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The Impact of Air Pollution on Labor Participation of the Elderly: Evidence from China

School of Society, Soochow University, No. 199, Ren’ai Road, Suzhou Industrial Park, 215123 Suzhou, Jiangsu, P. R. China

E-mail Address: zcliuhuan@126.com

Huan Liu and Tiantian Hu are the co-first authors of this paper

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Tiantian HU

https://orcid.org/0009-0009-7364-5284

Shenzhen Futian District Economic Development Promotion Association, Shenzhen, Guangdong, P. R. China

Qiaocheng Consulting (Shenzhen) Co., Ltd., No. 1301, Yinglong Exhibition Center, Shatou Street, Futian District, 518049 Shenzhen, Guangdong, P. R. China

E-mail Address: krebecca@yeah.net

Huan Liu and Tiantian Hu are the co-first authors of this paper

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, and

Meng WANG

https://orcid.org/0000-0001-6288-0646

School of Public Administration, Zhejiang University of Finance & Economics, No. 18, Xueyuan Street, Xiasha Higher Education Park, 310018 Hangzhou, Zhejiang, P. R. China

E-mail Address: wangmengbnugeo@gmail.com

Corresponding author.

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https://doi.org/10.1142/S2345748124500052Cited by:0 (Source: Crossref)

Abstract

Based on the three-year survey data from China Health and Retirement Longitudinal Study (CHARLS) database, in combination with the environmental statistical data of 122 cities, this study empirically tests the effect of air pollution on the labor participation of the elderly and the mechanism. Using the panel data model, two-way fixed effect method, and instrumental variable method, the results show that air pollution significantly reduces the labor participation of the elderly, with a decrement of 0.43%. With the respect of transmission mechanisms, air pollution affects the overall labor participation behavior of the elderly mainly through the number of working days per week and working hours per day. At the same time, along with the cumulating of the days of Air Quality Index (AQI) $\geq 100$ , the labor participation of the elderly is significantly reduced. In addition, the impact of air pollution on the labor participation of the elderly shows apparent heterogeneity divided by the gender, education level, urban-rural, and regional economic-level, and there are obvious substitution effects and income effects. This study confirms that air pollution affects the total labor participation of the elderly through the number of working days per week and working hours per day, and this impact reaches a peak when AQI is in the range from 100 to 150.

Keywords:

1. Introduction

In recent years, a series of environmental regulation policies have been implemented by the China’s central and local governments, thus the air pollution problem caused by China’s extensive growth model has been improved significantly, but the situation is still not optimistic. According to Report on the State of the Ecology and Environment in China 2021, 202 cities among 337 prefecture-level and higher cities reached air quality standard in 2020, accounting for 59.9%. While 337 cities experienced 345 days/per year of severe pollution and 1,152 days of very severe pollution, with PM $_{10}$ and PM $_{2.5}$ being the primary pollutants, accounting for 22% and 77.7% of the days with severe pollution and above, respectively (Ministry of Ecology and Environment of the People’s Republic of China, 2021).

Research shows that air pollution not only directly leads to health damage and excess mortality (Huang et al., 2018; Jiao et al., 2018; Kim, 2021; Liao et al., 2021; Markandya et al., 2018; Newell et al., 2018), but also affects labor participation and productivity (Aragón et al., 2017; Porto et al., 2021), and consequently affects the economic development of a country or a region (Chanel et al., 2014; Lanzi et al., 2018). With rapid deterioration of ambient air quality, population aging is also an irreversible social phenomenon in China in the 21st century (Liu, 2021a; Liu and Hu, 2022). For instance, China has 267.36 million people aged 60 and above in 2021, accounting for 18.9% of the national population, and 200.56 million people aged 65 and above, accounting for 14.2% of the national population (data from the seventh national census by the National Bureau of Statistics of the People’s Republic of China, 2021).

This study investigates the impact and path of air pollution on the labor participation behavior and supply intensity of the elderly by using the three phases micro-tracking survey data from the China Health and Retirement Longitudinal Study (CHARLS) database in 2013, 2015, and 2018, and also the data of air quality in 122 cities. From the policy viewpoint, studying the impact of air pollution on the labor participation of the elderly population will help the government fully understand the sustainability of the present development path and more accurately analyze the investment income in environmental investment decision-making. Considering China’s aging population and fewer children, it will be an important task for governments at all levels to explore how to more effectively utilize the dividends of the elderly population and promote their labor participation. The accurate identification of the impact of air pollution on the labor participation of the elderly will also help the government to recognize the negative effect of air pollution and to improve the social policies from the perspective of environmental governance.

2. Literature Review

The impact of air pollution on labor participation has attracted the attention of scholars for a long time. Based on the current research methods and conclusions, the literature concerning air pollution and labor participation can be divided into three parts: the impact of air pollution on labor participation, the influence path/effect of air pollution on labor participation, and the mechanism of air pollution affecting labor participation.

First, the effect of air pollution on labor participation was studied. Existing research conclusions mostly focus on the large and significant impact of air pollution on labor participation behavior. For example, in early studies, researchers mainly investigated the concentration of particulate matter or a single pollutant of the air pollution, and the results show that with the increment of the concentration of particulate matter or single pollutants (mainly SO₂), the probability of workers losing jobs will increase significantly (Archsmith et al., 2018; Hanna and Oliva, 2015; He et al., 2019; Ostro, 1983). In terms of overall air pollution, research shows that when workers are exposed to the environments with high air pollution for a long time, not only the labor participation of workers is affected but also their labor productivity would be affected (Hanna and Oliva, 2015; Kim et al., 2017; Zivin and Neidell, 2012).

Simultaneously, several studies show that the “substitution effect” of air pollution on the labor participation of workers is higher in economically developed areas, and the “income effect” of air pollution on the labor participation of workers is likewise higher in underdeveloped areas (Evans et al., 2011; Rad et al., 2014; Hanna and Oliva, 2015; He et al., 2019). The substitution effect refers to the reduction of negative work utility caused by the improvement of air quality, and the enhancement of worker’s willingness to increase their working hours. The income effect refers to the possibility of increasing the marginal income of workers due to the improvement of air quality, so that workers can reduce their working hours and obtain the same income, resulting in a decrease in their supply time. In terms of labor participation time, existing studies have mainly focused on the total annual labor participation time or working days per week, and research conclusively demonstrates that air pollution also significantly reduces the supply time of regional workers (Hanna and Oliva, 2015; Kim et al., 2017; He et al., 2019; Sarmiento, 2022; Zhou and Zhang, 2023).

Second, the mechanism of air pollution impacting on labor participation was studied, mainly from the perspective of workers’ health, particularly their physical and mental health. Hence, health is a key factor affecting workers’ continuous labor participation. However, there are few discussions on the direct transmission mechanism of health from the perspective of air pollution, and most studies examine the impact on labor participation independently from the health perspective. For example, studies show that due to long-term exposure to environments with high air pollution concentrations, the morbidity of malignant tumors and other diseases of workers will increase significantly (Pope et al., 2002; Zhang et al., 2018). Moreover, the acute health impact will reduce workers’ labor participation rates, and even lead to their withdrawal from the labor market or early retirement (Disney et al., 2006; Eric, 2010; García-Gómez et al., 2013; Liu, 2021b). It is also worth noting that compared with the employed workers, the unemployed ones suffer higher psychological stress and lower physical health levels (Mckee-Ryan et al., 2005; Zhang et al., 2017; Liu and Wang, 2022). Simultaneously, chronic diseases also affect the labor participation. For example, research shows that chronic diseases significantly impact the labor quality and productivity of a country or region (Gertler and Gruber, 2002; Stuckler, 2008; Huang et al., 2021; Wang et al., 2022a). Long-term exposure to air pollution significantly aggravates workers’ suffering from chronic mental diseases, such as depression and anxiety (Shepherd, 1975; Petrowski et al., 2021; Wang et al., 2022b). Thus, it can be seen that the main path of the air pollution impacting on the labor participation is through the indirect impact on labors’ health, and then transmitting to the labor participation.

