Trading with the Enemy

Transcription

1 Tradng wth the Enemy Mchelle R. Garfnkel Unversty of Calforna, Irvne Constantnos Syropoulos Drexel Unversty Current Verson: March 1, 2017 Abstract: We analyze how trade openness matters for nterstate conflct over productve resources. Our analyss features a terms-of-trade channel that makes securty polces trade-regme dependent. Specfcally, trade between adversaral countres reduces ther ncentves to arm gven the opponent s armng. If they have a suffcently smlar mx of ntal resource endowments, a move to trade brngs wth t a reducton n resources dverted to conflct and thus wasted, as well as the famlar gans from trade. Otherwse, a move to trade can nduce greater armng by one of them and thus need not be welfare mprovng for both. Moreover, when the two adversaral countres do not trade wth each other but nstead trade wth a thrd (frendly) country, a move from autarky to trade ntensfes conflct between the two adversares. Buldng on the welfare mplcatons, we also analyze the endogenous choce of trade regmes. JEL Classfcaton: D30, D74, F10, F51, F52. Keywords: resource nsecurty, nterstate dsputes, conflct, trade openness, comparatve advantage We are heavly ndebted to Stergos Skaperdas for extensve dscussons and nsghtful comments on earler drafts of ths paper. We also thank Mostafa Beshkar, Rck Bond, Kamal Sagg, Jun Xang, Yoto Yotov, Ben Zssmos and partcpants of the ASSA Meetngs 2015, the WEAI Annual Conference 2015, the Mdwest Economc Theory Conference at Purdue Unversty 2016, and the Internatonal Economcs Workshop at Vanderblt Unversty. Emal: mrgarfn@uc.edu Emal: c.syropoulos@drexel.edu

2 1 Introducton Internatonal trade takes place wthn an anarchc settng. Absent an ultmate adjudcator and enforcer, countres nevtably have unresolved dsputes and nearly all expend resources on defense to prepare for the possblty of outrght conflct or to mprove ther barganng postons under the threat of conflct. Despte such anarchy prevalng n nternatonal relatons, the classcal lberal perspectve vews greater trade openness among potental adversares as reducng or even elmnatng conflct (e.g., Polachek, 1980). 1 One argument n support of ths perspectve s that conflct precludes the realzaton of at least some of the gans from trade; then, countres actng collectvely and wantng to reap those gans would have a greater nterest under trade n mantanng a peaceful order and avodng war. However, t s well-known wth the prsoners dlemma beng a stark and smple example that n many economc, socal and poltcal nteractons, collectve ratonalty need not and often does not lead to a stable, equlbrum outcome. Instead, nteractons guded by ndvdual ratonalty more often lead to bad outcomes. Indeed, the realst/neo-realst perspectve, emphaszng self-nterest and ndvdual ratonalty as well as the anarchc nature of nternatonal relatons, argues contrary to the classcal lberal vew that trade can aggravate conflct between natons (e.g., Waltz, 1979). Specfcally, the benefts from freer trade can fuel frctons and conflct, as some states perceve that they (or ther rvals) wll develop a mltary edge n securty competton. 2 Our central objectve n ths paper s to dentfy and explore some key mechansms at play n determnng how the expanson of nternatonal trade affects the ntensty of conflct. The analyss s based on a varant of the Rcardan model of trade, sutably extended to allow for nternatonal dsputes. As n the canoncal Rcardan model, there are two large countres that possess dfferent (but constant returns to scale) technologes for producng two consumpton goods from a sngle nput. The dfference n technologes generates comparatve advantage that provdes the ratonale for mutually advantageous trade, even f one country s more effcent n producng both goods. However, n contrast to the standard Rcardan model, ours supposes that consumpton goods are produced wth an ntermedate nput, whose level depends on two prmary factor nputs. Moreover, at least some porton of one of these factors s 1 See Glpn (1987, pp ) for an overvew. 2 Pushng ths logc one step further, one could argue that actual or potental rvals would not trade wth each other (e.g., Greco, 1990; Gowa, 1995). See Barber and Schneder (1999), who survey the theoretcal and emprcal lterature regardng nternatonal trade and conflct.

3 contestable. It could be ol, mnerals, tmber, land, or water resources. 3 The dvson of the contested resource depends on the countres arms or guns, whch are also produced domestcally. Snce armng s endogenous, so too are the prmary resources avalable to each country to produce consumpton goods. As armng rses, reflectng more ntense conflct, producton of consumpton goods falls and hence securty costs rse. The model employed here s a smple one. Frst, t abstracts from many salent features of today s world economy, such as the presence of ncreasng returns, heterogeneous frms, foregn nvestment, and endogenous growth. But, employng such a smple framework allows us to dentfy clearly the possble role that endogenously determned world prces play n nfluencng the countres ncentves to arm namely, the terms-of-trade channel that, to the best of our knowledge, has not been formally explored n the lterature. 4 Second, the model does not dstngush between the moblzaton of resources for conflct and the potentally destructve deployment of those resources, nor does t consder explctly the dsruptve effect of conflct to shutdown trade between warrng natons. 5 mltary expendtures, we focus on armng. 6 Instead, motvated by the emprcal relevance of Insofar as resources are absorbed nto 3 Although we have seen a sharp drop n nterstate wars snce WWII, nterstate conflct over resources remans relevant n nternatonal affars. One ongong dspute nvolves the countres surroundng the Caspan Sea (Russa, Kazakhstan, Turkmenstan, Iran, and Azerbajan) over how to dvde the rghts of exploraton and explotaton for ol. Another dspute nvolves Chna, Tawan, Vetnam, the Phlppnes, Indonesa, Malaysa, and Brune for control over the Spratly and Paracel slands n the South Chna Sea, where there are suspected ol reserves. See Klare (2012), who provdes many examples where the competton for scarce resources (ncludng but not lmted to ol), for whch property rghts are not well defned or enforceable, has turned or can turn volent. 4 Indeed, the lterature that explores the possble effects of trade on armng s scant, and the few papers that do exst consder, for the most part, small-country settngs where world prces are treated as exogenously determned (e.g., Skaperdas and Syropoulos, 2001; Garfnkel et al., 2015). One excepton s Skaperdas and Syropoulos (2002) who consder nteractons between countres n the context of an exchange model. That analyss dffers from the present one n that t focuses prmarly on how the antcpaton of exchange affects armng ncentves va ts mpact on the dvson of resources based on Nash barganng. 5 Ths s not to deny the mportance of conflct s dsruptve effect. To the contrary, ths effect s emprcally relevant and can be vewed as an opportunty cost of conflct that serves as the bass for classcal lberal vew as descrbed above. Whle some have found that conflct has lttle to no sgnfcant effect on trade (e.g., Barber and Levy, 1999), Glck and Taylor (2010) fnd compellng evdence of a negatve and sgnfcant effect that perssts over tme. In related research, we are studyng the adversaral countres armng choces and ther subsequent decson to ether fght (war) that would preclude trade between them or negotate a peaceful settlement (armed peace). 6 SIPRI researchers estmate that, n 2015, global mltary expendtures accounted for 2.3 percent of global GDP; whle many countres devoted less than 1 percent of ther GDP to armng, others allocated n excess of 10 percent. See Perlo-Freeman et al. (2015) for more detals. 2

