DP2024-28

Industry Dynamics with Cartels: The Caseof the Container Shipping Industry*

RIEB Junior Research Fellow

S u g u r u O TA N I

August 21, 2024

* The Discussion Papers are a series of research papers in their draft form, circulated to encourage
discussion and comment. Citation and use of such a paper should take account of its provisional
character. In some cases, a written consent of the author may be required.

* This Discussion Paper won the Kanematsu Prize (FY 2023).

Industry Dynamics with Cartels: The Case of the Container
Shipping Industry∗
Suguru Otani
First version: October 27, 2023
Current version: August 26, 2024

Abstract
I investigate how explicit cartels, known as “shipping conferences”, in a global container shipping
market facilitated the formation of one of the largest globally integrated markets through entry, exit, andshipbuilding investment of shipping firms. Using a novel data, I develop and construct a structural modeland find that the cartels shifted shipping prices by 20-50% and encouraged firms’ entry and investment. In
the counterfactual, I find that cartels would increase producer surplus while slightly decreasing consumer
surplus, then may increase social welfare by encouraging firms’ entry and shipbuilding investment. This
would validate industry policies controlling prices and quantities in the early stage of the new industry,
which may not be always harmful. Investigating hypothetical allocation rules supporting large or small
firms, I find that the actual rule based on tonnage shares is the best to maximize social welfare.

1

Introduction

The ocean-going shipping industry, as a main engine in international trade, has developed to this day, bearing
the burden of the nation’s rise and fall. The history of the industry is older than that of competition law. So,
the international practice has been based on the “principle of freedom of shipping,” i.e., not giving priority
to the transport of cargo to and from one’s own country by one’s own merchant fleet and ships of one’s
own flag. It has been an international practice for governments not to intervene in the choice of shipping∗ suguru.otani@e.u-tokyo.ac.jp, Market Design Center, University of TokyoI thank my advisor Jeremy Fox for valuable advice. I also thank my committee members, Yunmi Kong, Maura Coughlin,
and Arun Gopalakrishnan. I benefited from extensive comments from Isabelle Perrigne, Yinghua He, Takeshi Murooka, Naoki
Wakamori, Yuta Toyama, Takuma Matsuda, Shosuke Noguchi, Taisei Noda, and Yuri Matsumura as well as participantsat the Summer Workshop on Economic Theory, the 18th Applied Econometrics Conference, the 18th Annual Economics
Graduate Student Conference at Washington University in St. Louis, Kanematsu prize, and the Japan Society of Logistics andShipping Economics Kanto region. This work won the Kanematsu Prize from Research Institute for Economics and Business
Administration (RIEB), Kobe University in 2023.

1

companies and vessels. Under this principle, the ocean-going shipping industry has developed in many
countries around the world without much regulation of market entry, exit, or business activities. In addition,
for more than 130 years, consortia and international cartels have been formed among shipping companies,
and these cartels have been allowed in most countries.1 In the shipping industry, international shipping
cartels are called “shipping conferences,” which control shipping prices and quantities of member firms by
centralized decisions of the members.2 The breakdown of shipping conferences caused drops in shipping
prices in the 1980s, historically known as the “container crisis” (Broeze 2002). This paper disentangles theeffect of the cartel breakdown on prices, firms’ entry, shipbuilding investment, and welfare by analyzing theshipping conferences.
Global containerization which refers to the use of standardized shipping containers to transport goods
around the world changed the industrial structure. Global containerization has the effect of dramaticallylowering the entry barriers for new shipping companies in developing countries. In addition, the existenceof shipping conferences became strongly perceived as an impediment to the entry of developing countries’
shipping industries into the world trade market. In response to this trend, in 1974, the United Nations
Convention on the Charter of the Liner Shipping Union was concluded and allowed new shipping companies
to participate in shipping conferences.
While containerization was progressing, as part of the deregulation policy under the Reagan administration in the United States, the new Shipping Act was enacted in June 1984. Its aim was first to allow member
carriers to make individual agreements with shippers on freight rates and services, and second to unbind
shippers from shipping alliances so that shippers could make their own choices of shipping companies. As aresult, the enactment led to a change from the collusive regime by shipping conferences controlling shipping
prices and quantities to the competitive regime.
Although the industry has been the subject of policy debates for about 150 years, quantitative researchhas been limited. To overcome data limitation, I construct a unified dataset based on several publishedbooks and publicly available data sources and study the relationship between industry growth and cartels,in particular, collusive markups and inner allocation mechanism within cartels.3 Concretely, I explore how
global containerization and explicit cartels formed one of the largest globally integrated markets via entry,
1 The Transport Policy Council (2007) of the Ministry of Land, Infrastructure and Transportation in Japan defines a shipping
conference as an agreement on freight rates and other business matters to restrain competition among container shipping lines
for the same routes. A consortium is a technical agreement between several shipping lines to form a group and operate a joint
service for services diversification, a reduction in the investment scale, and a cost reduction in the liner service. In addition,
consortia include alliances that are widely used.
2 There is an important difference between shipping conferences and alliances: Conferences are organized by specific routes
and directions, while alliances are formed globally. There may exist one conference covering trade on the transatlantic route andanother covering trade between Northern Europe and US Gulf ports. In addition, firms do not always participate in conferenceson all routes and directions they serve. Thus, conferences are very heterogeneous in their structure and membership.
3 See Otani and Matsuda (2023a) for more information on data construction.

2

exit, and shipbuilding investment of shipping firms by exploiting the route-year-level variations of freightrates, shipping quantities, and competition regimes.
Using the new dataset, I analyze the historical shipping price reductions in the 1980s known as the“container crisis” (Broeze 2002). It is anecdotally known that the crisis has been associated with two events:(1) the withdrawal of Sea-Land, which was the largest cartel member from shipping cartels in 1980 and (2)the enactment of the Shipping Act of 1984. The first event changed the market share of shipping cartels
significantly, while the second event neutralized the shipping cartels. To motivate my structural model, I
evaluate the effect of the above two events on shipping prices using regressions. I find that after the two
events, shipping prices decrease by 51%, which illustrates the effect of the industry regime on shipping prices
during 1966-1990.
However, it is not possible to disentangle the different explanations for the observed price reduction
using only reduced-form regression results. Therefore, I focus on the period between 1973 (i.e., the postOil-Shock period in the main three markets) and 1990 (i.e., before the initial year of the strategic alliances)and construct a dynamic structural model of firms’ entry, exit, and investment decision in homogenous
good markets under collusive and perfect competition regimes, which are exogenously determined by theenactment of the Shipping Act of 1984. Understanding the effect of shipping conferences with a structuralmodel contributes to the literature on competition law and industrial policy which have been investigatedin the shipbuilding and shipping industry (Kalouptsidi 2017, Barwick et al. 2019, Juhász et al. 2023).
I construct a structural model with explicit cartels. In the static competition analysis, I extend Porter(1983) to estimate cartel effects when firms and researchers are aware of the transition from a collusive
market regime to a competitive one. In the dynamic competition analysis, I apply the sequential dynamic
game approach proposed by Igami (2017) to market-year-level data on entry, exit, and investment, when themarket regimes are known. For each set of candidate parameters, I solve firms’ entry, exit, and investment
problems for a type-symmetric perfect Bayesian equilibrium (PBE) using backward induction. Then, I
construct the likelihood of observing the actual choices in the data and estimate parameters maximizing the
likelihood, rationalizing the observed entry, exit, and investment patterns.
Under static competition, I find that cartels increased shipping prices by $1,106 before 1979 and $440
during the 1980-1983 period. Specifically, cartel effects led to approximately a 20% increase in prices on the
Asia-to-Europe route before 1979 and a roughly 50% increase on the transatlantic westbound route. Under
dynamic competition, market heterogeneity in dynamic parameters can explain the observed data patterns.
Furthermore, I find that the estimated investment costs for all markets are higher compared to previous
studies on the global HDD industry (Igami 2017) and the recent container shipping industry (Jeon 2022),
which reflects the unique high sunk costs in shipbuilding and collusive pricing during the early stages of the3industry.
In counterfactual simulations, I evaluate the welfare performance of policies regarding cartel effects andinner allocation. Specifically, I analyze how the cartel effects and inner allocation mechanism would impact
entry, exit, and shipbuilding through the shifting static profit function. First, prohibiting cartels affects firms’
entry and shipbuilding investment, but the impacts are economically small due to the inelastic demand andlarge dynamic sunk costs relative to the present discounted value of the static markup in future periods.
Second, prohibiting cartels would not always lead to an increase in social welfare prior to 1984. This is due tosmaller profits, which in turn leads to a decrease in the number of firms entering the market and investing in
shipbuilding, resulting in a smaller market-level capacity and shifting up the supply equation while shifting
down the equation by neutralizing the cartel effects. This finding may provide an empirical justification forindustry protection policies that involve price and quantity control through a centralized mechanism in theearly stages of a new industry and underscore dynamic considerations that are necessary to assess welfare.
Third, I find that the actual inner allocation rule of shipping conferences based on tonnage shares is the best
to maximize social welfare. Specifically, under the hypothetical inner allocation rule supporting large firms,
producer surplus would increase, and consumer surplus would decrease, then social welfare would decrease.
Also, under the hypothetical inner allocation rule supporting small firms, producer surplus would slightly
decrease, and consumer surplus would not change, then social welfare would not change at an economicallysignificant level.

Related literature This paper contributes to three strands of the literature, namely, the analysis of theeffect of an explicit cartel, market dynamics of investment and entry/exit, and recent industrial policy andantitrust studies in the shipping industry. As far as I know, this paper is the first paper combining explicit
cartels and investment dynamics with known and simple inner allocation rules.
First, this paper empirically evaluates the effect of the shipping cartel on the market outcome and welfare.
While several papers empirically investigate the consequences of welfare under cartels in several industries
and auction formats using structural models, see the recent survey by Asker and Nocke (2021), this paper
focuses on the shipping conferences as a single explicit cartel entity, and departs from the traditional focus
on tacit collusion in the literature, e.g., Porter (1983), Bresnahan (1987), Miller and Weinberg (2017), andByrne and De Roos (2019). This paper contributes to the empirical literature on explicit cartels. Several
cartels have been analyzed as case studies, for example, sugar production (Genesove and Mullin 1998, 2001),
Norwegian domestic cement cartels (Röller and Steen 2006), bidding rings (Asker 2010b), gasoline pricing(Clark and Houde 2013, 2014), global coffee cartels (Igami 2015), collusive beer pricing (Miller and Weinberg2017), trade association of gynecologists (Alé-Chilet and Atal 2020), global oil industry (Asker et al. 2019),

4

global vitamin cartels (Igami and Sugaya 2022), and Joint Operating Agreements in the U.S. local daily
print newspaper industry (Tiew 2022). Each of these studies investigates specific features of each cartel.
Shipping cartels studied in my paper are recognized in survey papers such as those by Levenstein and
Suslow (2006), and Asker and Nocke (2021). Some studies, such as those of Morton (1997) and Podolny
and Morton (1999), examine the specific shipping cartels in the UK in the 1800s. Wilson and Casavant(1991) provide evidence on the regime change by the Shipping Act of 1984 using quarterly data of freightrates and shipping quantities of five selected commodities only on the transpacific route. However, they
do not exploit cross-sectional variations, especially between non-US and US routes. My data contain crosssectional variations of the freight rates. Thus, to the best of my knowledge, due to data limitations, nopapers investigated shipping cartels on six main routes after the global containerization in the 1970s.
The institutional background and approach are close to Igami (2015). Igami (2015) studies the impact ofmarket power on international coffee prices and evaluates the effect of a cartel treaty on coffee prices and its
global welfare consequences under counterfactual competition regimes, i.e., collusion versus Cournot–Nash ina single homogenous good market. Miller and Weinberg (2017) adopt a similar strategy for a specific merger
to test a conduct parameter between Bertrand–Nash and collusion in the US beer industry in differentiatedgoods markets. Clark and Houde (2013, 2014) study explicit price-fixing cartels in the Canadian gasoline
market by applying a differences-in-differences (DID) approach to collusive and competitive markets. I
cannot use a DID approach on my data because the cartel breakdown impact may propagate in the wholeindustry. Like these papers, I exploit the regime change of the whole industry caused by the exogenous cartel
breakdown events.
Second, this paper contributes to the literature on industry dynamics with a model including firms’
decisions on entry, exit, and investment. The shipbuilding investment size and technology adoption areclosely related in the container shipping industry because the size of a container ship captures technology
generation. Specifically, new generation ships are known as “Panamax” ships because of the size limits
for ships traveling through the Panama Canal. As the size of the capacity increases, the marginal cost of
shipping decreases. Each firm determines each year whether to pay a fixed cost to build large-capacity ships
or not conditional on the number of firms for each log-capacity level. Empirical applications include Ryan
(2012), Igami (2017), and Igami and Uetake (2020). My paper complements their findings with shipping
cartels inducing the collusive markup and inner allocation mechanism.
Third, this paper connects to the industry’s history from its beginning to its development after 2000,
which has gained attention in the industrial organization literature (Aguirregabiria et al. 2021).4 The most
4 The ocean shipping industry before the introduction of global container transportation is also studied. For example, Otani(2021) investigates Japanese shipping consolidation in 1964 by a structural matching model.

5relevant paper is Jeon (2022). She examines the relationship between demand uncertainty and firm-marketyear-level investment decisions by using container shipping demand and freight rate data between 1997 and2014. To facilitate her learning-based model, she needs to obtain initial prices and demand in the container
industry. Due to data limitation, she considers imputation and truncation approaches for missing shipping
demand data from 1966:Q2 to 1996:Q4 and confirms that the truncation approach performs well. Unlike
this paper, I use actual data and model shipping cartels explicitly. On cartel issues in a similar industry,
the most relevant paper is Asker (2010a). He studies how the presence of a cartel affects market conduct
following its dissolution, and how the dissolution might be affected by the obligations imposed on firms whoseek leniency in the tanker shipping market between 2001 and 2002. Kalouptsidi (2014), Brancaccio et al.
(2020), and Greenwood and Hanson (2015) investigate the bulk shipping industry after 2000. Bai and Li(2021) study the tanker market during 2017-2020 and investigate how the imbalance between the demandand supply of shipping services determines congestion. Although these industries are closely related to thecontainer shipping industry, each of these industries is differently characterized because market structure
and competition are different. Also, Kalouptsidi (2017) and Barwick et al. (2019) study the shipbuilding
industry, which is an upstream industry for the container and bulk shipping industries. These papers relyon the use of the Clarksons Research database and focus on the period after 2000.
This paper provides quantitative insights into the anecdotal evidence and theoretical models discussed
in the literature on maritime economics. As a unified survey, Sjostrom (2013) finds that most work on
shipping conferences has involved four kinds of models: monopolistic cartels, contestable markets, destructive
competitive, and empty cores. From the viewpoint of the industrial organization literature, the choice
between these models determines the pre-act supply-side behavior involving a markup. Regarding the
Shipping Act of 1984, Pirrong (1992) tests the model prediction of core theory using data of two specifictrade routes between 1983 and 1985. Clyde and Reitzes (1998) study the relationship between market power
and the market share of shipping conferences after the act.
In the international trade literature, Bernhofen et al. (2016) use country-level panel data on containerization adoption for the period 1962–1990. They focus on the effect of containerization adoption on the tradequantity, so they refer to the Containerization International Yearbook only for obtaining the first presenceof container technology in each country. Rua (2014) adds port-level data to their study and investigates the
diffusion of initial adoptions of containerized transportation. Coşar and Demir (2018) exploit rich Turkish
export data and examine modal choice between containerization and breakbulk shipping. My paper complements their findings by providing firm-market-year-level evidence and investigates market dynamics andwelfare. Like these papers, I exploit the change in competition regimes associated with the Shipping Act.

6

2

Data and institutional background

I provide details about the data in Section 2.1. I introduce the institutional background of the shipping
conference and the early history of the container shipping industry and discuss two key events associatedwith the change of competition regime in Section 2.2.
From the point of view of a firm’s entry and exit decisions, a market in this industry is a non-directional
location pair, i.e., if a firm operates a container ship in the eastbound of the transpacific, then it should
operate the ship in the westbound. A route is a directional trip, e.g., westbound and eastbound of thetranspacific.

