The Non-Linear Relationship between Air Pollution, Labor Insurance and Productivity: Multivariate Adaptive Regression Splines Approach

Abstract

This study explores the non-linear relationship between air pollution, socio-economic factors, labor insurance, and labor productivity in the industrial sector in Taiwan. Using machine learning, specifically multivariate adaptive regression splines (MARS), provides an alternative approach to examining the impact of air pollution on labor productivity, apart from the traditional linear relationships and parametric methods employed in previous studies. Examining this topic is imperative for advancing the knowledge on the effects of air pollution on labor productivity and its association with labor insurance, employing a machine learning framework. The results reveal that air pollution, particularly PM₁₀, has a negative impact on labor productivity. Lowering the PM₁₀ level below 36.2 μg/m³ leads to an increase in marginal labor productivity. Additionally, the study identifies labor insurance as a significant factor in improving productivity, with a 9% increase in the total number of labor insurance holders resulting in a substantial 42.9% increase in productivity. Notably, a link between air pollution and insurance is observed, indicating that lower air pollution levels tend to be associated with higher labor insurance coverage. This research holds valuable implications for policymakers, businesses, and industries as it offers insights into improving labor productivity and promoting sustainable economic development.

1. Introduction

In recent years, there has been an increasing number of studies examining the effects of air pollution on human health. These studies have found that air pollution not only negatively impacts physical health but also affects psychological health and cognitive performance. Particulate matter (PM), particularly PM₁₀ and PM_2.5, has been identified as a major air pollutant that poses a significant risk to human health. Research conducted by Chen and Kan [1], as well as Chen et al. [2], has highlighted the harmful effects of air pollution on physical health, such as alterations in pulmonary functions and the cardiovascular systems, and even life expectancy. However, recent findings suggest that air pollution also has a detrimental impact on psychological health and cognitive performance. Zare Sakhvidi et al. [3] conducted a study that found air pollution, particularly PM, to be a significant risk factor for both psychological health and cognitive performance.

Moreover, recent research has highlighted a clear association between air pollution and human capital, particularly in terms of labor productivity [4,5]. Investigations have shown the impact of ground-level ozone on workers in the agricultural sector, including both those employed outdoors and indoors, as well as highly skilled workers [6,7,8]. These findings demonstrate the detrimental effects of air pollution on workforce performance and underscore the significance of implementing air pollution control policies [4]. Nevertheless, despite the existence of prior studies, our understanding of the nonlinear correlation between air pollution and labor productivity remains limited. Furthermore, the relationship between air pollution, labor insurance, and their combined impact on productivity has received insufficient attention, despite labor insurance playing a vital role in enhancing productivity [9,10,11]. To bridge these knowledge gaps, this study employs state-of-the-art machine learning techniques renowned for their exceptional predictive capabilities and capacity to model nonlinear relationships [12,13,14], particularly among air pollution, labor insurance, other economic factors, and labor productivity.

This study focuses on the interaction between air pollution, labor insurance, and labor productivity in Taiwan’s industrial sector. The significance of providing health insurance to employees cannot be overstated, as research has demonstrated that employee absences due to sickness can harm firm productivity [15]. While the link between air pollution and labor productivity has been extensively studied, the relationship between air pollution, labor insurance and worker productivity has been overlooked. Interestingly, Dizioli and Pinheiro [9] found that workers with health insurance have a lower tendency to lose working hours compared to workers without insurance, with a reduction of 76.54%. This finding suggests that health insurance has a positive impact on worker performance. This channel of interaction is significant as it highlights the potential role of labor insurance in mitigating the adverse effects of air pollution on worker productivity. Furthermore, other research has indicated that investing in insurance necessities can have a cumulative effect on promoting economic growth [16].

This research builds on the findings of previous studies that have demonstrated the negative impact of air pollution on human health and cognitive performance [4]. However, this study employs a novel approach by utilizing the multivariate adaptive regression splines (MARS) model, which is a non-parametric method for analyzing complex relationships between multiple variables. The MARS model is particularly useful in examining the impact of air pollution on labor productivity because it allows for the examination of non-linear relationships between air pollution and labor productivity, as well as the identification of the specific levels of air pollution that have the most significant impact on labor productivity.

