Journal of International Economics 114 (2018) 331–345

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Journal of International Economics

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Shipping inside the box: Containerization and trade☆

A. Kerem Coşar a,⁎, Banu Demir b,⁎a University of Virginia, Department of Economics, United Statesb Bilkent University, Department of Economics, United States

☆ For their comments and constructive suggestions, wHarrigan, Eduardo Morales, Andrés Rodriguez-Claparticipants. Demir thanks CESifo/Ifo Institute for theirprovided valuable research assistance in the early stagGönül Şengül for suggesting the current title of the paper⁎ Corresponding author.

E-mail addresses: kerem.cosar@virginia.edu (A.K. Coşa(B. Demir).

1 Breakbulk is defined as shipping goods in bags, balesships' hold, instead of in standardized containers. This shcargo such as grains, coal and ores.

https://doi.org/10.1016/j.jinteco.2018.07.0080022-1996/© 2018 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 3 January 2017Received in revised form 27 July 2018Accepted 30 July 2018Available online 4 August 2018

Research Data Related to this Submission:https://data.mendeley.com/datasets/chskxfbc7y/1

We quantify the effect of container technology on transport costs and trade by estimating the modal choice be-tween containerization and breakbulk shipping using micro-level trade data. The model is motivated by novelfacts that relate container usage to shipment, destination and firm characteristics. We find container transportto have a higher first-mile cost and a lower distance elasticity, making it cost effective in longer distances. Atthe median distance across all country pairs, the container decreases variable shipping costs between 16 and22%. Containerization explains a significant amount of the global trade increase since its inception: a quantitativeexercise suggests that, in the absence of containers, Turkish and U.S. maritime exports in a typical sector to theaverage destination market would have been about two-thirds, and aggregate maritime exports 14 to 21%lower than what they are today, respectively.

© 2018 Elsevier B.V. All rights reserved.

1. Introduction

The introduction of containers in the second half of 1950s marked amajor innovation in transportation: the standard container (referred towithin the industry as “the box”) improved efficiency by allowing auto-mation in cargo handling, connecting sea transport with intermodal in-land transport, and reducing spoilage/pilferage on and off the ship. Allthese benefits generated economies of scale and slashed transit times(Levinson, 2008; Hummels, 2007). Despite its ubiquity, themechanismsthrough which containerization affected world trade are still unex-plored. Understanding the drivers of container usage at the decision-making level is key to themeasurement of transportation costs affectingthe volume and pattern of international trade.We provide the first suchanalysis using micro-level data on Turkish exports at the firm, productand destination level for the year 2013.

We start by documenting novel facts from Turkish micro data andU.S. aggregate data: despite the perception that international maritimetrade is now highly containerized, there is still an important margin ofmodal choice for exporters between container and breakbulk.1 As of

e thank Zouheir El-Sahli, Jamesre, and numerous seminarhospitality. Sümeyra Korkmazes of this work. We also thank.

r), banup@bilkent.edu.tr

, packed in cartons or pallets inould not be confused with bulk

2013, of the total maritime Turkish and U.S. exports of general cargo(excluding oil, fertilizers, ore, and grain) by weight, only 41 and 46%were containerized, respectively. By export value, these figures were54 and 58%.2 To the best of our knowledge, comparable data on con-tainer share in world maritime trade by value is not available. Availablestatistics onworldwide usage are usually by weight or by volume. For in-stance, Rua (2014) documents that the global share of containers ingeneral cargo (i.e.,excluding oil, fertilizers, ore, and grain) by volumereaches 70% by mid-2000s; see Fig. 1 in her paper.

The data shows large variation in container usage across firms, prod-ucts and destinations. We find four patterns in this variation: first, it isby and large explained by firms, rather than by products and destina-tions. Second, container usage increases with distance to the destina-tion. Third, container usage also increases with shipment size butdecreases with unit prices. Finally, container usage increases with firmsize and labor productivity. These findings imply that, conditional onphysical feasibility due to product characteristics and the necessary in-frastructure being available in both the origin and the destination,exporting firms still face a choice on the mode of maritime transporta-tion and only some of them find it profitable to ship in containers.

2 By dropping bulk commodities, the definition of general cargo eliminates some butnot all the products for which container shipping is not feasible due to their physical prop-erties. Such goods are typically transported by specialized vessels, such as roll-on/roll-off(ro-ro) ships for cars and trucks. To account for this, we also check the container sharesby restricting the sample to containerizable goods according to two available classifica-tions. Using the 1968 German Engineers' Society classification from Bernhofen, El-Sahli,and Kneller (2016), 54 and 53% of Turkish andU.S. 2013maritime exports (by value)werecontainerized. Using a more recent and restrictive OECD definition by Korinek (2011), therespective figures become 75 and 67%.

3 The entire dataset spans 10 years from 2003 to 2013. We work with the latest avail-able yearwhen the container usage in Turkey peaks and the effects of the Great Recessionsubsides.

332 A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

Informed by these facts, we propose and estimate amodel of self-se-lection into containerized shipping by heterogenous firms. In the firststage, we estimate the variable cost of container shipping relative tobreakbulkwithoutmaking any assumption onfirms' productivity distri-bution, using observed firm-product-destination level export revenuesby mode. In the second stage, we use these estimates along with addi-tional structure on firm productivities and parameter values from theliterature to recover relative fixed trade costs by mode.

Our contribution is threefold. First, to the best of our knowledge, thisis the first paper to usemicro-level data at the firm-product-destinationlevel to estimate the structural parameters of shipping technologies in amodelwith heterogeneous firmsmakingmodal and product quality de-cisions. The firm margin in shipping has so far not been considered inthe empirical international trade literature. The detailed micro-leveldata enables us to estimate the parameters of interest in a very preciseway using demanding specifications and controlling for various factorsthat affect maritime transport modal choice such as product character-istics, destination country characteristics, and more importantly, self-selection of firms into destination countries.

Second, the structural estimation onmicro-level data allows us to doquantitative counterfactual analysis to evaluate the impact of reducedtrade costs on trade: In the absence of containers, Turkish and U.S. mar-itime exports in a typical sector to the average destination would havebeen about two-thirds, and aggregate maritime exports 14 to 21%lower than their level in 2013, respectively. In the case of full adoptionof container technology, Turkish and U.S. maritime exports to the aver-age destinationwould increase by 13 and 19% in a typical sector, respec-tively. We also show that these quantitative results are invariant towhether transport costs are additive ormultiplicative as long as the for-mer specification takes into account the endogenous quality choice forexports.

Third, we provide supporting evidence for the conjecture that con-tainer shipping is subject to a higher scale but has a lower distance elas-ticity, facilitating increased trade with more distant destinations. At themedian distance across all country pairs (10,400 km), the container de-creases variable shipping costs between 16 and 22%. We corroboratethis evidence using direct measures on insurance and freight chargeson U.S. imports.

Our paper relates to an empirical literature that investigates the ef-fect of technological advancements in transportation on trade. Usingdata from19th century India, Donaldson (2018) estimates that railroadsreduced the cost of trading, narrowed inter-regional price gaps, and in-creased trade volumes. Pascali (2018) estimates the impact of steam-ships on the first wave of trade globalization. Focusing on airplanes,Harrigan (2010) investigates how geography and the choice of shippingmode interact in shaping comparative advantages and trade patterns.Hummels and Schaur (2013) use variation in transport modes acrossUS imports at the origin-product level to identify the ad-valorem equiv-alent time costs of shipping. Micco and Serebrisky (2006) estimate thatthe liberalization of air cargo markets reduces air transport costs byabout 9% by enabling the efficiency gains. Clark, Dollar, and Micco(2004) estimate the cost-reducing effects of port efficiency and contain-erization in US maritime imports. Brancaccio, Kalouptsidi, andPapageorgiou (2017) analyze the effect of matching frictions on tradecosts and volumes in bulk shipping.

As to the impact of containerization, Hummels (2007) estimates thatdoubling the share of containerized trade decreases shipping costs be-tween 3 and 13%.Moreover, he finds no evidence of decline inmaritimeliner shipping price index over the past five decades (see his Fig. 4),conjecturing that unmeasured quality changes in transportation—faster,more precise delivery services—could explain this finding. In a study ofport efficiency, Blonigen andWilson (2008) find that a ten percentage-point increase in the share of containerized trade between US and for-eign ports reduces import charges by around 0.6%. These seeminglylow estimates pose a puzzle in the face of container shipping beingpraised as a technological revolution. In contrast, Bernhofen, El-Sahli,

and Kneller (2016) find a large effect. Using a panel data of industry-level bilateral trade for 157 countries, they identify the effect of contain-erization through countries' differential dates of adoption of containerfacilities. Their results suggest that containerization contributed moreto the increase of world trade during the 1962–1990 period than tradepolicy changes such as GATT tariff cuts and regional trade agreements.

Finally, our model shares with Rua (2014) the widely-used elementof depicting a technology—in this case containerization—which lowersvariable costs in return for a high fixed cost in a Melitz (2003) type het-erogeneous firm model of trade (e.g.,Bustos 2011). As a result, onlymore productive firms prefer containerized shipping to break-bulk.Rua (2014) embeds this firm-level problem into a model of country-level technology adoption in order to derive testable implications onthe international diffusion of container technology. Using country-level data, she finds that fixed costs and network effects are the maindeterminants of the adoption of containerization. In contrast, we focuson the firms' choice of shipping mode and estimate the cost structureof shipping in order to quantify the role of containerization in trade vol-umes. The structural estimation in turn allows us to do quantitativecounterfactual analysis.

The next section introduces the data and documents the facts moti-vating our model and estimation.

