4.1. Regression analysis of social participation of empty nesters on their health
The results of the impact of social participation of the empty nesters on their health are shown in Table 1. Economic participation is beneficial to the health of empty nesters, i.e., the participation of empty nesters in economic activities significantly improves their health status. This phenomenon may be due to the fact that engaging in economic work can expand the social network relationships in their later life, and good social networks and social relationships make the empty nesters' thinking exercise. By participating in economic activities, empty nesters not only receive corresponding labor income, but also make friends in different fields, and may extend such interpersonal relationships to other aspects outside of work. Social participation is beneficial to the health of empty nesters, i.e., the participation of empty nesters in social activities can improve their health. Participation in social activities such as club activities, training courses, and door-to-door visits by empty nesters can help guide them to actively get out of the house and participate in outdoor activities as they enjoy their old age, slowing down the decline in physical function. At the same time, participation in social activities can promote emotional communication, cognitive stimulation and maintain a sense of social integration, reducing their cognitive dysfunction such as depression and loneliness. Family involvement showed positive effects on the health of empty nesters, i.e., participation in family affairs was beneficial to enhance the health of empty nesters. Family involvement increases the time spent by empty nesters in caring for their offspring, while children spend more time with them, which is conducive to improving the mood of empty nesters and delaying the decline of cognitive function; the elderly enjoy more financial support from their children in the process of caring for their offspring, which promotes them to use more elderly resources to protect their health and have the conditions to purchase more material products to improve their living standard; the empty nesters help their children to take care of Empty nesters help their children to take care of children, clean up the house and eat daily, which increases the possibility of moving their bodies and exercising their minds, thus promoting the health of empty nesters. Empty nesters' participation in volunteer activities has not shown any significant effect on their health, which may hinder the realization of the idea of "active aging". At present, the domestic volunteer service system and practice channels are still in the stage of improvement, and the volunteer service for the empty nesters lacks institutional regulation and guidance. The participation of empty nesters in volunteer services is mostly in the form of informal "spontaneous help" between streets and communities, which has little effect on the health of empty nesters and may even reduce their willingness to volunteer.
In terms of control variables. In addition to family participation, age was statistically significantly negative for the health of empty nesters at the 1% level for all three social participation categories: economic, social, and voluntary participation, indicating that participation in these three types of activities is not conducive to health improvement for older empty nesters. As age increases, the health capital depletion of the elderly begins to accelerate, and the health depletion of the empty nesters is more obvious, and their ability to participate in social activities is gradually decreasing. Instead of getting a positive impact, participation in social activities by elderly empty nesters may be counterproductive and induce the emergence of various health problems. In terms of marriage, all four social participation items were statistically significant positive for the health of empty nesters at the 5% level, suggesting that empty nesters with spouses or harmonious marriages have a beneficial effect on their health by participating in these four types of activities. This may be due to the fact that empty nesters need to rely more on each other as partners, and a harmonious marriage makes the other person not perceive an increased burden on them, but more like a mutual support and companionship in their later life, thus having a positive impact on health. Chronic disease passed a negative test at the 5% statistical level for all four social participation items. This indicates that empty nesters with chronic diseases have a low positive effect on health by participating in social activities compared to empty nesters who do not contain chronic diseases. Weakly healthy empty nesters may try to avoid time-consuming and labor-intensive activities for their own practical reasons, and the health-promoting effect is not as obvious. Participation in social activities by empty nesters with chronic diseases may lead to the sudden onset of their diseases, which not only fails to play a good role in promoting health, but also aggravates the diseases of empty nesters and is not conducive to their health improvement.
