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1 econstor Der Open-Access-Publikationsserver er ZBW Leibniz-Informationszentrum Wirtschaft The Open Access Publication Server of the ZBW Leibniz Information Centre for Economics Qu, Zhan; Raff, Horst; Schmitt, Nicolas Working Paper Inventory control an intermeiation in global supply chains Kiel Working Paper, No. 993 Provie in Cooperation with: Kiel Institute for the Worl Economy (IfW) Suggeste Citation: Qu, Zhan; Raff, Horst; Schmitt, Nicolas (05) : Inventory control an intermeiation in global supply chains, Kiel Working Paper, No. 993 This Version is available at: Nutzungsbeingungen: Die ZBW räumt Ihnen als Nutzerin/Nutzer as unentgeltliche, räumlich unbeschränkte un zeitlich auf ie Dauer es Schutzrechts beschränkte einfache Recht ein, as ausgewählte Werk Rahmen er unter nachzulesenen vollstänigen Nutzungsbeingungen zu vervielfältigen, mit enen ie Nutzerin/er Nutzer sich urch ie erste Nutzung einverstanen erklärt. Terms of use: The ZBW grants you, the user, the non-exclusive right to use the selecte work free of charge, territorially unrestricte an within the te lit of the term of the property rights accoring to the terms specifie at By the first use of the selecte work the user agrees an eclares to comply with these terms of use. zbw Leibniz-Informationszentrum Wirtschaft Leibniz Information Centre for Economics

2 Inventory Control an Intermeiation in Global Supply Chains Zhan Qu Horst Raff Nicolas Schmitt No. 993 March 05

3 Kiel Institute for the Worl Economy, Kiellinie 66, 405 Kiel, Germany Kiel Working Paper No. 993 March 05 Inventory Control an Intermeiation in Global Supply Chains* Zhan QU, Horst RAFF an Nicolas SCHMITT Abstract: The paper evelops a sple theoretical moel of inventory control in global supply chains. It ientifies a role for intermeiaries in managing inventory, an shows that inserting an intermeiary as an aitional link in a supply chain is profitable when eman volatility is high. It also provies conitions uner which the intermeiary hanling inventory is locate in the exporting versus the porting country. Trae liberalization in the form of less lumpy trae is shown to expan the role of export an port intermeiaries but to have potentially negative effects on the volume of international trae an social welfare in the porting country. Keywors: international trae, supply chain, inventory, intermeiation, lumpy trae. JEL classification: F, F3, L Zhan Qu Technical University Dresen Horst Raff Corresponing author Kiel University, Kiel Institute for the Worl Economy an CESifo Wilhelm-Seelig-Platz, D 48 Kiel, Germany, raff@econ-theory.uni-kiel.e Nicolas Schmitt Son Fraser University, an CESifo *We woul like to thank the Social Sciences an Humanities Research Council of Canaa for financial support. The responsibility for the contents of the working papers rests with the author, not the Institute. Since working papers are of a prelinary nature, it may be useful to contact the author of a particular working paper about results or caveats before referring to, or quoting, a paper. Any comments on working papers shoul be sent ly to the author. Coverphoto: uni_com on photocase.com

4 Introuction A large an quickly growing share of international trae is organize in global supply chains that link increasingly fragmente prouction processes (Balwin, 0). Coorinating prouction along these chains is a complex taskthathasbeenstuieextensivelyinthemanagementliterature. This literature has ocumente that one of the key management problems inherent in the spatial unbunling of prouction is how to eal with the growing size of inventories. Inventories arise naturally in this context, because prouction has to occur before consumption(or further processing) an eman is typically uncertain. In fact, using over 500,000 transactions from USpublicfirms,Jainetal. (04)estatethata0%shiftinsourcing from omestic to global suppliers increases average inventory investments by8.8%. Economists have not yet given much thought to the issue of inventories in global supply chains, at least as compare to management scientists. For instance, only recently has it been recognize by Alessanria et al. (04, 0, 00a,b) that the size of trae-goo inventories matters for economic performance,specificallyfortheynamicsofinternationaltraeflows. But we still know very little about the economic forces that etermine (i) the size of these inventories, (ii) how an by whom inventories are manage, an (iii) what the economic consequences are not only for the volatility of trae, butalso forthevolumeoftraeansocial welfare. The purpose of the current paper is to construct a theoretical moel of a global supply chain that helps us aress these questions. We start with a sple moel of a supply chain, in which we enogenize both the size of inventories an the length of the chain in the sense that inventory control may be elegate to an intermeiary (as an aitional link in the chain). We show that aing an intermeiary may reuce inventory an that such a strategy is optal when final eman is sufficiently volatile. We then a borers by assuming that prouction takes place in a ifferent country than consumption. This allows us to enogenize the location of the intermeiary an thus to consier whether the supply chain inclues an export or an port intermeiary. Ientifying an export intermeiary as one allocating goos across estination markets an an port intermeiary as one allocating goos across te within a given estination market, we See, for instance, Belavina an Girotra (0a, b), Biyalogorsky an Koenigsberg (00), Chen an Gavirneni(00) an references herein for recent examples. This literature has a very ifferent focus with respect to our paper since it eals mainly with issues linke to management strategies an oes not offer insights on international trae issues an social welfare. UsingUSinustryata,Alessanriaetal. (00b)estatethataninustrythatuse only porte inputs while exporting all of its output woul hol nearly three tes as much inventory as an inustry that prouce only for the omestic market using omestic inputs.

