One-o� Export Events: Some theory and

insights from monthly transactions data

Ingo Geishecker∗ Philipp J.H. Schröder† Allan Sørensen‡

PRELIMINARY and incomplete - July 2016

Abstract

An astonishing 40% of all �rm-product-destination export spells

in Danish micro-data turn out to be isolated single-month one-o� ex-

port events (observed once in a 36 month window). For the average

�rm, such one-o� exports account for 17% of total export sales. These

patterns cannot be explained by the lumpiness of trade (e.g. seasonal

shipments), nor do they sit well with available models of trade. To

reconcile the data with theory, we propose a model that introduces

reactive (i.e. buyer-side driven) one-o� exporting in addition to the

customary proactive export channel. This framework guides our em-

pirical investigation. In line with theory, we �nd that one-o� exporting

is associated with lower productivity and smaller �rm size; moreover,

it is more likely to occur for exports to far away, low income or unstable

destinations.

JEL: F12, F14, L10, D40

Keywords: Reactive exporting, proactive exporting, lumpy trade, tem-

porary trade, �rm level data, heterogeneous �rms.

∗European University Viadrina, Faculty of Business Administration and Economics,Germany. Tel.:+49 335/5534-2290, E-mail: geishecker@europa-uni.de .

†Aarhus University, Business and Social Sciences, Department of Economics and Busi-ness Economics, Denmark. Tel.: +45 87164971, E-mail: psc@econ.au.dk.

‡Aarhus University, Business and Social Sciences, Department of Economics and Busi-ness Economics, Denmark. Tel.: +45 87164989, E-mail: allans@econ.au.dk.

Acknowledgements: Ingo Geishecker and Philipp Schröder acknowledge �nancial supportfrom the Tuborg Foundation.

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1 Introduction

Two separate empirical phenomena of export patterns have emerged in recentyears. Firstly, the predominance of temporary or discontinued export spells.Secondly, the lumpiness of trade, i.e. prolonged breaks between individualshipments. The present paper uncovers an additional layer below these twophenomena, namely the surprising prevalence of isolated single month one-o� exporting episodes. Examining a total of 232,752 �rm-, commodity-,destination-speci�c export spells of manufacturing �rm in Denmark, we �ndthat over half (159,206 episodes) classify as temporary, lasting for less thanfour years. However, the lion share (93,380; i.e. 58.7%) of these temporaryexport spells are in fact one-o� export events: a single month of exportingwithin a 36 month window. Thus about 40% of all export spells that enterempirical analysis, say based on annual observations, are, at least in our data,in fact single month one-o� export transactions. Moreover, for the average�rm, such one-o� exporting accounts for 17% of their total export sales.

Despite of the presumably widespread presence of the one-o� export phe-nomenon in micro data, it is not re�ected in international trade theory. Inthe current workhorse models of heterogeneous �rms trade (e.g. Melitz, 2003;Bernard et al., 2003) �rms will conditional on their individual productivityrealization and/or other �rm characteristics, decide if (and how) to service agiven foreign market. In other words, the �rms conceptualized in the avail-able theories, would not go through the hustle of starting to export just todrop the activity after one single transaction. Yet this is exactly the dom-inant type of export spell in the data. In contrast, temporary trade, thatis short durations of export relationships � but not one-o� trade � has beensuccessfully embedded, for example by including demand uncertainty or pro-ductivity shocks, e.g. Besedes and Prusa (2006), Eaton et al. (2011), Békésand Muraközy (2012). Similar, the lumpiness of trade is readily explainedby theories of inventory management, seasonality or per-shipment costs, e.g.Alessandria et al. (2010) and Hornok and Koren (2015).

The available theories of temporary or lumpy trade have in common, thatthey focus on the proactive exporting behavior of �rms. Yet, what must bepresent in the data as well � and what could explain one-o� export events �is a certain degree of reactive exporting, say unsolicited one-o� orders fromabroad. While the seller side of an export relation has been the central fo-cus in economics, other disciplines have observed the equal importance ofthe buyer side. Export development models or exporter stages models ininternational business and international marketing research have for sometime distinguished reactive (passive) from proactive (active) exporters. Inparticular, so called `external change agents', such as foreign customers, ex-

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port/import agents, or wholesalers, rank high in explaining export initiation;see the seminal synthesis of Bilkey (1978).1 Importantly, reactive exportingepisodes require inducement from outside the �rm. Relevant cases of reactiveexporting associated with one-o� export events are for example, intermedi-aries that need to resolve an out-o� stock issue, wholesalers who continuouslyalter their product portfolio, trial and error (search) import demand or singlecustomer demand driven by a perfect match product variety.

Against this backdrop, the present paper proposes a simple extension ofthe Melitz (2003) model that includes proactive permanent exporting, proac-tive temporary exporting and reactive one-o� exporting. We allow for a widerange of �rm-speci�c and destination-speci�c heterogeneity (e.g. �rm-speci�ctransport costs). We maintain the customary proactive export decision, i.e.�rms compare the costs of exporting to the �ow pro�ts from the activity, andcapture temporary exporting by �rm-speci�c demand �uctuations. Firmsdisengage from proactive exporting once hit by a weak demand realization.In this dimension our framework mirrors models such as Eaton et al. (2011)and Nguyen (2012). Departing from existing formulations, we also introducereactive exporting. Even though a �rm has � based on its realized vectorof �rm-speci�c parameters including productivity � decided to abstain fromproactive exporting to a given destination, is may receiving an unsolicitedsmall-scale one-o� export order from that market. In this case, the �rm stillhas to decide wether or not to service the order.

The conceptual model arrives at a number of results on the selection of�rms into di�erent export patterns. First, for any given destination, proac-tive exporters are on average more productive than reactive exporters, whichagain are more productive than non-exporters. Second, for any given desti-nation permanent exporters are on average more productive than temporaryexporters. Third, for any given destination average productivity among �rmsservicing smaller one-o� export orders will in fact be higher compared to �rmsservicing larger one-o� orders. Finally, smaller markets and destinations re-quiring higher marketing costs or featuring larger �uctuations will see moreone-o� and temporary exporting.

We use this model to guide our empirical investigation. In our empiri-cal section we establish novel stylized facts on one-o� export events utilizing

1The international business and international marketing literature on reactive versusproactive exporting is truly vast. For reactive exporters one-o�, small or discontinuedorders are a frequent issue. In fact the seminal Johanson and Vahlne (1977) in developingthe so called Uppsala model trace the irregular export activity of early stages to sporadic`o�ers of demand' from abroad. In their bibliographic analysis of 50 years of businessresearch into exporting, Leonidou et al. (2010) identify that studies dealing with proactiveversus reactive export stimuli are one out of 25 major research themes.

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business account and trade data for the universe of Danish manufacturing�rms, including monthly transactions data for the period 1993-2012. In linewith our theory, we �nd that one-o� exporting is associated with lower pro-ductivity and smaller �rm size; moreover, it is much more likely to occur forexports to far away, low income or unstable destinations.

