Threshold Effects of PM_2.5 on Pension Contributions: A Fuzzy Regression Discontinuity Design and Machine Learning Approach

Abstract

Air pollution risk significantly impacts social and economic systems. Given the critical role of the pension system in socioeconomic stability, it is crucial to explore the impact of air pollution on pension contributions. Utilizing panel data from eight Chinese provinces between 2014 and 2024, this study quantifies the impact of Particulate Matter (PM_2.5) on pension contributions and explores its nonlinear and lagged effects through a fuzzy regression discontinuity design (FRDD) coupled with double machine learning (DML) techniques. Through the application of the FRDD, we found that pension contributions are significantly reduced when the PM_2.5 concentration exceeds the standard annual threshold of 35 $\mu g/m^3$, and the effects differ between the Urban Employees Basic Pension Insurance (UEBPI) and the Urban and Rural Residents’ Pension Scheme (URRPS). Further, the DML approach validated these findings and suggested that a complex hysteresis response mechanism exists in relation to air pollution. Additionally, it indicated that when PM_2.5 concentrations do not exceed the threshold, this similarly has a negative effect on pension contributions. These findings emphasize the need for policymakers and pension fund managers to integrate environmental considerations into pension sustainability strategies to increase resilience to ongoing environmental risks.

1. Introduction

According to the United Nations’ 1956 report “The Ageing of Populations and its Economic and Social Implications” [1], a country or region is considered to be experiencing population aging when individuals aged 60 and above constitute more than 10$\mathrm{\%}$ of the total population. The 2023 Asia-Pacific Population and Development Report [2] noted that individuals aged 60 and above now constitute 14.2$\mathrm{\%}$ of the total population in the Asia-Pacific region, indicating that the region has officially entered an aging period. Meanwhile, Chen and Giles [3] highlighted that, although European and North American countries entered an aging period earlier than their Asian counterparts, the pace of population aging is accelerating more rapidly in Asia. In response to this trend, pensions—as the primary source of income after retirement—play a vital role in ensuring the economic security of millions of individuals [4]. Consequently, ensuring the long-term sustainability of pension systems and fostering the growth of the pension industry have become key policy priorities for many Asian countries.

Using panel data from 30 Chinese provinces, Zeng [5] showed that, as population aging accelerates, the growth rate of pension income tends to decelerate while pension expenditures accelerate, widening the income–expenditure gap and raising the risk of structural imbalance in the pension system. Building on this macro perspective, a growing body of the micro literature examines how individual-level factors shape contribution behavior, particularly financial literacy, peer effects, mental accounting, and personal experience [6,7]. Furthermore, James employed the sociology of economic life framework to illustrate how pension decisions are deeply embedded in the social and cultural meanings constructed through everyday life experiences [8]. Additionally, government policy is also an important determinant of pension contributions. Li et al. [9] utilized differences in value-added tax enforcement to conduct an empirical analysis and found that stricter tax enforcement improves compliance with wage-linked social insurance contributions. Du et al. [10] studied the reform of the social insurance contribution base and found that adjusting the base affects enterprises’ wage declaration and contribution behaviors, thereby expanding coverage and contribution inflows. Tang and Fang [11] analyzed the impact of social security contribution reform on firm entry, exit, and growth and show that system restructuring can be transmitted to the contribution base through firm dynamics, which reveals the role of the system reform channel.

However, air pollution, recognized as a major public health issue and identified as the fifth leading risk factor for mortality [12], also results in substantial economic and social welfare losses, thereby posing a major threat to sustainable socioeconomic development [13,14]. Although the literature has established the considerable negative effects of air pollution [15,16], and Huang and Huang [17] have demonstrated the negative impact of air pollution on corporate social security contributions, theoretical and empirical research on the impact of air pollution on pension contributions is still limited. Consequently, understanding the impact of air pollution on pension contributions is imperative for formulating effective policies and developing sound risk-management strategies in the insurance and government sectors.

In this study, we selected PM_2.5 as the exposure factor to quantify air pollution and investigated whether changes in PM_2.5 concentrations affect pension contributions to assist the government and insurance companies in promoting pension system reform and the construction of an ecological civilization. We used data from China because of its status as the world’s second-most populous country, its substantial elderly population, and the rapid pace at which its population is aging [18,19]. Therefore, the potential future pension shortfall in China is a concern. We selected the total pension contribution data of urban employees and rural residents and PM_2.5 concentrations from 2014 to 2024 across eight provinces distributed in China’s four economic regions to construct our models and provide new insights into the impact of air pollution on pension contributions. Huang and Huang [17] adopted a geographic regression discontinuity design methodology based on the industry firm data to assess the impact of air pollution on corporate social security contributions empirically. Our study adopts a fuzzy regression discontinuity design (FRDD) model to estimate the local average treatment effect (LATE) in the provinces above the standardized line by using annual PM_2.5 concentrations that exceed 35 $\mathrm{\mu }g/m^3$ as a threshold, thus determining the effect of PM_2.5 concentrations exceeding the threshold of the pension contribution growth rate as well as the value of the contribution. We further used the education and government invention levels as the control variables for Urban and Rural Residents Pension Scheme (URRPS) modeling [20,21] and the tax liability level and industry structure as the control variables for Urban Employees Basic Pension Insurance (UEBPI) modeling, drawing on findings from prior research [9,22]. Then, we employed the bandwidth analysis to check the robustness of the FRDD. Adetutu [23] identified a nonlinear relationship between life insurance demand and pollution risk, and Wang et al. [24] reported a nonlinear relationship between PM_2.5 concentrations and crop insurance indemnity. Therefore, we adopted double machine learning with a nonlinear learner to capture the potential nonlinear and lagged effects of PM_2.5 concentrations on pension contributions across time and space. Additionally, double machine learning can provide a flexible, nonparametric estimation of the global average treatment effect (ATE) and provide further evidence of the impact of the actual value of PM_2.5 concentrations on the actual value of pension contributions for URRPS and UEBPI.

In summary, only a few studies have measured the impact of air pollution risks on pensions based on pension contribution data. Our study adds to the existing body of knowledge by systematically examining how air pollution affects pension contributions under both the UEBPI and URRPS, thereby shedding light on the heterogeneous effects of environmental risks across China’s dual-track pension system. Furthermore, we identify the LATE of pollution concentration exceedance on pension contribution behavior through a fuzzy regression discontinuity design, which enhances the robustness of causal inference. And the double machine learning framework with nonlinear learners is introduced to flexibly estimate the global average treatment effect (ATE) of pollution on pension contributions to capture potential nonlinear and lagged effects. Ultimately, this study provides valuable insights for the improvement of risk management practices within the framework of basic pension insurance, and the introduction of modern causal inference methods into the study of pension economics further helps to expand the research methods and paths in the field of social security in the context of sustainable development.

The remainder of the paper is organized as follows. Section 2 summarizes previous studies on the negative effects of air pollution and factors affecting pension contributions. Section 3 details the data sources and methodology. Section 4 expands on the empirical results, discusses the Fuzzy RDD and DML, and explores the nonlinear relationship and lag effects between PM_2.5 concentrations and pension contributions of URRPS and UEBPI, respectively. Section 5 highlights the implications of our findings and potential applications. Finally, Section 6 summarizes the originality and relevance of the research results and explains the limitations and future research directions.