5 show that an export intermeiary is preferre when emans are negatively correlate across estination markets an that an port intermeiary is preferre when these emans are positively correlate. Two examples help to illustrate the role of port an export intermeiariesinglobalsupplychains. ConsierfirstthecaseofO NeillInc., aus manufacturer of apparel an accessories for water sports. Because of low prouction costs, it manufactures its proucts in Asia resulting in a long lea te for prouction (3 months), forcing this manufacturer to prouce well before the selling season. O Neill allows for two types of orers from US retailers(cachon, 004): one place well before the selling season(with pre-book iscount an elivery guarantee), which means that retailers take possession of the goos, manage inventories an bear the risks associate withemanuncertainty. Theothertypeoforercanbemaeonshortnotice an is honore provie inventory is available in O Neill s istribution centre in San Diego. In this case, it is the port-intermeiary unit which acts as an porter, controls inventories an bears the risk. The secon example is from the toy market. At the en of the 990s the US toy market represente nearly half of the worl market, an it was ominate by two large firms (Mattel an Hasbro) whose prouction ha largely move to low-cost Asian countries. Moving prouction far from consumers was not without loss of flexibility in managing supply as prouction quantities ha to be specifie months before the holiay season an there were long transit tes, custom elays, quota restrictions, an communication barriers [making] managing the supply of proucts flowing from Asia a challenge (Johnson, 00, p. 8). Moreover, the eman for toys is characterize by a heavy concentration of sales in November an December (45% of US annual sales; Johnson, 00), a very uncertain success rate as very few toys are typically successful uring the Christmas season, an a heavy emphasis on new toys as the most successful ones are rarely so over multiple years. These features suggest that one of the main concerns of the toy firms is to make sure that supply meets eman across ifferent consumer markets, more than to allocate goos through te. This is precisely why Mattel an Hasbro put in place large wholesaling facilities able to ivert proucts to Europe or the US epening on inventory nees (Johnson, p. 0). This example is best associate with the type of export-intermeiation activity that wehave inmininthispaper. Whether these intermeiaries are affiliates of the manufacturers or inepenent firms is not critical. Thus, intermeiaries coul be thir-party logistics (3PL) firms (i.e., firms managing inventory storage in their own warehouse) manate by manufacturers to brige the gaps between prouctionanconsumptionanto helpcontrol inventories. 3 3 Inustry Canaa (008) reports that thir-party logistics (3PL) firms play an essential role in global supply chains involving Canaian firms. Accoring to the report (see

6 What avantages o intermeiaries have in controlling inventory relative to ownstream firms, say retailers or ownstream proucers, who in principle coul also hol inventory? Following the market microstructure literature (Spulber, 999), our theory of intermeiation is built on the assumption that intermeiaries possess market power. 4 In fact, we show that market power creates a role for intermeiaries in controlling inventory even if they o not possess a superior technology relative to competitive ownstream firms. The economic mechanism behin this is sple. An intermeiary with market power hols inventory to equalize toay s marginal revenue with tomorrow s expecte marginal revenue, whereas competitive ownstream firms hol inventory so as to equalize toay s price with tomorrow s expecte price. This plies that inventories are smaller an trae volatility is reuce when inventory is controlle by an intermeiary, which also explains why intermeiaries are especially useful when final eman is very volatile. Sply put, the intermeiary s incentives to control inventory are better aligne with the interests of the manufacturer because the intermeiary intertemporally segments sales perios whereas, in its absence, competitive ownstream firms integrate them. The intermeiary s avantage outweighs the resource cost of intermeiation in volatile markets where inventories ten to be big. This basic avantage of intermeiaries in controlling inventory carries over to the other environments we examine, namely to the case where the intermeiary may be locate in the exporting or the porting country. We then expan the moel by aing an international trae friction by assuming that trae may be lumpy in the sense that any shipment across borersneestocovermorethanonesalesperio. 5 Thefactthatlumpiness backgroun material to Figure 9), the number of meium an large 3PL firms in Canaa has increase from 98 firms in 998 to 443 firms in 007, an increase of nearly 50%. At the same te there was consierable consoliation in the inustry with the number of smallfirmsfallingfrom 586 to446. Thusthetotalnumberof3PLfirmswasnearlystable, but given the shift towar bigger firms the portance of 3PL activities has certainly increase. Worl Bank (04) reports that 3PL firms ha an estate global market of $677 billion in 0 ($36 billion in Asia, $70 billion in the US an $56 billion in Europe). 4 Spulber (999, p. xvii) argues that any market microstructure theory requires intermeiaries to have at least some market power so that they can set prices an balance supply an eman across te. Proviing "meiacy services", that is, staning reay to buy an sell goos at ifferent points in te is seen as a key role of intermeiaries. 5 The Worl Bank s Doing Business project (see fins that the te necessary to complete ocumentation, custom, inspections, port an terminal hanling for a container transporte by ocean shipping as an average elivery lag of 9- ays for exports from an ports to high income OECD countries an ays for exports from an ports to South Asian or Sub-Sahara African countries. See also Hummels an Schaur(03), Crista, et al. (03). The Great Recession has le financiallystrappe ocean carriers to cut fuel costs by reucing vessel spees from 5 to knots, which as up to three ays to the - ays voyage between Asia an North America (Bonney an Leach, 00). Interestingly, the protracte 04 West Coast longshore contract negotiations have le US retailers to port back-to-school an holiay merchanise 3

