**3. Data**

Hence, to investigate the impact of IHEGs on individual health, an internet survey via a website was conducted by a third-party company in Japan in 2015 and 2017. The third party company has provided lots of reliable website survey services in recent decades, and the company also has an extensive panel that allows the conducted sample to match the population distribution by regional area, age, and gender constitution. The original survey was conducted from 2015 to 2017, and data regarding demographics, household income, education level, SRH, mental health, and objective health were collected by matching country-level population age and gender. While web-based surveys randomly select respondents, compared to interview-based surveys, web-based surveys tend to select well-educated respondents because non-internet users are excluded. To address this problem, we carefully analyzed the respondents with high and low education levels separately. The detailed description regarding this original survey is included in [46].

The original cross-country survey data were comprised of 32 developing and developed countries on six continents: Asia, Europe, North America, South America, Africa, and Australia. Thirty-two countries were assessed using a web-based survey, and five countries were assessed using an interview-based survey that was web-based. The information on these specific country-level observations is available upon reasonable request. The countries surveyed in each continent are as follows:


The dependent variables were three indices. (1) An individual's SRH was a scale variable from one to five. We coded the health status numbers as "5 = very good, 4 = good, 3 = neither, 2 = poor, and 1 = very poor". (2) The mental health index was a mental health score, which was calculated based on the 12 survey items related to mental health. All answer options for the 12 survey items were from 1 to 4, which indicated mental health status from the worst status to the best. The 12 survey items included concentrating ability, sleeping quality, feelings of stress, behavioral control, depression, feelings of confidence, and positive e ffects. The 12-item general health questionnaire in the survey was a general short version of the World Health Organization's 60-item questionnaire. (3) Objective health was a dummy variable that was equal to 1 if an individual did not experience an illness or surgery in the past half-year (healthy = 1, unhealthy = 0). Objective unhealthy includes physical illness and mental illness.

The main independent variable was IHEG. Two indices were utilized in this study: (1) IHEG value (IHEG1) and (2) IHEG dummy variable (IHEG2). IHEG1 was a continuous variable which denotes the di fference between the educational attainment level of an individual minus their partner's education level. IHEG2 was a IHEG dummy variable (equal or unequal). The scale value of educational attainment level was as follows: never attended school = 1; dropping out of primary school = 2; primary school = 3; junior high school = 4; senior high school = 5; vocational school = 6; college = 7; university = 8; graduate school (master's degree) = 9; and graduate school (doctor degree) = 10. Education gap was a scale variable that ranged from −9 to 9 that was calculated by the scale number of the respondent's education minus that of his/her partner's education. For example, a value of −9 indicates that an uneducated individual married a partner who had a doctorate degree, and a value of 9 is the opposite. The education gap based on years of schooling was also conducted to improve the robustness of the results (the results using years of schooling are available upon request). As mentioned above, since there are both negative and positive e ffects on the relationship between the education gap and health, the results of the e ffect of the education gap on health are not clear. When the negative e ffect was greater than the positive effect, the coefficient of the education gap variable (IHEG1 or IHEG2) was negative, and the value was statistically significant and vice versa. These results are reported in the following section.

Thus, to address the endogenous problem, instrumental variables were utilized, which are as follows. (1) Parents' highest educational attainment, which is a scale variable from 1 to 10 (a parent's highest education level was evaluated as follows: never attended school = 1; dropping out of primary school = 2; primary school = 3; junior high school = 4; senior high school = 5; vocational school = 6; college = 7; university = 8; graduate school (master) = 9; and graduate school (doctorate) = 10.) (2) The dummy variable of a parent's advanced educational attainment (also known as tertiary education (International Standard Classification of Education (ISCED) levels 5 to 8—tertiary education included both commonly accepted academic education and advanced vocational or professional education) defined by UNESCO or higher education referred to as World Bank, mentioned by the World Bank) [47,48].

It is possible that a parent's educational attainment level does not directly influence an adult child's health level but affects the child's educational attainment. The overidentification test was used to test the validity of these instruments. First, the range in evaluated educational attainment was 1 to 10, from the lowest level (uneducated) to the highest level (individuals having doctorate degrees). The mandatory number of years of education differs by country and area, and this type of data was largely missing in the survey; therefore, measurement error may have occurred. Thus, the range score of evaluated education from 1 to 10 was a better variable than the years of schooling variable. Second, nine dummy variables of a parent's highest educational attainment level were utilized as instrumental variables: (1) dropping out of primary school dummy, (2) primary school, (3) junior high school, (4) senior high school, (5) vocational school, (6) college, (7) university, (8) graduate school (master), and (9) graduate school (doctorate). We will discuss the validity and violation of the instrument variables in the following section.

The other explanatory dummy variables were as follows: female dummy variable; work status dummy variables (e.g., individual unemployed, full-time employee, part-time employee, company owner, governmen<sup>t</sup> employee, professional worker such as physician and professor, self-employed, student, and housewife or househusband); education level dummy variables (e.g., senior high school or lower, vocational school, college or university, and graduate school); housing status dummy variables (e.g., rent and house owner); age dummies (e.g., less than 30 years old, 31–39, 40–49, 50–59, and 60 years or older); number of children dummy variables (e.g., no child, one child, two children, and three or more children); five household income dummy variables (e.g., first quintile to the fifth quintile); and country dummy variables were used to control country-level heterogeneity. The original data comprised 32 countries, including developing and developed countries on six continents (Asia, Europe, North America, South America, Africa, and Australia).

The following variables were utilized as dependent variables to investigate the potential channel of the impact of education gaps on health and a sustainable lifestyle. The dummy variables were income satisfaction, weekly working days, overcoming difficulties (based on the question "Have you recently felt that you could not overcome your difficulties?"), the overcome difficulties variable is constructed as "4 = not at all, 3 = no more than usual, 2 = rather more than usual, and 1 = much more than usual"), and satisfaction with health or medical care. Regarding a sustainable lifestyle, six dummy variables are constructed as sustainable lifestyle indices based on Akenji and Chen [2]. Attend environmental activities as volunteers (yes = 1, no = 0), donate to environmental activities (income) (yes =1, no = 0), donate to environmental activities (goods) (yes = 1, no = 0), purchase energy-saving household products (yes = 1, no = 0), energy-saving activities (yes = 1, no = 0), sorting or reducing rubbish (yes = 1, no = 0).

In the robustness check, the variables (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) were selected.

The statistical descriptions of the variables utilized in this study are summarized in Table 1.


**Table 1.** Descriptive statistics.


**Table 1.** *Cont.*

Note: Calculated based on the original international survey from 2015 to 2017. IHEG1: Difference between individual's own educational attainment level and the partner's level. IHEG2: having an education gap dummy variable (1 = having a gap, 0 = no gap).