MARS is a method that has the ability to model high-dimensional data in a flexible manner. It does so by utilizing a piecewise linear series to represent non-linear connections between input and output variables. The efficacy of MARS as a modeling technique has been demonstrated in numerous studies [12,17]. The present study employs MARS to examine the relationship between air pollution and labor productivity. The main objective is to explore not only linear relationships but also potential non-linear relationships, particularly those that involve a time lag between the effects of air pollution and labor productivity. By extending the linear model, MARS provides several advantages, one of which is the ability to measure the interactions between variables [17]. The use of MARS in this study allows for the capture of complex relationships that may not be readily apparent using traditional linear modeling techniques. This is especially important in the context of air pollution and labor productivity, where the relationship may be influenced by a variety of factors.

The primary aim of this study is to extensively investigate the non-linear relationship between air pollution and labor productivity while simultaneously examining its interaction with labor insurance using the multivariate adaptive regression splines (MARS) approach. By adopting this approach, we aim to expand the existing literature on the determinants of labor productivity and provide a comprehensive understanding of the direct link between air pollution and labor productivity. Moreover, as environmental factors, particularly air pollution, play a significant role in this relationship, our study offers novel insights into this area of inquiry. Secondly, by employing the MARS approach based on machine learning techniques, our research provides a broader and more multifaceted perspective on analyzing labor productivity. Using this alternative analytical tool, we can obtain a comprehensive understanding of the complex and interconnected variables involved. Notably, this study stands out as the first to employ a machine learning model, specifically the MARS model, to assess the impact of air pollution on labor productivity. The MARS model is recognized for its exceptional ability to capture intricate relationships among variables. Lastly, the empirical findings of this research hold practical implications for policymakers, particularly those in the industrial sector. We meticulously examine the various factors that can potentially influence labor productivity within this sector, along with their interplay. Consequently, our study offers valuable insights that can inform the decision-making processes of policymakers striving to enhance labor productivity within the industrial sector.

The remaining sections of this paper are structured as follows: Section 2 presents a review of the relevant literature pertaining to this study. Section 3 and Section 4 outline the data collection process and research methodology employed in this study. Section 5 presents the measurement findings and offers a comprehensive discussion of the results. Section 6 concludes the study, while Section 7 discusses the policy implications derived from the research.

2. Literature Review

In a general sense, productivity is commonly defined as measuring efficiency within the production process, specifically the output generated from a given set of inputs [18,19]. With respect to labor productivity, it can be understood as the output achieved per unit of labor input, as explained by Dua and Garg [20]. This definition also often applies to other fields, such as in the construction sector [21]. This concept is influenced by various factors that have evolved over time, encompassing aspects such as capital, workforce expertise, knowledge accumulation, institutional quality, and other macro-level determinants. Labor productivity is also interconnected with factors relating to health, environmental conditions, and even air pollution [5]. In the present investigation, labor productivity is gauged using the index of output per labor on a monthly basis in the industrial sector of Taiwan.

The topic of the impact of air pollution on labor productivity has garnered the attention of researchers ever since the ground-breaking study by Graff Zivin and Neidell [8]. Their research, which utilized panel data for labor productivity in the agricultural sector of California, demonstrated robust evidence that ozone levels below national standards substantially affected labor productivity. Specifically, they found that a mere 10-unit (ppb) increase in ground-level ozone resulted in a significant 5.5% reduction in farmer productivity.

Air pollution has been found to have negative impacts on not only physical health but also cognitive abilities. A study by Zare Sakhvidi et al. [3] found a correlation between increased levels of PM_2.5 and decreased performance in semantic fluency tests among participants of the CONSTANCES cohort. Additionally, Zhang et al. [22] observed that long-term exposure to air pollution was linked to decreased cognitive abilities, particularly in the areas of verbal and mathematical skills. It has also been noted that the effects of air pollution on brain function worsen with age. Although there is evidence that outdoor air pollution affects the central nervous system (CNS), leading to decreased brain performance [23], more research is needed to confirm this [24].

Particulate matter is comprised of small liquid or solid droplets that can enter the respiratory tract upon inhalation and result in severe health implications [25]. PM exposure may elicit short-term (acute) or long-term (chronic) effects on the human body [26]. Inhalation of particles smaller than 10 μm may lead to respiratory issues and subsequent bloodstream infiltration. Fine particles with a diameter of less than 2.5 μm may result in more severe health implications, and in many instances, even fatalities [27,28,29,30]. In addition to PM, there is a growing body of evidence linking other pollutants such as ground-level ozone (O₃), carbon monoxide (CO), nitrogen oxide (NO₂), sulfur dioxide (SO₂), lead, polycyclic aromatic hydrocarbons (PAHs), volatile organic compounds (VOCs), and dioxins to detrimental health effects in humans [26].

