# Exploring the Mechanism Analysis of Men’s Retirement and Physical Activity Participation Based on the IV-Probit Model

Authors: Jinhao Wu
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The issue of population aging is of great concern to all countries in the world, and China is one of the countries with more serious population aging. Under the situation of increasingly serious population aging, we should pay more attention to the life of the elderly after retirement. Paying attention to the health behavior and living conditions of the elderly population will contribute to the process of successful aging. Retirement is a critical point, and the transition period will have different effects on the health of the retired population, with some literature suggesting negative effects on the health of individuals after retirement, and others suggesting positive effects on health. Retirement has caused a lifestyle change in older adults, and few studies have addressed the impact of retirement on individuals’ choices of specific healthy lifestyles, particularly the impact of retirement on physical activity participation. In this study, we used data from the 2015, 2017, and 2018 China Social Tracking Survey (CGSS) to explore the effect of retirement on individual male physical activity participation using the sample size of retired male individuals from the three data periods and using the IV-Probit model. The results showed that retirement had a significant positive effect on individual men’s physical activity participation. In terms of the influence mechanism, physical health, psychological health, active learning during leisure time, and Internet use of retired individuals may be the main reasons for increasing physical activity participation. It provides a channel for China to encourage and support older adults to expand their physical exercise participation after retirement and improve their physical and mental health and to promote the shift of older adults’ postretirement lifestyle toward an active and healthy lifestyle.


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## Body

## 1. Introduction

Population aging is of great concern worldwide, and China is one of the countries with more serious population aging. By the end of 2021, China is a large agricultural country with more than 40% of its population in agriculture, and it is mainly located in rural areas of towns and villages, so it can be said that there is no real national fitness without the strong health of farmers [1]. With the rapid development of China’s economy and society, the phenomenon of aging is emerging, and young people in poor rural areas have to leave their hometowns and start their own business for a better life, which has caused the phenomenon of empty nest elderly in many poor rural areas, which is a problem worthy of social attention. Although economic conditions have improved, they are facing new problems such as empty nest syndrome, reduced care from children, and loneliness. The more frequently they participate in sports activities, the higher the happiness index and the lower the loneliness of the empty nesters. In view of this, we should pay more attention to the postretirement life of the elderly in the face of an increasingly serious population aging [2]. The exercise situation of the elderly in China is shown in Figure 1.Figure 1
The physical exercise situation of retirees from 2015 to 2020.Paying attention to the health behaviors and living conditions of the elderly population will promote the process of successful aging. Retirement is a critical point, and the transition period will have different effects on the health level of the retired population, with some literature suggesting a negative effect on the health level of individuals after retirement, and others suggesting a positive effect on health after retirement [3]. It is evident that the findings of domestic and foreign scholars on this research topic are controversial. The most important feature of the retirement transition is the reduction or loss of occupational routines, income, social connections, and status, and this change in personal status may stimulate changes in behavior, which will influence healthy lifestyle choices [4]. Some scholars have found that retirement makes lifestyle changes such as socializing, sleeping, smoking, and drinking, which affect one’s health level. Our scholar Jinzhen Ye, on the other hand, argued that retirement will change habits that were developed in the short term, and for habits that have persisted over time cannot be changed by the event of retirement alone [5]. The behavioral changes caused by individuals experiencing retirement will also affect the changes in their own health levels, and among these healthy lifestyles, participation in physical activity is one of the most important health behaviors among retired older adults, and exercise is conducive to improving the physical and mental health of individuals, while exercise plays a crucial role in the process of active anti-aging [6]. However, there are few studies investigating the causal relationship between retirement and physical activity participation, in which there is a complex causal relationship between retirement policies and retirement age restrictions on individual participation in physical activity in different countries, which makes it very difficult to identify the effects between the two [7]. An overview of the existing literature mostly explores the effects of retirement on health from empirical quantitative analyses, with less research on causal inferences about health behaviors, such as the lack of literature examining the effects of retirement on physical activity participation. This may be due to the fact that the most difficult issue to identify the effect of retirement on participation in physical activity is model endogeneity [8]. Therefore, the causal effects of physical activity participation can be identified using the mandatory retirement age as an instrumental variable. The methodology for exercise among older adults is shown in Figure 2.Figure 2
Approaches to exercise among older adults.This study uses data from CGSS 2015, 2017, and 2018 to conduct the analysis. The contribution of this study is reflected in, first, the use of the instrumental variables approach to address the endogeneity of the model, which makes the findings robust and error-free. Second, the analysis of the impact of retirement behavior on individual male physical activity participation is helpful to understand the changes in individual male physical activity participation after retirement [9]. Third, to analyze the mechanism causes that affect individual male physical activity participation. Fourth, it provides a channel for China to encourage and support older adults to expand their physical activity participation after retirement and improve their physical and mental health and to promote the change of elderly people’s postretirement lifestyle toward active and healthy.


## 2. Research Background

To promote physical activity participation as a healthy lifestyle, there is little literature that deals with causal inference exploration studies of retirement and physical activity participation alone [10].The literature review is centered on the following sections: first, studies on the impact of retirement on participation in physical activity, which are mostly used in the foreign literature to study the impact relationship between the two using leisure physical activity as a proxy variable for participation in physical activity. The findings are divided into two parts, with some scholars arguing that retirement increases participation in leisure physical activity and others arguing that retirement decreases physical activity participation or that there is little change in exercise participation before and after retirement, and existing studies have not formed consistent conclusions [11]. The reason for the inconsistent findings is partly attributed to the fact that the definition of the concept of physical activity participation has gradually become broader among people of different age groups: participation in physical activity initially included participation in sports or organized exercise; in middle and old age, the scope of physical activity participation was expanded to include activities such as housework, caring for family members and children, or gardening. Another part of the reason is attributed to the slightly different perspectives from which research scholars cut their studies, distinguishing the intensity of exercise participation or the impact on physical activity participation in the long and short term after retirement will cause differences in the results [12]. This is shown in Figure 3.Figure 3
Principles of physical activity among the elderly.Second, the influence of other factors such as family on post-retirement participation in physical activity was studied. According to foreign scholars, spouse’s retirement was found to reduce their personal physical activity. There are also studies where there is no significant correlation between the two, probably due to individual habits, and there are few cases where both spouses participate together or influence each other’s participation in physical activity. Considering the household level, the effect of retirement on physical activity participation has gender differences, which may be due to the fact that physical activity participation after retirement includes household physical activity, which is reflected in higher physical activity participation of men than women after retirement.Third, scholars’ different choices in the selection and use of research methods and research theories for both can cause some bias in the research results. In the descriptive analysis scholars mostly use research methods such as the chi-square test andt-test; in the inferential analysis, they mostly use basic models such as the general linear regression model and logistic regression model for inference. However, descriptive analysis is simple and limited by a single perspective, and it may not be possible to present the correct results in complex cause–effect relationships. One of the most important problems facing the selection of models for inferential analysis is that the models themselves have endogeneity problems, and if they are not solved, then the inferred results will also be biased [13]. Some other scholars have inferred the relationship between the two through qualitative studies, and this approach has some limitations. The theoretical aspect is mainly studied in the theory of health needs. The health analysis theory assumes that the retired group faces two different constraints of time and income when making health investment decisions. Time and income may be important reasons for individuals to reduce/increase their physical activity participation because physical activity participation takes place outside of work hours and the occurrence of retirement behavior lifts the time constraints, meaning that more time can be spent in physical activity [14]. By comparing retired individuals experiencing different retirement life states after retirement, foreign scholars found that individuals who retired to part-time jobs or were in a completely nonworking position had higher rates of physical activity compared to those who remained in full-time jobs after retirement. Since China is a mandatory retirement policy and foreign countries are flexible retirement policies, individuals may have different effects on their attitudes toward physical activity participation when faced with different situations of retirement policies. Foreign scholars have found that mandatory retirement does increase the physical activity of individuals, and it is further noted that the two are mediated through leisure time [15].In summary, the method of causal inference between the postretirement male population and physical activity participation in China has not been fully applied to this field; therefore, the present study on the analysis of the influence and mechanism of postretirement male individuals on physical activity participation will make up for the shortcomings of previous studies and help to explore how the postretirement male population can further maintain their health level and actively promote the successful aging process and improve the healthy living behavior of retired individuals.