2. Data and four empirical facts

2.1. Basic features of the data

The confidential micro-level data accessed from the premises of theTurkish Statistical Institute is based on customs forms and contains allTurkish export transactions that took place in 2013.3 Each transactionrecords the identity of the exporting firm, 8-digit Harmonized System(HS) product code, value, weight (in kilograms) and quantity (in spec-ified units, e.g. pair, number, liter, etc.) of the shipment, destinationcountry, and the mode of transportation (truck, rail, vessel, air, pipe-line). A separate binary variable informs us whether goods wereshipped in a container or not. For reasons related to disclosure restric-tions, our data excludes HS heading 27—mineral fuels, oils, waxes, andbituminous substances—and HS heading 93—arms and ammunition,parts and accessories. In the baseline analysis, we keep all other prod-ucts and capture their containerizability by fixed effects. Followingcommon practice, we also drop small transactions (firm-product-destination exports with an annual value of less than USD 5,000) fromthe dataset as they are likely to introduce noise into our estimates.

Unsurprisingly, containerization is associated with maritime ship-ments: 97.8% of all containerized exports by value are by sea. Only0.3% and 1.2% of air and land exports are containerized, respectively.Therefore, we restrict the sample to vessel exports to coastal countries.Excluded landlocked destinations constitute a small share of exports(8%), and an even smaller share of containerized exports (1.9%).

Table 1 presents further relevant summary statistics from our data.Our dataset covers 27,241 exporters, 5,557 8-digitHS products, and139 destination countries. The top panel of the table shows the fractionof observationswith no containerization or full containerization. The re-spective fractions are small at the destination or product level: share ofcontainerized exports lies strictly between zero and one to almost alldestinations in about 75% of 8-digitHS product codes. Nevertheless,the extensive margin contributes significantly to the variation in con-tainer use at the firm-level: about one-third of Turkish exportersnever shipped in containers, and another one-third shipped only in con-tainers in the year 2013. The share of containerized exports is eitherzero or one for about 90% of observations (firm-product-destinationlevel). The lower panel of Table 1 presents the relevant summary

Table 1Summary statistics for Turkish export data.

Panel A: All products

Level of observation

Firm Product Destination Firm-product-destination

Fraction of zeros (no containerization) 0.335 0.107 0.000 0.360Fraction of ones (full containerization) 0.337 0.143 0.029 0.533Share of containerized exports 0.524 0.556 0.598 0.527Share of containerized exports (excl. Zeros & ones) 0.571 0.551 0.586 0.568

Number of

Firms Products Destinations ObservationsVessel exports 27,241 5557 139 220,993Non-containerized 18,070 4762 135 103,259Containerized 18,112 4961 139 141,454

Mean Median

Value (USD) Quantity (Kg) Value (USD) Quantity (Kg)

Non-containerized 378,407.7 378,274.7 28,673 4201(5,046,657) (5,945,869)

Containerized 241,333.4 183,440.4 29,253 6789(1,943,938) (2,997,263)Panel B: Containerizable products only

Level of observation

Firm Product Destination Firm-product-destination

Fraction of zeros (no containerization) 0.337 0.100 0.000 0.361Fraction of ones (full containerization) 0.338 0.134 0.050 0.533Share of containerized exports 0.524 0.558 0.737 0.594Share of containerized exports (excl. zeros & ones) 0.573 0.553 0.723 0.572

Number of

Firms Products Destinations ObservationsContainerizable vessel exports 25,846 4865 139 206,659Non-containerized 17,112 4212 132 96,602Containerized 17,136 4377 139 132,067

Mean Median

Value (USD) Quantity (Kg) Value (USD) Quantity (Kg)

Non-containerized 194,114.1 71,934.9 26,893 3595(1,232,342) (808,124.3)

Containerized 217,471.8 92,438.7 27,881 5849(1,635,886) (785,887.8)

Notes:This table presents the summary statistics for the annualized data. Panel A is based on all products, regardless of their containerizability. Panel B restricts the sample tocontainerizable products based on the classification suggested by Korinek (2011). The following products are excluded from the sample: dry and industrial bulk, tankers, and bulk shippedgoods, goods shipped in tankers, motor vehicles, trailers and non-mechanically propelled vehicle n.e.s., aircraft, spacecraft, satellites, ships, boats and other floating structures. Standarderrors are in parentheses.

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statistics from a smaller sample that includes intrinsicallycontainerizable products only. We now proceed to a more nuancedanalysis that controls for compositional effects in order to tease out sa-lient patterns on container usage from our data.

4 To account for potential seasonal effects in container ship schedules, we pair destina-tions with months but suppress the time subscript, i.e.,d refers to a destination-monthpair.

2.2. Four facts about container usage

We now present four facts about the use of containerization. In eachcase, we first summarize the stylized evidence and then explain the un-derlying analysis. These facts subsequently guide our modeling choicesin estimating the parameters of shipping technologies.

To check for similar patterns, we use publicly available aggregateU.S. maritime trade data at the level of 10-digit HS products, trade part-ner, port, and container use (Schott, 2008). While it does not inform usabout firms, the import side of the U.S. data reports freight and insur-ance charges, which we subsequently use in the empirical analysis.

Fact 1: A large share of the variation in containerization is explainedby firms, rather than by products and destinations.

As reported above, around half of all annual vessel exports are con-tainerized, with varying fractions of full or no containerization acrossproducts, destinations and firms. We now explore the components ofthe overall variation in container usage. A priori, one may expect

product characteristics to be the primary determinant of whether ashipment will be containerized or not. After all, bulk commoditiessuch as ores or grains are hardly fit for the standard container, whereasanecdotes of global trade convey the image that some goods, such as ap-parel and consumer electronics, are stackable and thus highly contain-erized. Similarly, one may expect that the characteristics of thedestination country, such as the existence of the appropriate infrastruc-ture or level of development, to be key determinants since the technol-ogy is presumably expensive and dependent on specialized ports andintermodal logistics.

For visual inspection, we plot the intensive-margin distribution ofcontainer share—i.e.,excluding extensive margin mass points at zeroand one—in vessel exports aggregated over months in Fig. 1. Evidently,there is large variation across shipments (Panel A), with high heteroge-neity across all dimensions (Panels B–D). For statistical analysis, we runa series of fixed-effect regressions and analyze their fit in Table 2. Wedenote firms by a, products by j, and destination countries by d.4 The di-rect effects in the first column are the adjusted Rk

2’s from regressingcontainer shares, including the mass points at zero and one, on single

Fig.1.Distribution of Container Shares for Turkish Exports. Notes: Histogram of container shares, excludingmass points at 0 (no containerization at all) and 1 (full containerization). PanelA: 23,720 observations, Panel B: 4,166 8-digit HS products, Panel C: 135 destinations, Panel D: 8,941 firms.

Table 2Explaining the Variation in Containerization (Fact 1).

Direct effect Coefficient of partial determination

Panel A: Turkish exportsFirm (a) 0.557 0.509Product (j) 0.180 0.066Destination (d) 0.240 0.205Firm-product (aj) 0.620 0.603Firm-destination (ad) 0.909 0.896Product-destination (jd) 0.442 0.381Panel B: U.S. exportsPort (p) 0.020 0.015Product (j) 0.054 0.049Destination (d) 0.019 0.014Port-product (pj) 0.133 0.128Port-destination (pd) 0.076 0.071Product-destination (jd) 0.150 0.146

Notes: First column reports adjustedR2’s from regressing container sharesContShrajd on in-dividual (top panel) or paired (bottom panel) fixed effects. As an example, for firms, thiswould be the Ra2 from the regression ContShrajd= μa where μa represents firmfixed effects.Second column reports the coefficient of partial determination capturing the proportion ofvariation that cannot be explained in a reduced model without the particular elementamong the fixed effects. As an example for firms (k= a), take the Ra, jd2 from the regressionContShrajd = μa + μjd + ϵajd, where μjd represents product-destination pair fixed effects.Dropping the fixed effect for the dimension of interest a, the regression ContShrajd = μjd+ ϵajd yields Rjd2 . The coefficient of partial determination for firms is then (Ra, jd2 − Rjd

2 )/(1− Rjd

2 ), that is the fraction of the unexplained variation captured when firm fixed effectsare included. Destination refers to a destination-month pair.

334 A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

fixed effects k ∈{a, j, d} in the top panel and on pair fixed effects k ∈{aj,ad, jd} in the bottom panel. In order to purge out compositional effects,we report in the second column the coefficients of partial determinationisolating the unique contribution of each component.5

We first conduct the analysis using the Turkish micro export data,and report the results in panel A of Table 2. In terms of individual effects,product categories and destinations have relatively little explanatorypower. Firm-specific factors, both in terms of direct and isolated effects,account for a substantial fraction of the variation.6 Looking at joint ef-fects, the partial coefficient of firm-destination pairs equals 0.9, suggest-ing that containerization in international trade is predominantlydetermined by firms' modal choices that vary across countries.

Using the aggregateU.S. export data,which does not contain informa-tion about exporting firms, pairwise combinations of individual effects

5 That is, for each k, we first regress container shares on fixed effects (μk, μ−k) and findthe fit. For instance, for firms (k= a), that would be the Ra, jd2 of the regression ContShrajd= μa + μjd + ϵajd, where μjd represents product-destination pair fixed effects. We thendrop the factor of interest k = a to find Rjd

2 from the regression ContShrajd = μjd + ϵajd.The coefficient of partial determination is the ratio of the difference Ra, jd

2 − Rjd2 over the

variation unexplained 1− Rjd2 without contribution of the factor of interest a. This method

is robust to sequence sensitivity when comparing the fit across specifications that addfixed effects in a progressive manner (Gelbach, 2016).

