Trade From Space: Shipping Networks and The Global
Implications of Local Shocks∗
Inga Heiland†

Andreas Moxnes‡
Karen Helene Ulltveit-Moe§
Yuan Zi¶
March 2021

Abstract
This paper examines the structure of the shipping network and its implications
on global trade and welfare. Using novel data on the movements of container ships,
we calculate optimal travel routes. We then estimate the impact of a shock to the
network on global trade by analyzing the effect of the 2016 Panama Canal Expansion.
Trade between country pairs using the canal increased by 10% after the expansion.
While the building costs were borne by Panama alone, a model-based quantification
analysis shows that the welfare gains were shared by many countries, due to the network
structure of shipping.
We would like to thank participants at various seminars and conferences for valuable comments anddiscussion. We thank Clarksons Platou for providing us with access to the Clarksons World Fleet Register,and Bjørn Bodding at Clarksons Platou for valuable discussions. This project has received funding fromthe European Research Council under the European Union’s Horizon 2020 research and innovation program(grant agreement 715147).
†
University of Oslo & Statistics Norway & CEPR & CESifo, inga.heiland@econ.uio.no‡
University of Oslo & CEPR, andreas.moxnes@econ.uio.no§
University of Oslo & CEPR, k.h.ulltveit-moe@econ.uio.no¶
University of Oslo & CEPR, yuan.zi@econ.uio.no
∗

1

1

Introduction

Container ships are the engines of global trade. Levinson (2006) and Bernhofen et al. (2016)detail the seismic changes that the worldwide adoption of container shipping technology
has brought about in international trade. As documented by Rua (2014), by now, nearly
all countries have container ports, constituting the nodes of the global container shipping
network. However, there is scarce empirical evidence on the structure of the shipping network, e.g. which route a container might travel from the dock of port i to port j. At thesame time, the structure of the shipping network is an essential determinant of the costs oftrade, and there is increasing evidence suggesting that connectivity is at least as importantas geographical distance in determining freight costs.1 The networked environment also implies that a shock to a port, or a link, in the network, such as improvements in shipping
infrastructure, may affect shipping costs and trade flows for many more countries than thosethat are directly affected. In this paper, we use satellite data on the movement of container
ships to establish novel evidence on the routes that form the global shipping network. Thisin turn allows us to analyze the global reach of local shocks to the shipping network withrespect to trade costs, trade flows and real incomes.
Our contribution is threefold. First, we document salient features of the world container shipping network based on unique novel data covering the worldwide movements of
all container ships in 2016. Second, we calculate optimal shipping routes, inferred from thesatellite data, and estimate the impact of a local shock on global trade. We do so by using
the Panama Canal expansion in 2016 as natural experiment: From the optimal routes, we
infer which port-pairs use the canal. This enables us to estimate the reduced-form impactof the expansion on global trade. Third, we quantify the trade and welfare effects of theshock using a quantitative model of trade. In contrast to standard trade models, our modelfeatures a shipping network, as observed in the data, and routes form endogenously basedon the cost of shipping between ports. Comparing the welfare effects arising based on our
network model with those that would arise from a model without a shipping network, ouranalysis shows that the existence of the shipping network translates into heterogeneous andwidespread changes in trade costs, trade flows and real income.
Our empirical analysis of global container ship movements has become possible due to therapid advent of the global Automated Identification System (AIS) over the last years. AISreporting of vessel positions offers a degree of automation in data processing and aggregationthat was not previously possible.
Using an exhaustive data set based on AIS of all port calls made by container ships in2016, we document novel facts about the container shipping network. First, container ships
typically operate on fixed routes, i.e. they serve a stable set of ports, akin to buses serving
a fixed number of stops in a city. Second, shipping activity is highly concentrated acrossports, with some nodes (ports) in the network handling almost two orders of magnitude
more ships than the median port. Third, the network is very sparse in the sense that only
few countries have direct shipping routes to their trade partners. Less than 6% of all 22,562
pairs of countries with container ports are directly connected.
See Limao and Venables (2001) on the weak relationship between geographical distance and shipping
costs, Wilmsmeier and Hoffmann (2008) on the importance of connectivity, and UNCTAD (2015) for a reviewof the role of distance and connectivity.
12While the AIS data provides unprecedented detail about the movement of ships, one
cannot observe the movement of the cargo itself, i.e. the actual route of a shipment fromcountry i to country j. To make progress, we use the observed shipping network along withactual travel times between all direct port-pair links and calculate the fastest route between
any potential port pair. Consider, for example, a shipping network with direct links between
New York-London, New York-Hamburg, London-Oslo and Hamburg-Oslo. The fastest route
between New York and Oslo might then be New York-London-Oslo if this route minimizes
the sum of travel times of each leg of the journey, including waiting time at intermediate
ports Of course, the actual route chosen might be determined by other factors than speed,
such as port costs. However, it is widely recognized that the overall cost efficiency of aship depends on the total time it takes the ship to complete a voyage, see e.g. Cullinane
and Khanna (2000). As such, the calculated fastest route is an approximation to the actual
unobserved route. The fastest path calculations reveal that 50% of all country-to-country
connections involve stops in more than two other countries in between.
Besides adding to the distance traveled by a container, indirect routes expose bilateralflows to the shipping infrastructure of other countries. To demonstrate the importance of
exposure to third-country infrastructure, we analyze the global trade effects of a large improvement in local shipping infrastructure in 2016: the expansion of the Panama Canal.
After 10 years of construction, the extended Panama Canal opened on June 26th of 2016.
The $5.25 billion massive construction project was a modern engineering marvel: it nearly
doubled the capacity of the canal by adding a wider and deeper third lane.2 Our information on shipping routes allows us to explore how exporters and importers worldwide weredifferentially affected by this local change in the shipping infrastructure. Using a differencein-difference approach, we find that country pairs whose fastest connection passed throughthe Panama Canal prior to the expansion traded 10% more after the expansion comparedto other country pairs.
Finally, we develop a spatial model of trade to quantify the general equilibrium effectsof the Panama Canal expansion. In contrast to standard trade models, goods are passing
through a shipping network when traveling from a source to a destination location. The
model allows for economies of scale in shipping, so that larger ships on a given route may
potentially lead to lower average transport costs. We build on the work of Allen and Arkolakis(2020), but while their application is on urban economics, our focus is on international trade.
Using the model to quantify the effects of the Panama Canal expansion on global trade, we
assess the welfare impact of the canal expansion. The increase in world real income wereorders of magnitude greater than the construction costs, and while the building costs wereborne by Panama alone, the gains per capita were shared by many countries. Furthermore,trade costs declined substantially, both for location-pairs directly connected by the canal(e.g., Panama Pacific to Atlantic side), and also for locations indirectly connected (e.g.
Long Beach to Hamburg via intermediate ports).
We contrast these counterfactual results to a similar model without a shipping network,
i.e. where goods travel directly from source i to destination j. The decline in trade costs isgreater, and more smoothly distributed, in the network model compared to the no-network
The project required 5 million cubic meters of high-strength concrete - enough to build a highway fromNew York to St. Louis (Business Insider, 2016).
2

3

model, as goods in the network model may pass through segments (e.g., the canal) wheretransport costs declined. Therefore, the network model also generates greater increases intrade and real income compared to the no-network model. In sum, we conclude that the
network structure of shipping is of first order importance to assess the impact of changes intransport costs on trade and welfare.
Our paper is closely related to the growing number of studies using satellite data for
economic analysis. Donaldson and Storeygard (2016) provide an overview of applications
which so far has focused on environmental, development and spatial issues. This paper
explores how shipping satellite data can be used within the field of international trade.
There are only a few recent papers that have used shipping satellite data to explore issues
related to trade. Brancaccio et al. (2017) study the role of the transportation sector in world
trade focusing on search frictions and the endogeneity of trade costs. They use AIS data fordry bulk ships, which typically carry commodities such as iron ore, coal, grain and sugar. Our
focus is instead on container ships, which typically carry manufactured goods and accountfor around two-thirds of world trade based on values. In recent, and parallel, work, Ganapati
et al. (2020) study the role of shipping hubs for global trade and welfare. While our paper
focuses on the role of the global shipping network and use the Panama Canal expansion asa natural experiment, their paper instead estimates a quantitative model to assess the roleof hubs in transportation.
Our paper also aims to contribute to the literature on the effects of containerization. Besides having spurred global trade as documented by Bernhofen et al. (2016), new port technology has been shown to have significantly altered countries’ economic geography (Brooks
et al., 2018 and Ducruet et al., 2019). Finally, this paper is related to the literature thatstudies the impact of canal openings or closings. Maurer and Rauch (2019) analyze how
the Panama Canal changed U.S. population patterns, whereas Feyrer (2009) studies therelationship between trade and the closing and opening of the Suez Canal.
The rest of the paper is structured as follow. Section 2 documents the satellite data andthe construction of the shipping network and presents salient features of the network. Section
3 analyzes the global impact of the Panama Canal expansion on trade. Section 4 presents aspatial model of trade capturing the network features of the global shipping network, while
Section 5 uses the model to quantify the general equilibrium effects of the canal expansion
and compare them to those that would arise without a network environment. Section 6
concludes.

