Quantifying the Influence of Market Concentration on Maritime Freight Rates for Sustainable Transport: A Case Study of the Asia–North America Container Route

Abstract

The determination of freight rates in liner shipping is influenced by the market dynamics and the strategic decisions of shipping alliances. This study investigates the effect of non-alliance tonnage on freight rates along the Asia–North America West Coast route, employing a quantile regression method. A dataset covering July 2021 to June 2023 was used, with bunker prices and the Dow Jones Index serving as control variables. The results reveal that the non-alliance share has a significant and negative impact on lower quantiles, suggesting that enhanced competition reduces freight rates when the prices are low. In contrast, this effect disappears at higher freight levels. Bunker prices and the stock market index also exhibit varying effects, depending on the quantile, with demand-side variables being more influential during low-freight conditions. These findings suggest that market concentration affects price-setting power, and quantile-based approaches offer deeper insights into these complex relationships than linear models. These insights contribute to the sustainable development of maritime transport by promoting fair competition, improving pricing transparency, and supporting efficient policy interventions in global liner shipping.

1. Introduction

Container shipping alliances are horizontal agreements among several shipping companies designed to share vessels, routes, and operational resources to improve efficiency and save costs. As of early 2023, the three following principal global alliances govern container transportation: the 2M Alliance (comprising MSC and Maersk), the Ocean Alliance (containing CMA CGM, COSCO Group, and Evergreen), and THE Alliance (composed of Hapag-Lloyd, Yang Ming, HMM, and ONE). These alliances, established by firms that collectively dominate over 80% of the worldwide container ship fleet, employ only a fraction of their overall capacity under alliance agreements. The total capacity allocated by firms for alliance utilization represents around 39% of the global container fleet [1]. The Ocean Alliance possesses the highest percentage of global fleet capacity at around 16%, succeeded by the 2M Alliance at 11% and THE Alliance at 9%. Prospectively, alliance members have made substantial orders for new vessels—up to 25% of the current alliance capacity—while the Ocean Alliance’s new orders account for 32.4% of its existing capacity, similar to the total capacity of the 2M Alliance [2]. However, alliances are based on fixed-term agreements and can undergo modifications. MSC and Maersk have said that their 2M Alliance deal, initiated in 2015 and scheduled to conclude in 2025, will not be extended [3,4]. This transition signifies wider alterations in strategic priorities within the sector, as major carriers increasingly adopt independent growth strategies and operational flexibility beyond conventional alliance frameworks.

Agreements among container shipping companies can exert diverse influences on the market. The primary effect to note is the augmentation of business volume achieved by alliances, leading to the enhancement of the economies of scale. Companies that maintain distinct company volumes when operating independently will attain greater business volume and reduced unit expenses due to pooling [5]. This cheap cost may also be passed on to the clients, depending on the circumstances. The second consequence is the optimization of services resulting from diminished competition. As enterprises utilize more frequent and idle vessels to enhance competitiveness, the optimization of transportation services may occur with the reduction in competition and the augmentation of resource sharing within alliances [6]. Consequently, the geographical coverage area is likewise augmented.

Nonetheless, alliances may not invariably result in reduced freight charges for clients. The augmented market share resulting from the collaboration can enable corporations to monopolize the market. Specifically, if they have monopoly or oligopoly strength on some routes, they might elevate client costs by diminishing service frequency or augmenting freight charges. They may execute their freight-increasing decisions autonomously from expenses as a stipulation of common policy. Secondly, shipowners will have greater influence over freight pricing, as competition diminishes due to alliances. They will have the capability to drop to exceedingly low levels at their discretion. They can also use this condition to deter new market entrants. When a smaller company competes with coalitions on the same route, the alliances can transport goods at significantly reduced freight rates due to economies of scale, rendering small enterprises unable to compete in the long term. This technique, which temporarily lowers freight charges, ultimately places customers at the mercy of the alliances in the long term. Cargo owners pass on rising freight costs, which then trickle down to all individual customers. Governments are routinely scrutinized to ascertain compliance with antitrust rules to avoid unchecked power activities.

This study examined the impact of excluding tonnage from the alliance on freight rates along the Asian and North American routes. Asia and North America, the two principal regions in transit capacity, constitute one of the most active and significant trade routes globally for the liner shipping sector, facilitating east–west trade [7,8]. The route entails the conveyance of commodities through container ships between prominent ports on the East Coast of Asia, including those in China, Japan, South Korea, and Taiwan, and ports on the West Coast of North America, chiefly in the United States and Canada. Cost and demand, significant elements influencing freight rates, were incorporated as control variables in the model [9,10,11]. The study established the average bunker price from 20 global locations for cost and utilized the USA Dow Jones Index as a proxy variable for demand.

The quantile regression method was selected for the analysis. The quantile method is preferred because it works well with data that does not follow a normal distribution, is strong against unusual data points, provides different results at various points in the data, and does not rely on strict rules. The fact that the dependent variable, the freight index, does not follow a normal distribution and shows tail effects supports the use of the quantile technique as a better choice. Furthermore, the pricing strategies of alliances may fluctuate based on the freight market conditions; for instance, rivalry among alliances may intensify during periods of elevated freight rates and diminish during periods of reduced freight rates. The quantile method enables the identification of distributional disparities.

To address gaps in the literature—specifically the limited understanding of how non-alliance capacity affects freight rates across different market conditions, the neglect of distributional heterogeneity in previous models, and the absence of causality testing between market structure and pricing—this study seeks to answer the following research questions:

• How does the share of non-alliance carriers influence container freight rates along the Asia–North America West Coast route under varying market conditions?
• To what extent do cost-related and demand-side factors interact with market structure to shape freight rate behavior across different quantiles?

The findings indicate that the influence of the independent variables on the dependent variable varies across quantiles. The impact of the non-alliance share on freight rates is notably significant and negative, ranging from the first quantile to the median quantile. Additionally, the effect becomes smaller, meaning that having fewer alliances in the low-freight market helps increase competition and lowers freight rates. Under elevated freight conditions, the ratio of non-alliance carriers and fluctuations in the stock market do not significantly influence freight rates. Only the bunker price exhibits a substantial positive influence at two quantiles. This evidence indicates that the primary price determinants in the market prioritize cost exclusively under high freight conditions, while independent carriers adhere to alliance pricing and eschew competition. This study is, to the authors’ knowledge, the first to elucidate the impact of market concentration on freight by considering its distribution features. Understanding the dynamics of the container transportation industry is beneficial, as it operates independently of market equilibrium regarding pricing determination. By shedding light on the effects of market concentration and strategic behavior in liner shipping, the study contributes to the promotion of more transparent, competitive, and sustainable freight systems aligned with global transport efficiency goals.

