**4. Results**

### *4.1. Impact of a Couple's Education Gap on Health: OLS and Instrumental Variable Two-Stage Least-Squares (IV-2SLS) Estimations*

The first stage was based on the OLS model. It estimated various influence factors that included the effect of a parent's highest education level on the IHEG. The results are shown in Table 2. The dependent variables in Model 1 and Model 2 were labeled as "IHEG1," and in Model 3 and Model 4, they were labeled as "IHEG2." The main independent variables were a parent's highest level of education, which was described as instrumental variables in the two-stage least squares (2SLS) model. Stock et al. [45] suggested that if the *F*-statistic values were greater than 10 for one of the endogenous variables based on the 2SLS estimation, then the selected instrument variable was not weak. From Model 1 to Model 4, the *F*-statistic values for the joint significance on the coefficients of the instruments were 704.550, 159.136, 230.902, and 60.043, respectively, which were all larger than 10. Therefore, it is clear that the selected instruments in this study are not weak.

The estimation results are summarized as follows. (1) A parent's highest level of education was negatively correlated with both IHEG1 and IHEG2 in Model 1 and Model 3 (−0.092 in Model 1, −0.025 in Model 3), and the results were significant at the 1% level. (When using the number of years of schooling of parents as the educational attainment index of parents, the results were similar. However, the mandatory minimum number of years of schooling differs by country and area. Moreover, the number of years of schooling for individuals who dropped out was unable to be counted, which resulted in measurement errors. Therefore, we determined that the evaluated education from 1 to 10 was more appropriate than transforming the results into years of schooling.) The coefficient of parents with an advanced education was −0.106 in Model 1, and it was statistically significant at the 1% level. The results indicate that the IHEG was smaller for individuals with highly educated parents.

Table 3 presents the estimation results by using various health indices (SRH, the mental health index, and objective health) and various methods of analysis (the OLS and IV-2SLS methods). The dependent variable for Model 1, Model 2, and Model 6 was SRH. The dependent variable for Model 3, Model 4, and Model 7 was the mental health index, and the dependent variable for Model 5 and Model 8 was objective health. The results of the OLS model are shown in Models 1 and 3. The results of the IV-2SLS method are shown in Models 2 and 8. The results of the overidentification tests in Model 2 and from Model 4 to Model 7 were statistically insignificant at the 5% level. These findings indicate that the instruments are statistically exogenous in these models and that the instrument variable methods

should be utilized to address the endogeneity problem. This means that there was bias in the results based on the OLS model. Therefore, we report mainly the results based on the IV-2SLS method in the following section. We also compare the results to those based on the OLS model. The main results are as follows.

First, to compare the results obtained by the OLS and IV models, although the coe fficients in both the OLS (Model 1) and IV-2SLS (Model 3) were statistically significant at the 1% level, the coe fficient of IHEG1 was −0.020 for the OLS model and −0.046 for the IV-2SLS model. Similar results were observed in Models 3 and 4; the coe fficient of IHEG1 was −0.003 for the OLS model (Model 3) and −0.029 for the IV-2SLS model (Model 4). The magnitudes of the coe fficients in the IV-2SLS model were greater than those in the OLS model, which suggests that the impact of IHEG1 on health might be underestimated by the OLS model. Consistent results were obtained by additionally controlling health insurance satisfaction, alcohol consumption, and smoking.

Second, regarding the impact of IHEGs on health, there were two outcomes. (1) The coe fficients of IHEG1 were negative values (−0.046 in Model 2; −0.029 in Model 4; and −0.015 in Model 5; Table 3), and they were statistically significant at the 1% and 5% levels. These findings sugges<sup>t</sup> that health status (SRH, mental health, and objective health) was worse for individuals with a higher level of education than for their partner. Because a negative e ffect of IHEG1 on health was found for both husbands and wives, we investigate the above e ffects by gender in the following section. (2) The coe fficients of IHEG2 (couples with education gaps) were negative values (−0.205 in Model 6; −0.137 in Model 7; and −0.062 in Model 8—when using the educational attainment dummy variables, it was also found that the IHEG negatively a ffected objective health status, and the result was statistically significant at the 5% level—and they were statistically significant at the 1% and 10% levels. These findings indicate that, compared with the health statuses of couples with equal levels of education, health status (SRH, mental health, or objective health) was worse for couples with intra-education gaps.