2

Data and Descriptives

2.1

Data

AIS data. Our point of departure is containerized trade. Containerized seaborne tradecaptures the majority of merchandise world trade (see UNCTAD, 2016), and is responsible
for approximately 60 percent of the value of all seaborne trade in 2016 (Rajkovic et al.,2014). We build a comprehensive data set for the global container shipping network based onsatellite data for ships. The satellite data comes from AIS (Automatic identification System)
data and is provided by Marine Traffic. AIS is an automatic tracking system used on ships
4and by vessel traffic services (VTS). Vessels send out AIS signals identifying themselves
to other vessels or coastal authorities, and the International Maritime Organization (IMO)
requires all international voyaging vessels with above 300 Gross Tonnage and all passenger
vessels to be equipped with an AIS transmitter. This requirement ensures a nearly universal
coverage of container ships in our data, as over 99% of container-shipments around the world
are made by containerships that are above 500 tonnage.
Our data set is based on a ship’s port calls, i.e. the signal sent by a ship when it entersand leaves the geo boundary of a port. For each observation, we observe the ship’s ID, its
time stamp, transit status3 , and current draught (i.e., by how much a ship is under water),as well as port information (name, country, and geographic coordinates). We use data on all
port calls tracked by the AIS satellite system during the calendar year 2016. We merge thedata with container ships’ technical information provided by Clarkson World Fleet Register.
After adjusting for some reporting errors, we were able match 93% of global container ships
sailing in 2016.
The Clarkson data provides information on each ships’ scantling draught (i.e., draught
when fully loaded) and dead weight tonnage (i.e. the maximum tonnes of goods that a ship
can carry). Combining the two with a ship’s current draught, we can back out how muchcargo a ship was carrying using formulas from the marine traffic literature (see Appendix
Section B for details). Appendix Section A reports in detail our variables and how we havecleaned the data. Our final dataset includes 4,941 container ships and 514 ports for the year
2016.
Other data sets. The analysis in Section 3 requires data on trade flows, which we obtainfrom COMTRADE for the years 2013-2019. We aggregate monthly bilateral trade data to
the quarterly level to reduce volatility that is due to seasonal effects or to lagged reporting.
The analysis also requires variables such as distance and contiguity, which we obtain fromthe gravity database of CEPII. Data on free trade agreements come from the WTO’s RTA
databases. The analysis in Section 4 requires additional information about expenditure alongwith a few other variables, which we obtain mainly from the Eora Global Supply Chain
Database and supplement with data from the Worldbank’s World Development Indicatorsand from INSEE; we gather data for 149 countries for the 2015 cross-section. Appendix G
provides additional details.

2.2

Stylized Facts on the Global Shipping Network

We start by documenting three salient features of the global shipping network that will guidethe subsequent analysis.
Fact 1: Container ships typically operate on fixed routes. Table 1 provides descriptive
statistics on the number of ports passed per ship as well the number of ships that arrive anddepart per port. A key feature of container ships is that they typically visit the same port
many times. The table shows that the average number of distinct ports passed per ship isroughly one sixth of the total number of ports passed per ship (12 versus 68).
Fact 2: Shipping activity is highly concentrated in space. A few ports act as major hubs
in the shipping network. While the median port only serves around 200 ships per year, the3A ship is called ’in transit’ at a port if it is not lading or unlading cargos.

5

Table 1: Ships and Ports
Variable:

Obs

Median

Mean

Sd

Min

Max

Ships:# ports passed# distinct ports passed

4,941
4,941

64
12

67.81
12.48

40.16
6.94

1
2

312
48

Ports:# incoming ships# outgoing ships

514
514

206
201

651.82651.82

1,457.89
1,454.97

5
5

14,486
14,421

Port pairs:# shipsdeadweight tonnes (in millions)

4,158
4,158

38
0.70

80.58
2.08

168.864.98

59.66×10−3

2,779
95.95

Note: Summary statistics are based on the port calls made by container ships in 2016. Only ships
with deadweight tons>15,800 and trips with non-zero duration are used. Summary statistics include
only routes taken by at least 5 ships and only routes between ports that appear both as arrival anddeparture ports.

top ports serve close to 14,500 ships per year. The same pattern is observed at the port-pairlevel, i.e. there are a few links in the network that account for a large share of total shipping
activity.
Fact 3: Only 6 percent of all country pairs have a direct shipping connection. We calculate
the in-degree as the number of ports to which a port is directly connected based on incoming
ships, and the out-degree as the number of ports to which a port is directly connectedbased on outgoing ships. Table 2 shows that most ports are connected to rather few otherports. However, there is great variation between ports in how well connected they are.
Nevertheless, even the best connected ports are only directly connected to around one sixthof the total number of ports. The 514 ports in our data are allocated across 154 countries.
Only 6 percent of all country pairs have a direct shipping connection.4 Trade between thesecountries accounts for only 54 percent of world trade. Therefore, a large share of global tradedoes not travel on direct routes, but on routes with multiple hops.
The share of directly connected pairs is impacted by the restrictions we have imposed on the sample.
If we include connections with less than five ships and sailings by very small ships, the share of directly
connected country pairs is still only 11%.
4

6

Table 2: Port Networks
IndegreeOutdegree

Obs
514
514

Mean
8.09
8.09

Sd
10.26
9.85

Min
1
1

p50
4.5
5

p90
18
19

p95
31
27

p99
50
46

Max
84
82

Note: Summary statistics are based on the port calls made by container ships in2016. Only ships with deadweight tons>15,800 and trips with non-zero duration
are used. Summary statistics include only routes taken by at least 5 ships and only
routes between ports that appear both as arrival and departure ports.

2.3

Calculation of Fastest Routes

This paper investigates the impact of the Panama canal expansion on trade by exploiting
information on the underlying shipping routes. To do so, we need to identify the shipping
route between departure country i and arrival country j. This information enables us todetermine to what extent trade between two countries is exposed to the Panama canal
expansion.
While the AIS data provides unprecedented detail about the movement of ships, one
cannot observe the movement of the cargo itself, i.e. the actual route of a shipment fromcountry i to country j. This section documents our methodology to calculate routes andshows descriptive statistics on those routes.
Based on the schedule of departure and arrival times of all container ships in our dataset(inferred from the time stamps indicating arrival at and departure from a given port), we
compute the optimal path in terms of travel time from any port i to any port j at a any start
time h during the year 2016 using a simple algorithm described in Appendix C.5 Amongthe set of optimal paths connecting two ports at different points in time, we select the route(the sequence of intermediate ports) that is used most frequently.6
Figure 1 visualizes the fastest routes for U.S. exports to all other countries based on our
calculation.7 The figure shows that the routes typically go through hubs, e.g., U.S. shipping
to Europe tends to pass through Germany and the Netherlands, whereas U.S. shipping toAfrica goes through a hub in Spain.
Figure 2 plots the fastest travel times between all port pairs against geodetic distance.
Distance is strongly correlated with direct travel time, represented by the light blue dots inthe figure. However, we observe that for indirect routes, represented by the dark blue dots,
geodetic distance is much less informative for travel times.
To understand further the role of shipping hubs and indirect routes in the shipping
network, we examine the number of hops on the fastest shipping routes between all ports
The algorithm finds all optimal paths for a predetermined maximum number of intermediate stops. For
computational reasons, we set the maximum number of intermediate ports equal to 15.
6
In those cases where more than one route occurs with the same highest frequency, we average over thecharacteristics of these routes when producing summary statistics.
7
The figure displays only one route per country pair, namely the fastest one among the routes connecting
all U.S. ports to the port(s) in the partner country.
5

7

Figure 1: Fastest Travel Times.

Note: The figure plots the fastest routes from the U.S. to othercountries. All computations are based on observed arrival and departure times of container ships with deadweight tonnes>15,800
in 2016. Routes with less than 5 ships are dropped. The plottedroute is the fastest one among the routes connecting any U.S. port
and any port in the destination country.

8

Figure 2: Travel time and distance across port-pairs.

Note: The figure plots travel times on the fastest route between two ports against
their geodetic distance.

in the network. Figure 3 shows the frequency of hops after aggregating ports by country.8
Most country pairs are connected by routes involving at leastone to four hops.9
Our calculation of routes relies on the assumption that the fastest route will be thecost minimizing route. Appendix Section D.1 provides empirical evidence on the correlation
between freight costs and travel time that supports this assumption. To verify that our
calculated fastest routes captures the actual routes taken, Appendix Section D.2 compares
our computed routes with the actual routes for Chinese trade, based on detailed Chinese
customs data. The comparison shows that there is a high degree of overlap between thefastest-time routes and the actual routes in the Chinese data.
Having established the global shipping network and thereby the routes connecting all
trading partners, we move on to analyze the role of the network for the propagation of local
shocks.
For countries with multiple ports, we use the minimum number of hops across multiple connections to
the partner country.
9
Figure 3 shows that the share of country pairs with zero-hop routes is lower than the 6% percent of
directly connected country pairs reported above. This is due to the fact that in some cases the route thatwas optimal in terms of travel time most often in 2016 was an indirect one.
8

9

Figure 3: The distribution of the number of hops across country-pairs.

Note: The figure shows the distribution of the number of hops (intermediate countries) along the fastest route between all country pairs in the sample. The average(median) is 2.6. (3). For countries with multiple ports, the number of hops refers
to the route with the lowest number of hops.

3

The Impact of the Panama Canal Expansion on Global
Trade

Guided by the stylized facts on the shipping network presented in Section 2, we now investigate how a shock to a particular link in the network not only affects trade between
ports/countries on either side of the link, but also trade between any port/country thatis using that link indirectly. We use the Panama Canal expansion in 2016 as a naturalexperiment.

3.1

The Panama Canal Expansion

The Panama Canal opened in 1914 and is one of the important links of worldwide maritime
trade. The motivation for the 2016 expansion was twofold. First, because of the rapid
increase in global trade, the Panama Canal had started to reach its capacity constraint.
Second, container ships were getting larger, and many of them were too big to use the canal.
By the turn of the millenium, the Panama Canal was already a bottleneck for American andAsian-American-East coast trade. According to Wilson and Ho (2018), only 41 percent ofcontainer ships and 52 percent of dry bulk ships would have been able to pass through theoriginal canal.10 Therefore, in 2006, the Panama Authority decided to expand the canal by
Wilson and Ho (2018) provide a comprehensive case study of the Panama Canal. They calculated thecited figures based on numbers from Fairplay in 2015.
1010

adding a new, deeper and wider lane of traffic. The expansion project was approved in April
2006, and the construction began in 2007 with an estimated total cost of US$5.25 billion.11
The Panama Canal Authority initially announced that the Canal expansion would becompleted by August 2014 to coincide with the 100th anniversary of the opening of the
Panama Canal. But various setbacks, including strikes and disputes with the construction
consortium over cost overruns, pushed the completion date back several times. There was,therefore, substantial uncertainty about exactly when the expanded canal would open. The
expanded canal began commercial operation on 26 June 2016.
The enlarged canal was a formidable feat of modern engineering: it doubled the shipping
capacity of the canal, allowing for around 90 percent of the world’s containerships to pass. In
particular, the expanded canal allowed for the passage of so-called Neopanamax ships, whichcarry more than twice as much cargo as the older Panamax ships.12 As the new lane opened,a new toll structure was introduced that differentiated across ship size. It implied higher
rates for bigger ships on a per-ship basis, but lower rates for bigger ships on a per-container
basis (see Wilson and Ho, 2018). From June to December 2016, the share of Neopanamax
ships passing through the canal increased from 0 to 15 percent. In 2017, the canal container
tonnage increased by 22%.13
Overall, the Panama Canal expansion serves as an ideal natural experiment for our study
for several reasons. First, the canal is one of the most important hubs in the global shipping
network; as such the expansion is likely to have a large aggregate impact. Second, the oldcanal continued to operate both during and after the construction period, facilitating clean
identification of the impact of the expansion on global trade and container traffic. Third,
uncertainty about the exact opening date of the expanded canal suggests that anticipation
effects around the time of opening was limited.
A potential concern is that, although the opening date was subject to uncertainty, knowledge about a future expanded canal might have encouraged the building of larger ships andinvestment in port capacity. These general equilibrium effects are not identified in this paper. However, based on a detailed analysis of the development of shipbuilding we find noevidence of an escalation in the building of Neopanamax ships from the announcement ofexpansion of the canal and onwards. The building of such ships was relatively stable between
the announcement and completion year. Appendix Section E provides details on the analysis
and a more extensive discussion of the container shipping market.

