Militarized Disputes, Uncertainty, and Leader Tenure

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1 Militaized Disputes, Uncetainty, and Leade Tenue Badley C. Smith William Spaniel June 28, 2018 Abstact How do new leades impact cisis negotiations? We ague that opposing states know less about such a leade s esolve ove the issues at stake. To fully appeciate the consequences, we develop a multi-peiod bagaining model of negotiations. In equilibium, as a popose becomes close to cetain of its opponent s type, the duation and intensity of wa goes to 0. We then test whethe inceases to leade tenue decease the duation of Militaized Intestate Disputes. Ou estimates indicate that cises involving new leades ae 25.3% moe likely to last one month than cises involving leades with fou yeas of tenue. Moeove, such conflicts ae moe likely to esult in highe fatality levels. These esults futhe indicate that leade tenue is a useful poxy fo uncetainty. We ae gateful to Phil Aena, Eik Gatzke, Chales Gochman, Hein Goemans, Katja Kleinbeg, Amanda Licht, Paul Poast, William Reed, Scott Wolfod, two anonymous eviewes, and the paticipants of the 2016 Empiical Implications of Bagaining Theoy wokshop fo constuctive feedback. Depatment of Political Science, Vandebilt Univesity, Nashville TN (badley.cal.smith@gmail.com, Depatment of Political Science, Univesity of Pittsbugh, Pittsbugh, PA (williamspaniel@gmail.com,

2 1 Intoduction On Septembe 22, 1980, Iaq invaded Ian, hoping to expand its bodes. The wa lasted yeas, with casualty counts only supassed by Wold Wa I and Wold Wa II. Conflict between the counties was nothing new disputes between these counties wee fequent in the decades pio. Iaq had long sought contol of the Khuzestan Povince, an oil-ich egion in southwest Ian (Shemiani, 1993), while Ian disputed access to wateways nea thei shaed bode (Kash, 2002). Those pevious conflicts ended compaatively quickly; the Ian-Iaq Wa was unique in its length and intensity. One potential explanation fo the duation discepancy is tunove in leadeship in Ian. Duing those pevious conflicts, Iaq had dealt with a known entity Shah Mohammad Reza Pahlavi eigned fom 1941 to By 1980, though, Ayatollah Khomeini had eplaced the Shah. Thus, thoughout the wa, all the accumulated knowledge about the Shah s pefeences and toleance to un isks wee endeed ielevant. Histoy was no longe as poweful a guide. Iaq in tun spent the bette pat of a decade leaning that the Islamic Republic would not easily concede its teitoial possessions. Of couse, by only looking at one case, it is not possible to daw geneal conclusions about the elationship between the length of a leade s tenue and the duation of disputes. 1 nevetheless suggests that newe leades bing geate uncetainty to a dyad, causing was to last longe as thei opponents filte out potentially less esolved types. We ask whethe this mechanism holds on a lage scale. Ou stategy is two-fold. While many scholas have peviously theoized about leade tenue and the initiation of conflict (Gaubatz, 1991; Gelpi and Gieco, 2001; Chiozza and Goemans, 2003; Potte, 2007; Bak and Palme, 2010), discussion of tenue and duation of conflict is notably absent. We theefoe develop a model of bagaining and fighting, which boows fom the liteatue on watime convegence. 2 Compaative static analysis shows that as uncetainty about a leade s esolve disappeas, the expected duation of wa goes to 0. This theoetical esult suggests that the case might not be unique but athe is eflective of an undelying tend. Second, we investigate the elationship between leade tenue and duation with a lage-n 1 Indeed, Weisige (2013, ) and Hio (1989, 36-37) ague that Iaq sought to exploit a tempoay weakness in Ianian militay powe following the evolution. 2 These models investigate how poposes might sceen out less poweful advesaies ove the couse of fighting and bagaining. Ou setup is closest to Filson and Wene s (2002) model, though ou inteest is in uncetainty ove esolve, something intinsic to leades athe that a county s militay powe. Only Powell s (2004) model allows fo uncetainty ove esolve in his model. Wolfod, Reite and Caubba (2011) also featue uncetainty ove costs (which implicity coves esolve due to utility standadizations) but in a moe complex envionment with shifting powe. It 1

