An Evaluation of Port Environmental Efficiency Considering Heterogeneous Abatement Capacities: Integrating Weak Disposability into the Epsilon-Based Measure Model

Abstract

As pivotal hubs in maritime logistics networks, ports bear a growing responsibility to harmonize economic activities with environmental stewardship. Evaluating and enhancing port environmental efficiency (PEE) is therefore imperative for maritime decarbonization and sustainability. However, conventional approaches often assume homogeneous abatement capacities across heterogeneous ports, which may distort evaluation results. To address this flaw, we develop a modified EBM-Undesirable model embedding weak disposability and non-uniform abatement factors, explicitly accounting for heterogeneity the in port’s abatement capabilities. Drawing on panel data from China’s major coastal ports during 2013–2022, this study further employs the Global Malmquist Index and Dagum Gini coefficient to investigate dynamic characteristics and regional disparities in PEE. Key findings reveal: (1) PEE exhibits a modest yet volatile upward trend, accompanied by pronounced inter-port divergence; (2) Total factor productivity (TFP) demonstrates sustained improvement attributable to technical efficiency advancements, yet reveals untapped potential in technological level; (3) Substantial spatial heterogeneity persists, dominated by interregional differences, though overall inequality is gradually converging. Given the observed regional disparities and technological potential, policy suggestions are proposed to advance port decarbonization, regional coordination, and maritime sustainability.

1. Introduction

Maritime transport, which carries over 80% of global trade by volume, has experienced rapid expansion in recent decades [1], thereby intensifying global energy demand and contributing to the continued rise in carbon emissions [2]. Currently, maritime transport emits around 1056 million tons of CO₂ emissions annually, contributing to more than 3% of global anthropogenic CO₂ emissions, a share that continues to rise [3]. Emissions from the shipping industry are predominantly attributed to vessels and ports. Among these, ports serve as pivotal hubs and sources of carbon emissions and play an instrumental role in the global management and control of CO₂ emissions [4]. It is estimated that ports contribute about 2% of total global CO₂ emissions, with levels rising by 5.6% to 740 million tons between 2012 and 2018. If left unchecked, projections under business-as-usual scenarios suggest a further rise of up to 50% by 2050 [5]. In this context, ports are under increasing pressure to reduce emissions and advance sustainable transition. An exclusive concentration on carbon emission reduction may be inappropriate, as overly stringent decarbonization measures could impose constraints on port productivity and hinder economic growth. Enhancing port environmental efficiency (PEE), defined as the capability of ports to maximize desirable outputs while minimizing undesirable emissions under given inputs, emerges as an effective approach to reconcile shipping-related carbon emissions and sustained economic development [6]. Scientifically evaluating port environmental performance is therefore essential to support informed policy-making and promote long-term maritime sustainability.

Given the significance of PEE, scholars have engaged in extensive discussions on its measurement. Currently, the measurement and evaluation methods for port efficiency primarily encompass Stochastic Frontier Analysis (SFA) [7] and Data Envelopment Analysis (DEA) [8]. Among these, DEA stands out as a nonparametric method, requiring no predetermined parameters, which endows it with strong applicability. Hence, it has emerged as the most commonly used method for efficiency evaluation at present [9]. Initially, most studies employed conventional models like CCR and BCC to calculate port efficiency without considering undesirable outputs, particularly CO₂ emissions [10,11]. Amid growing environmental concerns, scholars have increasingly integrated undesirable outputs into the evaluation framework. A variety of DEA models, such as the directional distance function (DDF) [12], network DEA (NDEA) [13], slack-based measure DEA (SBM-DEA) [14], and range adjusted measure DEA (RAM-DEA) [15], have been widely applied to assess PEE.

While incorporating undesirable outputs has enhanced the environmental relevance of port efficiency assessments, most existing studies largely depend on either radial or non-radial DEA models, both of which exhibit inherent limitations. Radial DEA models assume proportional adjustments in inputs and outputs while overlooking non-radial slacks, which may not hold in certain contexts [16]. In contrast, non-radial DEA models account for slack but may sacrifice original proportionality, potentially compromising efficiency estimates [17]. Therefore, a composite evaluation framework compiling the strengths of both approaches is required, enabling a more reasonable and accurate evaluation of port efficiency.

In addition, the treatment of undesirable outputs in many studies remains grounded in the strong disposability assumption. Under this assumption, undesirable outputs, such as CO₂ emissions, are treated as freely reducible without compromising desirable outputs. However, this is rarely the case in actual production settings, where emission reductions typically involve trade-offs, such as increased costs or reduced output [18]. To address this limitation, the recent literature has increasingly adopted the weak disposability assumption, which offers a more realistic representation of environmental constraints by recognizing that pollution abatement is not costless and often requires a sacrifice in economic performance.

Moreover, PEE is often calculated under the assumption of a homogeneous abatement factor across all ports, implicitly overlooking the heterogeneous carbon-reduction characteristics that exist in practice. Substantial disparities exist among ports in terms of operational scale, technological endowment, and environmental governance, which often lead to heterogeneous abatement capabilities. Consequently, disregarding this heterogeneity by applying a uniform abatement factor may lead to systematically biased efficiency scores [19].

To fill these aforementioned research gaps, this study proposes a novel evaluation framework to comprehensively evaluate port environmental performance. First, we employ an epsilon-based measure model with undesirable outputs (EBM-Undesirable) that combines radial and non-radial features, allowing for a more precise evaluation of PEE. Building on this foundation, the EBM-Undesirable model is further extended by integrating the weak disposability assumption and non-uniform abatement factors. This approach allows port operators to differentially adjust their production activity levels to curtail undesirable outputs, explicitly reflecting the heterogeneity in abatement capacity. On this basis, the dynamic characteristics and regional disparities of PEE are examined via the Global Malmquist index and the Dagum Gini coefficient. Drawing from this, the study answer encompasses the following: How does the overall trend in PEE unfold? What is the predominant driver affecting the TFP of ports? How has the spatial heterogeneity of PEE evolved?

This article’s marginal contributions include: First, an EBM-Undesirable model was developed by incorporating weak disposability of undesired outputs to facilitate a precise evaluation of PEE. Second, heterogeneous carbon abatement capabilities across ports were accounted for in the efficiency measures, preventing the overestimation that can occur with a uniform abatement factor. Third, the Global Malmquist index and Gini coefficient of PEE are deeply decomposed, enabling the accurate identification of underlying drivers and the sources of regional disparity, underpinning targeted port development strategies.

The paper unfolds as follows. Section 2 presents the literature review. Section 3 proposes the methodology and data descriptions. Section 4 expounds the results and discussion. Section 5 summarizes the conclusions and proffers several recommendations.

2. Literature Review

2.1. DEA Application in Port Efficiency Evaluation

Port efficiency refers to the effective utilization of inputs to generate maximum possible outputs, or conversely, to achieve target outputs with minimal resource consumption [20]. The DEA approach is extensively utilized for quantifying port efficiency, with an emphasis on economic efficiency, environmental efficiency, and other applications [21].

In terms of economic efficiency evaluation, Tovar and Wall [22] implemented a DEA-Malmquist using meta-frontier analysis to calculate the efficiency, uncovering that port complexity and its scale are major determinants. Liu et al. [23] undertook benchmarking by assessing port efficiency of six typical Chinese Pilot Free Trade Zones (PFTZs), which revealed that the establishment of PFTZs positively influenced port efficiency. Agüero-Tobar et al. [24] utilized the DEA method for evaluating port operating performance in Chile and proposed a way for better understanding the economic effects of efficient operations. Moya et al. [25] employed the DEA meta-frontier approach to quantify port technical efficiency by adding an indicator of berth duration. Furthermore, Zhu et al. [14] explored the geographic disparities and changing tendency of inland waterway transportation efficiency. Kong et al. [26] established an integrated framework incorporating economic, environmental, and social elements for benchmarking port sustainable efficiency.