4 the producton of arms and thus are unavalable for the producton of goods traded n world markets, these expendtures represent an mportant addtonal opportunty cost of conflct. Gven our focus, ths paper can be thought of as offerng an analyss of a modfed verson of the classcal lberal vew, one that apples to cold wars. 7 Wthn the settng of our model, we compare the outcomes under two polar trade regmes, autarky and free trade. As one would expect, gven the amount of resources allocated to armng, a shft from autarky to free trade unambguously results n hgher payoffs to both countres. However, such a swtch also nfluences armng ncentves. Under autarky, where countres can consume only what they produce, each one chooses ts armng (or ts securty polcy) so as to equate the margnal beneft of capturng the contested resource to the margnal cost of dvertng resources from the country s own producton and thus consumpton. At the same tme, each country s armng choce adversely affects the opponent by reducng ts access to the contested resource. In equlbrum, where both countres gnore ths negatve securty externalty, armng s strctly postve. Importantly, trade nduces each country to nternalze, at least partally, the negatve externalty of ts securty polcy on the resources avalable to ts rval. The result s to lower armng ncentves gven the rval s polcy. To be more precse, as n the case of autarky, when the two countres trade wth each other, each one chooses ts armng to balance ts margnal beneft wth ts margnal cost. In the case of trade, however, each country s payoff depends on the producton of ts adversary s exportable, whch the adversary produces relatvely more effcently. Accordngly, an ncrease n one s own arms has an addtonal cost under trade: a reducton n the adversary s share of the contested resource and thus a reducton n the adversary s producton of ts exportable. Ths added cost, whch s reflected n a deteroraton of the mportng country s terms of trade that lowers the margnal beneft of armng relatve to the margnal cost, means that a country s ncentve to arm, gven the adversary s armng 7 Acemoglu and Yared (2010) fnd emprcally that mltary expendtures and the sze of the mltary n terms of personnel are negatvely related to trade volumes. Although that analyss treats the mltary varables (reflectng the natonalst or mltarst sentments) as exogenous, the negatve relatonshp found can be vewed as prelmnary evdence n support of the modfed verson of the classcal lberal vew we consder here, focusng on mltary expendtures. More recently, Setz et al. (2015) lnk emprcally trade, wars and mltary spendng from 1993 through 2001, a perod when nter-state wars were qute rare. They fnd that trade brngs added benefts largely through ts effect to dampen defense spendng, not only by tradng partners, but other countres as well. These added benefts are, accordng to ther estmates, comparable to the drect welfare benefts of greater trade openness. 3

5 choce, s strctly lower under free trade than under autarky. The effect of a swtch from autarky to free trade on equlbrum armng and welfare, however, depends on the dstrbuton of the resource that s partly contested (what we call captal ) and the uncontested resource (what we call labor ) across the adversaral countres. Specfcally, when the rato of captal to labor s roughly even across countres such that ther margnal costs of armng (dependng postvely on the wage rate relatve to the unt prce of captal) are smlar, the countres securty polces are also smlar such that they jontly satsfy a suffcent (but not necessary) condton for trade to nduce less armng namely, the absence of strategc substtutablty n the neghborhood of the autarkc equlbrum. 8 Snce trade s no worse than autarky for a gven level of armng, the reducton n armng due to trade renders trade unambguously superor to autarky. And, the dfference n payoffs exceeds what s predcted by tradtonal trade theory that admts no possblty of conflct at all. In partcular, the reducton of armng relatve to autarky s an added beneft of trade that s consstent wth the sprt of classcal lberalsm and the wrtngs of authors such as Angell (1933) who extolled the vrtues of trade openness and globalzaton. 9 Whenever the mx of labor and captal resources s unevenly dstrbuted across countres, the country havng the hgher rato of captal to labor faces a greater margnal cost of armng, and as such tends to arm less heavly then ts opponent n the autarkc equlbrum. The resultng asymmetry could mply that the less powerful country s best-response functon exhbts strategc substtutablty n the autarkc equlbrum; but, that alone need not overturn the results descrbed above. Nevertheless, there do exst suffcently asymmetrc dstrbutons of labor and captal resources such that the less powerful country s nduced to ncrease ts arms as ts opponent reduces ts armng n response to a shft from autarky to free trade. What s more, the resultng adverse strategc effect realzed by the more powerful country could swamp ts gans from trade to render trade unappealng. 8 How the dstrbuton of resources across countres matters n determnng whether ths condton s satsfed depends partly on the conflct technology and partly on the technology for producng the ntermedate good. 9 Of course, Angell wrote the frst edton of hs book just before the outbreak of World War I, an event that can be consdered a sgnfcant counterexample to the optmsm of classcal lberalsm. However, see Gartzke and Lupu (2012), who n examnng the nterplay of the networks of economc nterdependence and mltary allances n the perod leadng up to World War I offer a more favorable nterpretaton of that major conflct n relaton to the lberal theory. 4