## 3. Materials and Methods

### 3.1. Basic Theory

#### 3.1.1. Retirees’ Physical Exercise

With the improvement of people’s living conditions and the improvement of the social medical security system, the life expectancy of the population continues to increase and the number of elderly people continues to grow, which also intensifies the development of aging in the world. Therefore, the physical and mental health, social well-being, and quality of life of older adults are of great concern to society, yet older adults often suffer from physical illness as well as social isolation and family loneliness, and subjective well-being can reflect an individual’s mental health, which is a holistic assessment of the evaluator’s own quality of life based on certain self-defined criteria. In this study, by reviewing the literature, we found that physical activity can improve subjective well-being [16]. For example, Eyler et al. [17] found that after 10 weeks of physical activity, it was able to significantly improve the quality of life and reduce depressive symptoms in older adults. Antunes et al. conducted an experimental study of 46 sedentary older adults aged 60–75 years and found that those who participated in a 6-month experiment with a fitness program had significant decreases in depression and anxiety scores and significant improvements in quality of life, while the control group showed no significant changes. Bandura [18] included data from studies of older adults with only nonclinical conditions, but included data from clinical patients with spinal injuries and related research studies. Based on the existing studies, this meta-analysis study provides the results of empirical studies by foreign scholars in recent years and summarizes the available evidence for the best intervention effect [19]. Suitable sports for older adults are shown in Figure 4.Figure 4
Sports suitable for the elderly.


#### 3.1.2. Main Evaluation Method

This study uses algorithms of neural networks in addition to the IV-Probit model for computational probing. All other kinds of algorithms require relevant mathematical mapping relationships. The artificial neural network algorithm involved in this study does not require a large number of mathematical mapping relations, so it does not need to input a large number of mathematical equations in the first place, because it needs to be able to learn some additional basic mathematical rules systematically through the training of data in advance, so that it can output the required mathematical calculation results and simulate the mathematical model better given certain function values and mathematical function values. One of the main core functions of artificial neural networks, as a relatively complex discipline in computer science and mathematics and statistics, when performing mathematical calculations and information statistics, is the training algorithm [20].The process of the BP algorithm mainly consists of output signal, error forward, and backward linear propagation process. That is, the signal error can be adjusted according to the two input directions from the actual input signal direction to the actual expected signal output, respectively, to calculate the signal output, from the direction of the real expected signal output and then to the real expected input direction of the two directions, respectively, to calculate the signal error to adjust the signal error weight range and error threshold. In the study of the propagation method after the forward superposition of the signal, the input node signal is mainly the node on the actual output of the signal after the inverse superposition through the role of the hidden layer, and the actual output node signal can be generated through the non-linear transformation process [21]. If we find that the actual signal output node position does not coincide with the actual output node direction position of the actual input node expectation signal, the process of backward feed-back propagation method for signal error compensation will be easily generated. The principle of error input signal back propagation processing system is that the system will automatically back propagate its various output signals or error information values to each error input layer of the system through the hidden layer nodes layer by layer, and will sequentially transfer its output error signal value distribution to the nodes on each layer corresponding to all other layers of the system error input signal elements, with the system in each layer of the system nodes obtained. The output error input signal values obtained by the system at each layer node are used as the basis for its calculation to automatically adjust the weights among the system’s error output signal elements [22].Neural network is essentially a nonlinear predictive model and, as its name suggests, an algorithm that imitates the human and animal nervous systems for computation. It is based on imitating the human and animal-like brain neural network system to perform the computation and then to process the content of each module. Neural network algorithm is a derivative of data mining technology, which is one of the types of data mining technology that can be used for big data mining, such as analysis, classification, aggregation, and other data mining functions. Its advantages and disadvantages are very clear, the first advantage is that it is extremely resistant to interference, and the second is that it is capable of deep learning and better memory in a nonlinear situation, and can handle more complex situations. At the same time, it has two disadvantages. First, its computation and processing results are low-dimensional and cannot be adapted to a high-dimensional environment, so it has a hard-to-interpret nature. The second is that whether it is supervised or unsupervised learning, it requires a long learning time and the data are collected using a more traditional neural network approach.In this study, we use fuzzy neural networks. This type of neural network (FNN for short) is first, a deep combination of fuzzy theory and neural network algorithms. In the process of data mining and information processing by neural network algorithms, fuzzy theory is incorporated to improve the mapping and the relevance of mathematical relationships. The efficiency of supervised learning and unsupervised learning is better improved. The algorithmic formulas of such neural networks and the related structural diagrams are more commonly used and common and can be found in general textbooks. This type of neural network is shown in the figure, and it goes through five layers in supervised and unsupervised learning. In the beginning two layers, the required computational range doubles as the number of layers increases, but gradually decreases as it enters the third, fourth, and fifth layers. Of course this type of graph is first tested for dimensionality at this node in the input layer when the input is made. The specific value assumes that the dimension value isn and the node that needs to be input is n. Depending on the number of nodes needed, it is passed all the way to the layer of the dimensionality function and the related layer of further computed functions, as well as finally to the output layer. This type of fuzzy theory combined neural network has the same nature as the wavelet neural network and the neural network combined with the generalized theory, which both use the traditional gradient form of computation downward to calculate the centroid of the affiliation and the associated required width value and the final output value and the weights that we need. This is shown in Figure 5.Figure 5
Fuzzy neural network.


### 3.2. Model Setting and Variable Selection

In order to solve the endogeneity problem with unbiased estimation in the above study, instrumental variables are selected in this study to solve the endogeneity problem. Because of the unique advantages of the instrumental variables approach used in this study compared to the limitations of other research methods, the data in this study have exceptionally excellent statistical significance.