In terms of environmental efficiency evaluation, Chin and Low [27] incorporated environmental externalities into their port performance assessment framework and examined Asian port efficiency. In addition, Li et al. [28] and Wang et al. [29] respectively carried out studies on port environmental efficiency from the viewpoints of CO₂ and PM emissions. Castellano et al. [30] benchmarked the environmental efficiency of Italian ports, demonstrating that considering negative externalities and green policies is of utmost importance for assessing port competitiveness. Wang et al. [31] discovered that the green port efficiency is generally poor and unevenly developed, with most ports displaying a fluctuating growing trend within five years. In addition, Sun and Zhao [32] assessed the efficiency of China’s port-region (PR) system, demonstrating that overall efficiency is rising, with management level being a crucial impetus affecting efficiency. Lin et al. [33] evaluated the port environmental efficiency of the Yangtze River Delta Pilot Free Trade Zone (YRD PFTZ) from both static and dynamic perspectives and found that these ports generally exhibit a high level of environmental efficiency.

Regarding the evaluation of other application fields in ports, a relatively limited number of existing studies are found. In this regard, Nguyen et al. [34] investigated market concentration in Southeast Asian container ports and observed an association with operational efficiency. Kong and Liu [35] gauged port-cities’ sustainability by combining internal and external dimensions, emphasizing the implication of port-city interactions on sustainability. Additionally, Zhang et al. [36] undertook benchmarking the rail-water intermodal transport system efficiency. Jiang et al. [37] compared the efficiency and dynamic variations in the hinterland transportation system, concluding that road-rail transport shows exemplary efficiency. Zhang et al. [38] examined the low-carbon performance of the “ship-port” system and found that port system efficiency exhibited a sustained upward trend, whereas ship system efficiency experienced a volatile decline.

2.2. DEA Based on Weak Disposability (WD) Assumption

The conventional DEA model typically assumes strong disposability (SD) for undesired outputs in the production process, as posited by Färe et al. [39]. Under this axiom, undesired outputs, such as pollution, can be reduced independently and without cost, which neglects the potential impact of diminishing undesired outputs on desired outputs. However, this assumption may contradict economic rationality, especially when dealing with carbon emissions and other pollutants. In response to this issue, researchers progressively took a more realistic approach to managing undesirable outputs. Färe and Grosskopf [40] presented the concept of WD, which proposed that undesired outputs should be reduced in coordination with desired outputs rather than being disposed of independently and without cost. They argue that reducing undesirable outputs usually entails sacrificing some quantity of desired outputs or adding extra inputs. The traditional SD approach may cause estimation biases of production efficiency.

Early research on WD predominantly adopted a single abatement factor to reduce undesired outputs. While this approach is straightforward and intuitive, it disregards the heterogeneity across different firms in mitigating undesired outputs. Kuosmanen [41] put forward a method of multiple abatement factors that allows for a more accurate simulation of WD within non-parametric production models. Specifically, Kuosmanen’s approach permits firms to utilize non-uniform abatement factors tailored to their specific characteristics, thereby decreasing undesired outputs more effectively. This approach offers a more realistic reflection of production and averts the problem of efficiency overestimation caused by adopting a uniform abatement factor.

In practical applications, Chang et al. [42] modified the constraint of the SBM model such that undesirable outputs increase proportionally with improvements in output slack, thus aligning with the WD assumption. They applied this adjusted model to assess global airlines’ economic efficiency. Similarly, Jo and Chang [18] and Taleb et al. [43] benchmarked the port environmental efficiency by utilizing the SBM-DEA model with WD. It is worth noting that our previous study [44] also adopted the SBM-DEA framework with the weak disposability assumption to evaluate port environmental efficiency. Nevertheless, both studies relied on a uniform abatement factor to tackle the issue of WD within the DEA model framework. In contrast, Yu and See [45] utilized non-uniform abatement factors to compute the efficiency of airlines in diminishing undesired outputs such as CO₂ emissions, thereby obtaining unbiased efficiency estimates for airlines. However, there are scarce studies that have benchmarked the port’s environmental efficiency considering WD with the non-uniform abatement factor.

A review of the existing literature (see

Table 1. Summary of literature evaluating port efficiency with DEA model.

	Research Object	Method	Type	Inputs	Outputs
[10]	19 container ports	CCR, BCC	R	Terminal area, Quay length, Quay crane, Yard equipment, Maximum draft	Throughput
[11]	Kaohsiung Port	CCR, BCC	R	Gantry crane capacity, Gantry crane number, Berth length, Container yard area, Fixed costs, Variable costs	Total loading and unloading capacity
[12]	26 Spanish ports	DDF	R	Labor, Capital, Intermediate	Ships, Cargo traffic, Passenger traffic, CO2 emissions
[13]	13 global ports	Dynamic NDEA	NR	Fleet capacity, Expenses, Employees	Lifting, Revenue
[14]	11 Chinese ports	SBM	NR	Employees, Motor ship, Urban fixed asset investment	NOx emission, Passenger volume, Cargo volume
[15]	10 Chinese ports	RAM	NR	Staff members, Annual cash investment, Production berths	Container throughput, Cargo throughput, Main business income, CO2 emissions
[22]	26 Spanish ports	DEA-Malmquist	R	Labor, Intermediate consumption expenditures, Capital assets, Deposit surface area	Liquid bulk cargo, Solid bulk cargo, Container cargo, General non-container cargo, Passengers
[23]	6 Chinese ports	Super-SBM	NR	Berth number, Terminal length, Net asset, Cost of goods sold, Employees	Cargo throughput, Container throughput, Sales revenue, SO2 emission, NOₓ emission
[24]	12 Chilean ports	CCR, BCC	R	Maximum draft, Quay length, Berth number	TEUs transferred, Number of vessels
[25]	19 Mediterranean ports	CCR	R	Berth length, Yard area, Quay cranes number	Number of TEU handled per hour
[27]	13 East Asian ports	SBM	NR	The frequency of shipping services, Bilateral trade flows	Container capacity flows, Gaseous emissions
[28]	16 Chinese ports	SBM	NR	Labor, Fixed assets	Container throughput, Cargo throughput, CO2 emission
[29]	11 Chinese ports	DDF	R	Terminal length, Berth quantity, Labor, Total assets	Container throughput, PM emission
[30]	24 Italian ports	CCR, BCC	R	Investments, Terminal area, Employees, Green Port Efforts (GPE)	Solid bulk, Liquid bulk, Containers, Environmental Quality Index (EQI)
[31]	18 Chinese ports	Cross-efficiency model	NR	Berth number, Terminal length, Employees, Total fixed assets	Cargo throughput, NOx emissions, SOx emissions, Solid waste containers
[32]	22 Chinese ports	DDF	NR	Berth number, Terminal length, Employees, Barges	Cargo throughput
[36]	14 Chinese ports	NDEA	NR	Length of railways, Railway labor, Berth quantity, Port labor	Railway-port freight volumes, Cargo throughput, CO2 emission

Note: R = radial, NR = non-radial.

) shows that most studies employed either radial or non-radial models to compute port efficiency. These models are limited in their ability to simultaneously integrate radial and non-radial dimensions, potentially leading to deviations in the evaluation results. Hence, emerging radial and non-radial merits are essential for constructing an integrated framework to assess port performance. Additionally, many prior studies have disregarded the implications of the disposability assumption on port efficiency evaluation, merely considering SD or WD with the unified abatement factor, ignoring the distinct abatement technology characteristics across disparate ports. This oversight typically gives rise to an overestimation of efficiency. Consequently, there is a clear need for further research that incorporates WD with a non-uniform abatement factor, permitting port operators to modulate their production activity levels in varying proportions to abate undesired outputs. This approach would enable a more refined and accurate evaluation of PEE.

3. Methodology and Data Descriptions

3.1. An EBM Model with Non-Uniform Abatement Factors

Conventional DEA models are typically either input-oriented or output-oriented. In these models, decision-makers can improve the efficiency of DMUs only by reducing inputs or increasing outputs but cannot optimize both inputs and outputs simultaneously. Furthermore, most of these models are radial DEA models, implying that decision-makers can only reduce inputs or increase outputs in equal proportions. Consequently, the traditional radial DEA approach struggles in tackling the slackness of inputs and outputs, together with overlooking undesired outputs [46]. To overcome these limitations, Tone [47] introduced the SBM model, incorporating slack variables within the objective function. This model helps avoid the deviation caused by differences in radial and oriented models. Despite this refinement, the efficiency values are underestimated due to the objective function of the SBM model, which aims to maximize input-output inefficiencies [17]. Subsequently, Tone and Tsutsui [48] proposed the EBM model, which is distinguished by its ability to merge radial proportions and non-radial slacks, thereby facilitating a more precise efficiency evaluation.

