A quantile perspective on the effects of supply chain,digitalization,and government spending on air pollution in Vietnam

Abstract

This study examines the asymmetric effects of supply chain (SC) activity, digitalization (DI), economic growth (GDP), energy consumption (EN), and government final consumption expenditure (GE) on air pollution (AP) in Vietnam over the period of 1996–2023. To capture distribution-dependent heterogeneity, the analysis employs Quantile-on-Quantile Regression (QQR), Quantile-on-Quantile Granger Causality (QQGC), and Kernel Regularized Least Squares (KRLS). The results reveal pronounced asymmetric effects across pollution regimes. In particular, EN and SC have positive effects on AP at higher quantiles (0.75–0.95), with QQR coefficients reaching significant magnitudes, indicating substantial pollution amplification under high-emission conditions. In contrast, DI and GE reduce AP at lower to middle quantiles (0.20–0.50), but their mitigating effects weaken or reverse at upper pollution quantiles. The QQGC results confirm significant distribution-dependent predictive relationships from macroeconomic factors to AP, while KRLS estimates corroborate the dominant nonlinear patterns identified by the quantile-based analysis. Overall, the findings highlight that the environmental impacts of economic and policy variables in Vietnam are regime-specific, underscoring the need for differentiated and quantile-informed policy interventions targeting energy use, SC intensity, and digital transformation.

Keywords

GDP energy consumption digitalization government expenditure air pollution quantile analysis

Introduction

Air pollution has escalated into a major global challenge, with far-reaching consequences for human health, environmental quality, and long-term economic sustainability.^1,2 Fine particulate matter (PM2.5 and PM10), nitrogen oxides (NOₓ), sulfur dioxide (SO₂), and carbon dioxide (CO₂) are among the most harmful air pollutants.³ These substances have been scientifically connected to a range of negative health problems, including acute and chronic respiratory illnesses, cardiovascular diseases, and premature mortality. In addition, their role in accelerating climate change poses further risks to ecosystems and socioeconomic stability. The key sources of these pollutants include industrial manufacturing, vehicular emissions, and fossil fuel-based energy production, which emphasize the complicated correlation between economic development and environmental degradation.^4,5 As economies grow and urbanize, the demand for energy, transportation, and infrastructure increases, thereby intensifying pollution unless sustainable development measures are implemented.⁶ It is therefore vital to carry out an in-depth analysis of how energy consumption, supply chain (SC) activities, digital transformation, economic development, and government expenditure interact to mitigate air pollution (AP) and its detrimental effects. A deeper understanding of these relationships is essential for formulating integrated strategies that effectively reduce pollution while sustaining economic productivity.⁷

Vietnam, as a developing country, is experiencing quick economic growth, urbanization, and industrialization.⁸ Nevertheless, these advances have led to dramatic environmental pollution problems.⁷ In response, the Vietnamese government has committed to reducing emissions by enforcing strict environmental policies, including limiting coal consumption, transitioning to natural gas, and improving energy efficiency. To tackle the harmful impacts of climate change, policymakers are actively working to cut AP. Since the 1990s, global emissions have increased, particularly in low- and middle-income countries.³ Scholars identify economic growth and energy consumption as key drivers of emissions at both global and regional levels.^49–11 As a result, the transition toward energy-efficient and environmentally friendly economic development has become a central focus of the sustainable development agenda.

The internet and technological improvements represent both opportunities and challenges in tackling AP.^12–14 On the positive side, they promote operational efficiency, optimize resource utilization, and facilitate innovations such as smart grids and predictive analytics. Hung⁷ reports a significant positive impact of digitalization (DI), green investment, and financial development on economic sustainability in Vietnam, suggesting that investments in green technology and financial infrastructure are vital to achieve sustainability. In addition, Hung⁸ documents that the asymmetric interplay between digital innovation, energy intensity, demographic changes, and economic growth in Vietnam is significantly positive. Complementing these findings, Xuan and Hung¹⁵ indicate that green renewable energy positively impacts environmental quality in the short and medium term. Besides, economic growth, financial globalization, and fossil fuel consumption are found to positively affect the green investment–emissions nexus.

Governments use fiscal policies to influence environmental outcomes by providing significant economic policies that shape behavior. Evidence indicates that global investments in sustainable infrastructure, clean energy, and public transportation reduce emissions.^16–18 On the other hand, continued support for fossil fuels through subsidies results in higher AP. Bulus and Koc¹⁸ uncover that in Korea, higher levels of FDI, GDP, energy consumption, and imports are associated with increased CO2 emissions. However, government spending, renewable energy usage, and exports contribute to reductions in CO₂ emissions. Similarly, Samah et al.¹⁹ report that in Malaysia, CO₂ emissions and manufacturing output significantly influence government expenditure. Wu and Song²⁰ unveil that in Belt and Road Initiative (BRI) economies, GDP, public spending on health and research and development, and FDI drive an increase in green finance, while higher emissions tend to reduce the level of green finance.

The association between economic development and AP is mixed and nonlinear.^21–23 In the early stages of economic growth, industrialization and increased energy demand tend to exacerbate environmental degradation, often resulting in severe pollution problems.^17,24 Nonetheless, as economies advance, there is typically a shift toward cleaner technologies and stricter environmental regulations, resulting in a decrease in AP.²⁵ This inverted U-shaped relationship is described by the Environmental Kuznets Curve (EKC) hypothesis.

Government spending plays a prominent role in advancing green technology and achieving long-run environmental quality.¹⁸ As urbanization and economic growth fuel the industrial construction sector, adopting sustainable construction strategies becomes increasingly essential. The Vietnamese government has committed to sustained efforts to control AP over the long term in order to enhance environmental quality and reduce the frequent occurrence of severe haze events. In this context, the present study seeks to examine the influence of macroeconomic factors, such as economic growth, energy consumption, SC, government spending and DI on AP. The outcomes are expected to provide scientific insights and policy recommendations targeting critical industries, thereby supporting improved air quality and promoting sustainable development.

Despite the growing body of literature employing quantile-based approaches to explore the relationship between economic development and pollution, several crucial conceptual gaps remain, particularly in the context of emerging economies such as Vietnam. First, existing quantile-based articles primarily concentrate on a limited set of macroeconomic indicators, most commonly economic growth and energy consumption while largely overlooking the integrated roles of SC activities and DI, both of which are increasingly central to pollution dynamics in rapidly industrializing countries. Second, prior studies have mainly employed conventional quantile methods, which capture heterogeneity across the conditional distribution of AP but fail to account for asymmetric interactions between different quantiles of independent variables and environmental outcomes. Third, the causal mechanisms underlying these heterogeneous associations remain insufficiently explored, as most studies emphasize association rather than distribution-dependent causality.

This study contributes to both theory and policy by examining the relationships between SC, DI, GDP, energy consumption (EN), government expenditure (GE), and AP in Vietnam, providing valuable insights for formulating more effective strategies to address climate and development challenges. In other words, this study addresses these gaps by investigating SC, DI, GDP, EN, and GE within a quantile-on-quantile framework. By integrating Quantile-on-Quantile Regression (QQR), Quantile-on-Quantile Granger Causality (QQGC), and KRLS, the analysis captures both nonlinear dependence and distribution-sensitive causal effects across different pollution regimes. These approaches enable a more nuanced understanding of how macroeconomic and structural factors influence AP under different economic and environmental conditions, thereby providing straightforward insights beyond those offered by conventional quantile-based studies.

Practically, this study offers important policy implications for addressing AP in Vietnam. It recommends targeted interventions to decrease the environmental impact of SC and DI, including investments in energy-efficient technologies and environmentally conscious government spending. The findings also underscore the importance of boosting renewable energy investments and strengthening SC systems to boost green growth. These actions are important for achieving Sustainable Development Goals (SDGs) targets in connection with clean energy, sustainable growth, resilient infrastructure, urban sustainability, and climate action.