4.2. Classification discussion of the effects of social participation of empty nesters on their health
4.2.1. Regression analysis of social participation of empty nesters on their physical function
Table 2 depicts the effects of different types of participation on the physical function of the empty nesters, and it can be seen that all four social participation items passed the test at the 5% statistical level. Regardless of the type of participation, the empty nesters were able to ensure different levels of physical activity, avoiding the possibility of weak health due to long-term lack of exercise. Voluntary participation did not show a significant effect in Table 1, but had a more significant effect on physical function, which may be related to the fact that health is a variable under multiple dimensions. Age showed a significant negative effect in all four social participation items, i.e., the older the empty nesters were, the less likely they were to improve their physical functioning through social participation. The statement that as age increases, empty nesters are more likely to have decreasing health status and less likely to be socially involved, which is detrimental to physical functioning, is also consistent with health needs theory. Chronic diseases also showed a significant negative effect on the four social participation items, i.e., empty nesters with chronic diseases were less likely to improve their physical functioning through social participation. This is the same finding as in Table 1. Both variables, marriage and old-age insurance, showed significant positive effects. In terms of marriage, empty nesters who live with their spouses can take care of each other and give each other more care and companionship to ensure their social participation without any worries, thus contributing to the improvement of physical function. In terms of pension insurance, empty nesters who have pension insurance can achieve a certain degree of economic independence and are in a position to meet their own needs, and social participation is less likely to be subjectively influenced by others, thus promoting physical functioning. Gender only shows significant characteristics in family participation. Women have inherent advantages over men in terms of family participation, such as maternal love and emotional involvement, and they have more experience than men in caring for their offspring, which has been a female role since ancient times. Education shows significant characteristics in economic participation and voluntary participation. This may be because the higher the education level, the less likely the empty nesters are to engage in physical participation, mostly reemployment from their former units or relatively easy jobs that do not harm their physical functions. The scope and content of volunteer participation and education are related. Empty nesters with higher education levels have relatively more resources and contacts, and are more likely to participate in higher-level volunteer activities, which have a more obvious effect on physical function. The variable ethnicity showed significant effects in the 3 economic, social, and voluntary participation, indicating that Han residents have a promotion effect on physical function by participating in the above 3 social participation. There was no significant effect in family participation, which is related to the fact that family participation is not race-specific.
4.2.2. Effects of social participation on the cognitive function of empty nesters
Table 3 describes the effects of different types of social participation on the cognitive functioning of the empty nesters. Unlike the results of other studies in this paper, only social participation had a significant effect on the cognitive functioning of the empty nesters. By participating in club activities and training courses, the empty nesters can use different channels to achieve social role transition, maintain social network relationships and keep modern social ties, prevent memory decline and weakened thinking, and thus contribute to cognitive function. Age is a significant negative effect in all four models, which indicates that increasing age reduces the effect of social participation on the cognitive function of empty nesters. The older the age, the less mental activity of the empty nesters, the weaker their thinking ability and calculation ability, and some of them may even develop Alzheimer's disease, which is not conducive to the social participation of the empty nesters and thus has a negative health effect. The effect of marriage on the cognitive function of empty nesters passed the test at the 1% statistical level in all four models. This, like the regression results in Table 1, also validates the importance of marriage, i.e., living with a spouse is very important. Pension insurance also showed a significant effect in all 4 models and a larger effect than the effect of physical functioning. This may be due to the fact that pension insurance ensures that empty nesters have a stable income, which allows them to participate in various activities autonomously and has a more significant effect on cognitive functioning. The variable of education was statistically significant at the 1% level in all four models, indicating that the higher the education level of the empty nesters, the more they were able to improve their cognitive functions through social participation. The higher the education level, the higher the cognitive level of thought, the clearer the social resources and their needs, and the clearer the idea of improving their cognitive functions. The influence of residence on cognitive function was positive at the 1% level, and the urban areas had more activities and a larger population than the rural areas.
