# Price discrimination between freight forwarders and carriers: Evidence from the container shipping industry

Pierre Cariou, Haiying Jia, François-Charles Wolff

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Pierre Cariou, Haiying Jia, François-Charles Wolff. Price discrimination between freight forwarders and carriers: Evidence from the container shipping industry. Transport Policy, 2025, 170, pp.1-11. 10.1016/j.tranpol.2025.05.005. hal-05242590

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# Price discrimination between freight forwarders and carriers: Evidence from the container shipping industry

Pierre Cariou<sup>a, ID</sup>, Haiying Jia<sup>b, * ID</sup>, François-Charles Wolff<sup>c, ID</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

**Keywords:**

Container shipping

Freight forwarder

Freight

Price discrimination

TEU

## ABSTRACT

Freight forwarders often serve as intermediaries in the container shipping industry, facilitating reservations and negotiating container freight rates between shippers and carriers. This study empirically investigates whether these freight forwarders experience price discrimination compared to shippers who engage in direct price negotiations with carriers. The analysis uses a unique dataset consisting of approximately 1.5 million real-world transactions from 2018 to 2023. The results show that, on average, freight forwarders incur a 5 % premium for short-term contracts but receive a 3 % discount for long-term contracts. Moreover, the premium was more pronounced during the COVID-19 pandemic, peaking at 18.1 % in 2021–2022. This finding is corroborated by a robust estimation that matches contracts negotiated by freight forwarders with comparable contracts negotiated directly by shippers.

## 1. Introduction

Container shipping is the workhorse of the world economy, transporting 50–60 % of the value of international trade (UNCTAD, 2024). The impact of disruptions caused by COVID-19 on international trade demand and port connectivity has highlighted the importance of container shipping, more than ever before (Notteboom et al., 2021). In this market, many transactions involve freight forwarders, who serve as intermediaries between sellers (carriers) and buyers (shippers) (Murphy and Daley, 1997; Wong et al., 2009).

The main functions of freight forwarders include consolidating individual shipments from shippers into larger quantities, securing cargo space, and negotiating prices. They also provide a full range of additional logistics services such as packaging, documentation, warehousing, and inland transportation (Song, 2021). Due to the high uncertainty and volatility in the industry, shipping companies often allocate a portion of their capacity to freight forwarders or shippers to provide some stability through long-term contracts (Wei et al., 2024). The balance between long-term and short-term contracts is influenced by political situations, natural disasters, and supply-demand relationships. These factors can induce severe price fluctuations and expose companies to sudden risks in the supply prices of shipping services

(Zhang and Liu, 2019).

The implications for shippers who choose freight forwarders instead of negotiating directly with carriers are ambiguous and have not been extensively studied. Freight forwarders, due to their ability to consolidate large volumes, can often secure more competitive freight rates than shippers who negotiate directly with carriers. However, carriers may discriminate against freight forwarders and prefer to negotiate directly with shippers, potentially as a means of increasing their profit margin.

Economic theory suggests that negotiations can lead to several types of price discrimination, including (1) first-degree price discrimination, where shippers may have different willingness to pay (List, 2009); (2) second-degree price discrimination, where different volumes shipped may lead to bulk or loyalty discounts (Verboven, 2002; Becchetti et al., 2020); and (3) third-degree price discrimination, where shippers exhibit different demand elasticities based on factors such as income or geographic location (Corniere et al., 2023). The absence of arbitrage opportunities increases the prevalence of these types of price discrimination in services such as transportation. This is because the service product cannot be stored and sold at different prices in different markets (Becchetti et al., 2020). Finally, sellers or service providers may raise prices for certain customers in order to enhance profitability.

This paper investigates the potential for price discrimination by

<footnote><sup>a</sup> Kedge Business School, Bordeaux, France</footnote>

<footnote><sup>b</sup> Norwegian School of Economics, Bergen, Norway</footnote>

<footnote><sup>c</sup> Nantes University, Nantes, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: pierre.cariou@kedgebs.com (P. Cariou), haiying.jia@nhh.no (H. Jia), francois.wolff@univ-nantes.fr (F.-C. Wolff).</footnote>
carriers against freight forwarders in liner shipping, and whether carriers' strategies towards freight forwarders change over time. To do so, we use a unique dataset of over 1.5 million container transactions from 2018 to 2023 and consider several aspects in the empirical analysis. First, we assume that price differences may vary with contract length (short-term versus long-term contracts) based on the theory that contract length can balance power between buyers and sellers (MacKay, 2022). Second, we consider that price differences may vary across markets due to trade imbalances and patterns (Gouvernal and Slack, 2012; Notteboom et al., 2021), and compare our results for the Far East-North Europe and for the Far East-US West Coast routes. Third, given the substantial increase in container shipping freight rates during the COVID-19 period, we explore the possibility that price discrimination has changed over time, and provide separate investigations for the pre-, during-, and post-COVID periods.

Our research makes several important contributions to the existing literature. First, we present a dataset of unparalleled depth and scope in the academic literature. This dataset was made possible by recent advances in the digitalization of the shipping industry, coupled with the generous cooperation of the data provider. Second, we analyze the data using comprehensive econometric modelling techniques that account for the fixed effects associated with contract duration, shipping routes, and temporal variation. Our model allows for a thorough examination, ensuring the validity of the findings and a comprehensive treatment of the research question. Third, our results provide important insights into the pricing strategies of carriers and the balance of power among shippers, carriers and freight forwarders. The implications are therefore relevant to a wide range of stakeholders.

The remainder of the paper is organized as follows. Section 2 reviews the relevant literature. Section 3 introduces the dataset, followed by the econometric strategy, which is presented in Section 4. The empirical results are analyzed in Section 5. Section 6 provides discussions and implications, followed by conclusions in Section 7.

## 2. Literature review

The container liner shipping networks are designed to facilitate shipments along regular routes with fixed schedules, utilizing large-capacity vessels. This system aims to provide reliable service (Sun et al., 2020) and take advantage of economies of scale (Cullinane and Khanna, 1999). To access this service, shippers may hire freight forwarders (Coyle et al., 2008).

As intermediaries between carriers and shippers, freight forwarders play a crucial role in many shipping routes (Wei et al., 2024). They generate profit by booking container slots from shipping companies and subsequently selling these slots to shippers (Wirjodirdjo et al., 2021). Pope and Thomchick (1985) were among the first to highlight the importance of freight forwarders in this market, suggesting that they provide transportation services to shippers by purchasing the services of existing carriers. The literature also refers to this profession as third-party logistics (Razzaque and Sheng, 1998) or logistics agents (Yang et al., 2010). Freight forwarders have the ability to provide shippers with efficient and reliable supply chain (Chu, 2014), which can translate into a competitive price advantage (Ben-Shahar and White, 2006). Freight forwarders typically represent smaller groups of customers and improve supply chain efficiency and reliability (Chu, 2014) through their coordination and freight consolidation functions.

Despite their importance, there has been limited research on the role of freight forwarders within the transportation system. Instead, some survey studies have explored the key characteristics that enterprises consider when choosing freight forwarders, such as expertise and

geographic deployment (Murphy and Daley, 1997; Perlman et al., 2009). Among the reasons for using freight forwarders, their ability to secure space and to negotiate prices are the two most important. Price (used interchangeably with freight rates in this paper<fnref n="1" />) has been identified as the most important criterion in relation to factors such as frequency of sailings, transit time, directness of sailings, reputation for reliability that influence shippers' choices (Brooks, 1990). This finding was confirmed in a series of studies conducted by Brooks (1984, 1985, 1990) on surveys of shippers' choices in selecting carriers.