6 That the potental for greater trade openness to pacfy nternatonal relatons may be lmted n such cases s remnscent of the vew expressed by realsts/neorealsts n the nternatonal relatons lterature that hghlghts trade s effect to generate uneven gans to tradng partners and thereby dfferentally nfluence ther armng and thus the balance of power. But, n our analyss, the dfferental nfluence of trade on the two countres armng choces and the mpled nfluence on the balance of power hnges on sharp dfferences n the mx of ther ntal holdngs of secure captal and labor, not smply on dfferences n the sze of ther economes. 10 Our fndng of a possble lmt of trade openness to reduce the severty of nternatonal conflct at least n terms of resources devoted to armng also complements the more recent theoretcal work n the economcs lterature based on extensons of Heckscher-Ohln models that emphasze dfferences n factor endowments nstead of dfferences n technologes. In partcular, Skaperdas and Syropoulos (2001) and Garfnkel et al. (2015) study settngs wth two small countres that do not trade wth each other; yet, they possbly trade wth the rest of the world. A shft from autarky to trade n such settngs changes product prces and thus relatve factor prces, thereby alterng the cost of combnng resources n the producton of arms. 11 They fnd that, dependng on world prces, trade can ntensfy competton for resources used to produce tradables to such an extent that the added armng and the assocated conflct costs outwegh the gans from trade and thus render autarky preferable to free trade. Another possble lmt to the noton that the expanson of trade can nduce lower equlbrum armng follows from a modfed verson of our settng, consstng of three countres: two adversaral countres as before and a thrd, frendly country. Suppose, n partcular, that the two adversaral countres are dentcal n every respect so that, even n the absence of barrers to trade, they would not trade wth each other. Also, suppose that there exst technologcal dfferences between these two countres on the one hand and the thrd country on the other hand that can, gven the resources 10 Also see Bonfatt and O Rourke (2014), who consder the role of ncreasng trade dependence for two adversaral countres wth the rest of the world, n a dynamc, leader-follower settng, to nfluence the lkelhood of a preemptve war by the follower. In that analyss, smlar to ours, understandng the emergence of conflct between the two countres does not hnge on dfferences n the sze of ther economes. But, n Bonfatt and O Rourke s analyss, one fundamental sort of asymmetry s crtcal that s, the leader s ablty to block mports (necessary for armng) to the rval. 11 We abstract from ths mechansm n the current model, to solate the mportance of the endogenety of the countres terms of trade for armng ncentves, wth trade patterns beng determned by technology as emphaszed n Eaton and Kortum (2002). Of course, n more general (and largecountry) settngs, both mechansms could be present. 5

7 allocated to armng, make trade mutually advantageous. In ths case where the two adversaral countres compete n the market for the same good exported to a thrd country, there s an added margnal beneft to armng under trade namely, a postve terms-of-trade effect mplyng ncreased armng ncentves under trade relatve to those under autarky. That expanded trade opportuntes wth another (frendly) country can ntensfy conflct between two adversares s smlar n sprt to Martn et al. (2008), who show n the context of a new trade model wth product dfferentaton that ncreasng the opportuntes for trade among all countres reduces the nterdependency between any two and thus can make conflct between them more lkely. However, whle that analyss emphaszes the mportance of the dsruptve effects of conflct, ours hghlghts the mportance of the endogenety of armng and ts trade-regme dependence. Furthermore, our analyss, lke Skaperdas and Syropoulos (2001) and Garfnkel et al. (2015), suggests that, n ths case, trade between frends could make the adversares worse off. 12 Our analyss also has mplcatons for the endogenous determnaton of trade regmes. To examne these mplcatons, we extend the model to allow the contendng countres to choose non-cooperatvely and smultaneously autarky or free trade, before they choose securty polces. As expected n the two-country settng, when a shft to free trade nduces lower equlbrum armng by both countres, free trade s a subgame perfect equlbrum of the extended game. We cannot, however, rule out the possblty of autarky as another equlbrum outcome. In the three-country case, free trade wll emerge as the unque subgame perfect equlbrum, provded that the added securty costs are lower than the tradtonal gans from trade for the two contendng countres wth the thrd, frendly country. By contrast, f the added securty costs exceed those gans, then the subgame perfect equlbrum s necessarly asymmetrc. One contendng country trades freely wth the thrd, frendly country, whereas the rval chooses autarky. 13 Smlar to the fndngs of Matsuyama (2002), the 12 It s mportant to note, though, that the result n ths paper s due to the benefcal effect that a country s armng has on ts own terms of trade to add to armng ncentves, whereas the result n Skaperdas and Syropoulos (2001) and Garfnkel et al. (2015) derves from the mpact of world prces to ncrease armng ncentves through factor prces. A smlar result has been found n settngs where there s conflct over some resource between groups wthn a sngle (small) country that trades wth the rest of the world (see Garfnkel et al. (2008) and references cted theren). 13 Snce the two adversares are dentcal ex ante, whch one trades freely and whch one remans n autarky cannot be determned. The asymmetrc nature of ths equlbrum contrasts sharply wth Garfnkel et al. (2015), who fnd n a dfferent settng, where two small and dentcal adversares potentally trade wth the rest of the world, that the equlbrum s symmetrc. For all world prces 6

8 possblty of trade wth a thrd, frendly country s symmetry-breakng. Although the adversares arm dentcally, the one that engages n trade enjoys a hgher payoff. In what follows, the next secton presents the basc model, focusng on just two countres that trade wth one another. Secton 3 derves the countres payoff functons under the regmes of autarky and trade, showng that, for gven arms, autarky s weakly domnated by trade. In Secton 4, we characterze the countres ncentves to arm under each trade regme. Secton 5 studes how equlbrum armng and payoffs compare across trade regmes, dentfyng condtons under whch ncreased trade openness nduces lower armng by both countres and those under whch t can nduce greater armng by one of them to possbly render trade unappealng to the other country. We extend the framework by ntroducng a thrd (non-adversaral) country, n Secton 6, to explore the mportance of the nature of the tradng relatonshp between the contendng natons n determnng how ncreased trade openness can nfluence equlbrum armng and payoffs. Secton 7 examnes the countres non-cooperatve choce of trade regmes n both the two- and three-country cases. Concludng remarks follow n Secton 8. All techncal and supplementary detals are relegated to appendces. 2 Contestng a Resource n a Rcardan Settng Consder a world wth two countres, ndexed by a superscrpt = 1, 2. Each country holds secure endowments of two productve resources: labor denoted by L and captal denoted by K. Captal could be land, ol, mnerals, tmber or water resources. In contrast to standard trade models, we suppose that there s an addtonal amount of captal, denoted by K 0, that s nsecure and contestable by the two countres. Each country has the capacty to produce two goods for fnal consumpton, X j (j = 1, 2), and guns (or arms), G. 14 Guns should be vewed as a composte good reflectng the country s mltary strength that s deployed n an effort to take control of the nsecure resource K 0. Specfcally, the share of K 0 captured by country s that ensure the Pareto domnance of autarky, free trade s a possble subgame perfect equlbrum; and, for a subset of those prces, t s the unque equlbrum. 14 Our analyss focuses on adjustments at the ntensve margn, but could be extended to consder a contnuum of consumpton goods, as n Dornbusch et al. (1977). We chose the two-good verson of the model n vew of economsts general famlarty wth t, and because t allows us to dentfy the welfare mplcatons of trade n the presence of conflct for large, asymmetrc countres. 7