Why is a mapping and understanding of one-o� export events important?Our work can (i) assist the interpretation of disaggregated trade data, (ii)guide future theoretical developments and (iii) inform policy makers. First,our paper o�ers insights and an explanation for the presence of very shortexport spells in the data. Importantly, we pinpoint patterns in the datathat are not disclosed by annual data, but matter a great deal. In particu-lar, short export-spells found in annual data need to be carefully interpreted,since some of those observations could be singular one-o� export events. Sec-ond, increased attention to the buyer side of the export relation appears animportant alley for future theoretical developments. Our results suggest thatreactive exporting is potentially driving part of the patterns found in data.Finally, policy design needs to acknowledge the prevalence of one-o� exportevents. Knowledge of the particular microstructure of exporting has implica-tions for whether and which policies will trigger lasting export relationships,and possibly alter our understanding of the gains from trade. Export ini-tiation through promotion programs might not always have a lasting e�ect,i.e. long term monitoring of participating �rms is essential. Moreover, tradefacilitation should be tailored and di�erentiated when aiming at the exportrelations seller or buyer side, respectively. Finally, promotion programs thataim at far away and volatile markets might be particularly prone to triggeringdisappointing singular export events with little lasting impact.

Even though the present paper with its application of monthly transac-tions data at the �rm-product-destination level is the �rst to pinpoint theprevalence of one-o� export events, there are a number of important previousworks. Exemplary for a closely related literature on the duration of exportrelationships are Besedes and Prusa (2006a,2006b and 2011). These papershave � inter alia � pinpointed the role of destination market characteristics� a dimension we accordingly also explore in the current paper. Yet theirworks are based on country-pair annual data at the product level and not�rm-product-destination level monthly data. Monthly transaction data isemployed in the afore mentioned Hornok and Koren (2015) and Allessandriaet al. (2010) to address the lumpiness of trade, focusing on delivery lagsand transport technologies.2 However, these works do not include the �rm

2The application of monthly data is not unusual in macro-type studies, for examplesearching for the pass-through of shocks. But these applications are unrelated to the

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dimension, but focus instead at the product-destination level.The papers closest in spirit to the current work are perhaps Békés and

Muraközy (2012) and Gullstrand and Persson (2015) since they examineexport spells at the �rm-product-destination level and propose theoreticalextensions to match the data. In fact the current paper applies the �lteringmechanism proposed by Békés and Muraközy (2012), in order to distinguishbetween permanent export-spells (de�ned as having durations of four yearsor longer) and temporary trade (spells up to three years). Moreover, they�nd in annual Hungarian data that a large fraction of export spells are tem-porary, a �nding that we replicate in the Danish data. Based on their �nd-ings Békés and Muraközy (2012) propose a model to explain the signi�cantshare of temporary trade spells by time-varying �rm productivity combinedwith an endogenous choice of trade technology. More recently, Gullstrandand Persson (2015) formalize the idea that proactive exporting �rms can en-dogenously decide on core and peripheral markets, depending on the sunkcosts they spend. In peripheral markets �rms will more readily exit fromexporting. They con�rm the implications of their model with annual �rm-product-destination data for the Swedish food sector. We go beyond boththese papers by evoking monthly transaction data, which allows us to uncov-ers the prevalence of one-o� export events. In addition, to reconcile existingtheory with this new empirical phenomenon we propose a model extensioncapturing reactive exporting.

The remainder of the paper is structured as follows. Section 2 gives a�rst look at the data and maps the prevalence of one-o� exporting. Sec-tion 3 presents the conceptual model based on a partial equilibrium versionof the Melitz (2003) model augmented with reactive exporting, and arrivingat permanent, temporary and one-o� exports. We use the model to guideour further empirical investigation in Section 4. We examine a wide rangeof destination characteristics and �rm characteristics associated with one-o�exporting. Section 5 concludes.

2 A First Look at the Data

Our data consist of Danish �rm-level register data and business accountinformation for the years 2001 to 2012 provided by Statistics Denmark. Thesedata are merged with monthly destination- and commodity-speci�c exportinformation for each �rm which are available for the years 1993 to 2012.Starting from the universe of all Danish �rms, we exclude non-manufacturing�rms and �rms with missing sales or minimum sales in the sample period

questions addressed in the current paper and du not use �rm-level monthly data.

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below DKK 100,000 (about USD 18,000). Firm-level export informationby destination, goods-type and year is obtained from the External trade ofDenmark database which essentially covers all measurable export events ofDanish �rms. In combination with monthly transaction data we are able todistinguish one-o� exports from temporary exports, i.e. short-run destinationspeci�c export spells. In particular we apply the de�nition of temporaryexports developed by Békés and Muraközy (2012), i.e. export spells of up tothree successive years.

In order to study true temporary and one-o� exporting we constructa balanced �rm-sample for the years 2003 to 2011, excluding exiting andentering �rms. Since monthly destination- and commodity-speci�c exportinformation is available for all exporting �rms since 1993 left truncation ofexport spells is not a relevant issue for the present analysis. To avoid right-truncation we must observe at least one full year in the data after an exportspell has potentially ended. Since the last match between �rm-level registerdata and monthly export data is possible for the year 2012, our balancedsample thus ends in 2011.

The resulting sample consists of n = 5496 surviving �rms, of which nX =3022 at some point over the period 2002 to 2011 export. For each �rmwe de�ne export spells drawing on the respective export destination andtwo-digit Harmonized System (HS) product classi�cations as reported in the�rm-level External trade of Denmark database. Following the methodologyproposed in Békés and Muraközy (2012) we start by classifying an exportspell as permanent when the commodity-destination-speci�c export activitytakes place for more than three years in a row. Using our annual trade datafor this steps circumvents the issues associated with the lumpiness of trade.Following the same logic, commodity-destination speci�c export events thatonly occur for up to three years in a row are de�ned as temporary.3 Di�erentfrom Békés and Muraközy (2012) export spells are not assessed at the six-digit but at the two-digit HS level. This makes our de�nition of termination ofan export spell somewhat more lenient. Product switching in an establishedexport destination that would count as a discontinued export activity at a�ner aggregation level are at the two-digit level still counted as permanent.For example, a shoe producer that ships to the same destination, but switches

3Our monthly export data allows for alternative de�nitions of temporary exports bydirectly measuring the export spell length in months. However, due to the lumpiness oftrade, export activities frequently are interrupted for several months, for instance due toa summer holiday break or inventory management and shipment constraints, resultingin extremely short export spells. Allowing for an up to 11 months pause between �rm-product-destination export events would come close to the de�nition of permanent andtemporary based on annual data.

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the exported product from waterproof footwear to shoes with uppers madefrom textile will be recorded as a continuing exporter at the two-digit HSlevel but not at the six-digit HS level.

Going beyond existing research we search for one-o� export events in thedata, i.e. we further di�erentiate temporary exports by using monthly as op-posed to yearly export information. We classify a �rm-product-destinationexport episode as a one-o� export event when there is only recorded one sin-gle month export transaction within three successive years. More precisely,a �rm-product-market transaction that we have observed only once in oneyear, and not the previous or subsequent year. Thus these one-o� transac-tions are sandwiched between a minimum of 35 month of non-exporting, ofwhich at least 12 month of non-exporting have taken place either before orafter we observe the transaction. These rules eliminate even the most ex-treme sporadic export patterns that are known from the lumpiness of tradeliterature (i.e. annual or seasonal shipments), and leave us with true one-o�export episodes. To be clear, these spell de�nitions purposefully ensure thata single year export observation that is composed from two separate monthof export transactions is still labeled as a temporary export spell.