In a more recent study, Chang et al. [6] investigated the impact of different types of pollutants, including PM_2.5, on the productivity of indoor workers at a pear packaging factory. Their research revealed that an increase in PM_2.5 concentration led to a substantial decrease in labor productivity. Surprisingly, outdoor pollutants such as ozone, which cannot infiltrate indoor environments, had a negligible impact on labor productivity.

Although these studies may appear unrelated, their findings hold crucial implications for policymakers and stakeholders in the industrial sector. The evidence indicates that air pollution adversely affects labor productivity, a crucial factor in any industry. Therefore, policymakers must consider these insights when formulating strategies to mitigate the impact of air pollution on labor productivity. In particular, the industrial sector must create safe and healthy work environments that promote optimal labor productivity while safeguarding the welfare of workers. This aligns with the conclusions drawn from Li et al. [31], which highlights that the enforcement of laws and regulations can serve as a valuable tool for environmental preservation. Notably, variations in outcomes between developed and developing nations exist.

Air pollution does not only affect workers in the agricultural sector, but it also has negative implications for high-skill workers. Archsmith et al. [7] conducted a study that examined the short-term impact of air pollution on quality-focused workers, such as Major League Baseball (MLB) umpires. The study found that even a modest increase of 1 ppm in carbon monoxide (CO) led to an 11.5% increase in incorrect calls by umpires. Similarly, PM_2.5 and other pollutants also have a significant impact, where a 10 μg/m³ increase in PM_2.5 was associated with a 2.6% increase in the error rate. These findings have far-reaching implications for various industries that require high-skill labor. Policymakers must consider the negative impact of air pollution on labor productivity and worker health when developing and implementing environmental regulations.

He et al. [5] conducted a study that focused on the impact of PM_2.5 on manufacturing workers in two industrial sites in China’s Jiangsu and Henan provinces. By examining the exogenous effect of atmospheric ventilation on air pollution, the study found that a 10 μg/m³ increase in PM_2.5 over 25 days resulted in a 1% reduction in the daily output of workers. These findings have important implications for the industrial sector and highlight the need for effective measures to mitigate the impact of air pollution on worker productivity.

The extant literature exploring the nexus between labor insurance and worker productivity remains sparse. The empirical investigation conducted by Dizioli and Pinheiro [9] is of particular interest to this study, as it examines the underlying mechanisms by which insurance impacts productivity. The research findings are noteworthy as they provide empirical evidence that offering health insurance to workers can reduce the likelihood of illness-related absenteeism. This finding aligns with prior research conducted by Lofland and Frick [32], who reported that workers with health insurance are 17% less likely to miss workdays due to illness. Recent studies have also corroborated the significance of labor insurance for the labor market and labor supply, as reported by Aizawa and Fang [11] and Shen et al. [10]. In this study, labor insurance refers to the labor insurance program from Taiwan’s labor insurance bureau, which offered benefits for holders, including maternity, injury, sickness, disability, old-age, and death benefits, and a new pension program.

This study employs the multivariate adaptive regression splines approach (MARS) to examine the relationship between inputs. MARS is a non-parametric method that captures the relationship between input and dependent variables without relying on specific assumptions [17]. MARS is a popular machine learning algorithm widely used in engineering due to its adaptive nature that tailors itself to specific problems [33,34]. MARS has several advantages over other methods, including its ability to produce simple and interpretable models and measure the contribution of inputs, as well as its computational efficiency [35,36]. By using MARS, this study can provide a broader and more diverse input to studying labor productivity. The use of MARS in examining the impact of air pollution on labor productivity is unprecedented and thus can contribute to the development of literature on this topic.

MARS has been applied in several studies across different fields due to its ability to model and predict efficiently and simply. Zhang and Goh [35] applied MARS to analyze geotechnical engineering systems and compared it to BPNN, where the results showed that MARS is more efficient and interpretable compared to BPNN, despite having similar accuracy and generalization, even though BPNN is actually a form of deep learning [37,38,39]. Adoko et al. [40] predicted tunnel convergence with MARS and ANN and concluded that MARS has a better level of flexibility and computational efficiency compared to ANN, despite producing slightly lower accuracy. Zhang and Goh [41] applied MARS to predict pile drivability, and their study showed that MARS is more efficient than BPNN. In addition to engineering, MARS has also been applied in air pollution modeling [13], geotechnical engineering [42], and solar and renewable energy [14].