9 gven by φ = φ(g, G j ) = f(g ), j = 1, 2, (1) f(g ) + f(g j ) where f( ) > 0, f(0) s arbtrarly close to 0, f ( ) > 0, and f ( ) 0. Ths specfcaton of the conflct technology, also known as the contest success functon, s symmetrc so that G 1 = G 2 0 mples φ 1 = φ 2 = 1 2 ; t also mples φ s ncreasng n country s own guns (φ G > 0) and decreasng n the guns of ts adversary (φ G j < 0, j ). 15 The nfluence of guns on the dvson of K 0 between the two countres can be thought of as the result of ether open conflct (wthout destructon) or a barganng process wth the countres relatve mltary strength playng a promnent role. 16 Guns are produced wth secure labor and/or captal endowments. Let w and r be the compettve rewards pad to labor and captal n country, respectvely. Now defne ψ(w, r ) as the cost of producng one gun n country. Ths unt cost functon, whch s dentcal across countres, s ncreasng, concave and homogeneous of degree one n factor prces. By Shephard s lemma, ts partal dervatves ψ w and ψ r gve the condtonal demands respectvely for labor and captal n the producton of one gun. Thus, the quanttes of labor and captal dverted to contestng K 0 n each country are respectvely ψ wg and ψ rg, wth ψ r/ψ w representng the correspondng captal-labor rato. Throughout, we assume that the secure labor and captal resource constrants do not bnd n the producton of guns for ether country : L ψ wg > 0 and K ψ rg > 0. Once guns have been produced and the dsputed resource has been dvded, the resdual quanttes of labor and captal avalable to country are respectvely L Z = L g ψ wg and K Z = K g ψ rg, where L g L and K g K + φ K 0 denote gross quanttes of these prmary resource factors. Each country combnes ts own resdual resources, L Z and K Z, to produce an ntermedate nput, Z. Both factors are essental, and the technology s descrbed by the unt cost functon c(w, r ). 17 Ths 15 Ths specfcaton dffers modestly from the rato or power form typcally assumed (e.g., Hrshlefer, 1989; Skaperdas, 1996).e., f(g) = G b wth b (0, 1] n that t does not mply a dscontnuty of φ n guns at G 1 = G 2 = 0. That s to say, wth f(0) > 0, φ G (0, 0) = f (0)/4f(0) s defned. One example s f(g) = (δ + G) b wth b (0, 1] and δ > 0. Assumng that f(0) s postve but arbtrarly close to 0 s helpful n our proofs of exstence of equlbrum n armng choces under the trade regmes studed. 16 See Anbarc et al. (2002) for an analyss of how alternatve barganng soluton concepts translate nto rules of dvson that dffer n ther senstvty to guns. 17 Below, we also consder brefly the possblty that the factor nputs are perfectly substtutable n 8

10 functon, lke that for guns, s dentcal across countres, and ncreasng, concave and lnearly homogeneous n factor prces. Furthermore, c w and c r gve the condtonal demands respectvely for labor and captal n the producton of a unt of Z, wth c r/c w ndcatng the captal-labor rato demanded n that sector of the economy. The ntermedate good Z, n turn, s used to produce goods for fnal consumpton. Suppose, n partcular, that to produce one unt of good j (= 1, 2) producers n country (= 1, 2) need a j > 0 unts of Z. Then, wth Xj denotng the supply of good j n country, the followng expresson descrbes the producton-possblty set of country s tradables: a 1X 1 + a 2X 2 = Z, where X j 0. (2) Observe from (2) that, as n the canoncal 2-country, 2-good, one-factor Rcardan trade model, comparatve advantage s drven by nternatonal dfferences n technology (.e., productvty) and not by dfferences n factor endowments. 18 To fx deas, we assume that country has a comparatve advantage n good. That s, a 1 1/a 1 2 < a 2 1/a 2 2, whch states that the opportunty cost n country to produce good (= 1, 2) s lower than the correspondng opportunty cost n country j ( ). To economze on notaton and emphasze the mportance of other varables of nterest, we normalze a (= 1) for = 1, 2 and let α = a j > 1 for j = 1, 2. Note, n any case, ths model dffers from the Rcardan trade model n a sgnfcant way. Specfcally, each country s producton of Z (and thus each country s productve potental and ncome) depends on the securty polces of both countres (G for = 1, 2), whch are endogenous. Brngng the essental elements of the model together, the sequence of events s as follows: Stage 1. The two countres ( = 1, 2) smultaneously choose ther guns G usng ther secure endowments of labor and captal. the producton of Z. As wll become obvous, mperfect substtutablty of nputs n the producton of Z (along wth a sharp uneven mx of labor and captal endowments across countres) s a necessary condton for trade to nduce greater armng gven non-bndng resource constrants n the producton of guns. 18 We mpose ths producton structure wth an ntermedate nput for convenence only. An analytcally equvalent approach would be to assume that the producton functons of traded goods n each country dffer by a Hcks neutral factor of proportonalty, but not n factor ntenstes. Abstractng from dfferences n factor ntenstes allows us to rule out factor-endowment based ratonales for trade patterns and the possble adjustments n armng decsons due to trade related factor-prce effects (as n extensons of the Heckscher-Ohln model) and focus nstead on terms-of-trade effects. 9