The determinants of container freight rates are a widely studied area of research (see among others Luo et al., 2009; Gouvernal and Slack, 2012; Nielsen et al., 2014; Hirata, 2017; Munim and Schramm, 2017; Yin and Shi, 2018). Freight rates have been analyzed using either univariate models (Munim and Schramm, 2017), multivariate models (Luo et al., 2019), or more recently, machine learning algorithms (Saeed et al., 2023). However, most research in freight rate modeling uses aggregate prices, either average rates by route (Saeed et al., 2023) or market indices. To date, price heterogeneity has not been adequately addressed in the literature.

Gouvernal and Slack (2012) point out that container freight rate quotations are very complex and can vary from customer to customer, even for the same route and service. The oligopolistic market structure associated with container shipping would influence price levels (Cariou, 2008; Sys, 2009) due to the high concentration of market share, which is often achieved through strategic alliances (for a comprehensive review, see Ghorbani et al., 2022). As of 2023, more than 80% of the container shipping market is operated by the top three shipping alliances (Nerja and Sánchez, 2023). Price dispersion would depend on the degree of competition on a given route (Ardelan and Lugovkyy, 2019, 2023) and on the intensity of competition (Hummels et al., 2009; De Oliveira, 2014). Political elements also come into play, such as the recent move of the European Commission (EC) to limit the antitrust block exemption for liner shipping in April 2024 (EC, 2023), which led to the dissolution of the 2M alliance between MSC and Maersk.

Pricing by freight forwarders would tend to stimulate or suppress demand by adjusting prices according to market conditions (Xu et al., 2014). During the shipping off-season, the freight forwarder will lower the price of container slots to obtain more goods. During the peak shipping season, the freight forwarder should take the initiative to raise the price as long as it can book the container slot. If there is a lack of demand information, freight forwarder could also respond conservatively and reduce the price of container slots.

As global supply chains have recently faced widespread disruptions (Sun and Zhang, 2022; Arvis et al., 2024), one of the most immediate and noticeable effects was the COVID-19 pandemic, which led to severe port congestion and delays. Notteboom et al. (2021) point out that COVID-19 caused major disruptions in port operations due to health protocols, workforce shortages, and changes in shipping schedules. Nonetheless, there remains a need for a more comprehensive understanding of the full scope of disruptions in the container shipping sector and how they have affected the relationships between carriers, shippers, and freight forwarders.

Our research examines the factors that determine container freight rates at the transaction level. Contractual prices between carriers and consignees (which include shippers and freight forwarders) reflect the comprehensive information exchanged during price negotiations. Our rationale is that, given the potential for large variations in container prices, both between buyers and over time, the use of transaction data is paramount to understanding the pricing mechanism in the container shipping market. Therefore, we investigate the following three main hypotheses.

<footnote n="1">¹ Container freight rates are quoted in USD per container, which can be measured in TEUs (twenty-foot equivalent units) or FEUs (forty-foot equivalent units).</footnote>
**H1.** Freight forwarders face price discrimination from carriers, which is likely to be more pronounced for short-term contracts than for long-term contracts.

**H2.** Price discrimination is more pronounced in tight market conditions, such as those during the COVID-induced price hikes.

**H3.** The degree of price discrimination varies across routes due to different market conditions.

### 3. Data and descriptive statistics

The data used in this study consists of container freight contracts. The data was obtained through a signed agreement with a leading company (hereafter “The Co.”) that provides global benchmarks for ocean and air freight rates. Unlike studies that typically rely on aggregate container indices, this research uses individual contract information. This approach allows for the estimation of price equations that control for both observed and unobserved heterogeneity at a very granular level.

The period examined spans six years, from January 2018 to December 2023. Due to data limitations, we had access to only two major trade lanes: Far East to North Europe (FE-NE) and Far East to US West Coast (FE-USWC). In 2022, global container trade volumes (UNCTAD, 2024) were estimated at 23.8 million TEUs from the Far East to North America and 15.6 million TEUs from the Far East to Europe. These trade lanes ranked 2nd and 3rd in the world, behind container trade within Asia (42.1 million TEUs), but well above the flows from the Far East to Latin America (6.7 million TEUs), from Europe to the Far East (4.9 million TEUs) or from Europe to North America (4.6 million TEUs). Container traffic from Asia to North Europe and the US West Coast is related to the dominant position of East Asia as a global manufacturing powerhouse. This high production capacity requires shipping routes to deliver products to European and North American consumers, who have a high demand for imported goods.

The database contains information on shipper and carrier identification numbers, freight rates or transportation prices in USD per TEU, shipment dates, contract durations, and origin and destination ports. The key feature is the distinction between two types of buyers, freight forwarders and shippers. Following the classification used by the data

provider, we have distinguished between short-term contracts, defined as those with a duration of 31 days or less, and long-term contracts, defined as those with a duration of 88 days or more. Contracts between 32 and 87 days are considered unusual by the data provider and the industry. They are not classified as either short-term or long-term and typically correspond to prolonged negotiations due to special events. These abnormal intermediate contracts, which represent only 3 % of the contracts in the sample, have been removed. In addition, for each combination of trade lane category (FE-NE versus FE-USWC) and duration category (short-term versus long-term), the top and bottom 0.5 % of freight rates were excluded to mitigate the impact of potential outliers.

Table 1 provides a statistical description of freight rates and the number of contracts, categorized by trade lane, and divided into three periods: 2018–2020 (pre-COVID), 2021–2022 (during-COVID), and 2023 (post-COVID), and by contract type (short-term versus long-term). Although the COVID pandemic appeared in the first half of 2020, freight rates started to increase sharply in 2021; therefore, 2021 and 2022 are grouped together. The total number of contracts in our sample is 1 694 646. Most of them have a short-term duration, with 1 548 194 short-term contracts (91.4 %) and 146 452 long-term contracts (8.6 %).

Approximately two-thirds of the contracts (67.9 %) originate from Far East Asia and are destined for Northern Europe. This proportion is very similar for both short-term and long-term contracts, at 68.2 % and 67.8 %, respectively. For the FE-NE trade lane, the main origin ports include Shanghai (7.3 %), Ningbo (6.8 %), Yantian (6.7 %), Qingdao (6.4 %), and Hong Kong (6.4 %). The main destination ports are Rotterdam (20.6 %), Antwerp (20.1 %), Hamburg (19.8 %), and Le Havre (17.0 %). Notably, a higher proportion of long-term contracts originate from Shanghai, which accounts for 11.2 % of long-term contracts compared to 6.9 % of short-term contracts. In the FE-USWC trade lane, the top five origin ports are similar, but listed in a different order: Shanghai (9.4 %), Yantian (8.5 %), Ningbo (8.1 %), Hong Kong (7.4 %), Qingdao (7.2 %). There are only five destination ports in this lane: Los Angeles (24.9 %), Long Beach (23.6 %), Oakland (20.5 %), Seattle (18.3 %), and Tacoma (12.8 %). Los Angeles is notably overrepresented in long-term contracts, with 34.9 % compared to 24.0 % for short-term contracts.