2.1

Data

I use route-year-level and firm-market-year-level data of the container shipping industry. I define an operator
firm and a group as a firm. Each route (market) is divided into conference and non-conference routes(markets). For example, the transatlantic eastbound conference route is a single route and the transatlantic
conference market is a single market. A conference market is a market where all conference firms conducted
collusive behavior under the shipping conferences before the Shipping Act, but have competed since then.
A non-conference market is a market where all non-conference firms compete throughout the whole period.
As far as I know, price data in non-conference markets are not available.5 In this paper, I treat the nonconference markets as competitive fringe markets, remove them from the model, and focus solely on theconference market.

Shipping prices and quantities

First, I use route-year-level data of container freight rates and shipping

quantities for the conference routes. Collecting these data, in particular before 1994, is not trivial because
there is no single data source that covers the period between 1966 and 1993. Otani and Matsuda (2023a)
provide various data sources and a detailed guide on data construction for each of the container freight rates
and shipping quantities on major six routes: mainhaul and backhaul (separately) on the transpacific (Asiaand North America), transatlantic (North America and Europe), and Asia-Europe routes. Finally, I use
price and quantity data in the six conference routes between 1966 and 2009. Prices are adjusted by the U.S.
CPI in 1995.
Figure 1 illustrates the nonstationary trends of container freight rates and shipping quantities in theconference routes between 1966 and 1990. Container freight rates decrease with fluctuations and suddenly
5 Based on interviews with ex-practitioners in shipping companies, container freight rates for nonmember carriers were 20% to
30% lower than conference firms on the same routes. However, there was no data available on the trends in freight rates offeredby the non-conference carriers. In addition, although I checked The Japan Maritime Daily, the newspaper of the maritime
industry, I could not find any articles that continuously reported onfreight rates offered by non-conference carriers.

7

drop tremendously. However, the transitions of freight rates on Asia-Europe eastbound (Europe-to-Asia)
and westbound (Asia-to-Europe) routes are more unstable than that on transpacific and transatlantic routes
in the 1970s and 1980s. It might be because the strength of the shipping conference on the Asia-Europe
route declined, and its impact was more significant.6 The conference shipping quantities in all routes increase
monotonically between 1973 and 1990.7
The withdrawal of Sea-Land and enactment of the Shipping Act of 1984 in the US divide the conference
market’s regime, which is illustrated in the trend of the container freight rates in Figure 1. Under thelegislation of the Shipping Act of 1984 in the US, shipping conferences were easier to form and lost privileges.
Also, after 1984, the transpacific and transatlantic routes experienced severe price reductions via market
competition. The change of the industry regime shaped the container crisis.

(a) Price(b) Quantity

Figure 1: The trends of the container freight rates and shipping quantities.
Note: The container freight rates before 1992 refer to conference prices. The container freight rates after 1993 are the unified
prices based on the conference and non-conference prices, and the difference between them is known to be vanished due to the
Shipping Act of 1984. The latter data are standard and are often used in the literature such as Jeon (2022).
Sources: Otani and Matsuda (2023a)

Tonnage share across conference and non-conference markets

Second, I use ship-level data from aseries of the Containerization International Yearbook (CIY). I use the information on the build year, the nameof the ship operator, the deployed route, and the shipping capacity measured by the twenty-foot equipment
units (TEU). I assign the main three routes (that is, transatlantic, transpacific, and Asia-Europe) to all ships
6 Based on an interview with an ex-executive of a Japanese shipping company, conferences related to Asia-Europe had astrict membership screening process, and the number of voyages by member companies was clearly defined (closed conference).
In addition, some members of the conference pooled their freight and then redistributed them. In contrast, the conferences fortranspacific routes were free to join or leave (open conference), and freight pooling was explicitly prohibited under the Shipping
Act of 1916 in the US.
7 See Otani and Matsuda (2023a) for an analysis on the trends of the freight rate and quantity after 1990. It is anecdotally
known that the decrease of shipping prices between 1976 and 1978 might be caused by the reopen of Suez canal.

8(a) Transpacific(b) Transatlantic(c) Asia-Europe

Figure 2: Conference and non-conference market shares in the whole industry
Note: Conference and non-conference market shares are calculated by the tonnage share of ships deployed in the westboundand eastbound of the market. I highlight the market share of Sea-Land, which had a key role in the conference market.
Sources: Containerization International Yearbook

deployed on the routes, including subareas. Almost all ships are deployed in eastbound and westbound routes
in each assigned route.8 I combine the ship-level data with the firm-market-year-level data of entry/exit in
the market and joining/leaving conference and non-conference markets from various data sources.9
Based on the tonnage share of the firm-market-year-level data, I calculate the shipping tonnage shares of
the conference and non-conference firms.10 For example, the transatlantic eastbound route has conference
and non-conference routes independently. Figure 2 illustrates the transitions of market shares of the conference and non-conference firms and Sea-Land in each market, aggregating eastbound and westbound routes.
Throughout all periods, the transatlantic market was competitive because of the growing number and size of
non-conference firms. In contrast, the Asia-Europe market was dominated by conference firms, particularly
before 1980. The transpacific market is the middle case. Remarkably, the withdrawal of Sea-Land fromshipping conferences would affect the change of conference shares because it had the largest share in thetranspacific and transatlantic markets.

Investment pattern within a conference market

Figure 3 shows firm-year-level investment patterns

measured by TEU in each conference market except for Sea-Land. First, the largest firm remained in thesame position for many years. Second, almost all active firms accumulated tonnage size, and investment
booms and patterns are similar within each market. These two features not only provide an actual dynamic
8 The tonnage of ships deployed in multiple main routes is treated as the shipping capacity in “Multiple” routes and omitted
in the analysis because I could not identify the allocation of deployed ships to multiple routes. The ships deployed in multiple
routes were going to be common only after 1980. Thus, the effect of omitting these ships is limited.
9 See Otani and Matsuda (2023a) for additional details. This uses (Department of Transportation, the United States 1992,
Maritime Industry Research Institute 2004, Pace 1981, Gilpin 1983, Van Ham et al. 2012) and information from the website of
the port of Long Beach (https://polb.com/port-info/timeline/). See the industry-year-level merger patterns between 1966
and 2022 in Otani and Matsuda (2023b).
10 In the literature, the shipping quantity share is approximated by the capacity share because the utilization rate washigh. For example, in one of the oldest data, the utilization rate in the transpacific was 60% to 100% between 1997 and2000 (https://www.mol.co.jp/ir/data/cfh/pdf/data0105_2.pdf) even in the mature stage of the industry. I could not findevidence that firms strategically controlled utilization rates before 1990.

9equilibrium path but also help state discretization in the dynamic estimation part. See Section 3.

(a) Transpacific(b) Transatlantic(c) Asia-Europe

Figure 3: Firm-market-year-level capacity transition
Sources: Containerization International Yearbook

Table 1: Summary statistics of route-year-level and market-year-level variables

Quantity in conference route (1 mil TEU): Qrt
Quantity in nonconference route (1 mil TEU): Qnonrt
Price in conference route ($1000 per TEU): Prt
Log ($ GDP of destination area): Xrt
MarketType

Asia and Eur

CartelNoncartel

Transatlantic

CartelNoncartel

Transpacific

CartelNoncartel

N

mean

sd

min

max

138
138
138
138

0.61
0.42
2.79
28.26

0.47
0.33
1.23
0.73

0.00
0.00
0.89
26.33

2.05
1.30
6.65
29.42

Num of firms: Nmt
Total tonnage (1 mil TEU): Smt
Num of firms: Nmt
Total tonnage (1 mil TEU): Smt
Num of firms: Nmt
Total tonnage (1 mil TEU): Smt
Num of firms: Nmt
Total tonnage (1 mil TEU): Smt
Num of firms: Nmt
Total tonnage (1 mil TEU): Smt
Num of firms: Nmt
Total tonnage (1 mil TEU): Smt

mean

sd

min

max

20.93
0.19
28.12
0.11
14.90
0.11
81.67
0.18
14.70
0.17
30.36
0.12

4.68
0.05
8.91
0.07
2.58
0.04
26.15
0.07
3.91
0.09
8.67
0.06

2.00
0.00
2.00
0.00
6.00
0.01
3.00
0.00
1.00
0.00
4.00
0.01

25.00
0.26
37.00
0.21
17.00
0.18
102.00
0.25
19.00
0.31
38.00
0.19

Note: The data spans 25 years (1966-1990) for six routes. Transatlantic routes opened in 1966, transpacific routes in 1967, andAsia-Europe routes in 1971. For panel (b), the shipping prices before 1992 refer to conference prices, while the shipping prices
after 1993 are the unified prices based on the conference and non-conference prices and the difference between them vanished
due to the Shipping Act of 1984. The latter data are standard and are often used in the literature such as Jeon (2022).
Sources: Containerization International Yearbook and Otani and Matsuda (2023a)

Table 1 shows the summary statistics of route-year-level and market-year-level variables. The subscripts
r, m, and t are the route, market, and year index, respectively. It displays the route-year-level variablesof the conference and non-conference shipping quantities Qrt and Qnon
rt , conference shipping price Prt , andGDP of the destination area, Xrt between 1966 and 1990. Also, it countains the number of firms, Nmt andtotal tonnage, Smt in each market. The key feature is that the number of firms in non-conference markets
10Table 2: Summary statistics of firm-market-year-level variables(a) Firm-market-year-level variables of conference firms (1966-1990)

MarketAsia and Eur

Transatlantic

Transpacific

Num of ships
Total tonnage (1000 TEU)
Quantity share: qimt /Qmt
Quantity share: qimt /Qwholemt
Num of ships
Total tonnage (1000 TEU)
Quantity share: qimt /Qmt
Quantity share: qimt /Qwholemt
Num of ships
Total tonnage (1000 TEU)
Quantity share: qimt /Qmt
Quantity share: qimt /Qwhole
mt

mean

sd

min

max

5.57
8.87
0.05
0.04
7.59
7.35
0.07
0.04
9.60
11.08
0.08
0.04

4.59
10.04
0.08
0.06
7.46
10.62
0.09
0.05
8.28
11.76
0.12
0.05

1.00
0.60
0.00
0.00
1.00
0.10
0.00
0.00
1.00
0.31
0.00
0.00

20.00
40.70
0.57
0.47
36.00
66.55
0.50
0.32
28.00
47.22
1.00
0.27

(b) Firm-market-year-level variables of non-conference firms (1966-1990)

MarketAsia and Eur

Transatlantic

Transpacific

Num of ships
Total tonnage (1000 TEU)
non
Quantity share: qimt
/Qnon
mt
non
Quantity share: qimt /Qwholemt
Num of ships
Total tonnage (1000 TEU)
non
Quantity share: qimt
/Qnon
mt
non
Quantity share: qimt /Qwholemt
Num of ships
Total tonnage (1000 TEU)
non
Quantity share: qimt
/Qnon
mt
non
Quantity share: qimt /Qwhole
mt

mean

sd

min

max

3.99
3.42
0.05
0.02
3.17
2.15
0.02
0.01
4.63
3.55
0.04
0.02

4.92
5.05
0.09
0.07
3.18
3.14
0.04
0.02
4.50
5.20
0.06
0.04

1.00
0.11
0.00
0.00
1.00
0.10
0.00
0.00
1.00
0.13
0.00
0.00

30.00
28.01
0.88
0.88
26.00
29.81
0.54
0.34
24.00
32.37
0.53
0.51

Note: The large market shares capture the early stage of the industry where only a few active firms exist.
Sources: Containerization International Yearbook11

is larger and the average tonnage is smaller than in conference ones, which implies that the assumption ofcompetitive fringe is reasonable.
Panel (a) in Table 2 shows firm-market-year level variables in the conference markets for the numberof ships, total tonnage, and shipping quantity share as measured by tonnage size relative to the conference
market and whole market, qimt /Qmt and qimt /Qwhole. The mean of the number of ships varies from 5.57 tomt
9.60. The mean quantity share in the conference market is 5.57% in the Asia-Europe market, 7.59% in thetransatlantic market, and 9.6% in the transpacific market. Panel (b) in Table 2 displays firm-market-yearlevel variables in the non-conference markets. The average non-conference shipping quantity shares in thewhole market are less than half of conference ones. This again suggests that the assumption of competitive
fringe is reasonable as in the market-year-level data.

2.2

Industry Background

I provide some key features of shipping conferences, that is, an internal mechanism for conference firms
and an external mechanism for non-conference firms. See Otani and Matsuda (2023a) for additional details.
Before introducing the container shipping industry, I summarize the shipping conferences in the liner shipping
industry whose subset was a container shipping industry at that time.

Shipping conferences The main purpose of shipping conferences in the liner shipping industry is market
stabilization by controlling entry via excess capacity (Fusillo 2003), predatory pricing (Morton 1997, Podolny
and Morton 1999), price discrimination (Fox 1992, Clyde and Reitzes 1998), loyalty contracts (Marin andSicotte 2003), and so on. To this aim, the shipping conferences agreed on a variety of other issues between
the shipping companies in addition to freight rates. The content of the agreements can be roughly divided
into three categories: (1) alternatives to suppress freight rate competition among the member shipping
companies, (2) alternatives to prevent the outflow of shippers to non-conference shipping companies, and (3)alternatives to directly exclude non-conference vessels.
To avoid freight rate competition, rate agreements and vessel allocation agreements are concluded among
member shipping companies. The rate agreements are signed by conference members to agree on rates foreach product and to update rates jointly. The vessel allocation agreements adjust the amount of tonnage
to be allocated, the number of voyages, ports of call, operation schedules, and cargo to be loaded. Thesefeatures have been modeled as price and quantity-fixing cartels. According to United Nations Conference ofPlenipotentiaries On A Code Of Conduct For Liner Conferences, the service quantity was determined basedon the tonnage capacity share.11 This feature is incorporated in the supply side model of Section 3.
11 See United Nations Conference of Plenipotentiaries On A Code Of Conduct For Liner Conferences published by United12Conference tariff rates (freight rates) decided by these agreements had public notice, and no specific entry
restrictions were imposed on the ocean shipping market. Thus, the market is always subject to competition
from non-conferences’ vessels and new entrants. For this reason, the shipping conferences introduced theDual Rate System, the Fidelity Rebate System, and the Differed Rebate System to ensure the effectivenessof the freight rate agreements and prevent shippers from flowing to non-conference shipping companies thatoffered lower rates than the conferences’ tariff rates.12 These systems are recognized as entry deterrents topromote the stability of the freight rate and liner services.13
Conferences also used “fighting ships,” which are vessels temporarily put into service at a similar schedule
as non-conference shipping companies and at lower rates.14 Fighting ships were used to force non-conference
shipping companies to leave the route. All the members shared the losses associated with the operation offighting ships.
On the modeling across conference and non-conference markets, I assume that non-conference markets
are competitive fringe markets. That is, I treat non-conference markets out of the model. Also, I assume
that shippers’ decisions on the use of conference or non-conference ships are exogenous. That is, I treat thedemand for shipping as a variable in the data. These assumptions are needed due to the data limitation andare restated in Section 3.
After the 1960s, the circumstances and nature of shipping alliances rapidly changed. In particular,
shipbuilding investment was centered on containerizations explained later and pro-competitive amendments
to shipping laws in the United States have had a major impact on the functioning of shipping alliances andmarket competition in the shipping market.
The history of container shipping began with Malcolm P. McLean, the founder of the US land transportaNations in 1975. Section Article 2, PARTICIPATION IN TRADE, 5 in this article provides that, “If, for anyone of thecountries whose trade is carried by a conference, there are no national shipping lines participating in the carriage of that trade,the share of the trade to which national shipping lines of that country would be entitled under article 2, paragraph 4 shall be
distributed among the individual member lines participating in the trade in proportion to their respective share.” The issue ofnational shipping concerns trade between developed and developing countries. In the three main markets in this period, mydata contain no national shipping. Thus, this statement applies to my paper.
12 In the Dual Rate System, a shipper and a shipping conference conclude an exclusive patronage contract/loyalty agreement
and provide transportation service for the specific route. The contract rate is lower than the spot rate under the condition
that the shipper uses only conference member carriers’ service within a specific contract period. The Fidelity Rebate refunds
a portion of the freight if the shipper uses only the conference carriers within a specified period (4-6 months). The Differed
Rebate System is also an incentive to use conference carriers. Under the system, if a shipper had used only members’ services
for a specified refundable period (4-6 months), and if it does not use any non-conference members’ service for the deferment
period following the refundable period, a certain amount of money is refunded upon the shipper’s request. The refund amount
was usually around 10% of the freight. Fox (1992) uses the US port pair-level data in 1977 to examine the effect of the dual
rate contract and consumer loyalty.
13 For instance, Marin and Sicotte (2003) examine the economic effects of exclusive contracts of ocean shipping cartels during
the 1950s between firms and the ultimate consumers of their product. They record that, “During the congressional investigationsof shipping conferences in the late 1950s and early 1960s documents obtained from an ocean carrier contained an admissionthat ‘the entire contract system is a fighting measure to get rid of outside competition’ ” (p.198).
14 See Marshall and Marx (2014) (page 148) and Harrington et al. (2018) for reference to put the strategy of shipping
conferences in general cartel literature. Harrington et al. (2018) classify the general response of cartels to the expansion of
non-cartel supply into four strategies: takeover, starvation, coercion, and bribery. The fighting ships are classified into coercion
strategy.