3. Data

To examine the suggested model, monthly data from January 1998 to October 2022 was obtained from various sources, including data released by the Taiwanese government, such as the National Statistics Bureau of Taiwan [43], the Environmental Protection Administration [44], the Ministry of Health and Welfare, and Central Weather Bureau of Taiwan [45]. These sources provide comprehensive and reliable data necessary for the proposed model’s analysis. By utilizing this data, this study aims to provide a more comprehensive understanding of the impact of air pollution and labor insurance on the labor productivity in Taiwan’s industrial sector.

Table 1. Descriptive statistics and variables description.

Description	Observation	Mean	Standard Deviation	Min	Max	Coefficient Variation
Labor productivity index for industrial sector (2016 = 100)	286	85.496	22.361	48.11	147.2	0.2615
Fine suspended particulates with size less than 10 μm (μg/m3)	286	50.634	16.740	16.8	96.2	0.3306
Total monthly salary of industrial sector’s workers (NT$)	286	45,535.28	11,493.15	34,403	104,527	0.2524
Number of labor insurance holders (people)	286	9,231,670	1,002,672	7,563,319	10,809,587	0.1086
Commodity price index (2016 = 100)	286	103.691	9.593	87.55	124.84	0.0925
Monthly working hours for industrial worker (Hours)	286	182.359	14.973	129.9	208.6	0.0821

presents a comprehensive breakdown of the descriptive data’s particulars.

4. Research Methods

This study uses the multivariate adaptive regression splines (MARS) approach to analyze the relationship between inputs. MARS is a non-parametric method that captures the relationship between input and dependent variables without making any specific assumptions. Several studies have shown that MARS is more efficient and interpretable than other methods, such as back propagation neural networks (BPNN) and artificial neural networks (ANN) [35,40,41].

The equation used in this study is based on the labor productivity model proposed by He et al. [5] and Chen and Zhang [4]. This model is represented by the following equation:

$$\begin{array}{c}{Labor}_t={\alpha }_0+{PM}_t+{Salary}_t+{Insurance}_t+{Price}_t+{Hours}_t+{\epsilon }_t\end{array}$$

(1)

where ${Labor}_t$ shows the labor productivity index in industrial sector from January 1998 to October 2022. ${PM}_t$ denotes the rate of fine particulate matter in the air, ${Salary}_t$ is average labor wages in industrial sector for each month, ${Insurance}_t$ denotes the number of labor insurance holders, ${Price}_t$ is the commodity price index, and ${Hours}_t$ represents the mean number of hours worked per month by workers in the industrial sector. ${\epsilon }_t$ is the idiosyncratic error term.

Following the linearity testing, this study proceeds with the estimation process using MARS to further analyze the data. According to Zhang and Goh [41] and Friedman and Roosen [17], assuming a matrix x of n input variables and a target dependent response y, it is assumed that the data is produced from an unidentified “true” model. In the case of a continuous response, this model can be represented as:

$$\begin{array}{c}y=f\left(x_1,\dots ,x_n\right)+e\end{array}$$

(2)

The MARS model, denoted by f, is constructed using BFs that are spline piecewise polynomial functions, and $e$ is the fitting error. The MARS model, $f\left(x\right)$, which combines a basis functions (BFs) and their interactions to form a linear model, is expressed as follows:

$$\begin{array}{c}f\left(x\right)={\beta }_0+{\displaystyle \sum _{m=1}^m}{\beta }_m{\lambda }_m\left(x\right)\end{array}$$

(3)

where ${\beta }_0$ and ${\beta }_m$ are values determined through calculation to achieve the best possible fit for the data. The value of m represents the number of basic functions in the model. In the MARS model, a basis function can be a single univariate spline function or a combination of multiple spline functions for different predictor inputs [12]. The spline basis function (BFs), denoted by ${\lambda }_m\left(x\right)$, can be defined as:

$$\begin{array}{c}{\lambda }_m\left(x\right)={\displaystyle \prod _{k=1}^{k_m}}\left[S_{km}\left(X_{v\left(k,m\right)}-t_{k,m}\right)\right]\end{array}$$

(4)

$S_{km}$ is the position of the corresponding step function, 1 or −1. In addition, $k_m$ is the number of knots, $v(k,m)$ represents the label of predictor variable, and $t_{k,m}$ represents the location of knot. Based on the MARS framework proposed by Friedman and Roosen [17], MARS employs generalized cross-validation (GCV) to reducing duplicate BFs.