6 These factors do not include firm location and access to ports as all international portsin Turkey also have container terminals. In other words, firm location does not matter forthe relative access to container shipping.

Table 4Economies of Scale and Unit Values in Containerization (Fact 3).

All Differentiated Non-differentiated

(1) (2) (3)

CONTajdm CONTajdm CONTajdm

lnweightajdm 0.0099⁎⁎⁎

(0.0008)0.0116⁎⁎⁎

(0.0009)0.0057⁎⁎⁎

(0.0016)lnUnitValueajdm −0.0070⁎⁎⁎

(0.0017)−0.0077⁎⁎⁎

(0.0018)−0.0030 (0.0040)

Observations 711,742 532,277 179,465R2 0.690 0.697 0.682Firm-product-month FE + + +Destination-month FE + + +

Notes: The dependent variable CONTajdm is a binary variable that takes the value one ifthere is a positive containerized flow at the firm-product-destination level in a givenmonth. Column headings refer to the sample used to produce them. Product differentia-tion is based on the classification developed by Rauch (1999). lnweightajdm denotes thelogarithm of the weight (kg) of the export flows. lnUnitValueajdm denotes the logarithmof the unit value, defined as value per quantity. Robust standard errors clustered at theproduct-destination-level in parentheses. Significance: * 10%, ** 5%, *** 1%.

335A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

explain no more than 15% of the variation in container usage (panel B).Inthe Turkish data, pairwise combinations involving firms explain asmuch as 91% of the variation. The large portion of the variation left unex-plained in the U.S. data is consistent with the importance of firms.

Fact 2: Container usage is increasing in distance.Given the substantial contribution of the destination margin to the

firm-destination variation in container usage presented in panel A ofTable 2, we aggregate Turkish and U.S. export data to a common sampleof destination countries. Regressing container shares in maritime tradeto the logarithm of the sea distance to the trade partner, we find thatcontainerization increases with distance (Table 3). The positive and sig-nificant distance gradients are of remarkably comparable magnitudesfor the two exporter countries and remain robust to controlling forother destination characteristics such as income per capita, adjacencyand being in a free-trade agreement with Turkey or the U.S.

Fact 3: Container usage is increasing in shipment size and decreasingin unit value of the shipment.

Container shipping displays economies of scale due to high infra-structure costs and the large vessel sizes required to utilize these invest-ments (see Stopford, 2009, chapter 13). Also called the “first-mile cost”in logistics, thedecline in unit costswith scale and distance is a key char-acteristic of how transportation and shipping technologies affect trade.This cost structure is plausibly passed on from shipping companies totrading firms—as corroborated by minimum shipment requirementsand differential pricing practices for full-container load and less-than-container load shipments. We can thus expect container usage and itsgeographic determinants to correlate with parcel size.

Table 4 confirms this conjecture: container usage is increasing intransaction size. It also shows that container usage is correlated withunit value of shipments, defined as shipment value per quantity mea-sured in physical units.7 In particular, controlling for shipment weight,lower unit values within a firm-product pair are associated with highercontainer usage. Second and third columns split the sample to differen-tiated and non-differentiated goods according to the Rauch (1999) clas-sification. Results show that the negative association of container usagewith unit values holds for differentiated goods only, suggesting a rela-tionship between firms' quality and transport mode choices. In particu-lar, if transport costs are additive and unit shipping costs are higher inbreakbulk, for a given firm-product pair, Alchian-Allen effect implies anegative relationship between container usage and quality. To accountfor this mechanism, we will incorporate endogenous quality differenti-ation to the model presented in the next section.

Fact 4: Container usage is increasing in total sales, employment andproductivity of the exporter, with no economies of scope.

Per Fact 1, the most significant factor in explaining modal choice isthe identity of exporting firms. Theoretically, heterogeneity in

Table 3Distance and Containerization (Fact 2).

(1) (2) (3) (4)

ContShared ContShared ContShared ContShared

lndistd 0.088⁎⁎⁎

(0.023)0.118⁎⁎⁎

(0.030)0.088⁎⁎⁎ (0.024) 0.117⁎⁎⁎

(0.030)lnGDPpcd −0.016

(0.022)0.010 (0.010) −0.016 (0.022) 0.010 (0.014)

MajorFTAd −0.161⁎

(0.057)−0.030(0.040)

−0.157⁎⁎⁎

(0.054)−0.030(0.041)

Exporter Turkey U.S. Turkey U.S.Method OLS OLS Fractional logit Fractional

logitR2 0.217 0.175 – –Observations 103 103 103 103

Notes: The dependent variable is the share of containerizedmaritime exports in totalmar-itime exports in 2013 for Turkey (column 1)and the U.S. (column 2). lndistd is the shortestsea distance to the destination country. lnGDPpcd is (log) per capita GDP of the destinationcountry. MajorFTAd is a dummy taking the value one for major free trade agreements,which is the EU for Turkey and NAFTA countries for the U.S. Fractional logit coefficientsare average marginal effects. Significance: * 10%, ** 5%, *** 1%.

productivity or quality, together with fixed costs of container shipping,could induce firms to sort into using the technology (Rua, 2014). To in-vestigate this, Table 5 reports the results from regressing containerusage on various firm-level characteristics. Across all specifications, itis important to control for shipment size to ensure that the effect isnot going through the shipment-specific scale economies documentedin Fact 3, and for compositional effects through product-destinationfixed effects. Total firm exports, employment, sales, and sales perworker are all positively and significantly correlated with containerusage (columns 1–4). When total exports and sales per worker arejointly controlled for in column5, only the former is significant, suggest-ing that total export volume is a better proxy for firm selection in ourdata. In column 6, we include the number of 8-digit HS productsexported by the firm to a given destination and find no evidence ofeconomies of scope for container usage.

In concluding this section, we reiterate that the micro-level tradedata show substantial variation in containerizationwithin narrowprod-uct categories and destination countries, with the overall variationlargely accounted for by firms. Moreover, container usage is systemati-cally increasing in firm productivity and distance to the destination.Next section presents a transportmode choicemodel for heterogeneousfirms that is consistent with these stylized facts and is amenable toestimation.

3. Model

To explain the choice between containerization and breakbulk at thefirm-level, we now present a simple partial-equilibrium trade modelwith heterogeneous firms. Taking as given the demand in export desti-nations, monopolistically competitive firmsmake optimal pricing, qual-ity and mode of transport choices. By depicting containerization as ahigh fixed-low marginal cost shipping technology, we share somewidely-used elements with the model proposed by Rua (2014). In linewith mounting evidence (Hummels and Skiba, 2004; Irarrazabal,Moxnes, and Opromolla, 2015), we assume per-unit transport costs asour baseline specification. To take into account the potential Alchian-Allen effect—increased relative demand for high-quality products inthe presence of additive transport costs—we incorporate qualitydifferentiation to the model. This framework helps us characterize theconditions under which there is positive selection into containerusage, and yields estimable equations that pin down the structural pa-rameters of the two transport technologies.We later present an alterna-tive version of the model with iceberg trade costs and without quality

7 Unit of measurement does not vary within a given 8-digitHS product code.

Table 5Firm Characteristics and Containerization (Fact 4).

(1) (2) (3) (4) (5) (6)

CONTajdm CONTajdm CONTajdm CONTajdm CONTajdm CONTajdm

lnweightajdm 0.0144⁎⁎⁎ (0.00189) 0.0172⁎⁎⁎ (0.00287) 0.0162⁎⁎⁎ (0.00284) 0.0171⁎⁎⁎ (0.00293) 0.0149⁎⁎⁎ (0.00284) 0.0145⁎⁎⁎ (0.00280)lnexportsa 0.0169⁎⁎⁎ (0.00197) 0.0169⁎⁎⁎ (0.00329) 0.0179⁎⁎⁎ (0.00355)lnemploymenta 0.0104⁎⁎ (0.00473)lnsalesa 0.0191⁎⁎⁎ (0.00371)ln(sales per worker)a 0.0136⁎⁎⁎ (0.00461) 0.00158 (0.00536) 0.00288 (0.00605)NumProductsad −0.000133 (0.000237)Observations 711,743 437,208 437,208 437,208 437,208 437,208R2 0.673 0.725 0.726 0.725 0.726 0.726Product-destination-month FE + + + + + +

Notes: The dependent variable CONTajdm is a binary variable that takes the value one if there is a positive containerized flow at the firm-product-destination level in a given month.lnweightajdm denotes the logarithm of the weight (kg) of the export flows. lnexportsa is the logarithm of the total value of exports of firm i, lnemploymenta the logarithm of the averagenumber of paid employees, lnsalesa the logarithm of total sales, and ln(sales per worker)a the logarithm of total sales divided by the number of workers. Robust standard errors in paren-theses are clustered at the firm-level. Significance: * 10%, ** 5%, *** 1%.

9 All else being equal, optimal quality (equation 5) is increasing in the specific cost t. Tosee the intuition, note that the (fob) origin price elasticity of quality-adjusted demand zq isϵ= σ . p/(p+ t). At a given price p, the firm perceives its demand to be less elastic forhigher values of t. To meet the quality-adjusted demand zq, with t being paid per unit of

336 A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

differentiation. As will be demonstrated and explained below, thechoice between the two versions of the model does not affect our em-pirical strategy, and the predictions obtained from a counterfactual ex-ercise about the effect of containerization on trade remain invariant tothe specification of transport costs.

Demand There is one source country exporting to multiple destina-tions indexed by d. It is populated by a large number of firms, whichare heterogenous in productivity a and produce a continuum of hori-zontally and vertically differentiated varieties. As now standard in theliterature, we use the productivity index to represent varieties producedby these monopolistically competitive firms.