With respect to SDGs, this study advances literature by empirically connecting multiple SDGs through various macroeconomic indicators within an econometric framework. Importantly, DI captures progress toward SDG 9 (industry, innovation, and infrastructure) and SDG 12 (responsible production), EN reflects SDG 7 (affordable and clean energy), GDP corresponds to SDG 8 (decent work and economic growth), GE presents policy commitment and institutional capacity relevant to SDG 16 (effective institutions) and SDG 13 (climate action), while AP serves as a measurable outcome for SDG 3 (good health and well-being) and SDG 11 (sustainable cities).

By modeling the asymmetric and distribution-dependent interrelationships among these variables using quantile-on-quantile techniques, the study provides empirical evidence on how progress in one SDG dimension would reinforce or emphasize results in other SDGs under different pollution and economic conditions.

The remainder of the article is structured as follows: the literature review and theoretical mechanism section presents a review of the related literature and outlines the theoretical framework. The methodology section describes the dataset and methodology. The empirical results section analyzes the impact of economic factors on AP. Finally, The conclusion section 5 concludes the article and offers policy recommendations.

Literature review and theoretical mechanism

Although the existing literature often examines SC, DI, and GE as separate determinants of AP, their effects are interdependent, particularly in emerging economies such as Vietnam. SC directly influences AP through energy-intensive production processes, transportation, and logistics operations.^26,27 However, the magnitude of this environmental influence largely depends on technological capacity and policy intervention. In addition, DI plays a key moderating role by improving SC efficiency through enhanced logistics coordination, reduced energy intensity, optimized inventory management, and real-time monitoring of production and emissions.¹² These technological developments can reduce pollution by reducing waste, lowering fossil fuel dependence, and enhancing cleaner production practices. At the same time, GE shapes this nexus by providing the institutional and financial support necessary for digital infrastructure development, environmental regulation, renewable energy investment, and green logistics systems. Well-targeted public spending can amplify the pollution-reducing effects of digitalized SCs, whereas growth-oriented expenditure without environmental safeguards may intensify emissions.

DI and AP

The interaction between DI and AP can be understood through several theoretical frameworks, including environmental economics, technology diffusion, and structural transformation theories. DI fosters technological innovation, boosts energy efficiency, and promotes the growth of cleaner production models, thereby improving environmental quality. According to neoclassical production theory, digital technologies improve operational efficiency and resource allocation by optimizing logistical and industrial processes, which can reduce emissions. In addition, the EKC theory suggests that DI can facilitate shifts away from pollution-intensive sectors, contributing to improved air quality.

Numerous studies have found that the digital economy contributes to reductions in AP. DI has driven significant transformations in energy consumption and environmental management. Qi et al.¹² analyze the impact of industrial upgrading and the digital economy on AP in China, suggesting that industrial upgrading most effectively decreases PM2.5, while the digital economy has the greatest impact on lowering SO₂ emissions. Wang et al.,²⁸ using data from listed companies in Shanghai and Shenzhen, confirm that AP significantly constrains economy-wide digital transformation. Shen and Zhang,²⁹ applying a two-way fixed effects model to data from 269 Chinese cities, indicate that digital advancements significantly reduce fine particulate matter, supporting cleaner air and better environmental protection. Similarly, Wu et al.³⁰ uncover that growth in the digital economy leads to lower AP levels, with reductions more pronounced in Central and Western China than in the Eastern region. Yang et al.³¹ illustrate that DI decreases AP intensity through structural and technological mechanisms by promoting environmental investment and green innovation.

Nevertheless, a limited number of studies suggest that the digital economy may exacerbate AP. Several scholars argue that the expansion of the digital economy has contributed to increased emissions, negatively impacting environmental quality. Vadurin et al.³² highlight the need for improved digital tools to monitor AP in Ukraine, reporting that the BATS model often outperforms ARIMA for key pollutants, emphasizing the importance of automated model selection. Chen et al.³³ reveal that AP positively influences firms’ digital transformation.

Some researchers suggest that the digital economy has a nonlinear impact on AP. Given its mix of positive and negative effects, the digital economy might influence emissions in a complex, nonlinear manner. For instance, Wang and Ding³⁴ investigate mechanisms through which the digital economy both increases and reduces AP using panel data from 30 Chinese provinces. The authors suggest that emission reduction effects are more significant, attributed to the asymmetric bilateral impacts of the digital economy. Wang and Xu³⁵ examine how DI affects haze pollution through direct and indirect channels using data from 81 countries. Their study uncovers a statistically significant pollution-reducing effect, though this effect covaries significantly depending on country-specific factors.

Energy consumption and AP

The nexus between AP and EN can be better understood through four main theories: the EKC, the Pollution Haven Hypothesis, the Porter Hypothesis, and the Energy Efficiency Paradox. These frameworks explain the dynamic changes in pollution levels over time, with higher EN, particularly from nonrenewable sources, typically driving increased AP.

In recent years, rising EN from nonrenewable sources has been closely linked to heightened environmental pollution, prompting significant research attention on environmental degradation. Alvarez-Herranz et al.¹ provide insights into the interplay between energy regulation, GDP, and carbon emissions, demonstrating that energy innovation has a substantial positive effect on reducing pollution across 17 OECD countries between 1990 and 2012.

Focusing on China, Yuan et al.² investigate how economic development affects EN and AP. Their results reveal that the Resource and Environmental Performance Index, which measures the costs associated with energy and environmental impact, does not align with provincial variations in energy use or AP. Similarly, Wu and Qiao⁶ identify significant spatiotemporal patterns in urban heat island intensity, energy consumption, CO₂ emissions, and concentrations of PM2.5 and O₃, characterized by a north-south gradient and elevated levels in eastern China. Chen et al.³⁶ suggest that renewable energy reduces AP in China, while nonrenewable energy increases it, indicating a unidirectional causal linkage between energy source and emissions. Xiong and Xu³⁷ explore the effects of energy expenditure and environmental pollution on economic development, noting that although renewable electricity generation contributes to environmental degradation, its impact is significantly lower than that of nonrenewable sources.

In Latin America and the Caribbean, Koengkan et al.³⁸ demonstrate that economic growth and fossil fuel consumption are positively correlated with CO₂ emissions, while renewable energy consumption correlates negatively with emissions. Magazzino et al.³⁹ provide a comprehensive evaluation of the associations between information and communication technology, electricity consumption, and environmental pollution in the European Union. Chien et al.³ look into carbon emissions and PM2.5 concentrations in relation to renewable and nonrenewable energy consumption, environmental taxes, and ecological innovation across leading Asian economies from 1990 to 2017. The authors confirm that renewable energy, ecological innovation, and environmental taxes significantly reduce carbon emissions and PM2.5 levels in both the short and long term. Furthermore, Androniceanu et al.¹⁶ observe that while most countries have experienced economic progress since 2014, the pace of advancement varies significantly. This variation reflects the complexity of national development trajectories and the effectiveness of government efforts to achieve sustainable growth with minimal energy use and environmental impact.

Economic growth and AP

Both theoretical perspectives and empirical evidence generally support the existence of an inverted U-shaped relationship between GDP and AP, commonly known as the EKC. Qirjo and Pascalau⁴ study how rising per capita income influences five key air pollutants. They reveal that higher income levels are strongly associated with increased emissions of greenhouse gases and nitrous oxide (N₂O), particularly when accounting for trade dynamics linked to the proposed Transatlantic Trade and Investment Partnership. Similarly, Shafique et al.⁴⁰ explore the interplay between transportation, GDP, and environmental degradation in ten Asian economies. Their results highlight an endogenous relationship where both economic growth and transport sector activities drive CO₂ emissions and environmental degradation.