3.2

Empirical Strategy

Combining the AIS based network data with COMTRADE data on bilateral world trade, weinvestigate how the Panama Canal expansion affected global trade. We do so by employing
a simple differences-in-differences analysis:
https://web.archive.org/web/20110721055325/http://www.acp.gob.pa/eng/plan/documentos/propuesta/acpexpansion-proposal.pdf
12Foradetailed
descriptionoftheexpansion
project,seee.g.
https://www.nationalgeographic.com/news/2014/8/140815-panama-canal-culebra-cut-lake-gatun-focus/
13
http://www.pancanal.com/common/maritime/advisories/2017/a-02-2017.pdf
andhttps://www.moodys.com/research/Moodys-Upgrades-Panama-Canal-Authority-to-A1-Outlook-stable-PR_396338
11

11

yijt = βP ostt × P anExposureij + δ · Zijt + δij + δit + δjt + εikt ,(1)

where yikt is log of imports from country i to country j in quarter t.14 The variable P ostt
is a dummy that takes on the value one if the date is after June 2016, and zero otherwise.
Exposure to the Panama Canal expansion is captured by the variable P anExposureij , whichtakes on a value between zero and one. Zikt refers to a set of bilateral controls: a dummy
for joint membership in a free trade agreement (FTA), bilateral geographical variables (distance, contiguity and common language) and the share of deadweight tonnes traveling on
Neopanamax ships on the route connecting i and j prior to the expansion, all of which areinteracted with the P ostt dummy.15 Hence, we allow for trends in trade that may differ
according to observed geographical characteristics and for trends among pairs relying differentially on Neopanamax ships prior to the expansion. We also include a large set of fixed
effects: source country-time δit and destination country-time δkt fixed effects will control fortrends in overall exporting and importing for each country, while source-destination country
fixed effects δik control for time-invariant country pair characteristics.
Panama Canal exposure. The exposure measure is constructed as follows: We define
exposure at the route level equal to one if the route passes the Panama Canal and zerootherwise.16 For country pairs with multiple ports we average over the exposure of all portto-port connections using the source and destination port size as weights, where port size ismeasured in terms of total incoming (outgoing) tonnes in 2016. We also explore alternative
ways of inferring Panama Canal exposure in Appendix Section I.
Table 3 presents summary statistics for the Panama Canal exposure measure in 2016.
There are 3,623 country pairs (14% of 25,025 pairs with positive trade flows) which areconnected by a fastest route passing the Panama Canal. The value shipped between thesecountries accounts for 12% of global trade. The table shows that the majority of countries
are in some way exposed to the Panama Canal: 66% of all importers have at least one
fastest connection to a trade partner that passes through the canal. Across all importers,
the average share of imports exposed to the Panama Canal is 7%. Figure 4 shows the shareof imports passing through the Panama Canal by country, and illustrates the importance of
the Panama Canal as a shipping route for the Americas.
The exposure variable is calculated based on the observed container traffic data prior tothe opening of the expanded canal. The exposure variable is relatively stable over time. We
calculate the same variable for the post period (i.e., second half of 2016), and find that thecorrelation between the pre- and post-period exposure measure is 0.95. Furthermore, 95.3%
of port pairs experience zero change in exposure between the pre and post period, 2.5%
(2.2%) increase (decrease) their exposure. Hence, we find no large or systematic changes
towards a higher exposure in the post period.
The methodology relies on the fastest time algorithm correctly predicting port-to-portconnections that actually use the canal. This is more likely to be true if alternative routes
We use imports by country of consignment, rather than country of origin. Country of consignment iscountry where the last ownership change occurred before goods arrive in the importing country.
15
A Neopanamax ship is the term that characterizes the maximum ship size for crossing the expandedcanal.
16
In cases where the most frequent route is not unique, we average over the binary exposure measure ofthese routes.
14

12

Table 3: Panama Canal Exposure: Summary Statistics for 2016.
Country pairs
with exposure

Global trade
exposedImporterswith exposure(1)# pairs(2)% of total(3)
value in trn $(4)% of total(5)# importers(6)% of total

3,623

14 %

1.8

12 %

144

66 %

Note: The table shows in column 1 (2) the number (share) of country pairs with a fastest
and most frequent connection passing the Panama Canal; in column 3 (4) the value of (shareof global) trade between country pairs whose fastest and most frequent connection passes
the Panama Canal; in column (5) and (6), respectively, the number of importers with atleast one fastest connection passing the Panama Canal and their share in the total numberof importers.

Figure 4: Panama Canal Exposure by Country.

Note: The figure shows the share of imports passing through the Panama Canal in total imports
by country.

13

would take much longer time. To address this, we perform the following thought experiment.
First, we identify all the paths that pass the Panama canal according to our algorithm.
Second, we remove the canal from the shipping network and recalculate new, second-fastest,
paths using our algorithm. Third, we compare travel time before and after removing thecanal. The result of the experiment is illustrated in Figure 12 in the Appendix. On average,
travel time increases by 14 days (67%) if the canal cannot be used. For 97.6% of the affected
paths, travel time increases by 3 days or more. This suggests that other factors that may
affect the choice of alternative routes are a secondary concern and, furthermore, that it isunlikely that other cost factors would change a “treated” country pair to an “untreated” one,or the other way around.
.

3.3

Empirical Results

We estimate the empirical specification in equation (1) using quarterly COMTRADE trade
data for the period 2013Q1 to 2019Q4 as the dependent variable. Table 12 in the Appendix
Section G summarizes the estimation sample.17 Estimation results are reported in Table
4. Columns (1)-(2) report results for the baseline specification without and with controls,
respectively. In both cases, we find that bilateral trade between country pairs whose fastest
route passes the Panama Canal, increased by around 10 percent after the expansion.
Heterogeneity. We also explore whether the treatment effect is heterogeneous acrosscountry pairs. One hypothesis is that country pairs with fewer hops along the route will
have a greater treatment effect than country pairs with many hops. For example, if the
expansion reduces shipping costs due to the adoption of larger ships, then the cost savingsin percent will be higher on routes with fewer hops. In Column (3) in Table 4 the main
regressor is interacted with an indicator variable for whether the number of hops between
i and j is below or above the median number of hops. The estimation results support the
hypothesis; the treatment effect is 30% higher for country pairs with below median numberof hops as compared to to those with above median hops.
Pre-trends. Figure 5 shows the estimated coefficient β by quarter. We find that thequarterly treatment effects in the post period are positive though not individually significant,but the sum of them, which corresponds to the regression is in Column (2) in Table 4, isstrongly significant. Importantly, the figure illustrates the absence of pre-trends, indicatingthat the identifying assumption holds.

3.4

Robustness

To check the robustness of our results, we re-estimate the specification from column (2) ofTable 4 with a modified set of controls, for a shorter time span, for a balanced panel, formonthly data and with alternative Panama Exposure measures. The results are reported inTable 5. Overall, we find that the results are relatively insensitive to various perturbationsof the data, underscoring the robustness of the baseline results.
17
Our estimation sample covers about 82% of global imports reported to COMTRADE. The missing 18%
are due to countries not reporting trade data to Comtrade on a monthly basis (which are aggregated to thequarterly level).

14

Table 4: The impact of the Panama Canal expansion on trade
P ostt × P anExposureij

(1)

(2)

.105***(.038).108***(.040)(3).126**(.052).098**(.044)

×[#hops ≤ med]
×[#hops > med]

Controls
FEs

Noij,it,jt

Yesij,it,jt

Yesij,it,jt

Observations
Exporters/Importers
adj. R2

199,177
140/105.937

199,177
140/105.937

199,177
140/105.937

Note: Dependent variable is the log of imports from country i to country j in quartert over the period 2013Q1 − 2019Q4. The control variables are: an FTA indicatorand geographical variables (distance, contiguity and common language) interactedwith P ostt , and the share of deadweight tonnes traveling on Neopanamax ships
on the route connecting i and j in the pre period interacted with P ostt . The tripleinteraction term in column 4 is an indicator variable for whether the number of hops
between i and j is below of above the median number for the treated group. Standard
errors are clustered by i, j. Significance levels: ∗p < 0.1, ∗ ∗ p < 0.05, ∗ ∗ ∗p < 0.01.

15

Figure 5: Panama Canal Exposure Coefficient by Quarter.

P2019:q4
Note: Graph illustrates regression equation: yikt = β q=2013:q1 I[t = q]×P anExposureij +δ·Zijt + δij + δit + δjt + εijt where Zijt includes ln Dist interacted with quarter dummies. Solidlines indicate 90% confidence intervals.

Column (1) shows that the estimated magnitude is not driven by the disproportionately
large effect in Q4 of 2019 visible in Figure 5. Column (2) document that limiting thesample to the 38 importing countries that reported monthly trade flows in every month inour sample period does not change our results. Therefore our findings are not driven bycountries entering or exiting the sample or by an increase inreporting activity by particularcountries. Next, we estimate a specification based on monthly data. This produces a slightly
smaller coefficient estimate (.082; see Column (3) ). This is consistent with measurement
error in monthly flows due to lagged reporting, which is smoothed out by aggregating toquarters.
Finally, we construct two alternative Panama exposure measures using all optimal paths
found by our algorithm, instead of relying on the most frequent routes. In Column (5) the
Panama exposure measure at the port-to-port level is the simple average across the binary
exposure measure of all paths that were optimal at least once in the first half of 2016. In
Column (4), the paths are weighted by the amount of time during which they were optimal
during the first half of 2016. Aggregation from the port-to-port level to the country-pairlevel is done in a similar way as above.