#### 3.2.1. Model Setting

A Probit model of whether retired male individuals participate in physical activity was first established with the following standard normal distribution equation:(1)Pyi=1=Φβ0+β1Si+β2Xi,where yi=1 indicates that retired men i have participated in physical activity. Si denotes whether retired Xi or not is a series of personal and other variables such as age, education, income, and health self-satisfaction. Equation (1) can actually be written in the following form:(2)yi∗=β0+β1Si+β2Xi+εi,yi=1yi∗>0,where εi is the yi∗ error term, then yi∗>0 is a latent variable, yi=1, i.e., if, then, the unbiased estimator CovSi,εi=0 is obtained. And the instrumental variable probability ratio model (IV-Probit model) can be represented by the following set of equations:(3)yi∗=β0+β1Si+β2Xi+εi,yi=1yi∗>0,(4)Si=γ0+γ1Zi+γ2Xi+ε.In this system of equations, mustCovZi,εi=0 satisfy, Covε,εi=0 and. CovZi,Si≠0. Using the two-stage method, equation (4) is regressed in the first stage and then the Si predicted values Si∧=y0∧+y1∧Zi+y2∧Xi are obtained. In the second stage, the used inside Si equation Si∧ (3) is regressed after replacing it to obtain the unbiased estimator.


#### 3.2.2. Data Sources

The data used in this study are all reference data and processed data. The source of the data in this study is mainly from a demographic research institute of a university in Beijing. The relevant statistics conducted include those of a project with a three-year period. The project covered more than 400 villages and related village committees, and each village committee also surveyed more than 20 households. A total sample size of 40,762 was obtained. The data covered basic personal information, family situation, health, work, retirement, and community information for people aged 17–117 years. After eliminating the samples with missing data, this study finally determined and collated 29,419 valid sample data.


#### 3.2.3. Variable Definition and Descriptive Statistics

Dependent variable: physical activity participation. This study focuses on the impact of retirement on physical activity participation. This study uses the combined data from CGSS 2015, 2017, and 2018 to measure this indicator of physical activity participation. The answers to the questions in the original questionnaire were divided into five categories, and this study re-established a dichotomous variable as the dependent variable through the above questions and answers, where residents who had participated in exercise, regardless of frequency, were recorded as 1; those who did not participate once or never participated in exercise were recorded as 0.Independent variable: retirement variable. In this study, the retirement variable was reassigned as a dichotomous variable, and the selection item retired was defined as the retirement status and reassigned as 0. The rest of the variables were set as the active status and assigned as 1.(1) Control Variables: demographics, socioeconomic status, and self-health level. There are many factors affecting retirement and physical activity participation that must be controlled for in the model as much as possible, and the control variables in this study include three categories.This study examines the effect of retirement on physical activity participation in the male population, so the gender all retains the male sample size. The average age among retired men was around 67 years old, and individual men with partners were higher than working men, with education levels basically close to the secondary school level. The education levels were classified as elementary school and below education, secondary school, and university and above, where secondary school included middle school and high school.Socioeconomic status characteristics variables including household registration and so on are not normally distributed. The province of residence, according to economic development, is divided into eastern, central, and western regions.Health and behavioral characteristics variables: respondents’ self-evaluation of health and social activities (Internet use) in their free time were included. Activities engaged in during free time included Internet use and study, both of which were assigned as dichotomous variables.


## 3.1. Basic Theory

### 3.1.1. Retirees’ Physical Exercise

With the improvement of people’s living conditions and the improvement of the social medical security system, the life expectancy of the population continues to increase and the number of elderly people continues to grow, which also intensifies the development of aging in the world. Therefore, the physical and mental health, social well-being, and quality of life of older adults are of great concern to society, yet older adults often suffer from physical illness as well as social isolation and family loneliness, and subjective well-being can reflect an individual’s mental health, which is a holistic assessment of the evaluator’s own quality of life based on certain self-defined criteria. In this study, by reviewing the literature, we found that physical activity can improve subjective well-being [16]. For example, Eyler et al. [17] found that after 10 weeks of physical activity, it was able to significantly improve the quality of life and reduce depressive symptoms in older adults. Antunes et al. conducted an experimental study of 46 sedentary older adults aged 60–75 years and found that those who participated in a 6-month experiment with a fitness program had significant decreases in depression and anxiety scores and significant improvements in quality of life, while the control group showed no significant changes. Bandura [18] included data from studies of older adults with only nonclinical conditions, but included data from clinical patients with spinal injuries and related research studies. Based on the existing studies, this meta-analysis study provides the results of empirical studies by foreign scholars in recent years and summarizes the available evidence for the best intervention effect [19]. Suitable sports for older adults are shown in Figure 4.Figure 4
Sports suitable for the elderly.


### 3.1.2. Main Evaluation Method

This study uses algorithms of neural networks in addition to the IV-Probit model for computational probing. All other kinds of algorithms require relevant mathematical mapping relationships. The artificial neural network algorithm involved in this study does not require a large number of mathematical mapping relations, so it does not need to input a large number of mathematical equations in the first place, because it needs to be able to learn some additional basic mathematical rules systematically through the training of data in advance, so that it can output the required mathematical calculation results and simulate the mathematical model better given certain function values and mathematical function values. One of the main core functions of artificial neural networks, as a relatively complex discipline in computer science and mathematics and statistics, when performing mathematical calculations and information statistics, is the training algorithm [20].The process of the BP algorithm mainly consists of output signal, error forward, and backward linear propagation process. That is, the signal error can be adjusted according to the two input directions from the actual input signal direction to the actual expected signal output, respectively, to calculate the signal output, from the direction of the real expected signal output and then to the real expected input direction of the two directions, respectively, to calculate the signal error to adjust the signal error weight range and error threshold. In the study of the propagation method after the forward superposition of the signal, the input node signal is mainly the node on the actual output of the signal after the inverse superposition through the role of the hidden layer, and the actual output node signal can be generated through the non-linear transformation process [21]. If we find that the actual signal output node position does not coincide with the actual output node direction position of the actual input node expectation signal, the process of backward feed-back propagation method for signal error compensation will be easily generated. The principle of error input signal back propagation processing system is that the system will automatically back propagate its various output signals or error information values to each error input layer of the system through the hidden layer nodes layer by layer, and will sequentially transfer its output error signal value distribution to the nodes on each layer corresponding to all other layers of the system error input signal elements, with the system in each layer of the system nodes obtained. The output error input signal values obtained by the system at each layer node are used as the basis for its calculation to automatically adjust the weights among the system’s error output signal elements [22].Neural network is essentially a nonlinear predictive model and, as its name suggests, an algorithm that imitates the human and animal nervous systems for computation. It is based on imitating the human and animal-like brain neural network system to perform the computation and then to process the content of each module. Neural network algorithm is a derivative of data mining technology, which is one of the types of data mining technology that can be used for big data mining, such as analysis, classification, aggregation, and other data mining functions. Its advantages and disadvantages are very clear, the first advantage is that it is extremely resistant to interference, and the second is that it is capable of deep learning and better memory in a nonlinear situation, and can handle more complex situations. At the same time, it has two disadvantages. First, its computation and processing results are low-dimensional and cannot be adapted to a high-dimensional environment, so it has a hard-to-interpret nature. The second is that whether it is supervised or unsupervised learning, it requires a long learning time and the data are collected using a more traditional neural network approach.In this study, we use fuzzy neural networks. This type of neural network (FNN for short) is first, a deep combination of fuzzy theory and neural network algorithms. In the process of data mining and information processing by neural network algorithms, fuzzy theory is incorporated to improve the mapping and the relevance of mathematical relationships. The efficiency of supervised learning and unsupervised learning is better improved. The algorithmic formulas of such neural networks and the related structural diagrams are more commonly used and common and can be found in general textbooks. This type of neural network is shown in the figure, and it goes through five layers in supervised and unsupervised learning. In the beginning two layers, the required computational range doubles as the number of layers increases, but gradually decreases as it enters the third, fourth, and fifth layers. Of course this type of graph is first tested for dimensionality at this node in the input layer when the input is made. The specific value assumes that the dimension value isn and the node that needs to be input is n. Depending on the number of nodes needed, it is passed all the way to the layer of the dimensionality function and the related layer of further computed functions, as well as finally to the output layer. This type of fuzzy theory combined neural network has the same nature as the wavelet neural network and the neural network combined with the generalized theory, which both use the traditional gradient form of computation downward to calculate the centroid of the affiliation and the associated required width value and the final output value and the weights that we need. This is shown in Figure 5.Figure 5
Fuzzy neural network.