3 empiical analysis of all militaized intestate disputes between 1816 and Dawing fom the compaative static, we hypothesize that moe uncetainty leads to longe and moe violent conflicts. Howeve, measuement of uncetainty is often a baie to empiical eseach on intenational conflict. To ovecome this difficulty, boowing fom Thyne (2012), Ride (2013), Spaniel and Smith (2015) and Uzonyi and Wells (2016), we poxy fo uncetainty using leade tenue. The esults ae stiking, statistically significant, substantively impotant, and obust to multiple altenative specifications. We estimate that disputes involving new leadeship ae 25.3% moe likely to last longe than a month than a cisis involving leades with fou yeas of tenue. Futhe, though thee ae many cases of long disputes involving newe leades, dyads with long-seving leades vitually neve initiate disputes against one anothe. Oveall, ou pape contibutes to a gowing liteatue on leades, uncetainty, and inefficient conflict. Specifically, we use the theoetical esults fom the model to claify the causal mechanism linking leade tenue to intenational conflict. Led by Wolfod (2007), this liteatue agues that leadeship change acts as an exogenous shock to the geopolitical infomation stuctue. 3 Faced with geate uncetainty, an opposing paty is moe likely to miscalculate its optimal offe, leading to wa. As such, newe leades ae moe likely to expeience militaized disputes. Although this infomational mechanism has stong theoetical suppot, a numbe of othe mechanisms that tie leadeship tunove to intenational conflict have been poposed in the liteatue. These altenative causal mechanisms all lead to the same conclusion: leades who have ecently enteed office ae moe likely to be involved in the initiation of a conflict than longe-tenued leades (Gelpi and Gieco, 2001; Chiozza and Goemans, 2003; Bak and Palme, 2010). We theefoe choose to look fo empiical evidence of a connection between leade tenue and uncetainty by investigating the duation of conflict. Commitment issues o divesionay incentives have ambiguous effects on conflict duation. In contast, ou model has a cisp implication: as uncetainty disappeas, the expected duation of conflict goes to 0. Focusing on conflict duation also allows us to daw theoetical expectations about the destuctiveness of conflict. Ou theoetical esults indicate that as uncetainty disappeas, the numbe of costly battles also diminishes. Dawing fom this, we expect a negative elationship between leade tenue and the numbe of fatalities esulting fom an intestate dispute. If ou focus wee on the initiation of disputes, athe than thei duation, we could not daw this implication about conflict intensity fom ou theoetical famewok. We believe this povides an additional justification fo ou focus on conflict duation as an outcome of inteest. By 3 Oigins of theoetical mechanism date back futhe to connections between new leades and incentives to build eputations fo toughness (Dallek, 2003, ). 2

4 focusing on this outcome athe than initiation, we both allow ouselves to distinguish among poposed causal mechanisms as well as daw additional empiical expectations elated to duation. On this font, we find that newe leades coelate with highe casualty ates. This empiical finding is what we would expect in envionments with geate uncetainty, as opposing states have geate incentive to sceen out less esolved opponents unde such cicumstances. Ou pape thus contibutes by poviding futhe evidence indicating that uncetainty has a substantively impotant effect by testing a hypothesis that would hold fo the uncetainty mechanism but might not hold fo othes. We also indiectly contibute to the civil wa liteatue. Uzonyi and Wells (2016) show that longe-tenued leades coelate with shote civil was but only when the state featues constaining domestic institutions. 4 They theoize that long-tenued leades in unconstained envionments have solidified eputations and thus ae moe likely to face the post-wa commitment poblems that cause civil conflicts to dag on (Walte, 1997). But long-tenued leades in constained envionments can moe easily make cedible commitments, theeby allowing the infomational mechanism to popely wok. The issues of post-civil wa commitment do not apply to intestate was. Theefoe, if Uzonyi and Wells theoy is coect, the length of intestate was should decease in leade tenue, and this effect should not be conditional on institutional constaints. We find evidence fo this in the data. The emainde of the pape poceeds as follows. In section 2, we develop a simple gametheoetic model that ties leade tenue to the duation of disputes. The pupose of the model is to develop a tanspaent empiical implication: as disputants become moe cetain about thei opponents, the expected duation and intensity of conflict diminishes to nothing. With this hypothesis obtained fom ou fomal theoetical esults, we tun to statistical analysis in section 3. Using leade tenue as a poxy fo uncetainty, we evaluate the implication of ou theoetical model. The findings ae consistent with ou expectation that leades with shote tenues, because they intoduce geate uncetainty, beget lengthy disputes. In the emainde of section 3, we discuss the obustness of the esults. Finally, in section 4, we conclude with a discussion of the esults in the context of the boade liteatue, consideing the implications of ou esults fo both academic and policy communities. 4 Thyne (2012) finds this effect fo tenue but does not check fo inteactive effects with institutional constaints. 3