Generally speaking, the research contents regarding the impact of existing air pollution on labor participation are comprehensive, the research conclusions are consistent, and the research perspectives are rich. For example, the impact of air pollution on labor participation is discussed from multiple perspectives, such as total supply, impact mechanism, and the influencing path. These studies provide fundamentally theoretical support for future research. However, the existing literature still needs to be further explored. At first, the scope of the research object is limited. The existing research mainly involves the working-age population, and there is rare research literature focusing on the elderly population. Since the elderly are more vulnerable to health problems, the previous research is insufficient. Also, as the elderly are more sensitive to air pollution and cannot easily achieve higher quality of employment matching through mobility and migration as the working-age population do, the need for addressing the air pollution problem is more urgent.

Being an important social resource, the elderly can still play corresponding roles in the social development, such as experiential support for essential positions, although they may not be able to adapt their original work due to natural decline of the physical function. At the same time, due to the accelerated population aging across the world, improving the labor participation of the young elderly is one of the important ways to expand labor resources. On the one hand, labor participation of the elderly can alleviate the plight of the universal shortage of labor supply, on the other hand, it can optimize the labor supply structure and maximize the social value of the young elderly. Therefore, based on the lessons from the existing research, this study empirically investigates the impact of air pollution on the labor participation of the elderly and its influencing path by matching the micro-data of individual tracking survey and macro data of environmental quality in China, using the panel data model and taking the elderly as the main body. The main contributions of this study are as follows: (1) From the research perspective, the analysis of the impact of air pollution on the labor participation of the elderly fills the gaps of the current research in the field of the impact of air pollution on labor participation of working-age population, and thus provides policy guidance for the elderly to participate in social activities and give full play to their value. (2) Regarding the research methods, the accuracy of the selection of primary data was improved by matching macro data of air pollution with micro-individual survey data. The panel model is used to empirically investigate the impact of air pollution on the labor participation of the elderly and its impacting path. Also, the instrumental variable method and two-way fixed effects method are used to reduce the estimation bias and ensure the reliability of the research conclusion. (3) In terms of the research content, we highlight the labor participation of the elderly and empirically investigate the impact of air pollution on their labor participation behavior. This study discusses the realistic path of air pollution that affects the labor participation of the elderly from three aspects: the annual intensity of labor participation, the weekly intensity of labor participation, and daily intensity of labor participation. Besides, the impact of different levels of pollution intensity and different pollutants on the labor participation of the elderly is investigated to improve the robustness and reliability of the research findings and improve the relevant conclusions of the existing research. In addition, to improve the pertinence of the environmental governance and policies, this study also analyzes the group heterogeneity of the impacts of air pollution on the labor participation of the elderly in the dimensions of age, gender, education level, urban and rural partition, and regional economic development level (regional GDP).

3. Methods

3.1. Theoretical derivation and model building

Because of the exogenous characteristics of external air pollution that impact individuals, to highlight the marginal effect of air pollution on the labor supply of the elderly, we attempt to build a simple local equilibrium model that includes factors of air pollution and labor supply of the elderly (Friedlander and Ravimohan, 2002; Bosi et al., 2015; Yang and Xu, 2020; Aguilar-Gomez et al., 2022). Assuming that the utility of the elderly is not disturbed by other factors such as health under certain circumstances, the individual’s total utility would depend on the individual consumption (c) and labor supply (l). Subsequently, taking the air pollution condition as the constraint condition, the individual utility function can be set as $u = u (c, l; AQI)$ . Air Quality Index ( $AQI$ ) is the measurement index of air pollution, which comprehensively reflects air quality and $AQI$ will directly affect the choice between the labor supply and the consumption of the elderly. Based on this, the utility maximization function and budget constraints of labor supply for the elderly can be set as follows :

max u (t, w; AQI) = ϕ (AQI) \cdot w \cdot t - g (t; AQI), <math display="block" altimg="eq-00007.gif"><mo>max</mo><mi>u</mi><mo stretchy="false">(</mo><mi>t</mi><mo>,</mo><mi>w</mi><mo>;</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo><mo>=</mo><mi>ϕ</mi><mo stretchy="false">(</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo><mo>\cdot</mo><mi>w</mi><mo>\cdot</mo><mi>t</mi><mo>-</mo><mi>g</mi><mo stretchy="false">(</mo><mi>t</mi><mo>;</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo><mo>,</mo></math> (1)

g (t; AQI) = - \int t o u t (x; AQI) d x, <math display="block" altimg="eq-00008.gif"><mi>g</mi><mo stretchy="false">(</mo><mi>t</mi><mo>;</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo><mo>=</mo><mo>-</mo><msubsup><mrow><mo>\int</mo></mrow><mrow><mi>o</mi></mrow><mrow><mi>t</mi></mrow></msubsup><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo>;</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>,</mo></math> (2)

s.t w t + Y - p c = 0 . <math display="block" altimg="eq-00009.gif"><mstyle><mtext mathvariant="normal">s.t</mtext></mstyle><mspace width="1em" class="quad"></mspace><mi>w</mi><mi>t</mi><mo>+</mo><mi>Y</mi><mo>-</mo><mi>p</mi><mi>c</mi><mo>=</mo><mn>0</mn><mo>.</mo></math> (3)

The left side of Eq. (1) represents the maximum of individual utility of the elderly under the environmental impact of air pollution. The first term $ϕ (AQI)$ on the right represents the marginal utility brought by wage income under the optimal labor supply decision; w represents the labor wage income level of the elderly under air pollution; $w \cdot t$ represents the final lifetime income of the labor supply of the elderly for a long time; $g (t, AQI)$ represents the negative effect of labor provided by the elderly themselves when air pollution is certain, such as higher medical consumption expenditure due to further reduction of health condition. The expanded formula is shown in Eq. (2): Therefore, from Eq. (1), the maximum utility of labor supply for the elderly under the environment with air pollution is equal to the difference between the total utility of labor supply for the rest of life to obtain wage income and the negative utility caused by labor supply for the elderly. Equation (3) represents constraints. Here, we assume that the non-working income of the elderly is mainly from the social security, family assets, and children’s economic support; that is, Y in the formula is independent from air pollution and p represents consumer price. Equation (3) indicates that the lifetime labor income of the elderly under air pollution plus other incomes is equal to their total consumption. Therefore, according to this assumption, the equilibrium solution of maximizing personal utility can be obtained by constructing a Lagrange function, which is set as follows :

L (λ, c, l) = u (c, l; AQI) + λ [w (AQI) \cdot t (AQI) + y - p c (AQI)] . <math display="block" altimg="eq-00013.gif"><mi>L</mi><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>l</mi><mo stretchy="false">)</mo><mo>=</mo><mi>u</mi><mo stretchy="false">(</mo><mi>c</mi><mo>,</mo><mi>l</mi><mo>;</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo><mo>+</mo><mi>λ</mi><mo stretchy="false">[</mo><mi>w</mi><mo stretchy="false">(</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo><mo>\cdot</mo><mi>t</mi><mo stretchy="false">(</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo><mo>+</mo><mi>y</mi><mo>-</mo><mi>p</mi><mi>c</mi><mo stretchy="false">(</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>.</mo></math> (4)

Based on Eq. (4), we could calculate the partial differential of labor supply l and consumption c of the elderly and the second-order partial derivative of the air pollution index $AQI$ to obtain the marginal utility function of labor supply and consumption of the elderly with air pollution, as shown in Eqs. (5) and (6). Further, we calculate the first-order partial derivative of air pollution according to Eq. (3) and solve it according to Eq. (6) to obtain Formula (7). The details are as follows :

