Basic information of respondents with different numbers of children

As shown in Table 2, zero-child respondents (respondents with no children) account for 46% of the 1385 young people; one-child respondents (respondents with one child) account for 34.73%; two-child respondents (respondents with two children) account for 19.35%. From the perspective of age distribution, the proportion of zero-child respondents drops while the proportion of one-child respondents gradually rises with age; the 26–30-aged group account for 14.18% of the two-child respondents, and the 36–40-aged group account for 57.09%; zero-child respondents account for only 8.81% of the 36–40-aged group. From the perspective of hukou, the two-child respondents account for the highest proportion in the agricultural hukou group but the lowest proportion in the non-agricultural hukou group; the agricultural hukou group and the non-agricultural hukou have roughly equal proportions of the zero-child and one-child respondents. From the perspective of per capita household income, the two-child respondents account for the highest proportion in the low-income group, while zero-child and one-child respondents account for the roughly equal proportions in the low-income group; the high-income group has roughly equal proportions of zero-child, one-child, and two-child respondents (with a difference of less than 2%). From the perspective of educational level, two-child respondents make up the lowest proportion in those with higher educational levels (bachelor, master and above); on the contrary, two-child respondents make up the highest proportion in those with college or lower educational levels (the only slightly exceptional situation is that the proportion of one-child respondents in the high school group is about 1.5% higher than that of two-child respondents). From the perspective of occupational prestige, zero-child respondents have the highest occupational prestige, followed successively by one-child and two-child respondents; and the differences in occupational prestige of zero-child, one-child, and two-child respondents are not significant. Observed from the perspective of housing property, one-child respondents account for the lowest proportion in both the no-property group (respondents with no housing property) and three-or-more-property group (respondents with three or more housing properties). From the perspective of debt, zero-child respondents make up the highest proportion in the no-debt group and two-child respondents make up the highest proportion in the in-debt group. From the perspective of the number of siblings, zero-child respondents account for the highest proportion in the no-sibling group and the one-sibling group, while two-child respondents account for the lowest proportion in the no-sibling group and the one-sibling group; in contrast, two-child respondents account for the highest proportion of the two-or-more-sibling group, followed successively by one-child respondents and no-child respondents. In terms of living with grandparents, there is no significant difference between those without children and those with one child; however, the proportion of those with two children living with grandparents is noticeably higher than that of those with no children or one child.

Table 2 Means and distribution of dependent and control variables for respondents with different numbers of children (unit: %)

The mean value of the dependent variable self-efficacy for the full sample is 3.669; the self-efficacy value of one-child respondents is the lowest (3.647), followed by that of zero-child respondents (3.668), and that of two-child respondents is the highest (3.710). But are these small differences in self-efficacy really associated with the number of children? For example, as mentioned above, the proportion of respondents with higher educational levels in the two-child group (respondents with two children) is much lower than that of respondents with lower educational levels. Is it possible that people with higher educational levels are younger and haven’t completed childbirth because of longer education duration as a result of higher education popularization? Therefore, a matching approach should be applied to exclude confounding factors or avoid sample selection bias.

POM of self-Efficacy for respondents with different numbers of children

As shown in Fig. 2, the potential mean self-efficacy of respondents with different numbers of children is estimated using propensity score matching. The term “potential outcome means” (POM) is used because various scenarios, including the zero-child, one-child, and two-child cases, can be found in the observed data. POM refers to the self-efficacy of a group if all the group members are assumed to have no children, one child, or two children, which are counterfactual outcomes. When the full sample is observed, if all respondents are assumed to have no children, the average self-efficacy of the group is about 3.656; this figure decreases slightly to about 3.621 if all respondents have one child; and this figure increases substantially to about 3.759 if the group have two children. If the female group is assumed to have no children, their self-efficacy is about 3.685; if the female group is assumed to have one child, the self-efficacy decreases substantially by about 0.086%; if the female group is assumed to have two children, their self-efficacy increases to about 3.731. If the male group is assumed to have no children, their self-efficacy is the lowest (about 3.614). However, in stark contrast to women, men's self-efficacy shows almost no change when they have one child. Of course, similar to women, when men have two children, their self-efficacy also increases, but the increase is more pronounced, reaching a level of approximately 3.828.