However, the basic EBM model disregards negative effects generated during the production process, making it challenging to accurately reflect the true efficiency of decision-making units (DMUs). Therefore, this study considers undesirable outputs incorporating WD. In practical applications, different DMUs may operate under varying returns to scale. To reflect this, this study adopts the variable returns to scale (VRS) assumption, which allows for the possibility that the proportionate change in outputs may not be constant relative to the change in inputs [49]. Under VRS assumption, an EBM-Undesirable model imposing weak disposability (EBM-WD model) is developed, applying non-uniform abatement factors across disparate ports. Suppose there are $n$ DMUs, each input and output dimensions represented as $x\in R^m,y\in R^s,b\in R^q$, and corresponding matrices are: $X=[x_1,\dots ,x_n]\in R^{m\times n}$, $Y=[y_1,\dots ,y_n]\in R^{s\times n}$, and $B=[b_1,\dots ,b_n]\in R^{q\times n}$, where $X>0$, $Y>0$ and $B>0$. The model is formulated as follows:

$$\begin{array}{l}min\rho ={\displaystyle \frac{\theta -{\epsilon }_x{\displaystyle {\sum }_{i=1}^m\frac{w_i^{-}{s}_i^{-}}{x_{i0}}}}{\phi +{\epsilon }_y\left({\displaystyle {\sum }_{r=1}^s\frac{w_r^{g+}{s}_r^{g+}}{y_{ro}}+{\displaystyle {\sum }_{p=1}^q\frac{w_p^{b-}{s}_p^{b-}}{b_{po}}}}\right)}}\\ s.t.{\displaystyle \sum _{j=1}^n{X}_j}{z}_j+s^{-}=\theta x_0\\ {\displaystyle \sum _{j=1}^n{Y}_j}{z}_j{\delta }^j-s^{g+}=\phi y_0\\ {\displaystyle \sum _{j=1}^n{B}_j}{z}_j{\delta }^j+s^{b-}=\phi b_0\\ {\displaystyle \sum _{j=1}^n{z}_j}=1\\ \theta \le 1,\phi \ge 1\\ s^{-}\ge 0,s^{g+}\ge 0,s^{b-}\ge 0,z_j\ge 0,0\le {\delta }^j\le 1,j=1,2,\dots ,n\end{array}$$

(1)

where $z$ represents intensity variable; ${\rho }^{*}$ is the efficiency value; ${\delta }^j$ stands for the abatement factor, and ${\delta }^1\ne {\delta }^2\ne \dots \ne {\delta }^n$ enables each $DM{U}_j$ to be reduced by a distinct abatement factor; the constraints in model (1) are non-linear, and the intensity variables could be separated into two sections: $z_j={\lambda }_j+{\mu }_j$, that is, ${\mu }_j=(1-{\delta }^j)z_j$, ${\lambda }_j={\delta }^j{z}_j\dots$, the non-linear equations in model (1) can be converted into linear equations. By this setting, model (1) can be expressed as:

$$\begin{array}{l}min\rho ={\displaystyle \frac{\theta -{\epsilon }_x{\displaystyle {\sum }_{i=1}^m\frac{w_i^{-}{s}_i^{-}}{x_{i0}}}}{\phi +{\epsilon }_y\left({\displaystyle {\sum }_{r=1}^s\frac{w_r^{g+}{s}_r^{g+}}{y_{ro}}+{\displaystyle {\sum }_{p=1}^q\frac{w_p^{b-}{s}_p^{b-}}{b_{po}}}}\right)}}\\ s.t.{\displaystyle \sum _{j=1}^n{X}_j}({\lambda }_j+{\mu }_j)+s^{-}=\theta x_0\\ {\displaystyle \sum _{j=1}^n{Y}_j}{\lambda }_j-s^{g+}=\phi y_0\\ {\displaystyle \sum _{j=1}^n{B}_j}{\lambda }_j+s^{b-}=\phi b_0\\ {\displaystyle \sum _{j=1}^n({\lambda }_j+{\mu }_j)}=1\\ \theta \le 1,\phi \ge 1\\ s^{-}\ge 0,s^{g+}\ge 0,s^{b-}\ge 0,{\lambda }_j\ge 0,{\mu }_j\ge 0,j=1,2,\dots ,n\end{array}$$

(2)

Here, ${\mu }_j$ signifies the segment of $DM{U}_j$’s output that is mitigated through a decrease in activity level, while ${\lambda }_j$ corresponds to the segment of $DM{U}_j$’s output that remains active. $s^{-},s^{g+},s^{b-}$ respectively denote the slack of inputs, desirable outputs and undesired outputs. ${w_i}^{-},{w_r}^{g+},{w_p}^{b-}$ respectively depict the weights of inputs, desirable outputs and undesired outputs, and meet ${\displaystyle \sum _{i=1}^m{w}_i^{-}}=1$ and ${\displaystyle \sum _{r=1}^s{w}_g^{g+}+}{\displaystyle \sum _{p=1}^q{w}_p^{b-}}=1$. ${\epsilon }_x$ and ${\epsilon }_y$ are crucial parameters that signify the non-radial component’s significance in efficiency assessment, with feasible domain of [0, 1]. To prevent measurement inaccuracies, constraints on $\theta$ and $\phi$ are imposed, that is $\theta \le 1$, $\phi \ge 1$. Parameters $\epsilon$ and $w$ need to be determined beforehand. The projection values of multiple input and output metrics are derived via the SBM model with undesirable outputs, written as ${\widehat{x}}_{ik}=x_{ik}-s_i^{-},{\widehat{y}}_{rk}^g=y_{rk}^g+s_r^{g+},{\widehat{y}}_{pk}^b=y_{pk}^b-s_p^{b-}$, and the projection value matrix is built.

Taking input indicators as example and referring the treatment methods of [48,50], the steps for obtaining parameters ${\epsilon }_x$ and $w_i^{-}$ are outlined below:

Step 1: Projection values and substitutability interpretation.

The projection values of each input variable are obtained through the SBM model with undesirable outputs, denoted as ${\widehat{x}}_k(k=1,\dots ,m)$. The correlation between the projection values of two inputs ${\widehat{x}}_i$ and ${\widehat{x}}_j$ reflects their proportional relationship and indicates the degree of substitutability in the production process. A strong positive linear correlation suggests weak substitutability, implying a predominantly radial adjustment pattern; thus, $\epsilon$ should be close to 0. In contrast, a strong negative correlation implies strong substitutability and the adoption of non-radial adjustment, where $\epsilon$ should approach 1.

Step 2: Construct the diversity matrix R.

The diversity matrix $R={[R({\widehat{x}}_i,{\widehat{x}}_j)]}_{m\times m}$ reflects the pairwise linear relationships among the projected values of input indicators. For any two inputs ${\widehat{x}}_i$ and ${\widehat{x}}_j$, the corresponding element $R({\widehat{x}}_i,{\widehat{x}}_j)$ is computed as the Pearson correlation coefficient between their projection vectors. See Equation (3) for details.

$$R({\widehat{x}}_i,{\widehat{x}}_j)={\displaystyle \frac{{\displaystyle \sum _{k=1}^n({\widehat{x}}_{ik}-{\overline{x}}_i)({\widehat{x}}_{jk}-{\overline{x}}_j)}}{\sqrt{{\displaystyle \sum _{k=1}^n{({\widehat{x}}_{ik}-{\overline{x}}_i)}^2}}\sqrt{{\displaystyle \sum _{k=1}^n{({\widehat{x}}_{jk}-{\overline{x}}_j)}^2}}}}$$

(3)

where ${\widehat{x}}_i$ and ${\widehat{x}}_j$ represent the sequences of projection values for $i$ and $j$ for the $\mathit{k}$-th DMU, and ${\overline{x}}_i$, ${\overline{x}}_j$ are their respective means.

This definition ensures that R is a symmetric matrix with diagonal elements equal to 1, and effectively captures the similarity or substitutability among input indicators.