In the sample, the vast majority of transactions are contracted by

<table><caption>**Table 1**
Pattern of average contract prices ($/TEU).</caption><thead><tr><th rowspan="2"></th><th colspan="4">Short-term contracts</th><th colspan="4">Long-term contracts</th></tr><tr><th>All</th><th>Shippers</th><th>Freight forwarders</th><th>Difference</th><th>All</th><th>Shippers</th><th>Freight forwarders</th><th>Difference</th></tr></thead><tbody><tr><td colspan="9"><strong>Panel A. Container average price (in US$): 2018–2023</strong></td></tr><tr><td>All routes</td><td>3224</td><td>4060</td><td>3195</td><td>-865</td><td>2834</td><td>2959</td><td>2703</td><td>-256</td></tr><tr><td>Far East Main → North Europe</td><td>3477</td><td>4777</td><td>3442</td><td>-1335</td><td>2877</td><td>3089</td><td>2713</td><td>-376</td></tr><tr><td>Far East Main → US West Coast</td><td>2691</td><td>3256</td><td>2661</td><td>-595</td><td>2742</td><td>2778</td><td>2667</td><td>-111</td></tr><tr><td>Number of contracts</td><td>1 548 194</td><td>52 675</td><td>1 495 519</td><td></td><td>146 452</td><td>74 927</td><td>71 525</td><td></td></tr><tr><td colspan="9"><strong>Panel B. Container average price (in US$): 2018–2020 prior-COVID</strong></td></tr><tr><td>All routes</td><td>1539</td><td>1564</td><td>1538</td><td>-26</td><td>1325</td><td>1424</td><td>1252</td><td>-172</td></tr><tr><td>Far East Main → North Europe</td><td>1483</td><td>1420</td><td>1483</td><td>63</td><td>1277</td><td>1430</td><td>1194</td><td>-236</td></tr><tr><td>Far East Main → US West Coast</td><td>1734</td><td>1673</td><td>1736</td><td>63</td><td>1451</td><td>1416</td><td>1506</td><td>90</td></tr><tr><td>Number of contracts</td><td>692 228</td><td>10 456</td><td>681 772</td><td></td><td>71 825</td><td>30 323</td><td>41 502</td><td></td></tr><tr><td colspan="9"><strong>Panel C. Container average price (in US$): 2021–2022 COVID</strong></td></tr><tr><td>All routes</td><td>7535</td><td>6887</td><td>7573</td><td>686</td><td>5015</td><td>4743</td><td>5352</td><td>609</td></tr><tr><td>Far East Main → North Europe</td><td>8631</td><td>7656</td><td>8682</td><td>1026</td><td>5216</td><td>4946</td><td>5464</td><td>518</td></tr><tr><td>Far East Main → US West Coast</td><td>5262</td><td>5724</td><td>5228</td><td>-496</td><td>4586</td><td>4451</td><td>4918</td><td>467</td></tr><tr><td>Number of contracts</td><td>444 651</td><td>24 514</td><td>420 137</td><td></td><td>55 713</td><td>30 794</td><td>24 919</td><td></td></tr><tr><td colspan="9"><strong>Panel D. Container average price (in US$) 2023 post-COVID</strong></td></tr><tr><td>All routes</td><td>1401</td><td>1621</td><td>1392</td><td>-229</td><td>2143</td><td>2354</td><td>1573</td><td>-781</td></tr><tr><td>Far East Main → North Europe</td><td>1250</td><td>1595</td><td>1236</td><td>-359</td><td>2352</td><td>2650</td><td>1519</td><td>-1131</td></tr><tr><td>Far East Main → US West Coast</td><td>1563</td><td>1646</td><td>1559</td><td>-87</td><td>1925</td><td>2039</td><td>1626</td><td>-413</td></tr><tr><td>Number of contracts</td><td>411 315</td><td>17 705</td><td>393 610</td><td></td><td>18 914</td><td>13 810</td><td>5104</td><td></td></tr></tbody></table>

Source: authors’ calculations, data on container contracts from The Co. (2018–2023).
freight forwarders, accounting for 92.5 %. This percentage is slightly higher in the FE-USWC trade lane than in the FE-NE trade lane (93.8 % against 89.7 %). There are large differences in the duration of contracts. While the majority of short-term transactions are contracted by freight forwarders (96.6 %), the subsample of long-term contracts is much more balanced between shippers (51.1 %) and freight forwarders (48.8 %), although the total number of contracts is more limited.

Table 1 provides a comparison of average freight rates by contract term, trade lane, and period. From 2018 to 2023, the average freight rate paid by freight forwarders is 21.3 % lower than the freight rate paid when shippers negotiate directly with carriers for short-terms contracts (3195 USD compared to 4060 USD). There is also a negative premium for long-term transactions contracted through freight forwarders, although the difference is less pronounced (−8.7 %, 2703 USD compared to 2959 USD). The magnitude of the price difference varies by trade lane; however, the advantage (expressed as a negative variation) associated with freight forwarders remains consistent: −27.9 % in FE-NE compared to −18.3 % in FE-USWC for short-term contracts, and −12.2 % in FE-NE compared to −4.0 % in FE-USWC for long-term contracts.

Fig. 1 shows the pattern of transactions contracted with either freight forwarders or shippers over time. We notice a decrease in short-term contracts in 2020 and 2021, while the opposite pattern is found for long-term contracts. The situation has totally reversed since then, with a huge increase in short-term contracts in 2023. As we will see later, these changes are closely related to the level of freight rates before, during, and after the COVID. The high representation of freight forwarders in short-term contracts is consistent with the view that these operators offer a competitive advantage to shippers when there is a need to import or export containerized cargos with short notice, and usually for a small number of containers.

Freight forwarders typically serve SMEs that do not have sufficient cargo volumes to secure longer contracts with carriers. In such a situation, the expertise of freight forwarders, whose core business is the provision of transportation services, explains their competitive advantage in short-term contracts. Conversely, the number of long-term contracts is almost the same for both freight forwarders and shippers. These contracts are subject to a long-term tendering process which is set by shippers and are subject to negotiations with carriers. In this situation, the volume and the time available for negotiation means that it may

make sense for shippers and carriers to enter a direct negotiation, without the intermediary of freight forwarders.

Fig. 2 illustrates the monthly average prices by trade lane. It shows the huge increase in container freight rates as a result of the COVID crisis. Freight rates multiplied by more than 5 between the beginning of 2020 and the end of 2021, peaking at 12 500 USD for short-term FE-NE contracts (lower values are found during the pandemic for long-term contracts).

Several interrelated factors explain the surge in container freight rates observed during the COVID-19 pandemic. The pandemic caused widespread operational challenges, particularly for imports from Northeast Asia. The first factor is the imbalance between supply and demand. In early 2020, maritime container imports declined due to the spread of the pandemic. However, as lockdown measures ended and consumer demand rebounded, imports sharply increased, outpacing available shipping capacity. The second factor was a shortage of containers, as pandemic-related delays resulted in containers being held in various ports and on different ships. This shortage was particularly acute on the longer trade routes. The third factor was port congestion. Major ports experienced congestion due to increased cargo volumes and labor shortages, leading to longer waiting times for vessels and delayed shipments. According to data from Clarkson (2024), the average port waiting time for containerships over 8000 TEUs was 2.4 h in the last quarter of 2019, 3.4 h in Q4 2020, and peaked at 7.1 h in Q4 2021, before falling to 4.6 h in Q4 2022. This congestion has increased operational costs, which have been passed on to clients through higher freight rates.