The remainder of this article is structured as follows: Section 2 presents the theoretical background and market context. Section 3 describes the data and methodology. Section 4 reports the empirical findings. Section 5 provides a discussion of the results in light of the existing literature. Section 6 concludes the study with key insights, policy implications, and suggestions for future research.

2. Market Concentration and Strategic Power in Liner Shipping

This section provides the theoretical and structural basis for understanding how alliances and market concentrations shape freight rate dynamics. These insights serve as a foundation for the following empirical analysis, particularly in interpreting the role of the non-alliance share and its impact across different market conditions.

Liner transportation has not always fostered a very competitive environment. In the 1870s, as steamships supplanted sailing vessels, liner operators engaged in negotiations to circumvent unprofitable competition [12]. This agreement, referred to as a conference system, encompasses decisions pertaining to a specific common price and designated capacity on the established routes. Consequently, they sought to conduct lucrative shipping operations under their established parameters, rather than incurring losses and inflicting financial harm on one another by excessively lowering prices or augmenting supply. They asserted that coordination will improve due to the conferences, leading to enhanced capacity utilization and a reduction in freight charges. Furthermore, by maintaining a balanced trade flow, the availability of capacity and minimal freight volatility would be guaranteed [13].

Participants in the conference may identify and penalize those who secretly lower prices to boost business. The competition authorities permitted their existence for a period, despite ongoing objections from cargo owners regarding the conference’s pricing determination. The authorities believed that permitting them to refrain from price competition would lead to investments in newer, higher-quality boats, thereby enhancing capacity and service quality. Nonetheless, subsequent apprehensions arose regarding the conference system. Conference members excessively increase freight rates, exhibit insensitivity to cargo service due to a lack of competition among themselves, larger volume carriers are denied the advantage of reduced freight rates, and non-member shipowners are barred from competing. The conference system was progressively prohibited following the 2000s. The most recent significant conference concluded in 2018. Alliances for global liner shipping are acceptable as long as there is no collusion over freight rates [14].

Liner shipping is characterized as a monopolistic or oligopolistic market in the short term, influenced by elements such as geography, route, and country, while it evolves into a competitive market in the long term, as elucidated by different reasons [15]. Liner shipping possesses comparatively elevated entry and exit barriers. Proficient technical, commercial, and financial competencies are essential. Moreover, container vessels are comparatively more costly than other categories of ships, including dry bulk carriers and crude oil tankers. Liner shipping services may differ from other transport modes, but the sector’s main role is product transport. Service diversifications may include service speed, service frequency, the number of ports visited, and various distribution opportunities. Third, there is a limited number of companies offering services, particularly on certain routes. This indicates that the service provision is limited in quantity. Companies operating on certain routes may form alliances to reduce costs, leading to reduced competition and a diminished supply of services on that route. In summary, major entities in the liner market act as price setters, while smaller entities function as price followers [14]. Nevertheless, acknowledging that price wars and detrimental rivalry among liner businesses adversely impact the stability of international trade, these partnerships are permitted, despite resembling cartelization. This type of arrangement is purportedly the most efficacious organizational paradigm for international trade [16].

The present level of rivalry in container transportation, as measured by the Herfindahl–Hirschman Index (HHI), yields a value of 1021 when the market shares of the top 80 container businesses [2] are utilized. When treating each alliance as an individual entity, the calculated value is 2407. Antitrust rules stipulate that a score below 1500 signifies a competitive environment, a value between 1500 and 2500 denotes moderate concentration, and a value beyond 2500 implies significant concentration [17]. The score of 2407 suggests a scenario approaching high concentration. Certainly, with sufficient data, route-based computations may achieve more accuracy.

Companies perceive certain benefits in maintaining their operations via strategic alliances. Ghorbani et al. [6] categorized these aspects in their study via a systematic literature review: financial, marketing, customer support, operational, tactical, strategic, and managerial. Two pertinent factors related to our subject are financial considerations, which can be assessed through economies of scale [18,19,20], economies of scope [21,22], and diminished capital expenditures resulting from reduced investments in equipment and vessels [23,24,25]. Marketing and customer support factors include offering more frequent transport services [26,27], broadening the transport network [19,20], and stabilizing freight rates [23]. Additional variables comprise diverse derivatives of the aforementioned sub-factors and the requisite background they necessitate.

Upon reaching a consensus, the partners typically establish an agreement for a specified duration. Nonetheless, instabilities and issues may occasionally emerge within the coalition. Ghorbani et al. [6] aggregated these elements from the literature in their research. These issues may stem from reasons including the partner’s attributes, the nature of the relationship with the partner, and the intricacy of the collaboration. Things like having too few partners [28], competition between partners [29], how much trust there is between them [30], how complicated the organizations are [21], costs of working together [31], and changes in shipping prices [29] can weaken the alliance’s stability. Such elements can also be pivotal in the existence of alliances. This circumstance is anticipated to influence freight rates by impacting market concentration and competitive levels. Multiple studies in the literature validate the significant impact of shipping alliances [32,33] and market concentration [34,35] on freight rates.

Although strategic alliances and market concentration are crucial factors, they do not entirely account for freight rates. Freight prices are affected by numerous factors, as indicated in the literature. These factors include service frequency [36], distance [37,38], connectivity [37,39,40], maximum vessel size [41], port infrastructure [39], trade deficits [34,39], market competition [39], port utilization [42], geopolitical risk [43,44,45], and oil price [46,47].