∂c∂AQI=∂λ∂AQI⋅p−ucAQI(c,l;AQI)ucc(c,l;AQI),<math display="block" altimg="eq-00015.gif"><mfrac><mrow><mi>∂</mi><mi>c</mi></mrow><mrow><mi>∂</mi><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle></mrow></mfrac><mo>=</mo><mfrac><mrow><mfrac><mrow><mi>∂</mi><mi>λ</mi></mrow><mrow><mi>∂</mi><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle></mrow></mfrac><mo>⋅</mo><mi>p</mi><mo>−</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>c</mi><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle></mrow></msub><mo stretchy="false">(</mo><mi>c</mi><mo>,</mo><mi>l</mi><mo>;</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mi>c</mi><mo>,</mo><mi>l</mi><mo>;</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo></mrow></mfrac><mo>,</mo></math>(5)

∂l∂AQI=∂λ∂AQI⋅w+∂w∂AQI⋅λ−glAQI(l;AQI)gll(l;AQI),<math display="block" altimg="eq-00016.gif"><mfrac><mrow><mi>∂</mi><mi>l</mi></mrow><mrow><mi>∂</mi><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle></mrow></mfrac><mo>=</mo><mfrac><mrow><mfrac><mrow><mi>∂</mi><mi>λ</mi></mrow><mrow><mi>∂</mi><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle></mrow></mfrac><mo>⋅</mo><mi>w</mi><mo>+</mo><mfrac><mrow><mi>∂</mi><mi>w</mi></mrow><mrow><mi>∂</mi><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle></mrow></mfrac><mo>⋅</mo><mi>λ</mi><mo>−</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>l</mi><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle></mrow></msub><mo stretchy="false">(</mo><mi>l</mi><mo>;</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>l</mi><mi>l</mi></mrow></msub><mo stretchy="false">(</mo><mi>l</mi><mo>;</mo><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle><mo stretchy="false">)</mo></mrow></mfrac><mo>,</mo></math>(6)

∂λ∂AQI=[w(ulAQIull)−p(ucAQIucc)]+∂w∂AQI(wλull−l)−[(w2ull)+(p2ucc)].<math display="block" altimg="eq-00017.gif"><mfrac><mrow><mi>∂</mi><mi>λ</mi></mrow><mrow><mi>∂</mi><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced separators="" open="[" close="]"><mrow><mi>w</mi><mfenced separators="" open="(" close=")"><mrow><mfrac><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>l</mi><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle></mrow></msub></mrow><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>l</mi><mi>l</mi></mrow></msub></mrow></mfrac></mrow></mfenced><mo>−</mo><mi>p</mi><mfenced separators="" open="(" close=")"><mrow><mfrac><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>c</mi><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle></mrow></msub></mrow><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub></mrow></mfrac></mrow></mfenced></mrow></mfenced><mo>+</mo><mfrac><mrow><mi>∂</mi><mi>w</mi></mrow><mrow><mi>∂</mi><mstyle><mtext mathvariant="normal">AQI</mtext></mstyle></mrow></mfrac><mo stretchy="false">(</mo><mfrac><mrow><mi>w</mi><mi>λ</mi></mrow><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>l</mi><mi>l</mi></mrow></msub></mrow></mfrac><mo>−</mo><mi>l</mi><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo><mfenced separators="" open="[" close="]"><mrow><mfenced separators="" open="(" close=")"><mrow><mfrac><mrow><msup><mrow><mi>w</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>l</mi><mi>l</mi></mrow></msub></mrow></mfrac></mrow></mfenced><mo>+</mo><mfenced separators="" open="(" close=")"><mrow><mfrac><mrow><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub></mrow></mfrac></mrow></mfenced></mrow></mfenced></mrow></mfrac><mo>.</mo></math>(7)

In Eq. (6), $\frac{\partial λ}{\partial AQI} \cdot w$ represents the income effect of labor supply under the condition of certain air pollution; $\frac{\partial w}{\partial AQI} \cdot λ$ represents the substitution effect of labor supply brought by the increase of marginal income under the condition of certain air pollution, and in Eq. (7), $\frac{\partial w}{\partial AQI} (\frac{w λ}{u_{l l}} - l)$ represents the income growth brought by higher income levels and additional labor payments, which jointly produce the income effect. By combining Eqs. (6) and (7), it can be observed that the income effect of labor supply is large enough to exceed the sum of the substitution effect and the negative effect. The improvement of air conditions will promote the labor supply under other conditions; that is, air pollution will reduce the labor supply behavior of the elderly and then affect the labor supply quantity.

3.2. Empirical model

This study selects the panel data model for testing the effects of air pollution. The specific model setting is shown in the following equation :

Labor i j t = β 0 + β 1 Air_pollution j t + β 2 X i j t + β 3 Z j t + T t + π j + ε i j t, <math display="block" altimg="eq-00021.gif"><msub><mrow><mstyle><mtext mathvariant="normal">Labor</mtext></mstyle></mrow><mrow><mi>i</mi><mi>j</mi><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mstyle><mtext mathvariant="normal">Air_pollution</mtext></mstyle></mrow><mrow><mi>j</mi><mi>t</mi></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mi>j</mi><mi>t</mi></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi>Z</mi></mrow><mrow><mi>j</mi><mi>t</mi></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>+</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi><mi>j</mi><mi>t</mi></mrow></msub><mo>,</mo></math> (8)

where

${Labor}_{i j t}$ represents the labor participation of elderly i in area j at time i. Mainly two variables are used in selecting the proxy variables of labor participation of the elderly, which are the core explained variables of this study. The first is a dummy variables, that is, in the survey year, the labor participation of the elderly is 1, and no labor participation is 0, which is used to investigate or reflect the probability of annual labor participation behavior of the elderly. The second is the variable of labor participation intensity. Here, we select the number of months of labor participation each year for the elderly, the number of days of labor participation for the every week for the elderly, and the number of hours of labor participation everyday for the elderly as the agents in order to investigate the specific path of the air pollution impacting on the labor participation behavior of the elderly.

${Air_pollution}_{j t}$ represents the annual average air pollution in the region j at time i. This is the core explanatory variable in this study. First, we select the regional annual average AQI for the test. And then, the occurrence days of extreme pollution in area j at time i are classified to reflect the impact of different pollution intensities on the labor participation of the elderly. Here, the division of different pollution intensities is in accordance with China’s annual air pollution report index. For example, the cumulative number of days with $AQI \geq 100$ is defined as the first class, indicating the mild pollution. The cumulative number of days with $AQI \geq 150$ is classified as the second class, indicating the moderate pollution. The cumulative number of days with $AQI \geq 200$ is defined as the third class, indicating the severe pollution. The cumulative number of days with $AQI \geq 300$ is the fourth class, representing the extremely severe pollution. Moreover, we use different pollutants as the proxy variables of air pollution to investigate their impact on the labor participation of the elderly. In terms of different pollutants, we used the main pollutants reported in China’s air pollutants in the survey year and conducted the analysis with the help of API before the report of AQI (since AQI was only used in China after 2012). As a result, we select SO₂, NO₂, and PM $_{10}$ for agency analysis.

$X_{i j t}$ is the main control variable in this study. Based on the previous research that controlled individual characteristics and family income, we control relevant individual characteristics and family income variables in our model as well (Bosi et al., 2015; Zhang et al., 2018; Liu and Hu, 2021). Simultaneously, to ensure that air pollution is consistent with the changing law of labor participation for the elderly as much as possible, we also control the environmental characteristic variable $Z_{j t}$ in the area j at time i. Drawing on the research designs of Liu and Hu (2021) and Liu et al. (2021), we use the regional annual rainfall, total annual sunshine duration, regional average temperature, greening rate, regional annual financial expenditure, and regional population density as control variable as well. $T_{t}$ is a time dummy variable that controls the time change trend of labor participation for the elderly, $π_{j}$ is a regional dummy variable that controls the regional fixed effect, and $ε_{i j t}$ is the random disturbance term. The definitions and descriptive statistics of the core variables in the empirical model are shown in Table 1.