13

tion company Sea-Land Service. The first international container ship was employed by Sea-Land Service forthe transatlantic route in 1966, and for the transpacific route in 1967. For the Asia-Europe route, the first international semi-container ship, the Cornelia Maersk, was employed in 1967. However, the first international
full-container ship, the Kamakura-maru, was delayed to start in 1971, which is recognized as the first yearof global containerization. Dissemination of container shipping called global containerization induced thefollowing market changes between 1966 and 1990: (1) transforming the cost structure, (2) lowering barriers
to entry, and (3) stimulating the rise of (non-conference) shipping companies in developing countries. See
Otani and Matsuda (2023a) for details on each point.

Withdrawal of Sea-Land from shipping conferences in 1980 In the last years of the 1970s, a
substantial increase in competition for transpacific routes put pressure on rates. In 1979, Sea-Land introduced
eight SL-7 high-speed container vessels with a speed of 33 knots. These vessels worsen the profitability of
the company. The company withdrew from the shipping alliance to ensure its profitability.
However, because of the conference’s dual freight rate system, shippers who had contracts with conference
carriers were unwilling to pay the penalty to switch to Sea-Land. At the time, the double freight rate system
did not cover only port-to-port cargoes. Therefore, Sea-Land focused on import shippers and intermodal
cargoes that were not covered by the double-freight rate system. In addition, the fact that Sea-Land paid
the freight cost of returning containers from inland to the port rather than passing them on to shippers has
led to a reduction in freight rates.

The Shipping Act of 1984 in the US In the U.S., the new Shipping Act was enacted in June 1984 aspart of the deregulation policy under the Reagan administration. The aim of the act was to allow member
carriers to make individual agreements with shippers on freight rates and services and to unbind shippers
from shipping alliances so that shippers could make more appropriate choices. It drastically changed thecompetition regime, especially in the US-related routes.15
First, the Shipping Act of 1984 included the mandatory right to Independent Action (IA). IA refers toa behavior that a member firm may define independently its freight rates or services that deviate from theconference tariff rates. It guaranteed the right for the member carriers of the shipping conference to set theirown rates or services different from those of the alliance under the principle of openness.
Second, the act required conferences to allow the right to form service contracts (SC). SC refers to acontract in which the shipper commits in advance to load a specific quantity or more of cargo to the shipping
company during a specific period. Under this contract, the shipping company reserves the space necessary
15 Wilson and Casavant (1991) provide anecdotal evidence and a case study of the effect of the Shipping Act of 1984.

14

to carry the cargo and applies discounted freight rates.16
Third, the act prohibited the Dual Rate System. As such, the shipping conference lost its binding
power on shippers, and individual shipping companies frequently exercised their right of independent action,
which encouraged competition among shipping companies and led to a significant decline in freight rates on
US-related routes.17

2.3

Reduced form evidence on the Container Crisis

I quantify the effect of the withdrawal of Sea-Land and Shipping Act of 1984 on the shipping prices.18 I use
data of six routes between 1973 and 1990 to quantify the changes in the container freight rate before andafter the competition regime change induced by the Act. I drop data before the 1973 oil crisis and after
1991 because of the Soviet collapse in 1991 and the next deregulation act, the Ocean Shipping Reform Act(OSRA) of 1998.
I quantify the effect of the withdrawal of Sea-Land and Shipping Act of 1984 by least squares with dummy
variables for the two events, which are 1 after the event and 0 otherwise. I incorporate the variations of thedifference of cost shifters, that is, crude oil price, and specify the log container freight rate Prt in route r inyear t as:log Prt =β1 1(after 1980)rt + β2 1(after 1984)rt + β3 log Xrt + β4 log Wrt + τr + ξrt ,where log Xrt is the log of GDP for the destination area, log Wrt is the log of a mile-weighted crude oil price,τr is a route fixed effect, and ξrt is assumed to be an i.i.d. error term. We estimate parameters β1 , β2 , β3 , β4 ,and τr .19
Table 3 reports the regression results. The coefficients in Model 1 indicate that the withdrawal of SeaLand from cartels in 1980 decreased the container freight rate by 43% (i.e., exp(−0.570)−1 = −0.43). Model
2 also indicates that the enactment of the Shipping Act of 1984 decreases the container freight rate by 43%(i.e., exp(−0.556) − 1 = −0.43). Model 3 includes both dummy variables and shows that the after-1984
dummy explains the part of the price reduction given by the coefficient of the after-1980 dummy.
Models 4, 5, and 6 include route fixed effects and provide similar signs of the coefficients for the after1980 and after-1984 dummies. Incorporating route fixed effects significantly increases the adjusted R2 and16 The minimum number of containers promised by the shipper to the shipping company is called the MQC (Minimum
Quantity Commitment).
17 Japan Maritime Center (2008) pointed out that the Dual Rate System was the most effective way shipping companies kept
their shippers when the conference system was functioning.
18 Otani and Matsuda (2023a) show that a structural break test reveals that the container crisis occurred around 1980 in allroutes and the Shipping Act of 1984 heterogeneously boosted the container crisis in the US routes.
19 Note that adding fixed effects controlling unobserved heterogeneity within a year induces an overparametrization problemof the coefficients of dummy variables in my route-year-level panel data.

15

Table 3: Changes in log of the cartel’s freight rates, Prt .
Model 11(after 1980)

Model 2Model 3Model 4-0.424**(0.087)-0.047(0.161)0.179***(0.027)-0.556**(0.197)-0.100(0.159)-0.159(0.107)-0.491**(0.150)-0.404**(0.151)0.151(0.229)-0.018(0.066)

108
0.437
0.421
by: route

108
0.375
0.356
by: route

108
0.485
0.465
by: route-0.570**(0.177)1(after 1984)
log GDP: log(Xrt )log(crude oil price): log(Wrt )Route FE
Num.Obs.
R2
R2 Adj.
Std.Errors

Model 5Model 6-0.226+(0.098)0.152**(0.038)-0.306+(0.142)-0.349+(0.144)-0.051(0.056)-0.420**(0.074)-0.296*(0.111)-0.015(0.161)0.018(0.031)

X
108
0.804
0.789
by: route

X
108
0.757
0.737
by: route

X
108
0.824
0.808
by: routeNote: Estimation is with OLS. The dependent variable is the route-year-level average of the log of freight rate measured by US
dollars (adjusted to 1995 CPI) per TEU. The sample covers the period between 1973 (i.e., after the 1973 oil shock) and 1990
for six markets. Significance levels are denoted by + p < 0.1,∗ p < 0.05,∗∗ p < 0.01, and ∗∗∗ p < 0.001. The numbers between
parentheses give the standard errors, which are clustered at the route level.

reduces the levels and standard errors of the dummy variables by controlling market-year-level unobserved
heterogeneity. Model 6 shows that the withdrawal of Sea-Land from cartels in 1980 decreases the container
freight rate by 34% (i.e., exp(−0.420)−1 = −0.34) and the enactment of the Shipping Act of 1984 additionallydecreases it by 26% (i.e., exp(−0.296) − 1 = −0.26). The composite effect of the two dummies shows thatafter the container crisis of 1984, the price decreased by 51% (i.e., exp(−0.296 − 0.420) − 1 = −0.51). Thus,
estimation using a longer and route-year-level panel data suggests an overestimation of the effect of the
Shipping Act of 1984, as discussed in previous studies such as Wilson and Casavant (1991).
The reduced-form analysis yields several important insights into the container crisis. However, there areseveral potential reasons for observing this pattern. For example, marginal costs may have changed overtime. Alternatively, there may have been changes in the industry conduct. To disentangle these explanations
and gain much more detailed insights into the different channels, I develop a structural model in the following
section.

3

Model

I construct a structural model to investigate how the withdrawal of Sea-Land from cartels and the enactmentof the Shipping Act of 1984 reduce container freight rates through the markup reduction of cartels and affectthe entry/exit/investment dynamics in the industry. I assume that conference and non-conference routes
are mutually independent both on demand and supply sides and treat non-conference firms as price takers

16

in a competitive fringe. These assumptions provide a tractable model under limited data, i.e., without nonconference price data.20 Also, because the non-conference markets consist of many small firms relative to theconference markets, the competitive fringe assumption is reasonable. Consequently, the shipping quantities
of non-conference firms are excluded in the subsequent analysis. As before, I drop the data before the 1973
oil crisis and after 1991 because of the Soviet collapse in 1991 and the next deregulation act, i.e., the Ocean
Shipping Reform Act (OSRA) of 1998.
I consider a finite horizon and a nonstationary environment. For each market in each year, incumbents
and potential entrants observe a vector of all individual tonnages and exogenous demand as state variables.
Then, the static profit determined by the state and cartel effect is realized. Given some specified order,
each incumbent firm sequentially takes a discrete action from the action set consisting of exiting the market,
staying in the market without investments, and staying with investments after observing all previous actionsof all firms. Investment in this paper is shipbuilding investment increasing the tonnage size. After observing
all actions of all incumbents, each potential entrant takes an action from the action set consisting of entering
the market and exiting the market. After all firms decide actions, the state variables for the next year are
updated based on their actions.21 Thanks to the uniqueness of the equilibrium, I can solve the dynamic
equilibrium backwardly as in Igami (2017, 2018).

3.1

Demand and supply

Demanddenote the total shipping amounts in market m in year t and directed
and Qwhole
Let Qwholertmtroute r in year t, respectively. The market demand consists of the eastbound and westbound of the routedemand in market m. A container shipping route in route r in year t is divided into conference and nonnon
are total shipping amounts of conference= Qrt + Qnon
conference routes, i.e., Qwhole
rt , where Qrt and Qrt
rtand non-conference firms, respectively. For example, the transatlantic route has transatlantic conference andnon-conference routes. I do not model shipping customer behavior between conference and non-conference
20 Recently, Clark et al. (2018), Gabrielli and Willington (2020), and Caoui (2022) study the interaction of partial cartels
and non-cartel firms in auction formats and Harrington et al. (2018) study how the German cement cartel controlled the
expansion of non-cartel supply from Eastern European countries. I do not consider strategic interactions between conference
and non-conference firms because of the absence of non-conference price data.
21 Similarities and differences of my paper from Igami’s papers and Jeon (2022) are summarized as follows. Similarity with
Igami’s papers is in the dynamic part, that is, the equilibrium concept, key specification, and computational technique. The
difference from Igami’s papers is in the static part, i.e., cartel effects (ωimt ), and no static competition. Similarity with Jeon
(2022) is static parts, that is, specifications of log-log demand and supply side without cartel. The difference from Jeon (2022)
is the dynamic part, i.e., equilibrium concept, key specification, and computational technique. She incorporates learning of
demand into “moment-based Markov equilibrium” with additional variables such as the backlog and charter data in 2006-2014.
She solves the model by the full-solution method even under potential multiple equilibria. Her learning model finds that theinitial condition problem is ignorable based on an AR(1) interpolation. However, her assumptions are questionable because theindustry had cartels and nonstationary markets. Instead of her complicated model, I assume no learning and assume tractable
type-symmetric Perfect Bayesian Equilibrium with a rational expectation of cartel breakdown.

17

shipping services.22
Let Prt (srt , Drt , ζrt , ηrt ) denote the conference shipping prices where srt is endogenous observed state
capturing route-level capacities of all firms as defined later, Drt is exogenously determined observed demandstates, and ζrt and ηrt are i.i.d. demand and supply errors. Note that the errors are realized at the routeyear-level, not at the firm-route-year level. 23 Let Qrt (srt , Drt , ζrt , ηrt ) and Qnon
be the demand function
rtof conference and non-conference shipping. I assume that Qnon
is exogenously determined by fringe nonrt
conference firms and focus on Qrt (srt , Drt , ζrt , ηrt ) in the estimation.
Demand for container shipping of conference firms in route r in year t, Qrt (srt , Drt , ζrt , ηrt ), is assumed
to have constant elasticity and specified in the following parametrized form:24

Qrt (srt , Drt , ζrt , ηrt ) = exp(Drt )(Prt (srt , Drt , ζrt , ηrt ))α1 exp(ζrt ),(1)

where α1 is the parameter of the slope of the demand curve. I omit the i.i.d. errors ζrt and ηrt in the static
equilibrium prices and quantities because these are numerically determined on average by numerical draws
as in Igami (2017).

SupplySuppose Nrt firms exist in route r in year t. Each firm observes the state vector (srt , Drt ) =(sirt , s−irt , Drt ), where sirt is the individual discretized endogenous state, i.e., firm-level tonnage size, s−irt
rtis tonnage size of firm i’s rivals, srt = (sirt )N
i=1 = (sirt , s−irt ) is the industry discretized endogenous state,i.e., the vector of the individual discretized endogenous state, and Drt is the industry discretized exogenous
state. The discretization is discussed in the dynamic part. I assume that in the spot market, firms do notcontrol capacity strategically given their capacity constraints (Jeon 2022).
22 Customers can choose either or both conference and non-conference services. I collected data of whole quantity Qwhole (=mt
non
Qmt + Qnon
mt ) and recover conference and non-conference market quantity, Qmt and Qmt , as in the maritime literature.
Concretely, the market (quantity) share of conference and non-conference service can be approximated proportionally by tonnage
shares because the industry-level container utilization rate is 80-95% historically, and I did not find any evidence of a low
utilization rate. Here, Qnon
mt is determined by the sum of individual service quantities out of the model. Finally, Qmt =Qwhole− Qnonmt
mt is residual quantity determined by shipping conferences.
23 Conference firms “follow” prices and quantities determined by shipping conferences. Non-conference firms “set” prices andquantities based on individual decisions so the price data do not exist because they did not need to be report their prices
publicly. It is anecdotally known that the non-conference prices were lower than conference ones by 10-20% before 1984. Pricedifferences even in the homogenous service markets come from safety, reputation, unobserved quality, inertia, rich options, andso on.
24 I follow Kalouptsidi (2014) and Jeon (2022) in the static demand estimation. There are a few different points from thesestudies. First, my data do not contain quarterly-based variables before 1994, so my analysis is based on market-year-level
observations. This ignores short-run fluctuation of container freight and shipping quantities. Second, my data observe theinitial stage at which some price instruments used in these studies cannot be constructed. For example, the fraction of shipsthat are over 20 years old can be constructed only after 1986.

18

Individual supply equation Firm i’s marginal cost giving service quantity qirt is defined as

mcirt (qirt , sirt ) = γ0 + γ1

qirt
,
sirt

(2)

where γ0 and γ1 are cost parameters. If γ1 is positive, the marginal cost increases linearly as the firm’s
quantity decreases due to the difficulty of operations. If γ1 is negative, the marginal cost decreases linearly due to the cost efficiency. I leave the sign of γ1 as an empirical question. This specification assumes
that cost heterogeneity comes only from service quantity and tonnage size and there is no firm-level unobserved heterogeneity. Also, note that the tonnage size sirt is not exactly the firm-year-level shipping
capacity because I do not observe service frequency. The total cost of shipping qirt has the analytical form,
R qirtqirt 2
mcirt (q, sirt ))dq = γ0 qirt + γ1 2s+ C where C is a constant of integration. I assume that C = 00irt
and the constant cost is absorbed in the dynamic operation cost introduced later. Finally, note that theabove marginal cost specification is critical and may be the only specification that allows share-weighted
aggregation in a theoretically correct way and that other specifications using sirt are not available.
In a competitive market, the market price equals route marginal cost (route MC) which is the sum of
individual marginal costs (2) weighted by the tonnage share plus an i.i.d. route-year-level unobserved error
ηrt :

Prt =

Nrt
X
sirt

S
i=1 rtQrt
mcirt (qirt , sirt ) = γ0 + γ1
+ηrt ,
S|{z rt}
route MC

where Srt =PNrt

i=1 sirt . This specification is similar to Porter (1983).