11 Stage 2. The contested resource K 0 s dvded accordng to the φ combnaton nduced by these choces. Each country then uses all ts avalable nputs (L Z = L g ψ wg unts of labor and K Z = K g ψ rg unts of captal) to produce the ntermedate nput, Z. Stage 3. Each country uses output of Z to produce X and X j unts of consumpton goods and j respectvely. Stage 4. These fnal goods are traded domestcally and/or nternatonally dependng on the trade regme n place. In the subsectons to follow, we complete the specfcaton of the model and present some prelmnary analyss that allows us to subsequently analyze the equlbrum of ths model contngent on the prevalng trade regme. 2.1 Factor Markets and Producton of the Intermedate Input Whether the two countres trade or not, perfect competton wthn each one requres the prce of the ntermedate nput (p Z ) to be equal to ts correspondng margnal cost (c ); as such, we use these concepts nterchangeably. Addtonally, the amount of each factor used to produce Z and G must equal ts gross supply: c rz + ψ rg = K g ( K + φ K 0 ) (3a) c wz + ψ wg = L g ( L ), (3b) for = 1, 2. These condtons jontly determne the wage-rental rato ω w /r and output of Z that ensure factor markets n each country clear. To proceed, we now derve an expresson for the value of each country s producton of the ntermedate nput, whch we denote by R, gven the two countres gun choces. Specfcally, multply both sdes of (3a) by r and the two sdes of (3b) by w and sum them; rearrangng and usng the lnear homogenety of the unt cost functons n factor prces, then gve the followng: R = c Z = w L Z + r K Z = w L g + r K g ψ G. (4) Equaton (4) mplctly defnes Z as a functon of ω, L g, K g, and G. In partcular, solvng (4) for Z, whle agan appealng to the lnear homogenety of the cost functons 10

12 that mples ψ(w, r )/r = ψ(ω, 1) and c(w, r )/r = c(ω, 1), shows: Z (ω, K g, L g, G ) = w L g + r K g ψ(w, r )G c(w, r ) = ω L g + Kg ψ(ω, 1)G. (5) c(ω, 1) Ths functon, as wll become obvous below, plays a pvotal role n the defnton of the countres payoff functons and thus n our analyss of securty polces. For now, let kz K Z /L Z denote country resdual captal-labor rato, and observe that combnng (3a) and (3b) yelds c r c w = k Z K g ψ rg L g ψ wg. (6) Ths equaton mplctly defnes the equlbrum wage-rental rato ω w /r n country as a functon of K g, L g, and G : ω e ω e (K g, L g, G ). Then, usng ω e n the rght-hand sde (RHS) of (5) gves Z e Z e (K g, L g, G ), whch we refer to as the optmzed producton of the ntermedate nput Product Markets and Demand Let p j and D j respectvely denote the prce and quantty of consumpton good j (= 1, 2) demanded n country (= 1, 2). To keep the analyss as transparent as possble, we abstract from trade costs. 20 Compettve domestc (or nternal ) prcng n output markets always requres p = c for = 1, 2, snce country produces the good n whch t has a comparatve advantage (good ) whether or not t trades wth country j. Furthermore, absent trade costs, perfect competton requres that the prce of country s mportable good satsfy p j = mn[α c, c j ] for j = 1, 2. When trade s possble, at least one country wll cease to produce ts mportable; n ths case p j = p j j = cj for j = 1 and/or 2. But, f trade s smply ruled out, then p j = α c. Consumer preferences n each country are gven by U = U(D, D j) for j = 1, 2, whch we assume to be ncreasng, quas-concave, homogeneous of degree one and symmetrc over the two goods, wth a constant and fnte elastcty of substtuton, 19 Lemma A.1 presented n the Appendx shows how Z e and ω e depend on L g, K g and G. 20 However, as dscussed below n Secton 5.1, our fndngs regardng the negatve effect of trade openness on equlbrum armng and the resultng postve effect on welfare are robust to the presence of trade costs. 11

13 denoted n absolute terms by σ (0, ). 21 Let Y denote country s natonal ncome. Under both autarky and trade (absent tarffs), we have Y = R = c Z. Then, country s ndrect utlty functon can be wrtten as V = µ(p, p j)y = µ(p, p j)c Z, where µ µ(p, p j) = [(p ) 1 σ +(p j) 1 σ ] 1/(σ 1) for j = 1, 2 represents the margnal utlty of ncome, whch s decreasng and homogeneous of degree 1 n prces. 22 By Roy s dentty, the Marshallan demand functon for good j n country s D j = γ jy /p j = γ jc Z /p j, (7) where γ j γ j(p, p j) = ( µ / p j)/(µ /p j) = (p j) 1 σ /[(p j) 1 σ +(p ) 1 σ ] s the expendture share on good j (= 1, 2) n country (= 1, 2). Naturally, the relatve demand RD = D j/d for good j n country depends solely on prces. Defne p p j/p as the prce of good j n country relatve to the good n whch country enjoys a comparatve advantage, and let a hat ˆ denote percentage change (e.g., x dx/x). Then, we have RD = σ p, whch mples the relatve demand for the mportable good j n country depends negatvely on p, and more so the greater s σ. Furthermore, we have γ j/ p j = (1 γ j)(σ 1)(γ j/p j), whch shows that the expendture share for the mportable good s decreasng (ncreasng) n the prce of that good p j when σ s greater (less) than one. 3 Trade Regmes and Payoff Functons To explore how the two countres ncentves to arm depend on the trade regme n place namely, autarky and trade we frst analyze how equlbrum and thus payoffs are determned under each of these regmes for gven securty polces, G, and gross factor endowments, K g and L g. 21 Assumng CES preferences s not pvotal here, but helps smplfy notaton. Our assumpton that the consumpton goods are mperfect substtutes (σ < ) eases the exposton. As wll become clear, when σ =, the trade-dependency of armng ncentves dsappears. 22 More precsely, µ s the nverse of the prce ndex that s dual to the CES aggregator. Observe the lnear homogenety of utlty mples rsk neutralty; however, due to the concavty of the technology for Z n captal, ths assumpton does not mply the equvalence of the contest we are consderng and a wnner-take-all contest, wth φ equalng country s probablty of takng control of the entre quantty of the dsputed resource. As can easly be confrmed, under autarky gven ther guns choces, the two countres strctly prefer (ex ante) to share the dsputed resource accordng to (1). 12