5 2 Theoy A common souce of bagaining tensions in intenational elations is uncetainty ove how an acto values a good at stake elative to the cost of wa, also known as an acto s esolve. Although esolve is often associated with unitay acto states (Feaon, 1995), levels of esolve diffe by leade. This can be fo a vaiety of easons. At the most basic level, leades may simply value the same slice of teitoy o policy issue at hand diffeently fom one anothe. Similaly, they may just view violence as a moe useful altenative to diplomacy than othes (Goemans, 2000; Chiozza and Goemans, 2003; Hoowitz and Stam, 2014) o as a means to establish a tough eputation (Wolfod, 2007). Howeve, because esolve also incopoates a leade s sensitivity to costs, it also incopoates a numbe of domestic political factos. Fo example, one type of leade could seve a constituency that is moe insulated fom the costs of wa than anothe. (Bueno De Mesquita et al., 2005). Leades may be moe of less susceptible to challenges fom domestic opposition goups (Koch, 2009). Altenatively, some leades may fea the consequences of a foeign policy failue to a geate extent (Aena, 2008; Goemans, 2008; Debs and Goemans, 2010; Coco, 2011; Weeks, 2012). Moe bluntly, a leade could place geate value on the good at stake due to pivate benefits fom wa (Chiozza and Goemans, 2011). Fo intelligence agencies, knowing an opposing leade s level of esolve is a challenge fo two easons. Fist, esolve is manifestation of an individual s pesonal pefeences. Although publicly obsevable actions can eveal these types of pefeences to some degee, quantifying an exact figue is a difficult task. Second, a leade s willingness to fight depends on his o he domestic coalition and intenal political challenges. In tun, to obtain cetainty, intelligence agencies must undestand a lage numbe of individuals pesonal pefeences and also pedict how those pefeences will influence the leade s policy. To undestand how that uncetainty affects multi-peiod cisis negotiations, conside the following game. Two states, A and B, ae in a dispute ove an object woth 1. Failue to each an ageement leads to a seies of costly battles that andomly awads the object to one of the paties. Natue begins by dawing B s type as unesolved with pobability q and esolved with pobability 1 q. One can think of these daws as being possible pefeences fo wa that the leade of B may have. B sees its own type but A only obseves the common pio distibution. State A then demands a potion of the good x 1 [0, 1]. State B chooses whethe to accept o eject that amount. Accepting ends the game and implements the division, with A eceiving x 1 and B eceiving 1 x 1. If B ejects, the paties fight a battle. The battle costs A c A > 0 and B c B > 0. To model the uncetainty ove esolve, the two types of B intenalize this cost diffeently. 4

6 Explicitly, the esolved type functionally pays c B and the unesolved type pays c B, whee >. Dividing B s cost fo wa in this manne means that the esolved type is moe willing to spend blood and teasue to win the good at stake. As such, the esolve tem paameteizes a leade s sensitivity to the costs of wa. Wheeas standad bagaining models of wa teat combat as a game-ending costly lottey, we conside a moe complex scenaio whee militay victoy equies multiple successful battles fo state B. 5 In paticula, state A wins the battle with pobability p A, eliminating state B, and secuing the good fo itself. With pobability 1 p A, state B wins the battle, and both paties suvive to a second ound of bagaining. Hee, state A offes a division x 2 [0, 1]. If state B accepts, the paties implement that division. If state B ejects, they fight one moe battle. This time, the battle ends the game. State A pevails with pobability p A, state B wins with complementay pobability, and the both states pay the costs as befoe. 2.1 Equilibium Because this is an extensive fom game of incomplete infomation, we seach fo pefect Bayesian equilibia. Befoe addessing A s demand stategy in the fist stage, it is useful to undestand the incentives both paties face in the second stage. If B pevails in the fist battle, all payoffs associated with it ae ielevant fo the second stage; each paty has suffeed the costs of that battle and cannot ecoup them late. Each paty must theefoe maximize its payoff puely fo the second ound of bagaining. The fact that the fist battle s payoffs ae sunk pins down all possible esolutions fo the second stage. Indeed, A faces a staightfowad isk-etun tadeoff at that point. A s belief about B s type depends on the pobability each type accepted o ejected the fist stage s offe. The unesolved type any demand x 2 that leaves at least as much as its wa payoff fo the emainde of the game (excluding the sunk costs), 1 p A c B. Analogously, the esolved type s wa payoff fo the emainde of the game is 1 p A c B. This leaves A with only one of two possible optimal offes. Fist, it could demand p A + c B. Both types accept this amount is just baely enough fo the esolved type to accept, and so the unesolved type accepts as well because its costs to fight is lage. Second, A could demand p A + c B, which is just baely enough fo the unesolved type to accept. The esolved type theefoe ejects, as its cost of wa is lowe. An amount less than eithe of those is not optimal because it induces wa against both types, peventing A fom captuing any of 5 This is most simila to Filson and Wene (2002). One could intepet this setup as state A having two militay divisions that state B must defeat wheeas state B only owns one. Like Filson and Wene, we choose the two stage because it is sophisticated enough to allow us to daw compaative statics on wa duation but simple enough to solve with an explicit solution. See Slantchev (2003) and Powell (2004) fo simila models. 5