7 is an aitional reason for holing inventory an that it affects the ynamics of international trae is best seen through the example of a US steel wholesaler. This wholesaler purchases proucts both at home an abroa, with elivery of foreign steel proucts taking up to twelve weeks from the ateorersareplace(hallanrust,000). 6 Tablecontraststheaverage weight an average interval of omestic an foreign orers for 469 proucts that have both omestic an foreign purchase transactions. The relative lumpiness of foreign transactions shows up in the average weight of foreign orers,whichisnearlytwiceasbigasthatofomesticones,anintheaverage interval between orers, which is on average 9% longer for foreign than for omestic transactions. 7 Table also shows that the coefficients of variation (CV) associate with foreign transactions are lower for both weight an transaction interval than they are for omestic transactions. Hence, whether for weight or interval, foreign transactions exhibit more regularity, less ranomness aroun the mean than omestic transactions even for the same set ofproucts. 8 Table : US Steel Wholesaler s Purchasing Transactions Domestic Foreign # transactions 7,449 4,57 Average weight 6,47 9,8 Average interval(ays) 03 4 CV weight CV interval.39.6 We first show that the benefit of intermeiation within a supply chain may be smaller when trae is lumpy, an secon that lumpiness increases the relative attractiveness of an port intermeiary compare to an export intermeiary. We also prove that the welfare effects of intermeiation may epen on the lumpiness of trae. In particular, we argue that trae liberalization in the form of less lumpy trae may not only lea to more intermeiation but also to lower social welfare. The reason is not just that intermeiation involves a resource cost. Rather, by proving the allocation of goos across te, intermeiaries also allow the manufacturer to better much earlier than usual ahea of any potential problems (Lavigne, 04). 6 For each purchase transaction, we know the unit price, the number of units orere, the weight per orer, a coe inicating whether sourcing is omestic or foreign, the amount pai an the elivery ate. We thank George Hall an John Rust for making the ata available to us. See Alessanria et al. (00a) for aitional etails on this ata set. 7 The average intervalis an average ofaverages. Specifically we treat each set of transactions separately, we then compute the average interval at the iniviual prouct level before averaging these averages. Note that we isregar same ate transactions at the prouct level. The results are qualitatively the same if these transactions are inclue. 8 Areasonmaybethatthewholesalerregularlystocksforeignsourcegoos,lookingto omestic sources only when eman unexpectely excees the inventory of foreign source proucts (see for instance Allon an van Mieghem, 00). 4

8 extract consumer surplus, an in the process sales may fall. When trae is lumpy this potentially negative effect on welfare is less likely to occur, which uner certain conitions is enough to guarantee welfare gains from intermeiation. The paper can be seen as contributing to several strans of the literature. Our paper is linke to the literature on intermeiation in international trae, particularly to the articles investigating versus in exports (Ahn, Khanelwal an Wei, 0; Akerman, 0; Blum, Claro an Horstmann, 0; Crozet, Lalanne an Poncet, 03; Felbermayr an Jung, 0; Krauthe, 03; Schroeer, Trabol an Trueswetter, 005, among others). 9 To this literature we bring inventory consierations an enogenous port an export intermeiation. Inee, to our knowlege, our paper is the first attempting to istinguish between export an port intermeiaries. But our paper is more closely linke to two other literatures: the one on global supply chains, an the literature on inventories an the ynamics of international trae. With respect to the first literature(see, for instance, Balwin an Venables, 03; Costinot et al., 03; Fally an Hillberry, 04), the main contribution of our paper is to enogenize the number of linkswithinachainantoshowthatinventoriesaresmallerinalongerchain than they are in a shorter chain. This contrasts with articles (see for instance, Altomonte et al., 03) linking inventory volumes an the ownership structure of a supply chain. Their argument rests on the iea that a common flow of information about the state of final eman allows for quicker ajustments of orers an for lower inventories at each link along a supply chain within a multinational company an its affiliates compare to a chain in which firms eal at arm s length an face the so-calle bullwhip effect (Forrester, 96). Ownership consierations play no role in our moel; insteaitisthelengthofthesupplychainthatmattersforinventoryvolumes because of the avantage brought by intermeiation. With respect to the literature on inventories an the ynamics of international trae(alessanria, Kaboski an Mirigan, 04, 0, 00a,b; Hornok an Koren, 04; Kropf an Sauré, 03), our main contribution is to show that the plications for trae ynamics anwelfare are not the same epeningonwho engagesin international trae. Inee it is precisely because intermeiaries main role inourmoel istocontrolinventoriesthat the ynamicsoftraeansocial welfare are ifferent with respect those associate with no intermeiation. The paper is organize as follows. In Section we present the moel an solve for the equilibrium without intermeiation. In Section 3, we a intermeiation an establish when it benefits the supply chain. We then 9 See also Antras an Costinot (0) for trae intermeiaries engage in search an matching, Feenstra an Hanson (004) for the role of Hong Kong intermeiaries, an Bernaretal. (00,0)fortheportanceofintermeiationinUStraeaninItaly. 5

9 introuce borers an international trae in Section 4. This allows us to establish the relative merit of export an port intermeiation. In Section 5 we examine how the equilibrium of this sple moel changes when, in aition to a prouction lag, we have a trae lag an lumpy trae. In particular, we show how trae lumpiness affects further the relative merits of port an export intermeiaries an the benefit of intermeiation itself. In Section 6 we consier a more general eman function to ientify sufficient conitions uner which intermeiation may raise or lower the volume of trae an social welfare epening on trae lumpiness. Section 7 contains conclusions, an the Appenix collects the proofs of our results. A Sple Moel of Inventory Control Consier an upstream proucer (hereafter, calle the manufacturer) who supplies its prouct to a continuum of perfectly competitive ownstream firms. Downstream firms either manufacturers purchasing an intermeiate goo or retailers purchasing a final goo in turn sell to consumers. Final eman is ranom an all market participants are risk neutral. Therearetwoperios, t=,. Orersareplaceanprouctiontakes place at the beginning of each perio before eman is known. Consumption occursat the enofeachperio. Aprouctionlagthusoccurswithineach perio. 0 In this setting ownstream firms may hol inventory, i.e., carry overunsolgoosfromperioforsale inperio. Demanatte t=,isgivenbythelinearinverseemanfunction: p t =A s t +ε t,wheres t enotesfinalsalesanp t istheconsumerprice. The ranomvariablesε t [,]areintertemporallyinepenentanuniformly istributewithensity. Our assumptions about the prouction an istribution technologies are as sple as possible. The manufacturer incurs a constant unit cost of prouction c. The marginal prouction cost of ownstream firms is normalize to zero, as is the trae cost an the cost of holing inventory. There is no iscounting. We make the aitional assumption that the eman shock is nottoo big: (c+cw ) min 3, A c 4, A (c+c w), (A) (where c w is a per-unit cost of intermeiation that we will use in the next section). Assumption(A) rules out situations in which eman is(i) so high that there are stockouts in equilibrium, (ii) so low that when ownstream firmssellgoosattheenofperiotheconsumerpriceropstozero,an 0 SeeEvansanHarrigan(005),anRaffanSchmitt(007)forrelatemoelsapplie to ifferent issues. 6