Interestingly, the data suggests that the price gap between carriers and freight forwarders varies considerably over time. When examining the short-term contracts, the difference in average freight rates is positive and very low for both the FE-NE and FE-USWC trade lanes until 2020, after which the gap increases significantly. The price paid when contracting with a freight forwarder is more than 1000 USD higher for FE-NE during the COVID period, while the gap is negative for FE-USWC. In 2023, prices for transactions contracted with freight forwarders are consistently lower. A very similar pattern is observed for long-term contracts: freight rates with freight forwarders are lower before COVID-19 (except for FE-USWC contracts), higher during the pandemic, and lower thereafter. The magnitude of the price differentials also varies

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Proportion of freight forwarders in container contracts, by year
Source: authors' calculations, data from *The Co.* (January 2018–December 2023).</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 2. Monthly average container prices 2018-2023</figcaption></figure>

Source: authors’ calculations, data on container contracts from The Co. (2018–2023).

by trade lane.

Another observation from Fig. 2 is that there is a lag between price increases for shippers and those for freight forwarder during the COVID-19 period, particularly for long-term contracts. As intermediaries between shippers and carriers, freight forwarders may adjust their prices more swiftly in response to market changes due to their close proximity to market fluctuations and their need to secure capacity in a volatile market. The COVID pandemic caused significant disruptions in global supply chains, prompting freight forwarders, who are closer to the operational side, to feel immediate pressure to raise prices. They likely have better access to real-time market information and can anticipate price trends more accurately than shippers. Conversely, shippers may take longer to adjust their prices due to budgeting cycles and contract negotiations. Long-term contracts often involve more complex negotiations and may contain clauses that delay price adjustments. Freight forwarders generally have more flexibility to renegotiate terms with carriers than shippers, who may be locked into longer-term agreements with fixed pricing structures.

Overall, these descriptive statistics suggest that there may be instances of price discrimination in the container market, and that the disparity in freight rates paid by freight forwarders and shippers is contingent upon market conditions. In addition, this disparity may be influenced by other factors, such as the ports of origin and destination.

## 4. Econometric strategy

We assess whether freight forwarders experience price discrimination by considering that, if this occurs, freight forwarders and carriers receive different freight rates for contracts with identical characteristics, such as the origin and destination ports or the contract duration. For this analysis, let $\ln P_{i(t)}$ be the logarithm of the freight rate for a contract in effect at time t for the shipment of one TEU from an origin port to a destination port. Excluding the influence of contract characteristics, the difference in the average container freight rates paid by either freight

forwarders or direct enterprise shippers is:

$$ \Delta = E[\ln(P_{i(t)}|FF_{i(t)} = 1)] - E[\ln(P_{i(t)}|FF_{i(t)} = 0)] \quad (1) $$

where $FF_{i(t)}$ is a dummy variable such that $FF_{i(t)} = 1$ if the shipper is a freight forwarder and $FF_{i(t)} = 0$ if the shipper is a direct enterprise. The difference in average prices $\Delta$ can be estimated using a regression setting. The corresponding linear equation is as follows:

$$ \ln P_{i(t)} = \alpha + \delta*FF_{i(t)} + \varepsilon_{i(t)} \quad (2) $$

where $\alpha$ is a constant, $\delta$ measures the effect of the dummy $FF_{i(t)}$ on the logarithm of the freight rate, and $\varepsilon_{i(t)}$ is a residual such that $E[\varepsilon_{i(t)}] = 0$. From (2), $E[\ln P_{i(t)}|FF_{i(t)} = 1] = \alpha + \delta$ and $E[\ln P_{i(t)}|FF_{i(t)} = 0] = \alpha$, so $E[\ln P_{i(t)}|FF_{i(t)} = 1] - E[\ln P_{i(t)}|FF_{i(t)} = 0] = \delta$. The freight forwarder premium can be expressed as a percentage and is given by $(\exp(\delta) - 1)*100$. As emphasized earlier, the price associated with a contract will also depend on characteristics related to the transportation as well as more general market conditions. For instance, freight rates are expected to be higher when there is an increase in the demand for container transportation, with a limited change in supply. Equation (2) can be extended to account for such heterogeneity as follows:

$$ \ln P_{i(t)} = \alpha + \delta*FF_{i(t)} + X_{i(t)}\beta + \theta_r + \lambda_s + \gamma_t + \varepsilon_{i(t)} \quad (3) $$

where $X_{i(t)}$ is a set of control variables, $\theta_r$ is a route fixed effect with a route corresponding to the combination of an origin port and a destination port, $\lambda_s$ is a carrier fixed effect ($s$ is the company on which the container is transported), and $\gamma_t$ is a time fixed effect, with the time unit defined at the year-month level.

In (3), the premium $\delta$ is now adjusted for the influence of several sources of heterogeneity, both observed and unobserved. First, the vector $X$ includes the contract duration as a covariate, which is categorized into 4 groups: 0–7 days, 8–14 days, 15–21 days for short-term contracts, and 88–94 days, 95–149 days, 150–271 days, 272+ days for
long-term contracts. We also control for the number of contracts per company at the monthly level. A negative coefficient is expected due to the possibility of volume discounts. In addition, large companies may have a better knowledge of real-time conditions in the shipping market and be able to obtain cheaper prices. Second, the route fixed effect $\theta_r$ picks up the influence of distance, where longer trips should on average command higher prices. It also captures the intensity of competition on each route (unobserved in our data) and prices should on average be lower on routes served by a large number of companies. Third, the fixed effect $\lambda_s$ accounts for the influence of the carrier on which the containers are transported. There may also be some specific pricing strategies depending on companies. Fourth, the time fixed effect captures changes in supply and demand over time, as well as other time-varying factors related to transportation, such as fuel costs, port congestion or availability of container vessels.

Equation (3) defines a linear regression model with multiple fixed effects. In recent years, several estimators have been proposed to estimate high-order fixed effect models (Guimarães and Portugal, 2010; Correia, 2016). Iterative procedures have been proposed to solve the normal equations associated with the least squares estimates. Rios-Avila (2015) shows that fixed effects can be eliminated by iteratively demeaning the different variables. However, in the data, the dimension of each fixed effect remains rather small. For short-term contracts (1 548 194 observations), there are 72 months ($\gamma_t$), 287 routes ($\theta_r$), and 207 companies ($\lambda_s$), so the model can also be estimated by adding dummy variables associated with months, routes, and companies as covariates. Standard errors are adjusted to be robust to heteroskedasticity.