Consumer preferences in destination d are represented by a quality-augmentedCES aggregate as in Baldwin andHarrigan (2011) andKuglerand Verhoogen (2012):

Qd ¼Z

zd að Þqd að Þ½ �σ−1σ dG að Þ

� � σσ−1

;

where zd(a) denotes the quality, σ the elasticity of substitution, qd(a)quantity consumed and G(a) the distribution of firm productivity. Util-ity maximization yields the following demand for each differentiatedvariety:

qd að Þ ¼ XdPσ−1d zd að Þσ−1~pd að Þ−σ ; ð1Þ

where Xd is the spending allocated to imports from the source countryin destination d, ~pdðaÞ is the consumer price, and Pd is a quality-augmentedCES price index defined as:

P1−σd ¼

Z~pd að Þzd að Þ

� �1−σ

dG að Þ:

Supply Consumer prices (c.i.f.) differ from the producer prices (f.o.b.)because of trade costs, which have a specific component tdm that variesby destination and endogenously chosen transport mode m = {b, c}(for break-bulk or container), and an exogenous ad-valorem compo-nent τd N 1 that depends only on the destination8:

~pmd að Þ ¼ τd pmd að Þ þ tmd� �

: ð2Þ

In modeling quality production, we follow Feenstra and Romalis(2014) and assume that a firm with productivity a uses l units of labor(expressed in efficiency units of labor) to produce one unit of productwith quality z(a):

z að Þ ¼ a � lð Þθ;

8 A vastmajority of countries apply tariffs on transport inclusive prices—see footnote 10in Feenstra and Romalis (2014).

where θ ∈ (0, 1] represents diminishing returns in the production ofquality. The quality production function implies marginal cost of pro-duction given by

C a; zð Þ ¼ z að Þ1=θa

w; ð3Þ

where w is the unit cost of labor input and the numéraire. We now de-scribe firms' optimal pricing, quality and transport mode decisions.

Optimal Price and Quality Given mode m, firms maximize operatingprofits by solving

πmd að Þ ¼ maxpd ;z qmd að Þ � pmd að Þ−C a; zð Þ� ��

;

where qdm(⋅) captures the dependence of demand Eq.(1) on m through

the consumer price (2). First-order condition with respect to priceyields

pmd að Þ ¼ σC a; zdð Þ þ tmdσ−1

: ð4Þ

Similarly, first-order condition with respect to quality yields

zmd að Þ1=θ ¼ θ1−θ

� a � tmd ; ð5Þ

which varies by destination due to transport costs. Substituting (5) into(3) and then into (4) gives the following optimal price as a function ofunit transport costs:

pmd að Þ ¼ χ � tmd ; ð6Þ

whereχ ¼ 1σ−1 ð σθ

1−θ þ 1Þ is common to all firms.9 Eq.(6) describes a sim-ple linear relationship between f.o.b. prices and specific transport costs.

Given the profit-maximizing price and quality, the revenue of a firmwith productivity a exporting to destination d using transport technol-ogy m is given by:

rmd að Þ ¼ Θd � aθ σ−1ð Þ � tmd �− σ−1ð Þ 1−θð Þ

; ð7Þ

where Θd ¼ χðχ þ 1Þ−σ ð θ1−θÞ

θðσ−1ÞXdP

σ−1d τ−σ

d . Subtracting variablecosts at the optimal quality choice and rearranging terms, operating

q, the firmwould vary z as well. Of course, price and quality are both set optimally, whichleads to an equalization of perceived demand elasticities across firms at ϵ= σ·χ/(χ+1).We thank the referee for pointing this out.

10 For instance, HS heading 8703 refers to “Motor vehicles for the transport of persons,”which we consider as a sector. Finer 8-digit levels distinguish varieties according to bodytype, ignition type and engine capacity.11 Estimatingwith product fixed effects yields very similar estimates of both coefficientsof interest.

337A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

profits are given by

πmd að Þ ¼ χ þ 1

χσ� rmd að Þ: ð8Þ

Choice of Transport Mode A firm exporting to destination country dpays a mode-specific fixed cost fdm N 0. Net export profit for using eachtransport mode is simply:

Πmd að Þ ¼ πm

d að Þ− f md : ð9Þ

A firm exports to a destination in a container if Πdc(a) ≥Πd

b(a). Thefollowing condition is necessary and sufficient to induce productivity-based selection into containerization and thus make the model consis-tent with Fact 4:

f cdf bd

Ntcdtbd

!− σ−1ð Þ 1−θð Þ: ð10Þ

Similar to Rua (2014), this restriction on relative fixed and variabletrade costs is a modified version of the condition for selection intoexporting in Melitz (2003): only sufficiently productive exporterschoose container to breakbulk shipping by trading off higher fixedcosts with lower variable costs. Note that for the relevant levels of var-iable costs satisfying tc b tb, a higher tc pushes toward selection byrelaxing the constraint (10) on relative fixed costs: as the variable costadvantage of containerization diminishes, firms have to be more pro-ductive to self-select into container shipping. Moreover, this force getsstronger for lower returns to quality production θ: the costlier it is toproduce quality, the more productive an exporter has to be in order topass the selection threshold.

Finally, themarginal exporter uses break-bulk and can be character-

ized by ~abd satisfyingΠbdð~abdÞ ¼ 0. The marginal containerized exporter ~acd

is defined byΠcdð~acdÞ ¼ Πb

dð~acdÞ, and satisfies ~acdN~abd.

4. Estimation

The model of firm selection into exporting and containerization isbased on two novel sets of parameters that we wish to estimate:mode-dependent variable and fixed export costs (tdm, fdm). Progressingin two stages, we first parameterize and estimate relative variabletransport costs using observed firm-product-destination level exportrevenues by mode of shipping, controlling for selection through appro-priate fixed effects. This flexible approach allows us to estimate variablecosts without making a distributional assumption for firm productivity.In the second stage, we use these estimates along with additionalstructure on firm productivities to recover relative fixed trade costs bymode.

4.1. Estimation strategy

To derive estimating equations frommodel-based firm revenue andmode-choice rules, we specify variable transport costs by:

tmd ¼ tm � distδmd ; ð11Þ

where distd is the distance to destination country d. The parameters tmand δm capture the mode-specificfirst-mile costs and distance elastici-ties, respectively. Based on Fact 2 documented above,we anticipate con-tainerization to have a higher first-mile cost (tcNtb) and a lower distanceelasticity (δC b δb).

Under this parameterization, log revenues can be written as (seeAppendix A.1 for details)

lnrd að Þ ¼ lnrbd ~abd�

~abd� θ σ−1ð Þ

0B@1CA þ σ−1ð Þθ lna

þ 1−σð Þ 1−θð Þ ln tc �

− ln tb �� � � CONT

þ 1−σð Þ 1−θð Þ δc−δbð Þ � CONT � lndistd;

ð12Þ

where the indicator function CONT denotes container usage, i.e.,CONT=1 for a≥~acd and zero otherwise.

Eq.(12) forms the basis of our estimation. To implement anempiricalspecification,we have to consider two issues. First, each firm produces asingle variety j in themodel, whereas in the data, many firms operate inmultiple sectors and export multiple products belonging to a given sec-tor s(j). As discussed above, Fact 4motivates our abstraction from econ-omies of scope in container usage: multi-product firms makeindependent shipping mode decisions for each product. There may be,however, economies of scope in other activities leading to the emergeof multi-product firms. Accordingly, we group 8-digitHS productsunder 4-digitHS sectors, and use appropriate firm and sector fixed ef-fects to distinguish multi-product exporters' sales in different sectors.10

This approach also allows us to take into account demand variationacross sectors in a given destination, i.e.,Xsd denotes consumer spendingon sector s. Second, to attenuate the noise in the monthly data, we ag-gregate firm-product-destination-mode level export sales to the annuallevel.

The first term in (12) is common to all firms in sector s exporting todestination d, and thus can be captured by sector-destination fixed ef-fect (αsd). The second term contains firm productivity, and thus can becaptured by a firm fixed effect (αa). Our estimating equation can bewritten as:

lnrajdm ¼ 1−σð Þ 1−θð Þ ln tc �

− ln tb �� �

η1� CONTajdm

þ 1−σð Þ 1−θð Þ δc−δbð Þ η2 � CONTajdm � lndistd þ αsd þ αa

þ ϵajdm; ð13Þ

where the indicator function CONT is a dummy taking the value oneifthere is a containerized shipment in the observed firm-product-desti-nation level flow. Eq.(13) augments the theory-implied revenue Eq.(12)by an error term ϵ, which captures i.i.d. revenue shocks realized afterpricing and shipping decisions have been made, e.g.,exchange ratemovements, loss/damage of cargo in transit, or risk of non-payment.For another example where revenue shocks are orthogonal to the ship-ping decision, consider a buyer-seller pair contracting upon aminimumlevel of saleswith a particular delivery time, such as an initial order to bedelivered in a certain month, with the option of ordering an additionalamount to the same shipment. The initial level of demand irreversiblydetermines the optimal shipping mode. Then the shock is realized andthe exact level of demand—i.e.,whether the additional order comesinor not—is determined. This affects revenue but not the pre-deter-mined shipping mode.

4.2. Estimation results

Table 6 presents the results from estimating Eq.(13). Our dependentvariable is measured in terms of deviations from the respective 8-digitHS product means, lnðrajdm=r jÞ, where r j denotes the mean value ofexports at the product-level. We do this to control for differences inprice levels across products.11

Table 6Main Estimation: Inferring Containerization's Effects on Transport Costs from its Effect on Export Revenues.