10 (iii) so lowinperiothat shipmentsinperioarezero. Nextweescribethetingofevents. Atthebeginningofperiothe manufacturerannounces a proucerprice P. Downstreamfirms oreran take possession of q units of goos before eman in perio is known; then perio-one eman is reveale an the ownstream firms sell s q inperio,holingunsolunitsasinventoryforperio. Inperio,the manufacturer sets proucer price P, an ownstream firms orerquantity q, again before perio-two eman is known. Deman in perio is then revealeanownstream firms sell s q +(q s ). To erive the equilibrium, we first consier perio. After observing emanownstreamfirmssellall of the prouctsonhan, anhence s = q +q s, because they have alreay pai for these goos an, by (A), the consumer price is positive. Downstream firms orer goos at proucer price P before the eman shock is realize. Perfect competition among ownstream firms plies that they orer goos until expecte profits are zero,so that q satisfies: E (A q q +s +ε )(q +q s ) P q =0. () The manufacturer chooses P, respectively q, that maxizes its perio- expecte profit E (π )=P q cq. Using () to substitute for P q, it is easily shown that this expecte profit is maxize when ownstream firms oreranamountq = A c (q s ),plyingsalesinperioofs = A c. The expecteconsumerprice inperioisthusequal to E (p )= A+c. Noticethatinperio,afterε hasbeenreveale,theownstreamfirms ecie how much to sell now an how much inventory to keep for perio. Being price takers they sell the quantity that equalizes the consumer price in perioan the expecteconsumer price inperio, holing any surplus as inventory for perio. The consumer price in perio thus satisfies p = A s +ε = A+c, an therefore first-perio sales are equal to s = A c +ε. These first-perio sales can only be realize if s q so that there are no stockouts. Given that any unsol goos can be hel in inventory at no cost, it is optal to set proucer price P so that ownstream firms orer q = A c + an stockouts are avoie for any value of ε. In perio the quantity shippeis then equal to q =s (q s )= A c ( ε ). Here( ε )representsthelevelofinventoryhelbytheownstreamfirms. Thus a eman shock in perio, ε, leas to a change in inventory, an the latter affects the quantity shippein perio. 3 Obviously the greater Weexplainattheenofthenextsectionwhyassumption(A)antheassumptionof no inventory cost both bias our results against aing an intermeiary in the value chain. For now suffice it to say that these assumptions leave our results qualitatively unchange. Note that, if all the other competitive firms behave in this way, the best response for any given iniviual competitive firm is also to follow this strategy. 3 It is easy to see that this argument oes not epen on having only a two-perio 7

11 isthevarianceofeman,thegreateristhevarianceofshipments,whichis equal to Var(q )= /3. Finally we compute the manufacturer s expecte total profit. The total quantityorereoverbothperiosisq +q =A c+ε. Sinceinequilibrium ownstream firms make zero expecte profit, their expecte total revenue has to equal their expecte total spening on goos: A+c (A c+ε ) ε =P q +P q. () Using () the manufacturer s expecte total profit, E(π)=P q +P q E[c(q +q )], is E(π)= (A c). (3) 3 The Role of Intermeiaries in Inventory Control Suppose now that the manufacturer uses an intermeiary to control inventory an thus as a link in the supply chain. More precisely, the intermeiary takes over from the ownstream firms the inventory holing across perios; the ownstream firms sply sell in each perio whatever they buy from the intermeiary in that perio. For the intermeiary, just like for ownstream firms, the cost of holing inventory is zero. However, intermeiationinvolvesaresourcecost c w per-unitshippe. Themanufacturersets a two-part tariff for the intermeiary, consisting of the proucer price P t an a fixe payment (or transfer) T t for t=,. The intermeiary in turn chargesawholesaleprice w t. 4 The ting of the game is now as follows: at the beginning of perio themanufacturersetsatwo-parttariff(p,t ),theintermeiaryorersan takes possession of quantity q. Deman in perio is then reveale, the intermeiary chooses wholesale price w, ownstream firms purchase from the intermeiary an sell to consumers a quantity s q. In perio the intermeiary reorers a quantity q at the two-part tariff (P,T ). Then eman in perio is reveale, the intermeiary sets wholesale price w, ownstreamfirmsoreransell s q +(q s ). The equilibrium can be etermine as follows. In perio after eman has been reveale an given a wholesale price w, ownstream firms moel. Even in a setting with more perios ownstream firms have an incentive to hol inventory so as to equalize prices across te. Thus a eman shock in one perio will affect trae in the subsequent perio in the same way. 4 The intermeiary cannot eman a fixe payment from the ownstream firms, since they earn zero profit in equilibrium. The two-part tariff set by the manufacturer plies that, like in the case without intermeiary, the entire expecte profit generate by the value chain goes to the manufacturer. The manufacturer also has no incentive to use more than one intermeiary. 8