16

Table 5: Robustness
Robustness check:P ostt × P anExposureij
Observations
Exporters/Importers
adj. R2

2019Q4 dropped

Balanced sample

Monthly data

.102**(.040)
193,450140/105.937.097*(.054)
86,576133/36.947.082**(.040)
600,884
140/107.900

PanExposure: all paths
Weighted avg. Simple avg.
.103**.098**(.048)(.048)
199,177
199,177
140/105
140/105.937.937

Note: Dependent variable is the log of imports from country i to country j in quarter t over the period 2013Q1 −2019Q4 in columns (2,4,5). In column (1) the last quarter of 2019 is dropped. Column (3) is based on monthly data for
the full sample period. Column (2) is restricted to set of pairs for which trade flows exist in every quarter. All columns
include ij, it and jt fixed effects as well as controls. The control variables are: an FTA indicator and geographicalvariables (distance, contiguity and common language) interacted with P ostt , and the share of deadweight tonnes
traveling on Neopanamax ships on the route connecting i and j in the pre period interacted with P ostt . Columns (4)and (5) are based on a P anExposure measure computed as a weighted (column (4)) and simple (column (5)) average
across the exposure of all paths between two ports in i and j, rather than the exposure of the most frequent route.
Weights in column (4) are given by the amount of time for a which a certain path was optimal, that is, the numberof hours between the start date of the path and the start date of the previous optimal path relative to the length ofthe pre period. Standard errors are clustered by i and j in columns (1,2,4,5). In column (3) where the number ofimporters is very low, standard errors are clustered by ij. Significance levels: ∗p < 0.1, ∗ ∗ p < 0.05, ∗ ∗ ∗p < 0.01.

4

A Quantitative Trade Model with Optimal Routing

So far, the empirical analyses have provided evidence of the impact of the Panama Canal
expansion on global trade. This section introduces a parsimonious quantitative model ofworld container traffic and trade to quantify the general equilibrium and welfare effectsof the Panama Canal expansion. In contrast to standard trade models, goods are passing
through a shipping network when departing from an origin and arriving in adestination port.
Agents choose the optimal route endogenously in order to minimize transport costs. The
model also allows for economics of scale in shipping, so that larger ships on a given route
may potentially lead to lower average transport costs. We build on the work of Allen and
Arkolakis (2020) (henceforth, AA2020): while their application is on urban economics, whereindividuals choose where to live and commute, our focus is on international trade, where
goods move across borders subject to transport costs, but where individuals are immobile
across countries.
While the model allows for endogenous routes and reallocation of shipping across ports,
we have chosen to abstract from endogenous investment in ships and ports. There are twomain reasons for this. First, as documented in Section 3.1 and Appendix E, the first-ordereffect of the canal expansion was that more and larger ships could transit. Second, we do nothave a clean identification strategy for estimating these additional margins of adjustment.18
After presenting the economic framework, we quantify the effect of the expansion in
18

17Section 5. The quantification will allow us to assess the welfare impact of the canal expansion
and to assess the importance of ship size (economics of scale in transportation) in generating
those welfare gains. Finally, we contrast our results with a model with no shipping network.
This allows us to assess the role of the shipping network for trade and welfare.

4.1

Model Setup

Consider a world with N locations indexed by i and j, each is endowed with Li units of labor.
There is a continuum of varieties indexed by ν ∈ [0, 1]. Individuals have constant elasticity
of substitution (CES) preferences over varieties with elasticity of substitution σ ≥ 0. Labor
is the only input, and is inelastically supplied for producing and shipping goods. Shippingfrom an origin i to a destination j entails taking a route r through the network, which is
subject to multiplicative iceberg transport costs ΠK
k=1 trk−1 ,rk . Here, K is the number of links
on route r and trk−1 ,rk denotes the transport costs of traveling through the k th link of r. We
let Rij denote the set of all possible shipping routes from i to j. The efficiency of producing
and shipping each variety ν from i to j via route r is characterized by εij,r (ν). We assume
that εij,r (ν) is independently and identically Frechet distributed with level parameter Ai anddispersion parameter θ. Individuals purchase each variety from the cheapest location-routesource. The idiosyncratic shocks εij,r (ν) imply that not all varieties are traveling though
the same route even if the source and destination ports are the same, e.g. variety ν1 goingfrom Lisbon to Oakland may pass through Rotterdam while variety ν2 may pass throughHouston. A possible micro-foundation for the shocks εij,r (ν) is heterogeneity in the preferred
time of shipment, e.g. route planners report multiple routes between Lisbon and Oakland,
and those routes are available on different dates.19 Furthermore, it buys us tractability interms of producing analytical expressions for many key objects of interest.

4.2

General Equilibrium

We now turn to solving the general equilibrium and characterizing global trade and container
traffic.
We impose two market clearing conditions, total income Yi equals total sales, and total
expenditure Ei equals total purchases:
Yi =

X

Ei =

Xij

j

X

Xji ,

(2)

j

where Xij is the total value of goods shipped from i to j. Using the market clearing conditions
and the properties of the Frechet distribution, it can be shown that Xij equals
Xij = τij−θ

Yi Ej
−θ ,
Π−θ
i Pj

(3)

where


τij = 

K
X Y

−1/θ

t−θ
rl−1 ,rlr∈Rij l=119

See e.g. https://www.cma-cgm.com/ebusiness/schedules/routing-finder.

18

(4)

is the shipping cost from i and j. The variable Πi is the standard multilateral resistanceterm known from gravity models:−θ θ+1Π−θ,i = (Ai Li ) Yi

(5)

and Pj is the consumer price index:
Pj−θ =

X

τij−θ Yi Πθi .

(6)iWith balanced trade, Ei = Yi , we now formally define the equilibrium of the model:
Definition 1. Given {Li }, {Ai } and {τij }, an equilibrium is a output vector {Yi } , expenditures {Ei }, bilateral trade flows {Xij }, {Πi } and {Pi } that satisfies equilibrium conditions(2),(3), (5), (6), as well as the balanced trade condition, for all i, j.
At the bilateral level, the model aggregates to a standard Ricardian trade model. However, the shipping costs τij are no longer ’bilateral’; instead, they are an endogenous outcomeof consumers’ optimal routing problem. Its value depends on the number of routes available
linking locations i and j, and the transport cost of each route, which depends on the shipping
costs tkl of all segments on that route.
Since wages are the only source of income, we can solve for nominal wages wi in locationi using wi = Yi /Li . Welfare of individuals is then simply wi /Pi .
Solving for the EquilibriumhiDefining A ≡ t−θij , AA2020 shows that transport costs τij can be rewritten as−1/θτij = bij,

(7)

where bij is the elements of the matrix B = [bij ] and B is the Leontief inverse of A, B =(I − A)−1 . Using equation (7) along with the gravity equation and the market clearing
conditions, (3) and (2), we can write the equilibrium conditions as
X
Ei
−θ
+
t−θ
ij Πi
Pi−θ
j
X
Y
i
−θ
Pi−θ = −θ +t−θji Pj ,
Πij

Πi−θ =−θ/(θ+1)(8)(9)

When trade is balanced, Ei = Yi = Πi
(Ai Li )θ/(θ+1) , and given values of tkl , Ai and
Li , the 2N equations (8) and (9) can be solved for the 2N equilibrium outcomes Πi and
Pi . In the quantitative application below, we will write equations (8) and (9) in changes
following the “exact hat algebra” approach by Dekle, Eaton and Kortum (2008), to solve fora counterfactual equilibrium.

19

Trade and Traffic
We end this subsection by characterizing traffic flows according to the model. We define
traffic as the the total value of all cargo passing though a segment (k, l) in the network. It
can be shown that, in equilibrium, the value of traffic between k and l is−θ −θΞkl = t−θ
kl Pk Πl .

(10)

Furthermore, there is a simple mapping between trade and traffic.20 One can express equilibrium trade flows as:
Xij = cXij Yi Ej

(11)


−1

th
element of the matrix CX ≡ DX − Ξ , where DX is a diagonal
where cX
ij is the (i, j)Pmatrix with ith element di ≡ 12 (Yi + Ei ) + 21 j (Ξji + Ξij ) and Ξ = [Ξij ].

5

The General Equilibrium Effects of the Panama Canal
Expansion

We now turn to applying the model to quantify the impact of the Panama Canal expansion.
The empirical strategy is as follows. First, we estimate the impact of the expansion on thefollowing margins: container ship size, the frequency of ships and ship capacity utilization.
These steps will rely on the MarineTraffic traffic data between all port pairs, before andafter the expansion. Using the model, we can then back out the reduction in transport costs
caused by the canal expansion. Third, we perform a counterfactual simulation of the model,
where we use (i) the estimated change in transport costs and (ii) the MarineTraffic data,
to investigate the welfare impact of the expansion. Fourth, we estimate our reduced-form
model from Section 3.2 on the simulated data coming from the counterfactual. This enables
us to assess the importance of one specific mechanism, ship size, in generating the growthin trade that we estimated in Section 3.3. It also serves as a validation of the quantitativemodel. Fifth, and finally, we compare the counterfactual results based on the network modelwith a counterfactual from a model without a shipping network, i.e. where goods are shipped
directly from source i to destination j. This helps us isolate and understand the importanceof the shipping network in generating the main quantitative results on trade and welfare.

5.1

The Impact on the Margins of Shipping

The first step of the analysis is to determine the impact of the expansion on three margins
of shipping: (i) ship size, (ii) frequency (the number of ships) and (iii) ship utilization, i.e.
the percentage of used ship capacity. We proceed by creating a dataset of all threevariables from the MarineTraffic data, for every segment (port-pair kl) and for the 1st and2nd half of 2016. The construction of these variables is described in detail in Appendix
Section B. We estimate the following regression∆ ln ykl = α0 + βP anamaCanalkl + Dk + Dl + kl ,20

See AA2020 for detailed derivations.