Firm i’s static profit in route r in year t is defined as
Z qirtπirt (qirt , sirt , Drt ) = Prt (srt , Drt )qirt −mcirt (q, sirt ))dq,0

given demand state Drt , tonnage capacity sirt included in srt , and equilibrium price Prt (srt , Drt ). Taking. Solving this for qirt , firm
its first-order condition with respect to qirt , I obtain Prt (srt , Drt ) = γ0 + γ1 sqirt
irt
i’s individual supply equation qirt is defined byqirt (Prt (srt , Drt ), sirt ) =Prt (srt , Drt ) − γ0sirt .
γ1(3)

There are some remarks. First, aggregating individual supply equations gives route marginal cost, i.e.,
PNrt
Prt −γ0rt
Qrt =Srt gives route supply equation, Prt = γ0 + γ1 Q
i=1 qirt =γ1
Srt without shipping cartels.

19

Second, all firms provide service quantities up to the level at which their marginal costs equate the price,i.e., mcirt (qirt , sirt ) = Prt for all i, and then obtain positive profits. Third, in the container shipping industry,
the individual supply qirt (Prt (srt , Drt ), sirt ) is determined either by the allocation rule based on tonnage
share before 1983 or the above individual supply equation after 1984. Next, I discuss the choice of modeling.

Route supply equation with and without cartel behavior

The route supply equation is given as thecapacity-share-weighted sum of all firms’ supply equations plus the route cartel effect:

Prt = γ0 + γ1

Qrt
+ γ̃1(t ≤ 1983) ,
|
{z
}
Srt

(4)

route cartel effectwhere parameter γ̃ shifts the route supply equation.
The idea of the route cartel effect is the same as Porter (1983). Unlike this paper, however, I am agnostic
on the behavior of the shipping conferences which are explicit cartels with the breakdown timing known
to firms and researchers. I treat the route cartel effect as a deviation from a competitive price. Shipping
conferences shift up the original supply equation (i.e., route marginal cost) by route cartel effect as in Igami(2015). We can interpret as if they pretend to have higher marginal costs. The last term captures (partially)collusive markup directly instead of endogenizing (partially) joint profit maximization (i.e., the marginal
revenue equals the marginal cost) in homogenous goods markets. Although the above direct approach is
restrictive and gives no structural sense, I believe that endogenizing (partially) joint profit maximization
is not a good approximation for shipping conferences for the following reasons. First, container shipping
firms provide shipping services on fixed schedules between ports, so it might be difficult to adjust the total
service quantity to some target level shipping. Second, conferences can control prices to compete with nonconference firms out of the model. Third, the assumptions of Porter (1983) that capacity information does
not matter and the output shares of cartel members are relatively stable across the regimes are inadequate
in my data of a nonstationary industry history as shown in Section 2. Fourth, as a practical reason, thecollusive power as discussed in Section 2 is potentially time-varying and the sample size is not large enoughto conduct parameter estimation (Bresnahan 1982), discussed in Matsumura and Otani (2023a,b,c). See
Appendix C for the discussion of the trade-off of modeling choices and theoretical details. For the above
reasons, I take a direct approach in which the cartel effect γ̃1(t ≤ 1983) is a period effect that can be specified
more flexibly even under small sample.

20

3.2

Equilibrium price, quantity, and profit in spot markets

The industry regime is exogenously determined by the Shipping Act of 1984 and classified into two types,
i.e., collusive regime before 1983 and competitive regime after 1984.

Determinants of Prt in competitive regime after 1984 After 1984, Prt (srt , Drt ) is determined byan intersection of the demand and supply equations as perfectly competitive prices. Substituting (1) into∗(4) and solving the following for Prt given (α, γ), we numerically obtain an equilibrium price Prt(srt , Drt )as follows: Solving numerically the following fixed point problem for Prt given parameters, we obtain an∗
equilibrium price Prt(srt , Drt ).

Prt = γ0 + γ1

exp(Drt ) · (Prt )α1+ γ̃1(t ≤ 1983) .
{z
}
|
Srt
=0

Note that the fixed point is unique if α1 < 0, γ0 > 0, and γ1 > 0, that satisfy the standard downward demand
and upward supply equations.25

Determinants of Prt in collusive regime before 1983 Before 1983, shipping conferences consisting of
all conference firms set total quantities and quotas. The equilibrium price Prt is determined by the demandand price-quantity decision of shipping conferences. As discussed above, we do not explicitly model marketyear-level price-quantity decisions of shipping conferences. Instead, the effect is captured by the cartel effectterm in Equation (4). Larger the term, higher the market price by shifting up the supply equation.
Solving the following fixed point problem for Prt numerically given parameter values, we obtain the∗(srt , Drt ) as a solution ofequilibrium price Prt

Prt = γ0 + γ1

exp(Drt ) · (Prt )α1+ γ̃1(t ≤ 1983) .
|
{z
}
Srt
>0

∗
Finally, we obtain the equilibrium quantity Q∗rt (srt , Drt ) by substituting Prt(srt , Drt ) into (1).
exp(Drt )·(Prt )α1
and find the root of ∆(Prt ) = 0. Then, ∆(Prt ) is an increasing functionrt ) = Prt − γ0 − γ1
Srt∂∆(Prt )exp(Drt )α1 −1 > 0 and lim
=
1
−
γ
α
(P
)
rt
1
1
Prt →0 ∆(Prt ) < 0 where α1 < 0, γ0 > 0, and γ1 > 0. So, the
∂Prt
Srt

25 Define ∆(Pof Prt , i.e.,
solution is unique as the equilibrium price under these standard parameters. Estimated parameters in Section 5 satisfy thecondition.

21

Static profits in market m and route r

For the dynamic part, we derive market-year-level variables

by aggregating route-year-level ones. Firm i in market m in year t has the static profit defined as follows:

πimt (simt , smt , Dmt ) =Xπirt (sirt , srt , Drt ),

(5)

r∈m
∗
πirt (sirt , srt , Drt ) = Prt(srt , Drt )qirt −Z qirtmcirt (q, sirt ))dq,0s.t. qirt =Q∗rt (srt , Drt )ωirt

if t ≤ 1983∗
 Prt (srt ,Drt )−γ0 sirt

γ1

ωirt ∈ [0, 1], ∀i,otherwise ,Nrt
Xωirt = 1,i=1where ωirt is the service quota within the cartel and Dmt = (Drt )r∈m contains route-year-level demandstates of eastbound and westbound in market m in year t. In the data, shipping conferences impose ωirt =PNrt
sirt / i=1
sirt (= tonnage share) based on Code of conduct of liner conferences, Article 2. Note that routeyear-level tonnage is equivalent to market-year-level tonnage, that is, srt = smt because each ship is operated
in both eastbound and westbound routes. Changing the allocation rule on ωirt is insightful in counterfactuals.
Note that firms do not strategically control utilization rates by assumption. Thus, tonnage capacity
shares determine the profits directly and the profit is determined only by the states (smt , Dmt ) and there is
no strategic interaction with qirt in the spot market like Cournot competition.

(a) Transpacific πmt(b) Transatlantic πmt(c) Asia and Eur πmt

Figure 4: Estimated market-year-level prices, quantities, total tonnage, and firm’s profit of each level.
Note: Each element is derived from the discretized actual state in the data.

For initial insight, I establish a connection between static profits (5) and tonnage capacities sirt determined by dynamic decisions before delving into the dynamic model’s specifics. Figure 4 illustrates estimatedprofits for various capacity levels, as subsequently introduced, conditioned on actual capacity transitions.
Level-1 firms represent minimum capacity firms, while level-4 firms represent maximum capacity firms.
Larger capacity firms yield higher profits compared to their smaller counterparts, highlighting the incentive
for firms to augment capacities despite incurring substantial sunk investment costs. See more qualitative
analysis in Appendix C.2.
22

3.3

Dynamics

Time horizon

Given the static part and industry regime, I introduce a model where time is discrete witht = 1, 2, · · · , T . In this paper, t = 1 refers to 1973, i.e., the initial year of the post-Oil-Shock period andt = T = 18 refers to 1990, just before the dissolution of the Soviet Union.

MarketI model conference markets in which firms follow collusive behaviors determined by shipping

conferences in collusive periods before 1984, i.e., 1 ≤ t ≤ 12. Non-conference markets, which do notallow cartels, are not included in the model, and the aggregate quantities are exogenously determinedoutside the model. A market is defined as a round-trip route, which is the unit by which each ship
is deployed.

Let m ∈ M be a conference market, where M is a set of conference markets, that is,

M = {transpacific, transatlantic, and Asia-Europe} and M = |M| = 3. We assume that these markets
are independent for simplicity.

Player

Let Nmt be the set of incumbent firms, and Nmt be the number of incumbent firms. Suppose Nmtpebe the set of potential entrants. I
incumbent firms exist as players in market m in year t. Also, let Nmt

assume that four potential entrant firms exist as players across all periods, as is observed in the data, i.e.,pe|Nmt| = 4.

Actionpe
Potential entrant firm i ∈ Nmt
chooses action aimt ∈ Ape = {x, e} where aimt = x means quitting

the market, and aimt = e means entering the market. Incumbent firm i ∈ Nmt also chooses action aimt ∈Ainc = {x, k, b} where aimt = x means exiting the market, aimt = k means staying in the market without
investing, and aimt = b means staying in the market with investment. These actions change the evolution ofstate variables.

State

Let s̃imt ∈ R+ be the “actual” tonnage size of the incumbent firm i ∈ Nmt in market m in year

t. For dynamic estimation, discretization of continuous state variables is necessary. Let Smt be the setof discretized tonnage levels in market m in year t. I assume that the discretization grids are four. Then,
Smt = {1, 2, 3, 4}. Let simt ∈ Smt be the discretized tonnage level of the incumbent firm i ∈ Nmt in market min year t as a capacity level of actual tonnage size s̃imt . Concretely, based on data fitting, simt is determined23

by the following discretization formula:simt =




1







2



3







4

if s̃imt ≤ exp(8.5)
if exp(8.5) < s̃imt ≤ exp(9.5),

if exp(9.5) < s̃imt ≤ exp(10.5)
if exp(10.5) < s̃imtpe
and we call firm i a level-l firm if simt = l for convenience. I also assume that the potential entrant i ∈ Nmt

has simt = 0 as a null state.26
The industry state smt contains a set of discretized state variables that an individual firm uses to choose
an action in market m in year t. We define smt as follows:

1
2
3
4
smt = Nmt
, Nmt
, Nmt
, Nmt
,
l
l
=
represents the number of level-l firms in market m in year t, i.e., Nmt
where Nmt

Pi∈Nmt 1(simt = l). Letlbe the set of level-l firms for l = 1, 2, 3 and 4.
Nmt

The vector εimt represents the individual continuous unobserved exogenous state, defined as follows:

εimt =


(εaimt )a∈Ainc ,if i ∈ Nmt
(εaimt )a∈Ape ,pe
if i ∈ Nmt

which is firm i’s private information. I assume it is i.i.d. drawn from a type one extreme value distribution.
pe
In summary, firm i ∈ Nmt ∪ Nmt
knows (t, simt , smt , Dmt , εimt ), where simt and smt are endogenous statevariables, Dmt is an exogenous demand state variable given by the static model, and εimt is an exogenous
unobserved state variable drawn from a type one extreme value distribution. The researcher observes all thepestate variables that are common knowledge to firms: simt , smt , and Dmt for all i ∈ Nmt ∪ Nmt. The onlype
unobservables for the researcher are the private information shocks εimt of all i ∈ Nmt ∪ Nmt.
26 See Appendix A for details.

24

State Transition

peFirst, the transition rule for simt , representing the tonnage level of firm i ∈ Nmt ∪ Nmt

in market m in year t, is defined as follows:

simt+1 =simt + 1(aimt = b)




simt






1(aimt = e)if simt ∈ {1, 2, 3}
if simt = 4
if simt = 0

where 1(·) is an indicator function. The second case means that level-4 firms could not increase the level
which will be rationalized by the data with the assumption that level-4 firms’ choice-specific value functionof choosing aimt = b is zero, explained later. The last case means that entering the market implies moving
to the lowest state, i.e., simt+1 = 1, in the next period.
43
2
1) is directly determined as follows:
, Nmt
, Nmt
, Nmt
Second, the transition rule for (Nmt

1
1
Nmt+1
= Nmt
+

X

1(aimt = e) −

pe
i∈Nmt

2
2
Nmt+1
= Nmt
+

X

1(aimt = b) −X

1(aimt = b) −X

1(aimt = b) −X

X

1(aimt = x)X

1(aimt = x)

2
i∈Nmt

1(aimt = b) −

3
i∈Nmt

1(aimt = b) −

3
i∈Nmt

X

X
1
i∈Nmt

2
i∈Nmt

2
i∈Nmt

4
4
Nmt+1
= Nmt
+

1(aimt = b) −

1
i∈Nmt

1
i∈Nmt

3
3
Nmt+1
= Nmt
+

X

X

1(aimt = x)

3
i∈Nmt

1(aimt = x)

4
i∈Nmt

Finally, the exogenous demand state transition Dmt is not modeled and is equal to the estimated component
in the static model. Similarly, the transition of exogenous unobserved state εimt is determined by the i.i.d.
type-one extreme value distribution. These specifications satisfy the Conditional Independence Assumption(Rust 1987): conditional on simt , the realization of simt+1 is independent of εimt .
Per-period profit Let the per-period profit for incumbent firm i ∈ Nmt taking action aimt with per-period
shock εimt be:dπimt(simt , smt , Dmt ) = πimt (simt , smt , Dmt ) − ψ1(aimt = x)imt
− φ1(aimt = k) − (φ + I(simt ; ι1 , ι2 ))1(aimt = b) + εaimt,

where πimt (simt , smt , Dmt ) is the static profit, ψ is the common exit cost, φ is the common operation cost, andI (simt ; ι1 , ι2 ) is the incumbent’s investment cost of increasing simt with parameters ι1 and ι2 . I normalize the25profit to zero when the firm exits, that is, πimt (simt , smt , Dmt ) = 0. Using the same notation, the per-periodpeprofit for potential entrant firm i ∈ Nmt
taking action aimt with per-period shock εimt be

d
imt
,
πimt
(simt , smt , Dmt ) = −κe 1(aimt = e) + εaimt

where κe is the potential entrant’s entry cost.

Timing

All incumbents are deterministically ordered from level-4 firms to level-1 firms. That is, level-4

firms are the first movers, and the potential entrants are the last movers. This is because shipbuilding orders
to shipbuilding companies from large operator firms occupy a large amount of their shipbuilding capacity,so these are likely to be accepted earlier than small companies.
For market m in year t, the game timing proceeds as follows:27
pe
1. All firms face the current state (t, simt , smt , Dmt ) for all i ∈ Nmt ∪ Nmt,
d
2. Realize per-period profit πimt
(simt , smt , Dmt ) for all i ∈ Nmt ,3. Drawing and observing a private i.i.d. shock, εimt , from a known distribution, all level-4 incumbents
4
simultaneously take discrete action aimt conditional on the state,i = 1, · · · , Nmt

4. Drawing and observing a private i.i.d. shock, εimt , from a known distribution, and observing ai0 mt for4443i0 = 1, · · · , Nmt, all level-3 incumbents i = Nmt+ 1, · · · , Nmt+ Nmt
take discrete action aimt similarly,

5. Drawing and observing a private i.i.d. shock, εimt , from a known distribution, and observing ai0 mt for
4
3
4
3
4
3
2
i0 = 1, · · · , Nmt+ Nmt, all level-2 incumbents i = Nmt+ Nmt+ 1, · · · , Nmt
+ Nmt
+ Nmt
take discrete

action aimt similarly,
6. Drawing and observing a private i.i.d. shock, εimt , from a known distribution, and observing ai0 mt for
4
3
2
4
3
2
4
3
2
1
i0 = 1, · · · , Nmt
+Nmt
+Nmt
, all level-1 incumbents i = Nmt
+Nmt
+Nmt
+1, · · · , Nmt
+Nmt
+Nmt
+Nmt

take discrete action aimt similarly,
7. Drawing and observing a private i.i.d. shock, εimt , from a known distribution, and observing theactions of all incumbents, potential entrants i = 1, · · · , 4 take discrete action aimt similarly,pe
8. After observing the actions of all firms, update the state simt to simt+1 for all i ∈ Nmt ∪ Nmt.
27 My model follows Igami (2017). The specified order is deterministic like Igami (2017) and unlike Igami and Uetake (2020)
in which the order is stochastic and follows the pattern of month-level-action data. The stochastic alternating move cannot
apply to my data because the data on state transition is at the market-year-level, so updating state transition at a shorter time
length needs some conversion.