In the regression model presented in (3), there is a unique coefficient $\delta$ that measures the effect of freight forwarders on container prices. It is straightforward to relax this assumption and consider more flexible specifications allowing for heterogeneity, either by route or over time. In particular, as shown in Fig. 1, freight rates have changed considerably over the period due to the COVID-19 pandemic, resulting in an increased price difference between freight forwarders and carriers in 2021 and 2022. The hypothesis that the influence of freight forwarders may have changed due to COVID-19 shocks can be addressed by considering the following regression:

$$ \ln P_{i(t)} = \alpha + \sum \delta_t * FF_{i(t)} * \mathbb{1}_t + X_{i(t)}\beta + \theta_r + \lambda_s + \gamma_t + \varepsilon_{i(t)} \quad (4) $$

where $\mathbb{1}_t$ is a dummy variable such that $\mathbb{1}_t = 1$ during period $t$ and 0 otherwise. The model is estimated with two definitions of the time periods $t$. On the one hand, a distinction is made between the prior-COVID (2018–2020), during-COVID (2021–2022) and post-COVID (2023) periods. On the other hand, the possibility of a time-varying price difference at a more granular level is examined using $\mathbb{1}_t$ as a quarterly time trend, so that the coefficients $\delta_t$ represent the time-varying price difference by quarter.

## 5. Results

To test our first hypothesis (H1) that freight forwarders experience a price discrimination by carriers, which is likely to be more pronounced for short-term contracts than for long-term contracts, we estimate the impact of freight forwarders on prices using a stepwise modeling procedure. The estimation results are presented in Table 2. In the preliminary step, we regress the logarithm of the freight rate on a dummy variable that identifies freight forwarders, without including other controls.

Panel A reports the estimates for short-term contracts, while Panel B provides estimates for long-term contracts. As shown in column (1), the estimation results reveal a statistically significant coefficient $\hat{\delta} = -0.252$, indicating that the freight rate paid by a freight forwarder is 22.3 % ($1 - e^{-0.252}$) lower than the average price paid by shippers for short-term contracts and 14.0 % lower for long-term contracts. However, this basic analysis does not take into account composition effects related

<table><caption>**Table 2**
Price difference in container freight rate for freight forwarders.</caption><thead><tr><th>Variables</th><th>(1)</th><th>(2)</th><th>(3)</th></tr></thead><tbody><tr><td colspan="4"><strong>Panel A. Short-term contracts</strong></td></tr><tr><td>Freight forwarder</td><td>-0.252***<br>(-65.46)</td><td>0.049***<br>(10.47)</td><td></td></tr><tr><td>Freight forwarder, 2018–2020</td><td></td><td></td><td>-0.005 (-1.21)</td></tr><tr><td>Freight forwarder, 2021–2022</td><td></td><td></td><td>0.181***<br>(25.71)</td></tr><tr><td>Freight forwarder, 2023</td><td></td><td></td><td>-0.074***<br>(-12.78)</td></tr><tr><td>Contract duration 8–14 days</td><td></td><td>0.028***<br>(37.99)</td><td>0.027***<br>(37.41)</td></tr><tr><td>(ref: 0–7 days) 15–21 days</td><td></td><td>0.014***<br>(17.35)</td><td>0.014***<br>(16.93)</td></tr><tr><td>22–31 days</td><td></td><td>-0.031***<br>(-34.31)</td><td>-0.032***<br>(-36.12)</td></tr><tr><td>Monthly transactions per shipper (ln)</td><td></td><td>-0.004***<br>(-13.78)</td><td>-0.004***<br>(-15.39)</td></tr><tr><td>Month-year fixed effects</td><td>NO</td><td>YES</td><td>YES</td></tr><tr><td>Origin-destination fixed effects</td><td>NO</td><td>YES</td><td>YES</td></tr><tr><td>Supplier fixed effects</td><td>NO</td><td>YES</td><td>YES</td></tr><tr><td>Number of contracts</td><td>1 548 194</td><td>1 548 184</td><td>1 548 184</td></tr><tr><td>R<sup>2</sup></td><td>0.003</td><td>0.851</td><td>0.851</td></tr><tr><td colspan="4"><strong>Panel B. Long-term contracts</strong></td></tr><tr><td>Freight forwarder</td><td>-0.151***<br>(-36.63)</td><td>-0.031***<br>(-7.00)</td><td></td></tr><tr><td>Freight forwarder, 2018–2020</td><td></td><td></td><td>-0.114***<br>(-23.88)</td></tr><tr><td>Freight forwarder, 2021–2022</td><td></td><td></td><td>0.127***<br>(20.90)</td></tr><tr><td>Freight forwarder, 2023</td><td></td><td></td><td>-0.290***<br>(-27.41)</td></tr><tr><td>Contract duration 95–149 days</td><td></td><td>-0.004 (-0.65)</td><td>0.013** (2.33)</td></tr><tr><td>(ref: 88–94 days) 150–271 days</td><td></td><td>-0.131***<br>(-32.29)</td><td>-0.120***<br>(-29.97)</td></tr><tr><td>272+ days</td><td></td><td>-0.007**<br>(-1.88)</td><td>-0.013***<br>(-3.57)</td></tr><tr><td>Monthly transactions per shipper (ln)</td><td></td><td>-0.008**<br>(-8.41)</td><td>-0.005***<br>(-4.75)</td></tr><tr><td>Month-year fixed effects</td><td>NO</td><td>YES</td><td>YES</td></tr><tr><td>Origin-destination fixed effects</td><td>NO</td><td>YES</td><td>YES</td></tr><tr><td>Carrier fixed effects</td><td>NO</td><td>YES</td><td>YES</td></tr><tr><td>Number of contracts</td><td>146 422</td><td>146 404</td><td>146 404</td></tr><tr><td>R<sup>2</sup></td><td>0.009</td><td>0.646</td><td>0.653</td></tr></tbody></table>

Note: estimates from linear regressions, with robust t-values in parentheses. Significance levels are 1 % (***), 5 % (**) and 10 % (*).

Source: authors’ calculations, data on container contracts from The Co. (2018–2023).

for instance to time, route, and carriers.

The extended regression reported in column (2) includes control variables for contract duration, monthly transactions per shipper, as well as fixed effects for time, route, and supplier. The explanatory power of the regression is high, with $R^2 = 0.85$ for short-term contracts and $R^2 = 0.65$ for long-term contracts. Accounting for heterogeneity strongly affects the effect of freight forwarders on prices. On the one hand, freight forwarders pay on average a 5 % premium ($\hat{\delta} = 0.049$) for short-term contracts. On the other hand, the difference remains negative for long-term contracts, but with a much lower intensity, showing a change of -3.0 % compared to -14.0 % when no controls are applied. The correlation between freight rates and contract duration is mixed. For short-term contracts, compared to the baseline of 1–7 days, contracts with a duration of 8–14 days incur a 2.8 % higher price, contracts lasting
15–21 days incur a 1.4 % higher price, and contracts with a duration of 22–31 days receive a 3 % discount. For long-term contracts, the freight rate for a duration of 150–271 days is reduced by 13.1 % compared to the reference category of 88–94 days. For both short-term and long-term contracts, we find a negative association between the number of contracts held by each company and the price paid. However, the magnitude of the discount is quite small.

To test our second hypothesis (H₂) that price discrimination is more pronounced under tight market conditions, such as during the COVID-induced price hikes, we included the period-specific COVID dummies in the regression (column 3) to study whether the supply chain consequences of the pandemic shock affected the role of freight forwarders. On the one hand, the pandemic caused disruptions that led to delays in cargo handling at ports, creating bottlenecks that hindered the smooth movement of vessels and shipments. On the other hand, demand for container shipping remained strong due to the increased activities of online shopping by consumers confined to their homes. As a result, container shipping freight escalated to record high levels in 2021 and 2022.