20

(12)

Table 6: The Margins of Shipping: Results
Dependent variable
P anamaCanalkl

Controls
Source/destination FE
Obs∆ ln ShipSizekl
(1)
(2)
(3)
∗∗∗
∗∗
.22
.14
.12∗
(.05)
(.06) (.06)∆ ln F requencykl
(4)
(5)
(6)
.01
.02
.02
(.12) (.14) (.15)∆ ln U tilizationkl
(7)
(8)
(9)
.05
.02
.02
(.04) (.05) (.05)

No
No
3,595

No
No
3,595

No
No
3,595

Yes
No
3,566

No
Yes
3,403

Yes
No
3,566

No
Yes
3,403

Yes
No
3,566

No
Yes
3,403

Notes: The difference ∆ refers to the change from the 1st to 2nd half of 2016. ShipSizekl is calculated
as the average across all trips on a given segment. F requencykl is the number of ships using the segment. U tilizationkl is traffic Ξi relative to capacity (ShipSizekl ×F requencykl ). P anamaCanalkl isan indicator taking the value one if the segment uses the Panama Canal. Regressions are weighted by
the initial level of traffic Ξkl . Controls are: source- and destination country fixed effects, source anddestination port latitude and longitude, source and destination port capacity (total traffic), and average travel time between k and l. Source/destination FE refers to source- and destination port fixed
effects. Robust standard errors in parentheses. Significance levels: ∗p < 0.1, ∗∗p < 0.05, ∗∗∗p < 0.01.

where ∆ refers to the change between the 1st and 2nd half of 2016 (recall, the expandedcanal opened 26 June 2016), ykl is one of the three outcome variables described above andP anamaCanalkl takes the value one if the segment kl is using the canal and zero otherwise.
The variables Dk and Dl are origin and destination port fixed effects, respectively.
The estimation results are shown in Table 6. Columns (1), (4) and (7) show results without any controls, whereas columns (2), (5) and (8) are results with the following controls:source- and destination country fixed effects, source and destination port latitude and longitude, source and destination port capacity (total traffic), and average travel time between k
and l. Columns (3), (6) and (9) are estimation results when we instead include source- anddestination port fixed effects. We find that average ship size increased by .12−.22 log points,
depending on the specification, for Panama Canal segments relative to other segments. Thisis as expected, because the expansion facilitated much larger ships passing through the canal,
see Section 3.1. The other two margins, ship utilization and frequency, are estimated to bearound zero and are statistically insignificant.
By construction, the volume of traffic on a segment kl, ΞVkl , is the product of margins(i)-(iii):
ΞVkl = ShipSizekl × F requencykl × U tilizationkl .
Since margins (ii)-(iii) are both economically and statistically insignificant, our results suggest that the impact of Panama Canal expansion on trade traffic is mainly through allowing
bigger ships to operate on relevant links.

5.2

Transport Costs

In the next step, we use the results above to infer the change in transport costs due to thecanal expansion. We start by assuming that transport costs tkl are a log-linear function of21

ship size and other factors, such as travel time. Specifically, we assume thattkl = ShipSize−δ
kl fkl (.) ,(13)

where fkl (.) is a flexible function of all other factors (e.g., travel time). Recall that the model−θ −θ
gives us the following equilibrium expression for traffic flows: Ξkl = t−θkl Pk Πl . Taking logs,
differencing and inserting equation (13) yields∆ ln Ξkl = θδ∆ ln ShipSizekl − θ∆ ln Πl − θ∆ ln Pk − θ∆ ln fkl (.) .

(14)

where εkl ≡ −θ∆ ln Πl − θ∆ ln Pk − θ∆ ln f (.).
While the model gives us an expression for the value of traffic, Ξkl , our data has information about the volume of traffic, ΞVkl . We proceed by assuming that the volume and valueof traffic are proportional, i.e. Ξkl = αΞVkl , so that ∆ ln ΞVkl = ∆ ln Ξkl . We acknowledge
that this assumption may be overly restrictive in the cross-section, e.g. traffic between someport-pairs (k, l) may have higher unit values than between other port pairs (k 0 , l0 ). For the
purposes of inferring θδ, however, the key (and less restrictive) requirement is simply thatthe unit value of traffic through the canal does not change pre/post the canal expansion,
relative to the control group.
Using the finding above that the canal expansion led to larger ships, but not higher
frequency and capacity utilization, ∆ ln ΞVkl = ∆ ln Ξkl = ∆ ln ShipSizekl for Panama Canal
port pairs kl, we immediately infer that θδ = 1. In other words, since ship size is the only
margin of adjustment from the canal expansion, the change in the volume of traffic is thesame as the change in ship size.21 The estimate of θδ then allows us to infer the change intransport costs from equation (13), given knowledge about the trade elasticity θ. Specifically,a change in ship size, holding everything else constant, will lead to the following change intransport costs for the canal segments kl:
t̂kl = e−δβ ,(15)where β refers to the point estimate from the regression of ∆ ln ShipSizekl on P anamaCanalkl
from equation (12) above. For non-canal segments k 0 l0 , we have t̂k0 l0 = 1. In our baseline
specification we use the value θ = 8, which leads to a change in transport costs t̂kl ≈ 0.98
for Panama Canal segments kl.

5.3

The Welfare Effect of the Panama Canal Expansion

We have provided evidence above that the expanded canal led to bigger ships and lower
transport costs. In this section, we ask, given our estimated change in transport costs, whatis the welfare effect of the Panama Canal expansion?
The general equilibrium of the model can be written in changes, using the “exact hat
algebra” approach from Dekle, Eaton and Kortum (2008). Appendix H.1 shows that thesystem of equations can be simplified as:
An alternative approach is to estimate equation (14) and using the Panama canal indicator as an instrument for the change in ship size. This also produces a coefficient estimate close to one.
21

22

Table 7: Data and Parameters.
Variable

Description

Value

Source

θ
t̂kl
α
ΞVkl
Yi

Trade elasticity
Canal transport costs, change
The value per dwt of traffic
Initial traffic flows (volume)
Initial Expenditure

8.98
USD 1,734

Previous literature
Estimated, Sections 5.1 and 5.2
Calibrated, Appendix H.3
MarineTraffic, 1st half 2016
Eora Global Supply Chain Database, 2015;
World Development Indicators; INSEE

Π̂−θ
i =

Yi

−θ/(θ+1)

Π̂i

+

X

Yi + j Ξij P̂i−θj−θ/(θ+1)XΠ̂i
Yi+P̂i−θ =P−θ
Yi + j Ξji Π̂i
j
P

Ξij
P
Yi + j Ξij

!
−θ
t̂−θ
ij Π̂j(16)Ξjit̂−θ P̂ −θ .
P
Yi + j Ξji ji j

(17)

!

The data and parameters required to solve this system are modest: We need data on
initial (i.e. 1st half of 2016) traffic Ξkl , initial expenditure Yi , the estimated change intransport costs t̂kl and the elasticity θ, see Table 7. We set θ = 8, which is consistent withprevious estimates in the literature (e.g., Eaton and Kortum, 2002). As described above, we
assume that Ξkl = αΞVkl . The procedure to calibrate the value of α is described in Appendix
H.3.22
To calculate total expenditure by port, Yi , we use data for total country expenditure
and allocate expenditure to ports based on the relative port size, see details in Appendix
Section G.3. Recall that we assume labor immobility across locations. This is appropriate forcountries that only have one port, but is less ideal for multi-port countries. In our sample, 46
percent of countries have only one port, suggesting that the labor immobility assumption isa reasonable approximation (and better than assuming the opposite, perfect labor mobility).
Figure 6 shows the change in real income, wi /Pi , for the top 20 ports in our dataset. Not
surprisingly, the ports closest to the canal are gaining the most. However, we also observe
ports further away, such as in Colombia, Ecuador, Peru and the Caribbean, that obtainlarge welfare gains from the canal expansion. The weighted average of the real wage change
across all countries is 0.001%, or 128 billion USD, measured in 2015 prices. The gains fromthe canal expansion is much higher than its costs, which was estimated 5.25 billion USD in
2006.

5.4

Traffic, Trade and Trade Costs

Next, we explore the impact of the canal expansion on traffic, trade and trade costs. Using the−θ −θ
equilibrium objects P̂k and Π̂l found above, the change in traffic is simply Ξ̂kl = t̂−θkl P̂k Π̂l .
Furthermore, there is a mapping between traffic and trade, see equation (11). Given the
The quantification exercise is based on a slightly smaller set of ports (492) and countries (149), due tothe fact that it requires a balanced dataset of port-to-port flows for the 1st half of 2016.
22

23

Figure 6: Real income, % change. Top 20 ports.
0.6

Real income, % change

0.5

0.4

0.3

0.2

0.1

R
I
ES O H
M AI
M ER NAO
N AL , D
TE D
O
G AS
O
,E
BA C
N LIM Y,UJPO KU ON M
AL *, CRTO OF RF
SP A, TOAW CA IN*IL,
LE LLA TTOM,C AU STA PEOCDRPU KLA , C
W
N
S
C D*
H
R , NZPA IST
G PE I, U
BU USE
EN AYA TE
Q ,PA
PO VE UFIN NT IL,TE U ECA RA
FO CA PI , C
T
ROR
T TA RE,GG
DE
E
FR NA P,KI AN COCN
G E,
FR STO MQ
EE N
PO , JM
B
AL RT
M
AN B , BZA OA S*N
IL , P
LO A
*,
PA

0

initial and counterfactual matrix of traffic, Ξkl and Ξ0kl , we can then use equation (11) toinfer initial and counterfactual trade flows Xij and Xij0 . One can then back out the change
in bilateral trade costs, τ̂ij from the gravity equation (3):τ̂ij−θ =

−θ
Π̂−θ
i P̂j
X̂ij .
Ŷi ÊjFigure 7 shows the histograms of the % change in bilateral trade costs τij and bilateral
trade Xij . Trade costs decline by up to 4 percent and trade increases by up to 31 percent
in the aftermath of the Panama Canal expansion. In addition to the directly exposed portpairs, such as the Pacific and Atlantic Panama ports, indirectly connected port pairs, suchas between Ecuador and the U.S. East Coast, get large declines in trade costs. The averagechange in trade costs and trade across source-destination ports are -0.32 and 2.68 percent,respectively.