**Table 1. Descriptive statistics of variables.**
Variable	Definition	Mean	SD	Min	Max
If_work	Whether there is labor participation in one year, $yes = 1$ , $no = 0$	0.6987	0.1364	0	1
Work_month	Number of months with labor participation in one year, unit: month	7.6797	4.3136	0	12
Work_day	Number of days with labor participation in one week, unit: day	5.6366	1.8689	0	7
Work_hour	Labor participation time in one day, unit: hour	8.6579	3.7148	0	24
Family_income	Total household income in the survey year, unit: yuan (RMB)	4297.584	10043.86	0	1 million
AQI	Annual average regional AQI in the survey year	79.6995	22.9060	40	206
AQI_100day	Number of days with AQI $\geq$ 100 in the survey year	61.5820	37.5599	0	152.935
AQI_150day	Number of days with AQI $\geq$ 150 in the survey year	15.3360	15.0698	0	70.81
AQI_200day	Number of days with AQI $\geq$ 200 in the survey year	8.6554	17.5754	0	228.125
AQI_300day	Number of days with AQI $\geq$ 300 in the survey year	1.6319	4.0981	0	27.01
SO₂	Annual average of SO₂ in the survey year	21.6659	15.8191	5	141
NO₂	Annual average of NO₂ in the survey year	36.0157	14.1799	8	70
PM $_{10}$	Annual average of PM $_{10}$ in the survey year	91.9193	40.1566	32	277
Fiscal_expenditure	Regional annual fiscal expenditure, 100 million yuan/year	637.778	966.9111	18.5	8351.54
Sunshine_duration	Annual total sunshine hours in the region, h/year	1831.951	424.0223	954.3	2798.8
Annual_rainfall	Regional annual rainfall, mm/year	1055.94	539.4511	88.1	3012
People_density	Regional population density in the current year	505.1453	455.9146	5.135961	6521.55
Average_temperature	Regional annual average temperature, $^{\circ}$ C	15.3626	3.8020	4.8	23.4
Green_coverage	Regional greening rate in the current year	39.9430	7.1340	6.75	67
Grow_GDP	Regional annual GDP growth rate	7.6553	1.9996	0.2	13.3
Gender	$Male = 1$ , $Female = 0$	0.4758	0.4994	0	1
Bereft of spouse	Bereft of $spouse = 1$ , $no = 0$	0.2032	0.4024	0	1
Age	Actual age of respondents at the time of survey	68.0625	6.6385	60	115
Education	Highest diploma obtained by respondents at the time of the survey	3.0712	1.4911	1	10
Self_health	Rated health level by the respondents themselves from 1 to 5 as very bad, bad, average, good, and very good	3.0521	0.8419	1	5

Source: Made by the authors.

4. Data

The data for the study were obtained from the survey data of the CHARLS database in 2013, 2015, and 2018, and the data of AQI and others were obtained from meteorological statistics of cities in 2018 (air quality online detection and analysis platform, https://www.aqistudy.cn/) and monthly air quality report published by the Ministry of Ecology and Environment of the People’s Republic of China. The CHARLS data cover observations of 28 provinces, municipalities, and autonomous regions in the mainland of China. The survey subjects were the ones aged 45 and over, which can better reflect the basic characteristics of China’s elder population. Data from three follow-up surveys were selected for analysis. Through data screening and selection, and taking people aged 60 and over as the main body, 16,858 valid observations within a three-year period were finally obtained.

5. Results

5.1. Benchmark test

At first, based on the previous analysis, we investigate the results of benchmark test of the impacts of air pollution on the elderly’s labor participation. Here, Ordinary Least Squares (OLS) estimation was used for unbiased estimation. The results are presented in Table 2. Models (1)–(5) show the results of controlling different variables, in which Model (1) does not control the influence of other factors, Model (2) controls the influence of the annual total income of the family, Model (3) controls the variables of regional environmental characteristic, and Model (4) controls the variables of individual characteristics, and Model (5) presents the result of controlling the most of factors such as family annual total income, environmental characteristics, individual characteristics and the health level together.

**Table 2. Benchmark test of air pollution and labor participation of the elderly.**
	Explained variable: Work_time
Variables	(1)	(2)	(3)	(4)	(5)
lnAQI	$- 0.0057$ ***	$- 0.0057$ ***	$- 0.0048$ **	$- 0.0044$ **	$- 0.0043$ *
	(0.0021)	(0.0021)	(0.0023)	(0.0022)	(0.0023)
Family_income		$- 0.0000$	0.0000	$- 0.0000$	0.0000
		(0.0012)	(0.0013)	(0.0013)	(0.0013)
lnFiscal_expenditure			$- 0.0015$ **		$- 0.0017$ *
			(0.0016)		(0.0016)
lnSunshine_duration			0.0053*		0.0049*
			(0.0031)		(0.0031)
lnAnnual_rainfall			0.0004*		0.0003*
			(0.0018)		(0.0018)
lnPeople_density			0.0019		0.0020
			(0.0026)		(0.0026)
lnAverage_temperature			0.0001**		0.0003*
			(0.0052)		(0.0052)
Green_coverage			$- 0.0001$		$- 0.0001$
			(0.0001)		(0.0001)
Gender				$- 0.0001$	0.0004
				(0.0097)	(0.0097)
Age				$- 0.0000$ *	$- 0.0000$ *
				(0.0004)	(0.0004)
Education				$- 0.0005$	$- 0.0005$
				(0.0003)	(0.0003)
Bereft of Spouse				0.0007	0.0007
				(0.0006)	(0.0006)
Self_health					0.0002**
					(0.0006)
Constant	1.0234***	1.0234***	0.9787***	1.0188***	0.9815***
	(0.0090)	(0.0090)	(0.0349)	(0.0298)	(0.0450)
Observations	16858	16858	16858	16858	16858
Number of ID	10124	10124	10124	10124	10124
R-squared	0.0910	0.1210	0.2319	0.2413	0.2924

Notes: Standard errors in parentheses, *** $p < 0.01$ , ** $p < 0.05$ , * $p < 0.1$ .

Source: Made by the authors.

From Models (1)–(5), under the influence of different variables, the statistical index of air pollution (AQI) imposes significant and negative effect on the labor participation of the elderly, that is, if the air pollution gets more severe, the probability of the elderly’s labor participation will be significantly reduced. That is, if the regional annual average AQI increases by one unit; the probability of elderly’s labor participation is reduced by 0.43%. In terms of the impact of other variables, the test results show that few variables are significant. Noticeably, the total annual family income variable shows no significant impact on the labor participation of the elderly and the coefficient is particularly small. The self-rated health level of the elderly also shows the same impact.

Based on the investigation of air pollution’s impact on the labor participation behavior of the elderly, we also tested the impact of air pollution on the intensity of labor participation of the elderly. The results are shown in Table 3. Models (1)–(3) are tested from three aspects: annual labor participation intensity, weekly intensity of labor supply, and intensity of daily labor supply. Among them, the results of Model (1) indicates that air pollution has no significant impact on the annual labor participation of the elderly. The results in Model (2) show that the logarithm of AQI, the statistical index of air pollution, imposes significant and negative effect on the number of working days per week of the elderly; that is, along with the increase of the regional air pollution, the number of working days per week for the elderly is decreased, and when the regional annual average of AQI increases by 1 unit, the number of working days per week of the elderly will decrease by 0.44%. Likewise, the results of Model (3) show that air pollution imposes significant and negative impact on the daily labor participation time of the elderly; that is, if the air pollution gets severe, the daily labor participation time of the elderly will decrease significantly. Brought by 1 unit increase of the annual average AQI of the region, the daily labor participation hours of the elderly will decrease by 0.45%.