7 the suplus. An amount geate than eithe of those is not optimal because it gives away a needless concession. And an amount between those cannot be optimal because it povides a needless concession to the unesolved type while not changing the esolved type s decision to fight. Whethe A chooses the smalle o lage demand depends on its posteio belief that B is unesolved. If A thinks that B is vey likely esolved, then demanding the lage amount yields leads to wa too often. A instead demands the smalle amount to avoid suffeing the costs of fighting. Meanwhile, if A thinks that B is vey likely unesolved, then it is woth demanding the lage amount. This leads the esolved type to eject, but A is willing to un that isk so that it does not have to pay moe to the unesolved type than what is necessay. The cental stategic tension of the game is that the posteio belief in the second stage depends on the accept/eject decisions in the fist stage. Fo example, if the unesolved types all accept the initial offe, then A knows it is facing the esolved type in the second stage and accodingly demands the smalle amount. This gives the unesolved type a stong incentive to misepesent, which limits A s ability to sceen types in the fist stage. Nevetheless, A has substantial contol ove the fist ound of bagaining. In fact, A can easily elicit two types of behavios if it wishes. Fist, suppose that A demands an amount that gives B a shae at least as lage as the esolved type s payoff if a wa was fought to the finish. Doing so induces the esolved type to accept. This is because A s demands in the second stage egadless of its posteio belief eithe foce the esolved type to eject o gives the esolved type a peaceful settlement equivalent to its wa payoff. Such a demand also must induce the unesolved type to accept. Like the logic govening the second stage, this is because the unesolved type s wa payoff is wose than the esolved type s. Thus, if the esolved type wants to accept an offe, the unesolved type must as well. If A does not want to induce both types to accept immediately, it has a second option at its disposal. The main challenge A faces in sceening types is that the unesolved type might want to bluff esolve by ejecting in the fist stage, anticipating a demand geaed towad appeasing the esolved type in the second stage. Howeve, the esolved type and unesolved type pay diffeential pice fo wa. Consequently, A can find a demand that induces the esolved type to eject and the unesolved type to accept in the fist stage. 6 That demand hits a middle gound. It is smalle than the demand that induced both types to eject, as it now leads the esolved type to eject. But to convince the unesolved type to accept, it must be lage than the unesolved type s wa payoff; if it wee not, the unesolved type would eject and obtain the concessions geaed towad the esolved type. The esolved type 6 Without such a diffeential cost o isk of fighting, sepaating equilibia do not exist (Spaniel and Bils, 2018). 6

8 continues to eject because the demand is just small enough to convince the unesolved type to accept; with lowe costs of wa, the esolved type finds a stictly geate payoff in fighting. Some mino fomalization may help claify the intuition. Recall fom above that the lagest settlement B can expect to eceive in the second stage is 1 p A c B. If the unesolved type ejects the initial poposal, it eaches the second stage with pobability 1 p A and pays c B as the cost of the fist battle. Theefoe, the most the unesolved type can expect to eceive by fighting in the fist stage is: ( (1 p A ) 1 p A c ) B c B Thus, if the emainde of A s initial poposal (1 x 1 ) is lage than that quantity, the unesolved type must accept; even a successful bluff pays less than the amount B eceives in that case. These options set the stage fo Poposition 1. The equilibium of the game is geneically unique, but the bagaining stategies adopted depend on A s pio belief that B is unesolved. As a esult, the couse of wa can follow one of thee paths: Poposition 1. The duation of wa depends on A s pio belief: 1. If B is sufficiently unlikely to be the unesolved type, A demands a small amount in the fist stage. Both types accept with cetainty, and they fight no battles. 2. If the pobability B is the unesolved type falls in a middle ange, A demands a modeate amount in the fist stage. The unesolved type accepts with cetainty, but the esolved type ejects with cetainty. Updating its belief, A knows B is the esolved type in the second stage. A then demands a small amount, and the esolved type accepts accepts with cetainty. The states fight only one battle and only if A is facing the esolved type. 3. If B is sufficiently likely to be the unesolved type, A demands a lage amount in the fist stage. The unesolved type sometimes accepts and sometimes ejects, while the esolved type always ejects. Updating its belief, A know thinks it is moe likely facing the esolved type. Despite this, A demands a lage amount in the second stage. Only the unesolved type accepts. The states fight two battles if B is the esolved type and one battle with positive pobability if B is the unesolved type. The appendix contains a full poof, desciption of equilibium stategies, and deivation of 7