2. Literature Review

2.1. Negative Effects of Air Pollution

Air pollution has emerged as a considerable public health concern adversely affecting many fields, including human health, agricultural productivity, and social welfare. A growing body of scholarly research has concentrated on the adverse health externalities of air pollution. Severe air pollution not only negatively impacts mortality [25,26] and physical health, contributing to conditions such as cardiovascular disease [27,28], lung cancer [29], and diabetes [30], but also poses substantial risks to mental well-being [31,32]. Thus, the negative impacts of air pollution (especially those of ozone $O_3$ and PM_2.5) on agricultural output have attracted the attention of many researchers. Feng and Kobayashi [33] conducted a meta-analysis demonstrating that the ozone concentration $O_3$ (31–50 ppb) can reduce wheat, rice, and soybean yields by 9.7, 17.5, and 7.7$\mathrm{\%}$, respectively. Zhou [34] employed econometric modeling, incorporating fundamental agricultural inputs and climatic factors to provide empirical evidence of a negative correlation between PM_2.5 concentrations and agricultural yields in China, and Liu [35] reported average increases in corn and rice yields by 0.45 and 0.70$\mathrm{\%}$, respectively, when the PM_2.5 concentration reached the standard of 35 $\mathrm{\mu }g/m^3$ (secondary standard for ambient air quality). Additionally, at the socioeconomic level, the Organization for Economic Co-operation and Development (OECD) working paper [36] analysis based on European data indicates that air pollution negatively impacts market economic activity across the economy. Estimates suggest that a 1 $\mathrm{\mu }g/m^3$ increase in the PM_2.5 concentration (or a 10$\mathrm{\%}$ increase relative to the sample mean) leads to a 0.8$\mathrm{\%}$ decline in real GDP for the current year. Shi and Yu [37] highlighted that a 1 $\mathrm{\mu }g/m^3$ increase in the annual urban PM_2.5 concentration leads to a 7.7$\mathrm{\%}$ decline in residents’ subjective well-being, a reduction equivalent to 7.7$\mathrm{\%}$ of household disposable income. The detrimental effects of air pollution on the economy and social welfare have consequently drawn substantial attention from researchers.

The economic and social welfare impact of air pollution is predominantly examined in the context of health and healthcare expenditures. As early as 1970, Lave and Seskin [38] initiated research on the correlation between air pollution and mortality rates, aiming to quantify its economic costs. The study estimated that a 50$\mathrm{\%}$ reduction in air pollution across major cities could result in cost savings of approximately USD 1.222 billion in expenses related to respiratory diseases and USD 468 million in costs associated with cardiovascular diseases. Moreover, Chen and Chen [39] investigated the causal relationship between air pollution and medical expenditures, concluding that air pollution contributes to an increase in healthcare costs, with an elasticity coefficient of 10.013. Wang et al. [40] applied the Kriging interpolation method and provided evidence of a positive correlation between the PM_2.5 concentration and $O_3$ and medical expenditures, and Selin et al. [41] utilized the MIT Emissions Prediction and Policy Analysis-Health Effects (EPPA-HE) model to estimate that global economic losses resulting from $O_3$-related health issues will reach USD 580 billion by 2050.

There have also been studies that examine the broader economic and social welfare impacts of air pollution beyond health and healthcare expenditure. First, air pollution significantly affects household well-being. Gan et al. [42] utilized a baseline model to examine the relationship between air pollution and household participation in the stock market and found that households tend to mitigate financial risks by reducing their engagement in financial markets in response to high levels of air pollution. Meanwhile, Cai et al. [43] found a negative correlation between the PM_2.5 concentration and housing prices by using the instrumental variable (IV) method. Moreover, researchers analyzed the economic consequence of air pollution on labor productivity. GraffZivin and Neidell [44] indicated that a 10 ppb increase in $O_3$ leads to a 5.5$\mathrm{\%}$ decline in the labor productivity of American farmers. Chang et al. [45,46] identified a negative impact of air pollution on labor productivity, based on analyses of data from Chinese and American workers. Chen and Zhang [47] employed instrumental variable strategies to address the endogeneity issue of air pollution and found that a 10-unit increase in the air pollution index leads to a significant 4$\mathrm{\%}$ decline in labor productivity.

The aforementioned literature explores the economic consequences of air pollution from multiple perspectives, highlighting its negative externalities. However, in the context of an aging population, pensions serve as a critical social security mechanism that ensures the basic living needs of the elderly and covers their medical expenses; few studies have measured the impact of air pollution risks on pension income from an insurance data perspective. This study empirically examines the effect of air pollution on pension contributions among urban and rural residents as well as urban employees. By doing so, it not only expands the theoretical literature on air pollution but also offers new insights into the sustainable development of pension systems.

2.2. Factors Affecting Pension Contributions

China’s pension arrangements were historically highly fragmented along urban–rural lines. Throughout the 1990s and early 2000s, rural residents had very limited pension coverage, whereas urban workers in the state sector enjoyed relatively comprehensive pensions under the “iron rice bowl” system [48]. The basic pension insurance scheme for rural residents and urban non-employees has undergone three major changes. Following the introduction of the New Rural Pension Scheme in 2009 and the Urban Residents’ Pension Scheme in 2011 [49], a unified voluntary pension scheme, China’s Urban and Rural Residents’ Pension Scheme (URRPS), was established in 2014 to cover both rural residents and urban non-employees to realize comprehensive coverage of both urban and rural residents [48]. In design, the URRPS is a partially funded, two-tier system. Residents contribute voluntarily to an individual account, choosing their contribution level from preset tiers, and these contributions are fully accumulated in the account with matching subsidies from central and local governments [20].

As for the contributing factors of URRPS, the literature mainly focuses on institutional factors and individual characteristics. A recent county-level study finds that residents who are wealthier, better educated, and have more knowledgeable about pension policies are more likely to participate in the URRPS [20]. Additionally, some studies found that a higher trust in the government and in pension administration is associated with a greater willingness to enroll in the new rural/residents pension scheme; Chen et al. [21] found that for this older cohort, village-level characteristics (such as local promotional campaigns or peer enrollment rates) were more important in explaining whether a family enrolled. Thus, non-monetary factors such as system trust and the perceptions of benefit reliability, together with income and education levels, influence pension scheme participation decisions.

The other part of the first pillar of China’s pensions, together with URRPS, is the Urban Employee Basic Pension Insurance (UEBPI). UEBPI is China’s cornerstone mandatory pension scheme for formal sector workers, including enterprise employees and government and public institution staff. Employers and employees are legally required to make pension contributions, and the current standard arrangement is that employers contribute approximately 16% of their gross salary to a unified social pension fund, while employees contribute 8% of their salary to an individual pension account [49].

As for the contributing factors of UEBPI, the literature mainly focuses on system reform and enterprise contributions. Li et al. [9], Liu et al. [22], Li et al. [50], and Du et al. [10] separately examined the effects of the tax system, the minimum wage system, and the social security contribution base on social security and employee pension contributions. They concluded that the regulation of the tax and social security system and the establishment of the minimum wage system effectively contribute to the expansion of social and pension insurance coverage and the growth of the income of the social and pension insurance fund. It has also been shown that, while the UEBPI is mandatory for formal sector employees, actual compliance with this provision and the completeness of coverage depends on several factors. The key point is non-compliance by employers, especially small private businesses. High contribution rates have long been seen as a disincentive to business participation, leading many businesses to reduce their pension obligations by avoiding or understating wages [51]. Qian et al. [52] found that, while direct state oversight may be limited, the severity of government sanctions has a significant indirect effect: firms operating in environments where the threat of enforcement is more stringent are more inclined to enroll their employees in the program. Additionally, Huang et al. [17] applied the regression discontinuity design and found that air pollution reduces the level of social security contributions by lowering the production performance and innovation level of industrial firms, as well as lowering the total wages of employees.