In sum: apart from balancing our panel we have maintained all of thecharacteristics of the export data, keeping it fully comparable to data-setsused in previous research, i.e. allowing us to distinguish permanent from tem-porary exports. In addition, we have added the monthly export transactionsdimension which permits identi�cation of one-o� export episodes. Table 1displays the surprising results of a simple data count.

Table 1: Firm-product-destination export spells by category

Total Permanent Temporary One-o�excl. one-o�

Number 232,752 73,546 65,826 93,380Per cent - 32% 28% 40%

Notes: Permanent: spells of 4 or more years; Temporary: spells of 3, 2 or 1year length; One-o�: an isolated one-month-only export transaction within athree year period. See the main text for details on the spell de�nitions.

Of the total 232,752 �rm-, commodity- and destination-speci�c exportspells in our data, 159,206 (= 65,826 + 93,380) would be classi�ed as tempo-rary if one had to rely on annul data. Yet, consulting monthly data we �nd,

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that in fact 93,380 of these spells are one-o� export events. Thus, about 40per cent of all export spells in the data, are in fact one-o�, i.e. only occuronce in a single month within a three year time span.

We expect that the mechanisms driving such one-o� export events mustbe di�erent from the pro-active exporting that is usually pictured wheneconomist think about the export activity of �rms. In particular, we sus-pect that the buyer-side may be part of the cause for the high frequency ofone-o� exporting in the data, i.e. that �rms apart from proactive export-ing also experience reactive exporting, for example unsolicited orders fromabroad. Before we dive deeper into mapping the empirical phenomenon ofone-o� export events, we introduce a simple heterogeneous �rms frameworkaugmented to include reactive one-o� exporting. This model will structureour further empirical investigation.

3 A Conceptual Model of Proactive and Reac-

tive Exporting

Consider a standard heterogeneous-�rms trade framework of the Melitz(2003) type. Prior to entry a �rm, i, invests in a R&D activity which resultsin a blue-print for a �rm speci�c variety and a random vector of �rm-speci�cparameters γi = (φi, Fi, τi, Fx,i, Fm,i) where φi is productivity, Fi is �xed pro-duction costs, τi is a vector of destination speci�c iceberg trade costs, Fx,i isa vector of destination speci�c �xed export costs other than marketing costs,i.e. costs such as product adaption to the market that both proactive andreactive exporters have to endure and Fm,i is a vector of destination speci�cmarketing costs, i.e. the costs associated with proactive entry into an exportmarket. We assume that the �rms stochastic parameters are drawn inde-pendent from each other. Note that the assumed cost structure implies that�rms decisions to enter each of the potential export markets are independentfrom each other.4

Consider �rm i with productivity φi and its export decision regardingexport destination k at time t. The �rm may serve the market proactivewhich requires the �rm to pay both the �xed costs of exporting F k

x,i and the�xed costs of marketing F k

m,i. The pro�ts from this export mode read

πki,t,x−pro = Bk

t φσ−1i

(τ ki)1−σ − F k

x,i − F km,i (1)

4At the loss of generality we could impose more structure on the relations of the stochas-tic parameters, such that for example hierarchies of market entry, or similar stylized factscould be captured, see Eaton et al. (2011).

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where Bkt is a destination-speci�c time varying demand component and σ > 1

is the elasticity of substitution between any two goods.5 In particular, thetime changing Bk

t allows us to capture the idea that proactive exporters maystart or discontinue export spells depending on changing demand conditions,such that our speci�cation allows for permanent and temporary proactiveexporters. This feature mirrors the formalizations in Békés and Muraközy(2012) and Gullstrand and Persson (2015), albeit their speci�cations buildon di�erent mechanisms. In in Békés and Muraközy (2012) a central driveris time changing �rm productivity, where temporary exporters are those thatstop exporting after having received a negative shock to their productivity.In contrast, Gullstrand and Persson (2015) model the option value of enteringan export destination, and the uncertainty of future returns.

Changing demand, i.e. the model mechanism we employ, can be viewedas the summation of various events that change exporting conditions, such aspayment risks, taste changes, business cycle developments, i.e. events thatwould force a �rm to stop exporting to a speci�c destination.6

In addition to the proactive export mode giving access to the the entireforeign market, there is a chance of reactive exporting. We model this buyer-side of the export relation with a simple version of an external change agent,championed in the International Business and International Marketing liter-ature discussed in Section 1. In particular, we assume that foreigners (saydistributors) may approach the �rm and place an unsolicited export order.This occurs with probability zk > 0 which we assume to be exogenous. Inthat case the �rm still has to decide if it wants to service such one-o� order,since it faces the �xed costs of exporting F k

x,i although it does not incur thecosts of marketing the product, F k

m,i.7 To capture the idea that buyer-driven

reactive exporting only represents one or a few consumers � compared to thenumber of consumers reached when the �rm engages in proactive exportingwith a complete marketing/distribution network at cost F k

m,i - we assumethat �rms when receiving such external-to-the-�rm generated orders onlyface a fraction ρki,t of the consumers they would reach through the proactiveexport mode, where ρki,t ∈ (0, 1) is a stochastic variable being unknown when

5The functional form of the pro�t expression comes from an underlying CES demandstructure. The time-variation in Bk

t could be driven by business-cycle �uctuations orexchange rate shocks. Note that although Bk

t is endogenous in general equilibrium it isexogenous to the individual monopolistic �rm.

6Obviously, changes in demand could also stem from a changing competitive envi-ronment, were new �rms take customer shares from incumbent �rms, see Schröder andSørensen (2012) for a dynamic version of a Meltiz (2003) model along those lines.

7In this situation, it will not be worthwhile for the �rm to engage in �nding a secondcostumer in the destination, unless F k

m,i is very low.

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the �rm decides whether to engage in proactive export.8 The pro�ts fromreactive exporting read ρki,tB

kt φ

σ−1i

(τ ki)1−σ − F k

x,i. A �rm only services suchone-o� foreign order if it earns positive pro�ts from doing so. Positive pro�tsoccur once the fraction of consumers served in an unsolicited order is abovethe threshold share given by ρ̂ki,t ≡

Fkx,i

Bkt φ

σ−1i (τki )

1−σ . The expected �ow pro�ts

from reactive exports thus become

πki,t,x−re = zk

∫ 1

ρ̂n,ki,t

(ρBk

t φσ−1i

(τ ki)1−σ − F k

x,i

)dHk (ρ) , (2)

where Hk (ρ) is the cumulative distribution function.Despite this fairly general formulation, and without any additional struc-

ture on the model, we can make the following observations

∂πki,x−pro

∂φσ−1i

= Bkt

(τ ki)1−σ

>∂πk

i,x

∂φσ−1i

= Bkt

(τ ki)1−σ

zk∫ 1

ρ̂ki,t

ρdHk (ρ) > 0, (3)

∂ρ̂ki,t

∂φσ−1i

< 0 (4)

and∂ρ̂ki,t∂F k

x,i

> 0 and∂ρ̂ki,t∂τ ki

> 0. (5)

The inequalities in (3) state that in any given export destination �ow pro�tsfrom proactive exporting increases faster with productivity than expectedpro�ts from reacting on one-o� export orders. Hence, when a �rm is suf-�ciently productive it chooses the proactive export mode despite the larger�xed costs of doing so. The observations in (4) and (5) state that the re-quired size of an order (the fraction of consumers (ρki,t)) that is needed inorder to pro�table respond to unsolicited export orders from a given exportdestination, decreases with productivity and increases in �rm-destinationspeci�c trade costs. The thus extended framework, maintains all the wellknow properties of the Meltiz (2003) model, as well as standard � empiricalrelevant � extensions, such as asymmetric markets. For example, in the aboveformulation more productive �rms export (on average) to more markets.