**Table 3. Air pollution and labor participation intensity of the elderly.**
	Labor participation intensity: taking labor time as an example
Variables	Annual labor participation intensity (1)	Weekly supply intensity (2)	Daily supply intensity (3)
lnAQI	$-$ 0.0045 (0.0029)	$-$ 0.0044* (0.0024)	$-$ 0.0045* (0.0024)
Family_income	$-$ 0.00001 (0.0016)	0.00003 (0.0013)	0.00002 (0.0013)
lnFiscal_expenditure	0.000003 (0.0019)	$-$ 0.0016*** (0.0016)	$-$ 0.0014*** (0.0016)
lnSunshine_duration	0.0055 (0.0038)	0.0055* (0.0032)	0.0063** (0.0032)
lnAnnual_rainfall	0.0012* (0.0022)	0.0026** (0.0018)	0.0005* (0.0018)
lnPeople_density2	$-$ 0.0023 (0.0032)	0.0019 (0.0027)	0.0020 (0.0027)
lnAverage_temperature	$-$ 0.0002 (0.0064)	0.0012 (0.0054)	0.0010 (0.0054)
Green_coverage	$-$ 0.0001 (0.0001)	$-$ 0.0001 (0.0001)	$-$ 0.0001* (0.0001)
Gender	0.0003* (0.0119)	0.0005 (0.0101)	0.0004* (0.0101)
Age	$-$ 0.0000 (0.0005)	$-$ 0.0000 (0.0004)	$-$ 0.0000 (0.0004)
Education	$-$ 0.0004** (0.0004)	$-$ 0.0005** (0.0003)	$-$ 0.0004** (0.0003)
Bereft of Spouse	0.0011 (0.0008)	0.0007 (0.0006)	0.0006 (0.0006)
Self_health	$-$ 0.0001 (0.0007)	0.0001* (0.0006)	0.0002* (0.0006)
Constant	0.9864*** (0.0551)	0.9588*** (0.0466)	0.9674*** (0.0466)
Observations	16858	16858	16858
Number of ID	10124	10124	10124
R-squared	0.1920	0.2126	0.1727

Notes: Standard errors in parentheses, *** $p < 0.01$ , ** $p < 0.05$ , * $p < 0.1$ .

Source: Made by the authors.

5.2. Effects of different pollution intensities and pollutants on the labor participation behavior of the elderly

Second, we investigate the effects of different pollution intensities and pollutants on the labor participation behavior of the elderly. The results are presented in Table 4. Here, we use the number of days of extreme pollution (the number of days with AQI exceeds a specific value) in a particular area in a year as the proxy variable for pollution intensity; SO₂, NO₂, and O₃ are selected as the main proxy variables for different pollutants. Models (1)–(4) show the effects of different pollution intensities on the labor participation behavior of the elderly. From the results, it could be seen that AQI_100day imposes a significant and negative effect on the labor participation of the elderly; that is, severe air pollution could weaken the labor participation behavior of the elderly. In details, when the days of air pollution index $AQI \geq 100$ increases, the labor participation probability of the elderly will be reduced by 0.005%, but the influence coefficient is relatively small. Because the cumulative days of air pollution set as the explanatory variable in this model were not logarithmically processed, compared to the benchmark research results, the impact coefficient here appears much smaller, but it does not affect the results of significance of the coefficients. Moreover, AQI_150day, AQI_200day, and AQI_300day show no significant effect on the labor participation behavior of the elderly, and the influence coefficients are relatively small.

**Table 4. Air pollution intensity and labor participation of the elderly.**
	Explained variable: Work_hour
Variables	(1)	(2)	(3)	(4)	(5)
AQI_100day	$- 0.00005$ **
	(0.00002)
AQI_150day		$- 0.0001$
		(0.0000)
AQI_200day			$- 0.00001$
			(0.00002)
AQI_300day				$- 0.0001$
				(0.0001)
lnSO₂					$- 0.0020 *$
					(0.0011)
lnNO₂					0.0021
					(0.0019)
lnPM10					0.0004
					(0.0026)
Control Variable	Control	Control	Control	Control	Control
Observations	16858	16858	16858	16858	16858
Number of ID	10124	10124	10124	10124	10124
R-squared	0.1526	0.1122	0.1619	0.2320	0.1930

Notes: Standard errors in parentheses, ** $p < 0.05$ , * $p < 0.1$ . Control variable results are not listed.

Source: Made by the authors.

These results demonstrate that when the air pollution index (AQI) is greater than or equal to 100, air pollution would significantly affect the labor participation behavior of the elderly. However, when the AQI is greater than or equal to 150, the effects are no longer significant; which means there is a peak value of air pollution that could affect the labor participation behavior of the elderly, and this peak value is $100 \leq AQI \leq 150$ . In Table 4, the results of Model (5) show the impact of different pollutants on the labor participation behavior of the elderly, only SO₂ has significant and negative effect on the labor participation behavior of the elderly, and when the concentration of SO₂ in air pollution increases by 1 unit, the labor participation behavior of the elderly would be weakened by 0.20%. In addition, the concentrations of NO₂ and O₃ in air pollutants have no significant effect on the labor participation of the elderly. The differences of the impact of different types of pollutants (SO₂, NO₂, O₃) are mainly caused by differences of the pollution source and thus the effects of pollutants. The main source of SO₂ concentration comes from industrial production, coal consumption, and transportation. With higher possibility that the concentration of NO₂ and O₃ may come from non-industrial systems, the decrease of group health quality caused by SO₂ concentration would be comparatively greater, and thus indirectly affects labor participation of the elderly.

5.3. Group heterogeneity of the impact of air pollution on the labor participation behavior of the elderly

In terms of group heterogeneity, we conducted a comparative analysis from the aspects of age, gender, education level, separation of urban and rural areas, and regional economy level. The test results for age heterogeneity are presented in Table 5. We divided the groups by age under 60, 60–65, and above 65. Table 5 shows that air pollution imposes significantly negative effects on the labor participation behavior of the group under 60, and the marginal effect reaches $-$ 0.0074, which is much higher than that of the group of 60 above. In addition, there is no significant difference between the 60–65 years old group and $\geq 65$ year old group. That is, air pollution had no significant effect on the labor participation behavior of both groups.

**Table 5. Age heterogeneity of air pollution and labor participation behavior of the elderly.**
	Explained variable: Work_hour
Variables	Under 60 (1)	60–65 years old (2)	65 and over (3)
lnAQI	$-$ 0.0074** (0.0037)	$-$ 0.0046 (0.0042)	$-$ 0.0043 (0.0028)
Control Variable	Control	Control	Control
Observations	19253	6342	10516
Number of ID	11620	3826	6379
R-squared	0.2634	0.1759	0.1244

Notes: Standard errors in parentheses, ** $p < 0.05$ . Control variable results are not listed.

Source: Made by the authors.

Then, the heterogeneity of the impacts of air pollution on the labor participation behavior of the elderly is investigated from the perspective of partition of urban and rural areas. The test results are shown in Table 6. Models (1) and (2) are the tests of rural and urban observations, respectively. It appears that for the rural observations, air pollution has significant and negative effect on the labor participation of the elderly, and when the regional average annual AQI increases by 1 unit, the labor participation behavior of the rural elderly will decrease by 0.55%. However, for the urban samples, the impact of air pollution on the labor participation behavior of the elderly is not significant, and the coefficient is small, $-$ 0.0018, which is much less than that for the rural samples. It means that the labor participation behavior of the rural elderly is much more impacted by air pollution comparing to the urban elderly, with evident urban-rural heterogeneity.