5.5

Mechanisms and Model Fit

According to the model, the canal expansion caused trade to grow by X̂ij . This effect isentirely driven by the finding that the expanded canal caused bigger ships to pass throughthe canal. In order to evaluate the performance of the model, we estimate a version of the
reduced-form equation (1) from Section 3.2, but we replace real data with the simulated
data from the model (i.e. the left hand side variable).
The results are shown in Table 8. Column (1) performs the analysis at the port-pair level,
while column (2) aggregates the data to the country level, similar to Table 4 in Section 3.3.
24

Figure 7: Trade and trade costs, % change.
18

10 4

18

16

16

14

14

12

12

10

10

8

8

6

6

4

4

2

2

0
-10

0

10

20

30

0
-4

40

Trade, % change

10 4

-3

-2
ij

-1

0

, % changeInterestingly, the treatment effect using simulated data is very close to the treatment effectusing real data. This indicates that the main margin of adjustment based on the quantitative
analysis, namely ship size, is responsible for the growth in trade that we estimated in Section
3.3. The high adjusted R2 values also suggest that the model fits the data quite well. Recall
that the counterfactual model only required data on initial traffic Ξkl and expenditure Yi ,in addition to the change in transport costs t̂kl and the parameters δ and β. Therefore, themodel-generated growth in trade is an out-of-sample prediction, i.e. we did not use tradeflows, neither in levels nor in changes, when parameterizing the model.
A slight disconnect between the reduced form analysis in Section 3 and the model isthat the treatment (using the canal) in Section 3 was not inferred directly from the model.
We therefore also estimate the reduced form regression, but replace the treatment variable
P anExposureij with a Panama Canal exposure variable according to the model. Appendix
Section I provides details about the methodology and Table 13 presents the results. The
results are fully in line with our baseline results and are, if anything stronger and more
precise.

5.6

The Importance of the Shipping Network

Throughout the paper, we have emphasized the role of the shipping network for trade andwelfare. We end this section by comparing the counterfactual results reported above for the
network model with counterfactual results from a model without a shipping network, i.e.
where goods are shipped directly from source i to destination j.
To fix ideas, consider a world with three locations, i, j and k. In a canonical, no25

Table 8: Reduced-form regression: Simulated data.
Dependent variable: ln X̂ij (simulated)
P anExposureij
Source/destination FE
Observations
Dep. ports/Arr. ports
adj. R2

Port-pair.083***(.002)
Yes
240,064490/492.726

Country-pair.085***(.006)
Yes
10,253
138/102.736

Notes: Dep. var. is the relative change in exports from port i to port j
implied by the model, ln X̂ij . All columns in include i and j fixed effects.
Standard errors clustered by iand j. Significance levels: ∗p < 0.1, ∗ ∗ p <0.05, ∗ ∗ ∗p < 0.01.

network trade model, a change in transport costs between i and j, t̂ij can only affect kindirectly through general equilibrium effects. In our model, however, k may also be affectedby a network effect as goods shipped from i to k might pass though j. By comparing thecounterfactual results from the network model with the no-network counterfactual results,
we can isolate the network effects and quantify their relative importance on global trade.
We proceed as follows. In the absence of a shipping network, trade costs τij are exogenous.
Using the same definition of the equilibrium as described in Section 4, we solve the modelin changes, as before. Appendix J shows that the system of equations is
Π̂−θ
i =

X

τ̂ −θ
ij

Êj XijP̂j−θ Yi(18)τ̂ji−θ

Ŷj Xji
Ei
Π̂−θ
j

(19)

j

P̂i−θ =

Xj−θ/(θ+1)

After imposing trade balance, Êj = Ŷj , and using the fact that Ŷi = Π̂i, we can solve
this system of equations given data on initial trade flows Xij , expenditure Ei , output Yi , aswell as the change in trade costs, τ̂ij , and the elasticity, θ.
As in the counterfactual based on the network model, we set τ̂ij = 0.98 for port-pairs
directly using the canal, and τ̂ij = 1 otherwise.23 Initial trade flows Xij , expenditure Ei
and output Yi are calculated as follows. In the network model, we only used data for initialtraffic Ξij , and no data for trade Xij . To make the two counterfactuals comparable, theinitial values need to be consistent across models. We do this by first converting the traffic
data Ξkl to trade data Xij , using equation 11. Total income and expenditure is then simplyPP
the sum across rows and columns in the trade matrix, Yi = j Xij and Ei = j Xji . By
doing so, the two models are calibrated to the same initial steady state.
Figure 8 presents the changes in trade Xij and trade costs τij due to the Panama canal
expansion implied by the network and no-network model, respectively. Unsurprisingly, thechange in τij in the no-network model is 0 for the vast majority of port-pairs, and −2 percent
23

When goods are shipped directly from i to j, directed affected segments = directly affected port-pairs.

26

Figure 8: Trade Xij and trade costs τij , % change. Histogram.
14

10 4

2.5

10 5

Baseline
No-network

Baseline
No-network

12
2
10

1.5
8

6
1

4
0.5
2

0

0
-2

0

2

4

6

8

10 12 14-2

Change in bilateral trade Xij, %

-1.5

-1

-0.5

0

Change tauij, %for the very few port-pairs using the Panama Canal directly. In the network counterfactual,
however, the change in τij is much more smoothly distributed between −2 and 0%, because
many location-pairs are using the canal indirectly. For example, the network model suggeststhat trade costs between Hamburg and Long Beach (a port-pair which according to ourdata does not have a direct connection) would decline by 1-2%, while the no-network trademodel suggests a zero decline. The heterogeneous and widespread changes in trade costs,
τ̂ij , also translate into heterogeneous and widespread changes in trade flows. In the nonetwork model, trade creation in the aftermath of the canal expansion is limited to very few
port-pairs. While in the network model, many port-pairs are indirectly connected via thecanal, and therefore experience an increase in trade after the canal expansion. Based on
the network model, trade between Hamburg and Long Beach would increase by 14 percent,whereas the no-network model predicts an almost zero percent increase in trade.
Figure 9 reproduces the plot for the change in real income for our network model, but now
adds bars for the predicted increase in real income according to the no-network model. Not
surprisingly, the network model predicts higher gains from the canal expansion compared tothe model with only direct connections, mirroring that trade costs are declining more, andfor more location-pairs, in the network model than in the no-network model. For the top 20
locations, the real income gains are 69 percent higher in the network model as compared to
the no-network model. In sum, we conclude that the network structure of shipping is of firstorder importance to assess the impact of changes in transport costs on trade and welfare.
27

Figure 9: Real income wi /Pi , % change.
0.6
Baseline
No-network

0.5

Real income, % change

0.4

0.3

0.2

0.1

0

R
I
ES O H
M AI
M ER NAO
N AL , D
TE D
O
G AS
O
,E
BA C
N LIM Y,UJPO KU ON M
AL *, CRTO OF RF
SP A, TOAW CA IN*IL,
LE LLA TTOM,C AU STA PEOCDRPU KLA , C
W
N
S
C D*
H
R , NZPA IST
G PE I, U
BU USE
EN AYA TE
Q ,PA
PO VE UFIN NT IL,TE U ECA RA
FO CA PI , C
T
ROR
T TA RE,GG
DE
E
FR NA P,KI AN COCN
G E,
FR STO MQ
EE N
PO , JM
B
AL RT
M
AN B , BZA OA S*N
IL , P
LO A
*,
PA

-0.1

6

Concluding remarks

In this paper we exploit novel satellite data on all port calls made by container ships world
wide in 2016. This allows for the construction of a new comprehensive dataset on the
global shipping network and optimal shipping routes. We apply this dataset to analyze how
local shocks hitting a segment of the shipping network affect all trading partners worldwide
to varying degrees based on their exposure to the shock. Using the 2016 Panama Canal
expansion as a natural experiment, we show that the expansion not only had an effect on
trade flows directly exposed to the canal, but also had widespread indirect effects on world
trade due to countries’ indirect exposure to the canal through the global shipping network.
Based on counterfactual analyses we find that the Panama Canal expansion produced sizable
gains in terms of reduced trade costs, increased trade and higher real income, and that astandard trade model typically will underestimate the widespread gains arising from a local
shock to the transport infrastructure.

28

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30

Appendix
A

Constructing the Container Traffic Data Set

Our point of departure are the AIS data containing all port calls made by ships in 2016 thathas been provided by MarineTraffic. Based on the ship categories used by MarineTraffic, we
limit the data set to the ships categorized as “container ship” and “Cargo/containership”.
MarineTraffic provides each ship with a unique identifier (Ship ID). We start out with close
to 5,300 ships based on this identifier. We use this to identify each ship’s travel history. A
ship also has an IMO number and an MMSI number as well as a Ship Name. We use thisinformation to merge the AIS data set with the World Fleet register data base constructedby Clarkson, which has vessel specific information on a range of time invariant ship characteristics, such as the vessels carrying capacity measured in deadweight tonnes (dwt) andcargo capacity of container ship measured in twenty-foot equivalent unit (TEU).
Ideally there should be a perfect match between ship identifiers (IMO, MMSI and Ship
ID). However, for around 5% of the ships this is not the case. The mismatch could either
because of misreporting, or changing of owners (containerships typically change their MMSI
number when changing the owner). We correct for both misreporting and the change ofidentifiers by cross checking a ship’s IMO and MMSI number, as well as ship’s characteristics,
like its deadweight tons (dwt). We are able to correct for most of the misreporting and end
up with 5,165 distinct containerships. Finally, as we want to focus on global container traffic,
we introduce a threshold of 15,800 deadweight tons. This leaves us with 4,941 ships.
We then proceed by cleaning the routes of each container ship. The AIS data are veryrich with information on not just ports, but also on whether the ship is lading/unlading ina port, or is just in transit (e.g. due to need for additional fuels). In addition the data set
has information on anchorages, i.e. stops made by ships in places that are not ports.
We sort trips for each ship by their time stamp, so that their travel records are listed as
Arrival-Departure-Arrival-Departure, etc. A trip is defined as a direct port-to-port voyage. If
a ship departs a port A, makes several in transit stops at other ports, or stops at anchorages,
before finally arriving at port B, we define the voyage from A to B as one trip of the ship. We
use the draught reported when the ship reaches the arrival port as the draught of the trip.
Moreover, we drop a small number trips for which the arrival time stamp erroneously equals
the departure time stamp. Finally, we aggregate ports located within 30 kilometers of eachother and within the same country and we drop ports that do not appear both as arrivaland departure ports. We lose less than two percent of the shipped volumn by imposing theserestrictions on ship size, non-zero travel time, and the set of ports.