8Note that ρki,t could also capture that some "rents" that are transferred through e.g.double mark-up pricing to the local agent (e.g. a wholesaler) responsible for facilitat-ing/initating the one-o� trade relation. Moreover, we implicitly assume that foreignersfrom country k will not place unsolicited orders with �rms that proactively have estab-lished a marketing presence in country k.

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Of particular interest for the present paper are the insight concerningreactive one-o� exporting. Based on these observations we can state thefollowing results.

Result 1. Firms servicing one-o� export orders from market k are on aver-age more productive than �rms not exporting to market k.

Result 2. Proactive exporters to market k are on average more productivethan exporters servicing one-o� export orders from market k.

Result 3. Among the proactive exporters on market k prior to time t, itapplies that for any reduction in market demand Bk

t at time t, the �rmscontinuing to export (permanent exporters) are on average more productivethan those �rms discontinuing their export activity (temporary exporters).

Result 4. Among all �rms servicing one-o� export orders from market k,the �rms ful�lling smaller orders (smaller consumer shares, ρki,t), have onaverage higher productivity than the �rms servicing larger one-o� orders.

Result 1 extends the standard ranking of exporters versus pure domestic�rms, to the case of reactive exporting. The underlying mechanism � fo-cusing on the dimension of �rm productivity alone � is that the presence of�xed export costs, F k

x,i, forces low productivity �rms to reject one-o� orders.Result 2 establishes a new ranking between proactive and reactive exporters.Result 3 provides a ranking of permanent and temporary exporters, driven bythe presence of �xed marketing costs, F k

m,i, and mirrors the ranking derivedby Békés and Muraközy (2012) in their model with �rm-speci�c productivityshocks. Finally, Result 4 states that �rms have to be su�ciently productiveto pro�t from a given one-o� order. Thus, within the group of �rms reactingto one-o� export opportunities the most productive are more likely to alsorespond to smaller orders (involving a smaller portion of the consumers inthe destination market).

Figure 1 summarizes the above results, for the special case where �rmsare kept homogenous in all dimensions except for productivity, φ, and thecustomer share ρ of an unsolicited export order. ALLAN: WE NEED THEFIGURE REDONE TO READ "REACTIVE ONE-OFF EXPORTERS" IN-STEAD OF "UNSOLICITED EXPORTERS" - I BELIEVE YOU GOT THEFILE.

Albeit tempting and intuitively compelling, one cannot infer a generaland clear relation between exporter productivity premia and the degree ofreactive exporting from the fairly general model above. The relation may benon-monotone as the number of markets served is endogenous and dependson productivity. As productivity increases it becomes more likely that a �rm

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Figure 1: Export mode by customer share and productivity

serves a given market via proactive exporting. However, at the same time thehigher productivity makes one-o� export orders more pro�table and may inturn increase the number of markets served by the reactive export mode. Toarrive at unambiguous predictions one would need to put signi�cantly morestructure on the model, not least concerning the distribution of the attrac-tiveness (and thus hierarchy) of the various markets (see e.g. Lawless, 2009or Eaton et al., 2011). For our purpose, however, the model is fully su�cientto guide our empirical research design, allowing us to provide some �rst em-pirical evidence, proposing a distinction of export episodes into permanent,temporary and one-o� exports.

4 Empirical Analysis

The above model gives several directions for empirical investigation. Firstly,destination characteristics (that will a�ect the market speci�c costs of ex-porting) must be examined � this also mirrors the approach followed in thelumpiness of trade literature (REF). Secondly, we will address the preva-lence and volume of one-o� exporting events at the �rm-level. Finally, weprovide evidence on the characteristics, i.e. productivity, of �rms that aremore heavily engaged on one-o� exporting, or temporary and permanentexporting respectively.

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4.1 Destination-level Analysis

Once export spells are classi�ed as one-o� export events (see Section 2 for afull description of the data and spell de�nitions) one can assess the geographicdistribution and analyse destination-speci�c determinants of one-o� exports.Exporting �rms on average serve a total of 20 di�erent destinations between2002 and 2011, 34 per cent of which, however, are solely served throughone-o� exports. At the same time, there are marked di�erences in the setand relative importance of export destinations for one-o� vs. permanentexports. This becomes clear when looking at the Spearman rank correlationcoe�cient for one-o� and permanent export volumes to overlapping exportdestinations obtained by ranking export destinations according to their one-o� and permanent export volumes separately for each individual �rm. Overthe years 2002 to 2011 the Spearman rank correlation coe�cient betweenone-o� and permanent exports across all �rms is only 0.11. Thus, the set ofdestinations with high export volumes for permanent exports is very di�erentfrom the set of export destination with high one-o� export volumes.

We proceed by constructing destination speci�c indices for the relativeimportance of one-o� exports based on their share in all export spells towardsa given destination (Φ) and, respectively, their relative export volume (Υ):

Φd =

∑s∈Sd∩Sre

1∑s∈Sd

1(6)

Υd =

∑s∈Sd∩Sre

exs∑s∈Sd

exs

(7)

with s representing a �rm-commodity-destination speci�c export spell, Sre

the set of all one-o� export spells and Sd the set of all export spells belongingto destination d. The volume of a speci�c export spell is denoted as exs.

Figure 2 depicts the geographic distribution of one-o� export events. Wemap the destination speci�c share of one-o� export spells Φd for each of the217 export destinations of Denmark. While for half of all export destinations,the share of one-o� export spells is higher than 55 percent it is particularlyhigh for parts of Central and South America, Africa, the Middle East andPolynesian micro states. In comparison, Danish exports to the EuropeanUnion � Denmark's main trading partner � are much less likely to be one-o�. Still, even for EU 15 exports the share of one-o� export spells still is asurprising 25 per cent.

Turning our attention to the role of one-o� exports in the destinationspeci�c export volume Υd, Figure 3 reveals that for most export destinations

13

one-o� exports matter only little. For the 217 Danish export destinationsthe median share of one-o� exports in total export volumes is 20 per cent.However, for some export destinations that are either very small and far awaysuch as The Federal States of Micronesia and/or haunted by continuous warand con�ict such as Iraq, to pick some extremes, one-o� exports may accountfor 100 percent of the value of all exports to these destinations.