26

P∞
In the last period, each firm receives a terminal value defined as VimT (smt , DmT , εmT ) = ( τ =T β τ πimT ) =11−β πimT .

3.3.1

Dynamic optimization problem

Before describing the dynamic optimization problem, I will outline assumptions about the firm’s beliefs
concerning the evolution of endogenous and exogenous state variables and market regimes, which govern the
expectation of future profits.

BeliefFirst, I assume rational expectations regarding firm i’s beliefs about rivals’ moves, a−imt , where−i denotes i’s rivals. This means that firm i correctly expects how its rivals choose dynamic actions up to
per-period private shock ε−imt . This setup still allows for dynamic strategic interactions across differentlevel firms. Second, I assume perfect foresight regarding firm i’s beliefs about the evolution of the exogenousPddemand, Dmt , and the market-level marginal cost r∈m mcirt in the per-period profit πimt
. This means thatfirm i expects the evolution without any uncertainty. Third, I assume that firms perfectly predict the two
events in 1980 and 1984 for tractability. This means that all firms know the full history of market regimes
from the beginning of the whole period.

Value function

The dynamic programming problem for incumbent and entrant firms is defined as follows.

I start with level-4 firms. Level-4 firm i’s information set consists of industry state (simt (= 4), smt , Dmt , εimt ).
4dLevel-4 firm i ∈ Nmt
also knows the per-period profit πimt
(simt , smt , Dmt ) for all simt , smt , and Dmt for all
4knows the functional forms of the operation, exit, entry,
t = 1, · · · , T . Furthermore, Level-4 firm i ∈ Nmt

and investment costs and the distribution of private shocks, but not their realization. Then, level-4 firm4i ∈ Nmt
forms a belief about the actions of the level-3, level-2, and level-1 firms and potential entrants thathave not moved yet.
4(i.e., simt = 4) is defined as:
The value function of level-4 firm i ∈ Nmt

Vimt (4, smt , Dmt , εimt ) = πimt (4, smt , Dmt )
 b

x
k
+ max{V̄imt(4, smt , εximt ) , V̄imt
4, smt , εkimt , V̄imt
4, smt , εbimt ,27

and the choice-specific value functions (CSVF) are defined asxV̄imt(4, smt , εximt ) = −ψ + εximt ,

k
V̄imt
4, smt , εkimt = −φ + εkimt+ βE [Vimt+1 (simt+1 , smt+1 , Dmt+1 , εimt+1 ) | 4, smt , aimt = k, a−imt ] ,b4, smt , εbimt = −φ − I (simt ; ι1 , ι2 ) + εbimt
V̄imt



+ βE [Vimt+1 (simt+1 , smt+1 , Dmt+1 , εimt+1 ) | 4, smt , aimt = b, a−imt ] ,where β is a discount factor and (ψ, φ, ι1 , ι2 ) are the parameters for the incumbents. The expectations areover level-4 firm i’s belief about the choices of level-1, level-2, and level-3 firms that have not moved in yeart yet, and the potential entrants, as well as level-4 firm i’s rivals, and the realizations of their private costshocks. The expectation is derived as follows:

E [Vimt+1 (simt+1 , smt+1 , Dmt+1 , εimt+1 ) | 4, smt , aimt = k, a−imt ]
=

4
X

X

P (simt+1 , smt+1 |4, smt , aimt = k, a−imt )Vimt+1 (simt+1 , smt+1 , Dmt+1 , εimt+1 )

simt+1 =1 smt+1 ∈Smt

=

4
X

X

P (simt+1 |4, smt , aimt = k)P (smt+1 |smt , a−imt )Vimt+1 (simt+1 , smt+1 , Dmt+1 , εimt+1 )

simt+1 =1 smt+1 ∈Smt=

X

P (smt+1 |smt , a−imt )Vimt+1 (4, smt+1 , Dmt+1 , εimt+1 ) ,smt+1 ∈Smt

where the second equation is derived from exogenous Dmt+1 and i.i.d. εimt+1 , the third equation is obtained
from the independence of simt+1 and smt+1 in calculation of transitions, and the fourth equation is derived
from the transition specification of simt for level 4 firms, i.e., P (simt+1 |4, smt , aimt = k) is one if simt+1 = 4,zero otherwise. Similarly,

E [Vimt+1 (simt+1 , smt+1 , Dmt+1 , εimt+1 ) | 4, smt , aimt = b, a−imt ]can be decomposed asP

smt+1 ∈Smt P (smt+1 |smt , a−imt )Vimt+1 (4, smt+1 , Dmt+1 , εimt+1 ). The decompositionof P (smt+1 |smt , a−imt ) is shown in detail after introducing conditional choice probabilities.

28

Level-4 firm i solves the following problem:

max

aimt ∈Aincx
πimt (4, smt , Dmt ) + 1(aimt = x)V̄imt(4, smt , εximt )kb+ 1(aimt = k)V̄imt
4, smt , εkimt + 1(aimt = b)V̄imt
4, smt , εbimt .
4 ) is the optimal solution to this optimization
Level-4 firm i’s best response a∗imt (4, smt , εimt , (a∗i0 mt )i0 6=i,i0 ∈Nmt
pe
problem. However, note that the solution does not need to be conditioned on rivals’ actions (ai0 mt )i0 ∈Nmt ∪Nmt\ibecause of the rational expectation assumption on rivals’ moves and symmetricity. Therefore, the problem
is treated as a single-agent problem.
When it is the turn of level-3 firms to move, the information set of level-3 firm i consists of the industry
state (simt (= 3), smt , Dmt , εimt ) and the actions of level-4 firms that have already moved. Level-3 firmd3
also knows the per-period profit πimt
(simt , smt , Dmt ) for all simt , smt , and Dmt for all t = 1, · · · , Ti ∈ Nmtand is aware of the functional forms of the operation, exit, entry, and investment costs, and the distributionof private shocks, but not their realizations. Then, I construct the value function of level-3 firms as level-4∗
4 , (a 03 ) is the optimal solution
firms. Level-3 firm i’s best response a∗imt (3, smt , εimt , (a∗i0 mt )i0 ∈Nmt
i mt )i0 6=i,i0 ∈Nmt

to this optimization problem.
When it is the turn of level-2 firms to move, the information set of level-2 firm i consists of the industry
2
also knows
state (simt (= 2), smt , Dmt , εimt ) and the actions of level-3 and level-4 firms. Level-2 firm i ∈ Nmtdthe per-period profit πimt
(simt , smt , Dmt ) for all simt , smt , and Dmt for all t = 1, · · · , T and is aware of thefunctional forms of the operation, exit, entry, and investment costs, and the distribution of private shocks,
but not their realizations. Then, I construct the value function and best response of level-2 firms as level-3
firms.
When it is level-1 firms’ turn to move, level-1 firm i’s information set consists of industry state (simt (=11), smt , Dmt , εimt ) and the actions of level-4, level-3, and level-2 firms. Level-1 firm i ∈ Nmt
also knowsdper-period profit πimt
(simt , smt , Dmt ) for all simt , smt and Dmt for all t = 1, · · · , T and knows the functional

forms of the operation, exit, entry, and investment costs and the distribution of private shocks, but not theirrealization. Then, I construct the value function and best response of level-1 firms as level-2 and level-3
firms.
Finally, when it is potential entrant firms’ turn, potential entrant firm i’s information set consists of industry state (simt (= 0), smt , Dmt , εimt ) and the actions of level-4, level-3, level-2, and level-1 firms. Potential
dentrant firm i also knows per-period profit πimt
(simt , smt , Dmt ) for all simt , smt and Dmt for all t = 1, · · · , T

and knows the functional forms of the operation, exit, entry, and investment costs and the distribution of29

private shocks, but not their realization.
The value function of potential entrant firm i (i.e., simt = 0) is defined as follows:xeVimt (0, smt , Dmt , εimt ) = max{V̄imt(0, smt , εximt ) , V̄imt
0, smt , εkimt },where the expectation is taken over potential entrant firm i’s beliefs about the choices of all level firms, aswell as those of i’s potential entrant rivals, and the realizations of their private cost shocks. The CSVFs aredefined as follows:xV̄imt(0, smt , εximt ) = 0 + εximteV̄imt(0, smt , εeimt ) = −κe + εeimt+ βE [Vimt+1 (0, smt+1 , Dmt+1 , εimt+1 ) | 0, smt , aimt = e, a−imt ] .

Potential entrant firm i solves the following problem:x
max πimt (0, smt , Dmt ) + 1(aimt = x)V̄imt(0, smt , εximt )aimt ∈Apee+ 1(aimt = e)V̄imt(0, smt , εeimt ) ,peand potential entrant firm i’s best response a∗imt (0, smt , εimt , (a∗i0 mt )i0 ∈Nmt ∪Nmt\i ) is the i’s optimal solution

to the optimization problem. Under the rational expectation assumption on rivals’ moves and symmetricity,
the problem is treated as a single-agent problem.
Integrated Value Function The integrated value function of incumbent firm i ∈ Nmt can be written as

E[Vimt+1 (simt+1 , smt+1 , Dmt+1 , εimt+1 ) |simt , smt , aimt , a−imt ]
!
!
"
k
x
Ṽimt
(simt , smt , Dmt )Ṽimt(simt , smt , Dmt )
+ exp
+ exp
= σ γ + log exp
σ
σ

b
Ṽimt
(simt , smt , Dmt )
σ

!!#
,

a
a
where γ is an Euler constant, σ is a logit scale parameter, and Ṽimt(simt , smt , Dmt ) = V̄imt(simt , smt , Dmt , εaimt )−aεaimt is the deterministic part of the value function V̄imt
for all a ∈ Ainc .

30

peSimilarly, the integrated value function of potential entrant i ∈ Nmt
has the following analytical formula:

E[Vimt+1 (simt+1 , smt+1 , Dmt+1 , εimt+1 ) |simt , smt , aimt , a−imt ]
!
!!#
"
e
x
Ṽimt
(simt , smt , Dmt )Ṽimt(simt , smt , Dmt )+ exp,= σ γ + log exp
σσaawhere Ṽimt(simt , smt , Dmt ) = V̄imt(simt , smt , Dmt , εaimt ) − εaimt is the deterministic part of the value functionafor all a ∈ Ape .
V̄imt

Given these derivations, I can write the expected value functions from terminal period t = T to initialperiod t = 1 and numerically solve these by backward induction. For convenience, I define θπ as a set ofdynamic parameters, i.e., θπ = (ψ, φ, κe , ι1 , ι2 , σ).
Conditional choice probability

If εmt is drawn i.i.d. from T1EV, the CSVF gives the ex-ante optimal

conditional choice probability (CCP) of action a ∈ {x, k, b} of level-l incumbent i (i.e., simt = l) as follows:P rl (aimt = a|simt , smt , Dmt ) =where Wimt = exp



x
Ṽimt
(simt ,smt ,Dmt )
σ



+exp



exp



a
Ṽimt
(simt ,smt ,Dmt )
σ


,

Wimt

k
Ṽimt
(simt ,smt ,Dmt )
σ



+exp



b
Ṽimt
(simt ,smt ,Dmt )σ. Note that, givenlsymmetricity, P rl (aimt = a|simt , smt , Dmt ) = P rl (ai0 mt = a|si0 mt , smt , Dmt ) for i, i0 ∈ Nmt
so that we also

use P rl (almt = a|smt , Dmt ) as an expression of CCP of level-l firms.
Potential entrant i (i.e., simt = 0) has an analogous CCP of action a ∈ {x, e}:P rpe (aimt = a|simt , smt , Dmt ) =where Wimt = exp



x
Ṽimt
(simt ,smt ,Dmt )
σ



+exp



exp



e
Ṽimt
(simt ,smt ,Dmt )
σ

a
Ṽimt
(simt ,smt ,Dmt )
σ

Wimt



,

. Given symmetricity, we also use P rl (a0mt =a|smt , Dmt ) as an expression of CCP of potential firms.
Decomposition of P (smt+1 |smt , a−imt )l
For the decomposition of P (smt+1 |smt , a−imt ), let Kmt
be thelnumber of level l firms keep staying at the current level, EXmt
be the number of level l firms choosing exit,
l
l
l
l
l
Bmt
be the number of level l firms choosing building ships, and Nmt= Kmt+ EXmt+ Bmt
be the numberpepeof all level l firms. Also, let EXmt
be the number of potential entrants choosing exit, Emt
be the number ofpepepe
potential entrants choosing entry, and Nmt= EXmt+ Emt
be the number of all potential firms. Based on

the belief assumption, these determine the transition of smt+1 from smt . Then, the decomposition is written31

as follows:

P (smt+1 |smt , a−imt )
X

=

pe
pe
l
l
l
P (Nmt, EXmt, (Nmt, EXmt, Bmt)l=1,2,3,4 |smt ; θπ ),pepel ,EX l ,B l
smt+1 =Ψ Nmt
,EXmt
,(Nmt
mt )
mt

l=1,2,3,4,smt ,a−imt



pe
pe
l
l
l
P (Nmt, EXmt, (Nmt, EXmt, Bmt)l=1,2,3,4 |smt ; θπ )pe
pe
P pe (Nmt, EXmt| 0, smt ; θπ )

=

4
Y

!
l
l
l
P l (Nmt, EXmt, Bmt| l, smt ; θπ ) ,

l=1
l

l
l
l
P (Nmt, EXmt, Bmt| l, smt ; θπ )



l
l
l
N
−
EX
N
mt
mt 
mt  
EX ll= P r (almt = x | smt ; θπ ) mt

l
l
Bmt
EXmt


l
l
N l −EXmt−Bmt

× P rl (almt = k | smt ; θπ ) mt

Bl

× P rl (almt = b | smt ; θπ ) mt ,pepe
P pe (Nmt, EXmt| smt ; θπ )


pe
pe
 Nmt  pe
EX pe
N pe −EXmtpe=, P r (a0mt = x | smt ; θπ ) mt × P r (almt = e | smt ; θπ ) mt
peEXmt

where P rl (·) and P rpe (·) are CCPs of level l firms
 and potential entrants conditional on dynamic parameters n n!
θπ and rivals’ actions up to the current turn, , and the operator Ψ(·) produces the list of = k!(n−k)!
kfuture states from current states based on transition rules, that is,

pe
pe
pe
pe
l
l
l
1
1
1
Ψ(Nmt
, EXmt, (Nmt, EXmt, Bmt)l=1,2,3,4 , smt , a−imt ) = (Nmt+1= Nmt− EXmt+ (Nmt− EXmt
),
2
2
2
1
Nmt+1
= Nmt
− EXmt
+ Bmt
,
3
3
3
2
Nmt+1
= Nmt
− EXmt
+ Bmt
4
4
4
3
Nmt+1
= Nmt
− EXmt+ Bmt)

where a−imt up to the current turn is incorporated in the right hand side. The expression of P (smt+1 |smt , a−imt )captures market-level state transition consistent with data via the symmetric CCP of each level firm. Notethat P (smt+1 |smt , a−imt ) is updated for each turn of each level firm conditional on a−imt up to the current
turn.

32

3.3.2Equilibrium concept

I use a finite-horizon, sequential-move dynamic discrete game with private information and use a perfect
Bayesian Nash Equilibrium (PBE) in type-symmetric pure strategies as an equilibrium concept proposedby Igami (2017, 2018), and Igami and Uetake (2020). The CCP constitutes the type-symmetric equilibrium
strategy under the agents’ correct belief. The equilibrium focuses on across-level competition assuming
implicitly that there is no within-level competition. The model is equivalent to a single-agent problem (Rust
1987) where the decision timing is in sequential order. At each timing, firms make their dynamic discrete
choices to maximize their expected values under rational expectations of the evolution of endogenous statevariables and perfect foresight of the evolution of exogenous state variables. The “type” corresponds todiscretized state level-simt . Intuitively, if cartels exist, firms can enjoy higher per-profits and expected future
profits so that they want to invest more with collusive fixed prices. Otherwise, firms have low incentives toinvest more with competitive prices.
The existence and uniqueness of the equilibrium hold under strong restrictions such that: (i) the game hasa finite time horizon; (ii) firms are (ex-ante) homogeneous in their profit functions and transition probabilities;and (iii) at every timing within a year, only one firm can make an investment decision (Aguirregabiria et al.
2021). In this paper, restriction (i) is satisfied by specifying terminal period T , and restriction (ii) is satisfied
because private information εimt is drawn i.i.d. from the type one extreme value distribution and the samelevel firms are homogenous. The firm’s payoff is affected by its rivals’ cost shocks only through their actual
choices and not by the specific realizations of εa−imt for all a ∈ Ainc ∪ Ape . Restriction (iii) is also satisfied
because different types of firms move sequentially after observing the dynamic choices of earlier movers. At
its turn, only the same type of firms with symmetric strategies solve a single-agent problem based on their
expectation over the subsequent evolution of endogenous state variables.

