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.

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.

To estimate the relationship between marital bargaining based on fertility preferences and second-child fertility decisions, we use the following OLS regression model: twochild jp = β 0 + β 1 sheyes jp + β 2 heyes jp + β 3 sheyes jp × heyes jp + X jp γ + e jp (1) where j denotes household, p denotes province. twochild _jp represents the fertility decision of family j in province p on whether to have more than two children, sheyes _jp and heyes _jp are the wife’s and husband’s preferences, respectively, for having more than two children. All three are binary variables. X _jp represents a vector of control variables, and e _jp is the error term.

To estimate how one spouse’s fertility preferences might correlate to the other’s, we use the following two OLS regression models for husbands and wives: sheideal jp = α 0 + α 1 heideal jp + α 2 sexratio p + α 3 heideal jp × sexratio p + X jp θ + ϵ jp (2) heideal jp = π 0 + π 1 sheideal jp + π 2 sexratio p + π 3 sheideal jp × sexratio p + X jp σ + ν jp (3) where sheideal _jp and heideal _jp denote the ideal number of children for the wife and husband in household j in province p, and sexratio _p represents sex ratio in province p. These variables are expressed as deviations from their respective sample means to make the data more comparable and interpretable. We do not use sheyes _jp and heyes _jp , because they represent only the preference for a second child and overlook the heterogeneity in fertility preferences, potentially failing to capture the actual preference. By definition, a person who prefers two children and another who prefers eight are assigned the same value when using sheyes _jp or heyes _jp. Therefore, we instead use sheideal _jp and heideal _jp to better capture an individual’s preference for family size and their association with their partner’s preference. ε _jp and ν _jp are error terms.

The results are presented sequentially. First, we examine the relationship of different fertility preferences with the family’s decision to have a second child. Then, we explore how one partner’s fertility preference might be associated with the other partner’s preference.

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 decision to have a second child in a family.

We consider the situation with control for provincial fixed effects as the benchmark, as detailed in column (3). When a couple plans to have a second child, considering their fertility preferences, there are four possible outcomes: both agree to have the second one, both agree not to have it, the wife wants to have it but the husband disagrees, and the husband wants to have it but the wife disagrees. Our results show that when the couple reaches the agreement on the second child, it is associated with an increase in the likelihood of having a second child by more than 40% (0.148+0.106+0.178), the largest among the four outcomes. When a couple disagrees about having a second child, either spouse preferring a second child could be associated with an increased likelihood of having one. However, the wife’s preference tends to have a greater correlation with the household fertility decision. If only the wife agrees, her preference correlates to an increase in the household’s fertility probability by 14.8%, while if only the husband agrees, his preference correlates to an increase in the household’s fertility probability by 10.6%. All three estimators are significant at the 1% level and are robust across different specifications. This implies that to have a second child, both the wife and the husband need to cooperate to reach an agreement, especially when they have different second-child fertility preferences.

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 1,317 pairs of men and women both agreeing to have a second child, and 82 pairs agreeing not to have one. However, the actual numbers are higher: there are 1,459 and 224 households, respectively, that share the same fertility preference. Similarly, the households with couples share different fertility preferences are fewer than the 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.

In this section, we show correlation of wife’s and husband’s fertility preferences. The OLS results for wives and husbands are reported in Tables 4 and 5, respectively. In each table, columns (1) through (3) exclude self demographic characteristics, while columns (4) through (6) include them. Explanatory variables are added incrementally: we first introduce each spouse’s fertility preference in columns (1) and (4), then the provincial sex ratio in columns (2) and (5), and finally the interaction term between fertility preference and sex ratio in columns (3) and (6).

We consider the situation including self demographic characteristics as the benchmark, as detailed in column (6) of both tables. The results for both husbands and wives show that if they prefer more children, their partners also prefer more children. All estimators are significant at the 1% level. Specifically, if a husband’s ideal number of children is one more than the average male preference, his wife will likely prefer 0.4 more children than the average female preference. In contrast, if a wife’s ideal number of children exceeds the average female preference by one, her husband will likely prefer 0.5 more children than the average male preference.

Males and females exhibit asymmetry when considering the provincial-level sex ratio. We use the sex ratio for those aged between 20 and 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 decisions. In provinces where the sex ratio is one percentage point higher than the national average, a wife’s preference affects her husband’s preference much more strongly. Conversely, in such provinces, a husband’s preference affects his wife’s preference in a similar manner when the sex ratio becomes higher. More specifically, if the wife prefers one more child than the average female ideal number, then her husband will prefer 0.5 (0.495+0.668×1%) more children than the average male ideal number. Conversely, the husband’s fertility preference is not associated with his wife’s preference, regardless of the sex ratio in their resident province. This suggests that women’s increased bargaining power influences assortative matching, due to their smaller number in the marriage market. The greater bargaining power enables women to match with partners whose fertility preferences are associated with theirs.