14 3.1 Autarky We start our analyss of a closed economy wth two observatons. Frst, self-suffcency requres both consumpton goods to be produced n each country ; therefore, p = c and p j = α c, whch gve the equlbrum relatve prce under autarky: p A = p j/p = α. Second, wth the Marshallan demand functons (7), the just-descrbed market exchange rato between the two consumpton goods determnes the dvson of ncome between them. Ths dvson along wth the product market-clearng requrement that Dj = Xj for each good j determnes (by (2)) equlbrum quanttes. Usng the compettve prcng relatons noted above n µ(p, p j) and the fact that under autarky Y = R = c Z, the ndrect utlty functon of the representatve consumer n country can be wrtten as VA = µ(c, α c )Y = m AZ e (K + φ K 0, L, G ), = 1, 2, (8) where, snce µ s homogeneous of degree 1 n prces, m A µ(c, α c )c = µ(1, p A ), and where Z e Z (ω e, ) satsfes (5) and (6). An mportant feature of country s payoff functon under autarky (8) s that, snce p A = α and α s a constant parameter, m A s also a constant. Thus, each country s armng decson under autarky depends solely on how G nfluences ts optmzed producton of the ntermedate nput, Z e. 3.2 Free Trade Before examnng armng ncentves under autarky, we characterze the equlbrum payoff functons gven guns under trade. We focus on the case where each country specalzes producton completely n the good for whch t has a comparatve advantage: X = Z for = 1, 2. Thus, country s demand for good j s fulflled entrely by mports, and the equlbrum determnaton of world prces that clears the market for good j satsfes Dj + D j j = Xj j = Zj for j ( ) = 1, 2. To proceed, recall that compettve forces under free trade mply consumers face dentcal prces for each good: p j = p j j = cj for j = 1, 2. Snce consumers preferences are dentcal across countres, the equalty of the prces of good j across countres mples that ther expendture shares on that good are dentcal: γj = γ j j = γ j for j = 1, 2. Mantanng our focus on the market for good j, now let p T ( p j j /pj = c j /c ) denote the world (or domestc) prce of country s mportable (good j ) n terms of ts exportable good. Substtuton of the demand functons (7) wth the compettve prcng relatons nto the relevant market-clearng condton 13

15 shows p T = γ j Z /γ Z j, j, (9) where the expendture share on good j can be wrtten as γ j = (p T )1 σ /[1 + (p T )1 σ ] and γ = 1 γ j. 23 One can see the mpact of the relatve supply of the countres ntermedate nputs on p T and thus on country s terms of trade by logarthmcally dfferentatng (9), whle accountng for the dependence of the expendture shares on p T. After rearrangng terms, we have p T = 1 σ [Ẑ Ẑj ], (10) for j = 1, 2. An exogenous ncrease n the relatve supply of country s ntermedate nput Z /Z j expands the relatve supply of ts exportable and thus ncreases the relatve world prce of country s mportable p T a deteroraton of ts terms of trade that s decreasng n the elastcty of substtuton n consumpton σ > 0. Snce Y = R = c Z, we wrte country s payoff functon under trade as: V T = µ (p, p j)y = m T Z e (K + φ K 0, L, G ), j = 1, 2, (11) where m T µ(p, p j)c = µ(1, p T ) and Ze satsfes (5) and (6). Guns producton nfluences the payoffs under trade, lke the payoffs under autarky, through ts effect on the maxmzed value of the country s ntermedate output Z e. However, country s producton of guns nfluences VT through an addtonal channel namely, through ts effect on the relatve prce of country s mportable, p T. Specfcally, from (10), an ncrease n G, gven G j, ncreases Z and decreases Z j, and thereby ncreases the relatve prce of country s mportable good, p T. Snce m T = γ p T m j < 0, equaton T (11) mples an ncrease n p T alone reduces country s payoff under trade V 3.3 Incentves to Trade (for Gven Guns) Whle one of our prmary goals s to explore the trade-regme dependency of armng ncentves and the assocated welfare mplcatons, t s nstructve to see how payoffs 23 Of course, dependng on the countres securty polces, factor endowments, technology, and consumer preferences, p T could be determned by one country s autarkc prce. We revst ths possblty below. p T T. 14

16 under autarky and trade compare for gven guns. Based on a standard, gans-fromtrade argument usng (8) and (11), one can verfy the followng: Lemma 1 For any gven feasble guns and gross factor endowments, payoffs under autarky and trade are ranked as follows: VA V T, for each = 1, 2. Intutvely, when country s cost of mportng good j (p T ) s greater than ts opportunty cost α = p A, country produces both goods locally, mplyng dentcal payoffs under the two trade regmes. Trade flows between the two countres wll be strctly postve, gven guns, only when p T α wth strct nequalty for at least one country to make the payoffs for both countres under trade at least as hgh as they are under autarky and strctly greater under trade for at least one of them. 24 Any added payoff generated by a shft to free trade (gven armng) reflects the famlar gans from trade that follow from canoncal trade models based on comparatve advantage. 4 Endogenous Securty Polces We now turn to the determnaton of noncooperatve equlbra n securty polces and ther dependence on trade regmes. Inspecton of the objectve functons under autarky (A) n (8) and under trade (T ) n (11) reveals that the equlbrum producton of the ntermedate nput, represented by the envelope functon Z e, s of central mportance here. 25 As establshed n Lemma A.1 (presented n the Appendx), Z e and the equlbrum wage-rental rato ω e depend, under each trade regme, on guns and gross labor and captal endowments. Gven these quanttes, however, Z e and ω e are ndependent of the prevalng trade regme. Thus, as noted earler, our analyss rules out factor prces as a channel through whch a change n trade regmes can nfluence armng ncentves; nstead, the trade-regme dependency of armng ncentves operates solely through a terms-of-trade channel. 26 To set the stage for ths analyss, we make two addtonal observatons that can be verfed from (5). 27 Frst, the effect of a margnal ncrease n country s gross 24 To be more precse, comparng m A = µ(1, p A ) and m T = µ(1, p T ) shows that, f p T < p A = α holds for both countres, then each country specalzes completely n the producton of good, and both countres are strctly better off under trade. 25 Whle Z e mght appear to be a regular producton functon, t s best thought of as an equlbrum quantty that s jontly determned wth factor prces and wth gross nputs K g and L g beng employed (possbly) n dfferent proportons than n the producton of G. 26 By contrast, focusng on small countres, Garfnkel et al. (2015) abstract from the terms-of-trade channel, whle featurng nstead the factor-prce channel. 27 Also see the proof of Lemma A.1 presented n the Supplementary Appendx (B.1). 15