Fig. 2

Self-efficacy of Respondents with Different Number of Children. The observed value in the figure is reflected in the survey data, as shown in “Self-efficacy” row of Table 1

Overall, there is a gender difference in the quantitative relationship between the number of children and self-efficacy. Men’s self-efficacy shows a significant increase when they have an additional child; female self-efficacy stays at a high level when they have no children, falls to a low level when they have one child, and experiences a substantial increase when they have two children. However, male self-efficacy is always higher than female self-efficacy no matter whether they have one child or two children.

Comparison of potential self-efficacy among respondents with different numbers of children

As shown in Table 3, this part compares the potential self-efficacy of respondents with different numbers of children and checks its statistical significance at the confidence intervals of 90% and above. According to the comparison results of the full sample, the full sample has a statistically significant increase in self-efficacy when changing from having no children to two children or from having one child to having two children; the full sample has a slight decrease in self-efficacy when changing from no children to having one child, although there is not a significant probability (confidence level/probability below 90%) to infer the sample results to the overall population. The results for the female group indicate that, compared to women who have not given birth, those who have one or two children find it difficult to observe an increase in self-efficacy with a high probability (confidence level/probability of 90% or above); on the contrary, compared to women who have not given birth, the female have a high probability (of over 90%) of experiencing an about 0.079 decrease in self-efficacy when changing from having no children to having one child; but the female have an about 0.123 increase when changing from having one child to two children, and the difference is statistically significant at the 95% confidence level. According to the comparison results of the male group, the male group have a statistically significant increase in self-efficacy when changing from having no children to one child and from having one child to two children; having only one child increases the male self-efficacy slightly by about 0.009, which is not statistically significant; having the second child increases the male self-efficacy significantly by about 0.216. The difference coefficient is statistically significant at the 99% confidence interval, so this increase is considered to be real. Overall, on the one hand, self-efficacy can increase only by having a second child (that is, having two children); on the other hand, there are gender role differences in the quantitative relationship between the number of children and self-efficacy.

Table 3 Comparison of potential self-efficacy among respondents with different number of children

Data in Table 3 comes from the results of multivalued propensity score treatment effects under the “effects ipwra” command; values in parentheses are robust standard errors (“Robust Std. Err.”); * denotes p < 0.1; ** denotes p < 0.05; *** denotes p < 0.01.

Table 4 further shows the balance of the multivalued propensity score matching. Compared with the two-valued treatment effects matching method (just setting experimental and control groups, two-valued score matching can be judged by if the p value of two groups is greater than 0.1. If p value is greater than 0.1 in all control variables, it can be seen that both experimental group and control group have passed the balance test and are comparable), multiple-valued matching can qualitatively judge the equilibrium situation by observing how close the Weighted Variance ratio is to 1. The closer the Weighted Variance ratio is to 1, the better the balance is. As shown in the table, after the “ipwra/Inverse probability weighted regression adjustment” for both the full sample and the gender-specific samples, the one-child group and the two-child group are quite close to the zero-child group in terms of the control variables such as age and hukou, indicating that the experimental group and the control group are comparable. Thus, it can be safe to say that the differences in self-efficacy, as shown in Table 3, are caused by the difference in the number of children but not the control variables.

Table 4 Balance test of multi-valued propensity score matchingRobustness tests

Different measures are used for robustness tests of the reliability of the above results. In the “ra” process of “ipwra”, the dependent variable is predicted using “poisson” (The default is linear prediction; “poisson” here is “exponential outcome model”). If consistent results can still be observed using different methods, it would enhance the credibility of the findings.

The results of the robustness tests are shown in Table 5. The test results in Tables 3 and 5 have minor differences in the numerical values but no differences in the coefficient sign or the significance level, indicating that the results are reliable.

Table 5 Comparison of potential self-efficacy among respondents with different number of children

Data in the table comes from the results of multivalued propensity score treatment effects under the “effects ipwra” command; values in parentheses are robust standard errors (“Robust Std. Err.”); * denotes p < 0.1; ** denotes p < 0.05; *** denotes p < 0.01.