Generalized cross-validation (GCV) is a widely used statistical measure in the field of machine learning that serves to quantify the overall performance of a given predictive model. It is computed as the ratio of the mean-squared residual error, which represents the discrepancy between the observed data and the predicted outcomes, to a penalty term that takes into account the complexity of the model. This penalty term is crucial to ensure that the model does not overfit the training data and can generalize well to unseen data [41]. The GCV is typically applied to training datasets that contain N observations and is mathematically expressed as per the formulation proposed by Hastie et al. [46] in their seminal work, as shown below:

$$\begin{array}{c}GCV=\frac{\frac{1}{N}{\sum }_{i=1}^N{\left[y_i-f\left(x_i\right)\right]}^2}{{\left[1-\frac{M+d\times \frac{M-1}{2}}{N}\right]}^2}\end{array}$$

(5)

where $M$ is the basis functions number, and the penalty for each basis function included in the sub-model that is created is represented by d. Meanwhile, N stands for the quantity of data sets, and the $f\left(x_i\right)$ signifies the predicted values of the MARS model.

In order to evaluate the estimation capabilities of MARS, this study conducts a comparative analysis with various machine learning models, namely decision trees, Gaussian processes, and support vector machines. The evaluation is based on key parameters, including the root mean square error (RMSE), mean absolute error (MAE), and R-squared (R²). It is important to note that this comparison is solely intended to assess the performance of MARS in relation to the aforementioned models and does not provide an extensive analysis of the estimation outcomes for each machine-learning model.

The decision tree model employed in this study is bagging CART (classification and regression Tree). Bagging CART is a bagging algorithm that utilizes decision trees. Unlike boosting, bagging constructs individual base models independently, without relying on previous model estimates. The fundamental principle of this approach involves recursively partitioning the training dataset into a binary tree structure, with nodes serving as stages for classifying the data. At each stage, the cases within the current node, referred to as the parent node, are divided into two child nodes based on a threshold value derived from a predictor variable. The predicted value within a terminal node is simply the average of the response values within that specific node [47,48,49,50].

Furthermore, this study employs Gaussian processes with radial basis function kernel as a comparative model for MARS estimation. Gaussian processes are non-parametric machine learning models commonly utilized for addressing non-linear models characterized by a high uncertainty regarding the true function of the model. In the Gaussian learning process, data is modeled as a Bayesian estimation problem, assuming that the parameters of the Gaussian process are random variables [51]. Lastly, this study uses the support vector machine (SVM) as another model. SVM is a computer algorithm that learns to assign labels to objects based on examples. SVM represents a non-parametric machine learning approach that generally achieves a favorable balance between predictive accuracy and the ability to generalize trained models [52,53].

Moreover, to assess the performance of MARS with the models mentioned earlier, this study estimates the RMSE, MAE, and R² values for each model. RMSE and MAE are widely recognized absolute error measures commonly employed in machine learning and data mining [54]. These measures are frequently utilized for model fitting and comparison [37,54], particularly in research studies that leverage machine learning techniques [55].

$$\begin{array}{c}RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n}{\left({\widehat{Y}}_i-Y_i\right)}^2}\end{array}$$

(6)

$$\begin{array}{c}MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n}\left|{\widehat{Y}}_i-Y_i\right|\end{array}$$

(7)

$$\begin{array}{c}{R}^2=\frac{\sum _{i=1}^n{\left(Y_i-{\stackrel{-}{Y}}_i\right)}^2-\sum _{i=1}^n{\left(Y_i-{\widehat{Y}}_i\right)}^2}{\sum _{i=1}^n{\left(Y_i-{\stackrel{-}{Y}}_i\right)}^2}\end{array}$$

(8)

where $Y_i$ is actual value, ${\stackrel{-}{Y}}_i$ is mean of actual value, ${\widehat{Y}}_i$ is the estimated value, and n is number of observations.

5. Results and Discussion

Prior to performing MARS analysis, this study assessed the validity of the linearity assumption through a linear regression model. Residual diagnostics were conducted to evaluate whether the suggested model satisfies the prerequisites for implementing a linear model.

The first test was carried out by looking at the relationship between the variables used in this study and the standard residuals of the linear regression in the proposed model. Based on Figure 1 it can be seen that the variables labor, PM, salary, and insurance show an almost similar pattern, which is not constant around 0. This indicates a violation of the assumption of linear regression. The term misspecification in this context pertains to the non-linear relationship between the data for each predictor variable and the standard residual. It is commonly used to indicate deviations from the assumptions of linearity in linear regression. To add to the consideration, this study also tests the linearity of the data by comparing the residual value with the fitted value of the proposed model. The results of this test can be seen in Figure 2.