Step 3: Establish the affinity matrix S.

The new affinity matrix $S={[S({\widehat{x}}_i,{\widehat{x}}_j)]}_{m\times m}$ is constructed from the diversity matrix R via the specified formula $S({\widehat{x}}_i,{\widehat{x}}_j)=0.5+0.5R({\widehat{x}}_i,{\widehat{x}}_j)$, which allows it to quantify both the strength and direction of correlation among the indicators.

Step 4: Compute the parameters ${\epsilon }_x$ and $w_i^{-}$ from the affinity matrix S. The parameters ${\epsilon }_x$ is obtained as:

$${\epsilon }_x=\left\{\begin{array}{lll}{\displaystyle \frac{m-{\rho }_x}{m-1}}& ,& m>1\\ 0& ,& m=1\end{array}\right.$$

(4)

And the weights are normalized as:

$$w_i^{-}={\displaystyle \frac{w_{ix}}{{\displaystyle \sum _{i=1}^m{w}_{ix}}}}$$

(5)

where ${\rho }_x$ is the largest eigenvalue of affinity matrix S, $W_x=(w_{1x},w_{2x},\dots ,w_{mx})$ represents its corresponding eigenvector.

The methods for calculating parameters ${\epsilon }_y$ and $w_r^{g+},w_p^{b-}$ are consistent with the above steps.

3.2. The Global Malmquist Index

The DEA model typically provides a static analysis based on a time cross-section. When the evaluation unit involves panel data with multiple consecutive time points, the Malmquist Productivity Index (M index) is employed for dynamic analysis [51]. Nevertheless, the conventional M index can only compare productivity changes between adjacent periods and cannot facilitate intertemporal comparisons. Furthermore, it is prone to issues of infeasibility under VRS. To address these shortcomings, Pastor and Lovell [52] proposed the Global Malmquist Productivity Index (GM index). This index uses a joint frontier constructed by all periods, thus overcoming the defects of the traditional M index and possessing the advantage of intertemporal comparability. To incorporate undesirable outputs into the study, the GM index is further extended and utilized to calculate the TFP of the DMUs. Assume the study period is T; the production possibility set (PPS) in period t is expressed as:

$$P^t=\left\{\left(x^t,y^t,b^t\right):x^{t}canproduce(y^t,b^t)\right\}$$

(6)

The global PPS is constructed as the union of all period-specific PPSs and is formally defined as follows: $P^G=P^1\cup P^2\cup \dots \cup P^T$.

The GM index via formula outlined below:

$$G{M}_{t,t+1}(x_{t+1},y_{t+1},b_{t+1},x_t,y_t,b_t)={\displaystyle \frac{D^G(x_{t+1},y_{t+1},b_{t+1})}{D^G(x_t,y_t,b_t)}}$$

(7)

where $(x_t,y_t,b_t)$, $(x_{t+1},y_{\mathrm{t}+1},b_{t+1})$ are the input and output direction vectors for period $t$ and period $t+1$, respectively.$D^G(x,y,b)$ represents the global hybrid distance functions, while $D^t(x,y,b),D^{t+1}(x,y,b)$ depict the distance functions in two periods. A value of $GM>1$ suggests TFP growth over time; whereas $GM<1$ indicates a degradation.

Additionally, this study decomposes the GM index into two components: GM efficiency change (GMEC) and GM technological change (GMTC).

$$\begin{array}{l}G{M}_{t,t+1}(x_{t+1},y_{t+1},b_{t+1},x_t,y_t,b_t)\\ ={\displaystyle \frac{D^G(x_{t+1},y_{t+1},b_{t+1})}{D^G(x_t,y_t,b_t)}}\\ ={\displaystyle \frac{D^t(x_{t+1},y_{t+1},b_{t+1})}{D^t(x_t,y_t,b_t)}}\times \left[{\displaystyle \frac{D^G(x_{t+1},y_{t+1},b_{t+1})}{D^{t+1}(x_{t+1},y_{t+1},b_{t+1})}}\times {\displaystyle \frac{D^t(x_t,y_t,b_t)}{D^G(x_t,y_t,b_t)}}\right]\\ =GME{C}_{t,t+1}\times GMT{C}_{t,t+1}\end{array}$$

(8)

where $GME{C}_{t,t+1}$ and $GMT{C}_{t,t+1}$ represent changes in technical efficiency and technological progress between period $t$ and period $t+1$. Specifically, when $GMEC>1$, it suggests technical efficiency catch-up, and vice versa; while $GMTC<1$ demonstrates technological innovation, and vice versa.

3.3. Dagum Gini Coefficient

In examining regional disparities, many approaches such as the traditional Gini coefficient, variation coefficient, and Theil index, while possessing certain explanatory capabilities, have limitations in addressing the intersection and overlap of data distributions. To overcome the above drawbacks, Dagum [53] proposed the Dagum Gini coefficient, which divides the entire sample into distinct subgroups, and, respectively, examines the disparities within and between these subgroups, thereby providing a clearer understanding of the origins of these discrepancies. Furthermore, it adeptly resolves the issues of data intersection and overlap, as well as precisely revealing the relative difference features among different regions [54].

This study utilizes the Dagum Gini coefficient to explore PEE spatial disparities and sources, calculated as follows:

$$G={\displaystyle \frac{{\displaystyle \sum _{j=1}^k{\displaystyle \sum _{h=1}^k{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_h}\left|y_{ji}-y_{hr}\right|}}}}}{2n^2\overline{y}}}$$

(9)

where G signifies the overall Gini coefficient, the higher the value, more pronounced the general discrepancy. $y_{ji}$ ($y_{hr}$) stands for environmental efficiency of port $i(r)$ in the region $j(h)$. $\overline{y}$ indicates the average value of all port efficiencies, $n$ and $k$ respectively denote the number of ports and region divisions. $n_j$ ($n_h$) expresses the number of ports in region $j(h)$. It should be emphasized that before computing the Gini coefficient, sorting by the average port environmental efficiency in every region is required, outlined in Equation (10).

$${\overline{Y}}_h\le \dots \le {\overline{Y}}_j\le \dots \le {\overline{Y}}_k$$

(10)

If the approach of calculating the overall Gini coefficient is solely applied to region $j$, the intraregional Gini coefficient $G_{jj}$ of region $j$ can be obtained.

$$G_{jj}={\displaystyle \frac{{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_j}\left|y_{ji}-y_{jr}\right|}}}{2n_j^2{\overline{y}}_j}}$$

(11)

Similarly, the interregional Gini coefficient $G_{jh}$ can be derived.

$$G_{jh}={\displaystyle \frac{{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_h}\left|y_{ji}-y_{hr}\right|}}}{n_j{n}_h({\overline{y}}_j+{\overline{y}}_h)}}$$

(12)

The overall Gini coefficient $G$ can be further decomposed into the contribution of intraregional differences $G_w$, the contribution of interregional differences $G_{nb}$, and the contribution of the intensity of transvariation $G_t$, and it meets $G=G_w+G_{nb}+G_t$. The expression is as follows:

$$G_w={\displaystyle \sum _{j=1}^k{G}_{jj}{p}_j}{s}_j$$

(13)

$$G_{nb}={\displaystyle \sum _{j=2}^k{\displaystyle \sum _{h=1}^{j-1}{G}_{jh}(p_j{s}_h+p_h{s}_j)}}{D}_{jh}$$

(14)

$$G_t={\displaystyle \sum _{j=2}^k{\displaystyle \sum _{h=1}^{j-1}{G}_{jh}(p_j{s}_h+p_h{s}_j)}}(1-D_{jh})$$

(15)

In Equation (14), $p_j=n_j/n,s_j=n_j{\overline{y}}_j/n\overline{y}(j=1,2,\dots ,k)$, $D_{jh}$ depicts the relative disparities of port efficiency between region $j$ and region $h$, as given by Equation (16).

$$D_{jh}={\displaystyle \frac{d_{jh}-p_{jh}}{d_{jh}+p_{jh}}}$$

(16)

$$d_{jh}={\displaystyle {\int }_0^{\infty }d{F}_j}(y){\displaystyle {\int }_0^y(y-x)}d{F}_h(x)$$

(17)

$$p_{jh}={\displaystyle {\int }_0^{\infty }d{F}_h}(y){\displaystyle {\int }_0^y(y-x)}d{F}_j(x)$$

(18)

where $F_j(\cdot )$ and $F_h(\cdot )$ respectively represent the cumulative distribution functions of region $j,h$. $d_{jh}$ signifies the difference in the improvement of PEE across regions, while $p_{jh}$ is hypervariable first-order moment, which are, respectively, the mathematical expectation of the sum of all sample values $y_{ji}-y_{hr}>0$ and $y_{hr}-y_{ji}>0$ in region $j$ and $h$.