The estimates show that the pandemic has strongly affected the impact of freight forwarders on short-term contract prices. While the freight forwarder coefficient was near zero before COVID (−0.5 %) and negative after COVID (−7.4 %), there was a price discrimination effect of 18.1 % for freight forwarders in 2021 and 2022. This result is logical given the tight supply of shipping capacity during the COVID-19 disruptions, which forced freight forwarders representing more term contracts and SMEs to offer higher prices to secure transportation capacity. A similar pattern is observed for long-term contracts. Freight forwarders experienced discounts both before and after the pandemic (−11.4 % and −29.0 %, respectively), while they had to pay an additional premium of 12.7 % compared to enterprise shippers in 2021 and 2022.

To test our third hypothesis (H₃) that the degree of price

discrimination varies by route, we present the estimation results for quarterly time-varying price differences in Fig. 3. This figure includes both short-term contracts (top panel) and long-term contracts (bottom panel). The left-hand plots represent the time-varying price differences for the FE-NE trade lane, while the right-hand plots show those for the FE-USWC trade lane. The same scale is applied to the y-axis for the freight forward premium to facilitate comparison. The main finding is that there are significant variations in the price premium paid by freight forwarders when market power is more favorable to carriers. Focusing on FE-NE short-term contracts, we observe that there is almost no difference between freight forwarders and carriers until the end of 2020. Thereafter, the premium rises sharply, peaking at 120 % in the third quarter of 2021. After that, the premium declines rapidly, becoming negative in the second half of 2022, and finally gradually returning to zero by the end of 2023.

The situation is somewhat different for short-term FE-USWC contracts. From 2018 to mid-2022, freight forwarders offered higher prices, but the premium turned negative until the first quarter of 2023, before returning to positive values of around 30 %. For long-term contracts, the variation over time is less important for the FE-NE trade line than for the FE-USWC trade lane. For the former, freight rates are generally lower for freight forwarders until the end of 2020 and after mid-2023. For the latter, the premium was noticeably positive and substantial in the second half of 2018, continuously increasing from the beginning of 2020 and exceeding 60 % in 2021. Finally, the premium became negative from mid-2022 to the end of 2023.

Finally, we evaluate the extent to which the freight forwarder premium is influenced by market conditions. We correlate the four quarterly premiums shown in Fig. 3 with the average port waiting time (measured in hours) for containerships over 8000 TEUs. Our analysis reveals a strong positive correlation for contracts from the Far East to Europe, with an R² value of 0.38 for short-term contracts and 0.49 for

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Freight forwarder time-specific premiums by region
Source: authors' calculations, data on container contracts from *The Co.* (2018–2023).</figcaption></figure>

Note: the time-specific premiums are calculated using estimates from linear regressions explaining the logarithm of the container price as a function of contract duration, origin-destination fixed effects, supplier fixed effects, and a freight forwarder dummy interacted with the quarter-year dummies.
long-term contracts in the regression model explaining the estimated freight forwarder premium. In contrast, for contracts from the Far East to the US, we do not observe a significant correlation between the premium and the average port waiting time. Instead, we consider the port congestion index for containerships calling at ports on the West Coast of North America. We find a positive coefficient for the port congestion index in explaining the freight forwarder premium, with R² values of 0.16 for short-term contracts and 0.23 for long-term contracts. The fact that the factors influencing freight forwarder premiums differ across trade lanes may be due to differences in operational practices and market dynamics. Long-term contracts show a stronger relationship with congestion than short-term contracts, possibly due to longer exposure to market conditions and the need for more stable pricing structures.

Overall, our various estimates indicate that there may be substantial differences in freight rates, depending on whether contracts are with freight forwarders or with carriers, especially in the context of the COVID-19 pandemic. A key assumption in our regressions is that the choice of shippers is exogenous. The validity of this assumption may be problematic if some shippers systematically prefer either carriers or freight forwarders. For example, if firms with small volumes of containers to transport turn to freight forwarders (because they have better knowledge of real market conditions), while firms with larger volumes negotiate directly with carriers, then this may lead to systematic price differences that are not currently accounted for in the price equations. This, in turn, could bias the freight forwarder premium either upward or downward.

The differences in contract characteristics between freight forwarders and carriers can lead to potential selection bias, particularly when both agents operate on very different routes within a trade lane. To enhance the robustness of our analysis, we addressed this selection problem by focusing on observable characteristics. Specifically, we consider an exact matching procedure to estimate the freight forwarder premium for perfectly comparable contracts based on their observable characteristics, such as duration and date. The methodology and additional results are detailed in the Appendix, which demonstrates that the robustness analysis has minimal impact on the magnitude of the freight forwarder premium obtained by linear regression models.

# 6. Discussions and implications

Freight forwarders play a critical role in the logistics and supply chain industry, acting as intermediaries between shippers and carriers. They facilitate the efficient movement of goods. However, there are several reasons why freight forwarders may face price discrimination from carriers.

First, it can be argued that large companies are more likely to negotiate lower freight rates due to their substantial shipment volumes and long-standing relationships with carriers. In contrast, smaller businesses, often represented by freight forwarders, may have to pay higher rates for the same service. While this observation is largely true, it is critical to question whether this price discrimination is justified. If a freight forwarder can provide carriers with a steady stream of cargo, even if that cargo originates from multiple small businesses, why should they incur higher costs? Consequently, the pricing disparity raises important questions about the fairness and rationale of such price discrimination.

Second, we have demonstrated that freight forwarders are more active in short-term contracts than in long-term contracts. Long-term contracts provide carriers with greater stability and predictability, allowing them to plan service frequencies and allocate vessels more efficiently. As a result, contract duration emerges as a key determinant of price differences. After controlling for contract length, we find different roles and pricing treatments for freight forwarders: an average price premium of 5% for short-term contracts and an average price discount of 3% for long-term contracts. This finding is particularly interesting in light of the different treatment of freight forwarders across

different contract durations. We argue that the small share of shippers in short-term contracts is likely due to spillover from long-term contract clients who require urgent shipments. These short-term contracts can still secure favorable prices compared to those obtained by freight forwarders. However, in long-term contracts, carriers have less incentive to offer competitive prices to long-term clients due to the oligopolistic market structure in container shipping. In contrast, freight forwarders are flexible and can shop around among carriers, making them more likely to secure better prices than shippers negotiating directly with carriers, as they prioritize capacity security over price negotiation in long-term contracts.

Third, we argue that freight forwarders typically represent a fragmented set of small businesses that present a distinct risk profile for carriers. As a result, carriers may charge higher prices to compensate for the increased risks associated with the business brought by freight forwarders, taking into consideration differences in contract length and market conditions. In tight market conditions, such as during COVID-19 when the supply chain experienced significant disruptions, freight forwarders faced the harshest conditions and endured substantial price discrimination. During this period, they paid an average price premium of 18.1% for short-term contracts and 12.7% for long-term contracts, as carriers prioritized their longstanding corporate clients. This prioritization resulted in severe price discrimination against freight forwarders. However, as the market normalized post-COVID, the pricing dynamics shifted. Freight forwarders benefited from significantly higher discounts on long-term contracts, receiving discounts of up to 29%, compared to a 7.4% discount on short-term contracts. This post-COVID scenario highlights the fluctuating nature of price discrimination based on market conditions and contract duration.