## 3.1.1. Retirees’ Physical Exercise

With the improvement of people’s living conditions and the improvement of the social medical security system, the life expectancy of the population continues to increase and the number of elderly people continues to grow, which also intensifies the development of aging in the world. Therefore, the physical and mental health, social well-being, and quality of life of older adults are of great concern to society, yet older adults often suffer from physical illness as well as social isolation and family loneliness, and subjective well-being can reflect an individual’s mental health, which is a holistic assessment of the evaluator’s own quality of life based on certain self-defined criteria. In this study, by reviewing the literature, we found that physical activity can improve subjective well-being [16]. For example, Eyler et al. [17] found that after 10 weeks of physical activity, it was able to significantly improve the quality of life and reduce depressive symptoms in older adults. Antunes et al. conducted an experimental study of 46 sedentary older adults aged 60–75 years and found that those who participated in a 6-month experiment with a fitness program had significant decreases in depression and anxiety scores and significant improvements in quality of life, while the control group showed no significant changes. Bandura [18] included data from studies of older adults with only nonclinical conditions, but included data from clinical patients with spinal injuries and related research studies. Based on the existing studies, this meta-analysis study provides the results of empirical studies by foreign scholars in recent years and summarizes the available evidence for the best intervention effect [19]. Suitable sports for older adults are shown in Figure 4.Figure 4
Sports suitable for the elderly.


## 3.1.2. Main Evaluation Method

This study uses algorithms of neural networks in addition to the IV-Probit model for computational probing. All other kinds of algorithms require relevant mathematical mapping relationships. The artificial neural network algorithm involved in this study does not require a large number of mathematical mapping relations, so it does not need to input a large number of mathematical equations in the first place, because it needs to be able to learn some additional basic mathematical rules systematically through the training of data in advance, so that it can output the required mathematical calculation results and simulate the mathematical model better given certain function values and mathematical function values. One of the main core functions of artificial neural networks, as a relatively complex discipline in computer science and mathematics and statistics, when performing mathematical calculations and information statistics, is the training algorithm [20].The process of the BP algorithm mainly consists of output signal, error forward, and backward linear propagation process. That is, the signal error can be adjusted according to the two input directions from the actual input signal direction to the actual expected signal output, respectively, to calculate the signal output, from the direction of the real expected signal output and then to the real expected input direction of the two directions, respectively, to calculate the signal error to adjust the signal error weight range and error threshold. In the study of the propagation method after the forward superposition of the signal, the input node signal is mainly the node on the actual output of the signal after the inverse superposition through the role of the hidden layer, and the actual output node signal can be generated through the non-linear transformation process [21]. If we find that the actual signal output node position does not coincide with the actual output node direction position of the actual input node expectation signal, the process of backward feed-back propagation method for signal error compensation will be easily generated. The principle of error input signal back propagation processing system is that the system will automatically back propagate its various output signals or error information values to each error input layer of the system through the hidden layer nodes layer by layer, and will sequentially transfer its output error signal value distribution to the nodes on each layer corresponding to all other layers of the system error input signal elements, with the system in each layer of the system nodes obtained. The output error input signal values obtained by the system at each layer node are used as the basis for its calculation to automatically adjust the weights among the system’s error output signal elements [22].Neural network is essentially a nonlinear predictive model and, as its name suggests, an algorithm that imitates the human and animal nervous systems for computation. It is based on imitating the human and animal-like brain neural network system to perform the computation and then to process the content of each module. Neural network algorithm is a derivative of data mining technology, which is one of the types of data mining technology that can be used for big data mining, such as analysis, classification, aggregation, and other data mining functions. Its advantages and disadvantages are very clear, the first advantage is that it is extremely resistant to interference, and the second is that it is capable of deep learning and better memory in a nonlinear situation, and can handle more complex situations. At the same time, it has two disadvantages. First, its computation and processing results are low-dimensional and cannot be adapted to a high-dimensional environment, so it has a hard-to-interpret nature. The second is that whether it is supervised or unsupervised learning, it requires a long learning time and the data are collected using a more traditional neural network approach.In this study, we use fuzzy neural networks. This type of neural network (FNN for short) is first, a deep combination of fuzzy theory and neural network algorithms. In the process of data mining and information processing by neural network algorithms, fuzzy theory is incorporated to improve the mapping and the relevance of mathematical relationships. The efficiency of supervised learning and unsupervised learning is better improved. The algorithmic formulas of such neural networks and the related structural diagrams are more commonly used and common and can be found in general textbooks. This type of neural network is shown in the figure, and it goes through five layers in supervised and unsupervised learning. In the beginning two layers, the required computational range doubles as the number of layers increases, but gradually decreases as it enters the third, fourth, and fifth layers. Of course this type of graph is first tested for dimensionality at this node in the input layer when the input is made. The specific value assumes that the dimension value isn and the node that needs to be input is n. Depending on the number of nodes needed, it is passed all the way to the layer of the dimensionality function and the related layer of further computed functions, as well as finally to the output layer. This type of fuzzy theory combined neural network has the same nature as the wavelet neural network and the neural network combined with the generalized theory, which both use the traditional gradient form of computation downward to calculate the centroid of the affiliation and the associated required width value and the final output value and the weights that we need. This is shown in Figure 5.Figure 5
Fuzzy neural network.


## 3.2. Model Setting and Variable Selection

In order to solve the endogeneity problem with unbiased estimation in the above study, instrumental variables are selected in this study to solve the endogeneity problem. Because of the unique advantages of the instrumental variables approach used in this study compared to the limitations of other research methods, the data in this study have exceptionally excellent statistical significance.


### 3.2.1. Model Setting

A Probit model of whether retired male individuals participate in physical activity was first established with the following standard normal distribution equation:(1)Pyi=1=Φβ0+β1Si+β2Xi,where yi=1 indicates that retired men i have participated in physical activity. Si denotes whether retired Xi or not is a series of personal and other variables such as age, education, income, and health self-satisfaction. Equation (1) can actually be written in the following form:(2)yi∗=β0+β1Si+β2Xi+εi,yi=1yi∗>0,where εi is the yi∗ error term, then yi∗>0 is a latent variable, yi=1, i.e., if, then, the unbiased estimator CovSi,εi=0 is obtained. And the instrumental variable probability ratio model (IV-Probit model) can be represented by the following set of equations:(3)yi∗=β0+β1Si+β2Xi+εi,yi=1yi∗>0,(4)Si=γ0+γ1Zi+γ2Xi+ε.In this system of equations, mustCovZi,εi=0 satisfy, Covε,εi=0 and. CovZi,Si≠0. Using the two-stage method, equation (4) is regressed in the first stage and then the Si predicted values Si∧=y0∧+y1∧Zi+y2∧Xi are obtained. In the second stage, the used inside Si equation Si∧ (3) is regressed after replacing it to obtain the unbiased estimator.