9 the cutpoints on q. 7 Howeve, the intuition is as follows. Conside the fist outcome possible. If the pobability A is facing a esolved type is high, going though any sceening pocess looks unattactive. Indeed, suppose A demanded an amount in the fist stage that left B with less than the esolved type s payoff fo wa. Then the esolved type must eject. But the esolved type is elatively likely, meaning that A suffes the costs of wa with a high degee of pobability. Sceening out the unesolved type may yield a geate shae of the settlement fo A, but the odds of obtaining that outcome ae too low to justify the isk. Nevetheless, as the likelihood of the unesolved type gows, the isk declines and the incentive to sceen inceases. The second case coespondingly efes to a paamete space whee the following stategies unfold. In the fist peiod, A demands the peviously descibed sceening quantity. The unesolved type accepts, and the esolved type ejects. Updating its belief in the second stage, A knows that it must be facing the esolved type and theefoe lowes its demand. The esolved type accepts at this point. Despite giving moe geneous settlement tems to B in the second stage, the unesolved type still accept because of its highe functional cost of wa. 8 Note, howeve, that even this type of sceening demand ovepays the unesolved type. Again, this is because A must leave the unesolved type enough in the fist stage to disincentivize bluffing via ejection. Thus, if A believes B is vey likely the unesolved type, a thid paamete space exists. Hee, A demands an amount in the fist stage that gives the unesolved type its wa payoff. Obviously, this is not good enough fo the esolved type, which ejects. But it also does not induce the unesolved type to accept with cetainty eithe; if it did, A would demand an amount to appease the esolved type in the second stage, and so the unesolved type could pofitably bluff. Instead, the unesolved type mixes between accepting and ejecting in the fist stage. Upon eaching the second stage, A believes it is moe likely facing an esolved type than at the game s outset. Howeve, the pecentage of unesolved types that accept in the fist stage is elatively small. Consequently, in the second stage, A again tailos its demand to appease only the unesolved type. The esolved type ejects thoughout. Although A suffes its wa costs against that esolved type, it willingly accepts that inefficiency because the likelihood it is facing the esolved type is sufficiently low. Oveall, these stategies imply some wa in the fist stage and less wa in the second. 7 Poposition 1 s fist case applies when q < c A+ c B ( c A + c B c A + c B, (c c B A+ )( c A + 2c B c ) B (c A + c B ) 2 ). The thid case applies when q > (c A+ c B c A + c B. The second case applies when q )( c A + 2c B c ) B. (c A + c B ) 2 8 As the appendix details futhe, the unesolved type has a geate oveall wa payoff than the esolved type because each battle costs c B fo it athe than c B. 8