**Table 6. Group heterogeneity of air pollution and labor participation behavior of the elderly.**
	Explained variable: Work_hour
	Urban and rural		Regional economic development		Sex		Education level
Variables	Rural (1)	Urban (2)	High-GDP (3)	Low-GDP (4)	Male (5)	Female (6)	Low-education (7)	High-education (8)
lnAQI	$- 0.0055$ *	$- 0.0018$	0.0013	$- 0.0061$ **	$- 0.0064$ *	$- 0.0021$	$- 0.0059$ **	$- 0.0022$
	(0.0031)	(0.0037)	(0.0033)	(0.0031)	(0.0036)	(0.0031)	(0.0028)	(0.0145)
Control Variable	Control	Control	Control	Control	Control	Control	Control	Control
Observations	10144	6714	3893	12965	8290	8568	14708	2150
Number of ID	5990	4134	2675	8080	4980	5166	9429	1909
R-squared	0.2049	0.1734	0.1105	0.2439	0.1844	0.1937	0.2723	0.1581

Notes: Standard errors in parentheses, ** $p < 0.05$ , * $p < 0.1$ . Control variable results are not listed.

Source: Made by the authors.

In terms of heterogeneity from regional economic development, this study groups the observations by the ranking of annual GDP of 122 cities. Specifically, we define the regions where the GDP is higher than the average GDP of 122 cities as the high GDP group and those lower than the average as the low GDP group. Models (3) and (4) of Table 6 are the investigation results of heterogeneity of the effects by regional economic development. From Model (3), it could be found that air pollution has no significant impact on the labor participation behavior of the elderly for the high GDP group, and its impact coefficient is positive. However, according to the results of Model (4), air pollution shows significant and negative effect on the labor participation behavior of the elderly of the low GDP group, and when the regional annual average AQI value increases by 1 unit, the labor behavior of the elderly will decrease by 0.61%. From this result, it could be seen that significant regional economic heterogeneity does exist in the impact of air pollution on the labor participation behavior of the elderly.

Finally, group heterogeneity of the effects was investigated from two aspects: gender and education level. The test results for gender heterogeneity are shown by Models (5) and (6) in Table 6. The results of Model (5) indicate that for the males, air pollution does impose significant and negative effect on the labor participation behavior of the elderly, and the negative effect reaches $-$ 0.0064, which means if the regional annual average AQI increases by 1 unit, the probability of labor participation of the elderly would decrease by 0.64%. On the contrary, from Model (6), air pollution does not show significant effect on the labor participation behavior of the female elderly, and the influence coefficient is $-$ 0.0021, which is much smaller than that for the male elderly. This reveals that the impact of air pollution on the labor participation behavior of the elderly has significant gender heterogeneity and that the impact on the male elderly is higher and more significant. In terms of educational heterogeneity, the results of Models (7) and (8) show that air pollution imposes significant negative impact on the labor participation behavior of the elderly of low education level, and the effect reaches $-$ 0.0059; that is, while the regional average annual AQI value increases by 1 unit, the probability of labor participation of the elderly decreases by 0.59%. However, air pollution does not impose significant effect on the labor participation behavior of the elderly with high education level, and its coefficient ( $-$ 0.0022) is smaller than that of the elderly with low education. The above results further demonstrate that obvious educational heterogeneity also exists in the impact of air pollution on the labor participation behavior of the elderly. Specifically, the labor participation behavior of the elderly with higher education is less affected by the air pollution, but the labor participation behavior of the elderly with lower education is significantly affected by the air pollution.

5.4. Further analysis

5.4.1. Processing of sample-selective bias

The above benchmark test confirmed the significant and negative impact of air pollution on the labor participation behavior of the elderly. However, due to the influence of sample-selection bias and omitted variables, the test results may present estimation bias, thus it is necessary to further validate the benchmark test. For example, considering the environmental migration, when the air pollution in a certain area is severe, people of higher income will choose to migrate to the cities of less polluted environment in order to avoid the damage of air pollution on their own health. Consequently, the labor participation behavior of the elderly in areas of less air pollution would be less affected by air pollution, and hence the impacts might be insignificant. On the other hand, the labor participation behavior of the elderly in heavily polluted areas will be greatly affected by air pollution, showing significant characteristics. Therefore, this study deals with the estimation bias caused by the selection bias by controlling the environmental migration factor. By controlling the migration of the registered residence in the absence of domicile during the survey, the results are shown in Tables 7 and 8. Among them, the results of Model (1) in Table 7 show that air pollution has significant and negative impact on the labor participation behavior of the elderly, and the impact coefficient is $-$ 0.0045. In Model (2), the intensity of air pollution (AQI_100day) significantly reduces the labor participation behavior of the elderly, and the effect is $-$ 0.00005, which is slight. The results of Models (3)–(5) further indicate that AQI_150day, AQI_200day and AQI_300day still impose no significant effect on the labor participation behavior of the elderly. The above results demonstrate that after controlling the estimation bias caused by environmental migration, the benchmark test results are still robust. This confirms air pollution does impose negative impact on the labor participation behavior of the elderly, while only AQI_100day has significant impact.

**Table 7. Air pollution and labor participation of the elderly after controlling environmental migration.**
	Explained variable: Work_hour
Variables	(1)	(2)	(3)	(4)	(5)
lnAQI	$- 0.0045$ *
	(0.0025)
AQI_100day		$- 0.00005$ **
		(0.00004)
AQI_150day			$- 0.0001$
			(0.00004)
AQI_200day				$- 0.00001$
				(0.00003)
AQI_300day					$- 0.0001$
					(0.0001)
Constant	0.9805***	0.9514***	0.9571***	0.9521***	0.9502***
	(0.0481)	(0.0453)	(0.0456)	(0.0454)	(0.0453)
Observations	16344	16344	16344	16344	16344
Number of ID	9945	9945	9945	9945	9945
R-squared	0.1925	0.2327	0.1723	0.2020	0.1521

Notes: Standard errors in parentheses, *** $p < 0.01$ , ** $p < 0.05$ , * $p < 0.1$ . Control variable results are not listed.

Source: Made by the authors.

Also, by controlling the environmental migration, the test results of the impact of air pollution on the intensity of labor participation of the elderly are shown in Table 8. The results further reveal that while the air pollution does not significantly impact the annual intensity of labor participation of the elderly, it significantly and negatively affects the number of days of labor participation per week and labor participation hours per day. Thus, the benchmark test results are robust.

**Table 8. Air pollution and labor participation intensity of the elderly after controlling environmental migration.**
	Labor participation intensity: taking labor time as an example
Variables	Work_month (1)	Work_day (2)	Work_hour (3)
lnAQI	$-$ 0.0041 (0.0029)	$-$ 0.0046* (0.0025)	$-$ 0.0047* (0.0025)
Constant	0.9543*** (0.0576)	0.9567*** (0.0498)	0.9658*** (0.0498)
Observations	16344	16344	16344
Number of ID	9945	9945	9945
R-squared	0.2120	0.3427	0.2828

Notes: Standard errors in parentheses, *** $p < 0.01$ , * $p < 0.1$ . Control variable results are not listed.

Source: Made by the authors.

5.4.2. Processing of bias due to omitted variables

In order to avoid the estimation error probably caused by the omitted variables, we further use the two-way fixed effect and instrumental variable method for endogenous treatment. The two-way fixed effect method mainly refers to Liu and Hu (2021) who took the categorical variables as continuous variables and adopted the method of linear two-way fixed effect model estimation. This study also attempts to deal with the two-way fixed effect of the panel data, that is, the labor participation behavior of the elderly is processed as a continuous variable, and the variables of region and time are fixed at the same time. The results are shown in Tables 9 and 10. According to the test results in Table 9, by using the two-way fixed effect estimation, air pollution still shows significant and negative impact on the labor participation behavior of the elderly, and the AQI_100day still imposes significant and negative impact on the labor participation behavior of the elderly, indicating the robustness of the benchmark test results. Moreover, results of Models (3)–(5) show that the number of days of other pollution intensities does not significantly impact the labor participation behavior of the elderly, and thus the conclusion above is still robust.