Overall, the literature has examined the impact of some institutional factors on pension contributions from different perspectives, but most of the literature has neglected the impact of non-institutional factors on pension contribution behavior, and there are especially few studies on the pension contribution effect of air pollution. Therefore, focusing on the impact of non-institutional factors on pension contributions is also of great theoretical and practical significance.

2.3. Theoretical Links Between Air Pollution and Pensions

To provide a stronger theoretical basis for the subsequent empirical research strategy, we will next synthesize the theoretical association between air pollution and pensions based on summaries of the previous literature. In this paper, we argue that PM_2.5 affects pension contributions through the following channels. Firstly, through the labor force health and productivity channel, pollution exacerbates diseases such as heart disease, reducing working hours and earnings. Thus, the total wage bill that determines the UEBPI contribution base is compressed. Secondly, in terms of firm performance and costs, air pollution affects firms with different industrial structures differently. It increases firms’ operating and compliance costs and reduces the output quality, resulting in firms downsizing and reducing the total declared wage bill under the UEBPI pension system. Thirdly, in terms of household circumstances and trust in government systems, individuals’ trust in government and pension administrators, as well as their perception of benefit reliability, together with income level and education, influence participation and supplemental contribution decisions. These decisions are crucial for contributions to the UEBPI system, which relies on voluntary contributions. Based on these theoretical correlations, our study uses Fuzzy RDD to reveal contrasting effects around the national PM_2.5 standard threshold and dual machine learning to capture nonlinearities, hysteresis structures, and cross-provincial heterogeneity. This provides testable policy insights into the contribution mechanisms of the wage-linked UEBPI and the voluntary URRPS.

3. Date and Methodology

3.1. Data

In this study, we used historical PM_2.5 concentration data obtained from China Environmental Monitoring Center (CNEMC) [53]. Additionally, historical pension contribution data for urban employees and rural residents were sourced from China Stock Market and Accounting Research Database (CSMAR) [54]. Because China only formally established the existing URRPS in 2014, and there are some provinces with some missing values in the dataset, to exclude the effects of other disturbances, we selected eight representative provinces distributed in the four major economic regions of China, Hebei, Beijing, Henan, Shanxi, Liaoning, Heilongjiang, Xinjiang, and Neimenggu, as the objects of the study and then assessed the impact of air pollution on both urban employees’ and rural residents’ pension contributions from year 2014 to year 2024 by integrating these datasets.

3.1.1. Pension Contribution Database

The pension contributions for URRPS and UEBPI databases are sourced from CSMAR [54]. The CSMAR database, developed by GTA Information Technology Co., Ltd. (Shenzhen, China) is one of the most comprehensive and authoritative databases for Chinese financial and economic research. It provides standardized and well-structured data that align with international databases; it is also widely used for empirical studies in accounting, finance, and corporate governance. The data on pension contributions for URRPS and UEBPI are both categorized in the macroeconomic sub-database of the CSMAR.

For this analysis, we focused on the eight representative provinces, Hebei, Beijing, Henan, Shanxi, Liaoning, Heilongjiang, Xinjiang, and Neimenggu, which are distributed in the four major economical regions, East, Mid, East North, and West, and the database contains records spanning from 2014 to 2024. Figure 1 depicts the evolution of pension contributions for URRPS and UEBPI in these eight provinces over the specified timeframe, respectively. These figures showed a general upward trend in annual pension contribution for both URRPS and UEBPI, which might be related to China’s continued economic development and the improvement of government systems [55]. And pension contributions for UEBPI experienced a sharp decline in all provinces, which is likely related to the COVID-19 pandemic shock.

To effectively visualize the relationships within the data for modeling purposes, we processed the original pension contribution data by calculating the growth rate of pension contribution for URRPS and UEBPI. The plots for the growth rate of pension contributions are shown in Figure 2. The resulting plot exhibits a jagged shape, indicative of significant variation in the growth rate of pension contributions and reflecting the inherent uncertainty and variability in pension contribution risks. Certain sharp fluctuations can be explained by the influence of air pollution.

3.1.2. PM_2.5 Concentration

Annual PM_2.5 concentration data from the 8 provincial regions in China from 2014 to 2024 were sourced from CNEMC. In our analysis, the eight representative provinces we focus on are located in each of China’s four major economic zones, East, Mid, East North, and West; we then employ exposure-weighted PM_2.5 concentration to determine the average, maximum, and minimum levels of PM_2.5 concentration.

Provinces within the same economic region have similar trends in PM_2.5 changes, so we use Figure 3 to display average annual PM_2.5 concentration, highlighting the annual maximum, average, and minimum values across the four economic zones. The vertical bars in these figures indicate the standard deviation of the annual provincial PM_2.5 concentration for each year. The standard deviation of the maximum PM_2.5 concentration is the largest. It is evident from these figures that the PM_2.5 concentration has been decreasing in recent years, which showed the efficiency of the environmental regulations by the Chinese government. In the early years, the standard deviation of the maximum PM_2.5 concentration is particularly large in the East Region, and the maximum PM_2.5 concentration in some years in the East Region exceeds 100 $\mu g/m^3$, which is related to the fact that the majority of China’s industrial zones are situated in its more economically developed eastern regions and its heavy reliance on coal-intensive industries such as steel and cement, combined with widespread residential coal heating during winter [56].

3.2. Methodology

In this study, to comprehensively assess the impact of air pollution on pension contributions under the URRPS and UEBPI, we adopted a two-step identification strategy combining fuzzy regression discontinuity design (FRDD) and double machine learning (DML). FRDD exploits the regulatory threshold of 35 $\mu g/m^3$ for annual maximum PM_2.5 as an instrument to estimate the LATE in provinces just above the standard, leveraging quasi-random variations in pollution exposure. To complement this, DML provides a flexible, nonparametric estimation of the global average treatment effect (ATE), capturing potential nonlinear and lagged effects of PM_2.5 concentration on pension contributions across time and space. This dual approach strengthens causal identification by integrating threshold-based and data-driven strategies.

3.2.1. Fuzzy Regression Discontinuity Design

To estimate the causal effect of air pollution on pension contributions, we employ a fuzzy regression discontinuity design (Fuzzy RDD) using the national air quality threshold of 35 $\mu g/m^3$ for annual maximum PM_2.5 as the cutoff point. In China, this level represents the Grade II standard under the National Ambient Air Quality Standards (NAAQS), signaling the boundary beyond which air pollution is officially deemed harmful. Our identification strategy assumes that, although crossing this threshold does not deterministically assign treatment, it causes a discontinuous increase in the probability of experiencing adverse effects on pension contributions, thus justifying the use of a fuzzy rather than a sharp RDD [57].

The Fuzzy RDD is formally implemented using a two-stage least squares (2SLS) approach, as it involves endogenous treatment assignment. In the first stage, an indicator variable based on the cutoff (typically a binary instrument $Z$) is used to predict the probability of receiving the treatment variable $D$. This step identifies the discontinuous jump in treatment probability at the threshold and helps address endogeneity in the treatment variable. When the binary instrument $Z$ significantly affects the treatment variable $D$, the second stage can be performed. In the second stage, the predicted values of treatment from the first stage ($\widehat{D}$) are used to estimate its causal effect on the outcome variable. This yields an unbiased estimate of the $LATE$ around the cutoff.