14

Figure2:

Theshareofone-o�exportevents

inallexportspells,bydestination

(90,

100]

(80,

90]

(70,

80]

(60,

70]

(50,

60]

(40,

50]

(30,

40]

(20,

30]

(10,

20]

[0,1

0]

15

Figure3:

Theexportvolumeofone-o�exportevents

intotalexports,bydestination

(90,

100]

(80,

90]

(70,

80]

(60,

70]

(50,

60]

(40,

50]

(30,

40]

(20,

30]

(10,

20]

[0,1

0]

16

According to our theory from Section 3, exports to small far away desti-nations are, everything else equal, more prone to be discontinued. With high�xed exports costs or a small customer base even relatively small shocks maysu�ce to render exports to these destinations unpro�table. In addition, po-litical instability and con�ict give rise to potentially large demand and cost�uctuations. At the same time, uncertainty concerning true export costs andtrue demand may be particularly high for less obvious export destinations.This makes a testing the waters approach both on the customer side and theseller side more relevant. Thus in addition to uncertainty and shocks thatend proactive export episodes prematurely, our theory suggests that reactiveone-o� exporting will be highly important in such destination.

To analyze the determinants for one-o� exports more systematically weestimate variants of a simple descriptive model respectively regressing thedestination-speci�c share of one-o� exports in all export spells of industryj 9 and the share of one-o� exports in the total export volume to a given des-tination within industry j 10 on various destination-speci�c characteristics.This simple empirical model can, thus, be seen as a reduced aggregated formof our theoretical framework. Destination-speci�c demand (market size) isoperationalised by log destination country GDP (GDPd). Fixed marketingcosts, that conditional on customer base are decisive for whether a market isserved proactively or through reactive exports are approximated by log dis-tance (distd), as well dummies for common language (D : cld). Furthermore,regional trade agreement (D : rtad) and destination country membership inthe World Trade Organisation (D : wtod) as well as an industry �xed e�ects(αj) are included.11 Finally, shocks that may end otherwise continued proac-tive export episodes are modelled through controlling for political stabilityand violence in a speci�c destination drawing on the Worldwide GovernanceIndicator database (see Kaufmann, et al. 2010). A higher index value forthe variable PS implies a more stable environment.12 The corresponding

9More formally the industry-level one-o� export spell share is constructed as Φdj =∑s∈Sd∩Sre∩Sj

1∑s∈Sd∩Sj

1 with Sj denoting the set of all export spells belonging to industry j.

10Υdj =

∑s∈Sd∩Sre∩Sj

exs∑s∈Sd∩Sj

exs

11The respective control variables were obtained from the CEPII gravity database andupdated for the years 2007 to 2011 drawing on data from the World Bank, the UN, andthe WTO. We collapse our data to one observation per industry and destination yieldinga total of 3380 destination-industry-level observations. Accordingly, destination countryGDP is averaged over the period 2001-2011. All dummy variables take the value one if inthe period 2001 to 2011 they take the value one at least once.

12Since country coverage is somewhat smaller in this data base - we particularly lackinformation for a number of micro states - model speci�cations with the political stabilitycontrol are only estimated with 3351 observations.

17

regression equation with ξdj to be assumed i.i.d is:

Φdj|Υdj = αj + β lnGDPd + γ ln distd (8)

+ ηD : rtad + ϑD : wtod + κPSd + ξdj

.Table 2 shows that the one-o� spell share Φ and one-o� export volume

share Υ decrease in market size of the export destination and increase in dis-tance. Furthermore, the importance of reactive one-o� exports vs. proactiveexports is lower for export destinations that share a regional trade agree-ment or that are part of the WTO. This is in fact in line with our theoreticalprediction that lower demand and/or higher marketing costs render reac-tive one-o� exports relatively more pro�table. Furthermore, we also see thatone-o� exports are the less important the more stable and the less violent anexport destination is - a result well in line with the model's implication thatwith higher marketing costs reactive exports should gain importance.

We also �nd interesting di�erences in the magnitude and statistical signif-icance of coe�cients of determinants when explaining the relative frequencyof one-o� export events compared to the relative size of one-o� export vol-umes. This highlights the importance of di�erentiating between the extensiveand intensive margin of exports: As is already apparent from visual inspec-tion of the maps in Figures 2 and 3, one-o� exports, despite the prevalenceof the phenomenon, account for comparatively little of aggregate exports inmost destinations. Namely, Φd shows much less variation than Υd. Thus,regarding the proliferation of one-o� export events (its extensive margin),destination speci�c determinants as featured in Table 2 have less variation toexplain which should imply a lower magnitude of corresponding coe�cients.When looking at the share of one-o� exports in total export volume instead(Υd), we see that it generally responds much stronger to destination speci�ccharacteristics; possibly with the exception of distance. This is so, becausethis measure does not only re�ect the extensive margin of one-o� exportsbut also the intensive margin � in particular the sizable intensive margin ofpermanent exports (see Table 2, columns II and IV). More attractive exportmarkets with a larger customer base (re�ected in destination GDP) and/orwith lower �xed marketing costs (re�ected in lower distance and liberalizedtrade) are associated with a higher intensity of permanent exports amplify-ing the e�ects along the extensive margin captured in columns I and III ofTable 2. This corresponds to our theoretical framework, which conjecturesthat, conditional on customer base and everything else equal, lower market-ing costs will render the permanent proactive export mode relatively more

18

Table 2: Destination determinants of unsolicited export shares

(I) (II) (III) (IV)Φdj Υdj Φdj Υdj

lnGDPd -3.051*** -7.745*** -3.072*** -7.867***-0.18 -0.265 -0.182 -0.268

ln distance 4.357*** 4.314*** 4.165*** 4.279***-0.644 -0.946 -0.649 -0.953

D : rtad -6.970*** -10.748*** -6.325*** -9.903***-1.285 -1.888 -1.302 -1.913

D : wtod -4.845*** -6.364*** -4.233*** -5.603***-1.013 -1.489 -1.031 -1.515

PS -1.489*** -1.961***-0.434 -0.638

Constant 63.544*** 84.259*** 64.621*** 84.707***-5.93 -8.714 -5.946 -8.738

Observations 3,380 3,380 3,351 3,351R2 0.226 0.339 0.221 0.338

Notes:*,**,***Statistically signi�cant at the 10 percent, the 5 percent, the 1percent level, respectively. Standard errors in parentheses. All models controlfor industry �xed e�ects.

pro�table while high marketing costs foster reactive exporting as the modusoperandi.

4.2 Firm-Level Analysis of One-o� Exports

Based on the classi�cation of an export spell as reactive one-o� we can col-lapse all observed export spells and associated volumes into �rm speci�cshares of one-o� export spells and volumes over the period 2002 to 2011. Ac-cordingly, our �nal collapsed export related data consist of one observationper �rm. The two continuous measures Φi and Υi capture the importanceof reactive one-o� exporting for �rm i expressed in relation to the overallnumber of its export spells and its overall export volume respectively:

19

Φi =

∑s∈Si∩Sre

1∑si∈Si

1(9)

Υi =

∑s∈Si∩Sre

exs∑s∈Si

exs

(10)

with s representing a �rm-product-destination speci�c export spell, Sre

the set of all one-o� export spells and Si the set of all export spells belongingto �rm i. The volume of a speci�c export spell is denoted as exs.