Magazzino et al.³⁹ provide evidence that unsustainable economic growth contributes to increasing AP, specifically higher emissions of PM2.5 and NO₂ in New York State. More recently, Mirziyoyeva and Salahodjaev⁵ analyze the complicated interactions between economic growth, renewable energy use, globalization, and climate change, using CO₂ emissions as a pollution proxy. They confirm an inverted U-shaped association between GDP and CO₂ emissions, while renewable energy adoption and globalization contribute significantly to emission reductions.

In the context of China, Chai et al.²¹ investigate the impact of GDP targets on AP and identify a significant U-shaped relationship between growth constraints and pollution levels. Similarly, Li et al.,²³ using panel data from 30 Chinese provinces between 1998 and 2016, empirically validate the EKC hypothesis for PM2.5 emissions, indicating that AP has peaked as economic growth advances. Yu et al.¹⁷ further identify that when higher-level governments impose stringent growth targets on lower-level authorities, environmental regulations are relaxed, industrial upgrading stalls, and innovation is discouraged, resulting in increased pollution.

Government expenditure and AP

GE significantly impacts AP through targeted policies and investments. Funds allocated to environmental regulations, including monitoring and emissions control, help curb industrial and vehicular pollution. Investments in green infrastructure, such as public transportation and renewable energy, reduce reliance on fossil fuels, thereby lowering emissions. Moreover, research and development (R&D) funding and subsidies for sustainable industries can drive innovation in clean technologies, further decreasing AP. Nonetheless, ongoing support for carbon-intensive sectors may further deteriorate environmental quality. Effective governance and robust policy design are vital to ensure that government spending contributes to pollution reduction. The EKC suggests that as governments become wealthier, they tend to prioritize cleaner air and stronger environmental policies.

Building on prior research, this study draws on evidence from different countries and regions, employing a broad range of environmental indicators such as ozone (O₃), carbon dioxide (CO₂), sulfur dioxide (SO₂), particulate matter (PM₁₀), water quality, and deforestation. Although the impact of public expenditure on environmental quality remains somewhat inconclusive, existing results strongly support a positive relationship between government expenditure and AP mitigation.

For instance, Samah et al.¹⁹ highlight in Malaysia that GE is considerably influenced by CO₂ emissions. Bulus and Koc¹⁸ investigate Korea, suggesting that higher levels of FDI, GDP, energy consumption, and imports increase CO₂ emissions, while GE, renewable energy use, and exports contribute to emission reductions. Li et al.²³ point out the important governance role of environmental nongovernmental organizations, revealing their significant and robust contribution to improved environmental quality. Wu and Song²⁰ disclose that GDP, public spending, and FDI inflows positively influence renewable energy development in BRI economies.

Donkor et al.⁹ analyze Northern and Southern African countries from 2000 to 2016, suggesting that GE improves environmental quality in the North but worsens it in the South. They also note that in Northern Africa, both GDP and GE aid environmental quality, while CO₂ emissions have a small, statistically insignificant negative effect. Bao and Liu⁴¹ argue that heightened environmental awareness typically leads to stronger policies and increased spending on pollution control. Khan et al.⁴² determine a long-term positive association between GE, GDP, and CO₂ emissions. Azam et al.⁴³ assess France's energy and resource use, concluding that nuclear energy, natural resource management, and GE reduce CO₂ emissions, while GDP is connected to increased emissions.

SC and AP

The interaction between AP and SC activities can be analyzed through frameworks such as environmental economics, institutional theory, and operations management. SC activities, including transportation, sourcing, distribution, manufacturing, and end-of-life processes, significantly contribute to AP. From the perspective of environmental economics, AP presents a negative externality, as the environmental costs of emissions generated through SC operations are not borne by the producers alone. In other words, SC activities contribute to AP through EN and waste generation. Understanding this nexus is crucial for guiding improvements toward more sustainable SCs and informing policies aimed at reducing environmental degradation. By identifying the SCs that contribute most significantly to pollution, policymakers can better trace emissions from production to consumption and design targeted mitigation strategies.

Empirical studies confirm the substantial contribution of SC activities to AP, with emissions arising during production, transportation, warehousing, and disposal stages. Moran and Kanemoto⁴⁴ argue that linking consumers and SCs to emissions creates opportunities for broader engagement in pollution abatement, engaging not only primary emitters and local regulators but also additional stakeholders. Peng et al.²⁶ document that AP in China is remarkably influenced by two key SCs: “electricity, gas, and water supply/fixed capital formation” and “electricity, gas, and water supply/household consumption.” These patterns are largely driven by economic growth, shifts in input structures, changing consumption habits, and population growth.

Similarly, Song et al.²⁷ identify the Power and Heat, Metals Smelting, and Nonmetallic Mineral Products sectors as the primary sources of production-based emissions in China, while Construction, Equipment, and Services sectors predominantly contribute to consumption-based emissions. Karimi et al.²⁵ demonstrate that implementing models encompassing all dimensions of flexibility effectively advances sustainable development, substantially reducing both costs and environmental pollution in Iran. Zhao et al.¹³ highlight key sectors influencing PM2.5-related mortality from both production and consumption perspectives, suggesting that capital investment plays a vital role in cross-boundary pollution effects, largely due to reliance on equipment and construction products exported from resource-rich regions. Liu et al.⁴⁵ emphasize that regions such as Beijing-Tianjin-Hebei, parts of western China, and the Greater Bay Area, along with sectors like metal products, automobile manufacturing, and utilities, play central roles in CO₂ and AP reduction, driven by strong synergistic effects.

Although the present literature provides valuable insights into the determinants of AP, its findings remain mixed and, in some cases, contradictory. For example, while several studies report that DI and technological progress reduce AP through efficiency gains and cleaner production, others find that digital expansion may increase emissions due to rebound effects, rising energy demand, and uneven technological adoption. Similarly, economic growth and energy consumption are often identified as major drivers of environmental degradation, yet evidence supporting the EKC suggests that their impacts vary across development stages and pollution regimes. Government expenditure is likewise characterized by dual effects, as growth-oriented public spending may exacerbate emissions, whereas environmentally targeted expenditure can improve air quality. These inconsistencies indicate that the environmental effects of macroeconomic and structural factors are highly context-dependent, nonlinear, and heterogeneous across pollution levels. Consequently, approaches that rely on average or linear effects may obscure important distributional dynamics. This motivates the use of a quantile-based framework that explicitly captures asymmetric relationships and reconciles conflicting empirical evidence by examining how these effects vary across different pollution and economic conditions.

Methodology

In line with the insights drawn from the previous papers, this study adopts two advanced quantile-based techniques, namely QQR developed by Sim and Zhou⁴⁶ and QQGC proposed by Adebayo et al.⁴⁷ to explore the comparative influence of SC, DI, GDP, GE, and EN on AP in Vietnam. These methods are particularly suitable due to their capacity to capture nonlinear and heterogeneous dependencies among variables by analyzing their interactions across various quantiles.⁴⁷ While traditional mean-based models are useful for estimating average impacts, they assume homogeneous nexus across the distribution of AP. By contrast, the quantile-based models employed in this study suggest significant heterogeneity, asymmetry, and regime-dependent influences that would be obscured by simpler models.