In our study, we considered $Y_{it}$ to denote the annual pension contribution in province $i$ at year $t$ and let $D_{it}$ be defined as the pollution exposure which was measured as the three-year moving average of PM_2.5.

$$\begin{array}{c}{D}_{it}\equiv PM{2.5}_{ma3}={\displaystyle \frac{{PM2.5}_{it}+{PM2.5}_{it-1}+{PM2.5}_{it-2}}{3}} \end{array}$$

(1)

Additionally, the running variable is defined as

$$\begin{array}{c}{running}_{it}={PM2.5}_{it}-35\mu g/m^3\end{array}$$

(2)

where ${PM2.5}_{it}$ represents the annual maximum PM_2.5 concentration in city i during year t. We construct an indicator variable $Z_{it}$ that equals 1 if ${PM2.5}_{it}$ ≥ 35 and 0 otherwise. The Fuzzy RDD was then constructed using the following two-stage least squares (2SLS) procedure.

Stage 1 (first-stage equation):

$$D_{it}=\alpha +\pi \ast Z_{it}+{\gamma }_1{running}_{it}+{\gamma }_2{{running}_{it}}^2+{\gamma }_3\ast \left(Z_{it}\ast {running}_{it}\right)+{\delta }^{\prime }{X}_{it}+{\eta }_i+{\tau }_t+{\epsilon }_{it }$$

(3)

Stage 2 (second-stage equation):

$$\begin{array}{c}{Y}_{it}=\beta +\theta \ast {\widehat{D}}_{it}+{\rho }_1{running}_{it}+{\rho }_2{{running}_{it}}^2+{\rho }_3\ast \left(Z_{it}\ast {running}_{it}\right)+{\phi }^{\prime }{X}_{it}+{\eta }_i+{\tau }_t+v_{it }\end{array}$$

(4)

where $Y_{it}$ is the observed outcome (pension contribution amounts); ${\widehat{D}}_{it}$ is the predicted treatment from the first stage; $\theta$ identifies the local average treatment effect (LATE) of long-term PM_2.5 exposure for compliers at the threshold; $Z_{it}$ is the instrument indicating whether PM_2.5 exceeds the cutoff; ${\gamma }_i$ and ${\rho }_i$ are flexible coefficients of the running variable, the quadratic term of the running variable, and the interaction term; $X_{it}$ is a vector of observed control variables, as we have learned that the level of education, the level of richness of the population, and the degree of government intervention affects pension contributions of URRPS [20,21], and thus, $X_{it}$ includes log-transformed rural residents’ income, education level, government intervention, and rural population size when constructing models for URRPS. Based on the previous literature, when constructing the RDD models for UEBPI, we used different sets of control variables such as log-transformed urban employees’ income, urban employees’ population tax size, tax liability for enterprises, and provincial industrial structures. ${\eta }_i$ and ${\tau }_t$ represent province and year fixed effects, and ${\epsilon }_{it}$ and $v_{it}$ are the error terms for each stage.

This local instrumental variable (LIV) approach captures the LATE for cities whose probability of experiencing low pension contribution growth is discontinuously affected by crossing the PM_2.5 threshold. This method relies on standard assumptions of continuity in potential outcomes and absence of precise manipulation of the running variable near the threshold. We test these assumptions through the McCrary density test [58] and covariate balance checks around the cutoff.

To assess robustness, we further conduct bandwidth sensitivity analyses by estimating the model under multiple bandwidths around the threshold. Bandwidth selection is initially guided by the Imbens–Kalyanaraman (IK) and Calonico–Cattaneo–Titiunik (CCT) optimal bandwidth procedures [59], with sensitivity tests across ±25 to ±40 $\mu g/m^3$ windows.

Overall, employing a Fuzzy RDD framework with comprehensive diagnostic checks allows us to credibly estimate the localized causal impact of high PM_2.5 pollution events on pension contributions under URRPS and UEBPI. Our methodological rigor and explicit acknowledgment of assumptions and limitations contribute to the robustness and reliability of our empirical findings, thus offering great insights for policymakers addressing the economic impacts of environmental issues.

3.2.2. Double Machine Learning

To flexibly estimate the causal effect of air pollution on pension contributions while addressing high-dimensional and potentially nonlinear confounding, we employ the double machine learning (DML) framework, as developed by Chernozhukov et al. [60]. This method enables valid inference for treatment effects in the presence of complex covariate structures by combining machine learning with orthogonalized moment conditions and sample splitting.

In this study, we assumed the following partially linear model:

$$\begin{array}{c}{Y}_i=\tau \left(X_i\right)\ast D_i+g\left(X_i\right)+{ϵ}_i\end{array}$$

(5)

$$\begin{array}{c}{D}_i=m\left(X_i\right)+V_i\end{array}$$

(6)

where $Y_i$ is the observed pension contribution for Province $i$, $D_i$ denotes the treatment variable representing air pollution (e.g., maximum PM_2.5 or its lag), and $X_i$ is a vector of control variables including some economic and demographic factors. The functions $g\left(X_i\right)$ and $m\left(X_i\right)$ represent the potentially nonlinear relationships between the covariates and the outcome or treatment, respectively. The function $\tau \left(X_i\right)$ captures the causal effect of interest.

The DML procedure involves the following three key steps. First, the machine learning methods are used to estimate $g\left(X_i\right)$ and $m\left(X_i\right)$; in this study, we applied two nonlinear machine learners with the DML framework, including XGBoost [61] and Causal Forest [62]. XGBoost is employed to estimate the nuisance functions $m\left(X_i\right)$ and $g\left(X_i\right)$ under cross-fitting, and its strong predictive power for nonlinear databases improves orthogonalization to provide less biased and more stable inferences of the average treatment effect (ATE) of current and lagged PM_2.5, Meanwhile, the Causal Forest Learner can be used to directly estimate the heterogeneous treatment effect, portraying the change in effect across different provinces and structural conditions, such as a high industrial share or large population size. Under the Causal Forest Learner, causal average treatment effect (CATE) aggregation yields an ATE, which can be triangulated with the ATE of the DML-XGBoost model to improve the credibility of the machine learning conclusions, and, conversely, inconsistency suggests the presence of modeling bias in the machine learning model. The dual-learners comparison design can provide robust average effects and policy-relevant heterogeneous results simultaneously, complementing the local identification of Fuzzy RDD. Second, we computed the residuals $\widehat{{ϵ}_i}=Y_i-\widehat{g}\left(X_i\right)$ and $\widehat{v_i}=D_i-\widehat{m}\left(X_i\right)$ and then regressed $\widehat{{ϵ}_i}$ on $\widehat{v_i}$ to estimate the value of $\theta$ and explore the causal effect of the treatment.

In summary, DML is well-suited for our research context, given that the relationship between PM_2.5 and pension contributions under URRPS and UEBPI may involve threshold effects, lags effects, and nonlinear interactions with socioeconomic conditions. It not only identifies the overall causal effects of pollution but also captures nonlinear effects that are difficult to detect with traditional methods.

4. Results

4.1. Results from the Fuzzy Regression Discontinuity Design

In this study, our primary objectives were to determine whether PM_2.5 concentrations influence the level of pension contributions of URRPS as well as UEBPI. To demonstrate the potential improvements in model performance and predictive power, we introduced the maximum PM_2.5 concentration as the explanatory variable and constructed two different models for pension contributions of URRPS and UEBPI, respectively. The following two models were examined.

Case 1: The model was designed to determine the impact of PM_2.5 concentrations exceeding the policy threshold 35 $\mu g/m^3$ on the pension contributions of URRPS, alongside the year, province, log-transformed rural population size, log-transformed average years of schooling, log-transformed average disposable income for rural residents, and log-transformed degree of government intervention;

Case 2: The model was designed to determine the impact of PM_2.5 concentrations exceeding the policy threshold 35 $\mu g/m^3$ on the pension contributions of UEBPI, alongside the year, province, log-transformed urban employee population size, log-transformed average disposable income for urban employees, level of tax liability, and industry structure.