The findings of this research have significant implications for policymakers, pricing strategies, and market efficiency within the container shipping industry. First and foremost, the container shipping segment is characterized by an oligopolistic market structure, evidenced by a small number of dominant carriers serving a large customer base (Brock, 1983). This structure creates a unique competitive environment in which power in price negotiations shifts to the service providers and consequently affects the freight rates received by counterparties. The limited number of dominant carriers, particularly on long-haul trade routes such as those from the Far East to Europe or North America, means that not only do these carriers exert significant influence over prices, but also that the pricing decisions of one carrier directly affect the others in the market. As a result of this interdependence, the container freight rate market is often characterized by non-price competition, with the focus on customer relationship management and service improvements rather than price adjustments.

Second, while the traditional theory of oligopoly posits that prices tend to be rigid, due to the kinked demand curve (Sweezy, 1939; Hall and Hitch, 1939; Maskin and Tirole, 1988), our results reveal a more dynamic situation across different trade routes and market conditions, as illustrated in Fig. 3. On the Far East to North Europe trade route, freight forwarders consistently receive discounted prices for long-term contracts and, to a lesser extent, for short-term contracts, both before and after COVID-19, when the container freight market was relatively depressed. In contrast, the price differential for freight forwarders on the Far East to US West Coast trade route is less stable over the same periods. During the market boom caused by COVID-related disruptions, freight forwarders on both trade lanes experienced significant price discrimination. This suggests that while traditional oligopoly theory suggests price rigidity, our findings highlight the influence of market conditions and trade route-specific dynamics on pricing behavior, demonstrating the variability within the broader business environment.

# 7. Concluding remarks

This research presents the first comprehensive scientific investigation of pricing mechanisms in the container shipping industry, using a
unique dataset of nearly 1.6 million real-time freight contracts from January 2018 to December 2023. This novel dataset includes detailed information such as shipper and carrier identification, origin and destination, contract duration, and prices for two major trade routes: from the Far East to Europe and North America.

The extensive dataset allows for an in-depth analysis of pricing mechanisms during three significant time periods: before, during, and after COVID-19. These periods show different market conditions and freight market developments. Using fixed effect regressions to explain the contract prices, we reveal dynamic patterns in how freight forwarders experience price discrepancies relative to direct enterprise shippers across various trade lanes and time periods. The selected trade lanes represent a significant share of container shipping and are characterized by high volume. In contrast, price discrimination among freight forwarders may vary in less prominent trade lanes and intra-regional trade, where large and long-term shippers have a weaker presence. In these less competitive and lower-volume trade routes, freight forwarders may exercise greater market power.

This study provides critical insights into the evolving nature of freight rate pricing in response to market fluctuations and external disruptions. It also offers a critical understanding of the dynamics within this oligopolistic market, which have a significant impact on the overall efficiency and competitiveness of the industry. By leveraging these insights, carriers can better strategize their pricing and service offerings, while shippers can more effectively manage their negotiations and expectations within this competitive landscape.

However, there are limitations to the current research. There may exist selection bias, where the two selected major trade lanes selected

may not fully represent pricing behaviors in other regions with different competition situations. In addition, the study does not account for shipper characteristics due to data limitations. Future research could investigate the granular effects of pricing mechanisms by examining price differences across countries or specific corporations. This detailed analysis could uncover evidence that challenges the traditional economic theory of a single, uniform price. Such research would provide deeper insights into the variation in transportation prices and contribute to a more nuanced understanding of market behavior and economic principles in international trade. Future research could further explore how the individual characteristics of shippers may affect the price difference dynamics.

### CRediT authorship contribution statement

Pierre Cariou: Writing – review & editing, Writing – original draft, Investigation, Formal analysis, Conceptualization. Haiying Jia: Writing – review & editing, Writing – original draft, Investigation, Formal analysis, Conceptualization. François-Charles Wolff: Writing – review & editing, Writing – original draft, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Appendix. Exact matching and estimation of the freight forwarder premium

Let $\mathcal{F}^1$ be the set of treated transactions defined as contracts operated by freight forwarders, and $\mathcal{F}^0$ be the set of control transactions corresponding to shipper contracts. Each contract $j$ of $\mathcal{F}^1$ is then matched with all contracts of $\mathcal{F}^0$ that have exactly the same characteristics, with three possible cases: no counterfactual shipper contract, exactly one counterfactual shipper contract, more than one counterfactual shipper contract. The counterfactual freight rate is thus $\ln P_j^C = (\sum \ln P_k)/n_k$, where $n_k$ is the number of counterfactual contracts observed in the data. The premium is $\ln p_j - \ln P_j^C$, which means that this approach provides a non-parametric measure of the freight forward premium (in the sense that it varies for each contract).

The set of covariates chosen to match treated and control transactions is critical. With a very high number of covariates, the number of matched transactions is expected to be low, as it will be more difficult to find perfectly comparable treated and control contracts. The matching was carried out on the following two primary variables: first, the route, and treated contracts are matched only with control contracts operated on the exact same origin and destination ports; second, the starting date of the contract, since there is a lot of price variation over time, especially during the pandemic. Three different time periods are also considered: the exact start date (day), two weeks before and after the start date, and four weeks before and after the start date. Beyond four weeks, it is assumed that a shipper contract does not provide a valid counterfactual for any freight forwarder contracts. Since the monthly transactions per shipper is a continuous variable, it is not included as a matching criterion (otherwise, the number of matched contracts would be too small). However, this proxy for volume is controlled for in the regressions that provide the magnitude of the freight forwarder premium.

Table A1 presents descriptive statistics on the matching rate of contracts between freight forwarders and shippers. When the matching of treated and control contracts is based on the exact start date, about a quarter of the short-term contracts operated by freight forwarders have at least one corresponding contract operated by shippers with a similar route and a similar start date (day). As expected, the matching rate rises sharply when time windows increase. At four weeks, the matching rate is 61.5 %. However, this still means that in the OLS estimation discussed earlier, almost 4 out of 10 contracts correspond to very different situations (both geographically and in time). For long-term contracts, the matching rate is much higher at 67.7 % for the exact start date and 79.4 % for a four-week period.