Coefficient (1) (2) (3) (4)

lnðrajdm=r jÞ lnðrajdm=r jÞ lnðrajdm=r jÞ lnðrajdm=r jÞCONTajdm η1 0.296⁎⁎⁎ (0.0125) −0.289⁎⁎⁎ (0.101) −0.275⁎⁎ (0.125) −0.529⁎⁎ (0.250)CONTajdm ⋅ ln distd η2 0.0720⁎⁎⁎ (0.0123) 0.0741⁎⁎⁎ (0.0152) 0.114⁎⁎⁎ (0.0306)Observations 244,713 244,713 244,713 244,713R2 0.401 0.401 0.565 0.768Sector-destination FE + + +Firm FE + +Firm-sector FE +Firm-sector-destination FE +

Notes: The dependent variable is the logarithm of the value of export revenue at the firm-product-destination-mode level, measured in terms of deviations from the respective product-level means. CONTajdm is a binary variable that takes the value one if there is a positive containerized flow at the firm-product-destination level. Robust standard errors clustered at theproduct-destination level in parentheses. Significance: * 10%, ** 5%, *** 1%.

338 A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

In the first column,we start with the direct effect of containerizationwithout the interaction term to gauge whether containerization is asso-ciated with larger trade flows. Controlling for demand-related factorswith sector-destination fixed effects and supply-related factors (e.g.,firm productivity) with firm fixed effects, containerized exports are in-deed 35%(e0.296–1) larger than break-bulk exports.

The second column of Table 6 presents results from the estimation ofEq.(13). Contrasted with the first column, adding the interaction be-tween the container dummy and distance to destination reverses thesign of the coefficient η1 on CONTajdm to negative. This is consistentwith our hypothesis that containerization has a higher first-mile costthan breakbulk shipping: since σ N 1 and θ b 1, a negative η1 estimateimplies tcNtb . The coefficient η2 on the interaction between CONTajdmand lndistd is estimated to be positive and statistically significant,which implies a smaller elasticity of container shipping with respectto distance, δC b δb. In column 3, we replace firm fixed effects withfirm-sector level fixed effects to account for the possibility that multi-product firms may have different productivities in different sectors(Eckel and Neary, 2010; Bernard, Redding, and Schott, 2011), as wellas potential heterogeneity in productivity distributions or in the elastic-ity of substitution across sectors. The estimates of both η1 and η2 remainstable.

The specifications presented so far control for demand and supplyfactors related to sector-destination and firm-productivity pairs. Whilethe latter fixed effects control for productivity-induced firm selectioninto containerization, they do not adequately control for selection atthe relevant level of modal decision-making: a positive revenue shockat the firm-sector-destination level would increase the probability ofcontainerization, creating an upward bias in the estimate of η1 and driv-ing it toward zero. Note that a firm operating in sector s would prefercontainerized exports if Πsd

c (a) ≥Πsdb (a), where net profits depend on

revenues as derived in Eq.(9). Using the expressions for revenues inAppendix A.1, profit gains from shipping in a container can be derivedas follows:

Πcsd að Þ−Πb

sd að Þ ¼ χ þ 1χσ

� tcdtbd

!− σ−1ð Þ 1−θð Þ−1

24 35 � f cd− f bd�

� rbsd að Þ:

Since the expression above varies at the firm-sector-destinationlevel, selection into containerization can be accounted for by replacingsector-destination and firm-sector fixed effects in the estimating Eq.(13) with firm-sector-destination fixed effects αasd.

In this specification, the parameters of interest, η1 and η2, are identi-fied from variation in container usage within a firm-sector-destinationtriplet across products. We can consistently estimate the parametersas long as firms face revenue shocks that do not systematically varywith the mode of transport.

The fourth column of Table 6 presents the results. Compared to theestimates in column 3, estimates of both η1 and η2 are larger in absolute

value. In particular, the estimate of η1 more than doubles (in absolutevalue) when selection into containerization is accounted for. This resultis consistent with our prior that ignoring selection into containerizationwould drive the estimate of η1toward zero.

Robustness Checks Table7 presents a number of robustness checks.Columns 1 and 2 show the results from re-estimating our preferredspecification (last column of Table 6) on samples that exclude fromthe baseline intrinsically non-containerizable products based respec-tively on Korinek (2011) and Bernhofen, El-Sahli, and Kneller (2016).The coefficient estimates remain very close to their baseline values.We infer from this robustness check that the fixed effects included inbaseline already take into account the nature of the products in termsof their containerizability. In another robustness check presented in col-umn 3 of Table 7, we investigate whether within-firm quality differen-tiation affects our baseline estimates. A potential concern is that firmsmight ship higher quality products to richer or more distant destina-tions, and such selection could interact with their choice of shipmenttechnology and thus affect our estimates. To address this concern, werestrict the estimation sample to non-differentiated products, basedon the classification suggested by Rauch (1999), since we expect thatonly firms in differentiated-good sectors to exhibit quality-based com-petence (Eckel, Iacovone, Javorcik, and Neary, 2015). The robustnessof results rules out the possibility that our baseline estimates are drivenby within-firm quality differentiation across destinations.

Column4of Table 7 addsfinerfixed effects (product-destination andfirm-product) to the firm-sector-destination level fixed effects in thebaseline. This specification relies on variation in the use of containersat a more disaggregated level to identify the coefficients of interest.The similarity of the estimates to the baseline increases our confidencethat the latter identifies the coefficients of interest from variation incontainer usagewithin afirm-sector-destination triplet across products,relying mainly on product-specific random revenue shocks.

In the last column of Table 7, we allow the relative distance elasticityto be piece-wise linear. While the difference in distance elasticity be-tween breakbulk and container shipping increases with the bilateraldistance, the fit does not seem to improve compared to the parsimoni-ous functional form we assume in the baseline.

In the next section, wewill use our preferred estimates from the lastcolumnof Table 6, parameter values from the literature, and furthermo-ments from the data to recover the unobserved relative variable andfixed costs of containerization. Recovering these costs will allow us toundertake model-consistent counterfactuals, yielding predictions forthe contribution of containerization to the volume of trade.

5. Recovering trade costs

To recover transport technology parameters ðtm; δmÞ from the esti-mates of (η1, η2) in Eq.(13), we need to quantify σ and θ. As typical inthe literature (Anderson and Van Wincoop, 2004; Coşar and Demir,

Table 7Robustness Checks: Inferring containerization's Effects on Transport Costs from its Effect on Export Revenues.

Coefficient (1) (2) (3) (4) (5)

Containerizable Containerizable products Non-differentiated All All

products (OECD defn.) (Bernhofen, El-Sahli, and Kneller (2016)) products products products

lnðrajdm=r jÞ lnðrajdm=r jÞ lnðrajdm=r jÞ lnrajdm lnðrajdm=r jÞCONTajdm η1 −0.514⁎⁎⁎ (0.180) −0.532⁎⁎⁎ (0.175) −0.597⁎ (0.342) −0.647⁎⁎ (0.198)CONTajdm ⋅ ln distd η2 0.116⁎⁎⁎ (0.0221) 0.114⁎⁎⁎ (0.0214) 0.114⁎⁎⁎ (0.0412) 0.131⁎⁎⁎ (0.0243)CONTajdmI{distd ≤ 1000} η2 0.138⁎⁎ (0.0539)CONTajdmI{1000 b distd ≤ 4000} η2 0.361⁎⁎⁎ (0.0285)CONTajdmI{b4000 b distd ≤ 8000} η2 0.472⁎⁎⁎ (0.0408)CONTajdmI{8000 b distd ≤ 12,000} η2 0.535⁎⁎⁎ (0.0540)CONTajdmI{distd N 12,000} η2 0.593⁎⁎⁎ (0.0683)Observations 110,542 117,699 45,376 244,713 244,713R2 0.587 0.587 0.589 0.765 0.587Firm-sector-destination FE + + + + +Product-destination FE +Firm-product FE +

Notes: The dependent variable is the logarithm of the value of export revenue at the firm-product-destination-mode level, measured in terms of deviations from the respective product-level means. CONTajdm is a binary variable that takes the value one if there is a positive containerized flow at the firm-product-destination level. Column (1)restricts the sample tocontainerizable products based on the classification suggested by Korinek (2011); the following products are excluded from the sample: dry and industrial bulk, tankers, and bulk shippedgoods, goods shipped in tankers, motor vehicles, trailers and non-mechanically propelled vehicle n.e.s., aircraft, spacecraft, satellites, ships, boats and other floating structures. Column (2)also restricts the sample to containerizable products according to the classification employed by Bernhofen, El-Sahli, andKneller (2016). Column (3)drops differentiated goods as classifiedby Rauch (1999). Column (3)adds product-destination and firm-product fixed effects to the specification presented in the last column of Table6. Column (4)assumes a flexible functionalform for transport costs defined in Eq.(11). I{} are indicator variables which take on the value one if distance to destination satisfies the condition in parentheses, and zero otherwise. Ro-bust standard errors clustered at the product-destination level in parentheses. Significance: * 10%, ** 5%, *** 1%.

339A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

2016), the elasticity of substitution σ cannot be separately identifiedfrom the distance elasticity of trade costs. In our case, an additional pa-rameter θ, capturing the supply of quality, enters the picture.