4.1.1. Impact of Severe PM_2.5 Concentrations on Changes in Pension Contributions of URRPS

First, to identify the causal impact of severe PM_2.5 concentrations on changes in pension contributions of URRPS, we implemented a fuzzy regression discontinuity design (Fuzzy RDD) using a two-stage least squares (2SLS) framework. The cutoff value of the PM_2.5 is set at 35 $\mu g/m^3$, consistent with the Chinese national air quality standard. We defined a binary instrumental variable $Z=1$ if the annual maximum PM_2.5 concentration in a province exceeds this threshold and 0 otherwise. The results for first-stage regression and second-stage IV regression are detailed in

Table 1. Results for first-stage and second-stage IV regression for URRPS.

Dependent Variable	Treatment            Pension Contribution of URRPS
	First Stage	Second Stage (Clustered by Province)
pollution exposure		−34.36 ***
		(1.7868)
Z	−2.2978
	(1.9096)
running	14.1991 **	−0.6496
	(33.1006)	(1.1909)
poly(running,2)	−59.0698 ***	−0.75886 *
	(15.0759)	(0.0487)
I(running * Z)	1.0029 ***	1.3318
	(0.2646)	(2.5685)
log10 (disposable income)	314.9372 *	3220.059 **
	(97.1585)	(1372.846)
log10 (years of schooling)	168.3646	1319.7505 **
	(125.0312)	(467.2204)
log10 (government intervention)	2.14038	152.279 **
	(2.1665)	(10.375)
log10 (rural population size)	5.268	873.0824 **
	(3.4596)	(216.684)
F-statistics	116.2
	p-value: 0.00002
$R^2$	0.97

Notes: *, **, *** indicate statistical significance at the 10%, 5%, and 1% levels (two-tailed), respectively.

. For each control and independent variable, we showed the $\beta$ value for the parametric coefficient, the $p value$ (*, **, and ***), the standard deviation for the parametric coefficient, and standard errors clustered by province in the second-stage IV.

In the first-stage regression, the dependent variable is pollution exposure, which captures the three-year moving average of PM_2.5. The first-stage model includes $Z$ (the instrument), and the flexible polynomial in the running variable $(Max\_PM2.5-35)$, their interaction, as well as log-transformed control variables such as income, education level, government expenditure, and rural population, along with city and year fixed effects. The results showed that the cutoff indicator Z is not individually significant, whereas the interaction term $I(running\times Z)$ carried a positive and sizeable coefficient, suggesting that the slope shift at the cutoff is highly significant. This pattern was consistent with the specialization of the Fuzzy RDD, which states that the PM_2.5 crossing the standard 35 $\mu g/m^3$ changes the conditional relationship between the running and long-term exposure and thereby increases exposure probabilistically rather than deterministically. Meanwhile, the quadratic term of the running variable was significantly negative, indicated by a nonlinear trend near the threshold value. Additionally, the first-stage F-statistic $(F=116.2,p=0.00002)$ and an $R^2$ of 0.97 indicated that the instrument is informative and supports the validity of the Fuzzy RDD approach in this study. Then, we further validated the effectiveness of the Fuzzy RDD method in this study by applying the first-stage FRDD diagnostic figure, which captures the relationship between long-term PM_2.5 exposure near the threshold of 35 $\mu g/m^3$ and the running variable. Figure 4 shows that the mean jump in long-term exposure is limited at the threshold of 35 $\mu g/m^3$ for the PM_2.5, but exposure to the right of the threshold grows more rapidly with the running variable. This suggests that the threshold affects long-term exposure mainly by changing the marginal relationship between exposure–running variables, providing empirical evidence for localized IV identification by FRDD and consistent with the significant results of $I(running\times Z)$ in the first-stage regression.

In the second-stage IV regression, the dependent variable is the actual level of pension contributions of URRPS. The endogenous variable is the pollution exposure defined as the three-year moving average of PM_2.5, with instrumental variable estimation via a quadratic polynomial in the threshold indicator Z, an interaction term, and the same set of covariates in the first stage. The coefficient on the pollution exposure is negative and equal to −34.36, which is significant at the 1% level, suggesting that, within the neighborhood of the cutoff, a 1 $\mu g/m^3$ increase in PM_2.5 is associated with a decrease of about 34.36 units in URRPS contributions. Meanwhile, other covariates such as education level and government intervention show expected signs and significant effects, indicating that economic capacity and demographic structure also play substantial roles in the pension contributions of URRPS, which aligns with the results of previous studies. Taken together, these findings support the hypothesis that higher fine-particulate exposure causally reduces pension contributions among URRPS near the regulatory threshold, and these findings align with the first-stage evidence of a significant slope change at the cutoff, reinforcing the causality interpretation under the local RDD assumptions.

To further validate the negative impact of PM_2.5 on the pension contributions of URRPS, Figure 5 illustrates the nonlinear relationship between PM_2.5 exposure and the pension contributions of URRPS, using a quadratic polynomial regression around the policy threshold of 35 $\mu g/m^3$. The fitted curves reveal an upward trend in contributions under low pollution conditions, contrasted with a declining trend once pollution exceeds the threshold. This curve might be consistent with the mechanism by which economic activity rises in tandem with pollution in low-pollution zones, leading to increased contributions; however, after pollution exceeds the standard, health absenteeism and compliance costs become dominant, instead inhibiting the ability and willingness to contribute to the pension. Meanwhile, visible discontinuity at the cutoff supports the presence of a localized treatment effect, which is consistent with the two-stage IV estimate based on the Fuzzy RDD, suggesting that high pollution levels significantly undermine pension funding outcomes.

4.1.2. Impact of Severe PM_2.5 Concentrations on Changes in Pension Contributions of UEBPI

Next, to identify the causal impact of severe PM_2.5 concentrations on changes in the pension contributions of UEBPI, we applied a similar fuzzy regression discontinuity design (Fuzzy RDD) using a two-stage least squares (2SLS) framework. Also, unlike the set of control variables used in the previous study of PM_2.5 on pension contributions to UEBPI, the current study used a different set of control variables in the Fuzzy RDD.

From the results in the first stage of the Fuzzy RDD, we regress the pollution exposure that captures the three-year moving average of PM_2.5 on the instrumental variable Z (an indicator equal to 1 when the PM_2.5 exceeds the cutoff 35), the running variable $(PM2.5-35)$, and their interaction, alongside a series of control variables including log-transformed income, tax revenue, industrial structure, log-transformed population, provincial fixed effects, and year fixed effects. In terms of model fitting, the $R^2$ of 0.98 indicate a reasonably good model fit in the first stage.

The results are similar to the results of first-stage regression under URRPS, showing that, although the coefficient on the instrumental variable Z is −0.929, which is not individually significant, the slope changes sharply at the cutoff point since the interaction term is statistically significant and positive, indicating a stronger marginal association between the running variable and long-term exposure once the 35 $\mu g/m^3$ standard is exceeded. Meanwhile, the quadratic term in the running variable is negative, which is equal to −24.5217 and significant at the 1$0\%$ level, supporting the use of piecewise polynomial controls in the second-stage regression. Overall, the results of the first stage supported no sizable mean jump in exposure at 35 $\mu g/m^3$ but a statically pronounced kink. Thus, the cutoff indicators and their interactions provide exogenous local variations in long-term pollution exposure, satisfy the correlation condition in the first stage of the FRDD model, and provide a reliable basis for estimating the local causal effect of exposure on pension contributions under UEBPI in the second stage.

Table 2. Results for second-stage IV regression under UEBPI.