3.3.3

Technical specifications

I summarize the technical issues for fine-tuning the model. First, I specify incumbent’s investment cost ofincreasing simt by one unit, I (simt ; ι1 , ι2 ), as

I (simt ; ι1 , ι2 ) =




ι

1



ι2

if simt = 1, 2
otherwise.

Second, I fix the discount factor β = 0.9 which is a standard value. Third, I assume that level-4 firms’ CSVFb
of choosing building ships is zero, that is, V̄imt
4, smt , εbimt , to rationalize the fact that level-4 firms do notchoose to increase the level.
33

4

Identification and Estimation

4.1

Demand parameters

Taking the log of demand equation (1), I estimate the parameters α = (α1 , α2 , α3 , α4 , αr ) from:log(Qrt ) = α1 log Prt + α2 Xrt + α3 1(t ≤ 1979) + α4 1(1980 ≤ t ≤ 1983) + αr + ζrt ,(6)

and demand state is defined as Drt = α2 Xrt + α3 1(t ≤ 1979) + α4 1(1980 ≤ t ≤ 1983) + αr . However, routeyear-level price Prt is correlated with ζrt . To account for price endogeneity, I estimate (6) using instrumental
variables (IVs). The price is instrumented with the average age of ships deployed in each route and thetonnage share of 20-year-old ships. Both are used to capture the fact that old ships are less efficient than
new ones to use fuel energy, but both are uncorrelated with unobserved demand factors. The log GDP
for the destination area is used as a demand shifter Xrt . I add route fixed effects and regime dummies tocontrol route-regime level unobserved heterogeneity. Note that including the regime dummies does not mean
the existence of cartel effects on the demand side, but captures some coarse level of time trends. I keep a
consistency of regimes on demand and supply sides. I cluster the standard errors at the route level.
The demand parameters are identified from the time-series and cross-sectional variations across the main
six routes under constant elasticity functional form. Since ships have to go back and forth between the twoareas, two routes serving the same areas have the same level of supply while facing different demand shocks,
which helps the identification of the demand parameters.

4.2

Cost parameters

Based on supply equation (4), I estimate γ = (γ1 , γ2 , γ̃1 , γ̃2 , γr ) using IVs:

Prt = γ1

Qrt
+ γ2 Yrt + γ̃1 1(t ≤ 1979) + γ̃2 1(1980 ≤ t ≤ 1983) + γr + ηirt ,
Srt

(7)

where γ1 is a route-year-level supply slope, γ2 is coefficients of cost shifters, γ̃1 and γ̃2 are the cartel effects, γrrt
is a route fixed effect, and ηirt is an i.i.d. error term. Route marginal cost is defined as M Crt = γ1 Q
Srt + γr .

Cost shifters Yrt include the average age of ships deployed in each route, the tonnage share of 20-year-old
ships, and the average size of ships deployed in each route. These are used to capture the fact that old ships
are less efficient than new ones to use fuel energy and larger ships have smaller marginal shipping costs onrtaverage. The term Q
Srt is instrumented with a demand shifter, log GDP of the destination area, which is

excluded from the supply equation.

34

The cost parameters are identified by the time-series and cross-sectional variations across the main six
routes under the functional form assumption and known regime changes from institutional backgrounddiscussed in Section 2.

4.3

Dynamic parametersl
We estimate dynamic parameters, θπ , by Maximum Likelihood Estimation (MLE). Let Kmt
be the numberllof level l firms staying at the current level, EXmt
be the number of level l firms choosing exit, Bmt
be thellllnumber of level l firms choosing building ships, and Nmt= Kmt+ EXmt+ Bmt
be the number of all levelpepel firms. Also, let EXmt
be the number of potential entrants choosing exit, Emt
be the number of potentialpepepe
entrants choosing entry, and Nmt= EXmt+ Emt
be the number of all potential firms. Then, the jointlll) in year t in market m is
, Bmt
, EXmtlikelihood for observing (Nmtlll
P l (Nmt, EXmt, Bmt| smt , Dmt ; θπ ) = 






l
Nmt
l
EXmt




l
l
− EXmt
Nmt
l
Bmt

 l
EX l
 P r (almt = x | smt , Dmt ; θπ ) mtll
N l −EXmt−Bmt

× P rl (almt = k | smt , Dmt ; θπ ) mt
Bl

× P rl (almt = b | smt , Dmt ; θπ ) mt ,pepeand the joint likelihood for observing (Nmt
, EXmt) in year t in market m is


pe
N
mt 

EX pe
pe
pe
pe
| smt , Dmt ; θπ ) = , EXmtP pe (Nmt P r (a0mt = x | smt , Dmt ; θπ ) mt
pe
EXmt


pe
N pe −EXmt

× P rpe (a0mt = e | smt , Dmt ; θπ ) mt

.

all
l
all
l
all
l
Let Nmt= (Nmt)l=1···4,pe , EXmt
= (EXmt)l=1···4,pe and Bmt= (Bmt)l=1···4 . Then, the joint log-likelihood
all
all
all
for observing (Nmt
, EXmt, Bmt) in year t = 1, · · · , T in market m is defined as:llm (θπ ) =

T
X

log P

pe

pe
pe
(Nmt
, EXmt| smt , Dmt ; θπ )

t=1

4
Y

!!
l

l
l
l
P (Nmt, EXmt, Bmt| smt , Dmt ; θπ ).

l=1

The dynamic parameters are identified by the observed entry/exit/investment choices in the panel data ofglobal container shipping firms, together with estimated static parameters. For example, a large investment
cost decreases the predicted CCP of investing and increases the predicted CCP of staying at the same level.
I estimate θπ by the full solution method known as Nested Fixed Point Algorithm (NFP) proposed by Rust
(1987) in which the outer loop is MLE to find maximizers of the joint likelihood and the inner loop solves
35the finite horizon problem for each set of candidate parameters. At the equilibrium, fixed points of CCPs
generate corresponding value functions. I apply the algorithm of Igami (2017) and Kasahara and Shimotsu(2012). See the computation detail in Appendix A. I estimate the parameters for each market separately
because of computational simplicity and data fitting capturing market-level heterogeneity.

5

Estimation results

5.1

Demand for container shipping
Table 4: Estimation results of static parameters.
(a) Demand

1st (log(Prt ))log(Prt )log GDP: log(Xrt )1(t ≤ 1979)
1(1980 ≤ t ≤ 1983)
Avg ship age:
Share (20+ y.o. ships)
Route FE
R2
R2 Adj.

0.427*(0.161)
0.361*(0.110)0.082(0.070)-0.151**(0.023)3.187*(1.217)
X
0.862
0.847

(b) Supplyrt
1st ( Qsrt )2nd (log(Qrt ))-0.869**(0.308)0.434*(0.197)
0.396*(0.153)0.095+(0.052)

Qrt /Srt
Avg ship age
Avg ship size
Share (20+ y.o. ships)
1(t ≤ 1979)
1(1980 ≤ t ≤ 1983)
log GDP: log(Xrt )

X
0.860
0.847

Route FE
R2
R2 Adj.

-0.808*(0.298)-6.688(3.653)34.360(24.333)-0.577(0.430)-1.521**(0.355)2.766+(1.088)
X
0.341
0.278

2nd (Prt )180.190+(108.322)-146.641(101.551)
1332.402+(787.465)
4259.866(6611.957)
1106.208**(362.205)440.663**(148.448)

X
0.663
0.630

Note: Sample size is 108, i.e., six routes in 1973-1990. The numbers in parentheses show the standard errors, which are clusteredat the route level. Significance levels are denoted by +p < 0.1, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001.

Table 4 (a) reports the demand estimates. The first column shows the first stage regression. The
coefficient of the average ship age is negative. The negative sign captures that shipping services via old ships
are provided at a lower price due to the inconvenience caused by service frequency and speed. The coefficientof the share of 20-year-old ships is positive and statistically significant, which means that old ships are worse
than young ones in terms of cost efficiency. The second column reports the second-stage results. I find thatthe estimated price coefficient is -0.869 which is statistically significant. When the shipping price increases
by 10%, the shipping quantity decreases by 8.69%. The demand is inelastic and below the lower boundfound in the literature. It captures the unique features of containerized transportation, which has no viable36

cheap alternative to carry general cargo in this period.28 Figure 5 (a) illustrates route-year-level demandtransition. The demand gradually increased in the 1970s and was stationary in the 1980s.

5.2

Cost parameters and cartel effects

Table 4 (b) reports the cost estimates. The first column shows the first stage regression. The coefficient of theaverage ship age is negative and statistically significant. This implies that markets with older ships provide
a smaller amount of shipping service given the route-year-level aggregate tonnage size fixed. The secondrtcolumn reports the second-stage results. I find that the supply equation is increasing in Q
Srt . Given route-year-level aggregate tonnage size Srt fixed, increasing route-year-level shipping service Qrt by Srt results ina $180 price increase. Also, cartel effects increased the price from route marginal cost by $ 1,106 before 1979
and $ 440 in 1980-1983. The impact on prices is significant. For example, cartel effects increased prices byroughly 20 % in the Asia-to-Europe routes before 1979, and by roughly 50% in the transatlantic westboundroute. Figure 5 (b) illustrates route-year-level route marginal cost transition. I find that the route marginal
cost decreased gradually. See data fitting in Appendix D.

(a) Demand state Drt(b) Route marginal cost M Crt

Figure 5: Estimated demand state and route marginal cost.

Given the estimated route-year-level primitives, Figure 6 provides an intuitive illustration of estimateddemand and supply equations in 1979, 1983, and 1984 which correspond to the regimes. The intersection
determines the equilibrium prices and quantities. In all markets, equilibrium prices decrease from thecollusive regime in 1979 to the competitive regime in 1984 mainly because of the absence of cartel effects in the
supply equation. The demand equations also slightly decrease from the collusive regime to the competitive
28 For example, the price coefficient is -1.03 in dry bulk shipping markets (Brancaccio et al. 2020) and -3.89 in recent container
shipping markets (Jeon 2022). Also, note that although the low elasticity seems to motivate shipping conferences to increaseprices to infinity, this theoretical reasoning is incorrect because consumers can use the non-conference firms.

37

(a) Transpacific WB(b) Transatlantic WB(c) Eur to Asia(d) Transpacific EB(e) Transatlantic EB(f) Asia to Eur

Figure 6: Estimated demand and supply equations
Note: The downward-sloping lines are given by the estimated demand equation. The upward-sloping lines are given by theestimated supply equation.

regime. This might be due to the growing demand for noncartel shipping out of my model. From thesecomponents, I compute market-year-level equilibrium prices, quantities, total tonnage, and profits throughdiscretization.

5.3

Dynamic parameters

Table 5 displays the results of the dynamic parameters for each market. The estimated dynamic parameters
exhibit heterogeneity across markets. For example, in the transatlantic market, the estimated entry cost (κe )is $10.9 billion, while the sign of the estimated entry cost is ambiguous for the Asia-Europe market. This
captures the observed pattern of a higher number of entrants in the Asia-Europe markets with low entry
costs compared to the other markets. Furthermore, the estimated exit cost (ψ) exceeds the estimated entry
cost, which rationalizes the small number of exiting firms observed in the 1980s. The estimated operation
cost (φ) is $10.3 billion in the transpacific market, $9.6 billion in the transatlantic market, and $10.5 billion
in the Asia-Europe market, indicating the homogeneity of the operation costs across markets. This indicatesthe homogeneity of shipping services in the industry as well as the estimated logit scale parameter (σ).
Regarding investment costs of level-1 and level-2 firms (ι1 ), the estimates are $15.2 billion in the transpacific38

market, $14.6 billion in the transatlantic market, and $7.6 billion in the Asia-Europe market. Investment
costs of level-3 firms (ι2 ) are higher than those of level-1 and -2 firms. Although direct comparison is difficult
due to the different data and definitions of investment actions, the estimated values of the sunk costs arehigher than previous studies on a global HDD industry (Igami 2017) ($2-3 billion). This reflects the uniquefeature of the large sunk costs of shipbuilding and collusive pricing in the early stage of the industry.
Figure 7 illustrates the actual and estimated state transition patterns. The estimated transition represents
the mean of equilibrium paths in 1,000 simulations based on CCPs and estimated parameters. The figuresuggests that the estimated model reasonably fits the data, albeit in a smoother manner. The analysis
reveals several key findings. First, the number of level-1 firms increases in the initial periods and stabilizes
in the 1980s. This indicates that collusive pricing before 1980 encouraged firm entry. Second, the number oflevel-2 firms increases monotonically in the 1970s. Third, the number of level-3 firms gradually increases inthe transpacific and Asia-Europe markets but decreases in the transatlantic market. These findings not only
explain the different patterns of shipbuilding between the transpacific and transatlantic markets but alsosuggest that collusive pricing before 1980 incentivized firms to invest in shipbuilding. Finally, the number oflevel-4 firms reaches approximately one to two, but the estimated path failed to capture the spike only after
1985 in the transpacific market. Although the estimated model does not precisely replicate all the peaks andfluctuations observed in the data, it provides a simple benchmark for comparing actual and counterfactual
scenarios in the next section.
Table 5: Dynamic parameters
ParametereEntry cost: κ
Exit cost: ψ

Operation cost: φ
Investment cost: ι1
Investment cost: ι2
Logit scale: σ

Log Likelihood

Transpacific

Transatlantic

Asia-Eur

0.055[0.010,0.060]
0.200[0.200,0.201]
0.103[0.103,0.104]
0.152[0.152,0.162]
0.162[0.162,0.167]
0.101[0.080,0.152]

0.109[0.020,0.109]
0.193[0.193,0.200]
0.096[0.096,0.097]
0.146[0.146,0.210]
0.256[0.256,0.800]
0.100[0.090,0.105]

0.001[-0.021,0.001]
0.302[0.302,0.310]
0.105[0.105,0.106]
0.076[0.076,0.080]
0.078[0.078,0.080]
0.078[0.063,0.093]-168.338-153.593-158.643

Note: Each market aggregates its eastbound and westbound routes. The 90 percent confidence intervals are in brackets. These
intervals are based on likelihood ratio tests (i.e., by comparing LL(θ̂π ) − LL(θ̃π ) with the corresponding critical values fromthe χ2 distribution, where LL(θπ ) is the joint log likelihood evaluated at a vector of parameter values θπ ; θ̂π and θ̃π represent
the MLE and its perturbed counterpart, respectively). Thus, the confidence intervals need not be symmetric like Wald-type
ones. Each value is measured by 100 billion USD.

39

(a) Transpacific(b) Transatlantic(c) Asia and Eur

Figure 7: State transition: Estimated (solid) and data (dotted).

Table 6: Welfare evaluation (benchmark)(a) Transpacific(b) Transatlantic(c) Asia-Europe

RegimeCS

PS

SW

RegimeCS

PS

SW

RegimeCS

PS

SW

1973-1979
1980-1983
1984-1990

2.12
0.64
0.67

0.10
0.02
0.01

2.22
0.66
0.68

1973-1979
1980-1983
1984-1990

15.63
4.76
5.17

0.19
0.04
0.04

15.82
4.80
5.21

1973-1979
1980-1983
1984-1990

11.80
3.54
3.73

0.17
0.02
0.02

11.97
3.56
3.75

Note: Each number is the sum of discounted present values at 1973 for each regime. Each value is measured by 1 billion USD.

Table 6 displays regime-market-level measures of consumer surplus (CS), producer surplus (PS), andsocial welfare (SW) by summing up the present value of each measure for each regime. The table highlights the following key findings. First, market heterogeneity is evident in each welfare measure, with thetranspacific market exhibiting smaller CS and PS compared to the other two markets. Smaller PS in thetranspacific market is due to the large marginal cost shown in Figure 5 (b). Second, PS represents lessthan 5% of CS, primarily due to the limited number of level-4 firms generating substantial profits before
1990. However, there is a significant increase in the number of level-4 firms after my data period, aligningwith industry history. Third, during the first collusive regime (1973-1979), the observed surplus is about
three times larger than that of the subsequent competitive regime (1984-1990). Notably, PS experiences asubstantial reduction, reaching only 10 to 25% following the breakdown of the cartel. In contrast, the second
collusive regime (1980-1983) demonstrates a surplus similar to the competitive regime, indicating that a
welfare-related container crisis mainly occurred around 1980, just before the actual cartel breakdown.