Following Sim and Zhou,⁴⁶ the QQR framework examines how the $θ^{t h}$ quantile of an independent variable (X) affects the $τ^{t h}$ conditional quantile of AP. Specifically, the $τ^{t h}$ conditional quantile of $A P_{t}$ , given the $θ^{t h}$ quantile of $X_{t}$ , is expressed as:

Q_{A P_{t}} (τ | X_{t}) = α (τ, θ) + β (τ, θ) (X_{t} - Q_{X_{t}} (θ)) + ε_{t} (τ)

(1)

where

Q_{A P_{t}} (τ | X_{t})

denotes the

τ^{t h}

conditional quantile of AP,

Q_{X_{t}} (θ)

represents the

θ^{t h}

quantile of the explanatory variable,

α (τ, θ)

is the intercept term, and

β (τ, θ)

captures the dependence between the

τ^{t h}

quantile of AP and the

θ^{t h}

quantile of the explanatory variable. The term

ε_{t} (τ)

denotes the quantile-specific error term. This formulation allows the relationship between variables to vary across both the distribution of AP and the distribution of the explanatory variables.

Quantile-on-quantile Granger causality

After identifying the direction and magnitude of the influence of the regressors on AP with QQR, we utilize the QQGC model to estimate whether the selected macroeconomic variables have causal impact on AP in Vietnam using the following equations:

Q_{A P_{t}} (τ | F_{t - 1}) = ψ (τ) + \sum_{j = 1}^{p} α_{j} (τ) A P_{t - 1} + \sum_{j = 1}^{p} β_{j} (τ, θ) (X_{t - 1} - Q_{X} (θ)) + u_{t} (τ, θ)

(2)

where

F_{t - 1}

represents the information set available at time

t - 1

, p denotes the lag length,

α_{j} (τ)

captures the autoregressive effect of AP at quantile

τ

, and

β_{j} (τ, θ)

measures the predictive content of the

θ^{t h}

quantile of

X_{t}

for the

τ^{t h}

quantile of AP. The null hypothesis of no quantile-based Granger causality is:

H_{0} : β_{j} (τ, θ) = 0 \forall τ \in (0, 1), θ \in (0, 1)

Rejection of the null implies that deviations of $X_{t}$ from its $θ^{t h}$ quantile help predict movements in AP at quantiles $τ$ beyond its own history.

Kernel regularized least squares

For the robustness check, we employ Kernel Regularized Least Squares (KRLS), which offers a suitable approach for regression analysis, particularly in cases where the relationship between variables is nonlinear, as suggested by Hainmueller and Hazlett.⁴⁸ The KRLS estimation equation is represented as follows:

\hat{y} = K (K + λ I)^{- 1} y

(3)

where

\hat{y}

denotes the predicted values vector;

λ

is the regularization parameter; K stands for the kernel matrix; I and y represents the identity matrix and the observed response, respectively. The kernel function

k (x_{i}, x_{j})

can be positive as follows:

k (x_{i}, x_{j}) = e^{- \frac{| | x_{i} - x_{j} | |^{2}}{2 σ^{2}}}

(4)

where

σ

is a parameter controlling for the kernel's spread. The KRLS method estimates the coefficients by minimizing the regularized least squares criterion, as outlined below:

min_{α} | | y - K α | |^{2} + λ α^{T} K α

(5)

where

α

indicates coefficients in vector form. We estimate KRLS using a Gaussian kernel, which flexibly captures nonlinear relationships in the covariate space. The kernel bandwidth parameter

σ

and the regularization parameter

λ

are selected through data-driven tuning to balance goodness-of-fit and smoothness. Specifically, we adopt cross-validation to choose

(σ, λ)

that minimize out-of-sample mean squared prediction error.

Figure 1 presents the sequential steps of empirical analysis.

Data sources and descriptions

This study utilizes a comprehensive time-series dataset to investigate the effects of SC activities, DI, economic growth (GDP), energy consumption (EN), and government final consumption expenditure (GE) on air pollutant emissions (AP) in Vietnam during the period 1996–2023. The study explores the interconnections among these factors and their influence on emissions of various air pollutants, including nitrogen dioxide (NO₂), sulfur dioxide (SO₂), carbon monoxide (CO), black carbon, ammonia, and nonmethane volatile organic compounds. These pollutants share popular emission sources such as fossil fuel combustion, industrial activity, transportation, and SC operations and reflect overall air quality and health risks.²⁹ Aggregation also reduces multicollinearity among highly correlated emission series and allows the analysis to focus on the broader environmental burden relevant for macro-level policy evaluation. SC is proxied by global air transport, registered carrier departures, as this indicator captures a key logistics-intensive component of modern SCs that is closely linked to trade integration, time-sensitive goods movement, and industrial connectivity. For Vietnam, while this measure does not capture all dimensions of domestic SC activity, it serves as a consistent and observable proxy for SC intensity that is widely used in macroeconomic analyses. We acknowledge this limitation and note that future research could incorporate alternative indicators to capture domestic logistics more comprehensively. A summary of the variables and their data sources is presented in Table 1.

Table 1.

Data descriptions.

Variable name	Measurement	Code	Source
Emissions of air pollutants	(i) Nitrogen dioxide (NO2) (ii) Sulfur dioxide (SO2) (iii) Carbon monoxide (CO) (iv) Black carbon (BC) (v) Ammonia emissions (NH2) (vi) Nonmethane volatile organic compounds emissions	AP	Our world in data
Supply chain	Air transport, registered carrier departures (number of departures registered in Vietnam; proxy for logistics-intensive supply chain activity)	SC	WDI
Digitalization	Using the internet. Percentage of population	DI	WDI
Energy consumption	Primary consumption	EN	BP statistical review of world energy
General government final consumption expenditure	Government final consumption expenditure (% of GDP)	GE	WDI
Real gross domestic product	Gross domestic product per capita	GDP	WDI

Note: AP: air pollution; DI: digitalization; EN: energy consumption; GE: government expenditure; SC: supply chain.

Air transport departures are used as a proxy for supply chain activity, as they capture the logistics intensity and connectivity of time-sensitive and export-oriented production networks. For Vietnam, air transport is closely linked to high-value manufacturing, trade integration, and modern supply chain operations.

In order to perform the quantile-based models, we transform the annual data into quarterly frequency using the quadratic match-sum method, as suggested by Haseeb et al.⁴⁹ and Hung.⁷ This method is particularly suitable for converting low-frequency data into higher-frequency series, as it preserves the original annual totals while generating smooth intraperiod dynamics. Additionally, the quadratic match-sum approach helps minimize end-to-end deviations and interpolation bias, thereby maintaining the underlying structure of the data.^7,8,49

Table 2 represents the descriptive statistics for the selected variables in this study, including the mean, median, maximum, minimum, standard deviation, and results of the Jarque–Bera test. The average AP at the national level is 1.29, with values ranging from a minimum of 1.25 to a maximum of 1.32. The mean level of DI is relatively low at 7.9%. Other variables show average values ranging from 2.2 (GDP) to 16.1 (EN), reflecting persistently high levels of traditional energy consumption in Vietnam. Regarding volatility, DI and GE exhibit the highest standard deviations, indicating greater variability, while AP, GDP, and SC demonstrate the lowest volatility. Additionally, the skewness and kurtosis coefficients suggest that none of the variables follow a normal distribution, a finding confirmed by the Jarque–Bera test.

Table 2.

Descriptive statistics.

	AP	DI	EN	GDP	GE	SC
Mean	1.293051	7.983484	16.17143	2.215587	5.720847	2.841976
Median	1.298956	7.129297	16.82070	2.216435	5.747737	2.864933
Max	1.322037	19.79453	21.33117	2.379911	6.093620	3.187500
Min	1.252219	0.001751	9.594375	2.038864	5.346014	2.523929
Std. dev	0.019981	6.868004	3.432761	0.100420	0.294045	0.196485
Skewness	−0.680066	0.351090	−0.299811	−0.051326	−0.065064	0.059734
Kurtosis	2.313187	1.746889	1.858319	1.792533	1.229257	1.709120
Jarque–Bera	10.83446**	9.628942***	7.760588*	6.853063*	14.71149***	7.843001**

Note: AP: air pollution; DI: digitalization; EN: energy consumption; GE: government expenditure; SC: supply chain.