Dependent Variable	Pension Contribution of UEBPI
	Second Stage
pollution exposure	−27.5573 *
	(2.8643)
running	−5.01516
	(12.45714)
poly(running,2)	4.5838 *
	(0.5478)
I(running*Z)	51.2796
	(29.6008)
log10 (urban employee disposable income)	−7638.48
	(5913.91)
tax liability	478.1058
	(619.8445)
industrial structure	16,641.28 **
	(1806.081)
log10 (urban employee population size)	−2624.235 ***
	(499.11178)
$R^2$	0.973
adjusted $R^2$	0.946

Notes: *, **, *** indicate statistical significance at the 10%, 5%, and 1% levels (two-tailed), respectively.

reports the results of the second stage. For each control and independent variable, we showed the $\beta$ value for the parametric coefficient, the $p value$ (*, **, and ***), and the standard deviation for the parametric coefficient.

The results of the second stage showed that the increase in PM_2.5 exposure significantly contributes to the decrease in the level of actual pension contributions under UEBPI within the neighborhood of the threshold. The coefficient on treatment is positive, which is equal to −27.5573 and significant at the 5% level, suggesting that the provinces that experienced a significant decrease in pension contributions of about 27.5573 units under UEBPI within the neighborhood of the cutoff is with a 1 $\mu g/m^3$ increase in PM_2.5. Further, although the interaction term was not significant in the resultant realizations, the quadratic term of the running variable was positive and significant at the 10% significance level (coefficient estimate = 4.5838, p-value < 0.1), suggesting that there is a localized upward trend in pension contributions near the PM_2.5 threshold. Additionally, several control variables further supported this economic interpretation. The coefficient of urban employee population size was negative and strongly significant at the 1% level, where the estimated value is −2624.235 and the p-value is <0.01, suggesting that more populous provinces may be more vulnerable to pollution shocks in terms of pension system performance. The industrial structure variable had a positive and significant effect at the 1% level, suggesting that service-driven economies may be better able to sustain pension growth under unfavorable environmental conditions. These findings suggest that severe PM_2.5 pollution may inhibit the ability of local governments or employers to sustain strong pension contribution growth when PM_2.5 exceeds a pollution threshold of 35 $\mu g/m^3$, even when underlying economic conditions may support such growth.

Overall, the Fuzzy RDD empirical results of the UEBPI and the URRPS present several commonalities despite the significant differences in system design. First, both types of pension insurance systems exhibit statistically significant breakpoint effects around the PM_2.5 national annual pollution standard, which is equal to 35 $\mu g/m^3$, suggesting that air pollution can significantly affect pension contribution levels through behavioral adjustment mechanisms in both urban and rural environments, and the LATE estimation results support the causal effect of PM_2.5 in both cases. Meanwhile, the estimation coefficients of the interaction term of instrument variable Z and the running variable in the first stage are significant in both models, indicating a stronger marginal association between the running variable and long-term exposure, and the exceedance of the pollution threshold provides an exogenous source of pension contribution changes [63].

4.1.3. Robustness of Fuzzy Regression Discontinuity Design Estimates

To validate the robustness of our regression discontinuity design (RDD) estimates, we performed a bandwidth sensitivity analysis. The choice of bandwidth in RDD is crucial, because it determines the range of data around the cutoff used for local estimation. A narrower bandwidth may lead to high variance due to a small sample size, while a too wide bandwidth may introduce bias by including observations far from the threshold, potentially violating the local randomization assumption [57,64]. Therefore, following standard practice, we estimate the treatment effects across multiple alternative bandwidths and assess whether the results remain consistent. This diagnostic procedure helps ensure that the estimated causal effects are not sensitive to arbitrary bandwidth choices, thereby reinforcing the credibility of the findings [65].

In our study, to assess the robustness of the estimated treatment effect of PM_2.5 on rural pension contributions under the RDD, we applied Calonico et al.’s [59] method to check the optimal bandwidths and conducted the bandwidth sensitivity analysis using multiple thresholds around the policy cutoff of 35 $\mu g/m^3$. Figure 6 demonstrates that the point estimates at different bandwidths are all negative, indicating that the local average treatment effect of the negative association between long-term PM_2.5 exposure and pension contributions is directionally robust within the threshold neighborhood. The absolute values of the point estimates converge from approximately −3.5 to approximately −2 as the bandwidths expand from ±25 and ±30 $\mu g/m^3$ to ±35 and ±40 $\mu g/m^3$. At ±35 $\mu g/m^3$, the 95% confidence intervals are all below zero, which is statistically significant. The results are consistent across reasonable bandwidths, supporting the conclusion that long-term PM_2.5 exposure and pension contributions are negatively related to the localized average treatment effect.

4.2. Results from the Double Machine Learning with XGBoost and Causal Forest Learner

Based on the results of FRDD, we found that PM_2.5 and other control variables have a nonlinear relationship with pension contributions. Meanwhile, the Fuzzy RDD can only use the threshold of the PM_2.5, which is equal to 35, as an instrument variable to estimate the LATE for provinces, whereas we would like to estimate the global average treatment effect (ATE) of PM_2.5 on pension contributions, and thus, we need to understand the specific relationship between the actual value of PM_2.5 and pension contributions through machine learning. Then, we applied the double machine learning (DML) framework, combining the XGBoost and Causal Forest (Ranger) as nonlinear learners. The dependent variable is the total pension contributions of URRPS and UEBPI, respectively, and the key treatment variable is the annual maximum PM_2.5 concentration (Max_pm2.5). We further extend the model by introducing a one-year lag variable for PM_2.5 (Max_pm2.5_lag) to assess the potential lag effects. The results from the double machine learning with XGBoost are detailed in

Table 3. DML with XGBoost learner results for URPPS.

Variable	Estimated Value	Standard Error	T-Value	p-Value	Significant Level
Max_pm2.5	−0.2022	0.0964	−2.1	0.0361	**

Notes: ** indicate statistical significance at the 5% levels (two-tailed).

,

Table 4. DML with XGBoost learner results for UEBPI.

Variable	Estimated Value	Standard Error	T-Value	p-Value	Significant Level
Max_pm2.5	−4.5156	2.5686	−1.76	0.0787	*

Notes: * indicate statistical significance at the 10% levels (two-tailed).

,

Table 5. DML with lagged effects and XGBoost learner results for URRPS.

Variable	Estimated Value	Standard Error	T-Value	p-Value	Significant Level
Max_pm2.5	−0.4145	0.2017	−2.05	0.0399	**
pm2.5_lag	−0.4976	0.1838	−2.71	0.0068	***

Notes: **, *** indicate statistical significance at the 5%, and 1% levels (two-tailed), respectively.

and

Table 6. DML with lagged effects and XGBoost learner results for UEBPI.

Variable	Estimated Value	Standard Error	T-Value	p-Value	Significant Level
Max_pm2.5	−9.0280	4.9685	−1.95	0.0510	*
Max_pm2.5_lag	−9.6969	4.2957	−2.1	0.0356	**

Notes: *, ** indicate statistical significance at the 10%, 5% levels (two-tailed), respectively.

.

