisions from the perspective of the marital bargaining process.

Figure 1. Total Population, Birth, and Natural Growth Rates in China, 2001-2023.

Note: The short-dash, dash, and long-dash lines denote the starting times of the Double-Single, Selective, and Universal Two-Child Policies, respectively.

Theoretical models highlight the importance of the bargaining process in fertility decisions and illuminate how bargaining over fertility may differ between developed and developing countries. Fertility choices in developing countries are often dominated by a single decision-maker, typically males, who usually prefer a larger family size and possess greater bargaining power. These significant disagreements between spouses about fertility preferences imply that increasing women’s bargaining power could enable them to influence fertility decisions (Doepke and Tertilt, 2018). In contrast, high-income economies often feature gender-equal labor laws and greater female participation in the labor market, where bargaining over fertility becomes significant because women and men achieve equal bargaining powers (Doepke et al., 2023). Doepke and Kindermann (2019) propose a veto model for fertility decisions, illustrating that in high-income countries, where men and women achieve equal bargaining power, both spouses have veto power over fertility. This model also considers the spouses’ ability to commit to future consumption. Manser and Brown (1980) integrate marriage decisions within a two-person bargaining framework, allowing husbands and wives with distinct utility functions and preferences to negotiate agreements on crucial aspects such as children, housing, and leisure. These agreements enable them to realize gains from the marriage that would not be possible if they remained single.

The argument above suggests that agreement between spouses on the desired number of children is important. This indicates that in the marriage market, both men and women have strong incentives to seek partners with similar preferences. If a husband and wife share similar views on family size, they may avoid the need for a bargaining process. Therefore, in the presence of heterogeneity in preferences regarding the number of children, assortative matching naturally occurs in the marriage market. Thus, it is crucial to examine the extent to which bargaining and matching based on preferences influence family size.

In this paper, thus, we examine fertility decisions regarding the second child, focusing on differing marital fertility preferences utilizing data from the 2018 China Family Panel Studies survey and applying Ordinary Least Squares (OLS) regression models. We further explore assortative matching based on fertility preferences, using the provincial-level sex ratio as a proxy for women’s bargaining power. To this end, we collected data on the number of males and females aged 20-39 from the 2020 China Population Census Yearbook and calculated the sex ratio by dividing the number of males by the number of females. This approach captures the potential population in the marriage market.

The findings reveal that to have a second child, both the wife and the husband need to cooperate when they have different fertility preferences. Additionally, we found that marriage matching is non-random; specifically, individuals are more likely to pair with partners who share the same preference regarding having a second child. Therefore, we further studied how one spouse’s fertility preference associates with their partner’s. Our conclusions indicate that females with greater bargaining power correlate positively with their husbands’ ideal family size, whereas males do not have a similar correlation.

This paper contributes to the literature on fertility decisions from the perspective of the bargaining process within the Chinese context. Previous research mainly studies fertility decisions from the perspective of females in their reproductive age, which considers the family as a unit that internalizes individual differences to make fertility decisions that maximize household utility. Becker (1960) first applies economic theory to understand fertility decisions in 1960, proposing that children can be regarded as a consumption good that contributes to household utility. The model assumes a unitary household utility function, internalizing differences between family members, where families make rational choices about the number of children based on their preferences, income, and the costs of raising children (Becker, 1960). Further research considering parental altruism toward children assumes that parental utility also depends on the utility of children in addition to their number, thus household utility includes both the quantity and quality of children. This leads to findings that higher parental altruism leads to higher fertility rates, increased investment in each child's human capital, and greater long-term economic growth due to more capital accumulation, as altruism links the welfare of all generations in a family (Barro and Becker, 1989; Becker and Barro, 1988). Subsequent research builds on Becker’s work, adapting it to different contexts. For example, Baudin et al. (2015) focus on childlessness in the United States and propose a theory explaining that childlessness among the poor is due to low resources, while among educated women it is due to the high opportunity cost of having children. A study on the Chinese case by Liu and Liu (2020) explores the effectiveness of the Universal Two-Child Policy in China within the same framework, suggesting a threshold for the policy estimated to be lower than two children per household, implying the policy's impact on fertility rates is limited. However, as an essential family decision, fertility is mainly determined by both spouses’ preferences, leading to potential bargaining processes. There is a large amount of empirical literature on other countries based on the perspective of bargaining processes (Doepke and Kindermann, 2019; Testa et al., 2014). Peng (2020) based on interviews with 53 urban parents in China, reveals that family negotiations significantly shape Chinese reproductive behavior more than individual preferences. However, the quantitative study from the bargaining perspective on the Chinese case is limited.