The residual plot in Figure 2 exhibits a discernible pattern, indicated by the non-horizontal red line at a value other than 0, indicating a potential issue with the linearity of the data employed. Consequently, the subsequent analysis employs MARS, a machine learning technique that can capture non-linear relationships. However, one of the challenges in using machine learning methods, including MARS, is the tendency for the estimation results to be overfitted. Therefore, it is crucial to properly tune the model parameters, such as degree and prune. By default, degree is set to 1, meaning that the model is built without considering interactions. To achieve optimal tuning, it is recommended to set the upper limit of the degree to an appropriate level of interaction [46,56]. In this study, we use five degree values, which aid in the interpretation of the model used. Lower degrees are preferable to higher ones, since the latter may result in prediction model inconsistencies [12]. Therefore, selecting a suitable degree value is essential to obtain an accurate and robust model that can capture the complex relationships among the variables.

Figure 3 displays the results of hyperparameter tuning based on the criteria proposed in this study. The figure demonstrates that degree 1 yields the most optimal optimization value, resulting in the lowest root mean square error (RMSE) value and the highest R² value of 0.046 and 0.962, respectively. Therefore, degree 1 is deemed the best parameter in the proposed model, and we utilize this parameter for subsequent analysis. Using degree 1, we estimate multivariate adaptive regression splines (MARS), and the results are presented in Figure 4. This figure also illustrates the selection of plot models that describe generalized cross-validation (GCV). The plot reveals the best model selection with optimal terms or prune at 13. By utilizing MARS and the best model selection, we can extract valuable insights and develop robust predictions, thus enabling us to achieve our research objectives.

Prior to conducting the basis function calculation for multivariate adaptive regression splines (MARS), this investigation undertakes a comparative analysis of the root mean square error (RMSE), mean absolute error (MAE), and R-squared (R²) values of MARS against various alternative machine learning models, including support vector machines (SVMs), Gaussian process (GP), and bagging-CART (B-CART). The comparison results are presented in Figure 5. By evaluating the MAE, RMSE, and R² results, it is evident that MARS exhibits the lowest RMSE and MAE value and the highest R² in comparison to the alternative models. This observation signifies the superior predictive performance of MARS over the aforementioned models.

After conducting testing and estimation using the MARS approach, this study identified the optimal hyperparameters of the proposed model, which are a degree of 1 and a prune of 13. With these hyperparameters, we then trained the data by applying the final model to evaluate its predictive performance. This step is a crucial component of the modeling process, as it allows us to assess the model’s ability to accurately predict future outcomes based on the data used for training.

$$\begin{array}{l}Labor=100.902+0.5014\times BF1+0.0001\times BF2+0.00002\times BF3-0.0001\times BF4\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \hspace{1em}+0.0005\times BF5-0.0006\times BF6-0.0008\times BF7-1.2229\times BF8\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -0.7353\times BF9+3.0923\times BF10-1.8235\times BF1+0.2388\times BF12\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -0.1714\times BF13\end{array}$$

Table 2. Basis functions and corresponding equations of MARS model.

Basis Function (BF)	Equation
BF1	$max\left(0,36.2-PM\right)$
BF2	$max\left(0,Salary-\mathrm{57,674}\right)$
BF3	$max\left(0,Insurance-\mathrm{9,745,790}\right)$
BF4	$max\left(0,10204900-Insurance\right)$
BF5	$max\left(0,Insurance-\mathrm{10,422,600}\right)$
BF6	$max\left(0,Insurance-\mathrm{10,626,100}\right)$
BF7	$max\left(0,Insurance-\mathrm{10,626,100}\right)$
BF8	$max\left(0,Price-97.34\right)$
BF9	$max\left(0,104.99-Price\right)$
BF10	$max\left(0,Price-104.99\right)$
BF11	$max\left(0,Price-110.48\right)$
BF12	$max\left(0,160-Hours\right)$
BF13	$max\left(0,Hours-160\right)$

provides a clear definition of the basis function used in the MARS equation. The table shows that each basis function is a combination of one or more predictor variables and a split point, which can be either numerical or categorical. The table also shows the coefficient value for each basis function, which represents the contribution of that function to the overall prediction equation. By using this table, researchers and practitioners can gain a better understanding of how MARS works and how it generates the prediction equation.

Table 2 presents the basis function and equation obtained from the MARS output, which enables the understanding and interpretation of the relationship between the features. To facilitate a more straightforward and clear comprehension of the relationship between the features, this study generates a partial dependence plot for each predictor variable and the interactions among these variables. In Figure 6, a partial dependence plot is presented to illustrate the relationship and interaction between labor productivity and each predictor variable. Specifically, the plot shows the relationship between labor productivity and air pollution indicated by PM. The plot suggests that an increase in particulate matter has a negative impact on labor productivity. Moreover, it indicates that a decrease in PM, especially PM₁₀, at a level lower than 36.2 μg/m³ will result in an increase in marginal labor productivity compared to when PM₁₀ levels are higher than 36.2 μg/m³.