17 endowment of captal Kg = K + φ K 0 on Z e s gven by ZK e = r /c and the effect of a margnal ncrease n ts armng G (gven Kg) on Z e s Z e G = ψ /c. Second, an ncrease n G also affects the rval s optmzed producton of the ntermedate good Z je through ts nfluence the rval s gross captal endowment, Z je K = rj /c j. Brngng these observatons together, whle notng from (1) φ j = φ G G, shows: dz e = K dg 0 φ G Ze K + Z e G = 1 [ r K c 0 φ G ψ] dz je = K dg 0 φ j Z je G K = 1 c j [rj K 0 φ G ], gven G j, for j = 1, 2. (12a) (12b) 4.1 Autarky As revealed by the payoff functons under autarky (8) and noted earler, country s armng choce nfluences VA only through ts effect on the maxmzed value of country s ntermedate nput, Z e. That s to say, snce m A s a constant, V A = Ẑe. Thus, from (12a), each country s frst-order condton (FOC) for the choce of guns G, takng G j as gven, can be wrtten as 1 m A V A G = dze dg = 1 c [ r K 0 φ G ψ] 0, = 1, 2. (13) The frst term n the brackets of the RHS of (13) reflects the margnal beneft of producng an addtonal gun for country. An addtonal gun ncreases the share of the dsputed resource that country captures n the contest (gven the rval s choce G j ) and thereby ncreases the country s ncome and payoff. However, as shown n the second term, that addtonal gun comes at a cost. In partcular, captal and labor resources are dverted away from the producton of the ntermedate nput used n the producton of consumpton goods. Each country s optmal securty polcy balances ths trade-off at the margn. Observe that the negatve nfluence of country s securty polcy on country j s payoff through ts effect on Z je (shown n (12b)) does not drectly enter ths calculus. Mantanng focus on the case n whch the secure resource constrants on guns (.e., K ψ rg 0 and L ψ wg 0) are not bndng, equaton (13) s an exact statement of country s FOC under autarky. Furthermore, the conflct technology (1) mples nteror solutons wth (13) holdng as an equalty. Snce Z e s concave n 16

18 the country s own guns G and n the country s gross captal endowment K g (see parts (c) and (e) of Lemma A.1) and K g s concave n G through the conflct technology (1), we can show that V A s strctly quas-concave n G. Ths property ensures the exstence of an nteror (pure-strategy) equlbrum n securty polces. Let (G 1 A, G2 A ) be an equlbrum par of guns. Some addtonal (but relatvely mld) assumptons mply the equlbrum s unque: Proposton 1 (Equlbrum securty polces under autarky.) An nteror equlbrum n securty polces exsts under autarky: G A > 0, for = 1, 2. Furthermore, f labor and captal are suffcently substtutable n the producton of arms and/or the ntermedate good, ths equlbrum s unque. Proof. See the Appendx. Observe from (13) that the equlbrum n securty polces under autarky s ndependent of the elastcty of substtuton n consumpton. Ths ndependence follows snce each country s problem under autarky s effectvely one of maxmzng ncome or, equvalently, the quantty of the ntermedate good used n the producton of traded goods. Matters dffer, however, n the case of trade. 4.2 Free Trade Securty polces under trade, lke those under autarky, affect payoffs through ther mpact on the output levels of the ntermedate good. However, when trade s possble between adversares, these output changes also affect world prces as shown n (10). Then, usng (10) and (11) and recallng that m T / p T m T /p T followng: = γ j, one can verfy the ( ) m V T = Ẑe + T / p T p m T /p T = Ẑe γ j (Ẑe ) T σ Ẑje, j = 1, 2. (14) The second term n the RHS of ths expresson shows the terms-of-trade effect. Combnng (12) wth (14), the FOC for country s armng choce becomes: 1 m T VT G = 1 {[ 1 γ j c σ ( ) ] r j /c j Z je γj [ r K r /c Z e 0 φ G σ 1 γ ] } j ψ 0, (15) σ for = 1, 2 and j. Smlar to the FOC under autarky (13), ths FOC conssts of two components: the margnal beneft and the margnal cost of an addtonal 17