3.4. Data Collection and Descriptions

This study selects the data from 2013 to 2022 and takes 23 major ports in the five port groups along China’s coastal ports as the research object, as shown in

Table 2. Port distribution within the port group.

	Port Group	Contains Port
1	Bohai Sea port group	Dalian Port, Yingkou Port, Qinhuangdao Port, Tianjin Port,
		Yantai Port, Weihai Port, Qingdao Port, Rizhao Port
2	Yangtze River Delta port group	Shanghai Port, Lianyungang Port, Ningbo-Zhoushan Port, Taizhou Port, Wenzhou Port
3	Southeast Coastal port group	Fuzhou Port, Xiamen Port
4	Pearl River Delta port group	Shantou Port, Shenzhen Port, Guangzhou Port, Zhuhai Port
5	Southwest Coastal port group	Zhanjiang Port, Beihai Port, Fangcheng Port, Haikou Port

. Given the availability of data and based on relevant literature [55,56,57], this study selected input-output indicators, as detailed in

Table 3. Port environmental efficiency evaluation index.

	Variable	Unit
Inputs	Quay length	m
	Berth number	pcs
	10,000 Ton Class Berth number	pcs
Desirable outputs	Cargo throughput	10,000 tons
	Container throughput	10,000 TEU
Undesirable outputs	CO2 emission	10,000 tons

, to calculate PEE from the perspective of port production and utilization.

Since official yearbooks do not provide precise statistics on coastal port carbon emissions, indirect estimation methods are commonly used. While bottom-up approaches can provide detailed estimates at the vessel level, they require high-frequency operational data that are not consistently available for Chinese coastal ports [58]. By contrast, the top-down approach calculates emissions by multiplying fuel consumption by emission factors, offering a practical solution for regional studies [59]. Accordingly, and following prior studies [44,57,60], this paper adopts a top-down method to estimate port carbon emissions, as outlined in Equation (19).

$$C=SC\times HC\times \alpha$$

(19)

Here, C denotes the CO₂ emissions of the port; SC refers to the standardized coal-equivalent energy consumption per 10,000 tons of port cargo throughput, expressed in metric tons of standard coal. Annual SC values covering the period 2013–2022 were obtained from the Statistical Bulletin on the Development of China’s Transportation Industry, as shown in

Table 4. Reference coefficient of port coal-equivalent energy consumption per unit.

Period	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
SC	2.9	2.7	2.6	2.5	2.4	2.3	2.1	2.0	1.9	1.75

(drawing on prior research [44]). HC stands for the annual cargo throughput of a given port (in 10,000 tons); and $\alpha$ is the carbon emission coefficient, referring to the unit CO₂ emissions consumed per ton of standard coal in the port, taking the value of 2.4589. This value is derived from the theoretical carbon-to-CO₂ conversion process during the complete combustion of standard coal: 1 ton of standard coal contains approximately 0.67 tons of carbon, and full oxidation of carbon generates 3.67 tons of CO₂ per ton of carbon, resulting in 0.67·3.67 = 2.4589 tons of CO₂ per ton of standard coal.

Table 5. Indicator data description Statistical analysis.

	Variable	Min	Max	Mean	SD
Total	Quay length	3949	126,921	29,714.89	25,957.33
	Berth number	15	1238	217.3	243.2
	10,000 Ton Class Berth number	7	224	64.41	46.84
	Cargo throughput of port	2078	126,134	29,260.64	24,637.02
	Container throughput of port	9	4730	853.47	1088.55
	CO2 emission	14,817.82	613,273.5	164,683.9	137,513.4
Bohai Sea port group	Quay length	3949	48,211	26,177.74	12,195.15
	Berth number	15	257	128.4375	66.87071
	10,000 Ton Class Berth number	12	131	72.5375	30.82821
	Cargo throughput of port	3730	65,754	34,804.93	16,447.94
	Container throughput of port	39	2567	730.6	699.9425
	CO2 emission	18,997.46	358,520.9	196,752	93,388.28
Yangtze River Delta port group	Quay length	11,361	126,921	50,856.74	44,364.47
	Berth number	53	1238	451.46	398.7322
	10,000 Ton Class Berth number	7	224	89.7	77.7196
	Cargo throughput of port	4901	126,134	41,503.86	39,115.48
	Container throughput of port	15	4730	1434.8	1640.272
Southeast Coastal port group	CO2 emission	25,036.52	613,273.5	233,099.5	216,859
	Quay length	23,025	33,274	28,414.95	3054.073
	Berth number	158	207	180.1	12.2942
	10,000 Ton Class Berth number	48	81	68.85	9.852998
	Cargo throughput of port	12,759	30,164	20,158.35	4500.461
	Container throughput of port	198	1243	663.6	392.3723
	CO2 emission	87,564.38	136,126.7	111,955.4	17,475.09
Pearl River Delta port group	Quay length	5013	56,055	27,764.78	16,000.29
	Berth number	34	621	235.925	187.8966
	10,000 Ton Class Berth number	11	96	49.1	26.95657
	Cargo throughput of port	3155	62,906	24,258.18	20,197.23
	Container throughput of port	88	3004	1236.175	1125.693
	CO2 emission	16,291.44	336,395.2	136,400.3	112,017.4
Southwest Coastal port group	Quay length	4563	23,577	12,961.98	5504.1
	Berth number	32	177	102.3	44.48117
	10,000 Ton Class Berth number	11	51	29.625	12.04199
	Cargo throughput of port	2078	30,185	12,421.68	7857.261
	Container throughput of port	9	215	84.75	61.18142
	CO2 emission	14,817.82	170,710.4	69,676.27	44,401.43

Note Data sources: National Bureau of Statistics, China Statistical Yearbook (2014–2023), China Port Yearbook (2014–2023).

presents the descriptive statistics of the indicators.

4. Empirical Analysis

4.1. Comparisons of the PEE Under Different Models

To validate the applicability of the proposed EBM-WD model, this study conducted a comparative analysis of PEE with several widely recognized DEA models. These models were selected to represent different approaches to efficiency measurement: the radial BCC model, the non-radial SBM model, and the hybrid EBM model. The comparative results are summarized in

Table 6. Comparisons of average PEE from 2013 to 2022 based on different models.

Model	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
BCC	0.809	0.827	0.834	0.811	0.858	0.853	0.846	0.773	0.785	0.761
SBM	0.652	0.704	0.726	0.673	0.742	0.799	0.705	0.578	0.660	0.648
EBM	0.744	0.836	0.821	0.750	0.807	0.827	0.752	0.703	0.778	0.740
EBM-WD	0.742	0.842	0.810	0.748	0.808	0.816	0.754	0.704	0.781	0.742

and

Table 7. Comparisons of average PEE between ports under different models.

Port	BCC	SBM	EBM	EBM-WD
Dalian	0.571	0.517	0.679	0.683
Yingkou	0.829	0.738	0.815	0.807
Qinhuangdao	0.814	0.226	0.655	0.652
Tianjin	0.798	0.819	0.829	0.830
Yantai	0.584	0.294	0.583	0.588
Weihai	0.734	0.657	0.534	0.533
Qingdao	1.000	1.000	1.000	1.000
Rizhao	1.000	1.000	1.000	1.000
Shanghai	1.000	1.000	1.000	1.000
Lianyungang	0.819	0.851	0.885	0.844
Ningbo-Zhoushan	1.000	1.000	1.000	1.000
Taizhou	1.000	1.000	1.000	1.000
Wenzhou	0.711	0.302	0.592	0.597
Fuzhou	0.487	0.377	0.545	0.549
Xiamen	0.557	0.534	0.514	0.514
Shantou	0.850	0.786	0.683	0.682
Shenzhen	1.000	1.000	1.000	1.000
Guangzhou	0.999	0.954	0.997	0.997
Zhuhai	0.682	0.373	0.596	0.597
Zhanjiang	0.920	0.615	0.906	0.910
Beihai	0.927	0.825	0.751	0.752
Fangcheng	0.542	0.100	0.381	0.389
Haikou	0.935	0.875	0.900	0.895
Mean	0.816	0.689	0.776	0.775

.