40

6Counterfactual

I evaluate the welfare performance of policies concerning cartel effects and inner allocation by conducting
counterfactual simulations. Specifically, how the cartel effects and inner allocation mechanism would affectentry, exit, and shipbuilding through shifting the static profit function. I aim to address two main questions.
First, if historical shipping cartels were not permitted, how would the market configuration in the industry
have evolved? Second, would different inner allocation rules have incentivized the entry of small firms or the
shipbuilding of large firms? To assess welfare implications, I compare the gaps observed in the estimatedbaseline model with those obtained from a counterfactual simulation.

6.1

With and without shipping cartels

The long-run effect of cartels is a fundamental question in empirical studies. In a first counterfactual
simulation, I hypothetically eliminate the cartel effect in the profit function and assume that individual
service supply is determined by Equation (3) in the whole period. The counterfactual of zero cartel effects
is similar to Kalouptsidi (2017) in which the Chinese shipbuilding industry would not receive any subsidy
in the counterfactuals. For this counterfactual scenario, I solve the model for a new equilibrium under zerocartel effects (i.e., γ̃1 = γ̃2 = 0) and use the equilibrium choice probabilities to run 1,000 simulations of theequilibrium path for each level firm in each market.
Table 7 presents state transition patterns of the benchmark model and a counterfactual model without
cartel effects. Cartel effects increase the entry and investment of firms in transpacific and transatlantic
markets by at most 0.5 firm units for all level firms. Although the effects on a dynamic decision seem small
relative to the dynamic sunk costs, the economic impacts are not negligible because the change of market
configuration for all level firms significantly affects firms’ profits. Cartel effects are small in the Asia-Europe
market because the effect is small relative to the average marginal cost and profit rather than in othermarkets. This suggests the market heterogeneity of the impact of cartels.
Table 8 presents a comparison of welfare measures between the benchmark model and a counterfactualmodel without cartel effects. Several key findings emerge from this analysis. First, in the counterfactual
scenario, PS is reduced by 50% (transpacific), 32% (transatlantic), and 29% (Asia-Europe) compared tothe benchmark model between 1973 and 1979. Second, the counterfactual non-cartel scenario results in
a 1-3% increase in CS. Although this increase is small, it is reasonable and intuitive when considering the
dynamic implications, the supply equation including shipping capacity information, and the quite low demand
elasticity. In other words, smaller profits discourage firms’ entry and shipbuilding investment, leading to adecrease in the total shipping capacity, and shifting up the supply equation while simultaneously shifting41

down the curve by the level of cartel effects. Notably, the most significant result is that the prohibition ofcartels would not result in an increase in social welfare before 1984 in all markets, i.e., would not be always
beneficial. This finding provides empirical support for industry policies involving centralized mechanisms forprice and quantity control during the early stages of a new homogenous goods industry, although the impact
may not be large economically and may be heterogeneous. Overall, the counterfactual analysis highlights
the impact of cartel effects on welfare measures and underscores the dynamic considerations, necessary tounderstand the observed results, which is also suggested by Fershtman and Pakes (2000) numerically.
Table 7: State transition: Benchmark (point) and non-cartel (dashed)(a) Transpacific(b) Transatlantic(c) Asia-Europe

Table 8: Welfare evaluation (non-cartel scenario)(a) TranspacificRegimeCS

PSSW

CS change

PS change

SW change

1973-1979
1980-1983
1984-1990

2.19
0.64
0.67

0.05
0.01
0.01

2.24
0.65
0.68

(0.03)(0.00)(0.00)(-0.50)(-0.50)( 0.00)( 0.01)(-0.02)( 0.00)(b) Transatlantic

RegimeCS

PSSW

CS change

PS change

SW change

1973-1979
1980-1983
1984-1990

15.97
4.80
5.16

0.13
0.04
0.04

16.10
4.84
5.20

(0.02)(0.01)(0.00)(-0.32)( 0.00)( 0.00)(0.02)(0.01)(0.00)(c) Asia-Europe

RegimeCS

PSSW

CS change

PS change

SW change

1973-1979
1980-1983
1984-1990

12.05
3.58
3.73

0.12
0.02
0.02

12.17
3.60
3.75

(0.02)(0.01)(0.00)(-0.29)( 0.00)( 0.00)(0.02)(0.01)(0.00)

Note: Each number is the sum of discounted present values at 1973 for each regime. Each value is measured by 1 billion USD.
The number in a bracket shows the proportional change from the benchmark model. For example, (-0.50) means that the
hypothetical welfare is (1 − 0.50) × 100 = 50% of the actual welfare.

42

6.2

Under different inner allocation rule“Market Share Division” within the cartels matters to function cartels (Marshall and Marx 2014). However,to the best of my knowledge, there is a lack of research quantifying the effect of “Market Share Division” onwelfare in both the short-run and long-run, primarily due to the unavailability of observed inner allocation
rules in typical data. The case of shipping conferences serves as an excellent example, as the inner allocation
rule is known and straightforward, as shown in ωimt in Equation (5). This feature allows us to treat thedecision to join or leave explicit cartels as a simple choice of entry and exit in cartel markets. Furthermore,
the inner allocation mechanism employed by shipping conferences is linked to industry subsidies for specificfirms, which are operated under the constraints of government budgets. Subsidy policies on static profits
under the constraints are more interpretable than subsidies on lump-sum entry cost, for example, examinedby Fan and Xiao (2015). It also may be worthwhile to numerically investigate the optimal inner allocation
mechanism for social welfare through analysis of entry, exit, and shipbuilding investment because answering
this question theoretically is challenging, as it involves the complex and dynamic strategic decisions of firms.
1
To highlight the role of the inner allocation rule, I change ωirt to the following rule ωirt
:

1
ωirt
= s̃irt /Nrt
Xs̃irt ,

i=1s̃irt =


1.25 · s

if sirt = 1, 2
0.75 · sirtotherwiseirt.

The rule has the same role of encouraging entry and investment of level-1 and level-2 firms as a subsidy forsmall firms under some budget constraints. This rule shares the same spirit as the policies encouraging theentry of small firms, discussed in the literature of auction (Krasnokutskaya and Seim 2011) and dynamic
entry (Fan and Xiao 2015).29
Second, I consider the policy of supporting large incumbent firms. I change ωirt to the following rule
2
ωirt
:

2
ωirt
= s̃irt /Nrt
Xs̃irt ,

i=1s̃irt =


1.25 · s

if sirt = 3, 4
0.75 · sirtotherwiseirt.

29 Fan and Xiao (2015) consider the direct subsidy on dynamic entry costs for small potential entrant firms, although thesubsidies imposed by the 1996 Telecommunications Act are implicit and thus difficult to quantify.

43

Figure 9 presents state transition patterns of the benchmark model and a counterfactual model under
1
2
counterfactual inner allocation rules ωirt
and ωirt. As a remarkable finding, both counterfactual rules reduce1, level-1 and -2 firms would receive larger profits but
entry and investment. Under the allocation rule ωirt
2
have smaller incentives for investment and smaller expected future profits. Under the allocation rule ωirt,

level-1 and -2 firms would receive smaller profits but have larger incentives for investment and larger expected
future profits. These conflicting benefits balance each other and reduce entry.
Table 10 presents the results. First, CS is almost invariant to the change of the inner allocation rule1
to ωirtbecause the total supply of shipping and the number of entry and exit would be almost invariant.
2
However, the change of the inner allocation rule to ωirt
would slightly decrease CS in the transatlantic and1
Asia-Europe markets. Second, the allocation rule ωirt
encouraging small firms would reduce PS by 6-25 %,2
whereas the allocation rule ωirt
encouraging large firms would increase PS by 16-50 % but decreases SW by

1-2%. This concludes that an inner allocation rule encouraging large firms would worsen social welfare forsome markets. Third, the transpacific market is invariant to the counterfactual rules, which implies market
heterogeneity of the impact of the inner allocation rule. In conclusion, an actual inner allocation rule basedon the tonnage share seems the best to maximize social welfare.
1
2
Table 9: State transition: Benchmark (point) and ωirt
(dashed) and ωirt
(dotted)(a) Transpacific7(b) Transatlantic(c) Asia-Europe

Conclusion

I investigate how explicit cartels, known as “shipping conferences” in a global container shipping market
facilitated the formation of one of the largest globally integrated markets through the entry, exit, andshipbuilding investment of shipping firms. Using a novel data, I develop and construct a structural modeland find that the cartels shifted shipping prices by 20-50% and encouraged firms’ entry and investment.
In my counterfactual simulation, I compare welfare outcomes with and without the cartels and other inner44

Table 10: Welfare evaluation (counterfactual allocation rule)(a) Transpacific (encouraging small firms)

RegimeCS

PSSW

CS change

PS change

SW change

1973-1979
1980-1983
1984-1990

2.12
0.64
0.67

0.10
0.02
0.01

2.22
0.66
0.68

(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)(b) Transpacific (encouraging large firms)

RegimeCS

PSSW

CS change

PS change

SW change

1973-1979
1980-1983
1984-1990

2.12
0.64
0.67

0.10
0.02
0.01

2.22
0.66
0.68

(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)(0.00)(c) Transatlantic (encouraging small firms)

RegimeCS

PSSW

CS change

PS change

SW change

1973-1979
1980-1983
1984-1990

15.65
4.76
5.16

0.17
0.04
0.03

15.82
4.80
5.19

(0.00)(0.00)(0.00)(-0.11)( 0.00)(-0.25)(0.00)(0.00)(0.00)(d) Transatlantic (encouraging large firms)

RegimeCS

PSSW

CS change

PS change

SW change

1973-1979
1980-1983
1984-1990

15.54
4.67
5.06

0.22
0.05
0.05

15.76
4.72
5.11

(-0.01)(-0.02)(-0.02)(0.16)(0.25)(0.25)( 0.00)(-0.02)(-0.02)(e) Asia-Europe (encouraging small firms)

RegimeCS

PSSW

CS change

PS change

SW change

1973-1979
1980-1983
1984-1990

11.80
3.54
3.73

0.16
0.02
0.02

11.96
3.56
3.75

(0.00)(0.00)(0.00)(-0.06)( 0.00)( 0.00)(0.00)(0.00)(0.00)(f) Asia-Europe (encouraging large firms)

RegimeCS

PSSW

CS change

PS change

SW change

1973-1979
1980-1983
1984-1990

11.79
3.53
3.71

0.18
0.03
0.02

11.97
3.56
3.73

( 0.00)( 0.00)(-0.01)(0.06)(0.50)(0.00)( 0.00)( 0.00)(-0.01)

Note: Each number is the sum of discounted present values at 1973 for each regime. Each value is measured by 1 billion USD.
The number in a bracket shows the proportional change from the benchmark model. For example, (-0.50) means that the
hypothetical welfare is (1 − 0.50) × 100 = 50% of the actual welfare.

45

allocation rules. I find that cartels significantly increase producer surplus, slightly decrease consumer surplus,
and then may increase social welfare by encouraging firms’ entry and shipbuilding investment, validating
industry policies controlling prices and quantities in the early stage of the new industry, which may not be
always harmful. Investigating hypothetical allocation rules supporting large or small firms, I find that theactual rule based on tonnage shares is the best to maximize social welfare.
A logical next step is to investigate the theoretical and numerical properties of the equilibrium concept
proposed by Igami (2017, 2018). This specific sequential game focuses on across-level competition, assuming
the absence of within-level competition to mitigate intractability and the potential for multiple equilibria
which is common in Markov perfect equilibria, and aims to provide a unique equilibrium solution for practicaland counterfactual models through a full-solution solution method. While the utilization of Markov perfectequilibria involves additional technical procedures for testing and estimation, as formally discussed in Otsu
and Pesendorfer (2023), recent survey papers on empirical dynamic game literature underscore the importance of achieving equilibrium uniqueness and tractability. These surveys also summarize various theoreticalconditions (Aguirregabiria et al. 2021). Alternatively, Abbring and Campbell (2010) develop an entry modelwith identical firms, assuming entry and exit decisions follow a last-in-first-out (LIFO) structure. This model
achieves a unique equilibrium by introducing assumptions about the demand process. It is worth noting that
this uniqueness result typically applies to identical firms. Extending their approach to nonstationary andasymmetric settings would be a significant contribution to the literature.
Another avenue for further research is to compare the current model with a cartel formation and breakdown model that incorporates well-documented institutional details and data. While this paper primarily
focuses on specific aspects of shipping conferences as a case study, investigating a general empirical modelthat encompasses both explicit and implicit cartel models as summarized in Marshall and Marx (2014) andAsker and Nocke (2021) would be a valuable contribution to the literature.

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51

Appendix (For Online Publication)
This Appendix is prepared for online publication and contains supplementary materials. Table 11 lists
the contents.
AppendixA
B
C
D

Contents
Computational details
Data details
Model details
Additional estimation results

Algorithm, Confidence Intervals, Computational time, Discretization
Data construction, Merger issues
The link between my model and Porter (1983)
Data fitting

Table 11: Contents of the Appendix

A

Computation details

A.1

Algorithm

I construct the algorithm by applying Igami (2017, 2018) to my model setting. I fix targeted parameter θπ .
For exposition, I focus on market m = 1. I vectorize all state variables into smt and it takes a value from 1
peto S. As in the empirical exercise, I fix the number of potential entrants, Nmt, to four. Note that, at theequilibrium, fixed points of CCPs generate corresponding value functions. The algorithm to compute valuefunctions via backward induction proceeds as follows.
Algorithm 1: Value Functions and CCPs
1. For t = T − 1, · · · , 1, obtain the value function at t + 1 denoted by Vimt+1 (smt+1 ). Given θπ , obtain
exit cost ψ, operation cost O, and investment cost I.
(a) For smt = 1, · · · , S, obtain the number of firms, Nmt , from smt .
(b) Initialize and obtain old E[Vimt+1 (smt+1 )|smt ] and old P r(aimt |smt ) for all aimt ∈ Ainc andi ∈ Nmt .
(c) Initialize and obtain old E[Vimt+1 (smt+1 )|smt ] and old P r(aimt |smt ) for all aimt ∈ Ape and i ∈
pe
Nmt
.

(d) Then, find fixed points of CCPs as follows.
l(i) For level l = 4 and for all aimt ∈ Ainc and i ∈ Nmt,
pe
A. Given old E[Vimt+1 (smt+1 )|smt ], old P r(aimt |smt ), Nmt , and Nmt, compute the joint

likelihoodpepe
P pe (Nmt, Xmt| smt ; θπ )

4
Y

!
l
l
l
P l (Nmt
, Xmt
, Bmt
| smt ; θπ )

l=1

B.

pe
pe
l
l
l
for l = 1, 2, 3, 4.
for all Nmt
, Xmt
, Nmt
, Xmt
, and Bmt
peGiven the joint likelihood, Nmt , and Nmt, compute the transition probability P (smt+1 |smt )for all s = 1, · · · , S.

52

C. Given the joint likelihood, the transition probability, and Vimt+1 (smt+1 ), compute thenew expectation
E[Vimt+1 (smt+1 )|smt ] =SXP (smt+1 |smt )Vimt+1 (smt+1 ),smt+1 =1

then update old E[Vimt+1 (smt+1 )|smt ] of corresponding actions to new E[Vimt+1 (smt+1 )|smt ].
D. Given the new E[Vimt+1 (smt+1 )|smt ], compute new P r(aimt |smt ). If the new probability
is overflown, go to 1 with new θπ .
E. Obtain (CCP gap of incumbents) = newP r(aimt |smt ) − oldP r(aimt |smt ).
F. Update oldP r(aimt |smt ) to (newP r(aimt |smt ) + oldP r(aimt |smt ))/2.
G. Update l = l − 1 and go to (A) until l = 1.
(ii) For potential entrants,pe
A. Given the old E[Vimt+1 (smt+1 )|smt ], old P r(aimt |smt ), Nmt , and Nmt, compute the joint

likelihood.
pe
B. Given the joint likelihood, Nmt , and Nmt, compute the transition probability.