10 2.2 Empiical Implications While Poposition 1 explains the outcome of the game, it lacks empiical claity. Being explicit about this is citical given the challenges of empiically intepeting incomplete infomation cisis bagaining games. Consequently, we tun to Poposition 2, which geneates a staightfowad compaative static with empiical implications: Poposition 2. As state A becomes cetain about state B s type (i.e., as q goes to 0 o 1), the expected duation of wa goes to 0. Note that q is a measue of uncetainty. One can obseve this in a couple diffeent ways. Fist, A s uncetainty ove B foms Benoulli distibution. The vaiance of Benoulli distibution minimizes at q = 0 and q = 1. Second, as q appoaches 0, state A becomes inceasingly cetain that it is facing the esolved type; and as q appoaches 1, state A becomes inceasingly cetain that it is facing the unesolved type. Indeed, when q = 0 o q = 1, the game conveges to the complete infomation case. Thus, Poposition 2 states that if state A can accuately identify whethe it is facing the esolved o unesolved type, the expected duation of wa eventually eaches 0. To see how Poposition 2 s claim woks, conside two cases. Fist, suppose q is appoaching 0 fom the ight side. Then we must investigate the duation of wa fo when q falls in the fist ange fom Poposition 1. But unde such conditions, state A demands the safe amount and avoids wa entiely. Consequently, the duation of wa equals 0. Second, suppose q is appoaching 1 fom the left side. This case falls in the thid ange fom Poposition 1. Discussions of convegence models often ovelook this type of semisepaating equilibium, which actually featues geate conflict than the moe commonlyknown sepaating equilibium in which the popose skims the vaious types. Nevetheless, we can still obtain a elationship between uncetainty and length of wa. The appendix shows that the unesolved type fights a battle with pobability (1 q)(c A+ c B ) hee, while the esolved qc B ( 1 1 ) type fights both battles. Multiplying each of these pobabilities by the pio distibution of types, the oveall expectation of one battle fought equals: q ( (1 q)(ca + c B ) qc B ( 1 1 ) ) (1 q) ( ca + c B c B ( 1 1 ) + 1 q Note that this value is stictly deceasing in q. Indeed, as q goes to 1, the pobability of obseving one battle goes to 0. ) 9

11 Meanwhile, note that the pobability of obseving two battles in this case is simply the pobability of dawing the esolved type, o 1 q. This value is stictly less than the pobability of obseving one battle and is also stictly deceasing in q and goes to 0 as q goes to 1. 9 Although ou focus thus fa has been on the duation of conflict, a coollay of Poposition 2 gives us empiical leveage on the expected costs suffeed: Coollay 1. As state A becomes cetain about state B s type (i.e., as q goes to 0 o 1), the expected costs of wa paid go to 0. This is a staightfowad implication Poposition 2. As the pobability of wa goes to 0, so must the expected costs paid if the states ae fighting vanishingly few battles, then the costs suffeed must be coespondingly small. All told, the key takeaways fom Poposition 2 and Coollay 1 is that we ought to expect the duation of fighting and the associated negative effects to decease when uncetainty about a state s esolve disappeas. We test two empiical implications of this compaative static below. 3 Empiical Analysis Befoe tuning to the data, we must tanslate Poposition 2 s compaative static into a testable hypotheses. The model shows that geat amounts of uncetainty ove esolve should not only lead to dispute initiation but longe conflict as well. This esult tanslates natually to a discussion of leade tenue. Although an individual leade s chaacteistics do not alte the deteminants of militay stength, she can influence when the state wields that powe. Futhe, opposing states cannot easily identify a leade s bottom line in cisis bagaining because less esolved leades have incentives to misepesent themselves as esolved (Feaon, 1995). Howeve, as Wolfod (2007) agues, uncetainty is not static ove time, with infomation gowing as days in office pass. This is fo a vaiety of easons. Intelligence is a pimay issue: wheneve a new leade entes office, opposing intelligence oganizations must discad thei files on the pevious leadeship and begin thei eseach pocess again. Similaly, a fesh leade ceates a gap in the heads-of-state netwok, inceasing the tansaction costs of obtaining new infomation. Meanwhile, as a leade pogesses in tenue, she cannot help but make publicly obsevable actions. Put togethe, these factos indicate that opposing states should 9 Beyond Poposition 2 s limit esult, it is also tue that deceasing the diffeence in type space (that is, educing the vaiance of types by deceasing 1 1 ) monotonically educes the size of the paamete space unde which long was occu (that is, was in which the paties fight two battles). This is an altenative conceptualization educing uncetainty because shinking 1 1 to 0 conveges to the complete infomation case and monotonically educes the vaiance of the esevation values (Reed (2003, 637); Spaniel and Smith (2015, 740)). 10