To proceed, we exploit furthermoments of the data related to the in-tensity of container usage in the aggregate and in the extensive margin.Under the assumption that the unconditional firm productivity a isdrawn from a Pareto distribution with domain a ∈ [1,∞] and shape pa-rameter k satisfying k N θ(σ− 1) similar to Chaney (2008), we can de-rive analytic expressions for destination-level share of containerizedexports, μd, and the fraction of firms using container shipping, μdext

(seeAppendix A.2 for the details):

μd ¼R∞~acdrd að ÞdG að ÞR∞

~abdrd að ÞdG að Þ

¼Δtdð Þ− σ−1ð Þ 1−θð Þ Δ f d−1

Δtdð Þ− σ−1ð Þ 1−θð Þ−1

� θ σ−1ð Þ−kθ σ−1ð Þ

1þ Δ f d−1Δtdð Þ− σ−1ð Þ 1−θð Þ−1

� θ σ−1ð Þ−kθ σ−1ð Þ � Δtdð Þ− σ−1ð Þ 1−θð Þ−1

h i ; ð14Þ

and

μextd ¼

R∞~acddG að ÞR∞

~abddG að Þ ¼ Δ f d−1

Δtdð Þ− σ−1ð Þ 1−θð Þ−1

! −kθ σ−1ð Þ

; ð15Þ

where Δfd = fdc/fdb denotes relative fixed costs, and Δtd = td

c/tdb denotesrelative variable trade costs. Using the functional form (11) for transportcosts,

Δtd ¼ tcdtbd

¼ tctb

� �� dist δc−δbð Þ

d : ð16Þ

The set of parameters to be calibrated is (σ, θ, k) as well as relativefixed costs Δfd. The elasticity of substitution σ and Pareto parameter kare widely estimated in the literature. We take σ = 4 and k = 4.25from Melitz and Redding (2015).

The following procedure pins down the quality production parame-ter θ alongwith relativefixed costs: from the data,we take the empiricalmoments (μd,μdext) as themedian across sectors for each destination. For

all values of θ ∈(0, 1], we back out ðtc=tbÞ and (δC − δb) from (η1, η2) es-timates of Eq.(13). Given distances,we use Eq.(16) to construct destina-tion-specific relative variable transport costs, Δtd. To back out Δfd, weplugΔtd and the parameter values (σ, k, θ) into Eq.(14) and use the em-pirical moment μd on the left hand side. We then use (Δtd, Δfd) alongwith parameter values (σ, k, θ) in Eq.(15) to calculate the model-im-plied extensive margin moment. The value of θ is picked such that themedian of this moment across destinations matches its empiricalvalue of mediand {μdext} = 0.74, yielding θ=0.267. The resulting corre-lation between the observed and model-implied extensive marginacross destinations is about 0.78.

Variable Trade Costs Given σ = 4, the calibrated value θ = 0.267andestimates of (η1, η2) from the last column of Table 6 imply ðtc=tbÞ ¼1:27, i.e.,thefirst-mile cost of container shipping is about 27% largerthanthat of breakbulk shipping. While it has a higher first-milecost, con-tainer shipping has a smaller distance elasticity: δC − δb =−0.05.

Top panel of Fig. 2 plotsdΔtd against distance. The solid line is drawnusing baseline parameter values, while the dashed line sets σ=6 (andre-calibratesθ) to check robustness to an empirically relevant highervalue of σ. The negative gradient of relative variable container costswith respect to distance is consistent with the observed pattern in thedata that container usage is increasing in distance to the destination(Fact 2). Using the benchmark estimates, variable cost savings from con-tainerization reach 24% when the distance variable reaches 20,000 km.Cost savings are large for major trading pairs, amounting to 19.5% forGermany-USA and 22% for China-USA. For the latter pair, the lowerbound for cost savings implied at thehigher level ofσ=6 is around13%.

Note that the combination of a higher first-mile cost and a lower dis-tance elasticity implies that container shipping becomes cheaper be-yond a breakeven distance. The horizontal line in the top panel ofFig. 2 marks the breakeven distance implied by our estimates, which is103 km. This rather short breakeven distance is consistent with theraw data in that all destination countries, however close they are inproximity to Turkey, receive some containerized maritime exports(see the first row of Table 1). Concurrently, it is consistent with the im-portance of firms, rather than destinations, in explaining containerusage (Fact 1): if all destinations are situated beyond the breakeven dis-tance, which is the case in our data, the large variation in containerusage should come from firm-destination level heterogeneity. In the

Fig.2. Relative Variable and Fixed Trade Costs (Additive Specification). Notes: The upper

panel shows the variable costdΔtd ¼ tcd=tbd against distance. Red (blue) point marks USA-

China (USA-Germany), and the horizontal line at 1 marks the breakeven distance. The

bottom panel is the histogram of relative fixed cost values ( dΔ f d ) calibrated todestination countries in the Turkish export data using the baseline value of σ=4.

340 A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

model, firm selection into container shipping is driven by relative desti-nation-dependent fixed cost of exporting Δfd = fd

c/fdb, which we presentnext.

Fixed Trade Costs Bottom panel of Fig. 2 plots the histogram of cali-brated relative fixed costs of containerized exports. Fixed cost of con-tainerization is 40 to 100% higher than that of breakbulk, with amedian of 70% across destinations.

Several channels could justify higherfixed costs associatedwith con-tainerization. For instance, container links between ports are less fre-quent than break-bulk links. This implies, for any given shipment, theexporter has to spend additional effort to better manage the productionand inventory scheduling. Another source is the importance of transac-tion-specific scale in container shipping: if the shipment size is largeenough to fill a container (full-container-load), firms can scheduledoor-to-door shipping services. Otherwise, if the shipment is less-than-container load, exporters have to purchase additional servicesfrom freight-forwarders who consolidate and store shipments at ports.Dueto the cargo handling involved, such services typically involve addi-tional costs.12

12 We abstract from potential heterogeneity in fixed costs across firms. Note that thisdoes not bias the estimation of relative variable costs, which is identified from the varia-tion in modal choices within firm-sector-destinations.

Iceberg Specification of Trade Costs The baseline model assumes thattrade costs are composed of an ad-valorem part τd and an additivepart tdm. We now investigate the implications of assuming that tradecosts take the multiplicative “iceberg” form. Since multiplicative tradecosts do not affect firm's choice of product quality, we set z(a) = 1 forall firms. We assume that trade costs can be written as the product oftwo terms: destination tariffs that do not vary between shippingmodes τd, and distance-mode dependent costs tdm ≥ 1, such that Tdm =τd ⋅ tdm units of a good must be shipped to destination d in order forone unit to arrive.

With this specification, consumer prices in destination d are givenby:

~pmd að Þ ¼ Tmd � p að Þ:

Since we abstract from quality differentiation, firms maximizeprofits with respect to price only, yielding

pmd að Þ ¼ σσ−1

� 1a� Tm

d :

Given demand in destination d for the variety exported by firm a, wecan write firm revenues as

rmd að Þ ¼ Θd � aσ−1 � tmd �1−σ

; ð17Þ

where Θd ¼ ð σσ−1Þ1−σXdP

σ−1d τ1−σ

d . Condition (10) for productivity-based selection into containerization becomes

f cdf bd

Ntcdtbd

!− σ−1ð Þ:

As in Appendix A.1, we can write revenues of firm a from its exportsales to a destination country d in terms of the revenues of themarginalfirm exporting to the same destination:

rd að Þ ¼rbd ~abd� a

~abd

!σ−1tcdtbd

!1−σ

a≥~acd

rbd ~abd� a

~abd

!σ−1

ab~acd

8>>>>><>>>>>:ð18Þ

Finally, container share for the model with iceberg-type trade costsbecomes

μd ¼Δtdð Þ1−σ Δ f d−1

Δtdð Þ1−σ−1

� σ−k−1σ−1

1þ Δ f d−1Δtdð Þ1−σ−1

� σ−k−1σ−1 � Δtdð Þ1−σ−1

h i : ð19Þ

Note that letting transport costs to be multiplicative does not

modifyour estimating equation. Using the same specification for tmd ¼ tm

�distδmd , revenue expressions (17)–(18) still imply the estimating Eq.(13)without the term containing θ. In other words, the model with additivetrade costs and quality differentiation delivers a reduced form equationthat is isomorphic to the one derived from a model with multiplicativetrade costs and no quality differentiation. This interesting result can betraced to the optimal pricing expression (6) derived under additivetrade costs being multiplicative itself due to the presence of the qualitymargin.

Using the baseline estimates of (η1, η2) from the fourth column ofTable 6, along with σ=4, we back out ðtc=tbÞ ¼ expðη1Þ=ð1−σÞ ¼ 1:19and (δC− δb) = η2/(1− σ) =−0.038. Using the impliedΔtd, we thenback out relative fixed costs Δfd from the empirical aggregate containershares μd using the expression above. Top and bottom panels of Fig. 3

Fig.3. Relative Variable and Fixed Trade Costs (Multiplicative Specification). Notes: The

upper panel shows the variable cost dΔtd ¼ tcd=tbd against distance. Red (blue) point

marks USA-China (USA-Germany), and the horizontal line at 1 marks the breakeven

distance. The bottom panel is the histogram of relative fixed cost values (dΔ f d) calibratedto destination countries in the Turkish export data using the baseline value of σ=4.

341A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

plot relative variable trade costs Δtd and histogram of relative fixedtrade costs Δfd. Note that the breakeven distance remains unchangedfrom Fig. 2 since it only depends on our estimates of η1 and η2.13

While relative variable costs look qualitatively and quantitatively simi-lar to its counterpart at the top panel of Fig. 2, iceberg specification im-plies smaller variable cost savings from containerization. This is evidentfrom the flatter cost gradient with respect to distance at top panels. Theimplied variable cost saving for a shipping between China and USA is16% when transport costs are deemed to be multiplicative, comparedto 22% when they are assumed to be additive. When the elasticity ofsubstitution is set higher to σ= 6, the implied cost savings are muchmore similar between multiplicative and additive specifications(dashed lines at the top panels of both figures).