<table><caption>**Table A1**
Matching rates of contracts</caption><thead><tr><th>Variables</th><th></th><th>All</th><th>Exact starting day</th><th>±14 days</th><th>±28 days</th></tr></thead><tbody><tr><td colspan="6"><strong>Panel A. Short-term contracts</strong></td></tr><tr><td rowspan="2">All routes</td><td>Nb of FF contracts</td><td>1495519</td><td>378670</td><td>661753</td><td>920029</td></tr><tr><td>Matching rate</td><td></td><td>25.3 %</td><td>44.2 %</td><td>61.5 %</td></tr><tr><td rowspan="2">Far East - > North Europe</td><td>Nb of FF contracts</td><td>1022518</td><td>273677</td><td>443160</td><td>594568</td></tr><tr><td>Matching rate</td><td></td><td>26.8 %</td><td>43.3 %</td><td>58.1 %</td></tr><tr><td rowspan="2">Far East - > US West Coast</td><td>Nb of FF contracts</td><td>473001</td><td>104993</td><td>218593</td><td>325461</td></tr><tr><td>Matching rate</td><td></td><td>22.2 %</td><td>46.2 %</td><td>68.8 %</td></tr></tbody></table>

(continued on next page)
<table><caption>**Table A1 (continued)**</caption><thead><tr><th>Variables</th><th></th><th>All</th><th>Exact starting day</th><th>±14 days</th><th>±28 days</th></tr></thead><tbody><tr><td colspan="6"><strong>Panel B. Long-term contracts</strong></td></tr><tr><td rowspan="2">All routes</td><td>Nb of FF contracts</td><td>71525</td><td>48428</td><td>52932</td><td>56765</td></tr><tr><td>Matching rate</td><td></td><td>67.7 %</td><td>74 %</td><td>79.4 %</td></tr><tr><td rowspan="2">Far East - > North Europe</td><td>Nb of FF contracts</td><td>56195</td><td>43617</td><td>45067</td><td>46231</td></tr><tr><td>Matching rate</td><td></td><td>77.6 %</td><td>80.2 %</td><td>82.3 %</td></tr><tr><td rowspan="2">Far East - > US West Coast</td><td>Nb of FF contracts</td><td>15330</td><td>4811</td><td>7865</td><td>10534</td></tr><tr><td>Matching rate</td><td></td><td>31.4 %</td><td>51.3 %</td><td>68.7 %</td></tr></tbody></table>

Source: authors' calculations, data on container contracts from *The Co.* (2018–2023).

We then consider a weighted version of equation (3) to evaluate the magnitude of the freight forwarder premium. All treated transactions that cannot be matched to a control contract are assigned a weight of zero. When matching is successful, the weight associated with each counterfactual contract is defined as the inverse of the total number of counterfactual contracts. The estimates are presented in Table A2, where each regression includes the freight forwarder dummy interacted with the before, during, and post-COVID dummies. The main finding is that the exact matching procedure leads to very similar conclusions.

For short-term contracts, the difference between the average freight rates of freight forwarders and shippers appears to be very small (ranging from –2 % to 3 %) before COVID, then it increases sharply during the pandemic in 2021 and 2022. The OLS coefficient tends to overestimate the freight forward premium, which is positive (about 20 %), at least when the matching is not at the exact start date (presumably due to the low matching rate in this case). In 2023, the freight forwarder discount is around 10 % for short-term contracts. For long-term contracts, the premium after matching is negative before COVID (about –10 points), positive during COVID (between 18 and 20 points, which is substantially higher than the OLS premium), and then negative after COVID in 2023, with a discount of about –30 %.

<table><caption>**Table A2**
Exact matching estimates of the logarithm of container prices</caption><thead><tr><th>Variables</th><th>(1) All</th><th>(2) Matching: Exact day</th><th>(3) Matching: ±2 weeks</th><th>(4) Matching: ±4 week</th></tr></thead><tbody><tr><td colspan="5"><strong>Panel A. Short-term contracts</strong></td></tr><tr><td>Freight forwarder, 2018–2020</td><td>–0.005 (–1.21)</td><td>0.030*** (11.75)</td><td>–0.013*** (–6.58)</td><td>–0.019*** (–10.98)</td></tr><tr><td>Freight forwarder, 2021–2022</td><td>0.181*** (25.71)</td><td>0.315*** (96.27)</td><td>0.149*** (60.72)</td><td>0.136*** (62.18)</td></tr><tr><td>Freight forwarder, 2023</td><td>–0.074*** (–12.78)</td><td>–0.066*** (–23.22)</td><td>–0.096*** (–47.20)</td><td>–0.122*** (–69.93)</td></tr><tr><td>Contract duration 8–14 days</td><td>0.027*** (37.41)</td><td>0.024*** (10.44)</td><td>0.033*** (29.23)</td><td>0.032*** (32.34)</td></tr><tr><td>(ref: 0–7 days) 15–21 days</td><td>0.014*** (16.93)</td><td>0.029*** (10.57)</td><td>0.018*** (12.94)</td><td>0.018*** (16.50)</td></tr><tr><td>22–31 days</td><td>–0.032*** (–36.12)</td><td>–0.058*** (–24.50)</td><td>–0.043*** (–35.46)</td><td>–0.037*** (–34.36)</td></tr><tr><td>Monthly transactions per shipper (ln)</td><td>–0.004*** (–15.39)</td><td>–0.008*** (–18.38)</td><td>–0.002*** (–5.30)</td><td>–0.002*** (–7.24)</td></tr><tr><td>Month-year fixed effects</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Origin-destination fixed effects</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Supplier fixed effects</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Number of contracts (unweighted)</td><td>1 548 184</td><td>758 789</td><td>1 534 328</td><td>2 299 492</td></tr><tr><td>R<sup>2</sup></td><td>0.851</td><td>0.810</td><td>0.798</td><td>0.777</td></tr><tr><td colspan="5"><strong>Panel B. Long-term contracts</strong></td></tr><tr><td>Freight forwarder, 2018–2020</td><td>–0.114*** (–23.88)</td><td>–0.131*** (–26.60)</td><td>–0.110*** (–22.20)</td><td>–0.091*** (–19.31)</td></tr><tr><td>Freight forwarder, 2021–2022</td><td>0.127*** (20.90)</td><td>0.166*** (23.84)</td><td>0.166*** (24.47)</td><td>0.184*** (27.90)</td></tr><tr><td>Freight forwarder, 2023</td><td>–0.290*** (–27.41)</td><td>–0.331*** (–21.05)</td><td>–0.329*** (–23.94)</td><td>–0.332*** (–26.49)</td></tr><tr><td>Contract duration 95–149 days</td><td>0.013** (2.33)</td><td>0.043*** (6.01)</td><td>0.013** (2.02)</td><td>0.009 (1.30)</td></tr><tr><td>(ref: 88–94 days) 150–271 days</td><td>–0.120*** (–29.97)</td><td>–0.093*** (–19.61)</td><td>–0.105*** (–23.47)</td><td>–0.093*** (–21.70)</td></tr><tr><td>272+ days</td><td>–0.013*** (–3.57)</td><td>0.002 (0.44)</td><td>0.010*** (2.68)</td><td>0.020*** (5.40)</td></tr><tr><td>Monthly transactions per shipper (ln)</td><td>–0.005*** (–4.75)</td><td>–0.003** (–2.36)</td><td>–0.001 (–1.26)</td><td>–0.000 (–0.42)</td></tr><tr><td>Month-year fixed effects</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Origin-destination fixed effects</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Supplier fixed effects</td><td>YES</td><td>YES</td><td>YES</td><td>YES</td></tr><tr><td>Number of contracts (unweighted)</td><td>146 404</td><td>121 240</td><td>162 093</td><td>205 512</td></tr><tr><td>R<sup>2</sup></td><td>0.653</td><td>0.719</td><td>0.695</td><td>0.686</td></tr></tbody></table>

Note: estimates from linear regressions (column 1) and weighted linear regressions after exact matching (columns 2, 3 and 4), with robust t-values in parentheses. Significance levels are 1 % (**%), 5 % (**) and 10 % (*).

Source: authors' calculations, data on container contracts from *The Co.* (2018–2023).

## Data availability

The data that has been used is confidential.

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