As shown in Table 6 and Table 7, the BCC model yields the highest mean PEE score of 0.816, while the SBM model provides the lowest at 0.689. This finding is consistent with the established literature [61]. The BCC model, as a radial measure, tends to overestimate efficiency by projecting inefficient DMUs onto the production frontier without fully accounting for non-radial slacks in inputs and outputs. Conversely, the SBM model, which is entirely based on slacks, often underestimates efficiency by neglecting the proportional relationship between inputs and outputs. The EBM model, as a hybrid approach, correctly addresses the limitations of both radial and non-radial models. Its mean PEE score of 0.776 lies between those of the BCC and SBM models, demonstrating a more balanced and realistic efficiency measure.

The mean PEE score of our proposed EBM-WD model (0.775) is very close to that of the conventional EBM model, and both fall within the range defined by the BCC and SBM models. This confirms that the EBM-WD model retains the hybrid strengths of the EBM framework while enhancing its environmental realism. Although the overall efficiency levels are similar, the results are not entirely identical: several ports experience shifts in their PEE rankings under the EBM-WD model, reflecting the differentiated impact of non-uniform abatement factors under the weak disposability assumption. These rank adjustments validate the methodological extension and underscore the necessity of incorporating non-uniform abatement factors to provide a more nuanced and realistic evaluation of port environmental efficiency.

4.2. Overall Analysis of Port Environmental Efficiency

This study utilizes the EBM-WD model to evaluate the environmental efficiency of China’s coastal ports from 2013 to 2022. The results are provided in

Table 8. The PEE values of China’s coastal ports from 2013 to 2022.

Port	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	Mean	SD
Dalian	0.611	0.948	0.687	0.637	1.000	0.658	0.506	0.420	1.000	0.358	0.683	0.220
Yingkou	0.910	0.969	0.855	0.868	1.000	0.944	0.655	0.615	0.596	0.661	0.807	0.150
Qinhuangdao	0.641	0.662	0.676	0.550	0.811	0.719	0.680	0.566	0.580	0.636	0.652	0.074
Tianjin	1.000	1.000	1.000	0.954	0.772	0.696	0.636	0.629	1.000	0.611	0.830	0.167
Yantai	0.525	0.733	0.757	0.603	0.483	0.666	0.545	0.501	0.513	0.553	0.588	0.093
Weihai	1.000	1.000	1.000	1.000	0.233	0.288	0.196	0.170	0.195	0.246	0.533	0.383
Qingdao	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.000
Rizhao	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.000
Shanghai	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.000
Lianyungang	0.797	1.000	0.644	0.646	1.000	1.000	1.000	0.708	0.645	1.000	0.844	0.162
Ningbo-Zhoushan	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.000
Taizhou	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.000
Wenzhou	0.591	0.586	0.625	0.568	0.571	0.561	0.592	0.603	0.645	0.627	0.597	0.026
Fuzhou	0.362	0.387	0.355	0.364	0.359	1.000	0.465	0.529	1.000	0.670	0.549	0.245
Xiamen	0.478	0.621	0.530	0.495	0.517	0.499	0.494	0.495	0.485	0.531	0.514	0.039
Shantou	0.376	0.477	0.471	0.478	0.772	0.659	0.590	1.000	1.000	1.000	0.682	0.233
Shenzhen	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.000
Guangzhou	0.972	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.997	0.009
Zhuhai	0.486	0.555	0.594	0.626	0.692	0.712	0.750	0.585	0.557	0.418	0.597	0.097
Zhanjiang	0.688	0.992	1.000	1.000	1.000	1.000	0.909	0.740	0.771	1.000	0.910	0.120
Beihai	0.238	1.000	1.000	0.364	1.000	1.000	1.000	0.536	0.755	0.630	0.752	0.280
Fangcheng	0.391	0.433	0.436	0.380	0.377	0.374	0.332	0.356	0.412	0.403	0.389	0.031
Haikou	1.000	1.000	1.000	0.680	1.000	1.000	1.000	0.737	0.814	0.721	0.895	0.132
Average	0.742	0.842	0.810	0.748	0.808	0.816	0.754	0.704	0.781	0.742	0.775	0.041

. As shown in Figure 1a, the overall PEE underwent a fluctuating increase throughout the research timeframe. A similar pattern was also observed in the study by Zhang et al. [38]. From 2013 to 2018, PEE increased gradually, with the mean value rising from 0.742 to 0.816, signifying a 9.973% enhancement. This growth can largely be ascribed to significant efforts in promoting smart ports, port integration, and prioritizing sustainable development [62,63].

However, from 2018 to 2022, PEE declined, with the average value falling from 0.816 to 0.742, a decrease of 9.069%. This downturn was primarily caused by the COVID-19 pandemic, which disrupted port operations through reduced cargo volumes, temporary shutdowns, and labor shortages [64]. These disruptions constrained the effective utilization of inputs and led to a decline in port efficiency [65]. Notably, these effects are largely temporary, and port efficiency is expected to rebound as trade flows and port operations recover. Furthermore, Figure 1b depicts the distribution of PEE, highlighting a gradual rise in the number of ports at the effective frontier over the research period.

As depicted by Figure 2, the mean PEE across all ports stands at 0.775, reflecting a relatively high overall efficiency level. However, pronounced inter-port disparities are observed, which can be attributed to differences in management practices, technological adoption, and environmental policy implementation. The ports with the top efficiency scores comprise the ports of Qingdao, Shanghai, Taizhou, Rizhao, Ningbo-Zhoushan, and Shenzhen, all attaining an average PEE score of 1, which signifies DEA efficiency. Following closely are Guangzhou Port and Haikou Port, boasting PEE scores of 0.997 and 0.910, respectively, indicating considerable advances in low-carbon port construction. These ports benefit from advanced operational management systems, significant investment in low-carbon technologies, electrification of port equipment, and rigorous enforcement of local environmental regulations, collectively sustaining their high environmental performance.

In contrast, Fangcheng Port, Xiamen Port, and Weihai Port showed unsatisfactory environmental performance, with average PEE values of 0.389, 0.514, and 0.533, respectively. To mitigate their environmental performance gaps, these ports should prioritize low-carbon transition strategies, encompassing the optimization of energy mixes and the implementation of targeted regulatory measures. Furthermore, it can be discerned from the last column of Table 8 that the standard deviations of PEE of Qingdao, Rizhao, Shanghai, Ningbo-Zhoushan, Taizhou, Shenzhen, and Guangzhou are relatively small during 2013–2022, illustrating that their environmental efficiency levels were relatively stable. On the contrary, the ports of Weihai, Beihai, Shantou, Fuzhou, and Dalian showed larger standard deviations in PEE, indicating relative volatility in their environmental efficiency performance.

Table 9. The PEE of five major group ports from 2013 to 2022.

Port Group	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	Mean	SD
Bohai Sea port group	0.841	0.836	0.914	0.872	0.826	0.787	0.746	0.652	0.613	0.735	0.633	0.769	0.097
Yangtze River Delta port group	0.881	0.878	0.917	0.854	0.843	0.914	0.912	0.918	0.862	0.858	0.925	0.888	0.029
Southeast Coastal port group	0.411	0.420	0.504	0.443	0.430	0.438	0.750	0.479	0.512	0.742	0.601	0.521	0.118
Pearl River Delta port group	0.743	0.709	0.758	0.766	0.776	0.866	0.843	0.835	0.896	0.889	0.854	0.812	0.061
Southwest Coastal port group	0.565	0.579	0.856	0.859	0.606	0.844	0.844	0.810	0.592	0.688	0.689	0.721	0.117

describes the PEE values of five major port groups from 2013 to 2022. During the research period, the Yangtze River Delta port group ranked first in seven years, consistently displaying a superior level. This high performance can be ascribed to the region’s advantageous geographical location, superior infrastructure, robust hinterland economy, and efficient management systems. The Pearl River Delta port group experienced steady growth in environmental performance, driven by recent policy and rapid regional economic development, which boosted the environmental efficiency of Shenzhen Port and Guangzhou ports. In addition, the PEE of the Southwest and Southeast coastal port group showed a fluctuating upward tendency with significant volatility, indicating substantial potential for further development. Conversely, the Bohai Sea port group’s PEE expressed a downward trend, owing mostly to improper resource allocation and overinvestment, resulting in poor overall environmental performance. These findings extend the research of Chen et al. [66].