### *4.2. Estimations by Various Groups*

To consider the heterogeneity in various groups, we also made estimations based on education, gender, age, income, and country. As a kind of human capital, a high level of education is associated with more working skills and higher incomes. A couple with a large education gap may also have grea<sup>t</sup> skill and knowledge gaps, resulting in communication di fficulties. Moreover, the probability of obtaining help from his or her partner may be lower for an individual with a higher level of education because he or she is more likely to do work that requires specific skills and knowledge. To consider the heterogeneity due to individual education level, we made estimations using two groups: (1) a high education level group that completed vocational school or higher (also referred to as tertiary education (ISCED levels 5 to 8) by The United Nations Educational, Scientific and Cultural Organization (UNESCO) (tertiary education included both commonly accepted academic education and advanced vocational or professional education) or higher education by the World Bank) [47,48]; (2) a low education level group that completed senior high school or lower (also known as primary or secondary education (ISCED levels 0 to 4)) by UNESCO). The estimations were also employed by gender (women and men), age (younger than 40 years and older than 40 years), continents (Asia, Europe, and North America, and South America and Australia), and by income (high-income countries and middle-income countries) groups. The results for the high- and low-education groups are summarized separately in Table 4 column (a) and column (b) The value of the IHEG (IHEG1) was used as the education gap index (IHEG) in the estimations. The dependent variables were SRH, mental health, and objective health. The independent variables were similar with those in Table 3, but only the results of the IHEG are summarized in Table 4. The main results are as follows.


*Sustainability* **2020**, *12*, 4623



based on the original international survey from 2015 to 2017.

First, in general, the coe fficients of the IHEG were negative values (−0.084 in (a) for SRH; −0.042 in (a) for mental health; and −0.024 in (a) for objective health), and they were all statistically significant at the 1% level. This finding indicates that for the group with a high education level that completed vocational school or higher, an education gap between a respondent and his or her partner may lower the respondent's SRH, mental health, and objective health status. Individuals with education levels that are higher than those of other family members may have more household financial responsibilities, which may result in long working hours and more feelings of stress. As a result, their mental health and physical health status may be poor.

Second, the e ffects of the IHEG on health di ffered in the di fferent groups. (1) For the high-education group (a), the coe fficients of the IHEG were negative for women (−0.106 in Model 1(a); −0.034 in Model 3(a) for mental health; and −0.057 in Model 5(a)), and they were all statistically significant at the 1% level. These results sugges<sup>t</sup> that when a wife has a higher level of education than her husband, her SRH, mental health, and objective health may be worse. The coe fficients for men were −0.063, −0.043, and −0.001 and were statistically significant at the 1% level for SRH and mental health. An education gap between wives and husbands also negatively a ffects the husband's health. Comparing the groups of husbands and wives, the negative e ffect of having a higher education than one's partner was greater for women regarding SRH and objective health. Accordingly, on average, wives have more housework. Therefore, work-family conflicts might be severe for a wife when she has an education level that is greater than that of her partner. However, for the low-education group, most coe fficients were not statistically significant for either wives or husbands. Compared with the high-education group, the negative e ffect of an IHEG seemed to be smaller for the low-education group. This finding indicates that work-family conflicts may be severe for both wives and husbands with high education levels.

(2) For the high-education group, although a negative e ffect of the IHEG on health was found in both the younger group and the older group, the e ffect was greater for the younger group based on SRH and mental health than for their counterparts. However, the e ffect was greater for the older group based on objective health. For the low-education group, most coe fficients were not statistically significant for either the younger or older groups.

(3) Comparing the results in various areas of the world, for the high-education group, the coe fficients of the IHEG were negative for Asian countries (−0.108 in Model 1(a); −0.057 in Model 3(a); and −0.045 in Model 5(a)), and they were all statistically significant at the 1% level. This finding suggests that, for the high-education group, an IHEG may worsen the SRH, mental health, and objective health of individuals in Asian countries. The coe fficients for Europe and North America were −0.082, −0.033, and 0.003, and they were statistically significant at the 1% and 5% levels in Model 1 and Model 2. Comparing Asian countries with European and North American countries, the negative e ffect of an IHEG on health was greater for individuals in Asian countries. However, for the low-education group, most coe fficients were not statistically significant for the Asian, European, and North American countries.

(4) Considering the results of lower and upper middle-income countries and high-income countries internationally, the negative e ffect of an IHEG on health was greater for lower and upper middle-income countries than for high-income countries regarding mental health and objective health for the lower and upper middle-income countries. This finding may be because high-income countries can provide universal public health insurance and advanced medical or health care service.

Third, for the low-education group, there may be a positive relationship between an IHEG and health. For example, the coe fficients of the IHEG were positive values (0.053 in Model 2(b) for the total; 0.020 in Model 6(b)), and they were statistically significant at the 1% and 10% level. This finding suggests that, for the low-education group, reducing the education gap may improve the health status of an individual, particularly regarding the mental health condition of women (0.076 and statistically significant at the 1% level in Model 4 (b) for women).



based on original international survey from 2015 to 2017.