As reported in Table 3 we �nd that 1nX

∑iΦi = 0.48, i.e. reactive one-

o� exports make up 48 per cent of an average �rm's export spells. Thiscorresponds to 1

nX

∑iΥi = 0.17, i.e. 17 per cent of an average �rm's over-

all export volume are accounted for by one-o� export episodes. These aresurprising �gures suggesting that reactive one-o� exporting indeed is an im-portant �rm-level phenomenon.13

To compare the prevalence of one-o� exports to that of temporary ex-ports as identi�ed by Békés and Muraközy (2012) we calculate the share oftemporary exports in �rm's export spells Λi and the respective export vol-ume share Θi. Naturally, one-o� exports are nested in Λi and Θi. Table 3therefore reports the respective �gures net of one-o� exports: Λi − Φi andΘi −Υi.14

For the average �rm temporary export spells excluding one-o� exportevents account for 29 per cent of all export spells. Accordingly, in terms ofprevalence one-o� exports dominate. Combining one-o� export spells withtemporary exports excluding one-o� exports accounts for about 77 percentof all export spells for the average �rm. This �gure is comforting similar tothe one reported in Békés and Muraközy (2012). In terms of export volumeshare temporary exports net of one-o� exports account for about 19 per centof the average �rm's export sales and thus are roughly on a par with one-o�exports.

13To rule out that these �gures are driven by sporadic exports of capital goods, whichmay be of particular relevance for small exporters, we identify capital goods exports at the8-digit level of the Combined Nomenclature and disregard them for the construction of Φand Υ as a robustness test. When doing so the mean of Φi is raised to 59 per cent andthe mean of Υi increases to 51 per cent. Furthermore, all descriptive �ndings presented inwhat follows remain essentially unchanged. We can conclude that sporadic capital goodexports do not drive results.

14Λi =∑

s∈Si∩St1∑

si∈Si1 and Θi =

∑s∈Si∩St

exs∑s∈Si

exswith St denoting the set of temporary exports.

20

The surprising prevalence and importance of one-o� export events at the�rm level clearly warrants additional investigation. In principle isolated sin-gle month exporting could be the result of proactive exporting being discon-tinued within the �rst month of transaction. This could be due to unexpectedcost spikes or negative productivity or demand shocks. However, we wouldexpect such shocks for each �rm to be evenly distributed across time. Thus,one would not observe a high frequency of spells ending exactly within onemonth. Our descriptive �ndings show the opposite, with 1

nX

∑iΦi = 0.48

about half of all export spells last only one month.Another explanation of our �ndings could be based on proactive exporters

that are testing the waters. The latter being pictured as a situation where�rms have uncertainty about the actual demand their products face and theactual exporting and marketing costs to a given destination. As a conse-quence when confronted with actual demand and cost �gures �rms may pullout of pro-actively served export markets ending the respective export spell,see e.g. Nguyen (2012) or Albornoz et al. (2012). Let us consider this possi-bility in more detail: Our calculations show that the average exporting �rmin our sample simultaneously serves 25 product-destination markets (the me-dian is 8) at any given year. Of all product-destination markets on average22 per cent are served exclusively through one-o� exports. Thus, to be con-sistent with the idea that the singe month one-o� export events found in thedata are in fact proactive exporters testing the waters, it would need to betrue that almost a quarter of the markets a �rm attempts to serve revealthemselves as being less attractive than expected. On average this seems tobe a fairly high proportion of wrongly assessed market opportunities. Fur-thermore, it is hard to accept that on average 17 per cent of a �rm's exportvolume and associated (arguably proportional) export e�orts are directed topro-actively unlocking new export markets which, ex-post, turn out to beinfeasible.

This hints at a potentially important role of reactive exporting. The viewthat a considerable degree of reactive exporting is taking place at the �rmlevel is further strengthened by disentangling the product and destinationmargins of exports. On average, exporting �rms in our balanced sampleexport 9 di�erent products (HS, two-digit) between 2002 and 2011. However,from the set of products ever exported by a �rm on average 45 per centare exclusively exported through one-o� exports. To bring this in line withan explanation based on proactive temporary exporting (see Section 3) themajority of all newly introduced export products would actually have to behit by unfavorable shocks or ex-post would reveal themselves as unfeasiblefor exporting to a given destination. Again, one average this would imply animplausibly bad judgement of actual market opportunities by �rms.

21

Against this backdrop, the view that a sizable share of the export activitymay in fact be reactive exporting, i.e. responding to buyer generated one-o�demand, seems plausible and in line with the data. Naturally, this does notreplace the proactive exporting mode that is customary pictured in currenttrade theories. On the contrary, our model in Section 3 shows that proactiveexport modes and reactive exporting can be simultaneously included in theworkhorse model of heterogenous �rms trade.

Table 3: Descriptive Statistics

Mean SD Bottom Decile Median Top Decile

Φi 0.48 0.24 0.25 0.44 0.82

Υi 0.17 0.31 0.00 0.02 0.79

Λi − Φi 0.29 0.19 0.00 0.27 0.50

Θi −Υi 0.19 0.28 0.00 0.04 0.69

4.3 Firm-level Stylized Facts

In the following section we relate �rm-characteristics to one-o�, temporary,permanent and non-exporting as suggested by the theory proposed in Sec-tion 3. We focus on the economically meaningful and important exportvolume share, i.e. how much of a �rm's total exports are generated by, forexample, reactive one-o� exporting. Results for the spell share, say the shareof one-o� export spells in a �rm's total number of export spells are similar.A brief example is shown at the end of the section.

Our theoretical framework (Results 1 to 4) suggests that proactive ex-ports would be associated with larger �rm size and higher productivity thanreactive exports. At the same time proactive exports that are temporary areexpected to be associated with smaller �rm size and lower �rm productivitythan permanent proactive exports. But what does the data actually say?

As previously explained, we collapse all observed export volumes into �rmspeci�c shares of one-o� volumes over the period 2002 to 2011. Similarly we

22

calculate the respective volume shares for temporary exports (excluding one-o� exports). According to Equation 10 Υi captures the importance of one-o�exports for �rm i expressed in relation to the �rm's overall export volume.In the same fashion Θi −Υi captures the export volume share of temporaryexports net of one-o� exports.

For the following empirical analysis we retrieve value added, full-timeequivalent employment and domestic sales information from �rm-level busi-ness accounts and combine them with the collapsed �rm-level export data.

To assess the association of �rm characteristics and the intensity withwhich �rms engage in one-o� exports, we estimate variants of the followingsimple descriptive model:

lnYi 2002 = αj + δYEXi + υYEXi ×Υi (11)

+ λYEXi × (Θi −Υi) + ϵi,

with lnYi 2002 representing start of sample �rm characteristics, namely logvalue added per worker and log domestic sales. The dummy variable EXtakes the value one if at any time during the sample period the �rm has beenan exporter. Industry �xed e�ects αj with i ∈ j control for potentially corre-lated industry-speci�c unobserved characteristics. The remaining error termϵi is assumed to be i.i.d. Recall that all �rm and time speci�c observationsare collapsed into one observation per �rm. This avoids the complexities oftime changing �rm-speci�c shares of one-o� and temporary export volumes.