12 have stonge beliefs about a leade s pefeences as tenue pogesses. Stated diffeently, leade tenue is an effective poxy fo uncetainty. Pevious studies have uncoveed such a elationship in ams aces (Ride, 2013) and sanctions (Spaniel and Smith, 2015). We can now diectly tanslate this to Poposition 2 s compaative static. As tenue inceases, the belief egading an opposing leade s esolve should convege to a paticula expectation. In tun, the expected duation of conflict ought to decease, eithe because the popose demands a safe amount and guaantees the peace o because the popose demands an aggessive amount but chances of guessing incoectly goes to 0. Regadless, this povides us with ou fist hypothesis: Hypothesis 1. The expected duation of conflict is deceasing in a leade s tenue at the beginning of the dispute. Although duation is ou pimay outcome of inteest, ou theoetical esults also cay testable implications with espect to combat fatalities. In the context of ou theoetical model, as uncetainty vanishes, the numbe of ounds of fighting diminishes to 0. Fom this, we daw a second testable implication fom the compaative static in Poposition 2. Specifically, moe ounds of fighting should be associated with highe fatality levels. This can be seen in Poposition 2 by consideing how, as uncetainty vanishes, so too does the numbe of times that each state pays the cost of wa in equilibium. Intepeting the cost of wa as the loss of both mateial esouces and human lives as the esult of combat, this means that as uncetainty is esolved, the numbe of fatalities esulting fom a militaized dispute should decease. Thus, as leade tenue inceases, we also expect the numbe of fatalities esulting fom extended peiods of destuctive conflict to decease. An altenative way to think of this is as follows. Cheap talk signaling does not wok unde nomal cicumstances because less esolved types have incentive to bluff stength. 10 In contast, the wa mechanism we study in the model above pemits meaningful communication because the two types pay diffeential costs fo fighting. Because the moe esolved type suffes a smalle cost, it is willing to fight unde a lage set of cicumstances than the unesolved type. As a esult, the costliness of wa sceens types. Howeve, when little uncetainty exists, thee is less of a need to pay costs to cedibly eveal infomation. Opeationalizing these costs as casualties fom wa gives us the following hypothesis: Hypothesis 2. The expected numbe of fatalities esulting fom conflict is deceasing in leade tenue. We find suppot fo these hypotheses below. Howeve, befoe developing ou statistical model, it is woth biefly discussing a couple eseach design issues. Fist, note that the 10 See Ramsay (2011), Satoi (2002), and Tage (2010) fo exceptions. 11

13 statistical esults do not imply that leade tenue only affects conflict though the hypothesized mechanism. Indeed, once in a conflict, many scholas ague that leade pesistence contibutes to both the duation and intensity of fighting (Goemans (2000); Stanley (2009); Coco (2015)). This is because leades have incentive to stay in disastous conflicts in hope of tuning the tide, which then would allow the culpable leades to stay in powe. In these cases, newe leadeship facilitates dispute temination. We view this theoy as consistent with ous fo two easons. Fist, ou focus is on leade tenue at the stat of disputes. And second, although a new leade bought in duing a conflict adds uncetainty, it also changes the leadeship s oveall pefeences fo wa and peace. Consequently, it is not supising that peace esults despite the spike in uncetainty. Second, we do not claim that all uncetainty about all leades is equal. Some leades come into office as vitual blank slates to foeign intelligence agencies, while othes ente having held thei ival s eye fo many yeas. Coding these diffeences is a challenge because it would equie knowing how clandestine agencies pedict leadeship tunove and whethe they can do so successfully. Instead, we view this poblem as stacking the deck against finding a statistically significant elationship. Fo known entities, the additional infomation accued ove time is athe small. We would thus expect the coelation between such leades tenues and conflict to be negative but small. In contast, leaning would be much moe significant fo unknown leades, geneating negative and lage coelation. Mixing these cases togethe theefoe suppesses the tue effect of leaning and infomation acquisition. It will theefoe be hade to find evidence fo the mechanism using leade tenue. The only eal poblem we would encounte is if uncetainty systematically inceased fo some subset of leades as time in office pogessed, and it is difficult to come up with a eason that would be the case. 3.1 Data To test ou hypotheses, we investigate the duation of militaized intestate disputes (MIDs). Thus, ou units of obsevation ae all dyadic MIDs fom 1816 to We daw the bulk of ou data fom two souces: the Coelates of Wa (COW) fo conflict data and Achigos (Goemans, Gleditsch and Chiozza, 2009) fo data on leade tenue. In the following sections, we fist descibe the data used in this study. 11 Next, we detail ou use of an appopiate statistical model, the well-known Cox popotional hazads estimato fo duation analysis, and odinay least-squaes egession fo ou analysis of fatality levels. Then we epot the esults and povide some substantive intepetation to demonstate the elevance of ou findings. Finally, we descibe vaious checks on the obustness of these esults befoe concluding. 11 We utilize the EUGene data geneating softwae to obtain all elevant COW data (Bennett and Stam, 2000) 12