The impact of salary, commodity prices, and average working hours on the marginal labor productivity of industrial sector workers in Taiwan was examined next. Figure 5 shows that an increase in salary has a small but positive impact on labor productivity. Specifically, a higher salary level of 57,674 NTD per month will lead to a greater increase in marginal labor productivity than a lower salary level. Regarding commodity prices, the PDP revealed a mixed effect on labor productivity. A commodity price index between 97.34 and 104.99 had a negative impact on marginal labor productivity, while a commodity price index higher than 110.48 had a positive effect on it. Lastly, the study found that the average length of working hours had a negative effect on marginal labor productivity. According to MARS estimation, average working hours of more than 160 h/month decreased marginal labor productivity compared to average working hours of less than 160 h/month. In conclusion, the findings suggest that, while salary and commodity prices have some impact on marginal labor productivity, the average length of working hours is a more significant factor affecting labor productivity in the industrial sector in Taiwan.

Furthermore, the next variable examined in this study is labor insurance, and in this study, labor insurance specifically refers to the labor insurance program provided by Taiwan’s labor insurance bureau. This program offers a range of benefits to its beneficiaries, including but not limited to maternity benefits, compensation for injuries and sickness, disability benefits, old-age benefits, death benefits, as well as a newly introduced pension program, which has been shown to have a significant impact on labor productivity in the industrial sector in Taiwan. The MARS estimation results interpreted by PDP in Figure 6 reveal that an increase in the number of labor insurance holders leads to a positive and significant increase in labor productivity. This finding is consistent with prior research on the positive impact of social security systems on labor productivity and suggests that labor insurance serves as an important institutional mechanism to promote labor productivity. The results show that an increase in the number of labor insurance holders to over 9,745,790 people leads to a greater impact on increasing marginal labor productivity compared to a lower number of insurance holders. Specifically, the MARS estimate shows that an increase of 9% in the total number of labor insurance holders has a substantial impact on labor productivity, leading to an increase of 42.9%.

The magnitude and importance of the impact of labor insurance on labor productivity can be seen in Figure 7, which shows the variable’s significance in the proposed model. The figure highlights the central role of labor insurance in promoting productivity in the industrial sector, underscoring the importance of considering this variable when examining labor productivity in this sector. The findings of this study underscore the significant role of labor insurance in promoting labor productivity in the industrial sector in Taiwan. The study highlights the need for policymakers to consider the impact of labor insurance on productivity when designing and implementing policies aimed at promoting labor productivity in this sector. This study provides valuable insights into the mechanisms that promote labor productivity and could inform future research and policy initiatives aimed at promoting labor productivity in Taiwan and other countries.

This study also examines the relationship between labor productivity, particulate pollution, and labor insurance. The MARS estimation results are interpreted using a partial dependence plot, which is shown in Figure 8. The figure reveals that an increase in air pollution, as indicated by an increase in particulate matter (PM), is associated with a reduction in labor productivity. On the other hand, an increase in the number of labor insurance holders is found to be positively associated with an increase in labor productivity.

The findings suggest that particulate matter is a significant negative factor that affects labor productivity, with higher levels of PM leading to a decrease in productivity. The negative impact of air pollution on labor productivity is consistent with prior research that has shown the harmful effects of air pollution on human health and cognitive function, which can in turn lead to reduced productivity. The results underscore the importance of addressing air pollution in efforts aimed at promoting labor productivity, and highlight the need for policymakers to take action to reduce air pollution in the workplace. In contrast, the results indicate that labor insurance is a positive factor that encourages an increase in labor productivity. The findings support prior research that has shown the positive impact of social security systems on labor productivity, suggesting that labor insurance serves as an important institutional mechanism for promoting labor productivity in the industrial sector in Taiwan.

Taken together, the findings suggest that both particulate matter and labor insurance are important factors that affect labor productivity in the industrial sector. The results of this study highlight the need for policymakers to take into account the impact of air pollution and labor insurance on labor productivity when designing and implementing policies aimed at promoting productivity in the workplace. This study provides valuable insights into the mechanisms that promote labor productivity and could inform future research and policy initiatives aimed at promoting labor productivity in Taiwan and other countries.