On the basis of the so obtained parameter estimates we can calculate thepercentage di�erences between exporters and non-exporters with respect totheir start of sample productivity (value added per worker) and domesticsales. These percentage di�erences do now depend on Υi as well as Θi.

(Y EX=12002

Y EX=02002

− 1

)= exp (δY + υYΥi + λY (Θi −Υi))− 1

Table 4 reports exemplary calculations for the bottom decile, median andtop decile of Υ and Θ−Υ.

First turning to labour productivity as measured by value added perworker. We �nd a concise sorting pattern. As expected, exporters in oursample are signi�cantly more productive than non-exporters. However, theexporter productivity premium is strongly associated with the predominantexport mode of the �rm. Exporters with predominantly permanent exports,i.e. exporters in the bottom decile of Υ and (Θ−Υ) are 40 percent more pro-ductive than non-exporters. To the extent that the share of one-o� exports

23

Table 4: Exporters vs. Non-Exporters depending on one-o� and

Temporary Export Volume Shares, in per cent

Υi

(Θi −Υi) Bottom Decile Median Top Decile H0 : Bottom = Top

(I) (II) (III)Labour Productivity

Bottom Decile 40.05 38.96 22.29 F=36.17***( 2.44 ) ( 2.35 ) ( 2.76 ) p=0.00

Median 39.36 38.28 21.69 F=36.21***( 2.39 ) ( 2.31 ) ( 2.73 ) p=0.00

Top Decile 14.57 13.68 0.05 F=36.76***( 2.79 ) ( 2.75 ) ( 3.01 ) p=0.00

H0 : Bottom = Top F=71.98 *** F=72.21*** F=73.41***p=0.00 p=0.00 p=0.00(I) (II) (III)

Domestic Sales

Bottom Decile 353.10 347.43 264.40 F=4.06**( 38.04 ) ( 36.50 ) ( 39.72 ) p=0.04

Median 347.75 342.15 260.10 F=4.07**( 37.14 ) ( 35.62 ) ( 39.07 ) p=0.04

Top Decile 179.32 175.82 124.64 F=4.12**( 32.88 ) ( 32.17 ) ( 32.68 ) p=0.04

H0 : Bottom = Top F=18.17*** F=18.38*** F=17.90***p=0.00 p=0.00 p=0.00

Notes:***Statistically signi�cant at the 1 per cent level. Υ and Θ denote the one-o� andtemporary export volume shares, respectively.

increases this productivity premium signi�cantly falls as becomes apparentby moving down Column (I) and by looking at the Wald test comparing thebottom and top decile of Υ in Table 4. All other things equal, exportersat the top decile of Υ, i.e. �rms with the highest proportion of one-o� ex-ports on average are only 14% more productive than the control group ofnon-exporters. At the same time, when the share of temporary exports netof one-o� exports (Θ−Υ) increases, the exporter productivity premium fallseven further: Moving from left to right in Table 4 and looking at the Waldtests comparing the exporter premium for the bottom decile of (Θ − Υ) tothe top decile one sees that regardless of the share of one-o� exports the ex-porter premium declines the higher the share of temporary exports are. Atthe top decile of Υ and (Θ−Υ), i.e. �rms that hardly have any permanent

24

export relations, there is no exporter productivity premium left. For thisgroup of �rms exporters and non-exporters are equally (un)productive. Thesame pattern holds with respect to �rm size as captured by domestic sales. Itis the largest �rms that select themselves into predominantly permanent ex-ports while less productive �rms have a higher proportion of reactive one-o�and interrupted proactive exports. As reported in the lower panel of Table 4�rms in the bottom decile of Υ and (Θ − Υ) are about 353 per cent largerthan non-exporters, a size advantage that drops to 125 per cent when movinginto the top deciles of Υ and Θ−Υ.

These �ndings mirror in fact our theoretical insights developed in Sec-tion 3. For example, according to Result 2 one would expect reactive one-o�exports are associated with lower �rm-level productivity, just as is the casein the data. Also, in line with Result 3 we �nd that temporary exporting, i.ediscontinued proactive export episodes, are associated with lower �rm-levelproductivity.

However, the resemblance between data and theory goes even further.According to Result 4 developed in Section 3 we should expect that �rmsservicing smaller one-o� export orders on average have a higher productivitythan �rms servicing large one-o� orders. We, thus, proceed by applying fur-ther restrictions to one-o� export episodes taking into account the relativesize of a product-destination export volume. More speci�cally, for this exer-cise we label export episodes as one-o� when they last only one month anddo not reoccur with three successive years and are at the same time of smallvolume. In particular, we require ω, the volume of the product-destinationtransaction as a percentage of total sales to be below 3, 1 or 0.1 percent.From the total of 93,380 one-o� export spells 92,315 account for less thanthree per cent, 90,031 account for less than one per cent while 74,435 ac-count for less than 0.1 per cent of the respective �rms' total sales. Thus,relatively speaking 99 per cent of all one-o� spells are small (ω < 3%), 96per cent are fairly small (ω < 1%), and 75 per cent are indeed very small(ω < 0.1%). We re-estimate our main model speci�cation with these threealternative measures of the share of one-o� exports Υi,ω<3;1;0.1%.

Table 5 reports the respective exporter productivity calculations againdi�erentiating between the the bottom decile, median and top decile of Υω

holding the temporary export share Θ constant at the median. When ap-plying the lenient size constraint requiring one-o� export spells to be smallenough to account for less than three percent of the respective �rm's salesin that given year (ω < 3%) the di�erences in the exporter productivity pre-mia between the bottom and top decile of Υω are somewhat less pronouncedcompared to the unconstrained �gure reported in Table 4 - the F-statisticof the corresponding Wald test drops from 72 to 45. When applying the

25

Table 5: Exporter productivity premium, one-o� exports � size con-

strained

ω < 3% ω < 1% ω < 0.1%Υω ΘMedian −Υω

(I) (II) (III)Labour Productivity

Bottom Decile 38.65 38.02 36.57( 2.33 ) ( 2.30 ) ( 2.21 )

Median 38.20 37.81 36.56( 2.30 ) ( 2.28 ) ( 2.21 )

Top Decile 24.05 31.97 36.38( 2.39 ) ( 2.21 ) ( 2.18 )

H0 : Bottom = Top F=45.07 *** F=18.65*** F=0.76p=0.00 p=0.00 p=0.38(I) (II) (III)

Domestic Sales

Bottom Decile 344.69 338.42 328.43( 36.08 ) ( 35.19 ) ( 33.45 )

Median 342.19 338.29 328.78( 35.53 ) ( 34.97 ) ( 33.45 )

Top Decile 267.04 334.69 335.26( 34.19 ) ( 35.17 ) ( 33.59 )

H0 : Bottom = Top F=5.74** F=0.03 F=3.97**p=0.02 p=0.86 p= 0.05

Notes:***Statistically signi�cant at the 1 percent level. Υ denotes the one-o� exportvolume share. ω represents the one-o� export volume relative to a �rms total sales inthe year in which the spell is classi�ed.