A notable differentiation of our study from analogous studies is the application of quantile regression analysis for model estimation. This approach was chosen for several technical advantages: (i) it is resilient to outliers, providing more dependable results amid extreme observations, (ii) it effectively addresses heteroscedasticity, (iii) it performs well even when variables diverge from a normal distribution, (iv) it captures relationships across various quantiles of the dependent variable, (v) it identifies asymmetrical relationships that may be missed by alternative methods, and (vi) it uncovers potential nonlinear patterns in the data. The benefits of quantile regression are especially pertinent to the liner shipping freight industry. Freight prices in this sector frequently experience substantial volatility, characterized by outliers and high price fluctuations resulting from varying demand, seasonal influences, and geopolitical occurrences. The resilience of quantile regression to outliers renders it an optimal instrument for elucidating these dynamics. Moreover, heteroscedasticity is a common problem in freight markets, characterized by increased rate variability during times of heightened demand or uncertainty, which quantile regression adeptly addresses. Due to the frequently non-normally distributed nature of freight rates and market situations, the adaptability of quantile regression in addressing non-normal data guarantees enhanced accuracy in estimations. This method enables a comprehensive analysis of the rate distribution, facilitating a nuanced knowledge of how market conditions influence freight rates at multiple tiers, hence uncovering asymmetries and nonlinear correlations prevalent in intricate global markets such as liner shipping.

3. Data and Methodology

The freight rate variable is China/East Asia to North America West Coast (USD/TEU) weekly data gathered from Freightos [48]. Bunker price is the Very Low Sulphur Fuel Oil (VLSFO) Global 20 Ports Average price (USD/Ton), which is obtained by taking weekly averages of daily prices from Ship & Bunker [49]. The Dow Jones Index (points) is one of the stock markets in the USA and the weekly data are gathered from Investing [50]. The index is considered a proxy variable for the economic situation and the demand for maritime transport in the USA. Given the weekly frequency of the dataset used in this study, no publicly available direct trade volume indicators exist at the corresponding temporal resolution. Therefore, the Dow Jones Index was selected as a high-frequency proxy for economic demand conditions. This choice aligns with the need to match the frequency of explanatory variables to that of the dependent variable in time series models, ensuring consistency and avoiding interpolation biases that could arise from using lower-frequency indicators. The share of non-alliance carriers in the Asia–North America West Coast (%) data are gathered from Sea Intelligence [51]. This variable is included in the model to measure the market concentration, a higher ratio indicates a decrease, while a lower one indicates an increase in the concentration.

Table 1. Variable definitions.

Variable	Acronym	Description	Source
Freight Rate	FREIGHT	China/East Asia to North America West Coast ($/TEU)	Freightos
Non-Alliance Share	NON-AL	Share of container capacity operated outside shipping alliances (%)	Sea-Intelligence
Bunker Price	BUNKER	Very Low Sulphur Fuel Oil (VLSFO) Global 20 Ports Average price ($/Ton)	Ship & Bunker
Dow Jones Index	DJI	Dow Jones Industrial Average (index points)	Investing

presents a summary of the variables used in the empirical analysis, including their acronyms, descriptions, and data sources.

These data consist of the moving average value of 3-week values. Due to data constraints, the form could only be reached in this version. For this reason, 3-week moving average values of other variables were used in the analysis. The dataset covers the period between 12 July 2021 and 19 June 2023 and consists of 102 weekly observations. A longer period for the analyzers would have helped us obtain more valid results, but we had to limit our search to this range as we could not obtain more variables. This limitation arises primarily from constraints in the availability of public data, as comprehensive non-alliance share figures are only accessible for a limited period. While the main findings are robust across different quantiles, the limited sample size should be considered when interpreting the results. Future studies may benefit from extending the observation period as additional data becomes available.

This study primarily investigates the relationship between market concentration, measured by the non-alliance share of carriers on the Asia–North America West Coast route, and container freight rates. Based on the theoretical framework and empirical patterns observed in the liner shipping industry, we propose the following hypothesis:

H1: 

An increase in the non-alliance share is associated with a decrease in container freight rates, reflecting greater competition on the trade route.

To accurately estimate this relationship, bunker prices and macroeconomic demand conditions (proxied by the Dow Jones Index) are included as control variables in the model. While these factors are expected to influence freight rates positively, they are not the central focus of hypothesis testing in this study.

Our model is designed as presented in Equation (1):

Freight Rate = f (Concentration, Bunker Price, Demand)

(1)

Figure 1 illustrates the trajectory of the series comprising 3-week moving averages over time. Container freight charges surged to unprecedented levels in 2021 following the COVID-19 pandemic. The factors contributing to this situation include the empty container crisis resulting from a supply-demand imbalance due to closures and restrictions, a reduction in ship voyages due to declining demand, disruptions in the global supply chain, the closure of the Suez Canal, escalating fuel prices, port congestion [52], and an increase in online shopping driven by extended time spent at home [53]. The elevated freight trend persisted until mid-2022, after which it reverted to pre-COVID-19 levels. Conversely, ship owners perceived the surge in freight as a significant opportunity for capital accumulation, resulting in an unprecedented container ship order volume of 1.8 million TEU in the first quarter of 2021 [54].

Figure 1 additionally presents a graph illustrating the proportion of the container fleet in the Pacific Ocean transporting goods from Asia to the North American West Coast that is not part of the alliance. In 2023, associated enterprises utilized only a portion of their resources for alliances, with the overall fleet of global alliances representing 82.4% [2], while the total allied resources accounted for 39% [1]. Alliances may vary based on contract year, nation, route, and port. The non-alliance rate in the Pacific varies from 8.2% to 19.5%, peaking during periods of elevated freight rates and then declining to lower levels in recent times, specifically when freight costs were significantly reduced. In other words, elevated freight costs enabled non-allied vessels to secure goods from the market. The prevalence of alliances has intensified in response to low freight rates, attributable to their cost benefits derived from economies of scale. A bidirectional relationship between the alliance rate and freight charges can be anticipated. Our analysis posits that an increase in the prevalence of non-alliance carriers will result in a decline in freight rates, as this indicates a partial enhancement of competition on the route and a subsequent reduction in prices. Conversely, the rise in the alliance’s tonnage is anticipated to lead to a heightened market concentration and diminished competition, resulting in an estimated increase in freight costs [55].

Bunker prices are significantly influenced by fluctuations in oil prices due to their tight correlation. Notable disparities in bunker pricing can be seen from one port to another [56]. There exists a substantial positive correlation of 0.91 between them within the specified period. The economic collapse resulting from COVID-19 in 2021 led to an excess of oil, causing the prices to decline. Beginning in 2022, the economic recovery commenced, leading to a resurgence in oil consumption, which subsequently resulted in an escalation of oil prices. Furthermore, Russia’s incursion into Ukraine generated volatility in the oil market, as Russia is a significant global oil supplier, resulting in price surges [57]. This conflict has interrupted the worldwide oil supply network [58]. Consequently, global ship bunker prices have risen. In 2023, oil prices fell below $80 due to macroeconomic concerns and restrictive monetary measures in response to rising inflation.