### 3.2.2. Data Sources

The data used in this study are all reference data and processed data. The source of the data in this study is mainly from a demographic research institute of a university in Beijing. The relevant statistics conducted include those of a project with a three-year period. The project covered more than 400 villages and related village committees, and each village committee also surveyed more than 20 households. A total sample size of 40,762 was obtained. The data covered basic personal information, family situation, health, work, retirement, and community information for people aged 17–117 years. After eliminating the samples with missing data, this study finally determined and collated 29,419 valid sample data.


### 3.2.3. Variable Definition and Descriptive Statistics

Dependent variable: physical activity participation. This study focuses on the impact of retirement on physical activity participation. This study uses the combined data from CGSS 2015, 2017, and 2018 to measure this indicator of physical activity participation. The answers to the questions in the original questionnaire were divided into five categories, and this study re-established a dichotomous variable as the dependent variable through the above questions and answers, where residents who had participated in exercise, regardless of frequency, were recorded as 1; those who did not participate once or never participated in exercise were recorded as 0.Independent variable: retirement variable. In this study, the retirement variable was reassigned as a dichotomous variable, and the selection item retired was defined as the retirement status and reassigned as 0. The rest of the variables were set as the active status and assigned as 1.(1) Control Variables: demographics, socioeconomic status, and self-health level. There are many factors affecting retirement and physical activity participation that must be controlled for in the model as much as possible, and the control variables in this study include three categories.This study examines the effect of retirement on physical activity participation in the male population, so the gender all retains the male sample size. The average age among retired men was around 67 years old, and individual men with partners were higher than working men, with education levels basically close to the secondary school level. The education levels were classified as elementary school and below education, secondary school, and university and above, where secondary school included middle school and high school.Socioeconomic status characteristics variables including household registration and so on are not normally distributed. The province of residence, according to economic development, is divided into eastern, central, and western regions.Health and behavioral characteristics variables: respondents’ self-evaluation of health and social activities (Internet use) in their free time were included. Activities engaged in during free time included Internet use and study, both of which were assigned as dichotomous variables.


## 3.2.1. Model Setting

A Probit model of whether retired male individuals participate in physical activity was first established with the following standard normal distribution equation:(1)Pyi=1=Φβ0+β1Si+β2Xi,where yi=1 indicates that retired men i have participated in physical activity. Si denotes whether retired Xi or not is a series of personal and other variables such as age, education, income, and health self-satisfaction. Equation (1) can actually be written in the following form:(2)yi∗=β0+β1Si+β2Xi+εi,yi=1yi∗>0,where εi is the yi∗ error term, then yi∗>0 is a latent variable, yi=1, i.e., if, then, the unbiased estimator CovSi,εi=0 is obtained. And the instrumental variable probability ratio model (IV-Probit model) can be represented by the following set of equations:(3)yi∗=β0+β1Si+β2Xi+εi,yi=1yi∗>0,(4)Si=γ0+γ1Zi+γ2Xi+ε.In this system of equations, mustCovZi,εi=0 satisfy, Covε,εi=0 and. CovZi,Si≠0. Using the two-stage method, equation (4) is regressed in the first stage and then the Si predicted values Si∧=y0∧+y1∧Zi+y2∧Xi are obtained. In the second stage, the used inside Si equation Si∧ (3) is regressed after replacing it to obtain the unbiased estimator.


## 3.2.2. Data Sources

The data used in this study are all reference data and processed data. The source of the data in this study is mainly from a demographic research institute of a university in Beijing. The relevant statistics conducted include those of a project with a three-year period. The project covered more than 400 villages and related village committees, and each village committee also surveyed more than 20 households. A total sample size of 40,762 was obtained. The data covered basic personal information, family situation, health, work, retirement, and community information for people aged 17–117 years. After eliminating the samples with missing data, this study finally determined and collated 29,419 valid sample data.


## 3.2.3. Variable Definition and Descriptive Statistics

Dependent variable: physical activity participation. This study focuses on the impact of retirement on physical activity participation. This study uses the combined data from CGSS 2015, 2017, and 2018 to measure this indicator of physical activity participation. The answers to the questions in the original questionnaire were divided into five categories, and this study re-established a dichotomous variable as the dependent variable through the above questions and answers, where residents who had participated in exercise, regardless of frequency, were recorded as 1; those who did not participate once or never participated in exercise were recorded as 0.Independent variable: retirement variable. In this study, the retirement variable was reassigned as a dichotomous variable, and the selection item retired was defined as the retirement status and reassigned as 0. The rest of the variables were set as the active status and assigned as 1.(1) Control Variables: demographics, socioeconomic status, and self-health level. There are many factors affecting retirement and physical activity participation that must be controlled for in the model as much as possible, and the control variables in this study include three categories.This study examines the effect of retirement on physical activity participation in the male population, so the gender all retains the male sample size. The average age among retired men was around 67 years old, and individual men with partners were higher than working men, with education levels basically close to the secondary school level. The education levels were classified as elementary school and below education, secondary school, and university and above, where secondary school included middle school and high school.Socioeconomic status characteristics variables including household registration and so on are not normally distributed. The province of residence, according to economic development, is divided into eastern, central, and western regions.Health and behavioral characteristics variables: respondents’ self-evaluation of health and social activities (Internet use) in their free time were included. Activities engaged in during free time included Internet use and study, both of which were assigned as dichotomous variables.


## 4. Results and Discussion

### 4.1. Analysis of Descriptive Statistical Results

Instrumental variable: statutory retirement age. According to the experience of instrumental variables often used in previous literature, this study chooses the statutory retirement age as the instrumental variable.This time, the retirees, specific physical exercise participation, household registration, marriage, education, health, depression, learning status, and Internet use were statistically analyzed, as shown in Figure6.Figure 6
Descriptive statistical analysis of retiree variables.The specific physical exercise participation, household registration, marriage, education, health, depression, learning status, and Internet use of on-the-job personnel were statistically analyzed, as shown in Figure7.Figure 7
Descriptive statistical analysis of on-job variables.In this study, the specific physical exercise participation, household registration, marriage, educational background, health, depression, learning status, and Internet use were statistically analyzed, as shown in Figure8.Figure 8
Descriptive statistical analysis of common variables of retirees and active personnel.In the description of model variables in this study, the first is the explained variable, physical exercise participation variable is a classification variable, representing in the past year, do you often engage in the following activities in your spare time, namely physical exercise 0 = do not participate in physical exercise; 1. Get physical. The second is the explanatory variable (endogenous); retirement is a categorical variable, representing the reason why you did not work last week 0 = in-service; 1 = retirement. Third, the explanatory variable (exogenous): (1) age is a continuous variable, unit: years. (2) Educational background is a categorical variable, 1 = primary school or below; 2 = middle school; University degree or above. (3) Marriage is a categorical variable, 0 = no partner; 1. (4) Household is a classification variable, 0 = agricultural household; 1 = nonagricultural household. (5) Region is a categorical variable, 1 = eastern region; 2. 3 = Western Region. (6) Health was a categorical variable, 0 = NO; 1 = yes. (7) Depression was a categorical variable, 0 = depression; 1 = no depression. (8) Learning status is a categorical variable, 0 = no learning; 1 = learning. (9) Internet use is a categorical variable, 0 = does not apply to the Internet. (10) Income is a continuous variable, unit: ten thousand yuan/year. Finally, the age of 60 for men as the legal retirement age is a categorical variable.