*, **, *** indicate significance at 10%, 5% and 1%, respectively.

Figure 2 presents the Quantile-Quantile (Q-Q) plots for the selected time series. Points that closely align with the orange reference line indicate an approximately normal distribution. However, noticeable deviations, particularly in the tails, suggest that the variables for Vietnam deviate from normality. Overall, the Q-Q plots confirm that all variables exhibit nonnormal distributions. Furthermore, as shown in Table 3, the BDS test was employed to detect nonlinear characteristics within the series. The results reveal significant nonlinearity and dependence between each regressor and AP across all embedding dimensions for Vietnam. Specifically, the variables DI, EN, GDP, GE, SC, and AP consistently demonstrate significance at the 1% level, reinforcing the presence of nonlinear associations. These outcomes considerably justify the use of nonlinear modeling techniques in the analysis.

Table 3.

Brock–Dechert–Scheinkman test results.

Dimension	AP	DI	EN	GDP	GE	SC
M2	0.186530***	0.200837***	0.205148***	0.205749***	0.204234***	0.201972***
M3	0.308736***	0.337615***	0.34767***	0.348846***	0.344319***	0.343227***
M4	0.388509***	0.431547***	0.446439***	0.449736***	0.440983***	0.440261***
M5	0.440493***	0.496712***	0.514583***	0.521839***	0.508073***	0.505706***
M6	0.474380***	0.542493***	0.561484***	0.574330***	0.555374***	0.549261***

Note: AP: air pollution; DI: digitalization; EN: energy consumption; GE: government expenditure; SC: supply chain.

*** indicates significance at 1%.

Figure 3 illustrates the Pearson correlation matrix among DI, EN, GDP, GE, SC, and AP in Vietnam over the sample period. The results reveal a significant correlation between DI and AP, while EN, GDP, GE, and SC do not exhibit evidence of a linear relationship with AP from 1996 to 2023. The weak linear correlations do not suggest measurement problems or conceptual mismatch between the selected variables and AP. Instead, they illustrate that the interactions are significantly nonlinear and heterogeneous across the distribution. This reinforces the motivation for adopting quantile-based approaches, which are specifically designed to uncover nonlinear and distribution-sensitive relationships that are not observable through conventional correlation analysis.

Although the descriptive statistics demonstrate a somewhat narrow range for the composite AP indicator, this reflects the normalization and aggregation of multiple pollutant series rather than a lack of underlying variability. Furthermore, quantile-based techniques do not rely on wide dispersion in raw levels but on differences in the conditional distribution and tail behavior of the variable. As shown by the Q-Q plots, BDS test results, and quantile unit root tests, the AP series exhibits significant nonlinearity, asymmetry, and distributional heterogeneity across quantiles. These properties confirm that the constructed indicator contains sufficient informational content to support quantile-on-quantile analysis.

Overall, the results from the Jarque–Bera and BDS tests indicate that the variables display asymmetric and nonlinear behavior. To effectively capture this complexity, econometric techniques such as QQR and QQGC are well-suited, as they accommodate the nonlinear interrelationship between time series.

Subsequently, we apply the Quantile Augmented Dickey–Fuller (QADF) and Quantile Phillips–Perron (QPP) tests to examine the stationarity properties of the variables across the full conditional distribution, following the approach of Ramzan et al.⁵⁰ Unlike the traditional ADF test, the QADF approach (see Figure 4) evaluates stationarity at different quantiles rather than at the mean, providing a more detailed characterization of distributional dynamics for AP, GDP, SC, GE, EN, and DI. The results reveal heterogeneity in test statistics across quantiles: for AP, DI, GDP, and EN, the statistics approach critical values at the distribution tails, indicating relatively weaker evidence of stationarity in those regions. However, none of the variables exhibits persistent unit root behavior across all quantiles, and no variable can be classified as integrated of order one at specific quantiles. The QPP test results (see Figure 5) yield consistent conclusions, reinforcing the presence of distributional heterogeneity rather than distinct integration orders. These findings highlight asymmetric and quantile-dependent dynamics, supporting the use of quantile-based methodologies rather than conventional unit root tests. Although the quantile-based unit root tests display fluctuations of test statistics around critical values, the potential risk of nonstationarity is confined to specific regions of the conditional distribution. In particular, the QADF and QPP results indicate that test statistics for AP, GDP, EN, and DI approach critical thresholds primarily at the extreme lower and upper quantiles, while remaining comfortably below critical values across the central quantile range. This pattern suggests localized tail sensitivity rather than pervasive nonstationarity, reflecting distributional heterogeneity instead of distinct integration orders.

Empirical results

QQR estimates

Although nonlinear patterns are evident in the QQR surface plots, asymmetry in this study is not inferred from visual inspection. Instead, asymmetry is analytically identified through differences in the sign, magnitude, and persistence of estimated coefficients across quantiles of both the independent variables and AP. Specifically, asymmetric effects are detected when the influence of a given determinant differs between lower and upper quantiles or changes direction across pollution regimes. The QQR allows for such asymmetric responses by jointly conditioning on the distributions of both variables. The consistency of these asymmetric patterns is further supported by the QQGC results, which reveal distribution-dependent predictive effects across quantiles.

Figure 6(a)–(e) represents surface plots derived from the QQR analysis, demonstrating the asymmetric and heterogeneous relationships between SC, DI, GDP, EN, GE, and AP in Vietnam. The left-side plot in each Figure illustrates the QQR output, while the right-side plot portrays the p-values. The red color in the p-values plot indicates the significant p-values (p < .05). These plots capture the interdependence across 19 quantiles, enabling the assessment of variations in the nexus under different economic and environmental conditions, including extreme scenarios. The slope estimates α₁(θ, τ) present how the θth quantile of each explanatory variable affects the τth quantile of AP, suggesting a nuanced perspective on their interaction across the entire conditional distribution. Following the quantile-based framework of Troster et al.,⁵¹ the quantile space is segmented into three regimes: lower quantiles (0.05–0.15) reflect extreme bearish conditions, upper quantiles (0.85–0.95) denote extreme bullish conditions, and mid-quantiles represent normal economic conditions. This categorization allows for a detailed understanding of both the magnitude and direction of dependence across different regimes. In the QQR surface plots, color intensity reflects the magnitude and sign of the estimated QQR coefficients, with warmer (reddish) tones indicating larger positive effects and cooler (bluish/green) tones indicating larger negative effects, while lighter shades correspond to coefficients closer to zero and thus weaker relationships at the respective quantile intersections. The results demonstrate considerable variation in the dependency structures between AP and its determinants, highlighting the importance of considering quantile-based methods to capture these nonlinear and asymmetric dynamics.

In the case of the nexus between DI and AP (Figure 6(a)), the analysis reveals that the influence of DI on AP is significantly negative. A strong and inverse association is observed across all quantiles of DI and the low to middle quantiles of AP, indicating that DI significantly contributes to improving air quality, particularly under moderate pollution conditions. These findings align with those of Shen and Zhang²⁹ and Wu et al.,³⁰ who report that DI improves environmental quality in both E7 and G7 economies. However, the results also show a notable positive relationship between the upper quantiles of AP (0.75–0.95) and the majority of DI quantiles. This suggests that under conditions of high pollution intensity, the effectiveness of DI in reducing emissions may diminish or even reverse, possibly due to structural constraints or lagged responses in technological adoption. Overall, the evidence supports the assertion that DI plays a vital role in lowering pollution emission intensity in Vietnam. This can be attributed to enhanced production flexibility and operational agility facilitated by digital technologies. Through digital transformation, the economy can more readily adjust production strategies in response to environmental demands, minimize waste via advanced manufacturing systems, and optimize resource use through improved materials management. These capabilities contribute to more sustainable and responsive production systems.