The influence of the bunker price on the freight rate, incorporated as a control variable in our model, is anticipated to be positive. The impact of bunker prices on total voyage costs fluctuates based on the ship’s age, voyage distance, machinery size, speed, and average bunker prices, potentially comprising 20% to 75% of total voyage costs [59]. The alteration in bunker prices positively influences the total journey costs and, consequently, freight rates. Nonetheless, this position may vary based on market demand and the degree of competition. Excessive demand for transportation or a monopolistic/oligopolistic market structure on the route may lead to an increase in freight rates, irrespective of bunker costs [60].

Stock market indexes are widely regarded as indicators of the economic conditions of nations [61,62]. This attribute allows them to serve as an indication of the demand for maritime transport [63,64], characterized by a derived demand structure [65]. Stock markets respond based on anticipated future conditions rather than the present circumstances [66]. Investors make decisions based on factors such as economic growth, the industrial output index, inflation, and national unemployment rates. Furthermore, investor mood, influenced by both macroeconomic indicators and global variables, is another significant determinant of stock market fluctuation. The interconnectedness of stock markets across time means that events in the global arena, particularly in major nations, influence local stock markets [67,68]. Economic developments, geopolitical events, trade regulations, and money movements across different global areas can influence stock markets independently of local economic conditions [69]. Figure 1 illustrates that the Dow Jones Index serves as a barometer for the economic condition in the USA, given its strong correlation with macroeconomic factors [70]. Furthermore, given that the USA is the world’s largest economy, the inverse correlation between stock market conditions and worldwide oil prices is distinctly observable. A notable negative connection of −0.40 exists between the WTI oil price and the DJI. Rising oil prices create inflationary pressure in countries, perhaps leading to anticipation of interest rate hikes, which may diminish demand for stock market instruments and subsequently result in a decline in the entire stock index.

The influence of the stock market index on freight, incorporated as a control variable in our research, is anticipated to be positive. Enhanced economic activities and optimistic future projections will lead to an escalation in the stock market. This condition will positively impact output and overseas trade, hence increasing the demand for maritime transport. Despite the supply–demand equilibrium in container shipping not being fully aligned with market conditions, it is anticipated that the rising demand will positively influence freight prices [63,64].

Table 2. Descriptive statistics.

	Bunker	DJI	Freight	Non-AL	Δ Ln Bunker	Δ Ln DJI	Δ Ln Freight
Mean	718.4	33,621.1	9042.0	0.133	0.0005	−0.0002	−0.0184
Median	661.6	33,763.9	8901.9	0.136	−0.0017	0.0005	−0.0141
Maximum	1096.7	36,173.5	19,967.9	0.195	0.1004	0.0388	0.2139
Minimum	530.3	29,206	1004.7	0.082	−0.0511	−0.0376	−0.2179
Std. Dev.	150.8	1561.7	6672.6	0.026	0.0246	0.0129	0.0691
Skewness	0.911	−0.691	0.056	−0.021	0.731	0.014	0.741
Kurtosis	2.76	3.20	1.33	2.18	4.57	3.62	5.79
Jarque–Bera	14.3	8.29	11.8	2.84	19.4	1.65	42.1
Prob.	0.00	0.01	0.00	0.24	0.00	0.43	0.00
Obs.	102	102	102	102	101	101	101

Source: Freightos [52]; Investing [54]; Sea-Intelligence [55]; Ship & Bunker [53].

presents the descriptive statistics of the variables, encompassing both the raw data and their logarithmic return form. The raw data statistics pertain to the moving averages of their 3-week values, since the non-alliance data are structured to ensure that other variables are similarly changed for data alignment. Logarithms of all data, excluding non-alliance data, were utilized in the analysis. Given that the non-alliance data are expressed as a percentage rate, utilizing their raw form was deemed appropriate. The table includes log return variables derived from the results of the unit root test. Due to the presence of unit roots in the Bunker, DJI, and Freight variables, first differences were employed in the regression analysis.

Due to the data being weekly and representing the 3-week moving average values, the weekly average return figures are rather modest, as moving averages diminish volatility. Conversely, upon analyzing the variability of the raw data (standard deviation/mean), the stabilities are as follows: DJI (5%), non-Alliance (20%), Bunker (21%), and Freight (74%). Although the DJI variable remains relatively consistent, freight exhibits significant variability and poses considerable risks for both shipowners and shippers. Moreover, variables in non-alliance data exhibit a non-normal distribution in the raw series. In the return series, DJI returns exhibit a normal distribution, however Bunker and Freight returns do not follow a normal distribution. The histograms depicting the distributions of the variables are given in Appendix A. The examination of the Bunker and Freight variables reveals significant tail effects, indicating that approaches based on normal assumptions may be inadequate. Diverse outcomes may be achieved for various quantiles when the freight variable is employed as the dependent variable. Consequently, we choose to employ quantile regression analysis for our model estimation rather than OLS regression analysis.

Quantile regression analysis [71] is a technique employed to assess the association between one or more independent variables and various quantiles of a dependent variable. This method yields more thorough results than conventional linear regression analysis by elucidating how various points in the distribution of the dependent variable react to the independent factors. Furthermore, due to its resilience to outlier observations and non-normality within the dataset, its assumptions are less rigorous than those of conventional regression analysis [72].

Linear regression analysis estimates the variation in conditional mean, whereas quantile regression analysis calculates the variation in conditional quantile. If the distribution of the dependent variable in the study is non-normal and heteroscedastic, conditional mean models will fail to accurately represent the variations [73]. Quantile regression facilitates a deeper comprehension of financial markets. In contrast to linear regression, it elucidates volatility by addressing the extreme values within the quantiles rather than solely focusing on the mean prices. Consequently, it enables the analysis of extreme events such as market bubbles and breakdowns [72]. Quantile regression (QR) has been increasingly adopted in maritime and transport-related studies to explore distributional effects beyond mean estimates provided by traditional OLS models. Unlike OLS, which focuses solely on the conditional mean of the dependent variable, QR estimates the relationship across different points of the conditional distribution, making it particularly suitable for skewed and heteroscedastic data. In the context of maritime transportation, QR has been applied to assess factors influencing port disruption spillovers [74], the effects of oil price uncertainty on freight indices [75], safe ship maneuvering based on AIS trajectory data [76], and CO₂ emissions across transport sectors [77,78]. These studies demonstrate that QR enables a more nuanced understanding of how explanatory variables affect outcomes under varying market or operational conditions, which is essential in dynamic environments like shipping and port logistics.