### 4.2. Estimated Results of the IV-Probit Model

The statistical results in this study have good statistical significance, where∗∗∗P<0.01, ∗∗P<0.05, P∗<0.1. This study presents the one-stage regression results of the IV-Probit model. The results of the first stage regression can also understand which factors are associated with the decision to participate in physical exercise. The level of annual income, the level of development in the region, and the level of health will have a significant positive impact on individuals’ participation in physical exercise after retirement. The parameter of age is significantly negative, indicating that the opportunity to participate in physical exercise decreases with the increase of individual age, which is consistent with the trend of people reducing physical activity with the increase of age. The coefficients of the first-stage regression instrumental variables were significant at a 1% level.This study presents the two-stage regression results of the IV-Probit model. Except for age square and marital status, the coefficients of other variables are significant at a 1% level, age is negative, and other variables are positive. In other words, the individual’s income, health level, years of education, and the area where they live after retirement all have a positive impact on physical exercise participation.In the analysis of the effect of retirement on physical exercise, variable names mainly include household registration (refer to: agricultural household registration): nonagricultural household registration, whose Probit model value is 0.411(13.70)∗∗∗, IV-Probit model value is 0.254(0.045)∗∗∗; Age, its Probit model value is −0.019(−4.08)∗∗∗, IV-Probit model value is −0.007(0.005)∗∗∗; Education background (refer to primary school and below): High school, its Probit model value is 0.236(0.029)∗∗∗, IV-Probit model value is 0.167(0.034)∗∗∗, university and above, its Probit model value is 0.851(0.047)∗∗∗, IV-Probit model value was 0.851(0.047)∗∗∗; Marriage (reference: no partner): there is a partner, whose Probit model value is −0.038(0.034), IV-Probit model value is −0.037(0.034); Region (see Western Region): in the eastern region, the Probit model value is 0.119(0.029)∗∗∗, IV-Probit model value is 0.105(0.029)∗∗∗, in the central region, the Probit model value is 0.118(0.032)∗∗∗, IV-Probit model value is 0.126(0.033)∗∗∗; Income, its Probit model value is 0.130(0.043)∗∗∗, IV-Probit model value is 0.088(0.017)∗∗∗; Retirement status (refer to: in-service): retirement, its Probit model value is 0.418(0.043)∗∗∗, IV-Probit model value is 1.167(0.178)∗∗∗; Health (reference: unhealthy): health, its Probit model value is 0.277(0.034)∗∗∗, IV-Probit model value is 0.259(0.034)∗∗∗.


### 4.3. Test of Tool Variables

Among many methods to identify causality, the IV instrumental variable has obvious advantages. Therefore, this study selects tool variables to solve the endogeneity problem of the model, and the function of tool variables after use will carry out an unbiased estimation of the estimation results. According to the experience of selecting instrumental variables in the previous relevant literature, this study chooses the statutory retirement age as the instrumental variable because legal retirement age is an exogenous variable under China’s compulsory retirement policy. Statutory retirement age is correlated with retirement but does not have a direct impact on the dependent variable physical exercise participation.One, the Hausman test of Endo-CAVALIer shows that the value of different is IV-Probit minus Probit. Nonagricultural household different value is −0.155; age difference value is 0.009; the different value of educational background is −0.008; the difference of having a partner is −0.006; the difference value of eastern region is −0.016; difference value of western region is −0.023; income difference value is −0.047; health difference is −0.047, and overallP value is 0.0046.The results show thatP=0.0046<0.05, rejecting null hypothesis H0: there is no systematic difference between a single equation and an instrumental variable equation. The results do differ, so instrumental-variable estimates should be adopted. The F statistic was significantly larger than the empirical value of 10 and significant at 1% P<0.001. That is to say, the instrumental variables selected in this study are strongly correlated with the dependent variables and will not lead to bias in the result estimators.


### 4.4. Mechanism Analysis of Influence of Retirement on Male Participation in Physical Exercise

Based on the above analysis results, it is found that the retirement variable has a significant positive impact on participation in physical exercise. Meanwhile, this study solves the endogeneity problem through an instrumental variable method, proving the causal relationship between the two. It is because of the unbiased estimation and the proof of the causal relationship between the two that the limitations of previous literature research can lay a foundation for the following mechanism research and analysis of this study. What is the influence mechanism of retirement on physical exercise participation? This study summarizes the following aspects from numerous studies. The first aspect of this study considers the physical and mental health of retired individuals. After retirement, the change in individual identity and status may stimulate the change of behavior, including physical exercise. The interaction between physical health variables and mental health variables (depression degree) and retirement variables was taken as the core independent variables affecting retired male individuals’ participation in physical exercise, and Probit regression analysis was conducted. If retirement affects residents’ participation in physical exercise through the above variables, then regression will show that the positive influence of variables interacting with retirement should be larger or further significant.In the first two models, the health variable and the depression variable interact with the retirement variable, respectively, and the retirement variable and their interaction variables show significant differences after controlling for demographic variablesP<0.001. Compared with reference variables, dissatisfaction with one’s own health status after retirement will significantly positively affect physical exercise participation behavior. According to the health needs theory, the investment in health after retirement depends on the marginal value of time and the importance that individuals attach to maintaining health. There is plenty of time after retirement, and individuals will increase their awareness of the importance of health as they get older and more experienced. So individuals will increase their participation in postretirement physical activity with the combined effect of more time and increased health awareness. After retirement, individuals who are satisfied with their own health will also increase their participation in physical exercise, which will increase their exercise behavior by 0.54 compared with those who are not satisfied with their own health. The difference between the two is because the choice of physical exercise behavior has been widely considered as an important nonmedical factor of health, physical exercise has become both a way for healthy people to further improve their health level and a way for unhealthy people to improve their health level. Foreign literature points out that individuals actively pursue their own hobbies and participate in sports activities after retirement, which have beneficial effects on physical and mental health. There is no significant difference in the influence coefficient of physical exercise between individuals without depression and those with depression after retirement, but both of them are significant at 1% level. In general, nondepressed individuals tend to engage in more physical activity than depressed individuals. Because physical activity may have an anti-depressant effect, retired individuals should actively play the anti-depressant effect of physical exercise and increase their participation in physical exercise in order to prevent depression. Some domestic and foreign scholars believe that retirement shock has a negative impact on men’s mental health. After retirement, men can regularly participate in physical exercise and reduce depression due to the disappearance of work pressure and the increase of time flexibility.In the latter two models, based on the subversive change of individual roles after retirement, the retired elderly are encouraged to continue to learn new skills and update their knowledge and concepts in order to better adapt to the aging life. This study chooses learning and Internet use as two variables for mechanism analysis. Learning variables and Internet use variables interoperated with retirement variables. Controlling for demographic variables, retired individuals’ Internet use had a significant positive effect on physical exercise participationP<0.001. This is in line with the findings of scholars WANG Shiqiang and KEARNS that the Internet promotes physical activity participation among older adults and increases the frequency of exercise. The impact of Internet use by retired individuals on physical activity participation increased by 0.47 compared to no Internet use, which is due to the fact that the Internet changes the values of retired older adults; accesses more information about physical activity; improves cognitive abilities; and also increases social activities of older adults, so it also promotes their physical and mental health more. Under the influence of learning factors, retirement and learning interacted, and controlling for demographic variables, active learning among retired individuals would have a significant positive effect on physical activity participation P<0.001. This is consistent with the findings of foreign scholars that active learning can improve health literacy, increase physical activity, and promote healthy lifestyles among older adults. This is because high health literacy is associated with good health behaviors. Learning is not only the ability to understand health information, but also includes the ability to assess and apply health information. This explains the 0.51 difference between learning and not learning respectively and retirement interaction on physical activity participation. Active and positive learning is very effective in increasing physical activity.