12 orer an then sell an amount s that satisfies the zero-profit conition (A s +ε )s w s =0. Thus, the intermeiary s expecte perio-two revenue is E [(A s +ε )s ] = (A s )s, an the expecte marginal revenue is E(MR )=A s. Silarly, in perio, after ε has been reveale, the intermeiary sets a wholesale price w an ownstream firms purchase an sell quantity s, suchthat(a s +ε )s w s =0. The intermeiary srevenue hence is equalto(a s +ε )s,anthecorresponingmarginalrevenueismr = A s +ε. To etermine the intermeiary s optal wholesale prices, respectively sales to ownstream firms in each perio, assume that the manufacturer charges the same proucer price in both perios, P =P = P (we explain below that it is inee what the manufacturer chooses to o), so that the intermeiary s marginal cost is equal to P + c w. To maxize its profit the intermeiary sells quantities such that MR = E(MR )=P +c w. It followsthat s =(A (P+c w )+ε )/ an s =(A (P+c w ))/. Theintermeiarycanavoiastockoutinperiobyoreringaquantity q =(A (P+c w )+)/, which guarantees that s q for all ε. This is inee optal given a zero cost of holing inventory. In perio the intermeiary thus orers q =s (q s )= A (P+c w) ( ε ). The level ofinventoryhelbythe intermeiary,( ε )/, isthusonly half as large as the inventory that woul be hel by ownstream firms in the absence of an intermeiary. The variance of shipments in perio with intermeiation is Var(q )= / an thus only a quarter as high as the variance in the absence of intermeiation. This proves our first result: Proposition Inventory is smaller an shipments are less volatile if the inventory is controlle by an intermeiary. This result is ue to the fact that an intermeiary with market power faces ifferent incentives to hol inventory than competitive ownstream firms. Recall from the previous section that ownstream firms, after observing eman in perio sell the quantity that equalizes the first-perio consumer price with the expecte secon-perio consumer price. When eman turns out to be low in perio, this plies that ownstream firms sell very little an thus hol a large inventory; but when first-perio eman is high, ownstream firms sell a lot an hol very little inventory. In fact, when ownstream firms control the inventory, first-perio sales iffer from expecte secon-perio sales by the amount of the eman shock: s s =ε. Bycontrast,whenanintermeiarycontrolstheinventory,sales inperioifferfromexpectesalesinperiobyonlyhalftheamountof theshock: s s = ε. Thereasonisthatafterobservingemaninperio the intermeiary chooses the wholesale price so as to equalize the marginal revenue in perio an the expecte marginal revenue in perio (which 9

13 is equal to the intermeiary s marginal cost). This plies that, compare to the case without intermeiation, the intermeiary inuces ownstream firmstosellmorewhenemanislowanlesswhenemanishigh,which reuces the volatility of shipments in perio. Since sales in high-eman statesaresmallerinthecaseofintermeiation,thequantitythathastobe orereto prevent astockout inperioisalso smallerinthiscase, which explains why an intermeiary hols less inventory than ownstream firms. Another way to unerstan why the manufacturer values the intermeiary is to recognize that if MR = E(MR ), then p = E(p ). Thus the intermeiary s strategy amounts to segmenting the two sales perios (intertemporal market segmentation). In the absence of intermeiation, by equating p an E(p ), the ownstream firms in effect integrate markets across perios (intertemporal market integration). The benefit an intermeiary brings to the supply chain eviently stems from the fact that its incentive to hol inventory is better aligne withthe interests of the manufacturer than the incentives of ownstream firms. This benefit has to be trae off against the cost of intermeiation, which sply isthe resourcecost of c w perunit. To show this trae-off formally notice that the total expecte profit of theintermeiaryforagivenproucerprice P antransfer T isgivenby: A A (P+c w)+ε A (P+cw )+ε +ε (P+c w ) ε expecte profit in t= + A A (P+c w) A (P+cw ) (P+c w ) T. expecte profit in t= After evaluating the integral this splifies to [A (P+cw)] + T. The optaltwo-parttariffhasthemanufacturersetp =csoastoavoiouble marginalization an set T so as to extract the intermeiary s entire expecte profit. It follows that the manufacturer s expecte profit when traing with thehelpofanintermeiaryisthengivenby E π int = [A (c+c w)] Comparing (4) with(3) we may state the following result: +. (4) Proposition The manufacturer uses an intermeiary to control inventoryifthevarianceofeman(anthus )issufficientlylarge. At this point it is useful to briefly consier how relaxing two splifying assumptions woul influence our results. Making inventory costly to hol 0

14 woul introuce a trae-off between reucing the possibility of a stockout by oreringalargerquantityinperioanlitingthecostofholinginventory by keeping the first-perio orer small. This trae-off woul eviently iffer between ownstream firms an the intermeiary, as ownstream firm face more volatile sales anthusrequire a largerorer to avoiastockout. The benefit of using an intermeiary woulthus be evenbigger inthe case of inventory costs. Relaxing(A) woul also not funamentally alter our results. First, consier allowing for the possibility of stockouts. This woul create interesting economic trae-offs only in combination with costly inventory. As explaine above, an intermeiary reuces sales volatility an thus the threat of a stockout, making the use of an intermeiary a more avantageous choice. Secon, allowing eman shocks to be so big that the consumer price may rop to zero in perio when ownstream firms ump their goos on the market woul also create an aitional incentive to use an intermeiary. The reason is that ownstream firms facing a threat of such "estructive competition" ten to orer less than an intermeiary who can always guarantee a positive consumerprice inperio. 5 In the following sections we consier two extensions that a an international ension to our analysis. We first consier a case where the manufacturer ships goos to more than one market. Combine with (plicit) trae costs, this raises the question of where the inventory shoul be hel. Secon, we consier the case of lumpy trae an investigate the changing role of intermeiaries as trae becomes less lumpy. 4 Export versus Import Intermeiaries Intheprevioussectionwefounout whenit paysthemanufacturertoa a link in the supply chain by elegating inventory control to an intermeiary. We now introuce a borer between the manufacturer an consumers plying that this intermeiary can be locate either in the exporting or in the porting country. The purpose of this section is thus to unerstan the circumstances uner which the manufacturer uses either an export or an port intermeiary. In orer to make this choice interesting, we introuce two new elements. First, we consier more than one consumption market. Specifically, we assume that the manufacturer ultately supplies competitive ownstream firms in two ientical countries, enote α an β. Secon, we assign separate roles to the export an to the port intermeiaries. Specifically, we let 5 See Raff an Schmitt (007) for a formal analysis of estructive competition uner silar circumstances. Also note that the case, also rule out by (A), where eman in perio is so small that there are no shipments in perio is rather silar to the case of lumpy trae iscusse below.