### *4.3. The Impact of IHEGs, Sustainable Lifestyle, and Health*

Next, we investigated the potential mechanism of the negative effect of IHEGs on health and sustainability lifestyle. We estimated the effects of IHEG1 (value) on (1) income satisfaction, (2) weekly working days, (3) overcoming difficulties (the impact of IHEGs on feelings of stress was also estimated, and the results were consistent with those for overcoming difficulties in the analyses. These results are available upon request), (4) satisfaction with health or medical care, (5) attending environmental activities as a volunteer, (we also explored the effect of IHEGs on the frequency of drinking alcohol and smoking behavior. The results indicated that the impact of a couple's education gap on healthy behavior was not statistically significant. An intrahousehold education gap may not worsen health behaviors) (6) donation to environmental activities (income), (7) donation to environmental activities (goods), (8) purchase energy-saving household products, (9) energy-saving activities, and (10) sorting or reducing rubbish.

As the mechanism may differ by education level, we made estimations for both the (a) high-education group (vocational school or higher)—this designation is known as tertiary education (ISCED levels 5 to 8) by UNESCO or higher education by the World Bank—and (b) the low-education group (senior high school education or lower). This designation is also known as primary/secondary education (ISCED 0 to 4) by UNESCO. The results are summarized in Table 5.

For the high-education group, all coefficients of the IHEG in the five models were statistically significant at the 5% or 1% level. Based on the results, four channels regarding the effect of IHEGs on health were determined. First, an individual with a high level of education is more likely to find a better job and have a higher income in the labor market than an individual with a low level of education. Therefore, he or she can accumulate more wealth and invest more to improve his or her health status and those of other household members (positive effect of income hypothesis). A high IHEG may decrease an individual's income satisfaction (−0.036) and health or medical care satisfaction (−0.016). These results do not support the positive effect of the income hypothesis. Therefore, the negative effects may be greater than the positive effects.

Second, regarding household responsibilities, a highly educated individual may have longer working hours than their less-educated partner. It was found that long working hours may negatively affect the health status of individuals (negative effect of longer working hours hypothesis). The coefficient of the IHEG was 0.017 for weekly working days, and −0.008 for attending environmental activities as a volunteer. These findings indicate that a highly educated individual with a higher IHEG may have to work longer and that the probability of participation in social activities is lower, which may worsen their health status (For the impacts of long working hours on mental health, please see [28–31]; for the impacts of volunteer activity on health, please see ref. [49–51]). These results support the negative effect of the longer working hours hypothesis. Third, the coefficient of the IHEG for overcoming difficulties was −0.008, which shows that the higher the IHEG, the lower the probability of overcoming difficulties. A couple's education gap may decrease the amount of help provided by a partner for individuals with high education levels. As a result, he or she has to address these problems alone, which may increase loneliness and stress when the individual faces difficulties in life and work. The results support the negative effect of the skill gap hypothesis.


**Table 5.** The potential mechanism by two different educational attainment groups.

Notes: (1) Standard errors in parentheses. \*\*\* *p* < 0.01, \*\* *p* < 0.05, \* *p* < 0.1. (2) The control variables are similar with those in Table 4, except for the respondent's educational attainment. (3) The OLS regression is utilized in Model 1 to Model 10. (4) High education: vocational school or higher; Low education: senior high school or lower. (5) The independent variable is intrahousehold education (value) Source: Calculated based on the original international survey from 2015 to 2017.

Third, regarding a sustainable lifestyle, the results sugges<sup>t</sup> that the intrahousehold education gap may decrease the sustainable lifestyle activities of improving environmental sustainability. For example, the coefficient for the intrahousehold education gap regarding volunteer attendance at environmental activities is −0.008 for the high-education group. Statistically, it is significant at 1%. It suggests that individuals who completed vocational school education or higher (high education) and experience an education gap in marriage are less likely to volunteer for environmental activities. On the contrary, for the low-education group, the coefficient is positive and statistically insignificant; it indicates that for individuals who completed high school or lower and experience a low-education gap in marriage are more likely to volunteer for environmental activities. Similar trends are found in income donation or goods donation to environmental activities (models 6 and 7). The results show that the negative influence of the education gap in marriage on the environmental activities may influence environmental sustainability. Regarding household-consumption-related environmental activities, there is a similar negative relationship with a sustainable lifestyle. For example, the coefficient of the education gap for energy-saving household products is a negative value for the low-education group, and it is statistically significant at the 1% level. It suggests that individuals who completed high school or lower and experience an education gap have a lower probability of purchasing energy-saving household products. However, no significant influence is found in the high-education group. Moreover, the results are almost similar for energy-saving actions and sorting or reducing rubbish (models 9

and 10). These results sugges<sup>t</sup> that the intrahousehold education gap may worsen the sustainability lifestyle (i.e., reducing the activities of improving environmental sustainability).