## 4.1. Analysis of Descriptive Statistical Results

Instrumental variable: statutory retirement age. According to the experience of instrumental variables often used in previous literature, this study chooses the statutory retirement age as the instrumental variable.This time, the retirees, specific physical exercise participation, household registration, marriage, education, health, depression, learning status, and Internet use were statistically analyzed, as shown in Figure6.Figure 6
Descriptive statistical analysis of retiree variables.The specific physical exercise participation, household registration, marriage, education, health, depression, learning status, and Internet use of on-the-job personnel were statistically analyzed, as shown in Figure7.Figure 7
Descriptive statistical analysis of on-job variables.In this study, the specific physical exercise participation, household registration, marriage, educational background, health, depression, learning status, and Internet use were statistically analyzed, as shown in Figure8.Figure 8
Descriptive statistical analysis of common variables of retirees and active personnel.In the description of model variables in this study, the first is the explained variable, physical exercise participation variable is a classification variable, representing in the past year, do you often engage in the following activities in your spare time, namely physical exercise 0 = do not participate in physical exercise; 1. Get physical. The second is the explanatory variable (endogenous); retirement is a categorical variable, representing the reason why you did not work last week 0 = in-service; 1 = retirement. Third, the explanatory variable (exogenous): (1) age is a continuous variable, unit: years. (2) Educational background is a categorical variable, 1 = primary school or below; 2 = middle school; University degree or above. (3) Marriage is a categorical variable, 0 = no partner; 1. (4) Household is a classification variable, 0 = agricultural household; 1 = nonagricultural household. (5) Region is a categorical variable, 1 = eastern region; 2. 3 = Western Region. (6) Health was a categorical variable, 0 = NO; 1 = yes. (7) Depression was a categorical variable, 0 = depression; 1 = no depression. (8) Learning status is a categorical variable, 0 = no learning; 1 = learning. (9) Internet use is a categorical variable, 0 = does not apply to the Internet. (10) Income is a continuous variable, unit: ten thousand yuan/year. Finally, the age of 60 for men as the legal retirement age is a categorical variable.


## 4.2. Estimated Results of the IV-Probit Model

The statistical results in this study have good statistical significance, where∗∗∗P<0.01, ∗∗P<0.05, P∗<0.1. This study presents the one-stage regression results of the IV-Probit model. The results of the first stage regression can also understand which factors are associated with the decision to participate in physical exercise. The level of annual income, the level of development in the region, and the level of health will have a significant positive impact on individuals’ participation in physical exercise after retirement. The parameter of age is significantly negative, indicating that the opportunity to participate in physical exercise decreases with the increase of individual age, which is consistent with the trend of people reducing physical activity with the increase of age. The coefficients of the first-stage regression instrumental variables were significant at a 1% level.This study presents the two-stage regression results of the IV-Probit model. Except for age square and marital status, the coefficients of other variables are significant at a 1% level, age is negative, and other variables are positive. In other words, the individual’s income, health level, years of education, and the area where they live after retirement all have a positive impact on physical exercise participation.In the analysis of the effect of retirement on physical exercise, variable names mainly include household registration (refer to: agricultural household registration): nonagricultural household registration, whose Probit model value is 0.411(13.70)∗∗∗, IV-Probit model value is 0.254(0.045)∗∗∗; Age, its Probit model value is −0.019(−4.08)∗∗∗, IV-Probit model value is −0.007(0.005)∗∗∗; Education background (refer to primary school and below): High school, its Probit model value is 0.236(0.029)∗∗∗, IV-Probit model value is 0.167(0.034)∗∗∗, university and above, its Probit model value is 0.851(0.047)∗∗∗, IV-Probit model value was 0.851(0.047)∗∗∗; Marriage (reference: no partner): there is a partner, whose Probit model value is −0.038(0.034), IV-Probit model value is −0.037(0.034); Region (see Western Region): in the eastern region, the Probit model value is 0.119(0.029)∗∗∗, IV-Probit model value is 0.105(0.029)∗∗∗, in the central region, the Probit model value is 0.118(0.032)∗∗∗, IV-Probit model value is 0.126(0.033)∗∗∗; Income, its Probit model value is 0.130(0.043)∗∗∗, IV-Probit model value is 0.088(0.017)∗∗∗; Retirement status (refer to: in-service): retirement, its Probit model value is 0.418(0.043)∗∗∗, IV-Probit model value is 1.167(0.178)∗∗∗; Health (reference: unhealthy): health, its Probit model value is 0.277(0.034)∗∗∗, IV-Probit model value is 0.259(0.034)∗∗∗.


## 4.3. Test of Tool Variables

Among many methods to identify causality, the IV instrumental variable has obvious advantages. Therefore, this study selects tool variables to solve the endogeneity problem of the model, and the function of tool variables after use will carry out an unbiased estimation of the estimation results. According to the experience of selecting instrumental variables in the previous relevant literature, this study chooses the statutory retirement age as the instrumental variable because legal retirement age is an exogenous variable under China’s compulsory retirement policy. Statutory retirement age is correlated with retirement but does not have a direct impact on the dependent variable physical exercise participation.One, the Hausman test of Endo-CAVALIer shows that the value of different is IV-Probit minus Probit. Nonagricultural household different value is −0.155; age difference value is 0.009; the different value of educational background is −0.008; the difference of having a partner is −0.006; the difference value of eastern region is −0.016; difference value of western region is −0.023; income difference value is −0.047; health difference is −0.047, and overallP value is 0.0046.The results show thatP=0.0046<0.05, rejecting null hypothesis H0: there is no systematic difference between a single equation and an instrumental variable equation. The results do differ, so instrumental-variable estimates should be adopted. The F statistic was significantly larger than the empirical value of 10 and significant at 1% P<0.001. That is to say, the instrumental variables selected in this study are strongly correlated with the dependent variables and will not lead to bias in the result estimators.