Figure 3 depicts an evolutionary trend in the national kernel density curve, initially moving rightward before gradually shifting leftward. This dynamic pattern indicates that PEE experienced an initial rise and a subsequent decline over the research duration. The peak of the curve became higher and narrower, signifying a heightened concentration of PEE. This observation underscores an increasingly pronounced agglomeration effect among ports. Furthermore, the curve’s distribution is right-skewed, implying that the majority of coastal ports demonstrate relatively high environmental efficiency. Notably, the primary peak shows a unimodal distribution, which suggests that the phenomenon of polarization is not notably evident.

4.3. Dynamic Characteristics Analysis of Port Environmental Efficiency

To further examine the dynamic characteristics of PEE throughout the research period, the GM index was utilized.

Table 10. Changes in the GM index and decomposition items from 2013 to 2022.

Period	GM	GMEC	GMTC
2013–2014	0.992	1.254	0.864
2014–2015	0.988	0.966	1.037
2015–2016	0.991	0.929	1.103
2016–2017	0.997	1.155	0.915
2017–2018	1.048	1.070	1.035
2018–2019	0.972	0.916	1.094
2019–2020	1.092	0.951	1.148
2020–2021	1.050	1.159	0.957
2021–2022	1.085	0.980	1.176
Mean	1.024	1.042	1.037

lists the GM index and its decomposition items.

The findings demonstrate that the mean annual GM index for China’s coastal ports during 2013–2022 is greater than 1, at 1.024, manifesting a slight upward tendency in TFP of the coastal ports with an average yearly growth rate of 2.4%. Regarding the GM index decomposition, GMEC and GMTC increased by 4.2% and 3.7%, respectively. These findings confirm the joint enhancement of technological level and technical efficiency has contributed to the rise in port productivity, which is in line with Li et al. [28]. The improvement in technical efficiency is the predominant driving element behind TFP growth.

Overall, the TFP trend for China’s coastal ports shows a pattern of initial decline followed by recovery. The TFP declined during 2013–2017 and 2018–2019 but rebounded between 2019 and 2022, indicating a positive trajectory in the recent development of coastal ports. As regards GMEC and GMTC, their overall fluctuations are pronounced, with alternating states of upward increases and downward decreases. However, there are few synchronized changes between the two, which suggests that the emphasis on technical efficiency and technological level varies during different periods of coastal port development. In agreement with Cui et al. [57], this result demonstrates that the effect of balancing the joint development of both is not ideal, leading to the overall port TFP not improving steadily.

As illustrated in Figure 4, 16 ports, accounting for 70% of the sample, exhibited a GM index surpassing 1, indicating an enhancement in their TFP. Shantou Port had the highest average GM value at 1.250, while Dalian Port had the lowest value at 0.954. Notably, there are pronounced spatial variations in TFP among coastal ports. The ports of Qingdao, Fuzhou, Shanghai, Beihai, Xiamen, and Ningbo-Zhoushan have demonstrated significant improvements in TFP, reflecting effective efforts in enhancing environmental performance through improved operational management and technological innovation. In contrast, ports such as Yingkou, Tianjin, and Shantou have experienced prolonged declines in TFP, suggesting persistent inefficiencies. To improve their environmental performance, these ports should consider optimizing governance mechanisms and accelerating the adoption of green technologies.

The decomposition results further reveal that for ports with increased TFP, such as Shanghai, Ningbo-Zhoushan, Guangzhou, Taizhou, and Shenzhen, GMTC has increased significantly more than GMEC, demonstrating that technological innovation serves as the primary impetus of TFP improvement. Conversely, for ports such as Shantou, Beihai, Fuzhou, Lianyungang, and Zhanjiang, the average growth rate of GMEC notably exceeds GMTC, suggesting that enhancements in technical efficiency predominate. For ports like Wenzhou, Fangcheng, Xiamen, Rizhao, and Qingdao, no marked distinction between GMEC and GMTC was observed, implying that both factors contribute equally to productivity fluctuations. Notably, ports exhibiting GMTC below the unity threshold, such as Qinhuangdao and Yingkou, demonstrate insufficient technological progress. These ports could benchmark against their high-performing counterparts to establish investment priorities and thereby enhance their environmental performance. The slight increase in GMTC for the ports of Zhuhai, Haikou, Weihai, and Tianjin was offset by a widespread decline in GMEC, thereby impeding productivity improvement.

The average GM index for the five major port groups is displayed in

Table 11. Mean values of GM index for five major port groups.

Port Group	2013/2014	2014/2015	2015/2016	2016/2017	2017/2018	2018/2019	2019/2020	2020/2021	2021/2022	Mean
Bohai Sea port group	0.967	1.001	1.012	0.877	1.123	0.857	0.984	1.020	1.043	0.987
Yangtze River Delta port group	0.956	0.951	1.029	1.075	0.991	1.018	0.941	1.100	1.203	1.029
Southeast Coastal port group	1.026	0.974	0.987	1.012	1.012	1.132	1.102	1.048	1.027	1.036
Pearl River Delta port group	1.039	1.008	1.000	1.058	0.955	1.059	1.516	0.967	1.043	1.072
Southwest Coastal port group	1.023	0.994	0.892	1.070	1.081	0.979	1.069	1.131	1.091	1.037

. Across all port groups, with the exception of the Bohai Sea, the average GM index surpassed unity, indicating a positive trend in TFP from 2013 to 2022. This suggests relatively effective resource allocation and operational management, contributing to advancements in environmental performance and reduced emissions. Notably, the Pearl River Delta port group demonstrated the most significant advancement, with its TFP amplified by 7.2%, reflecting considerable gains in enhancing port environmental performance [67]. Conversely, the Bohai Sea port group registered a GM index of 0.987, signifying a marginal decline in TFP and an average yearly reduction of 1.3%. This indicates areas where environmental efficiency and emission reduction strategies may need further attention in this region.

The average GM index and its decomposition items for the five port groups are illustrated in Figure 5. The primary inhibitory factor for the productivity growth in Bohai Sea port group is the decline in technical efficiency. Despite its abundant resources and infrastructure, this port group struggles to harness them effectively, thereby leading to reduced TFP. In contrast, technical efficiency has played a dominant role in driving the TFP growth of the Southwest and Southeast coastal port groups. Furthermore, the TFP growth observed in both the Yangtze River Delta and Pearl River Delta port groups can be attributed to the simultaneous improvement of both technical efficiency and technological progress. This indicates both port groups are both optimizing existing operations and embracing new technologies to boost PEE and cut emissions. In summary, these distinctions underscore the varying developmental stages and strategic priorities of each port group, suggesting that tailored approaches are necessary to further improve TFP and environmental performance within each region.

4.4. Regional Differences Analysis of Port Environmental Efficiency

To delve deeper into regional disparities in PEE, the Dagum Gini coefficient of PEE was calculated spanning 2013–2022. The findings are summarized in

Table 12. Dagum Gini coefficient and its decomposition.

Period	Total	Intraregional	Interregional	Intensity of Transvariation	Subgroup
					1	2	3	4	5
2013	0.194	0.035	0.102	0.057	0.120	0.093	0.069	0.208	0.279
2014	0.129	0.021	0.064	0.044	0.066	0.072	0.116	0.166	0.125
2015	0.145	0.025	0.058	0.062	0.084	0.104	0.098	0.162	0.123
2016	0.177	0.033	0.083	0.062	0.119	0.116	0.076	0.156	0.228
2017	0.159	0.032	0.068	0.059	0.175	0.075	0.090	0.083	0.138
2018	0.143	0.030	0.043	0.070	0.158	0.077	0.167	0.097	0.139
2019	0.182	0.034	0.096	0.051	0.204	0.071	0.015	0.111	0.162
2020	0.194	0.037	0.106	0.050	0.233	0.101	0.017	0.087	0.143
2021	0.165	0.036	0.052	0.077	0.207	0.099	0.174	0.093	0.111
2022	0.184	0.036	0.091	0.056	0.218	0.065	0.058	0.128	0.171
Mean	0.167	0.032	0.076	0.059	0.159	0.087	0.088	0.129	0.162

and the Gini coefficient trend illustrated in Figure 6.