19 gun. However, the negatve effect of an addtonal gun on country s terms of trade modfes these two components as compared wth autarky, thereby suggestng that whether trade s possble or not matters for the countres ncentves to arm. Before explorng that nfluence, we characterze the equlbrum under trade. Henceforth, we assume that σ > γ j for j = 1, 2, such that the margnal cost of armng s strctly postve for both countres. Ths assumpton, however, does not ensure that the margnal beneft, when evaluated at G = 0, s strctly postve. Dggng a lttle deeper, let us defne ξ j r /c Z e r j /c j Z je + r /c Z e = c j Z je /r j, for j. c Z e /r + c j Z je /rj The parameter ξ j reflects country j s relatve sze n terms of the countres GDP, net of armng and measured n domestc unts of the nsecure resource. Then, the sgn the margnal beneft for country (.e., the frst term n (15)) s determned by the sgn of (σ γ j /ξ j ). Hence, there exsts a crtcal value of σ, σ γ j /ξ j evaluated at G = G j = 0 for each country j = 1, 2, such that country s margnal beneft of armng when G = 0 s strctly postve (non-postve) f σ > σ (σ σ ). Snce γ 1 + γ 2 = ξ 1 + ξ 2 = 1, there are two dstnct possbltes to consder: () σ 1 = σ 2 = 1, whch arses when the two countres have dentcal secure endowments; 28 and, () σ > 1 > σ j for j = 1, 2, whch arses n the presence of asymmetres. Thus, f σ 1, the margnal beneft of armng must be non-postve for at least one country (the relatvely larger one) and possbly both; f σ > 1, the margnal beneft of armng must be postve for at least one country j (the relatvely smaller one) and possbly both. Also observe that the maxmum value of σ across, σ max[σ 1, σ 2 ], s greater than or equal to 1. Buldng on these deas and usng the FOC under trade (15), t s possble to verfy that an equlbrum always exsts. However, multple pure-strategy equlbra or mxed-strategy equlbra are possble. Nonetheless, provded that the strength of the two countres comparatve advantage, as determned by domestc opportunty costs and measured by α, s suffcently strong, a pure-strategy equlbrum that 28 Specfcally, as dscussed n Secton 5.1, a symmetrc equlbrum emerges wth Z e = Z je, γ = γ j = 1 2 and p T = 1 for = 1, 2. Snce equlbrum factor prces are dentcal across countres, we have addtonally ξ j = 1 2 n ths benchmark case. Thus, σ > 1 (σ 1) mples that the margnal beneft of armng s strctly postve (non-postve) at G = 0 for both. 18

20 dffers from the one under autarky exsts under free trade. 29 focuses on ths case, lettng (G 1 Proposton 2 T, G2 T ) denote that equlbrum: The next proposton (Equlbrum securty polces under free trade.) Suppose the condtons that ensure a unque equlbrum under autarky are satsfed and each country s comparatve advantage (α ) s suffcently large. Then, there exsts a pure-strategy equlbrum n securty polces under free trade that s dstnct from the equlbrum under autarky: () G T = 0 for = 1, 2 f σ σ max[σ1, σ 2 ] and () G T ( G A ) > 0 for = 1, 2 f σ (σ, ). Proof. See the Appendx. Clearly, the elastcty of substtuton n consumpton (σ) plays an essental role under free trade, as t determnes the magntude of the terms-of-trade effect. When the two goods are not close substtutes (.e., σ 1), then σ σ for one country = 1, 2, or both. Country s payoff under trade n ths case s hghly dependent on country j s producton, through relatve world prces. Even though an ncrease n guns by country, where ntally G = 0 and gven G j 0, generally mples a postve net margnal beneft of armng for gven world prces (.e., r K 0 φ G ψ > 0), that addtonal gun by country mples at the same tme a worsenng of ts terms of trade. More precsely, t nduces not only an ncrease n the supply of ts exportable good but also a decrease n the supply of ts mportable good. The terms-of-trade effect, then, tends to reduce the effectve margnal beneft of an addtonal gun by more than t reduces the margnal cost. Indeed, when the two consumpton goods are not suffcently substtutable (σ 1), the negatve net terms-of-trade effect swamps the postve net margnal gan gven world prces for at least one country,. Then, gven (1) wth φ G (0, ) at G = 0, country chooses to produce no guns at all. If, n addton, σ σ j, then G T = Gj T = 0. But, even f σ > σj whle σ σ, our specfcaton of the conflct technology (1) requrng that f(0) be arbtrarly close to zero (even f postve) mples that country j s best response to G = 0 s to produce 29 The potental problem, as analyzed n the Supplementary Appendx (B.1), s that p T can vary only wthn the range [1/α j, α ], gvng rse to a possble dscontnuty n country s best-response functon under trade such that t concdes wth country s best-response functon under autarky for some G j. Requrng that comparatve advantage α be suffcently large for both = 1, 2 ensures the exstence of a pure-strategy equlbrum n securty polces that s dstnct from the equlbrum under autarky. Nevertheless, even when ths requrement s satsfed, we cannot rule out the possblty that there exst multple pure-strategy, trade equlbra. 19

21 just an nfntesmal amount of guns. In ths case, securty costs are effectvely equal to zero. Hence, we wrte n the case where σ < 1 σ max[σ 1, σ 2 ], G 1 T = G2 T = 0.30 When the two consumpton goods are suffcently substtutable (.e., σ > σ 1), the negatve effect through the terms of trade channel s not large enough to wpe out the postve net margnal beneft of armng gven world prces when evaluated at G = 0 for ether country. The condtons specfed n the proposton along wth (1) ensure, n ths case, the exstence of an nteror equlbrum n securty polces under trade that dffers from the equlbrum under autarky. At ths nternal equlbrum, the favorable effect of an ncrease n the rval country s armng G j T on country s terms of trade s not suffcently large to swamp the negatve effect on country payoff for gven world prces. Put dfferently, the externalty of each country j s armng remans negatve n equlbrum: dv T /dgj < The Relatve Appeal of Free Trade We are now n a poston to compare the equlbrum payoffs under the two trade regmes, denoted by VA V A (G A, Gj A ) n the case of autarky and VT V T (G T, Gj T ) n the case of trade, for j = 1, 2. Combnng Lemma 1 wth the equlbrum analyss underlyng Propostons 1 and 2, the next lemma establshes that a suffcent condton for trade to domnate autarky s smply that trade nduce lower armng by both countres: Lemma 2 (Equlbrum payoffs under autarky vs. free trade.) Suppose that trade nduces both countres to arm less as compared wth autarky. Then, each one s strctly better off under free trade than under autarky (.e., V T (G T, Gj T ) > V A (G A, Gj A ) for j = 1, 2), and the dfference n payoffs for both s greater than the standard gans from trade. 30 Observe σ 1 s suffcent, but not necessary, for trade to effectvely remove both countres ncentves to arm; the same result obtans when σ > 1, as long as σ < σ. 31 To confrm ths clam, whch also holds true when σ > σ > 1 (such that country chooses not to arm whereas country j chooses an nfntesmal quantty of arms), evaluate dv T /dgj V = dze /dg j Z e γ j σ [ dz e /dg j Z e dzje /dg j ] Z je, usng the value of dze /dg j Z mpled by country j s FOC under trade (15) for an nteror soluton, to e fnd that a necessary and suffcent condton for dvt /dgj < 0 s that σ > 1. 20