15 an export intermeiary allocate goos across export estinations, an an port intermeiary allocate goos across te within a given estination market. An export intermeiary thus is a firm that takes possession of goos inthecountryoforiginanallocatesthemacrossthetwocountriesbutnot across perios. Hence, this export intermeiary oes not hol any inventory. By contrast an port intermeiary is a firm that takes possession of goos in the country of estination. There it may allocate goos across perios by holing inventory. But it oesnotallocategoosacrosscountries. 6 We make the following aitional ajustments to the moel an to the notation. Deman in country i = α,β at te t =, is given by the linear inverse eman function: p it = A s it +ε it, where s it enotes final sales an p it is the consumer price. The ranom variables ε it [,] are intertemporally inepenent, but in each perio may be correlate across thetwocountries. Inparticular,for t=,,let f(ε αt,ε βt )enotethejoint ensity function an assume that the marginal ensities are uniform so that f α (ε αt ) = f(ε αt,ε βt )ε αt an f β(ε βt ) = f(ε αt,ε βt )ε βt. Furthermore, suppose that f t(ε αt,ε βt ) = f α (ε αt )f β (ε βt ), an let the correlationcoefficient between ε αt an ε βt be ρ for t=,. It shoul be obvious from the above that our port intermeiary is ientical to the intermeiary analyze in the previous section. All we have one it to locate one in each estination market. We therefore concentrate onanalyzing the case ofthe export intermeiary. 7 Thetinginthecaseofanexportintermeiaryisasfollows. Inperio afterobservingthetwo-parttariff(p,t )theexportintermeiaryorers an takes possession of quantity q. After eman has been reveale, it sets wholesale prices w α an w β to allocate q across countries α an β. Downstreamfirmsthenselloutputtoconsumers,whereithastobethecase that s α +s β q. In perio, the export intermeiary faces proucer tariff (P,T ), reorers quantity q an resells it to ownstream firms at wholesalepricesw α anw β sothat s α +s β q. Analyzingthisgameis thus equivalent to consiering twice a one-perio case. So we can omit the te subscript t. Consier an export intermeiary who has taken elivery of a quantity of goos, q, an sets wholesale prices so as to allocate this quantity among 6 In other wors, it is the ability of allocating goos across te that prarily characterizes our port intermeiary. It oes not mean that an port intermeiary coul not also spatially allocate goos but that this role is seconary an thus ignore here. The same is true for our export intermeiary: the spatial allocation of goos is seen as the main role an the allocation across te is seconary, an thus ignore in our analysis. 7 Recallthatwithatwo-parttariffthe manufacturerhasnoincentiveto usemorethan one export intermeiary an, in the case of port intermeiaries, more than one in each estination country. We also assume that shipping costs are sufficiently high that while goos can be shippe to each estination country, it never pays to re-export them to the other estination country. That is, we assume away any parallel trae. See Raff an Schmitt (007) for a moel in which ownstream firms engage in parallel trae.

16 the two countries such that s α +s β = q. Facing a wholesale price w i competitive ownstream firms in country i = α,β orer an sell output until profitisequaltozero: (A s i +ε i )s i w i s i =0. Theintermeiaryearnsa totalrevenueinthetwocountriesof(a s α +ε α )s α +(A s β +ε β )s β. To maxize this revenue, the wholesale prices shoul be set so as to equalize marginal revenues across the two countries: A s α +ε α = A s β +ε β. Together with the conition s α +s β = q, this plies s α = q+(εα ε β) 4 an s β = q (ε α ε β) 4. That is, the export intermeiary is able to reallocate goos so that the market with the higher realize eman receives a proportionately larger quantity. How this may benefit the manufacturer is shown explicitly in the Appenix, where we erive the manufacturer s expecte profit per estination market when exporting through an export intermeiary: E(π ex )= [A (c+c w)] + ( ρ). (5) Comparing (5) with(4) yiels the following result: Proposition 3 Suppose trae is intermeiate. Then port intermeiaries are use if emans are positively correlate across countries(ρ > 0). An export intermeiary is use if emans are negatively correlate across countries(ρ<0). Even if channeling trae through an intermeiary is costly, it is still optal for a manufacturer to use an port or an export intermeiary when the eman volatility is sufficiently high. This is because an intermeiary allows for a better spatial or intertemporal allocation of goos from the manufacturer s point of view. 5 Trae Lumpiness an Intermeiation In aition to the prouction lag there may also be a te lag involve in shipping goos between the country of origin an estination countries α an β. A sufficiently long te lag makes trae lumpy proviing an aitional reason for keeping inventory. We efine lumpy trae as a situation, in which goosmayonlybeshippeatthebeginningofperioforconsumptionin periosan. Thequantity thathasbeenorereinperioforsale in country i,say Q i, hastolastfortwoperiossothattheownstreamfirms salesinthe two periossatisfy s i +s i Q i. Consier first the case where inventory is controlle by ownstream firms. 8 In this scenario the manufacturer sets a proucer price P i, then 8 Detaile erivations of the results for the case of no intermeiation, trae through port intermeiaries, an trae through an export intermeiary are provie in the Appenix. 3