B

Calculating Global Container Traffic

Based on the container traffic data set described above, we compute a set of measures tocharacterize the global container traffic for any port pair for a given period: (i) frequency,
i.e. the number of ships traveling between the two ports; (ii) ship size, i.e. average ship
size traveling in terms of deadweight tonnes (dwt); (iii) shipments (cargo), computed basedon AIS data matched with data on ship characteristics; and (iv) utilization, calculated as
31

shipments/(ship size × frequency).
Due to the availability of AIS data, the use of draught-based estimates of ships’ cargo
has recently emerged in the maritime transport literature, see e.g. Adland et al. (2017).
The draught of a ship refers to the vertical distance between the surface of the water andthe lowest point of a vessel. We build on this approach, and as we limit the analysis to
one type of ships, namely container ships, we are able to establish a relatively simple rule
for the computation of the ships’ container shipment. For each sailing ship we observe thedraught reported by the ship en route, HA , which will vary depending on the ship’s cargo.
A ship sailing without cargo is referred to as a ship sailing in ballast. In practice, a ship
sails in ballast if its draught is smaller than a given threshold value, which we refer to as
ballast draught (HB ). Specifically, we define HB = 0.55HS , where HS is the ship’s scantling
draught. Scantling draught is the draught the ship will have when it is fully loaded, and it isalso referred to as design draught, as it is this draught it is build for, and is thus a constant.
We have access to technical information on ships’ scantling draught as well as the vessel’s
carrying capacity (dwt) from the Clarkson World Fleet Database (see Section A above).
We use 0.55 as the weight to define ballast draught based on the maritime engineering
literature.24 Letting HA refer to the draught reported by the ship en route, we calculate theshipments carried by a ship on a specific voyage, as
Ef f ectiveDW T = dwt ∗ (HA − HB )/ (HS − HB ) .

(20)

A ship’s draught as well as estimated cargo relates to one specific trip, i.e. to a voyage
between two ports.
Table 9 shows that, based on our draught-based estimates, on average container ships
do merely 1% of their trips without cargo (in ballast). This stands in sharp contrast toother types of vessels that are typically involved in very different trades, and do not operateon “bus routes” like container ships. Brancaccio et al. (2017) focus on dry bulk ships andreport that 42% of the ships travel without cargo. We also observe that there is substantial
variation across trips with respect to draught, effective dwt, and across ports with respect
to total incoming and outgoing cargo.
The threshold for ballast water is chosen based on information from MarineTraffic supported e.g. David(2015).
24

32

Table 9: Ships, Trips and Port
Variable:

Obs

Mean

Sd

Min

Max

Ships:
Share of trips in ballast (<55%)

4,937

0.01

0.05

0

1

Trips:
Actual draught (% of scantling draught)
Effective dwt on loaded trips

331,249
331,249

0.94
26,113.93

0.07
24,559.94

0.55
1.23

1
199,744

Ports:
Total incoming effective dwt (in millions)
Total outgoing effective dwt (in millions)

514
514

16.83
16.83

44.36
44.34

0.01
0.01

498.70499.98

Note: Summary statistics are based on the port calls made by container ships in 2016. Effective
dwt is calculated based on dwt and draught and is used as a measure for cargo. Only ships withdeadweight tons>15,800 and trips with non-zero duration are used. Summary statistics include only
routes taken by at least 5 ships and only routes between ports that appear both as arrival anddeparture ports.

C

Fastest Route Calculation

Using the schedule of actual departure times and arrival times of all container ships in ourdataset, we compute the fastest path from port i to port j at time h, where h measures
hours since Jan 01 2016 00:00. The algorithm works as follows. Every time a ship leaves i toanywhere, we compute all possible paths to j through the network of connections available
at that point in time. To limit the computational burden, we consider only paths involving
up to 15 intermediate ports. From the set of possible paths, we drop all those that are
dominated by others, i.e. paths that start at the same time or later, but arrive earlier.
We also drop paths that are identical to others in terms of travel time and arrival time,
but involve more stops in intermediate ports. The result of the algorithm is a set of paths
between i and j that are optimal in terms of travel time at some starting time h in 2016.
The algorithm is programmed in Stata. We ran the algorithm in parallel on 514 cores(one for each departure port) endowed with an Intel Xeon-Gold 6138 2.0 GHz processoron the Saga supercomputer (https://www.sigma2.no/node/537). The average (maximum)
required CPU time per core denoted as hh : mm : ss is 01:55:55 (05:50:37), the total CPU
time is 993 hours. The maximum RAM required per core is 78920K. The result is 13,915,115
unique paths described by departure port i, arrival port j, departure time h, arrival time ha
and up to 15 intermediate ports.

33

D

Empirical Evidence on Shipping Costs and Actual
Shipping Routes

D.1

Freight costs and Fastest Routes

Our empirical analysis relies on the assumption that cargoes from a country i to a country
j are shipped on the fastest route between the two countries. To justify this assumption
we use trade data for the US by customs district and country of origin that allows us toback out freight costs and examine the correlation between freight costs and travel time on
direct routes observed in the AIS data. The results are reported in Table 10. The dependent
variable is freight costs computed as cif/fob margin relative to import value. The unit ofobservation is the freight cost of containerized imports by US customs district, country oforigin, and product (10-digit HTS code). U.S. customs districts are matched to U.S. container
ports based on names.Independent variables are travel time (lnHoursij ), geodetic distance(lnDistij ), total dwt of ships traveling to US port j from country i in 2016 (lnDW T ), total
number of ships traveling to US port i from country j in 2016 (lnShipsij ) and average ship
size based on the latter two variables (lnAvgDW Tij ). The analysis shows that there is apositive correlation between travel time and freight costs. This positive correlation remains
also when we control for other potential determinants of freight costs such as distance andcharacteristics of the cargo flow. We note that there is also a negative correlation between
freight costs and average ship size, indicating economies of scale in transport at the shiplevel.

34

Table 10: Correlations with Freight costslnHoursij(1).004***(.000)(2).005*(.001)

lnDistij(3).005***(.001)-.001(.001)

lnDW T(4).005***(.001)-.001(.001)-.000(.000)

lnShipsij
lnAvgDW Tij
FEs
Observations
Exporter/US ports

Products
adj. R2

j,p167,227
61/20
13,0860.152

j,p167,227
61/20
13,0860.152

j,p167,227
61/20
13,0860.152

j,p167,227
61/20
13,0860.152(5).004***(.001).002(.001)(6).004***(.001)-.001(.001)-.000(.001)-.005***(.000)
j,p
167,227
61/20
13,0860.152.000(.001)-.005***(.000)
j,p
187,011
61/20
13,2960.156

Note: Dependent variable is freight costs computed as cif/fob margin as share of the import value. Unit of observationis the freight cost of containerized imports by US port, country of origin, and product (10-digit HTS code). The
sample is based on US trade in 2016 and include only transactions where the US port of entry is also the port ofunlading. Columns (1)-(5) include only those port-country pairs where a US port is connected to only one port
in the partner country. Column (6) includes all port-country pairs and the values of all independent variables arecomputed as averages across multiple ports in the exporting country. All regressions include fixed effects for US
ports and products. Standard errors are clustered at the product level. Significance levels: *p < 0.1, **p < 0.05,***p < 0.01.

D.2

Evidence on Actual Routes of Chinese Trade

We have access to Chinese customs data for 2006, where we observe both transportation
method and one transit country. We can therefore check whether the transit ports according
to our fastest route algorithm overlap with the transit country in the Chinese data. We
perform the following analysis. First, we aggregate the Chinese data to the origin-transit
country-destination level (imports or exports), and only keep observations where transportation method is by sea. Second, for each origin-transit-destination triplet in the Chinese data,
we check whether we find a similar triplet according to the fastest route algorithm. We findthat 87% of the fastest-time routes we identified for Chinese imports and exports include
transit countries that are matched with origin-transit-destination triplets in the Chinese
data. At the same time 30% of the origin-transit-destination triplets in the Chinese data arematched with triplets in our constructed fastest-time data set. However, the trade values ofthe matched triplets are on average 10 times higher than the unmatched ones, in total making up about 81% of the Chinese marine trade in 2016. Our finding suggest that fastest-timeroutes correctly capture the main routes Chinese trade takes.

35

E

The Container Shipping Market

We have compiled data on the size distribution of all container ships over time. Specifically,using data from Clarksons, we can look the ship size distribution by year of construction.
Figure 10 plots the number of ships by different size bins and by construction year. Interestingly, the number of Neopanamax ships (i.e., ships that cannot pass through the old canal,
but can pass through the new canal), has been relatively stable between the announcement
year and completion year (marked by dashed lines in the figure). Except for ultra large
container ships, which cannot pass the Canal even after expansion, all three categories experienced a decline in newly build ships after the financial crisis (solid-line). The numbers
support our view that large ships (Post/Neopanamax ships) were already widely adopted
globally before the expansion project started, while the Panama Canal was a bottleneck ofglobal container shipping. The numbers strongly indicate that the canal expansion was not
sufficient to incentivize owners to invest in new ships. In addition to this, the container
shipping industry has been characterized by over-investment and idle ship capacity for many
years (see Figure 11), in the wake of the 2007 financial crisis and trade collapse, see e.g.
Zhang et al. (2014). Data from the consulting industry shows that around 5% of container
ships were idle over the period 2009 to 2016, see Figure 11.25 . Moreover, container freightrates have also been relatively low over the 2006-2016 time period, consistent with the findingthat there was ample capacity in the market, see e.g. Rau and Spinler (2016).
Figure 10: Ship Building

http://www.globaltrademonitor.com/2020/09/21/flexport-idle-container-ship-capacity-is-returning-tonormal-levels-after-increases-in-q2/
25

36

Figure 11: Idle Containership Capacity 2009-2020

F

Panama Canal Exposure

F.1

Summary Statistics
Table 11: Summary statistics on Panama Canal exposure

Rank

Importer

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

USA
MEX
CAN
CHN
JPN
KOR
DEU
GBR
CHL
COL
BRA
BLX
NLD
AUS
FRA

Share of total
imports passing PC
50.8
10.2
9.6
4.2
2.8
1.7
1.6
1.6
1.2
1.2
1.1
1.1
1.0
0.9
0.9

Share in world
imports
14.0
2.5
2.7
7.7
3.7
2.6
6.5
4.2
0.4
0.3
0.9
2.6
3.0
1.2
3.8

37

Exporter
USA
CHN
MEX
CAN
JPN
DEU
KOR
GBR
FRA
ITA
CHL
BRA
IRL
PER
COL

Share of totalexports passing PC
30.5
16.0
12.1
10.1
5.8
3.4
3.4
1.3
1.3
1.2
1.1
1.1
0.9
0.8
0.8

Share in world
exports
9.0
14.9
2.6
2.5
4.3
8.5
3.4
2.6
3.3
3.1
0.4
1.3
1.1
0.2
0.2

F.2

Sailing without the Panama Canal
Figure 12: Travel Time without use of the Panama Canal

Note: The figure shows the distribution of port-to-port travel timedifferences with vs. without the Panama Canal for the pairs thatare using the Panama canal according to our algorithm.