When variables X and Y are estimated by standard regression, $\widehat{\alpha }+\widehat{\beta }X$ equation is estimated for the conditional mean of Y. Thus, inferences can be made from the model by interpreting the coefficients and their significance. In quantile regression, the distribution of the dependent variable is involved, and the conditional quantile of Y is estimated. The equation estimated with the quantile becomes ${\widehat{\alpha }}_q+{\widehat{\beta }}_{q}X$. Here, the coefficients for each q are estimated as ${\widehat{\alpha }}_q$ and ${\widehat{\beta }}_q$. Since q takes values between 0 and 1, a wide range of information is obtained about the conditional distribution of Y [79]. Theoretically, quantile regression can be presented mathematically as in Equation (2). Separate constants (${\widehat{\alpha }}_q$) and coefficients (${\widehat{\beta }}_q$) for the independent variable are estimated in each quantile.

$${\widehat{Y}}_t={\widehat{\alpha }}_q+{\widehat{\beta }}_{q1}X$$

(2)

The model we estimated is presented in Equation (3). The equation generated as freight is a dependent variable, while the non-alliance rate, bunker price, and DJI are independent variables. In the model we estimated, we chose 10 as the quantile number (q) and applied our estimation. Thus, nine coefficients were obtained for each constant and independent variable.

$${Freight}_t={\widehat{\alpha }}_q+{\widehat{\beta }}_{q1}NonAlliance+{\widehat{\beta }}_{q2}Bunker+{\widehat{\beta }}_{q3}DJI$$

(3)

To address the possibility of a bidirectional causal relationship between non-alliance shares and freight rates, a Granger [80] causality test was conducted as a robustness check. While the primary analysis investigates the effect of non-alliance share on freight rates, it is also plausible that changes in freight rates may influence the non-alliance market share by attracting or discouraging non-allied capacity. To examine this, we performed Granger causality tests between the two variables. This robustness check enhances the reliability of the study by considering potential reverse causality effects.

Depending on the estimation results, the relationship between the variables may exhibit no causality, unidirectional causality, or bidirectional causality. A simple Vector Autoregression (VAR) model involving our two variables with a lag order of one can be illustrated as shown in Equations (4) and (5).

$${Freight}_t={\beta }_{10}+{\beta }_{11}{Freight}_{t-1}+{\propto }_{11}{NonAlliance}_{t-1}+u_{1t}$$

(4)

$${NonAlliance}_t={\beta }_{20}+{\beta }_{21}{NonAlliance}_{t-1}+{\propto }_{21}{Freight}_{t-1}+u_{2t}$$

(5)

4. Results

Unit root analysis is essential, although its significance fluctuates depending on the approach employed in the time series analysis. If the mean, variance, and other distribution properties of the series fluctuate with time, indicating the presence of a unit root, this diminishes the dependability of the conclusions produced. The present values of series exhibiting unit roots demonstrate dependency on their historical values, hence violating the concept of independence among observations. Making predictions with such a series is challenging due to the temporal variability of their mean and variance, as well as the shocks they endure. Consequently, unit root analysis must be conducted, and the series should be transformed as warranted by the findings.

Accordingly, we conducted augmented Dickey–Fuller (ADF) [81] and Phillips–Perron (PP) [82] unit root analyses by converting our data, excluding non-alliance share, into logarithmic forms, with the results displayed in

Table 3. Unit root test results.

Test	Variable	Level		First Difference		Conclusion
		Intercept	Intercept and Trend	Intercept	Intercept and Trend
ADF	BUNKER	−1.84	−1.67	−2.93 **	−3.22 *	I (1)
	DJI	−3.21 **	−3.57 **	−6.04 ***	−6.10 ***	I (0)
	FREIGHT	−0.23	−1.56	−5.49 **	−5.41 *	I (1)
	NON-AL	−1.33	−1.38	−4.30 ***	−4.27	I (1)
PP	BUNKER	−1.35	−1.05	−3.35 **	−3.47 **	I (1)
	DJI	−2.03	−2.10	−3.87 ***	−3.66 **	I (1)
	FREIGHT	0.10	−2.96	−3.37 **	−3.32 *	I (1)
	NON-AL	−2.95 **	−3.22 *	−17.75 ***	−26.21 ***	I (0)

Notes: (1) CVs for ADF and PP are −3.49 for *** 1%, −2.89 for ** 5%, −2.58 for * 10% at intercept; −4.05 for *** 1%, −3.45 for ** 5%, −3.15 for * 10% at trend and intercept. (2) Schwarz Information Criteria was used in the selection of lag length in ADF. (3) Barlett kernel spectral estimation and Newey-West Bandwidth methods were used in PP.

. Logarithmic forms offer superior distribution characteristics and facilitate the transition from discrete series to continuous forms. As the non-alliance share variable is already expressed as a percentage, we utilized it in its raw form to avoid complicating the interpretation. Both approaches’ null hypotheses examine the presence of a unit root. The PP approach is based on the ADF test and exhibits enhanced resilience to autocorrelation and heteroscedasticity in error terms. Upon examining the correlograms of the variables across 36 lags, a persistent substantial autocorrelation was noted at all delays. The series observations are not independent of previous values, making the application of the PP test perhaps more appropriate. The outcomes of both tests are identical, with the exception of the DJI and non-alliance variables, and indicate that the Bunker and Freight variables possess unit roots. For DJI, ADF signifies stationarity, whereas PP denotes the presence of a unit root. ADF suggests a unit root for non-alliance share, but PP shows stationarity. Given the presence of autocorrelations in all variables and the PP test’s superior resilience to autocorrelation and heteroscedasticity, its results were utilized as the foundation for subsequent investigation. All variables, with the exception of non-alliance share, exhibit a unit root, necessitating the use of their first differences in regression analysis. The conclusion derived from the stationarity of the non-Alliance share indicates that, despite fluctuations within a specific range, its mean and variance remain constant over the long term. The impacts of the shocks to which it is subjected are not enduring.