## 4.4. Mechanism Analysis of Influence of Retirement on Male Participation in Physical Exercise

Based on the above analysis results, it is found that the retirement variable has a significant positive impact on participation in physical exercise. Meanwhile, this study solves the endogeneity problem through an instrumental variable method, proving the causal relationship between the two. It is because of the unbiased estimation and the proof of the causal relationship between the two that the limitations of previous literature research can lay a foundation for the following mechanism research and analysis of this study. What is the influence mechanism of retirement on physical exercise participation? This study summarizes the following aspects from numerous studies. The first aspect of this study considers the physical and mental health of retired individuals. After retirement, the change in individual identity and status may stimulate the change of behavior, including physical exercise. The interaction between physical health variables and mental health variables (depression degree) and retirement variables was taken as the core independent variables affecting retired male individuals’ participation in physical exercise, and Probit regression analysis was conducted. If retirement affects residents’ participation in physical exercise through the above variables, then regression will show that the positive influence of variables interacting with retirement should be larger or further significant.In the first two models, the health variable and the depression variable interact with the retirement variable, respectively, and the retirement variable and their interaction variables show significant differences after controlling for demographic variablesP<0.001. Compared with reference variables, dissatisfaction with one’s own health status after retirement will significantly positively affect physical exercise participation behavior. According to the health needs theory, the investment in health after retirement depends on the marginal value of time and the importance that individuals attach to maintaining health. There is plenty of time after retirement, and individuals will increase their awareness of the importance of health as they get older and more experienced. So individuals will increase their participation in postretirement physical activity with the combined effect of more time and increased health awareness. After retirement, individuals who are satisfied with their own health will also increase their participation in physical exercise, which will increase their exercise behavior by 0.54 compared with those who are not satisfied with their own health. The difference between the two is because the choice of physical exercise behavior has been widely considered as an important nonmedical factor of health, physical exercise has become both a way for healthy people to further improve their health level and a way for unhealthy people to improve their health level. Foreign literature points out that individuals actively pursue their own hobbies and participate in sports activities after retirement, which have beneficial effects on physical and mental health. There is no significant difference in the influence coefficient of physical exercise between individuals without depression and those with depression after retirement, but both of them are significant at 1% level. In general, nondepressed individuals tend to engage in more physical activity than depressed individuals. Because physical activity may have an anti-depressant effect, retired individuals should actively play the anti-depressant effect of physical exercise and increase their participation in physical exercise in order to prevent depression. Some domestic and foreign scholars believe that retirement shock has a negative impact on men’s mental health. After retirement, men can regularly participate in physical exercise and reduce depression due to the disappearance of work pressure and the increase of time flexibility.In the latter two models, based on the subversive change of individual roles after retirement, the retired elderly are encouraged to continue to learn new skills and update their knowledge and concepts in order to better adapt to the aging life. This study chooses learning and Internet use as two variables for mechanism analysis. Learning variables and Internet use variables interoperated with retirement variables. Controlling for demographic variables, retired individuals’ Internet use had a significant positive effect on physical exercise participationP<0.001. This is in line with the findings of scholars WANG Shiqiang and KEARNS that the Internet promotes physical activity participation among older adults and increases the frequency of exercise. The impact of Internet use by retired individuals on physical activity participation increased by 0.47 compared to no Internet use, which is due to the fact that the Internet changes the values of retired older adults; accesses more information about physical activity; improves cognitive abilities; and also increases social activities of older adults, so it also promotes their physical and mental health more. Under the influence of learning factors, retirement and learning interacted, and controlling for demographic variables, active learning among retired individuals would have a significant positive effect on physical activity participation P<0.001. This is consistent with the findings of foreign scholars that active learning can improve health literacy, increase physical activity, and promote healthy lifestyles among older adults. This is because high health literacy is associated with good health behaviors. Learning is not only the ability to understand health information, but also includes the ability to assess and apply health information. This explains the 0.51 difference between learning and not learning respectively and retirement interaction on physical activity participation. Active and positive learning is very effective in increasing physical activity.


## 5. Conclusion

This study focuses on the study and analysis of retired men’s physical activity participation and solves the model endogeneity problem through an instrumental variables approach to achieve unbiased estimation. The estimated results show that, first, retirement leads to a significant increase in men’s physical activity participation. Second, further study of the effect mechanism suggests that the positive effect of retirement on men’s physical activity participation may be due to men’s own health status, mental health status, and active study or Internet use in their free time.In the first two models, the health and depression variables were interacted with the retirement variable, respectively, and the retirement variable showed significant differences with both interaction variables, controlling for demographic variablesP<0.001. Comparing the reference variables, postretirement individuals’ dissatisfaction with their health status would significantly and positively influence physical activity participation behavior. According to health needs theory, investment in health after retirement depends on the marginal value of time and the importance that individuals place on maintaining health, and individuals will increase their level of awareness of the importance of health after retirement when they have plenty of time and as their age and experience increases. Therefore, individuals will increase their participation in physical activity after retirement due to the dual effect of having more time and increased health awareness. Individuals who are satisfied with their self-health after retirement will also increase their participation in physical activity and will increase their exercise behavior by 0.54 compared to those who are not satisfied with their self-health. The difference between the two is due to the fact that the choice of physical activity behavior has been widely recognized as a healthy and important nonmedical factor, and physical activity has become both a way for healthy people to further improve their health and a way for unhealthy groups to improve their self-health. Foreign literature indicates that postretirement individuals who actively pursue their hobbies and participate in physical activity have beneficial effects on physical and mental health. The coefficients of the effects of physical activity for postretirement individuals who do not suffer from depressive states and those who suffer from depressive states do not differ significantly, but both are significant at the 1% level. Overall, physical activity participation tended to be higher in nondepressed individuals than in depressed individuals. Precisely because physical activity may have anti-depressant effects, retired individuals should be more active in the anti-depressant effects of physical activity and increase physical activity participation in order to prevent themselves from suffering from depression.In the latter two models, based on the disruptive shift in the role of individuals after retirement, retired older adults are encouraged to continue learning new skills as well as updating their knowledge perceptions in order to better adapt to aging life. In this study, two variables, learning and Internet use, were selected as the variables for mechanism analysis. The learning variable and the Internet use variable were interacted with the retirement variable, and a significant positive effect of Internet use on physical activity participation was found among retired individuals, controlling for demographic variablesP<0.001. This is in line with the findings of scholars WANG Shiqiang and KEARNS that the Internet promotes physical activity participation and increases exercise frequency among older adults. The effect of using the Internet on physical exercise participation increased by 0.47 for retired individuals than not using the Internet. This is due to the fact that the Internet changes the values of retired older adults; gets more information about physical exercise, improves cognitive ability, and also increases social activities of older adults, so it also promotes their physical and mental health development more. Under the influence of learning factors, retirement and learning interacted, and controlling for demographic variables, active learning among retired individuals would have a significant positive effect on physical activity participation P<0.001. This is consistent with the findings of foreign scholars that active learning can improve health literacy, increase physical activity, and promote healthy lifestyles among older adults. This is because high health literacy is associated with good health behaviors. Learning is not only the ability to understand health information, but also includes the ability to assess and apply health information. This explains why there is a difference of 0.51 between learning and nonlearning respectively and retirement interaction on physical activity participation.



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*Source: 7409857-2022-09-20.xml*