17 ownstream firms in each country i=α,β orer quantity Q i. In perio, aftertheemanshock ε i hasbeenresolve,ownstreamfirmseciehow much to sell in perio, an the leftover is sol in perio. We fin that trae lumpiness has no effect on the expecte total shipment to a country, (A c), nor on the manufacturer s expecte profit, which is still given by(3). The egree of lumpiness sply oes not affect the manufacturer s proucer price so that ownstream firms orer the same expecte quantity. Next consier the case of an port intermeiary. This intermeiary ajuststhewholesalepriceinperioafterobservingε inorertoallocate output across perios until the marginal revenue in perio is equal to expecte marginal revenue in perio. The manufacturer s total expecte profit from exporting to a country via an port intermeiary is E π l p = [A (c+c w)] + 4. (6) Like in the case of non-lumpy trae, it pays to introuce an port intermeiary when the variance of eman is sufficiently large relative to the cost of intermeiation. Notice, however, from(6) an(4) that the benefit of an port intermeiary is now smaller than in the case of non-lumpy trae. Thisis,ofcourse,uetothefactthattheintermeiarycannotreorergoos in perio. More precisely, when goos can be reorere in perio, the port intermeiary, after observing ε, not only equates marginal revenue inperiowithexpectemarginalrevenueinperio;italsoknowsthatit will be able reorer goos to make sure that the expecte marginal revenue in perio equals marginal cost. This ability to optally ajust sales in perio is absent when goos are orere only once at the beginning of perio. Finally consier trae intermeiate by an export intermeiary. The optal strategy of the export intermeiary after observing the eman shocks ε α an ε β is to set wholesale prices so that the competitive firms orer the quantities Q α an Q β that equalize marginal revenues across the two countries. The expecte profit of the manufacturer from exporting to a given country is E π l exp = [A (c+c w)] + ( ρ). (7) 48 Like in the case of non-lumpy trae, traing through an export intermeiaryisprofitableifthevarianceofemanislargerelativetotheresource cost of intermeiation, provie emans in the two countries are not perfectly correlate. But we observe from (5) an (7) that the avantage of using an export wholesaler is smaller than in the case of non-lumpy trae. The reason for this is that the intermeiary in the case of lumpy trae has only one opportunity to allocate inventory across countries. Once the 4

18 export intermeiary has complete this allocation, ownstream firms in the two countries face the "wrong" incentives wrong from the point of view of the manufacturer an of the intermeiary to allocate inventory across te, namely by selling until the first-perio price is equal to the expecte secon-perio price. This intertemporal "misallocation" of inventory oes not take place when there is non-lumpy trae. It is meiate from the above iscussion that trae lumpiness changes the relative benefit of using port compare to export intermeiaries, making port intermeiaries more attractive. We may therefore state: Proposition 4 When trae is lumpy the manufacturer strictly prefers port intermeiaries to an export intermeiary unless eman shocks in the two countries are perfectly negatively correlate(ρ = ). This is an interesting result because it inicates that lumpy trae penalizes more an export than an port intermeiary. It is the case because, unlike an port intermeiary, the export intermeiary loses control of the intertemporal allocation of proucts once they have been shippe. The analysis also plies that the use of intermeiaries an thus the length of supply chains epens on trae lumpiness. The benefit of using an port or export intermeiary is lower in the case of lumpy trae than with non-lumpy trae. That is, they are only use for higher levels of the variance of eman. The consequence of this is meiate: Proposition 5 As trae becomes less lumpy the likelihoo that trae is intermeiate an that it is intermeiate by an export rather than an port intermeiary rises. In other wors, as trae becomes less lumpy inventories are more likely to be manage by intermeiaries rather than by ownstream firms. The reason is clear: an intermeiary, whether on the port or on the export sie, is less constraine with non-lumpy than with lumpy trae an is thus more useful to a manufacturer as an aitional link within the supply chain. In aition, the avantage of an export intermeiary rises compare to that of an port intermeiary, as there are increase opportunities to allocate goos across countries. There is inee some evience that trae lumpiness has ecrease over te. Table showsinparticularthat thete anthe cost of oceanshipments associate with port proceures has fallen over the last eight years irrespectiveofthecountrygroup. 9 Becauseteancostaremeasure by 9 BaseonWorlBank sdoingbusinessatameasuringcountry-specificteancosts (excluing tariffs) associate with official export an port proceures (thus excluing the te an cost of transportation) of a stanar prouct traveling in a ry-cargo, 0- foot, full container loa weighing 0 tons with a value of $0,000. We use (Worl Bank) GDP eflators per country group to compute real values. The te an cost of export proceures show silar outcomes. 5