6. Additional evidence from the U.S. data

In this section, we use publicly available U.S. data to provide addi-tional quantitative and qualitative support for our relative variable

13 This follows from tbdðgdistÞ ¼ tcdðgdistÞ, which yieldsgdist ¼ expð ln ðtcÞ− ln ðtbÞδb−δc Þ ¼ expð−

η1=η2Þ.

transport cost (Δtd) estimates. The data, originally collected by the U.S.Census Bureau and made publicly available by Schott (2008), providesinformation about the value and weight of U.S. imports, as well asnon-tariff charges (freight and insurance) on them, broken down bymode of shipment, source country, 10-digit product, and the customsdistrict of entry. Themode of shipment is further broken down into con-tainerized and non-containerized vessel imports. We use data for 2013and aggregate product categories to 8-digit to facilitate comparisonwith our baseline estimates from the Turkish data. For the same reason,we exclude HS headings 27 and 93.

We start by checking the distribution of containerized importcharges relative to breakbulk. CIFjsm denotes charges for insurance andfreight per import weight for each product j, from each source countrys and by shippingmodem ∈{container, breakbulk}. Fig. 4 plots the histo-gram of CIFjsc /CIFjsb across product-source country (js) pairs. With a me-dian value of 0.804, import charges of containerized flows are lowerfor majority of import flows. This is direct evidence that for most desti-nations, breakbulk is themore expensive shippingmode in terms of var-iable costs. If, in addition, shipping costs have an additive component,the result is also consistent with the negative correlation between con-tainer usage and unit values (Fact 3)and justifies our modeling of en-dogenous quality differentiation to account for that.

Using the U.S. import data, we now directly estimate the transportcost function (11):

ln CIFmjs�

¼ α j þ αs þ β1 � CONTjsm þ β2 � CONTjsm � ln distsð Þþ ϵjsm;

where α's represent the set of product and source country-port of entryfixed effects. Qualitatively, β1 N 0 and β2 b 0 would be consistent withour finding that containerization has a higher first-mile cost and alower distance elasticity. Quantitatively, the magnitude of β2 providesa direct estimate for δC − δb.

Table 8 presents the results. In column 1, we report the baseline es-timate and in column 2, we include unit values in order to capture theeffect of import charges varying with prices such as insurance. Notonly do the coefficients have the anticipated signs, but the magnitude

of β2 ¼ δc−δb in column2 is consistentwith the value of 0.05 estimatedfrom the Turkish data.

7. Counterfactuals: Effect of containerization on trade

Having quantified the relative cost of maritime transport modes, wenow explore the extent to which the availability of container shippingincreases trade. To address this question, we calculate two statistics:we first compare the current level of exports to a destination to thecounterfactual level that would obtain if container shipping was notavailable:

ΔEXPd1 ¼

Z ~acd

~abd

rd að ÞdG að Þ þZ ∞

~acd

rd að ÞdG að Þ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}Current exportsZ ∞

~abd

rd að ÞdG að Þ|fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl}Breakbulk only counterfactual exports

:

The second method assumes that the selection equation in (10)holds with equality, i.e.,Δfd = Δtd−(σ−1)(1−θ) for all d, due to a counter-factual decrease in the fixed cost of container shipping. In this case, allexporters to all destinations prefer containerization to breakbulk

Fig.4. Relative Cost of Containerized Charges for U.S. Imports. Notes: This figure plotsinsurance and freight charges per weight for containerized 2013 U.S. import flowsrelative to breakbulk across 8-digit HS products and source countries.

Fig.5. Increase in Trade due to Containerization for the Median Sector. Notes: This figureplots ΔEXP1d, the ratio of current level of destination-specific exports for the mediansector in terms of container usage to the counterfactual level that would obtain ifcontainer shipping was not available. Each dot is an export destination from Turkey (toppanel) and the U.S. (bottom panel) as the source country.

342 A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

shipping. This statistic is given by

ΔEXPd2 ¼

Z ∞

acd

rd að ÞdG að Þ|fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl}Container only counterfactual exportsZ ~acd

~abd

rd að ÞdG að Þ þZ ∞

~acd

rd að ÞdG að ÞCurrent exports|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

;

where acd denotes the ability of the marginal exporter to destination dwhen Δfd = Δtd−(σ−1)(1−θ). While ΔEXP1d is informative about howmuch international trade has increased from the pre-container era tothe present due to the availability of the technology, ΔEXP2d is informa-tive about potential future increases due to further improvements inthe technology to the point of full adaption. In Appendix A.3, we derivethese statistics analytically:

ΔEXPd1 ¼ 1þ Δt− σ−1ð Þ 1−θð Þ

d −1� Δ f d−1

Δt− σ−1ð Þ 1−θð Þd −1

!θ σ−1ð Þ−kθ σ−1ð Þ

;

ΔEXPd2 ¼ Δt− σ−1ð Þ 1−θð Þ

d

1þ Δt− σ−1ð Þ 1−θð Þd −1

� Δ f d−1

Δt− σ−1ð Þ 1−θð Þd

−1

� �θ σ−1ð Þ−kÞθ σ−1ð Þ

:

Table8Transport Cost Estimation using U.S. Import Data.

Coefficient (1) (2)

ln(CIFjsm) ln(CIFjsm)

CONTjsm β1 0.777⁎⁎⁎ (0.184) 0.487⁎⁎⁎ (0.167)CONTjsm ⋅ ln dists β2 −0.103⁎⁎⁎

(0.020)−0.056⁎⁎⁎

(0.018)ln(Valuejsm/Weightjsm) 0.578⁎⁎⁎ (0.003)Observations 494,598 494,598R2 0.210 0.302Product FE + +Source country-port of entryFE

+ +

Notes: The dependent variable is the mode specific (breakbulk vs container) logarithm offreight and insurance charges per weight for 2013 U.S. import flows at the level of 8-digitHS-product j and source country-port of entry s. CONTjsm is a dummy for containerizedflows. lndists is sea distance from the source country. Robust standard errors clustered atthe product-source country level in parentheses. Significance: * 10%, ** 5%, *** 1%.

We conduct these counterfactual exercises for both Turkey and theU.S. For the latter, we calculate Δtd using our estimates and the sea dis-tances of export destinations to the U.S., and then back out Δfd from Eq.(14) using the median U.S. container share across sectors for each des-tination, μd.

Fig. 5 plots destination specificΔEXP1d against sea distances. Sincewerecover variable trade costs from a specificationwith sector fixed effectsand use the sectoral median container share μd to calibrate fixed costs,the interpretation of the counterfactual export change is also with re-spect to the median sector in terms of container usage. For both coun-tries, containerization implies a significant increase in the exports ofthe median sector: the average across 96 destinations in Fig. 5 is 46%for Turkey, and 40% for the U.S. In other words, current trade levelswould decrease by about a third in an average sector if container tech-nology did not exist (≈0.46/1.46). The gains reach 78% for the most re-mote trade partners.14

14 By construction, the exercise implies an increase of exports to all destinations. Suchdrastic changes in distance-related shipping costs, however, could potentially divert tradefromnearby trade partners in a general equilibrium framework.We also abstract from en-dogenous price setting by carriers, which is empirically relevant in the transportation in-dustry (Hummels, Lugovskyy, and Skiba, 2009). See Asturias (2018) and Wong (2018)for welfare analysis in general equilibrium when transportation costs are endogenous.

343A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

Potential increases in trade if container shippingwas fully adopted—to thepointwhere it is preferred by all exporters—are relatively smaller:the mean ΔEXP2d across destinations is 13% and 19% for Turkey and theU.S., respectively. The implication is that for the typical sector, most ofthe trade increasing effect of containerization has already been realized.This is not surprising given that while only 54% of Turkish exporters usecontainerization in a typical sector, remaining firms export smalleramounts. Therefore, full adoption would increase Turkey's exports inthat sector to the average destination by just 13% due to the diminishingreturns caused by firm selection.

To gauge the total effect on maritime exports, we aggregate ΔEXP1d

using as weights the export share of each destination country d. Sincetrade shares are decreasing in distance, the aggregate effect is smallerthan the simple average reported above. We find that total Turkishand American maritime exports would have been 14 and 21% lower inthe absence of containerization, respectively.

These results are invariant to transport costs being additive or mul-tiplicative since ΔEXP1d and ΔEXP2d are functions of the observables (μd,distd) and the estimates of (η1, η2)—see Appendix A.3 for details. Tosee the intuition, first note that the term Δtd−(σ−1)(1−θ) in ΔEXP1d andΔEXP2d depends only on distd and the estimates of (η1, η2). This is a directresult of both specifications yielding the same estimating equation. Sec-ond, we back out Δfd from the same empirical container share momentμd—depending on the cost specification, this is Eq.(14) or (19). As a re-sult, themodelwith additive costs and endogenous quality choice yieldsthe same trade increase due to containerization as themodel with mul-tiplicative trade costs and no quality margin, when both models arequantified using the same salient moments of the data. For the verysame reason, the values chosen for (σ, k) parameters do not matterfor the magnitudes of ΔEXP1d and ΔEXP2d.

The two specifications, however, differ in the implied elasticity oftrade to shipping costs. In the baseline (specific transport costs), con-tainerization decreases variable trade costs to a destination located atthe median distance from Turkey or U.S. by about 20%. As mentionedabove, exports to the average destination would be around 46% lowerin a typical sector for both countries. This implies trade elasticity around2.3 (≈0.46/| − 0.2|). Since the estimated variable cost decrease issmaller under iceberg specification—see top panels of Figs.2-3 and thediscussion in the previous section—implied trade elasticities are larger,around 3 (≈0.46/|− 0.15|).