In addition, this paper contributes to the literature on assortative mating based on fertility preferences. Existing literature primarily examines how assortative mating influences fertility behaviors, with a particular emphasis on educational sorting. For example, Bueno and García-Román (2021) study the Spanish case, indicating that couples with similar educational levels are more likely to have children, especially if both spouses are highly educated. Similarly, a European study finds that educational sorting significantly predicts fertility behaviors; couples with both partners highly educated tend to delay their first child but have more children later, whereas couples with a higher-educated husband and a lower-educated wife are less likely to have a second child (Nitsche et al., 2018). Tian et al. (2023) also highlight that educational sorting has the most significant impact on women’s fertility preferences compared to age and income sorting using Chinese data. Additionally, the study of marriage matching in China highlights the impact of hukou locality and intergenerational mobility on marital choices. Research from Shanghai indicates that possessing local hukou shapes these choices, enhancing the matching of highly-educated individuals while limiting interactions between hukou residents and less-educated non-hukou migrants (Qian and Qian, 2017). Urban males are empowered in the marriage market by being granted the same rights as women to pass hukou locality to their children (Han et al., 2015). Hu (2016) identifies significant associations between the occupational statuses of individuals’ fathers and those of their spouses, as well as with their fathers-in-law. To the best of our knowledge, no existing studies investigate the impact of fertility preferences on marriage matching within the Chinese context. Given these research gaps, this paper aims to provide new insights into how fertility decisions are made through bargaining processes and how fertility preferences could be associated with assortative mating.

The remainder of the paper is organized as follows: Section 2 presents the data and variables used for the empirical analysis. Section 3 outlines the empirical strategy. Section 4 explores how fertility decisions are made based on both spouses’ fertility preferences. Section 5 examines how one spouse’s fertility preference associates with their partner’s preference. Section 6 concludes the paper.

Methods

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 around 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 through a systematic sampling method, targeting 25 households per county to fulfill the study’s requirements.

Since we seek to understand the family’s fertility decisions for a second child through the bargaining process, 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 shown in Figure 2. Ultimately, the sample comprises 2,054 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=2,054.

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, 46.84% 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 80.72% 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 the family income. We assigned the income to be zero if the individuals are currently not employed. 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). In this paper, as we are interested in the marital bargaining process regarding family fertility decisions, 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 by dividing the number of males by the number of 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 between 20 and 39 across 31 provinces was 1.08, implying there are more males than females in the marriage market. The detailed summary statistics for all variables are shown in Table 1.

Table 1. Summary statistics.

VARIABLES	Mean	S.d.	Min	Max
Province
2020 sex-ratio (male/female)	1.0797	0.0529	0.9855	1.2086
2010 sex-ratio (male/female)	1.0428	0.0584	0.9536	1.2523
2000 sex-ratio (male/female)	1.0651	0.0440	0.9896	1.1884
Household
twochild (1 if having more than two children)	0.4684	0.4992	0	1
sheyes (1 if wife desiring more than two)	0.7941	0.4045	0	1
heyes (1 if husband desiring more than two)	0.8072	0.3946	0	1
number	1.4635	0.8301	0	7
income (in log function)	8.6801	4.4421	0	13.6412
Wife
age	30.8135	4.0334	18	37
ideal number of children	1.9119	0.6285	0	7
education years	10.4615	3.9976	0	22
employment status (1 if currently employed)	0.8252	0.3799	0	1
hukou (1 if urban)	0.2439	0.4295	0	1
Husband
age	31.3121	4.8175	16	61
ideal number of children	1.9416	0.6827	0	10
education years	10.3734	3.9628	0	22
employment status (1 if currently employed)	0.8442	0.3627	0	1
hukou (1 if urban)	0.2356	0.4245	0	1
N	2,054

Results

Conclusions

In this paper, we examine fertility decisions regarding the second child, focusing on differing marital fertility preferences by utilizing data from the 2018 China Family Panel Studies survey and applying Ordinary Least Squares regression models. We further explore assortative matching based on fertility preferences, using the provincial-level sex ratio from 2020 for the population aged between 20 and 39 as a proxy for women’s bargaining power, which captures the potential population in the marriage market. Our findings reveal that having a second child requires cooperation between the wife and the husband, especially when they have differing fertility preferences. Additionally, our research shows that marriage matching is not random; individuals are more likely to pair with partners with the same preference for having a second child. Further analysis demonstrates that females with greater bargaining power correlate positively with their husbands’ ideal family size, whereas males do not have a similar correlation. This paper contributes to the literature on fertility decisions from the perspective of the bargaining process within the Chinese context, as well as preference matching and sorting.