Figure 6(b) depicts the QQR surface plot illustrating the interactions between EN and AP. The results clearly indicate a significantly positive interplay across most quantiles, suggesting that increased energy consumption is generally associated with higher levels of AP in Vietnam. At the middle and upper quantiles of AP, EN exhibits a strong and increasingly positive effect, with coefficient magnitudes rising dramatically as both EN and AP move toward their upper quantiles. This indicates that under high pollution regimes, EN acts as a strong amplifier of environmental degradation. Although the coefficient magnitudes become particularly large in the upper-tail regions, these estimates should be interpreted with caution, as extreme quantiles are estimated using fewer effective observations and are more sensitive to tail behavior. Nevertheless, the smooth and systematic increase in coefficients across quantiles suggests that these effects reflect state-dependent amplification rather than random estimation artifacts. Conversely, at lower AP quantiles (0.05–0.30), a negative influence is observed across all quantiles of EN. This suggests that under conditions of relatively low pollution, energy consumption may exert a weaker or even marginally mitigating effect on AP, although this effect is neither consistent nor robust enough to serve as a reliable hedge against air degradation. The overall findings suggest the environmental consequences of Vietnam's persistent reliance on fossil fuels, particularly coal and oil, for electricity generation and industrial activities. As energy demand escalates due to rapid urbanization and industrialization, increased combustion of fossil fuels results in higher emissions of harmful pollutants. In addition, the ongoing use of outdated energy technologies and poor energy efficiency exacerbate emissions intensity, contributing significantly to environmental degradation. These outcomes are consistent with existing literature, such as Alvarez-Herranz et al.¹ and Chen et al.,³⁶ which provide empirical evidence supporting the strong and positive link between energy consumption and environmental deterioration. The findings thus highlight the urgent need for transitioning to cleaner energy sources and adopting energy-efficient technologies to mitigate the adverse environmental impacts associated with rising energy consumption.

Similarly, Figure 6(c) illustrates that the impact of GDP on AP in Vietnam is generally positive, particularly at the middle-to-upper quantiles of AP and the higher quantiles of GDP. This pattern suggests that as Vietnam's economy expands, the associated increase in industrial activity, EN, and infrastructure development tends to exacerbate AP. These outcomes align with the early stages of economic development, where growth is often accompanied by environmental degradation. Nevertheless, the QQR results also reveal a notable negative effect of GDP on AP at the lower quantiles (0.05–0.40), indicating a nonlinear and dynamic relationship. This mixed pattern highlights the dual role of economic growth—as both a driver of environmental pressure and a potential catalyst for environmental improvement. The relationship depends significantly on the stage of economic development and the structure of the economy. As an emerging economy, Vietnam initially experiences rising pollution with increased GDP due to its dependence on fossil fuels, rapid industrialization, and limited regulatory enforcement. Nonetheless, as income levels rise and the economy matures, further increases in GDP would support environmental improvements. This occurs through greater public awareness, stricter environmental regulations, and investments in cleaner technologies and sustainable infrastructure. Such a trajectory is consistent with the EKC hypothesis, which posits an inverted U-shaped relationship between environmental degradation and economic growth. In the early stages of development, pollution worsens with growth, but beyond a certain income threshold, further growth contributes to environmental improvements. Our findings support the EKC hypothesis and are consistent with prior studies such as Shafique et al.⁴⁰ and Magazzino et al.,³⁹ who observe similar turning points in the growth-pollution nexus in emerging economies.

Regarding the relationship between GE and AP, the results indicate both positive and negative linkages across different quantiles in Vietnam. Specifically, a strong positive relationship is observed between GE and AP at the 0.20–0.50 and 0.80–0.95 quantiles of AP, across low to high quantiles of GE. By contrast, the interplay turns negative at the 0.05–0.15 and 0.55–0.75 quantiles of AP, indicating that the impact of GE on AP is nonmonotonic and varies across the distribution. Importantly, the overall impact of GE on AP is negative, suggesting that increased government spending tends to reduce AP levels in Vietnam. This implies that GE, particularly when directed toward environmental initiatives, plays a vital role in mitigating pollution. Government expenditure on environmental protection encompasses a wide range of activities, including funding for pollution control, green infrastructure, renewable energy development, and regulatory enforcement. These results highlight the importance of strategic public spending in managing environmental degradation. Environmental funds should be targeted toward effective areas such as oil windfall management, green taxation mechanisms, and the promotion of sustainable policy frameworks. Consistent with the findings of Wu and Song²⁰ and Donkor et al.,⁹ the results suggest that GE influences environmental quality by shaping the demand for pollution reduction and sustainable practices in Vietnam. This further reinforces the critical role of fiscal policy in steering environmental outcomes in emerging economies.

We find a mixed effect of SC on AP in Vietnam. Specifically, at the low and middle quantiles (0.05–0.40) of AP, a negative relationship exists between SC and AP, suggesting that SC operations may help reduce pollution under certain conditions. In contrast, a positive association is observed at the higher quantiles of AP (0.45–0.95) across all quantiles of SC, indicating that higher levels of AP could be connected to intensified SC activities. This asymmetric relationship may stem from the dual nature of SC practices in Vietnam. On one hand, SCs have the potential to adopt cleaner production technologies, implement green logistics strategies, and incorporate environmentally conscious management practices. These innovations can contribute to pollution reduction. On the other hand, many SC activities—such as logistics, manufacturing, and transportation, still heavily rely on fossil fuels and outdated technologies, which contribute significantly to emissions. Therefore, the results suggest that while SCs can be part of the solution, they are also a contributor to environmental degradation in Vietnam. For sustainable development, it is essential that national SC systems transition toward eco-friendly models. This includes adopting waste-reducing practices, integrating renewable energy sources, and enhancing energy efficiency throughout the SC. These findings are consistent with prior research²⁵ that highlights the sophisticated and conditional influence of SCs on environmental outcomes.

QQGC results

Following this, the study employed the QQGC developed by Adebayo et al.⁴⁷ to examine how different levels of the selected independent variables influence AP in Vietnam. Figure 7 illustrates the QQGC results using a heatmap representation. Each cell corresponds to a specific combination of quantiles, where the horizontal axis presents the quantiles of the independent variable and the vertical axis shows the quantiles of AP. Color intensity reflects the magnitude of the test statistic: cooler colors (blue) indicate weak or insignificant causality, while warmer colors (yellow to red) indicate stronger causal effects. Statistical significance is denoted by asterisks within each cell, where *, ** and *** indicate significance at the 10%, 5% and 1% levels, respectively. Figure 7 presents the findings, which highlight both the direction and magnitude of causality across quantiles, thereby reinforcing the heterogeneous nature of these relationships. Following Adebayo et al.,⁴⁷ the analysis is conducted over a finite grid of quantiles {0.05, 0.10, 0.20, …, 0.90, 0.95} for both variables. The QQGC test is implemented using an optimal lag length of one, selected based on the Akaike Information Criterion, which is appropriate given the sample size and helps mitigate overparameterization.