**Table 9. Air pollution and labor participation of the elderly under two-way fixed effect.**
	Explained variable: Work_hour
Variables	(1)	(2)	(3)	(4)	(5)
lnAQI	$- 0.0028$ *
	(0.0017)
AQI_100day		$- 0.00002$ *
		(0.00001)
AQI_150day			$- 0.00002$
			(0.00003)
AQI_200day				$- 0.00001$
				(0.00002)
AQI_300day					$- 0.0001$
					(0.0001)
Constant	0.9811***	0.9658***	0.9650***	0.9635***	0.9637***
	(0.0259)	(0.0236)	(0.0239)	(0.0236)	(0.0236)
Observations	16858	16858	16858	16858	16858
R-squared	0.2339	0.1938	0.1627	0.1935	0.1806

Notes: Standard errors in parentheses, *** $p < 0.01$ , * $p < 0.1$ . Control variable results are not listed.

Source: Made by the authors.

Table 10 indicates that by using the two-way fixed effect estimation, the impact of air pollution on the annual labor participation behavior of the elderly is still not significant, but the impacts on the working days per week and working hours per day of the elderly are significant and negative. Note here that the impact coefficients are relatively smaller than the benchmark test results. Yet the results prove that the results of benchmark test are robust.

**Table 10. Air pollution and labor participation intensity of the elderly under two-way fixed effect.**
	Labor participation intensity: taking labor time as an example
Variables	Work_month (1)	Work_day (2)	Work_hour (3)
lnAQI	$-$ 0.0032 (0.0020)	$-$ 0.0029* (0.0017)	$-$ 0.0031* (0.0017)
Constant	0.9721*** (0.0310)	0.9632***(0.0270)	0.9744***(0.0264)
Observations	16858	16858	16858
R-squared	0.2334	0.1941	0.2640

Notes: Standard errors in parentheses, *** $p < 0.01$ , * $p < 0.1$ . Control variable results are not listed.

Source: Made by the authors.

In parallel, the method of panel instrumental variable is selected to deal with the problem of missing variables. By employing panel data, we are able to control the selection biases of restructuring and handle the problem of missing variables. Referring the existing studies (Liu and Hu, 2021) by using the proportion of mining industry employees in the total regional population regional as the instrumental variable, we also select the proportion of mining industry employees in the total regional population as the proxy variable of regional mineral resources. Then the two-stage panel instrumental variable method is used for estimation, and the results are shown in Tables 11 and 12. It can be seen from the results of the first stage Model (1) that mineral resources impose significant impact on regional air pollution, which indicates that the selection of instrumental variables is effective. In Table 11, Models (2)–(6) are the results of second stage estimation by using the two-stage method of panel instrumental variables. Among them, the results of Model (2) imply that after using the instrumental variable method, air pollution still significantly and negatively affects the labor participation behavior of the elderly, and its marginal effect becomes significantly larger (reaches 0.0906, which is much higher than 0.0043 in the benchmark test). Thus, along with 1 unit increase of the annual average AQI of a region, the probability of labor participation behavior of the elderly will reduce by 9.06%. The results of Models (3)–(6) show that after endogenous treatment of instrumental variables, the air pollution intensity AQI_100day still has significant impact on the labor participation behavior of the elderly, and the estimated coefficient increases to 0.0010, while AQI_200day and AQI_300day still have no significant effect on the labor participation behavior of the elderly. However, when the instrumental variable is processed, AQI_150day shows significant impact on the labor participation behavior of the elderly, and the coefficient reaches 0.0017. The above results further demonstrate that the benchmark test results are robust.

**Table 11. Endogenous treatment of the impact of air pollution on labor participation of the elderly.**
		Explained variable: Work_hour
Variables	First-stage (1)	(2)	(3)	(4)	(5)	(6)
lnAQI/Mineral_resources	3.1203***	$- 0.0906$ **
	(0.6183)	(0.0417)
AQI_100day	281.1983***		$- 0.0010$ **
	(68.2850)		(0.0005)
AQI_150day	166.9779***			$- 0.0017$ **
	(36.4757)			(0.0008)
AQI_200day	$- 72.6987$ *				0.0039
	(60.6475)				(0.0036)
AQI_300day	22.1315*					$- 0.0128$
	(13.7434)					(0.0095)
Constant	—	1.5540***	0.9815***	1.1515***	0.5135	0.8959***
	—	(0.2807)	(0.0502)	(0.1048)	(0.4187)	(0.0862)
Observations	16858	16858	16858	16858	16858	16858
Number of ID	10124	10124	10124	10124	10124	10124

Notes: Standard errors in parentheses, *** $p < 0.01$ , ** $p < 0.05$ , * $p < 0.1$ . Model (1) is the test result of the first stage of the corresponding instrumental variable method. Only the statistical results of the impact of Mineral_resources on air pollution in the first stage of each model are listed here, while the results of other control variables and constant terms are not listed.

Source: Made by the authors.

From Table 12, it could be seen that the estimation results of air pollution’s impact on the intensity of labor participation of the elderly are also robust after using instrumental variables. In detail, as shown in Models (3) and (4), air pollution does have an impact on the working days of the elderly per week and daily working hours. The influence coefficients are 0.0804 and 0.0857 respectively, which are much higher than the corresponding coefficients of the benchmark test, indicating that the benchmark test results are robust. Also, the results of Model (2) show that air pollution has significant impact on the annual intensity of labor participation of the elderly, and the coefficient reaches 0.1066.

**Table 12. Endogenous treatment of the impact of air pollution on the labor participation intensity of the elderly.**
		Labor participation intensity: taking time as an example
Variables	First-stage lnAQI (1)	Work_month (2)	Work_day (3)	Work_hour (4)
lnAQI/Mineral_resources	3.1203*** (0.6183)	$-$ 0.1066** (0.0508)	$-$ 0.0804* (0.0422)	$-$ 0.0857** (0.0425)
Constant	6.3544*** (0.2269)	1.6642*** (0.3419)	1.4630*** (0.2837)	1.5065*** (0.2862)
Observations	16858	16858	16858	16858
Number of ID	10124	10124	10124	10124

Source: Made by the authors.

5.5. Transmission mechanism of air pollution’s impacts

First, poor air quality can lead to inferior health quality of the workers and their family members, which increases medical consumption. In order to increase household income to cope with expenditure risks, workers will enlarge their labor supply, and this is the substitution effect of the air pollution. This study attempts to use the two-week physical pain index as a mediating variable to test whether the substitution effect of air pollution is valid. The results of Models (1) and (2) in Table 13 indicate that air pollution does impose significant impact on the two-week physical pain of the elderly, and the physical pain is subsequently transmitted to the impact on labor participation, thus clear substitution effect of air pollution is exhibited.

Second, when air quality is improved, production efficiency may increase, and also wage rate rises, thus the laborers would reduce labor supply. This is the income effect of air pollution. We attempt to use the regional air quality as an intermediary variable to test whether the income effect of air pollution is valid. The regional air quality is obtained by cross-referencing of the air quality of provinces and the province code. The regional air quality is from the air quality survey in the corresponding year. We define regions with AQI less than 100 as regions of good air quality, otherwise poor air quality. The province code is the numerical code of each province to reflect regional differences. The estimation results of the provincial air quality are shown in Models (3) and (4) in Table 13. Model (3) indicates that the impacts of air pollution do indeed show significant differences due to regional differences, and Model (4) shows that under the condition of controlling the air quality of a region, the air pollution index significantly and negatively affects the labor supply of the elderly, indicating that along with the improvement of air quality, the elderly will indeed reduce their own labor supply, thus a significant income effect of air quality is presented.