Following the unit root test outcomes, we computed the first differences in the logarithmic values of the bunker, DJI, and freight variables for the regression analysis. Figure 2 illustrates the distribution of freight values in log return form, our dependent variable, categorized by quantiles. Figure 2 indicates that the minimum value was −0.2179 and the maximum value was 0.2139. The values depicted in the figure are distributed between these two extremes. The region preceding quantile 0.1 comprises exceedingly low values, and the region following quantile 0.9 has exceedingly high ones. These two extremes both exhibit tail effects in the distribution.

To enhance the findings and substantiate the application of quantile regression, we initially estimated the regression equation using the linear OLS approach and displayed the results in

Table 4. OLS regression estimation results.

Variable	Coefficient	Std. Error	t-Statistic	Prob.
Δ Ln BUNKER	0.305892	0.306192	0.999019	0.3203
Δ Ln DJI	1.256307	0.461131	2.724405	0.0076
NONAL	−0.610369	0.343984	−1.774412	0.0791
C	0.063530	0.045102	1.408573	0.1622
R-squared	0.1335	Wald F statistic		4.0904
Adjusted R-squared	0.1067	Prob (Wald F stat.)		0.0088

Notes: (1) White heteroscedasticity test was applied to residuals and null of homoscedasticity was accepted. (2) Q-stat autocorrelation test was applied to residuals and null of no-autocorrelation was rejected. (3) Jarque–Bera normality test was applied to residuals and null of normality was rejected. (4) The model was re-estimated using the HAC covariance method to overcome autocorrelation problems.

. Our investigation of the model’s residuals revealed homoscedasticity, the presence of autocorrelation, and a deviation from normal distribution. Consequently, we implemented HAC correction to rectify the standard mistakes. The end results indicate that the model is substantial; the influence of bunker price is positive yet inconsequential, the effect of the stock market is both positive and significant, and the effect of non-alliance share is significant and negative. A 1% rise in the stock market results in a 1.25% increase in freight charges. The reaction of freight rates to stock market gains exceeds the stock market’s fluctuations, indicating a somewhat elastic relationship. A 1-point (%1) rise in non-alliance shares results in a 0.61% decrease in freight rates. Given the distinct distribution features of the variables and the residuals of the linear regression, it was determined that quantile regression would be more suitable.

The model estimated for the quantile regression is delineated in Equation (3). We initially estimated the model for the 0.5 quantile and provide the findings in

Table 5. Quantile regression estimation results.

Variable	Coefficient	Std. Error	t-Statistic	Prob.
Δ Ln BUNKER	0.325575	0.224033	1.453243	0.1494
Δ Ln DJI	1.048870	0.486801	2.154620	0.0337
NONAL	−0.292467	0.278283	−1.050969	0.2959
C	0.011843	0.034795	0.340375	0.7343
Pseudo R-squared	0.083160	Quasi-LR statistic		12.78826
Adjusted R-squared	0.054804	Prob (Quasi-LR stat)		0.005118

Notes: (1) The bootstrap procedure was implemented in EViews 12 using the XY-pair method with a Knuth random number generator and 1000 iterations. (2) Kernel and Hall-Sheater methods were used for Sparsity Estimation. (3) Rankit Quantile Method and Epanechnikov Kernel Method were used. (4) Initial value for the quantile to estimate was chosen as 0.5.

. The model is significant, at the 99% confidence level, based on Quasi-LR statistics. Of the variables, only the stock market index is substantial and exerts a positive influence on freight. The subsequent step involves examining the variation in coefficients over the specified quantile, as a relationship that lacks significance at 0.5 may exhibit significance in other segments of the dependent variable’s distribution.

Quantile regression estimation was conducted for 10 quantiles, and the resulting coefficients are displayed in

Table 6. Quantile process estimates.

	Quantile	Coefficient	Std. Error	t-Statistic	Prob.
Δ Ln BUNKER	0.100	0.277541	0.364157	0.762146	0.4478
	0.200	0.126175	0.278601	0.452889	0.6516
	0.300	0.079503	0.239255	0.332296	0.7404
	0.400	0.312075	0.181939	1.715278	0.0895
	0.500	0.325575	0.213659	1.523803	0.1308
	0.600	0.686988	0.252282	2.723096	0.0077
	0.700	0.560836	0.253038	2.216408	0.0290
	0.800	0.620955	0.416096	1.492336	0.1389
	0.900	−0.384328	0.946289	−0.406143	0.6855
Δ Ln DJI	0.100	1.353848	0.552149	2.451962	0.0160
	0.200	1.123021	0.535623	2.096661	0.0386
	0.300	1.385202	0.476628	2.906255	0.0045
	0.400	1.412222	0.396921	3.557939	0.0006
	0.500	1.048870	0.478998	2.189718	0.0309
	0.600	0.590009	0.467111	1.263103	0.2096
	0.700	0.404830	0.438208	0.923830	0.3579
	0.800	0.566824	0.765138	0.740813	0.4606
	0.900	0.522450	2.261016	0.231069	0.8177
NONAL	0.100	−0.908362	0.269015	−3.376626	0.0011
	0.200	−0.949232	0.244097	−3.888754	0.0002
	0.300	−0.702172	0.268286	−2.617251	0.0103
	0.400	−0.475029	0.245858	−1.932129	0.0563
	0.500	−0.292467	0.265484	−1.101637	0.2733
	0.600	−0.056070	0.252867	−0.221738	0.8250
	0.700	−0.055082	0.200712	−0.274431	0.7843
	0.800	−0.071209	0.310658	−0.229219	0.8192
	0.900	−0.466716	0.849972	−0.549096	0.5842
C	0.100	0.043045	0.033921	1.268956	0.2075
	0.200	0.064002	0.030327	2.110412	0.0374
	0.300	0.046918	0.032119	1.460746	0.1473
	0.400	0.027625	0.029796	0.927152	0.3561
	0.500	0.011843	0.031547	0.375417	0.7082
	0.600	−0.000790	0.030093	−0.026260	0.9791
	0.700	0.003404	0.025974	0.131066	0.8960
	0.800	0.019429	0.048794	0.398196	0.6914
	0.900	0.108490	0.141568	0.766347	0.4453