stricter size constraint of (ω < 1%) the productivity di�erence between thebottom and top decile of Υω, albeit still signi�cant, drops further. That is,�rms with the highest share of one-o� exports (with each one-o� spell nowaccounting for less value) are relatively more productive in comparison toour initial de�nition employed in Table 4. For example, the exporter produc-tivity premium for the top decile of Υi,ω<1% is 32 per cent compared to 14per cent for all one-o� export episodes regardless of size (compare Table 5,upper panel, column (II), Top Decile with Table 4, upper panel, column (II),Top Decile). When applying the strictest size constrained for one-o� exportsω < 0.1 we see that exporter productivity premia for the bottom and top

26

Table 6: Exporters vs. Non-Exporters depending on one-o� and

Temporary Export Spell Shares, in per cent

Φi

(Λi − Φi) Bottom Decile Median Top Decile H0 : Bottom = Top

Labour Productivity

Bottom Decile 51.88 40.71 32.04 F=18.09***( 4.72 ) ( 2.76 ) ( 2.46 ) p=0.00

Median 41.56 31.15 23.07 F=19.13***( 3.46 ) ( 1.99 ) ( 2.37 ) p=0.00

Top Decile 23.32 14.26 7.21 F=21.28***( 2.62 ) ( 2.57 ) ( 3.39 ) p=0.00

H0 : Bottom = Top F=43.11*** F=50.35*** F=57.04 ***p=0.00 p=0.00 p=0.00

Notes:***Statistically signi�cant at the 1 per cent level. Φ and Λ denote the one-o� andtemporary export volume shares, respectively.

decile of Υi,ω<1% almost perfectly align. What does this mean: Exporterswith a high share of very small one-o� exports are indistinguishable in termsof productive from exporters with a large share of proactive exporting (a lowshare or almost no one-o� export episodes).

We �nd something very similar for exporter premia in terms of domesticsales (compare the lower panels of Table 5 and Table 4). With a strictersize constraint for one-o� exports the percentage di�erence in domestic salesbetween the bottom and top decile of Υω disapears. When applying thestrictest size constraint ω < 0.1 we even see a reversal of the established sizeranking.

These �ndings correspond in fact to our theoretical derivations. To seethis consider Figure 1 and Result 4 depicting the downward sloping pro-ductivity threshold between reactive exporters and non-exporters, i.e. only�rms with fairly higher productivity will react to small volume one-o� exportorders. Put di�erently, the theory suggests that if �rms productivity is notsu�ciently high very small export orders might not be serviced. Accordingly,�rms with lower productivity might have a lower share very small one-o� ex-ports. This generates a counteracting a�ect that can render productivity orsize di�erences between �rms with a high share and �rms with a low shareof one-o� exports insigni�cant. Theoretically, it is even possible that thiscounteracting e�ect dominates. In our application this would correspond to

27

the pattern we �nd in Table 5 for (ω < 0.1%).For completeness, Table 6 brie�y shows the productivity premia results

when using the spell share instead of the export volume share, i.e. replac-ing the volume shares Υi and (Θi − Υi) of one-o� and temporary exportsused above with the spell shares Φi and (Λi − Φi). Results are similar tobefore. INGO:I HAVE DELETED THE LOWER HALF OF THIS TABLE"DOMESTIC SALES", SINCE THEY WHERE DEPARTING FROM RE-SULTS IN THE TABLE WITH VOLUME SHARES ABOVE. OR AM IREADING THINGS WRONG? THE ORIGINAL TABLE IS PRESERVEDAFTER "END DOCUMENT".

5 Conclusion

Using �rm-level data for Denmark including monthly export transactions, weestablish the following stylized facts: 40 per cent of all observed export spellsfor our balanced sample of surviving �rms between 2002 to 2011 are in factisolated single month one-o� export events. It is the very distant and smallexport destinations that have no mitigating advantages such as regional ormultilateral trade agreements and that are politically most unstable whichare served by an over-proportional share of such one-o� exporting. From the�rm perspective such one-o� exports are an important phenomenon account-ing for more than 17 percent of an average �rm's total export sales. Yet, forlarge �rms, that account for most of the aggregate export volume, this shareis considerably smaller.

We extend a standard heterogenous �rms trade model to reconcile theorywith the data. In particular, we employ a concept that has been champi-oned in the International Business and International Marketing literature:the distinction into proactive and reactive exporting. In addition to proac-tive permanent exports and proactive temporary exports (i.e. discontinuedonce hit by a shock) some unsolicited one-o� foreign demand reaches the�rm randomly and the �rm may choose to export reactively. In the model,proactive exporters turn out to be larger and more productive than reactiveone-o� exporters, which in turn are larger and more productive than non-exporters. Surprisingly, the mechanisms of our model also imply that smallerone-o� export orders will only be serviced by the more productive �rms. Thisformalization and its predictions guide our empirical investigation.

We �nd support for the productivity and size rankings and associatedpredictions in the data. Exporter productivity and size premia typically de-crease the higher a �rm's share of reactive one-o� exports becomes. Oursimple descriptive regression analysis indicates that exporters that select

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into proactive permanent exports as the predominant export mode enjoya start of sample productivity advantage of about 40 per cent and a startof sample size advantage of 353 percent in comparison to our control groupof non-exporters. Firms that select themselves into reactive one-o� export-ing and proactive temporary exporting as their sole mode of exporting, arefound to be equally (un)productive as non-exporter INGO: EQUALLY? ISTHAT RIGHT, IS THERE NO DIFFERENCE TO NON-EXPORTERS,AND NO DIFFERENCE BETWEEN TEMPORARY (EXCLUDING) ONEOFF AND ONE-OFF - MAYBE I READ THE TABLES WRONG? IDE-ALLY WE WANT TO BRIEFLY STATE HERE THE RANKING OF THETHREE TYPES: PERMANENT, TEMPORARY AND ONE-OFF and toenjoy a much smaller size advantage of only 125 per cent over non-exporters.In addition, we �nd evidence of a counteracting e�ect. At the extremes ofthe distribution we observe a reversal of the previously described productiv-ity and size ranking with respect to one-o� exports. Accordingly and in linewith our theory, the data suggests that �rms that react on very small one-o�export orders are more productive and larger than �rms only servicing largeone-o� orders. Finally, and also in line with theory, any destination coun-try characteristic that raises export marketing costs makes the respectivedestination more prone to one-o� exporting.

Apart from the contribution that our paper makes to the duration ofexports literature, the astonishing prevalence of one-o� export events thatwe pinpoint warrants future research. We see two particularly important di-rections. Firstly, theoretical models of international trade should elaboratefurther on the buyer-side of the export relation. Concepts from InternationalBusiness Studies and International Marketing might be a rich source of in-spiration for such formal extensions. Secondly, although the actual exportinitiation is never recorded in o�cial register micro data, several data-setsinclude some information on the imports of �rms. Future research could mapthe import behavior of �rms in more detail, for example, by identifying the�rm characteristics that are associated with a taste for one-o� import orders.

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