Besides the workload and income e ffects on the linkages between health and education gaps, our results show the negative role played by the intrahousehold education gap on reshaping the household's choice to harmonize environment through energy consumption, recycling, separate collection and reduction of rubbish, volunteer attendance, and charity. As highlighted by Tilman and Clark [42], the crucial relationship between sustainability lifestyle and public health is through environmental sustainability and food lifecycle. These results demonstrate the importance of the linkages between health and education gaps and a sustainable lifestyle and sugges<sup>t</sup> that education equality in marriage plays a crucial role in enhancing consumption and production sustainability.

#### *4.4. Robustness Check to Consider Intergeneration Influences in the Relation between Education and Health*

The exclusion restriction in this study was that the impact of a parent's educational attainment level on an adult child's health must be indirect (such as a child's education level or a couple's educational di fference) and not via direct channels [52–59]. As such, the two sets of selected instrumental variables using a parent's educational attainment for the endogenous variables of a couple's education di fference should satisfy this exclusion restriction condition. It has been argued that increasing the educational attainment level of parents improves the educational level of children [53,58]. When individuals attain a high education level (e.g., complete a doctorate degree in graduate school), well-educated individuals are more likely to have higher education levels than their partners. Therefore, it is acceptable that parents that are more educated may potentially a ffect their adult child's choice of an educated partner versus a less-educated partner, but a parent's education level is not directly associated with an adult child's health. As far as we know, evidence of a direct correlation of health status and parent educational attainment has rarely been shown.

The indirect e ffects of parental education on health may also result from reshaping an adult child's unhealthy behavior (such as smoking). Individuals with relatively better education levels are thought to exhibit healthier behaviors; for example, these individuals are more likely to have a ealthy weight, consume a healthy diet, exhibit healthier behaviors, have a reduced likelihood of disaster, and have an enlarged social network [52–59]. When parents are well educated, they have extensive knowledge on the harmful e ffects of smoking and consuming alcohol in large amounts and have a more e fficient way of selecting health insurance. These kinds of knowledge might influence the health behaviors or choices of their adult children, and as a consequence, their adult children may be healthy (indirect channel). To consider this possible indirect channel, we conducted a further robustness check by controlling additional control variables (Panel 2). The variables were (1) satisfaction with health/medical care, (2) nonsmoker, (3) alcohol consumption (drink alcohol every day; 4–5 times per week; 2–3 times per week; once per week; less than above; and do not drink alcohol). The regression results with the abovementioned additional controls for (1), (2), and (3) are summarized in Table 6 Panel 2 (Model 4(a)–Model 6(b)), where the individuals who completed vocational school or higher (this designation is known as tertiary education (ISCED levels 5 to 8) by UNESCO or higher education by the World Bank) are denoted in (a), and those who completed senior high school or had a lower education level are denoted in (b) [47,48]. The corresponding regression results omitting the above controls ((1), (2), and (3)) are displayed in Panel 1 (Model 1(a)–Model 3(b)) using the same sample.

The coe fficient of IHEG was −0.077 and statistically significant (Model 1(a)), whereas the coe fficient was −0.060 when controlling for the additional variables (the variables were (1) satisfaction with health/medical care, (2) do not smoke dummy variable, (3) alcohol consumption dummy variable (drink alcohol every day; 4–5 times per week; 2–3 times per week; once per week; less than above; and do not drink alcohol)), and the result was statistically significant (Model 4(a)). Similar results were also found in the other models, in which the coe fficients had a similar magnitude, were statistically significant, and had the same sign (Model 1(b) with Model 4(b); Model 2(a) with Model 5(a); Model 2(b) with Model 5(b); Model 3(a) with Model 6(a); and Model 3(b) with Model 6(b)). The di fference between the coe fficients of IHEG in Panel 1 and those in Panel 2 was small. This finding suggests that the indirect channel of the impact of parent education on adult children's health did not conflict with our main conclusions.

In addition, other factors a ffected health status. For example, (1) increasing levels of satisfaction with health/medical care also improved an individual's health status; (2) compared with the smoking group, the nonsmokers report better subjective health and mental health, whereas there was no grea<sup>t</sup> di fference between these two groups regarding objective health; and (3) drinking alcohol more frequently positively a ffected SRH and objective health, whereas alcohol consumption negatively affected mental health.