. Following standard practice in the applied quantile regression literature and considering the characteristics of the available dataset, 10 quantiles were selected for the analysis. This choice balances the need for detailed insight across different segments of the conditional distribution with the requirement to maintain statistical reliability, given the relatively limited number of weekly observations. By focusing on deciles, the study captures potential nonlinearities in the relationship between market concentration and freight rates across varying market conditions without compromising the robustness of the estimates. To assess the robustness of the quantile regression results, a bootstrap resampling procedure was conducted using the XY-pair method with 1000 replications. Given that there are 10 quantiles, nine coefficients are computed for each independent variable and the constant term. The results indicate that each independent variable significantly influences freight rates across various quantiles. A 1% variation in bunker price influences freight rates by 0.31% at the 0.4 quantile, 0.68% at the 0.6 quantile and 0.56% at the 0.7 quantile. The stock market index, conversely, substantially influences freight rates within the 0.1 to 0.5 quantiles. A 1% fluctuation in the stock market influences freight rates by 1.04% to 1.41%. This scenario typically aligns with periods when freight rates are likely to decline. The impact of the non-alliance rate on freight costs is large and negative within the 0.1 to 0.4 quantiles. A 1-point (%1) rise in non-alliance share affects freight rates by −0.47% to −0.94%. The impact coefficient diminishes as the quantile ascends. The effect is considerable when the propensity for freight to decline is significant, whereas it diminishes when the downward propensity is less pronounced. The fluctuating trajectory of the coefficients in relation to the distribution of the dependent variable is also illustrated visually in Appendix B. We employed the Wald slope equality test to ascertain if the coefficients exhibit significant differences across the quantiles of the distribution. The null hypothesis (non-Equality) is not rejected for 10 quantiles (Stat = 27.7, p = 0.27), while it is rejected for 4 quantiles (Stat = 11.7, p = 0.06). Despite the results from the test not aligning with the selected quantiles, they significantly bolster our assertion that the relationship between variables may fluctuate over various quantiles of the distribution.

To investigate the direction of the relationship between freight rates and the non-alliance share, and to enhance the robustness of the main regression results, a series of Granger causality tests were conducted. These tests assess the possibility of a bidirectional causal relationship between the two variables. The results, presented in

Table 7. Granger causality test results between freight rates and non-alliance share.

Null Hypothesis	Chi-Sq	df	Prob.
Non-alliance share does not Granger-cause freight rate	5.191	1	0.022
Freight rate does not Granger-cause non-alliance share	0.017	1	0.894
Non-alliance share does not Granger-cause freight rate	8.561	4	0.073
Freight rate does not Granger-cause non-alliance share	1.388	4	0.864
Non-alliance share does not Granger-cause freight rate	20.926	9	0.013
Freight rate does not Granger-cause non-alliance share	11.552	9	0.239

Notes: (1) Maximum lag for VAR equation was selected as 12 by using Schwert [83] rule. (2) Optimum lags offered are 1 by SC, 4 by HQ, and 9 by AIC.

, are based on optimal lag lengths selected using different information criteria (SC, HQ, and AIC). In all three cases, the null hypothesis of non-causality was rejected only in the direction from the non-alliance share to freight rates, indicating a unidirectional relationship and supporting the assumption of exogeneity in the model.

5. Discussion

The formation of alliances within the maritime shipping industry enables the creation of more extensive and efficient transport networks. By utilizing each other’s resources—such as ships, ports, and commercial and managerial expertise—alliance members can increase voyage frequencies, offer greater capacity, and ensure more reliable shipment timing. As a result, customer concerns about shipping schedules are alleviated. Furthermore, these alliances help significantly reduce unit transportation costs by spreading fixed expenses across a larger network and enabling economies of scale. However, while the formation of alliances brings economic benefits, it can also lead to an increase in freight rates. Typically, freight rates are determined through bargaining power between the ship owner and the cargo owner. As the concentration of alliances increases, the bargaining power of ship owners strengthens, allowing them to raise freight rates in their favor. Market concentration, which increases with stronger alliances, may shift the power dynamics, as noted by Shi and Voß [84]. Our research aimed to empirically assess how changes in the alliance concentration along the Asia to North American West Coast route affect freight rates, considering control variables such as bunker prices and stock market indices.

To estimate our research model, we adopted quantile regression analysis for several technical reasons. First, quantile regression is robust to outlier observations and heteroscedasticity, which are common in economic data. It also performs well when variables are not normally distributed and allows us to examine relationships at different points in the distribution of the dependent variable. This approach is particularly suitable for our study, as container freight rates are not solely determined by market forces, but can be influenced by monopolistic or oligopolistic conditions along specific trade routes. In our model, we included bunker price and demand variables as control factors. These variables undeniably impact freight rates, and excluding them would have undermined the validity of our results. We used the price average from 20 global ports as a proxy for bunker price, and the Dow Jones Index (DJI) as an indicator of maritime transport demand. Stock market trends reflect economic conditions and expectations, which in turn influence demand for maritime transport.

The key variable in our study is the non-alliance share in the Pacific region. We employed a specific market concentration measure tailored to a particular shipping route, offering a more precise analysis than the widely used Herfindahl–Hirschman Index (HHI). While the HHI assesses overall market concentration, it can oversimplify route-specific dynamics by aggregating data from larger markets. Our approach, focused on concentration at the route level, allows for deeper insights into competitive behavior and pricing power specific to the Asia to North American West Coast trade lane. Our unit root analysis revealed that only the non-alliance ratio is stationary, implying that its mean and variance remain stable over time, with fluctuations occurring within a certain range. In contrast, other variables displayed unit roots, indicating that they are subject to external shocks and cannot be reliably predicted using historical data [85]. Consequently, we used first differences for these variables in the regression analysis.