The mean Gini coefficient for the whole PEE was 0.167. The lowest value occurs in 2014, at 0.129, which suggests relatively balanced development in that year. The highest value of 0.194 appeared in 2013 and 2020, demonstrating a pronounced spatial imbalance in PEE during these two years. As indicated in Figure 6, the Gini coefficient for the overall environmental efficiency declines from 0.194 in 2013 to 0.184 in 2022, a decline of around 5.2%; the environmental efficiency gap is gradually narrowing. The trend can be characterized as fluctuating, with environmental efficiency gaps first narrowing and then widening across three distinct periods: 2013–2016, 2016–2020, and 2020–2022. Furthermore, the interregional Gini coefficient showed a similar evolution pattern, spanning 0.043 to 0.106. The Gini coefficient of intensity of transvariation is 0.057 in 2013 and then reaches above 0.070 in 2018 and 2021, separately, showing a certain degree of increase, and then drops to 0.056 at the end. In contrast, the intraregional Gini coefficient remained relatively stable, ranging from 0.020 to 0.040.

The tendency of the intraregional Gini coefficient is represented in Figure 7. In terms of intraregional differences, the five major port groups have average Gini coefficients that span 0.085 to 0.165. The Yangtze River Delta port group had the smallest average intraregional Gini coefficient at 0.087, indicating minimal environmental efficiency disparities within the group. This balanced development could be attributed to the strong economic foundation, robust infrastructure, policy support, and technological cooperation, which have collectively fostered coordination and cooperation across ports. On the contrary, the Southwest Coastal port group had the highest average intraregional Gini coefficient at 0.162, reflecting significant disparities due to factors such as limited economic development, challenging geographical conditions, and insufficient investment. As depicted in Figure 7, the Bohai Sea port group witnessed a rising Gini coefficient from 2014 onward, highlighting a growing imbalance, while the Yangtze River Delta maintained relatively balanced development. The Pearl River Delta port group demonstrated a general decline in its Gini coefficients, suggesting a narrowing of intraregional environmental efficiency gaps. The same pattern is seen in the southwestern coastal port group. In addition, the Southeast Coastal port group maintained stable equilibrium levels, except for fluctuations in 2019 and 2021.

Figure 8 visualizes the variations in the Gini coefficients among regions. Overall, the shaded areas in Figure 8 are generally decreasing, showing that the polarization of PEE among regions is diminishing during the observation period. It is noteworthy that the Yangtze River Delta and Pearl River Delta port groups have the smallest regional disparity (Gini coefficient = 0.122). This showcases similarities in economic development, port operations, resource allocation, and technological advancements. In contrast, the Southeast Coastal and Yangtze River Delta port groups showed the largest disparity, with a Gini coefficient of 0.274. This disparity may stem from variations in economic conditions, geographic features, investment levels, and policy support. The Gini coefficient among most port groups exhibit an alternating process of first falling and then rising, with an overall declining trend. This result demonstrates that the discrepancies among these port groups are gradually narrowing. In contrast, the Gini coefficient between the Bohai Sea port group and the Yangtze River Delta port group exhibits a slow rising trend, suggesting that the discrepancies between these two groups are widening.

Figure 9 illustrates the regional differentiation source and contribution rate. Interregional disparities accounted for the largest share at 45.1%, followed by the intensity of transvariation at 35.8%, and intraregional disparities at 19.1%. This demonstrates that the main sources of environmental efficiency discrepancies among China’s coastal ports are interregional disparities and the intensity of transvariation, with interregional disparities being the dominant factor. Over time, the impact of interregional discrepancies has diminished, whereas the contribution from the intensity of transvariation has exhibited a slow volatile trend. This indicates that the contribution of the variation stemming from the overlapping interactions among various regions is progressively increasing. In addition, the contribution rate of intraregional disparities exhibits slight volatility and remains stable.

5. Conclusions and Policy Implications

5.1. Main Conclusions

Enhancing PEE is crucial for fostering sustainable port development; consequently, refining PEE assessment is imperative, particularly when considering the heterogeneous abatement capabilities of individual ports. This study proposes a modified EBM-Undesirable model that incorporates weak disposability and non-uniform abatement factors to more accurately evaluate PEE. The Global Malmquist index and the Dagum Gini coefficient were further employed to analyze the temporal dynamics and regional discrepancies of PEE. The main conclusions are summarized as follows.

First, PEE exhibited a fluctuating upward trend from 2013 to 2022. Moreover, while the general environmental efficiency level is relatively high, significant heterogeneity persists among individual ports and across port groups. Regionally, the Yangtze River Delta and Pearl River Delta port groups demonstrate considerable environmental performance and green transformation capacity, whereas the Bohai Sea port group experienced a decline.

Second, the dynamic analysis indicates a moderate overall TFP growth, primarily driven by improvements in technical efficiency. However, there remains untapped potential in advancing technological levels. The sources of TFP improvement vary across port groups; some have benefited from technical efficiency gains or technological innovation, while others have experienced decline due to resource misallocation.

Third, the regional disparity analysis uncovers an imbalance in the spatial distribution of PEE. In general, regional development within and between port groups still exhibits discrepancies, albeit the overall gap is gradually narrowing. Interregional discrepancies and the density of transvariation are the predominant factors contributing to these disparities, while intraregional discrepancies play a comparatively minor role.

5.2. Policy Implications

Drawing on the discoveries, several key policy recommendations are proposed to facilitate the high-quality, sustainable development of the port sector. It can proffer valuable insights for policymakers in formulating sustainable port development strategies.

Firstly, the allocation of resources should be optimized. Ports with relatively low efficiency should enhance managerial capabilities and operational practices through targeted policy support and increased capital investment. Resource allocation should not only aim at expanding cargo throughput but also prioritize the implementation of energy-saving and emission-reduction initiatives.

Secondly, differentiated development strategies should be implemented. Ports should move beyond a one-size-fits-all approach and formulate strategies tailored to their specific characteristics, including location, development stage, and operational efficiency. At the port-group level, region-specific measures are recommended: the Bohai Sea group should prioritize improvements in operational management and technical efficiency; the Yangtze River Delta and Pearl River Delta groups should emphasize technological innovation and smart port transformation; and the Southwest and Southeast coastal groups should enhance regional coordination and infrastructure connectivity.

Thirdly, interregional cooperation and integration should be strengthened. The fragmented development of coastal ports has led to redundant competition and inefficient resource use. Establishing interregional cooperation mechanisms would facilitate the sharing of resources, technologies, and managerial expertise. Coordinated planning and policy alignment can improve the overall competitiveness of the port system and promote regional integration.

Lastly, the construction of smart ports should be continuously advanced. Advancing smart port construction is essential for future competitiveness. Ports should accelerate the development of intelligent infrastructure, such as big data platforms, IoT applications, and automated terminals, while also embedding low-carbon technologies, including shore power facilities, renewable energy integration, and intelligent energy management.

5.3. Research Limitations and Further Expansions

While this study provides a comprehensive evaluation of port environmental efficiency and spatio-temporal characteristics, several limitations should be acknowledged. First, the scope of this study is primarily confined to coastal ports. Future research should expand the analysis to inland ports and adopt a national-scale perspective. Second, owing to data availability and measurement constraints, certain input metrics, such as labor and assets, were not incorporated. Moreover, port CO₂ emission data was estimated indirectly from cargo throughput and standardized coal coefficients. Although this approach is widely used, it may not fully reflect port-specific energy structure. Future studies should address this limitation by pursuing collaborative research with port authorities or government agencies to gain access to more detailed, disaggregated data. This will enable a more nuanced and accurate assessment of port environmental performance.