In the baseline specification using XGBoost and including only the contemporaneous PM_2.5 measure, we find an economically meaningful negative effect under both pension systems. Specifically, a one-unit increase in the annual Max_pm2.5 is associated with a CNY 0.2022 billion decrease in total pension contributions under URRPS, and a one-unit increase in pm2.5 is associated with a CNY 4.5156 billion decrease in total pension contributions under UEBPI. This result suggests that current-year pollution levels may depress residents’ capacity or willingness to contribute to the pension system, and the coefficient on PM_2.5 under URRPS is smaller than the coefficient on PM_2.5 under UEBPI, which can be partly attributed to the institutional design of the URRPS, which relies less on wage-based payroll contributions and more on individual voluntary contributions and government subsidies, resulting in its pension contributions being less sensitive to external environmental shocks [66,67]. When we included the lagged PM_2.5 variable under the URRPS, the contemporaneous effect is still statistically significant, with an estimated value of −0.4145, and the lagged effect becomes highly significant at the 1% significance level, and the estimated value of the lagged effect is negative and equal to −0.4976; under the UEBPI, the lagged PM_2.5 variable is also more significant in the variation in pension contributions relative to the PM_2.5 variable. This shift in significance supports the hypothesis that the economic consequences of air pollution on pension contributions materialize with a temporal lag, potentially reflecting the delayed impacts on household health, labor supply, and informal sector income.

To further validate these findings and capture more flexible nonlinearities and interactions, we estimate the DML model using a Causal Forest (Ranger) Learner and, additionally, to analyze the interpretability of the treatment effects of heterogeneity across features. The results from the double machine learning with the Causal Forest Learner are detailed in

Table 7. DML with lagged effects and Causal Forest Learner results for URRPS.

Variable	Estimated Value	Standard Error	T-Value	p-Value	Significant Level
Max_pm2.5	−0.4722	0.2425	−1.95	0.0515	*
Max_pm2.5_lag	−0.5035	0.2245	−2.24	0.0249	**

Notes: *, ** indicate statistical significance at the 10%, 5% levels (two-tailed), respectively.

and

Table 8. DML with lagged effects and Causal Forest Learner results for UEBPI.

Variable	Estimated Value	Standard Error	T-Value	p-Value	Significant Level
Max_pm2.5	−4.6508	3.8301	−1.21	0.2246	--
Max_pm2.5_lag	−7.9637	3.9460	−2.02	0.0436	**

Notes: ** indicate statistical significance at the 5% levels (two-tailed).

, and the results of the coefficient of significance of heterogeneous treatment effects under URPPS and UEBPI are detailed in

Table 9. Coefficient of significance of heterogeneous treatment effects for URRPS.

Feature Variable	Significance Coefficient
Government	0.1607
Education	0.1522
Population	0.1462 factor
Rural_resident_income	0.1279
Factor(Province)	0.0066

and

Table 10. Coefficient of significance of heterogeneous treatment effects for UEBPI.

Feature Variable	Significance Coefficient
Industry Structure	0.1836
Urban_resident_income	0.1779
Population	0.1614 factor
Tax_level	0.1503
Factor(Province)	0.0012

.

The results reveal stronger and statistically more robust effects: both current and lagged PM_2.5s are negatively and strongly significantly associated with pension contributions under both pension systems. The estimated coefficient for Max_pm2.5 is −0.4722 (p = 0.0515) and for Max_pm2.5_lag is −0.5035 (p = 0.0249) under URRPS; the estimated coefficient for Max_pm2.5 is −4.6508 (p = 0.2246) and for Max_pm2.5_lag is −7.9637 (p = 0.0436) under UEBPI. These findings confirm that air pollution significantly reduces the level of pension contributions, suggesting that air pollution as a non-institutional factor has a significant impact on both types of pension contributions, and air pollution not only reduces pension contributions in the current period but exerts an even more pronounced lagged effect. This is generally consistent with the findings of Huang et al. [68] and Dong et al. [69] that long-term exposure to PM_2.5 has long-term effects on mortality, morbidity, etc., and thus, there are some lagged effects of air pollution risks. Additionally, the lag effect of PM_2.5 also affects the insurance sector; according to Brook et al.’s [70] empirical findings, long-term exposure to PM_2.5 has been shown to reduce life expectancy and alter survival curves, and this reduction in life expectancy has a lagged effect, leading to changes in the timing and size of life insurance and pension liabilities. Adetutu et al.’s [23] study revealed a correlation between rising pollution delay risks and changes in life insurance coverage. It also shows that insurance industries are sensitive to reductions in life expectancy and morbidity risks induced by air pollution. These findings are also consistent with the conclusion of our study that lagged PM_2.5 has a greater effect on pension contributions than the current PM_2.5.

As can be seen from Table 9 and Table 10, government financial spending, the level of education, population size, and income are the key factors explaining the differences in CATE under the URRPS pension system. This suggests that the impact of pollution on contributions varies more with these structural characteristics. The results also suggest that the sensitivity of pension contributions may be more pronounced in settings with high government financial input, high levels of education, and a large population. Furthermore, the insignificant contribution of provincial variables to the heterogeneity analysis indicates that provincial differences are not a significant factor in explaining fluctuations in CATE within the model and that socioeconomic characteristics are the primary drivers of heterogeneity rather than individual provincial variables. Meanwhile, under the UEBPI pension system, the heterogeneity analysis findings are consistent with those under the URRPS system. Structural and scale covariates, such as industrial structure, urban income level, population size, and tax level, mainly explain the differences in CATE within the DML model. The province-specific effects are negligible and suggest that more industrialized and larger provinces are more sensitive in terms of their pension contribution sensitivity to PM_2.5 exposure.

Additionally, understanding the importance of explanatory variables in predicting pension contributions provides valuable insights into the role of PM_2.5 concentrations as a potential predictor of pension contributions. The importance score serves as a measure of the contribution of a feature to the construction of double machine learning; thus, the more frequently a feature is utilized in building the DML, the higher its relative importance. Figure 7 presents the importance plot for URRPS, indicating that rural population size, local government expenditure, and education level emerge as the most important predictors of pension contributions, which are related to the existence of government subsidies and incentives in the UEBPI system, as well as the fact that the education level enhances financial literacy and trust in the system, which leads to a more stable pension contribution path. Meanwhile, industry structure emerges as the most important predictor of pension contribution under UEBPI based on Figure 8. This is directly linked to the fact that pensions under the system are linked to the wage base and the industrial structure leans towards high-value and standardized labor, which tends to result in a more stable level of contributions and a higher base. Importantly, both Max_pm2.5 and its lagged value rank among the top contributors under both different pension systems, reinforcing their substantive relevance to pension funding outcomes.

Combining the above empirical results, the outcomes obtained through Fuzzy RDD and DML correspond testably with the past literature in terms of direction, mechanism and strength. Firstly, the significant negative LATE of air pollution on pension contribution, as identified by Fuzzy RDD near the threshold, is consistent with Huang’s evidence [17] that pollution inhibits firms’ production and thus compresses the social security contribution base. Meanwhile, the acceleration in marginal effects observed in the DML model as pollution intensity rises reflects the findings of nonlinear risk responses in the insurance market. For example, both crop insurance [24] and life insurance [23] are nonlinearly sensitive to pollution risk. Additionally, this study revealed that incorporating lagged effects into the DML model amplifies the impact of pollution risk on pension contributions, which aligns with past studies indicating that long-term PM_2.5 exposure has a lagged effect on mortality and disease [25,70]. This suggests that air pollution shocks do not instantly affect pensions but rather manifest gradually. Furthermore, this study revealed that pension contributions under UEBPI are more sensitive to industrial structures, while the pension contributions under URRPS are more sensitive to income, education, and government spending. This is consistent with the notion that labor productivity is significantly impacted by pollution in manufacturing scenarios [44,47] and that pollution moderates residents’ welfare and financial behaviors [37,42]. Meanwhile, in contrast to the established literature, which mostly reveals the negative economic impacts of pollution from the perspectives of healthcare expenditure or firm performance [36,38], our study combines pollution risk with the level of pension contributions and found that, under both the URRPS and the UEBPI, the effect of pollution risk on pension contributions is consistent in terms of both the threshold and lagged effects. The above comparative evidence provides an empirical basis for in-depth discussion of the explanatory mechanisms, system differences, and policy implications.