For instance, EN demonstrates strong and significant causality across most quantiles from EN to AP, indicating that EN can reliably predict variations in AP. This is likely due to Vietnam's energy-intensive industrial activities and reliance on fossil fuels. Similarly, GDP shows consistent and robust causality across nearly all quantiles, particularly in the upper quantiles of AP, suggesting that higher levels of economic output, often tied to energy use and industrialization, have a substantial impact on pollution levels. In contrast, SC exhibits weaker and more sporadic causality across quantiles. This suggests that SC has limited predictive power over AP, potentially due to the heterogeneity in SC practices, uneven policy enforcement, or variations in infrastructure development across sectors.

For DI, the QQGC estimates are statistically significant, with moderate causality observed across low to middle quantiles of DI. This indicates that increased DI may improve air quality indirectly by enhancing data collection, environmental monitoring, and AP, thus enabling more targeted and effective interventions in AP. Likewise, GE also shows significant causality across multiple quantiles, with strong clusters appearing particularly in the higher quantiles of AP. This suggests that public spending, especially on environmental protection and infrastructure, can significantly influence AP levels, both directly and indirectly. The Vietnamese government's investment in public services and environmental initiatives appears to play a crucial role in mitigating pollution.

Overall, the observed heterogeneity in causality patterns across variables underscores that while economic activity influences AP, the intensity and direction of this effect depend on the specific economic structure and development stage of the country. Therefore, policy measures should be customized to the characteristics of each economic factor. It is essential for policymakers to consider the distributional dynamics of macroeconomic indicators when designing strategies aimed at improving environmental quality in Vietnam.

Robustness check

To validate the robustness of our empirical findings, we employ KRLS as an alternative nonparametric technique. KRLS is employed to augment the quantile-based analysis by providing a flexible, data-driven assessment of nonlinear relationships without imposing a predefined functional form. While QQR and QQGC focus on distribution-dependent heterogeneity across various quantiles, KRLS captures average marginal effects while allowing them to vary smoothly across the covariate space. This approach facilitates the identification of nonlinear response patterns that may remain obscured within quantile surfaces alone. Specifically, the KRLS approach is utilized to examine the effects of SC, DI, GDP, EN, and GE on AP across various quantiles. Robustness is established if the magnitude, direction, and distributional patterns of the estimated coefficients (β) obtained through KRLS are consistent with those derived from the QQR and QQGC models. This cross-methodological comparison enhances the credibility of the results by confirming that the observed relationships are not driven by model-specific assumptions or estimation techniques. The KRLS outcomes are reported in Table 4, providing further support for the presence of asymmetric and nonlinear interactions between the independent variables and AP in Vietnam.

Table 4.

Results of Kernel Regularized Least Squares for all parameters.

Parameters	Average	SE	Q25	Q50	Q75
DI	−0.001	0.000	−0.002	−0.001	0.001
EN	0.003	0.000	0.001	0.004	0.005
GDP	−0.052	0.011	−0.176	−0.068	0.110
GE	−0.018	0.003	−0.034	−0.017	−0.003
SC	0.035	0.006	−0.014	0.027	0.079

Note: AP: air pollution; DI: digitalization; EN: energy consumption; GE: government expenditure; SC: supply chain.

Table 4 reports the impact of SC, DI, GDP, EN, and GE on AP in Vietnam over the period 1996–2023, based on KRLS estimation. The average coefficient of GDP is −0.052, indicating a generally negative association with AP. However, an examination of the quantile-specific results reveals heterogeneity: while negative effects dominate at lower quantiles, a positive influence of 0.110 is observed at the 75th percentile (Q75). This suggests that the GDP–AP interplay is nonlinear and dependent on the level of pollution. Similarly, the other regressors, SC, DI, EN, and GE exhibit both positive and negative influences on AP across different quantiles, confirming the asymmetric and dynamic nature of their interactions with environmental quality. Notably, EN, GDP, and SC emerge as key drivers of AP, consistent with earlier findings. A comparison between the KRLS and QQR outcomes reveals strong consistency in both the direction and relative importance of key determinants of AP. Specifically, variables such as EN and SC show positive marginal effects in the KRLS framework, aligning with their significantly positive influence observed across middle and upper pollution quantiles in the QQR analysis. On the other hand, DI and GE display mitigating effects on AP in KRLS estimates, which corresponds to their negative or weakly positive effects at lower and medium quantiles in the QQR surfaces. Although slight variations in coefficient magnitudes are observed in the KRLS robustness analysis, the overall directional patterns remain consistent with those identified through the QQR and QQGC models. These results confirm the reliability and validity of the main empirical estimates and reinforce the conclusion that quantile-based approaches are well-suited for capturing the sophisticated, nonlinear environmental relationships in emerging economies such as Vietnam. The robustness of the results strengthens their relevance for both academic research and policy formulation.

Discussion

The quantile-based estimates of the selected variables on environmental degradation presented in this study provide a robust analytical framework that enhances a productive dialog between policymakers and scientists. This framework facilitates the development of data-driven strategies for the joint prevention and control of AP in Vietnam. The imperative for enhanced environmental monitoring, particularly concerning air quality, has become increasingly urgent amid global challenges such as climate change and localized industrial impacts.³² The current study addresses this need by investigating the asymmetric effects of SC, DI, GDP, EN, and GE on AP, thereby providing a detailed analysis to support the integration of advanced monitoring technologies with practical environmental policies and sustainable development initiatives.

In this study, the term structural constraints refers to persistent economy-wide characteristics that limit the effectiveness of pollution-mitigating mechanisms. In Vietnam, these constraints include heavy reliance on fossil-fuel-based energy generation, limited penetration of renewable energy, the dominance of energy-intensive manufacturing in export-oriented SCs, and uneven enforcement of environmental regulations. These factors are documented in national energy statistics and prior empirical studies and help explain why certain variables exhibit weaker or reversed environmental effects under high pollution regimes. Accordingly, the observed patterns reflect structural features of the economy rather than short-term policy or cyclical fluctuations.

Interestingly, the results reveal that the environmental impact of DI is heterogeneous and strongly dependent on pollution regimes. While DI exhibits a pollution-mitigating effect at low to middle quantiles of AP suggesting efficiency gains, improved monitoring, and cleaner production processes, this effect weakens and, in some cases, reverses at higher pollution quantiles. In highly polluted regimes, the expansion of digital infrastructure may increase energy demand, exacerbate rebound effects, or rely on carbon-intensive electricity sources, thereby offsetting potential environmental benefits. These findings imply that DI is not a guaranteed solution for reducing AP. Its effectiveness depends critically on complementary conditions such as clean energy availability, energy efficiency standards, and supportive environmental regulation. Accordingly, policies promoting digital transformation should be integrated with green energy transitions and emissions control measures to ensure that DI contributes to environmental improvement rather than unintentionally intensifying pollution under high-emission conditions. Overall, these findings suggest that DI promotes cleaner development pathways and highlight the importance of continued investment in digital infrastructure as a core component of Vietnam's environmental strategy. These results align with the findings of Qi et al.,¹² Wang et al.,²⁸ and Wu et al.,³⁰ who provide empirical evidence supporting the role of DI in strengthening the predictive accuracy of AP in Vietnam.