6. Conclusions

The impact of air pollution on society’s social and economic life has become a growing concern among researchers. The discovery of the harmful effects of air pollution on human cognitive abilities and health has sparked further interest in exploring the impact of air pollution on socio-economic activities. This study seeks to contribute to this area of research by examining the relationship between air pollution, specifically particulate matter, and human economic activity, namely labor productivity. Moreover, this study also investigates the relationship between social security factors of the community, particularly labor insurance, air pollution, and labor productivity. By utilizing the machine learning technique, namely MARS, this study aims to provide additional insights into this topic. Additionally, this study provides an alternative estimation model to address any violations of basic assumptions that may occur in a linear model.

Overall, this study makes a significant contribution to the existing body of literature by providing a comprehensive examination of the non-linear relationship between air pollution, labor insurance, worker salary, working hours, commodity price, and labor productivity. Second, the study employs machine learning techniques, particularly the multivariate adaptive regression splines (MARS) approach, to analyze the relationships among the variables. This application of advanced analytical methods allows for a deeper and more nuanced exploration of the relationships, offering novel insights into the interdependencies. Third, by utilizing the MARS model and machine learning techniques, this research introduces an alternative analytical approach to studying the relationship between the identified variables. This approach enhances the understanding of these complex relationships and provides a different perspective compared to traditional analytical methods. Fourth, the findings of this study have practical implications for policymakers, particularly in the context of promoting labor productivity in Taiwan and other regions facing similar environmental and social challenges. The insights gained from this research can inform policy initiatives aimed at improving labor practices, optimizing resource allocation, and mitigating the negative impact of air pollution on productivity.

The estimation results of MARS reveal that labor insurance has a significant impact on boosting labor productivity, especially in the industrial sector. The study establishes that an increase of 9% in the total number of labor insurance holders has a considerable impact on labor productivity, resulting in a 42.9% increase. Furthermore, this study shows that salary is not as crucial as average working hours for enhancing productivity, as indicated by the MARS estimation results and partial dependence plot. Additionally, employing machine learning techniques, the study validates that air pollution, specifically PM₁₀, has an adverse influence on labor productivity. The findings indicate that a decrease in PM, mainly PM₁₀, to a level lower than 36.2 μg/m³ can yield a rise in marginal labor productivity compared to when PM₁₀ levels exceed 36.2 μg/m³.

This study has several limitations that should be acknowledged. Firstly, the use of the MARS model and machine learning techniques introduces assumptions and constraints, which rely on the quality and representativeness of the training data. Addressing issues such as overfitting, model selection, and parameter choices is crucial to ensure accurate and reliable results. These issues have been previously addressed in studies that have employed machine learning techniques, as demonstrated by Bejani and Ghatee [57] and Shiau et al. [37]. Consequently, when it comes to the MARS model, it is essential to exercise caution during the process of model selection and parameter determination, as emphasized by Arthur et al. [58]. Secondly, relying on a single machine learning technique, the MARS approach, may restrict the exploration of alternative modeling approaches that could provide different insights. Employing multiple techniques or an ensemble approach would offer a more comprehensive analysis and enhance understanding by capturing a wider range of potential relationships. Additionally, establishing causality and determining the direction of relationships can be challenging due to the study’s reliance on observational data. Causal inferences are limited, emphasizing the need for caution in interpreting the findings. Future research should overcome these limitations by utilizing comprehensive data, considering a broader range of variables, and employing different research methods to enhance understanding in various contexts.

7. Policy Implications

The results of this study have significant policy implications for governments and policymakers seeking to improve labor productivity and mitigate the negative impacts of air pollution on economic activity. The finding that labor insurance has the greatest impact on increasing labor productivity in the industrial sector suggests that policies aimed at increasing the number of workers covered by labor insurance could have a substantial positive impact on productivity levels. Policymakers could consider introducing incentives for employers to provide labor insurance coverage or expanding social security programs to cover more workers.

Additionally, the finding that reasonable working hours are more important than salary in relation to increasing productivity highlights the need for policies that encourage employers to prioritize employee well-being and work–life balance. This could include implementing policies such as flexible working hours or offering more paid time off.

Furthermore, the negative impact of air pollution, particularly PM₁₀, on labor productivity underscores the importance of implementing policies aimed at reducing air pollution levels. This could include regulations aimed at reducing emissions from industrial sources, as well as encouraging the adoption of clean energy sources and incentivizing the use of public transportation. Overall, the results of this study suggest that policymakers should focus on improving working conditions and reducing air pollution levels in order to increase labor productivity and promote sustainable economic growth.