19 evaluating port an transit as well as ocumentation an custom proceures anfees, theyare largely inepenent ofthe size, the weight anthe value of shipments. Thus lower fixe costs per shipment shoul be associate with less lumpyshipments. 0 Table : Te an Cost of Import Proceures % Change High-Income Countries Te to Import (ays) % Cost to Import (constant USD) $,0 $980-3.% Upper-Mile Income Countries Te to Import (ays) % Cost to Import (constant USD) $,36 $,0-8.5% Lower-Mile Income Countries Te to Import (ays) % Cost to Import (constant USD) $,4 $, % Low Income Countries Te to Import (ays) % Cost to Import (constant USD) $,9 $, % 6 Trae Volume an Welfare Effects of Intermeiation Intermeiation in our moel affects the trae volume an hence social welfare in the estination countries only because it involves a resource cost. In particular, the expecte volume of shipments to a given country over two perios is (A c) without intermeiation an sply (A c c w ) with intermeiation, inepenent of whether the intermeiary is locate in the exporting or the porting country or whether trae is lumpy or not. This is not a general result, of course, but one that is riven by our splifying assumptions. These assumptions were useful, precisely because they allowe us to emonstrate why a supply chain may benefit by aing an intermeiary to control inventory or allocate goos across markets, even if it reuces overall sales. In this section we generalize the moel to explore whether intermeiation may have any effect on the expecte volume of trae an social welfare beyon that stemming from the resource cost. For this purpose, we set c w = 0 an go back to the general setup of Section 3, where we o not istinguish between an export an an port intermeiary. A reason to 0 Documentation an custom proceures an fees are more inepenent of weight an value than port an transit proceures an fees. See Hornok an Koren (04) for a iscussion on this point an estations with 009 US an Spanish trae ata showing that trae lumpiness is inee lower for estinations with lower ocumentation an custom proceure an fees. 6

20 suspect that intermeiation has such effects is that intermeiaries not only provetheallocationofgoosacrossteanspace,buttheyalsoallowthe manufacturer to better exercise market power in the estination countries, an this may be etrental to consumers. Specifically elegating pricing to an intermeiary with better information about the realization of eman permits more exact pricing to extract surplus from consumers. Consier the general eman function p it = p it (s it )+ε it, with p it <0 in country i=α,β at te t=,. Ignoring country an te subscripts, also assume: p (s) 0;p (s)+sp (s) 0;p (s) 0;3p (s)+sp (s) 0; (A) p (s)+sp (s) s(p (s)) /p (s) 0. This assumption is satisfie for linear eman functions. Obviously, the linear eman case is a specific an extreme case of (A) since it requires p =p =0. We prove the following result: Proposition6 Suppose that c w =0 anthe emansatisfiesassumption (A). Then an intermeiary reuces the expecte volume of trae an expecte social welfare in the estination country if trae is non-lumpy, an it increases the expecte volume of trae an expecte social welfare in the estination country if trae is lumpy. Proof: see Appenix. In the previous section, we establishe that an intermeiary raises the profit of the supply chain more when trae is non-lumpy than when it is lumpy. Clearly, the intermeiary s market power is better exercise in the presence of non-lumpy trae. Assumption (A) establishes then that there are eman characteristics for which the intermeiary s market power, through its ability to ajust wholesale prices, leas to lower overall expecte sales an welfare as compare to a supply chain without intermeiation. It is then not surprising that expecte sales an welfare are higher with lumpy trae since the intermeiary is unable to ajust its wholesale price in perio. But the proposition goes further an establishes that expecte sales an welfare are higher than without intermeiation. This result has interesting plications for trae, especially if we consieraworlinwhichtraebecomeslesslumpyoverte. Recallfromthe previous section that a reuction in lumpiness shoul lea to more intermeiation. But with less lumpiness intermeiaries may reuce social welfare. Hence trae liberalization in the form of less lumpy trae may have negative welfare consequences exactly when trae becomes intermeiate. Assumption(A)establishes,amongotherthings,thatMR (s)=p (s)+sp (s)<0 anmr (s)=3p (s)+sp (s) 0. 7

21 7 Conclusions This paper shows that aing an intermeiary to a supply chain is often an optal strategy to follow for manufacturers in an environment where customershavetoplaceorersbeforeemanisknown. Thisisthecaseeven if aing an intermeiary is costly an may even ecrease the overall volume of sales an welfare. The benefit brought by an intermeiary is shown to be especially portant when eman volatility is high, as an intermeiary is able to smooth shipments an to lower the nee to maintain inventories withinasupplychainwithrespecttoonewheresuchanintermeiaryisnot present. These are especially relevant results in an international trae context as lags between prouction an consumption, whether ue to the nature of prouction, the location of that prouction, the transportation technology or borerelays, make them far more prevalent thanin a omestic market environment. It is then not surprising that export an port intermeiaries continue to be portant agents aroun the worl. A corollary of our results is that uring a ramatic shock such as the worl financial crisis, the reuction in the volume of trae an the subsequent recovery can be expecte to be softer within a supply chain involving intermeiation than in one without it. This outcome has nothing to o with the ownership structure within the chain but everything to o with the incentives of ifferent agents in the chain to maintain inventories. But we go further by assigning istinct roles to port an export intermeiaries. Import intermeiaries are viewe as particularly useful whenever intertemporal arbitrage can be exploite, while export intermeiaries are useful when international spatial arbitrage is likely to be present. An avantage of thisapproachisthat it makesit possible to isentangle the relative role of an port an an export intermeiary, something that has, to our knowlege, not been consiere in the literature. The other avantage is its splicity. Showing that trae lumpiness affects the incentive to use intermeiaries in general an the type of intermeiary in particular allows us to cla that, insofar as trae nowaays is less lumpy than in the past, we shoul observe more intermeiaries in international markets, not less, whether they are export or port intermeiaries. But it is also true that, as international trae becomes less lumpy, we shoul observe a relatively higher proportion of export intermeiaries. The argument that intermeiaries are more useful thaneveranthiseveniftransportcostsantraebarriershavecomeown is not entirely new. Belavina an Girotra (0), for instance, argue that intermeiaries help firms aapt to a volatile environment, even if they are See PRWeb (006) for an example of a recent Chinese export intermeiary (Chinavision Wholesale) for electronic proucts. The fact that this intermeiary seems to accept any orer, whatever its size, suggests non-lumpy trae. 8