Economic growth and energy consumption reveal positive influences on AP, reflecting the classic environmental tradeoff inherent in Vietnam's development trajectory. Increased economic activities, including transportation, industrial production, and construction, drive higher energy demand, which is satisfied through fossil fuel consumption. This escalation in both GDP and EN results in significant AP, thereby contributing to deteriorating air quality. While GDP plays a vital role in improving living standards and reducing poverty, it often comes at the cost of environmental degradation. This underscores the urgent need for Vietnam to transition toward cleaner energy sources, enhance energy efficiency, and implement stricter environmental regulations. These findings align with prior research.^5,6,16

Our findings indicate that SC has a positive impact on AP in Vietnam, suggesting that activities related to the production, transportation, and distribution of goods contribute substantially to environmental degradation. Export-oriented and manufacturing sectors rely heavily on fossil fuel-based transportation and energy-intensive processes, which exacerbate AP. In addition, the growing demand for efficient logistics is likely to intensify pollution, especially in industrial and urban areas where freight movement is concentrated. These results highlight the urgent need for Vietnam to green its SCs by adopting cleaner production methods and investing in sustainable logistics infrastructure. Our conclusions are consistent with the findings of Peng et al.,²⁶ Zhao et al.,¹³ and Liu et al.⁴⁵

The results reveal that GE has both negative and positive effects on AP in Vietnam, reflecting the dual nature of public spending. On the one hand, investments in infrastructure, industrial development, and GDP can result in increased EN and construction activities, thereby contributing to higher emissions and environmental degradation. On the other hand, GE can significantly decrease AP by funding environmental protection programs, promoting clean energy, developing green infrastructure, supporting public transportation, and enforcing stricter environmental regulations. The influence of GE on AP is not unambiguously beneficial and depends critically on the composition and allocation of public spending. While our results indicate that government expenditure contributes to pollution mitigation at certain quantiles, suggesting the effectiveness of environmental regulation, public investment, and institutional support, this effect weakens or becomes insignificant in other regimes. This finding is consistent with the mixed evidence in the literature, which shows that growth-oriented or infrastructure-focused public spending may increase emissions, whereas environmentally targeted expenditure can improve air quality. These results are aligned with those reported in previous studies.^9,18,23

Conclusion

Commodity production and logistics remain major sources of AP, posing substantial environmental challenges for emerging economies such as Vietnam. This study examines the asymmetric and distribution-dependent effects of SC, DI, GDP, EN, and GE on AP over the period 1996–2023 using a comprehensive quantile-based framework. By employing QQR, QQGC, and KRLS, the analysis moves beyond average-effect models and provides nuanced insights into how these determinants operate across different pollution regimes.

The findings reveal clear heterogeneity in the determinants of AP. At lower pollution quantiles, GDP, EN, and SC tend to have weaker or even negative effects on AP, suggesting that during relatively low-emission periods, economic activity and logistics expansion do not necessarily intensify environmental degradation. However, at middle and upper pollution quantiles, these variables display strong and increasingly positive effects, indicating that under higher pollution and economic intensity, growth-related and supply-chain-driven activities substantially exacerbate AP. By contrast, DI and GE exhibit mixed and regime-dependent effects, mitigating pollution at low to moderate quantiles but losing effectiveness or reversing sign at higher pollution levels.

The QQGC results confirm that these variables possess significant predictive power for AP across the distribution, while the KRLS estimates corroborate the dominant nonlinear patterns identified by the quantile-based analysis. Overall, the results underscore that the environmental impact of economic, technological, and policy factors in Vietnam is fundamentally state-dependent. Consequently, effective environmental strategies require differentiated and quantile-specific policy interventions rather than uniform approaches, particularly emphasizing energy transition and SC restructuring under high pollution regimes.

The quantile-based analysis implies that policy interventions should be differentiated across pollution regimes rather than uniformly applied. At low to moderate pollution quantiles, DI and GE exhibit pollution-mitigating effects, suggesting that policies promoting digital transformation, smart logistics, and institutional capacity building are likely to be effective when environmental pressure is relatively contained. In contrast, at higher pollution quantiles, the effectiveness of DI weakens and, in some cases, reverses, while EN and SC have strong amplification effects. This indicates that under high-emission regimes, priority should be given to stricter energy regulations, accelerated renewable energy deployment, and the restructuring of carbon-intensive SC activities rather than relying solely on efficiency-enhancing digital investments. Similarly, the heterogeneous effects of GE suggest that fiscal policies should be targeted toward environmental protection and clean infrastructure, particularly in high-pollution contexts. Overall, the results highlight that environmental policy effectiveness is state-dependent, and quantile-specific strategies are essential for achieving meaningful pollution reduction.

Evidence from developing countries often reveals a tension between economic growth and environmental protection, suggesting the need for Vietnam to find a balanced and optimal policy approach. The results indicate an asymmetric effect of DI, SC, and macroeconomic factors on AP in Vietnam. To address these challenges, a targeted policy framework is essential to mitigate the environmental impact of these drivers.

Encouraging formalization can help enforce environmental standards, promote the adoption of cleaner technologies, and reduce emissions. Policymakers should facilitate the transition from informal to formal business operations through measures such as tax incentives, production subsidies, and the reduction of bureaucratic obstacles. The integration of digital tools for monitoring and supporting small businesses can further enhance compliance with environmental regulations.

Further, the results call for targeted policy interventions to promote sustainability in sectors directly affecting air quality, particularly economic development, EN, and SC operations. Ensuring access to high-quality, clean energy can accelerate the adoption of green technologies and promote more efficient use of natural resources. Technology plays a vital role in driving these improvements. Enhancing SC efficiency can further reduce avoidable emissions and energy waste. Policymakers should also introduce a combination of regulatory frameworks and incentive mechanisms to encourage the transition to cleaner and more environmentally sustainable technologies across industries.

While this study provides straightforward insights into how SC, DI, GDP, EN, and GE influence AP in Vietnam, it is not without limitations. The analysis is based on a limited set of macroeconomic indicators; future research could extend this work by incorporating a broader and more diverse range of variables. Additionally, by focusing exclusively on Vietnam, the study does not capture potential cross-country variations. Future studies should consider comparative analyses across multiple developing countries and examine these dynamics over time to understand how contextual factors and policy environments shape environmental outcomes.

Given Vietnam's significant economic and policy transitions over the period 1996–2023, potential structural breaks could affect the stability of estimated relationships. Although this study does not explicitly model structural break points, the quantile-based framework partially mitigates this concern by allowing interactions to vary across the conditional distribution rather than imposing constant parameters over time. By capturing heterogeneous and nonlinear dynamics across pollution regimes, the approach reduces sensitivity to regime shifts that would arise from gradual structural changes. Nevertheless, abrupt policy-induced breaks cannot be entirely ruled out, and future research could incorporate formal structural tests or regime-switching quantile models to further assess temporal stability.

In addition, as with most macro-level environmental studies, potential endogeneity might arise from bidirectional associations among GDP, EN, and AP. While the quantile-based models employed in this study allow for heterogeneous and nonlinear relationships across the conditional distribution, they do not fully eliminate endogeneity concerns. However, the combined use of QQR and QQGC helps mitigate simultaneity by examining distribution-dependent predictive dynamics rather than contemporaneous correlations. Moreover, the consistency of results across QQR, QQGC, and KRLS provides additional confidence that the identified patterns are not driven by a single estimation approach. However, the findings should be interpreted as conditional associations and predictive relationships rather than strict causal effects, and future research could extend this analysis using instrumental-variable or structural quantile methods.

In this study, the term robustness refers to the consistency of empirical patterns across complementary estimation techniques rather than to extensive sensitivity analyses involving alternative bandwidths, kernel functions, or quantile grid specifications. Specifically, robustness is assessed by comparing the dominant signs, magnitudes, and regime-dependent patterns obtained from QQR, QQGC, and KRLS. While alternative kernel choices or bandwidth selections may affect local smoothness, the focus of this paper is on identifying broad distributional dynamics rather than fine-grained sensitivity to tuning parameters. Future research could extend the analysis by formally testing sensitivity to alternative bandwidths and kernel specifications.

Footnotes

Acknowledgments

This research is funded by University of Finance-Marketing, Vietnam.

ORCID iDs

Ngo Thai Hung

Hoang Thi Xuan

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research is funded by University of Finance-Marketing, Vietnam.

Declaration of conflicting interests

The author declares that they have no competing interests.

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