G

Additional Data Sources

G.1

COMTRADE Trade FlowsThe monthly COMTRADE data was downloaded via the API call "https://comtrade.un.org/
api/get/plus?max=250000&type=C&freq=M&px=HS&ps=inserttimeperiod&r=insertreportercode&p=all
between Jan 8-10, 2021. We aggregate monthly observations to quarters and keep only quarters were trade flows were reported in every month. We use the total value of imports bydestination and country of consignment (i.e., the country from which goods were dispatchedto the final destination; see UN (2013, p 185)).

38

G.2

Estimation Data: Summary Statistics
Table 12: Summary Statistics of the Estimation Sample

Variableln Value (in $, by quarter)
FTA
ln DistanceContiguity
Common Language
Pan Exposure

N

Mean

Std. Dev

Min

Max

Source199,177
199,177
199,177
199,177
199,177
199,177

16.2
.30
8.66
.02
.14
.14

3.27
.46
.82
.15
.35
.35

1.39
0
4.55
0
0
0

25.74
1
9.89
1
1
1

monthly COMTRADEWTO RTA database
CEPII
CEPII
CEPII
AIS data

Note: Export data in rows 1 is aggregated from monthly to quarterly frequency and covers
the period 2013Q1- 2019Q4.

G.3

Data for the Model-based Quantification

We distribute total expenditure by country across ports according to the relative size of ports
measured by the total incoming tonnes in the first half of 2016, according to the AIS data.
Expenditure by country is taken from the Eora Global Supply Chain Database (MRIO)(https://worldmrio.com/). For 19 out of the 149 countries (small islands and overseas territories) expenditure data is not available. We construct the missing expenditure level using
GDP data for these countries obtained from the Worldbank’s World Development Indicatorsand from INSEE together with the average expenditure/GDP ratio of small islands for which
we do observe both expenditure and GDP.

H

The Theoretical Model

H.1

Solving the model in changes

This section shows how to solve the general equilibrium of the model in changes, using the“exact hat” notation developed in Dekle et al. (2007).
The first equilibrium condition is
Yi =

X

Xij

j

Yi X −θ Ej
τij −θ
Π−θ
Pj
i
j
X
Ej
Π−θ
τij−θ −θ ,
i =
Pj
j
Yi =

where we substituted in for the gravity equation and solved for Πi . In matrix notation, thiscan be rewritten as:
39

h

Π−θ
i

i

= [1 − A]
"

−1

"

Ei
Pi−θ

#

#

Ei
[1 − A]
=
P −θ
" i #
h
i
h
i
Ei
−θ
Π−θ
−
A
Π
=
i
i
Pi−θ
X
Ei
−θ
Π−θ
t−θ
i −
ij Πi =
Pi−θ
j
X
Ei
−θ
Π−θ
=
+
t−θ
i
ij Πi .
Pi−θ
j
h

Π−θ
i

i

In a similar fashion, the second equilibrium condition can be rewritten as:
Ei =

X

Xji

j

Ei X −θ YjτPi−θ j ji Π−θjX
YjPi−θ =
τji−θ −θ
Πj
j
Ei =

h

0 −1

i

Pi−θ = [1 − A ]
"

"

Yi
Π−θ
i

#

#

Yi
[1 − A ]
=
Π−θ
i
X
Y
i
−θ
t−θ
= −θ
Pi−θ −
ji Pj
Πi
j
X
Yi
−θ
Pi−θ = −θ +t−θji Pj .
Πi
j
0

h

Pi−θ

i

Expressed in changes, the two equilibrium conditions become

Π̂−θ
i =
P̂i−θ =

X
Ei
Ξij
Êi
+
P
P
−θ
Ei + j Ξij P̂iEi + j Ξij
j

Yi +

Yi

Ŷi

P

−θ
j Ξji Π̂i

!
−θ
t̂−θ
ij Π̂j

!

+

X
j

Ξji
t̂−θ P̂ −θ .
P
Yi + j Ξji ji j−(θ+1)/θ

Since trade is balanced, Ei = Yi . Furthermore, by using the fact that Π̂i = Ŷi

40

, we

can write the system as
Π̂−θ
i =

−θ/(θ+1)

Π̂i

Yi

+

X

P̂i−θ
j
−θ/(θ+1)XΠ̂i
Yi+P̂i−θ =P−θ
Yi + j Ξji Π̂i
j

H.2

Yi +

P

j Ξij

Ξij
P
Yi + j Ξij

!
−θ
t̂−θ
ij Π̂j(21)Ξjit̂−θ P̂ −θ .
P
Yi + j Ξji ji j

(22)

!

Algorithm for solving the equilibrium in changes

The system of equations (21)-(22) can be solved with a simple fixed point procedure. We−θ−θstart with a guess of Π̂−θi and P̂i . We then update equation (21) to get a new value of Π̂i .
−θ
We then update equation (22) to get a new value of P̂i . We iterate on the two fixed points
until the system converges.
P
World output is the numeraire, i Yi = Y W = 1. Specifically, when iterating on the fixed
points above, for each iteration, we rescale Π̂i and P̂i so that Ŷ W = 1 holds. We haveŶ W =Xi

X Yi −θ/(θ+1)
Yi
Ŷi =
Π̂
.
W
W i
Y
i Y

After each iteration of equation (21), we calculate Ŷ W and then rescale Π̂−θby dividing byiŶ W .

H.3

Converting ΞVkl to ΞklThis section describes how to calibrate the value α in the expression Ξkl = αΞVkl . The
methodology is as follows: First, start with a guess of the value of α, α0 , and obtain valuesof Ξkl . According to the model, there is a mapping between traffic Ξkl and trade Xij according
to equation (11). After converting traffic to trade, we calculate the value of world container
P
trade flows, i.e. X̃ W = ij,i6=j Xij , according to the model. If X̃ W is different than the true
value of world container trade, X W , i.e. X̃ W − X W 6= 0, we update the guess of α, andcontinue to do so until X̃ W − X W = 0. The value of α that delivers X̃ W − X W = 0 is USD
1734 per deadweight tonnage of traffic.
The world value of container trade, X W , is calculated as follows. According to Rajkovic
et al (2014), the global value of container trade was 5.6 trillion USD in 2010. According to
the WTO, world merchandise trade increased by 4.6 percent from 2010 to 2016. Under theassumption that the share of container trade in total merchandise trade is constant, worldcontainer trade in 2016 is 5.9 trillion USD (5.6 trillion USD×1.046)

I

Alternative Exposure Measures

This section shows the sensitivity of the baseline results in Section 3.3 when using a different
measure of Panama Canal exposure.

41

Table 13: Regressions with Panama exposure derived from the model
Exposure measure:P ostt × P anExposureij
Observations
Exporters/Importers
adj. R2

Travel timePA
> .3
continuous πij(1)(2).151**.086**(.065)(.042)
192,810
192,810138/102
138/102.936.936

Travel time & Ship sizePA
> .3
continuous πij(3)(4).130**.094**(.066)(.045)
192,810
192,810138/102
138/102.936.936

Note: Dependent variable is the log of imports from country i to countryj in quartert over the period 2013Q1 − 2019Q4. The control variables are: an FTA indicatorand geographical variables (distance, contiguity and common language) interactedwith P ostt , and the share of deadweight tonnes traveling on Neopanamax ships on
the route connecting i and j interacted with P ostt . Standard errors are clusteredby i and j. Significance levels: ∗p < 0.1, ∗ ∗ p < 0.05, ∗ ∗ ∗p < 0.01.

We parameterize transport costs tkl as
tkl =T ravelT imekl
ShipSizekl

!δ

,

(23)

where T ravelT imekl and ShipSizekl refer to average travel time and ship size across all
trips on a link kl. Using the values of δ and θ from Section 5, we calculate trade costs τij
by invoking equation (7). We can then calculate the likelihood of using a link kl for trade
between i and j. The likelihood is (see AA2020):
πijkl =

τij
τik tkl τlj!θ.

Define P as the set of links that use the Panama canal, according to the container traffic
data. The model-derived likelihood of using the canal is calculated as
πijP A = max πijkl .
kl∈PTable 13 repeats the regression analysis from Section 3.3 when replacing the baseline exposure
measure with πijP A .26 Column (3) uses the πijP A as the measure of exposure, while column (4)mimics the baseline regression by instead creating an indicator variable equal to one when
πijP A > .3. Columns (1) and (2) repeat the analysis, but instead of using tkl from equation(23), we use the simpler version tkl = T ravelT imeδ .

J

Solving the no-network model in changes

This section shows how to solve the general equilibrium of the no-network model in changes,
using the “exact hat” notation developed in Dekle et al. (2007).
26

PA
Similar to the baseline analysis, we aggregate πij
from port- to country-pair using port size as weights.

42

The first equilibrium condition is

Yi =

X

Xij

j

Yi X −θ Ej
τij −θ
Π−θ
Pj
i
j
X
Ej
Π−θ
τij−θ −θ ,
i =
Pj
j
Yi =

where we substituted in for the gravity equation and solved for Πi .
The second equilibrium condition can be rewritten as:
Ei =

X

Xji

j

Ei X −θ YjτPi−θ j ji Π−θjX
YjPi−θ =
τji−θ −θ .
Πj
j
Ei =

Expressed in changes, the two equilibrium conditions become
Π̂−θ
i =

X

τ̂ −θ
ij

Êj XijP̂j−θ Yiτ̂ji−θ

Ŷj Xji
.
Ei
Π̂−θ
j

j

P̂i−θ =

Xj43