8. Conclusion

This paper takes an important step toward better understanding andquantifying transport costs. Using micro-level Turkish export data, weestimate the effect of containerization on transport costs and trade byproviding the first systematic estimation of firms' modal choice be-tween containerized and breakbulk shipping. The results confirm therole of container technology in the global economy: it implies variablecost savings around 20% at distances that are relevant for major tradingeconomies, with a fixed cost around 50 to 100% higher than itsbreakbulk alternative. A counterfactual exercise suggests that in the ab-sence of containerization, Turkish and U.S. maritime exports in a typicalsector to an average destination would decrease by around a third. Ag-gregating over destinations, we predict that total maritime exportswould have been by about 14 and 21% lower for Turkey and the U.S., re-spectively. Container shipping is indeed a major driver of increased in-ternational trade in the past several decades.

We conclude by noting that our findings relate to the “distance puz-zle” in international trade, i.e.,the negative effect of distance on tradehas not decreased over time (Disdier and Head, 2008). In describingthe potential sources of the supposed death of distance, the literatureoften refers to technological advancements in transportation. Our resulton container shipping costs being less distance-elastic provides amech-anism and support for this idea. We do not, however, offer a resolutionto the puzzle itself. Neither do we interpret our result as predicting a

decline in the distance elasticity of overall trade due to an increasing in-tensity of container usage over time. The distance elasticity of trade de-pends not only on the distance elasticity of trade costs but also on thetrade elasticity with respect to trade costs. It is possible that changesin the sectoral or bilateral composition of world trade may have offsetthe decline in distance-related shipping costs. For instance, containeri-zation may have helped countries that are located further apart starttrading with each other. If trade between new partners is subject tohigher non-transport trade frictions than those between existing tradepartners, and if that discrepancy is correlated with distance (e.g.,dueto lingual or cultural differences), the compositional shift may offsetthe gains from lower shipping costs and keep the average distance elas-ticity constant (Head andMayer, 2013). Investigating the channels con-tributing to the distance puzzle despite declining shipping costs thusremains an important question for researchers.

Appendix A. Appendix

A.1. Derivation of the Revenue Function (Eq.12)

Using the expression for revenues in Eq.(7), we canwrite revenue ofafirm exporting to destination d using transport technologym as a func-tion of themarginal firm exporting to the same destination using trans-port technology m:

rmd að Þrmd ~amd � ¼ a

~amd

!θ σ−1ð Þ; ð20Þ

where ~amd denotes the productivity of the marginal firm using trans-port technology m. The revenue of the marginal exporter can bewritten as:

rmd ~amd � ¼ Θd � ~amd

�θ σ−1ð Þ � tmd �− σ−1ð Þ 1−θð Þ

; ð21Þ

where Θd is a function of, among other, destination country Xd seeEq.(7). For the marginal firm choosing containerization overbreakbulk, we have the following relationship between its revenuefrom containerized exports and its revenue from breakbulk exports:

rcd ~acd �

rbd ~acd � ¼ tcd

tbd

!− σ−1ð Þ 1−θð Þ: ð22Þ

Putting the two expressions together, we can write firm revenues asfollows:

rd að Þ ¼rbd ~abd� a

~abd

!θ σ−1ð Þtcdtbd

!− σ−1ð Þ 1−θð Þa≥~acd

rbd ~abd� a

~abd

!θ σ−1ð Þab~acd:

8>>>>><>>>>>:Using the specific trade cost function (11) and the indicator function

CONT denoting container usage, i.e.,CONT=1 for a≥~acd, and taking log-arithms yields the expression (12) in the text.

A.2. Derivation of the Container Share Eq.(14)

Firm productivity is distributed Pareto with the CDF,k is shapeparameter:

G að Þ ¼ 1−a−k; ð23Þ

344 A.K. Coşar, B. Demir / Journal of International Economics 114 (2018) 331–345

Share of containerized exports for a given sector-destination pair isgiven by:

μd ¼R∞~acdrd að ÞdG að ÞR∞

~abdrd að ÞdG að Þ :

Wecanwrite revenues in terms of revenues of themarginal exporterusing Eqs.(20) and (22) to obtain:

μd ¼R∞~acdrd ~abd�

Δtdð Þ− σ−1ð Þ 1−θð Þ a=~abd� θ σ−1ð Þ

dG að ÞR ~acd~abd

rd ~abd�

a=~abd� θ σ−1ð Þ

dG að Þ þ R∞~acd rd ~abd�

Δtdð Þ− σ−1ð Þ 1−θð Þ a=~abd� θ σ−1ð Þ

dG að Þ

¼ Δtdð Þ− σ−1ð Þ 1−θð Þ ~acd �θ σ−1ð Þ−k

~abd� θ σ−1ð Þ−k

þ Δtdð Þ− σ−1ð Þ 1−θð Þ−1h i

~acd �θ σ−1ð Þ−k

;

where Δtd = tdc/tdb.

Next, we use the profit functions in (8)and (9) to express marginalproductivities in terms of trade costs:

~abd� θ σ−1ð Þ

¼ χσχ þ 1ð ÞΘd

� tbd� σ−1ð Þ 1−θð Þ

� f bd~acd �θ σ−1ð Þ ¼ χσ

χ þ 1ð ÞΘd� 1

tcd �− σ−1ð Þ 1−θð Þ− tbd

�− σ−1ð Þ 1−θð Þ � f cd− f bd�

:

Substituting these in the expression for μd above and simplifyingyield the following:

μd ¼Δtdð Þ− σ−1ð Þ 1−θð Þ Δ f d−1

Δtdð Þ− σ−1ð Þ 1−θð Þ−1

� θ σ−1ð Þ−kθ σ−1ð Þ

1þ Δ f d−1Δtdð Þ− σ−1ð Þ 1−θð Þ−1

� θ σ−1ð Þ−kθ σ−1ð Þ � Δtdð Þ− σ−1ð Þ 1−θð Þ−1

h i ;where Δfd = fd

c/fdb. Derivation of μdext follows similar steps.

A.3. Derivations for the Counterfactual Exercise

The first measure, ΔEXP1, compares the current level of exports to adestination to the counterfactual level that would obtain if containershipping was not available:

ΔEXP1 ¼R ~acd~abd

rd ~abd�

a=~abd� θ σ−1ð Þ

dG að Þ þ R ∞~acd rd ~abd�

Δtdð Þ− σ−1ð Þ 1−θð Þ a=~abd� θ σ−1ð Þ

dG að ÞR∞~abdrd ~abd�

a=~abd� θ σ−1ð Þ

dG að Þ:

The numerator was derived in Appendix A.2, and the denominatoris:

rd ~abd�

~abd� −θ σ−1ð Þ

~abd� θ σ−1ð Þ−k

:

So, using the expressions for ~abd and ~acd in Appendix A.2, we obtain:

ΔEXP1 ¼ 1þ Δt− σ−1ð Þ 1−θð Þd −1

� Δ f d−1

Δt− σ−1ð Þ 1−θð Þd −1

!θ σ−1ð Þ−kθ σ−1ð Þ

: ð24Þ

The other measure, ΔEXP2, compares the counterfactual level thatwould obtain if the relative fixed cost container shipping would fallsuch that Δfd = Δtd−(σ−1)(1−θ) to the current level of exports to a desti-nation. Let acd denote the ability of themarginal exporter to destination dwhen Δfd = Δtd−(σ−1)(1−θ). Then, ΔEXP2 is equal to:

ΔEXP2 ¼R∞acdrd acd �

a=acd �θ σ−1ð Þ

dG að ÞR ~acd~abd

rd ~abd�

a=~abd� θ σ−1ð Þ

dG að Þ þ R∞~acd rd ~abd�

Δtdð Þ− σ−1ð Þ 1−θð Þ a=~abd� θ σ−1ð Þ

dG að Þ:

The denominator was derived in Appendix A.2. The numerator is

equal to rdðacdÞðacdÞ−k

, where rdðacdÞ ¼ χσχþ1Δt

−ðσ−1Þð1−θÞd f bd . Rearranging

terms, we obtain:

ΔEXPd2 ¼ Δt− σ−1ð Þ 1−θð Þ

d

1þ Δt− σ−1ð Þ 1−θð Þd −1

� Δ f d−1

Δt− σ−1ð Þ 1−θð Þd

−1

� �θ σ−1ð Þ−kÞθ σ−1ð Þ

: ð25Þ

To see that these expressions do not depend on the assumed values

of (σ, θ, k) or relative fixed costs,Δfd, defineWd ¼ ð Δ f d−1ðΔtdÞ−ðσ−1Þð1−θÞ−1

Þθðσ−1Þ−kθðσ−1Þ

to re-write the share of containerized exports to a given destination as:

μd ¼ Δtdð Þ− σ−1ð Þ 1−θð ÞWd

1þWd � Δtdð Þ− σ−1ð Þ 1−θð Þ−1h i ;

where (Δtd)−(σ−1)(1−θ) = exp (η1)distdη2. We can expressWd as a func-tion of observables (μd, distd) and estimates of (η1, η2):

Wd ¼ μd

exp η1 �

distη2d −μd exp η1 �

distη2d −1 � :

Next, re-write ΔEXP1 and ΔEXP2 as functions ofWd:

ΔEXP1 ¼ 1þ exp η1 �

distη2d −1 �

Wd;

ΔEXP2 ¼ exp η1 �

distη2d1þ exp η1

�distη2d −1

�Wd

:ð26Þ

The expressions in (24) and (25) for the model with iceberg tradecosts become:

ΔEXP1 ¼ 1þ Δt− σ−1ð Þd −1

� Δ f d−1

Δt− σ−1ð Þd −1

!σ−1−kσ−1

;

ΔEXP2 ¼ Δt− σ−1ð Þd

1þ Δt− σ−1ð Þd −1

� Δ f d−1

Δt− σ−1ð Þd

−1

� �σ−1−kσ−1

:

It is easy to see that the expressions above can be re-written as in(26) using the equation for the share of containerized exports in (19).

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