In initial linear regression estimations, we found that bunker prices had a positive but statistically insignificant effect, while stock market demand (DJI) had a positive and significant impact on freight rates. The non-alliance share was found to negatively and significantly influence freight rates. However, due to issues with non-normal residuals and autocorrelation, we re-estimated the model using quantile regression, which revealed varying effects across different quantiles of the freight distribution. Our quantile regression results showed that the impact of independent variables varies significantly across quantiles. Notably, the effect of the non-alliance share was most pronounced at the lower quantiles (0.1 to 0.4), where freight rates are lower. A 1% increase in the non-alliance share reduced freight rates by approximately 0.9%, suggesting that heightened competition among independent carriers puts downward pressure on freight rates. In periods when freight rates were relatively stagnant, changes in bunker prices were reflected in freight rates, but during periods of significant freight rate fluctuations, bunker price changes had little effect. This suggests that when competition is limited, ship owners tend to price based on demand rather than cost.

On the demand side, the stock market index (DJI) exhibited a positive impact on freight rates between the 0.1 and 0.5 quantiles, with a 1% increase in stock prices leading to a 1.04% to 1.41% rise in freight rates. This reflects the heightened demand associated with stronger economic activity, as rising stock markets signal positive future economic expectations. However, when freight rates were high, changes in the stock market had a diminished effect, as ship owners adjusted their prices to maximize profit rather than respond to demand fluctuations. The main variable, non-alliance share, consistently showed a negative impact on freight rates, with significant results between the 0.1 and 0.4 quantiles. This negative relationship suggests that a higher non-alliance share leads to lower freight rates. While this effect is not enormous, it is substantial enough to affect the competitiveness in the region. Specifically, a rise of 11.3 percentage points in the non-alliance share could reduce freight rates by up to 10%, assuming other variables remain constant.

Since the alliance fleet in the region has an average volume of 86.7%, independent carriers with an average of 13.3% cannot significantly affect the competition. It could be assumed that the independent carriers are not deliberately undercutting, as this could cause the alliance fleet to start a competitive war and wipe them out of the market. This situation can also be defined as destructive competition [86]. Or it may be moving the aggregate profit away from its maximum point, so they follow the prices of the strong alliances. In general, firms avoid destructive competition for various reasons. First, the excessive competition causes profit margins to fall. Second, constantly breaking prices can also damage brand value. Customers may perceive decreases in firms’ prices as a decrease in quality and may reduce demand. Third, the increased competition can force firms to do more promotions, advertisements, and campaigns, increasing costs. Finally, as a result of competition to increase market share, if all firms lower their prices, their market share will not change significantly. In this case, they will have the same market share with less profitability. In addition, the destructive competition can have consequences such as bankruptcies, merges, acquisitions, and voluntarily leaving the market [87]. Antitrust regulations must be strictly followed and enforced by authorities to protect cargo owners and final consumers from being overcharged, as price-cutting competition between alliances seems unlikely. The findings of this study are in line with the broader literature on liner shipping, which emphasizes the role of market concentration in shaping freight rate behavior. The observed negative relationship between the non-alliance share and freight rates, particularly under weak market conditions, aligns with earlier research suggesting that reduced competition enables dominant carriers to exert greater pricing power. Similarly, the asymmetric influence of cost and demand-side variables across different quantiles supports previous studies that highlight the varying sensitivity of freight rates to market fundamentals. Overall, the results confirm theoretical expectations from the literature and provide new evidence on how competitive structure interacts with freight pricing under different market conditions.

6. Conclusions

While alliances create efficiencies by reducing costs and increasing capacity, they also lead to market concentration, which strengthens the shipowners’ pricing power. The non-alliance share plays a crucial role in influencing freight rates, particularly in periods of low competition, and the stock market significantly affects demand-driven pricing. The empirical findings of this study highlight the negative effects of market concentration on freight rates, particularly during periods of weak market conditions. In light of these results, we propose several specific policy recommendations to enhance competition and improve freight market functioning. First, regulatory authorities could establish a minimum threshold for non-alliance capacity on strategic trade routes such as the Asia–North America corridor, in order to maintain a competitive balance and reduce pricing power concentration. Second, competition agencies and maritime regulators should implement regular monitoring systems to track the capacity shares of alliances and non-alliance carriers. This could be achieved through a collaborative framework involving port authorities and carriers, who would be required to report service deployment data on a monthly or quarterly basis. The aggregated data could be used to produce public transparency reports, enabling early detection of excessive concentration. Such measures would not only support a more competitive and resilient freight market, but also help policymakers respond proactively to emerging structural imbalances in global liner shipping.

Beyond statistical significance, the results of this study also carry substantial economic implications. For instance, the finding that a 1% increase in non-alliance share can lead to up to a 0.9% reduction in freight rates in certain quantiles suggests a meaningful competitive effect in price-sensitive market segments. Given the scale of container trade on routes such as Asia–North America, even marginal improvements in market structure can translate into significant cost savings for shippers and downstream industries. This effect is particularly relevant when considering the typically low price elasticity of demand in container shipping, where a small rate reduction can improve accessibility for marginal cargo flows or support trade recovery in weaker demand periods. Thus, encouraging non-allied participation not only enhances market competition but also contributes to greater pricing efficiency in global liner shipping. Although the R-squared value in the OLS model (0.1335) and the pseudo R-squared in the quantile regression (0.083) are relatively low, this is not uncommon in studies involving freight markets, where external shocks, unobserved variables, and market volatility can limit explanatory power. These values do not indicate poor model quality but rather reflect the complexity of the shipping industry, where pricing is influenced by numerous dynamic and often non-quantifiable factors. By promoting fair competition and transparency in freight pricing, the findings support broader sustainability goals in maritime logistics. Ensuring a balanced market structure contributes not only to economic efficiency but also to the long-term resilience and environmental responsibility of global shipping networks.

While our current study focuses on freight rate modeling via econometric methods, emerging research in the broader maritime domain—such as intelligent control systems that enhance vessel navigation efficiency under uncertain conditions [88] and advanced ship detection models leveraging deep learning for situational awareness and port operations [89]—illustrates the growing role of technological innovation in shaping sustainable and data-driven maritime transport strategies. These developments complement economic models by enhancing the operational foundation of modern liner shipping systems.

A limitation of the study is the relatively short sample period, which results from restricted public data availability regarding non-alliance shares. Although the dataset offers meaningful insights, the modest number of observations may limit the precision and generalizability of the quantile-specific estimates. Future research could address this limitation by extending the dataset. Also, further studies are needed to explore the dynamics of market concentration on other routes to develop a more comprehensive understanding of these market behaviors.