C. Given the joint likelihood, the transition probability, and Vimt+1 (smt+1 ), compute new
E[Vimt+1 (smt+1 )|smt ] from the old P r(aimt |smt ). Update the old E[Vimt+1 (smt+1 )|smt ]of corresponding actions to new E[Vimt+1 (smt+1 )|smt ].
D. Given the new E[Vimt+1 (smt+1 )|smt ], compute new P r(aimt |smt ). If the new probability
is overflown, go to 1 with new θπ .
E. Obtain (CCP gap of potential entrants) = newP r(aimt |smt ) − oldP r(aimt |smt ).
F. Update oldP r(aimt |smt ) to (newP r(aimt |smt ) + oldP r(aimt |smt ))/2.
(iii) Check (CCP gap of incumbents) + (CCP gap of potential entrants) < 0.01. If it is true,
newP r(aimt |smt ) is a fixed point. Otherwise, go to (i) again.
(iv) Given newP r(aimt |smt ) and newE[Vimt+1 (smt+1 )|smt ], compute value function Vimt (smt ).
By nesting the above Algorithm 1 for value functions and CCPs as an inner loop, we evaluate the joint
log-likelihood llm (θπ ) of observing choices in data as an outer loop. I use the Nelder-Mead algorithm forthe outer loop. For the inner loop 1-(d), I implement policy function iteration based on the updating rulesimilar to the algorithm of Kasahara and Shimotsu (2012) which shows a good contraction property.

A.2

Calculation of confidence intervals

I calculate 90% confidence intervals using likelihood ratio tests, which involve comparing ll(θ̂π ) − ll(θ̃π )with the corresponding critical values from a χ2 distribution. Here, ll(θπ ) is the joint logarithmic likelihood
evaluated at a vector of parameter values θ̂π , and θ̃π represents the maximum likelihood estimate (MLE)
and its perturbed counterpart, respectively. I do not use standard errors based on Wald-type tests because
the likelihood function exhibits a step function-like shape due to the game-theoretic nature of the model, as
discussed in Igami (2017, 2018) and Igami and Uetake (2020). Specifically, for each parameter, I calculate
the difference between the original likelihood and the likelihood evaluated at perturbed parameters, which
consist of the four original parameters and one perturbed parameter. The perturbed parameter is chosenfrom eleven-grid intervals centered on the corresponding point-estimated value. Then, find lower and upper53

bounds of the perturbed parameter satisfying that ll(θ̂π ) − ll(θ̃π ) is less than the χ2 critical value for thecorresponding degrees of freedom.

A.3

Computational time

The main computational burden comes from Algorithm 1, in particular, finding fixed points for all statevariables. Using appropriate starting values, it takes at least a week for the transatlantic market and twomonths for the transpacific market to estimate θπ . Depending on the grids of perturbed parameters, ittakes several days for all markets to calculate confidence intervals. It takes some minutes to simulate 1,000
equilibrium paths based on estimated CCPs.

A.4

Discretization details

To compute equilibrium outcome from discretized tonnage size in the static part, I need to recover “actual”
tonnage size from the corresponding discretized tonnage size. This procedure depends on the representativevalue between grid points. Because I use common grid levels for all three markets, which are heterogeneous,for consistent comparison in the dynamic part, I should not use common representative values for all markets.
To alleviate this limit in the view of data-fitting, I specify the representative values for each market basedon fitting the equilibrium prices, quantities, and total tonnage size to the data. I specify the representativevalues for the Asia-Europe market as



10.5




10.0
s̃imt =
9.0





8.0

if simt = 4
if simt = 3
if simt = 2
if simt = 1.

For the transpacific market,



10.5




9.5
s̃imt =


8.5




8.0

if simt = 4
if simt = 3
if simt = 2
if simt = 1.

For the transatlantic market,



12.1




10.1
s̃imt =


9.2




7.2

if simt = 4
if simt = 3
if simt = 2
if simt = 1.

Figure 8 shows that equilibrium elements conditional on the actual states in the data capture the data
patterns well, although some lags and deviations from the data exist due to the discretization. The equilibrium profits illustrate the market heterogeneity of the markup across all levels of firms.

54

(a) Transpacific Pmt(b) Transatlantic Pmt(c) Asia and Eur Pmt(d) Transpacific Qmt(e) Transatlantic Qmt(f) Asia and Eur Qmt(g) Transpacific Smt(h) Transatlantic Smt(i) Asia and Eur Smt(j) Transpacific πmt(k) Transatlantic πmt(l) Asia and Eur πmt

Figure 8: Estimated market-year-level prices, quantities, total tonnage, and firm’s profit of each level.
Note: Each element is derived from the discretized actual state in the data.

B

Data details

The route-year-level prices and quantities are constructed based on Otani and Matsuda (2023a). The
industry-year-level merger patterns between 1966 and 2022 are discussed in Otani and Matsuda (2023b).
Mergers in the ocean shipping industry before the introduction of global container transportation are studied
by Otani (2021) regarding Japanese shipping consolidation in 1964. In the period between 1973 and 1990,
55

two mergers occurred in 1986, three mergers occurred in 1988, and two mergers occurred in 1990. The final
two mergers do not affect my analysis because the data records ship-level information of merged firms in
1990. Although the other five mergers may affect my analysis, I treat merged firms as exiting firms fromshipping conferences and merging firms as investing firms if their state variables in the next period showlevel-up due to data limitation because there are at most two mergers at market-year-level and multiple
simultaneous mergers are difficult to model unlike month-industry-level sequential merger decisions of Igami
and Uetake (2020).

C

Model details

C.1

The link between my model and Porter (1983)

There is a link between my model and Porter (1983) who studies a “Joint Executive Committee railroad
cartel” in the U.S. railroad industry. Concretely, my model does not model strategic interaction in thestatic market but assumes that the static market is either collusive or perfectly competitive, and markup isdetermined by cartel effects which are constant and exogenously determined by cartels. In contrast, Porter(1983) models strategic interaction as quantity competition with conduct parameters that determine perfectcollusion to perfect competition, and the markup is determined endogenously by quantity competition under
specific conduct parameters. First, my model and Porter (1983) are equivalent in competitive markets except
for the tonnage size term which is given in the static model. Second, my model and Porter (1983) are different
in collusive markets because my model is agnostic about the cartel behavior and treats collusive behavior
as a deviation from perfectly competitive behavior, whereas Porter (1983) assumes that cartels choose thetotal quantity to maximize their joint profit. This difference comes from the difference in how a researcher
interprets prices in the collusive regime in data.
Porter (1983) assumes a constant elasticity demand model, log(Qrt ) = α0 + α1 log(Prt ) + ζrt as in (6)where I use the same demand parameters because it has the same role between my model and Porter (1983).
γ̃1 −1
Porter (1983) also specifies firm i’s marginal cost as mcirt (qirt ) = γ̃1 (air qirt
) where air is a firm-specificshift parameter and γ̃1 (> 1) is the parameter of the marginal cost different from γ1 in my model. Note thatin (2), the inverse tonnage size term, 1/sirt , captures
since my model assumes mcirt (qirt , sirt ) = γ0 + γ1 sqirt
irt
the similar but time-varying firm-specific shift parameter.
The firms’ actions under different behavioral assumptions can then be summarized byPrt (1 +θitγ̃1 −1) = mcirt (qirt ) = air γ̃1 qirt
α1

where θit is the conduct parameter Bresnahan (1982). If firms choose price noncooperatively or at a perfectlycompetitive level, they price at marginal cost, and so θit equals zero for all i and t. If instead they maximize
joint profits, θit equals one for all i and t. If firms produce at Cournot output levels, θit equals qirt /Qrt , i.e.,
the firm i’s market share in period t.
The individual supply equations are weighted by market shares and added up. Then, we get the industry
supply relationship
Prt (1 +X qirtθt)=mcirt (qirt ),
α1
Qrt
i∈Nrt

56

1/(1−γ̃ )where θt =

P

1
air
qirt
qirt
1/(1−γ̃1 )i∈Nrt Qrt θit . Porter (1983) shows that firm i’s market share, Qrt , is constant, P
a
i∈Nrt

ir

, for all t in each of the three cases above. Note that higher the value of the firm-specific variable cost shiftparameter, air , lower the market share of firm i. The supply relationship can now be written as
Prt (1 +X 1/(1−γ̃ )θtγ̃1 −11) = γ̃1 (ai)1−γ̃1 Qrt
.
α1
i∈Nrt

Suppose Irt is an indicator variable that equals one when the industry is in a cooperative regime and equals
zero when the industry witnesses a reversionary episode. Then, the supply relationship of the industry isgiven by!
log Prt = log γ̃1 (X

1/(1−γ̃1 ) 1−γ̃1ai)+ (γ̃1 − 1) log Qrt + log((1 +i∈Nrt= β̃0 + β̃1 log Qrt + log(

θrt −1) )α1α1)Irt ,
1 + α1 P
1/(1−γ̃1 ) 1−γ̃1α1).
and β̃1 = (γ̃1 − 1). Porter (1983) estimates β̃0 , β̃1 and log( 1+αwhere β̃0 = log γ̃1 ( i∈Nrt ai)
1
If the marginal cost is given by (2) in my model, the supply relationship can now be written as
Prt (1 +X qirtθtqirt)=(γ0 + γ1
)
α1
Qrt
sirt
i∈Nrt
X sirtqirt=(γ0 + γ1
)
Srt
sirt
i∈Nrt
γ0 X
γ1 X
=
sirt +
qirt
Srt
Srt
i∈Nrt

= γ0 + γ1

i∈Nrt

Qrt
,
Srt

where the second equation comes from the property that tonnage capacity shares determine service quantity
shares, the third equation comes from the constant cost parameters, and the fourth equation comes fromthe aggregations of individual capacities and quantities. First, this relationship implies that my model andPorter (1983) are equivalent in competitive markets except for the tonnage size term, Srt , which is givenin the static model. Second, to give a structural sense, it is necessary to additionally assume that cartels
choose their total quantity to maximize their partially joint profit, then the collusive additional markup isθt Prt−α1that depends on Prt . In other words, my model interprets observed collusive prices as competitive

prices plus cartel effects γ̃, whereas Porter (1983) interprets observed collusive prices as Prt (1 + αθt1 ).
In the main text, under the above trade-off, I choose to use the model in which I am agnostic on cartel
behavior. There are some reasons. First, container shipping firms provide shipping services on their fixedschedules between ports, so it is difficult to adjust the total service quantity to some target level. Second,shipping cartels can control prices to compete with non-conference firms out of the model so a joint profit
maximization model based on quantity competition might be inappropriate. Third, the assumptions ofPorter (1983) that capacity information does not matter in marginal costs and the output shares of cartel
members are relatively stable across the regimes are inadequate in my data on nonstationary industry
history with entry, exit, and investment of many firms, shown in Section 2. In my model, tonnage capacity
sirt determines the marginal cost efficiency of firm i and gives a link between static and dynamic parts of57

investment decisions, that are ignored by Porter (1983) assuming stationary markets. Fourth, as a practicalreason, the sample size of my route-year-level data is not large enough for estimating potentially time-varying
conduct parameters, discussed in Matsumura and Otani (2023a,b,c). My modeling choice is similar to Igami(2015) which recovers marginal costs from competitive regimes and calculates collusive markups as collusive
prices minus the average of recovered marginal costs without any model of the coffee cartels.

C.2

Qualitative analysis of an individual capacity on revenue, total cost, andprofitI analyze how dynamic decisions changing tonnage capacities affect static profits. Note that in the static
model, capacities for all firms, srt = (sirt , s−irt ), are given. Also, the dynamic decisions on capacities are
discretized, so the following analysis provides an approximated intuition treating capacities as continuous
variables.
In Equation (5), firm i in route r in year t has the profit defined as follows:∗
πirt (sirt , srt , Drt ) = Prt(srt , Drt )qirt −|{z}=RevenueQ∗ (s , D )ω
rt
irt
rt rt
s.t. qirt = P ∗ (s ,D )−γ
rt
rt
0
 rt
s
γ1

irt

Z qirt|0

mcirt (q, sirt ))dq ,{z}=Total cost

if t ≤ 1983

ωirt ∈ [0, 1], ∀i,otherwise ,Nrt
Xωirt = 1.

i=1First, I analyze the first term on revenue. Fixing rivals’ capacity, s−irt , and taking the first-order condition
with respect to sirt ,∗∂(Revenue)(srt , Drt )
∂Prt
∂qirt
∗
=
qirt + Prt(srt , Drt )
∂sirt
∂sirt
∂sirt
 ∗
(s
,
D
)
∂P
∂Q∗ (srt , Drt )
rt
rt
rt

∗
irt

(srt , Drt )( rt
qirt + Prt
ωirt + Q∗rt (srt , Drt ) ∂ω
if t ≤ 1983∂sirt )

∂s
∂s

irt
irt

{z
}
|
{z
}
|
>0
= ∂P ∗ (s<0 , D )∗(srt , Drt ) sirt
∂Prt

rt
P ∗ (s ,D )−γ
rt rt
∗

qirt + Prt (srt , Drt )(+ rt rtγ1 rt 0 )otherwise ,

γ

1

∂sirt
∂sirt

{z
}
{z
}
|
|
<0

<0

where the signs come not from solving fixed points of equilibrium prices and quantities in Section 3.2∗
because these cannot be derived as analytical forms. Due to dependency on the levels of qirt , Prt(srt , Drt ),sirt , estimated parameters γ0 and γ1 , and specification of ωirt , I emphasize that the signs of remaining
terms are not ex-ante determined. In my empirical application, the terms∗∂Prt(srt ,Drt )
∂sirt

and

∗
∂Prt
(srt ,Drt )∂sirt

are small because the marginal impacts of individual firms’ capacities out of more than ten firms on theequilibrium prices and quantities are limited. Also, under the standard allocation rule such that firms withirt
larger capacities provide more service quantities, it holds that ∂ω∂sirt > 0. Additionally, my static estimation∗
results confirm that γ1 > 0 and Prt(srt , Drt ) − γ0 > 0 for all routes, which means that equilibrium prices

are larger than the increasing marginal costs at zero quantity. Given these results of my specific application,∂(Revenue)
> 0.
∂sirt

Next, I analyze the second term on the total cost. Fixing rivals’ capacity, s−irt , and taking the first-order58

condition with respect to sirt ,∂(Total cost)∂
qirt 2=(γ0 qirt + γ1
+ C)
∂sirt
∂sirt
2sirt
qirt 2= −γ1 2 < 0.
2sirt
Therefore, taking the first-order condition of πirt (sirt , srt , Drt ) with respect to sirt ,∂πirt (sirt , srt , Drt )∂(Revenue) ∂(Total cost)
=
−
,
∂sirt
∂sirt
∂sirt
|
{z
}
<0

irt ,srt ,Drt )> 0 so that ∂πirt (s∂s
> 0. Figures 8 (j), (k),and given my specific empirical application, ∂(Revenue)
∂sirt
irt

and (l) show equilibrium profits conditional on actual states for each capacity level. This shows the above
qualitative static-dynamic link that increasing capacities in the dynamic part increases static profits.

D

Additional estimation results

D.1

Data fitting of the main models

Figures 9 (a) and (b) illustrate that the estimated route-year-level prices and quantities given in the demandpart fit the data reasonably well, replicating the regime changes, albeit in a slightly smoother manner. Table
12 shows that estimated market-year-level prices from the supply side model fit the prices in data reasonably
for each competition regime on average. However, the estimated standard deviation does not fit the standard
deviation in the data because the sample size is small.

(a) Prt : Estimated (solid) and data (dotted)(b) Qrt : Estimated (solid) and data (dotted)

Figure 9: Estimated route-year-level prices and quantities.

59

Table 12: Data fit for shipping prices for each regime.
RegimeMarket1973-1979

Asia and Eur
Transatlantic
TranspacificAsia and Eur
Transatlantic
TranspacificAsia and Eur
Transatlantic
Transpacific1980-1983

1984-1990(1) Mean P̂mt(2) Mean Pmt(1)/(2)3974.854
2864.721
3920.995
2569.928
1848.499
2979.180
1671.175
1186.535
2444.903

4172.739
2791.502
3810.528
2625.379
2047.711
2724.519
1672.949
1331.900
2297.765

0.953
1.026
1.029
0.979
0.903
1.093
0.999
0.891
1.064

Note: Market aggregates eastbound and westbound routes. Estimated prices P̂mt are calculated from the results of Table 4(b).

60