5. Discussion and Recommendations

We investigated the relationship between PM_2.5 air pollution and pension contributions in China, utilizing provincial panel data from eight provinces representing four economic regions from 2014 to 2024. We employed a fuzzy regression discontinuity design at the regulatory PM_2.5 threshold of 35 $\mathrm{\mu }g/m^3$, complemented by a double machine learning approach to uncover the significant causal impacts of air pollution on pension contributions across two distinct pension systems: the Urban Employees Basic Pension Insurance (UEBPI) and the Urban and Rural Residents’ Pension Scheme (URRPS).

Our empirical findings indicated that PM_2.5 concentrations above the 35 $\mathrm{\mu }g/m^3$ threshold significantly reduce the growth rate of pension contributions. Specifically, UEBPI contributions show a measurable decline during periods when air pollution exceeds the threshold, which may be driven by lower labor productivity, higher absenteeism, and higher employee healthcare expenditures. URRPS contributions, on the other hand, which are mainly voluntary contributions from the rural and urban informal sectors, are more sensitive to whether PM_2.5 exceeds the threshold, highlighting the greater vulnerability of low-income groups to pollution-induced economic pressures. Furthermore, our DML analysis identified nonlinearities and lagged effects, demonstrating that severe or prolonged exposure to elevated PM_2.5 concentrations amplifies the negative impact on pension contributions, with regional variations shaped by local industrial structures and demographic profiles. Moreover, the DML analysis helped us to identify the effect of PM_2.5 on the absolute value of pension contributions. Consistent with previous studies, our findings also support the conclusion that pollution leads to macroeconomic slowdowns and welfare losses. However, unlike previous studies, we mapped pollution shocks directly onto the income dimension of social security rather than limiting them to health or output domains [36,37]. Furthermore, in addition to the determinants of URRPS identified in previous studies (education, income, and institutional trust) [20,21], we found that environmental risk is an important non-institutional deterrent to voluntary pension contributions.

This study strengthens the causal inference of environment–socioeconomic interactions by integrating Fuzzy RDD and DML in the methodology. Fuzzy RDD clearly defines pollution thresholds and effectively controls confounding factors, while the DML methodology captures complex nonlinear relationships and lagged responses ignored by traditional linear models.

Our analysis focused on eight provinces distributed from four different economic regions. For future research, we can explore the generalizability and heterogeneity of these findings and expand the sample to the whole country or other countries and then verify whether the association between pollution and pensions is universal or context-specific. Additionally, we find that URRPS contributions are more sensitive to PM_2.5, so we could also look more deeply into urban–rural differences in the future and investigate whether migration, such as workers moving out of polluted areas, plays a role in the mediation of pension contributions, which is in line with the findings of selected labor mobility studies. Meanwhile, there is significant value in extending our analysis to other outcome indicators and policy instruments related to pensions in future research. One direction would be to examine whether air pollution affects not only the contribution but also the expenditure side of the equation. For future research, we could also evaluate policy interventions to assess whether the air pollution control policies implemented in China in the mid-2010s had a measurable impact on pension fund metrics in the subsequent years and to explore the role of protective public policies or private insurance mechanisms for pollution-related issues and then clarify strategies to strengthen the pension system against environmental risks. Additionally, our study formalized the lagged effect of PM_2.5 on pension contributions; we can therefore consider including multi-year lagged pollution variables in our models to better capture the chronic effects of air pollution on pension contributions and other insurance in the future.

From a policy perspective, these results emphasize that environmental regulation and pension sustainability are intertwined objectives. The International Association of Insurance Supervisors (IAISs) and the Sustainable Insurance Forum (SIF) jointly published the “Application Paper on the Supervision of Climate-related Risks in the Insurance Sector” on 24 May 2021, to help national regulators identify, monitor, and assess the impact of climate change risks on the insurance sector and mitigate the associated risks for financial stability. As these systems evolve, factors relating to air pollution could be incorporated into existing frameworks. Countries could develop risk-based regulatory policies appropriate to their circumstances, requiring air pollution risks to be incorporated into pension funds’ risk management and internal control processes. For example, green finance mechanisms could be adopted in pension contribution policies, whereby transferring a portion of environmental tax revenues or carbon pricing gains to pension reserves, especially in highly polluted areas, creates a feedback loop whereby polluters indirectly compensate the social sector. Similar initiatives have been introduced in Germany, the United Kingdom, and Sweden. Germany’s eco-tax reform involved raising energy taxes and using the proceeds to fund public pension schemes and reduce social insurance contributions [71]. Meanwhile, Sweden has offset some of its social security contributions through carbon tax revenue recycling [72]. China’s environmental protection tax, implemented in 2018, is currently used primarily for environmental protection purposes [73], but it could potentially form the basis of a system linking to pension contributions in the future. These advancements could increase the resilience of the government in addressing air pollution risks and ultimately contribute to the sustainability of the pension system.

6. Conclusions

In our paper, we examined the relationship between particulate pollution (PM_2.5) and pension contributions in China. We combined the fuzzy regression discontinuity design at the regulatory threshold of 35 µg/m³ with a double machine learning framework. We used data from eight representative provinces and found that exceeding the threshold significantly slows the growth of pension contributions, with the flexible DML estimator detecting the nonlinear relationship and the lagged effect of air pollution in addition to the additional effects on contribution levels. While these findings confirm that improved air quality enhances pension sustainability, our study also provides an empirical basis for reconciling environmental policy with the sustainability of social protection. Our findings highlight the importance of coordinating environmental regulations and pension management policies, such as incorporating air pollution indicators into contribution forecasting, stress testing, and the risk management of pension funds, exploring green finance linkages and using part of the proceeds from environmental taxes or carbon pricing for pension reserves in heavily polluted regions.

Unlike previous studies, this paper revealed that the impact of PM_2.5 exposure affects the pension contribution base, shifting the focus away from traditional health or mortality indicators. From a methodological perspective, the study employed Fuzzy RDD at the threshold of 35 $\mu g/m^3$ in conjunction with double machine learning and cross-fitting techniques. This approach enables the derivation of local causal estimates with internal validity and the construction of flexible global response surfaces, capturing nonlinear and lagged effects. Consequently, significant differences between the UEBPI and the URRPS are revealed. The heterogeneity of the two-track system, combined with the contribution level and growth rate evidence revealed by the double machine learning approach, provides a nuanced interpretation of complexities that are overlooked by traditional linear modeling and single-track analysis. In summary, we shift the perspective of the study of the environment–pension correlation from health or expenditure outcomes to the income dimension of social security, while revealing heterogeneity, lags, and nonlinear response characteristics under the two-track pension system that are ignored by standard linear designs.

Our study also has some limitations. Firstly, the FRDD model only identifies localized effects near the threshold and may not accurately predict changes in pension contribution levels in the event of extreme weather resulting in high or low levels of air pollution exposure. Secondly, while our study selected eight different provinces in four economic regions, measurement errors due to annual PM_2.5 use and limited provincial coverage may still weaken the estimates. Finally, despite the design of control variables in our model based on previous studies, certain unquantifiable shock factors and shocks to the pension system from healthcare data are still likely to persist. Therefore, future studies can expand the geographic scope, gather the complete daily panel data of PM_2.5, explore urban–rural mechanisms and migration responses, and correlate disease and health claim data to more clearly identify the risk that air pollution poses to the pension system.