4.2.3. the effect of social participation of empty nesters on their social integrity
Table 4 describes the effects of different types of social participation on the social integrity of the empty nesters. Economic participation passed the test at the 1% statistical level, which indicates that participation in economic activities is conducive to enhancing the life satisfaction of empty nesters. In the context of rapid development of the market economy, the level of life satisfaction is directly related to economic income, and empty nesters obtain considerable income through economic participation, which is conducive to the improvement of life quality and thus promotes their life satisfaction. Social participation, such as social activities, training courses, and dancing, can enlighten the wisdom of empty nesters, enhance their personality, cultivate their sentiment, and discover the richness and beauty of life, thus contributing more to life satisfaction. Age showed a significant positive effect on social completeness in all cases, indicating that the older the empty nesters were, the higher their life satisfaction was. Along with age, the wishes of the elderly may have been accomplished, such as having children and grandchildren, etc., and the happiness of their later life is high. The regression results for chronic diseases showed the same results as those in Tables 1 and 2, both showing a significant negative effect. The variable of education had a negative effect at the 1% statistical level in all four models, indicating that empty nesters with higher education are less likely to improve their life satisfaction through social participation. The higher education may have higher demands on life, and the high demands of life lead to the decrease of life satisfaction; the climbing mentality of empty nesters in the process of interpersonal interaction and the contemporary social climate condition all affect the life satisfaction of empty nesters. The effect of marriage on social integrity was basically consistent with the above regression results, indicating that marriage plays an important role in the health of empty nesters. Religious beliefs passed the significance test in all four models, indicating that religious beliefs can enhance the life satisfaction of empty nesters. Some studies have shown that religion is beneficial to physical and mental health and life happiness, such as quitting smoking and drinking, improvement of moral level, and decrease of divorce rate, etc.
4.3.Endogeneity treatment
Table 5 shows the effects of social participation on the health of empty nesters estimated by two-stage least squares (2SLS). Considering that voluntary participation did not affect the health of empty nesters, this section does not involve the test of voluntary participation. Based on the one-stage F-values of all three models exceeding 10, it can be determined that the regression does not have weak instrumental variables. Based on the p-values of the overidentification test for the three models, it can be determined that the instrumental variables are valid and reliable. The results of the first-stage regression showed that the effect of the instrumental variables was positive, i.e., savings and social relationships would promote economic participation, social participation, and family participation among empty nesters. In the model of economic participation, the results of the second-stage regression show that the coefficient of the effect of economic participation on the health of empty nesters is positive, indicating that economic participation promotes the health of empty nesters. the absolute value of the estimated coefficient of 2SLS is larger than the coefficient of OLS estimation, which indicates that economic participation has a more significant positive effect on the health of empty nesters after using the instrumental variables. The results of the two-stage regression showed that the 6 variables of gender, marriage, education, ethnicity, and pension insurance had a significant effect on the health of empty nesters. Marriage had a significant positive effect on the health of the empty nesters, indicating that the health of the empty nesters with a spouse was better compared to those who had no spouse or did not live with a spouse. Gender had a significant negative effect on the health of empty nesters, indicating that male empty nesters were relatively less likely to be healthy. In the model of social involvement, the effect of social involvement on the health of empty nesters remained positive, i.e., empty nesters who were socially involved were more likely to be healthy, and 2SLS estimates showed a more pronounced effect of social involvement. The effect of chronic disease on the health of empty nesters is significantly negative, suggesting that empty nesters with chronic disease have little likelihood of social engagement to enhance their health. The effect of marriage on the health of empty nesters remained positive. In the model of family involvement, the effect of family involvement on the health of empty nesters is still significantly positive, that is, family involvement is beneficial to enhance the health of empty nesters, and 2SLS estimation shows that the effect of family involvement is more significant. Chronic diseases have a significant negative effect on the health of empty nesters, i.e., empty nesters with chronic diseases are less likely to enhance their health through family involvement. Pension insurance has a positive effect on the health of empty nesters, indicating that empty nesters with pension insurance are more likely to be healthy. From the above study, it was also found that among economic participation, social participation and family participation, none of the health insurance variables had a significant effect on the health of the empty nesters. This is consistent with the results obtained from the underlying regression.