**Table 13. The transmission mechanism of air pollution’s impact on the labor supply of the elderly.**
Variables	First-stage two-week physical pain (1)	Second-stage Work_hour (2)	First-stage regional air quality (3)	Second-stage Work_hour (4)
lnAQI	$-$ 0.8077*** (0.0812)	0.0007** (0.0004)	$-$ 0.6501*** (0.0321)	$-$ 0.0046* (0.0024)
Two-Week Physical Pain		$-$ 0.0038** (0.0024)
Provincial Air Quality				$-$ 0.0003** (0.0009)
Constant	0.5189 (1.5627)	0.9812*** (0.0450)	1.8319*** (0.6185)	1.5065*** (0.2862)
Observations	16858	16858	16858	16858
Number of ID	10124	10124	10124	10124

Notes: Standard errors in parentheses, *** $p < 0.01$ , ** $p < 0.05$ , * $p < 0.1$ . Control variable results are not listed.

Source: Made by the authors.

6. Discussion

Labor participation of the elderly is an important measure to actively deal with population aging. In the existing research, more attention has been paid to measures to promote the social participation of the elderly, while less attention is focused on the restrictive factors of their labor participation. This study targets at the elderly and empirically tests the impact of air pollution and its intensity on the labor participation behavior and intensity of labor participation of the elderly, by matching the CHARLS survey database with the tracking survey data of air quality of 122 cities in China. The results show that annual average air pollution of a region significantly impacts the labor participation of the elderly, and the reducing effect reaches 0.43%. Most previous scholars have also stated significant and negative impacts of air pollution on residents’ labor participation in their empirical analysis (Aragón et al., 2017; Kim et al., 2017; Wang et al., 2020; Wu et al., 2023; Zhou and Zhang, 2023), but their research mainly focuses on the working-age population and few focus on the elderly population. Therefore, the conclusion of this study not only enriches the existing research conclusions but also further extends the analysis to the impact of air pollution on the labor participation behavior of the elderly.

Another conclusion of this study is that air pollution significantly impacts the intensity of labor participation of the elderly, especially impacting the working days per week and working hours per day for the elderly. This conclusion also contributes to the existing research regarding the impact of air pollution on the intensity of labor participation of residents and promotes the application of the existing research conclusions.

Moreover, based on the research on residents’ labor participation behavior or probability of the labor participation (Eric, 2005; Hanna and Oliva, 2015; Porto et al., 2021; Alem et al., 2023), strengthening the research on the intensity of residents’ labor participation has more crucial social policy implications, the significance not only relies on the optimizing of the incentive policy of the labor participation behavior of the elderly, but also the meeting of the needs of different intensity of labor participation of the elderly, and on the providing of important empirical support for the introduction of accurate labor policies.

Further, this study shows that different intensities of air pollution could influence the elderly’s labor participation. Specifically, when the regional annual average AQI is $> 100$ , more cumulative days lead to the significant reduction of the intensity of labor participation for the elderly. However, when the regional annual average AQI is $> 150$ and, the increase of cumulative days no longer significantly impacts the labor participation behavior or probability of the participation for the elderly. This conclusion demonstrates that an apparent peak value of regional AQI exists in the effect of air pollution on the labor participation behavior of the elderly, and the value ranges from 100 to 150, while the effect of intensity of air pollution intensity is rarely investigated in the existing research (García-Gómez et al., 2013; Zivin and Neidell, 2012; Liu et al., 2021; Wang et al., 2022a).

Moreover, this study deepens the existing research conclusions and shows that after air pollution reaches a certain value, its impact on the labor participation behavior of the elderly tends to be stable. Research on the impact of air pollution on the intensity of labor participation of the elderly has more practical value and political meaning. It can not only theoretically reveal the mechanism of air pollution impacting on the labor participation but also provide a practical path to optimize the policies of labor participation in terms of labor security (He et al., 2019; Rad et al., 2014; Wang et al., 2020; Yang and Xu, 2020; Aguilar-Gomez et al., 2022; Sarmiento, 2022). Therefore, when formulating the guiding policy of labor participation of the elderly, regional air pollution should be considered as an important index to stimulate the enthusiasm of elderly’s labor participation, and to improve their life quality, and to realize their self-value.

The main research advantage of this study is that it empirically investigates the impact of air pollution on the labor participation of the elderly by constructing a panel data model based on the matching of micro-tracking survey data of CHARLS with the macro-pollution survey data of 122 cities in China. First, we construct the basic data pool by matching the three-year micro-survey data with regional air pollution data. This operation can fully demonstrate the influence coefficients of regional individual labor participation by the change of regional air quality, and the results also may have high reliability. Second, in terms of the core contents of this study, we not only investigate the impact of air pollution on the supply behavior or probability of the labor participation of elderly but also the mechanism of air pollution impacting on the labor participation behavior of the elderly. Moreover, we analyze the impact of air pollution on the intensity of labor participation of the elderly from three aspects: the frequency of annual labor participation, weekly labor participation and daily labor participation, to promote the rigor and perfection of the research.

However, this study holds limitations which can be used as the basis for future development. For example, the observations covered by the CHARLS survey database are mainly determined by the health status of the middle-aged and elderly individuals who are over 45 years old. However, the representativeness of air pollution in these areas may not represent the characteristics of the most prominent areas, resulting in the unreliability of primary observations to a certain extent. The best way to solve this problem is to replenish the shortage of primary observations in this study through supplementary investigation that combines the statistics data of air quality of specific regions in China, which could also be the main contents for further research. At the same time, although this study compares the group heterogeneity of the impacts, there are also obvious differences of labor behavior between the working-age and non-working-age populations. For example, labor participation is an essential condition for personal and family survival for the working-age population, while the elderly may view labor participation as crucial part of their life quality, or in other words, a critical substitute for leisure. Therefore, in future research, we can further compare the labor participation behavior of the working-age population and the elderly population to investigate the mechanism of air pollution impacting on the different populations, and thus provide theoretical and empirical support for introducing more effective environmental governance measures.

7. Conclusions

The main conclusions of this study are as follows: First, regional air pollution significantly affects the labor participation behavior or probability of labor participation of the elderly, with an overall influential coefficient of 0.43%. Also, regional air pollution impacts the intensity of labor participation of the elderly, and especially affecting the weekly working days and daily working hours of the elderly. However, regional air pollution does not significantly impact the labor participation months of the elderly annually.

Second, the impact of air pollution intensity on the labor participation of the elderly is mainly reflected by the impact of AQI_100day, while the cumulative days of extreme pollution with an annual average AQI more than 100(AQI $>$ 100day) shows no significant impact on the labor participation behavior of the elderly. This result also demonstrates the peak value of air pollution where the impact of air pollution intensity on the labor participation behavior of the elderly appears. In terms of the impacts of different pollutants, it appears that the concentration of SO₂ in air pollution of a region significantly affects the labor participation behavior of the elderly.

Third, the impacts of air pollution on the labor participation behavior of the elderly show evident group heterogeneity, for the male elderly, the elderly of low-level education, the elderly in rural areas, and the elderly of low GDP output, the impacts are more significant. Yet, the impacts of air pollution do not have evident group heterogeneity regarding different ages.

At last, significant labor substitution and income effects exist in the impacts of air pollution, which together affect the labor supply of the elderly.

Data Availability Statement

The data that support the findings of this study are openly available at the following URL/DOI: http://charls.pku.edu.cn/.

Acknowledgments

The authors are very grateful for the financial support of The National Social Science Fund of China [23FGLB027] & National Natural Science Foundation of China [71904167; 2023hx125; 42001179]. At the same time, we are very grateful to Tang and other experts for their suggestions on revision and language polishing.

ORCID

Liu Huan https://orcid.org/0000-0001-8772-1545

Hu Tiantian https://orcid.org/0009-0009-7364-5284

Wang Meng https://orcid.org/0000-0001-6288-0646

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Vol. 12, No. 01

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Received 8 January 2024

Accepted 8 May 2024

Published: 6 June 2024

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This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 (CC BY-NC) License, which permits use, distribution and reproduction in any medium, provided that the original work is properly cited and is used for non-commercial purposes.

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