14 3.1.1 Dependent Vaiables Ou fist dependent vaiable of inteest is the duation of conflict. To measue this, we tun to the Coelates of Wa data. The specific dataset that we use is the Militaized Intestate Dispute data, which collects infomation at the conflict and paticipant level. Fotunately fo us, these data contain the stat and end date of each conflict included. Fom this, we calculate the numbe of weeks that a given conflict lasted and utilize this measue as ou dependent vaiable. 12 The second dependent vaiable in ou analysis is battle deaths esulting fom militaized conflict. Fo a measue of fatalities, we again tun to the Coelates of Wa data. We use the fatality level vaiable fo ou main analysis, which is an odinal measue of fatalities taking on values of 1 though 6. Because of issues with missing data, we defe use of the Coelates of Wa s pecise measue of fatalities fo the main analysis. While the pecise value would povide an ideal measue fo pesent puposes, of the 447 militaized intestate disputes with a positive fatality level in ou sample, 403 have missing values fo the pecise fatality measue. In contast, thee is no missingness in the pecise measue among disputes that involved zeo fatalities. Thus, we avoid use of this measue due to the clealy non-andom missingness. We believe that the odinal measue, while not ideal, is the best among all available altenatives Independent Vaiables Tenue. Ou independent vaiable of inteest in this analysis is leade tenue. We measue this by taking the minimum tenue among the conflict s oiginatos in each obsevation. To maximize the pecision of the measuement, we calculate this tenue as the numbe of days that leade has been in office at the time the dispute was initiated and then take the common logaithm of this value. We use a logged vaiable fo theoetical easons. Specifically, we expect that thee ae deceasing etuns to infomation acquisition. In this way, the maginal influence of each additional day of a leade s behavio deceases ove time. Put diffeently, the fist day in office povides moe infomation than the second, the second povides moe infomation than the thid, and so foth. Logging the numbe of days in office ensues that ou measue has this popety. 13 Because the unit of obsevation in this study is a militaized intestate dispute, it is necessay to make choices about how to measue tenue among many possible altenatives. 12 We also pefomed the analysis with days and months and the substantive esults ae unchanged. We opt fo weeks because it is the most fine-gained measue that we can use without having to discad too many obsevations due to missingness in the days vaiable. 13 Fo anothe use of this appoach, see Spaniel and Smith (2015). 13

15 The pimay difficulty aises because conflicts often include multiple paticipants. As such, we must incopoate leade tenue into ou empiical analyses with cae. In the absence of stong theoetical pios, a numbe of these measues appea valid. Howeve, ou theoetical agument fom section 2 povides us with a compass with which to navigate these competing options. We allow theoy to be ou guide hee given the notion that moe theoetically gounded statistical models fae bette at uncoveing existing elationships in the data (Aena and Joyce, 2011). The infomational logic of ou theoy pecludes many altenative measues. Two such options ae to simply sum the tenue of the leades of the oiginatos of a conflict o aveage the tenue acoss all leades involved. We believe that these ae theoetically inappopiate fo a numbe of easons. Fist, pe Poposition 2, militaized conflict is a costly fom of infomation tansmission; it ends when beliefs about the actos convege to the ealized type. Consequently, even if one side has conveged its beliefs about the second, conflict might continue until the second conveges its beliefs about the fist. This indicates that the least tenued leade is the citical case and that the sum of leade tenue is not. As such, we use the minimum tenue among all leades coded as oiginatos of a given conflict by the COW coding ules. Second, summing tenue leads the model to teat highly unelated cases as statistically identical. Fo example, with unlogged data, two leades with 10 yeas of expeience each would be identical to a dyad with a fesh leade and a leade with 20 yeas expeience. Ou theoetical model leads us to expect the second dyad to be fa moe fagile and equie substantially moe leaning than the fist dyad. All told, these two points indicate that we should opt fo the minimum tenue length in the dyad. Contols. The analysis also includes a numbe of contol vaiables to account fo othe factos that ae likely also elated to the duation of conflict. We descibe these contol vaiables below: Polity. Many pevious studies link democacy to duation and escalation of conflicts. The mechanisms ae manifold: govenments esponsive to thei people ae sensitive to casualties (Gelpi, Feave and Reifle, 2005), democacies accue audience costs moe quickly and theefoe can signal faste (Feaon, 1994), backing down has diffeential isks fo autocats than democatic leades (Debs and Goemans, 2010), and democacies ae geneally moe tanspaent (Schultz, 1998). Meanwhile, due to thei accountability and tem limits in some cases, democatic leades geneally seve shote tems, and eseaches have peviously used democacy as a poxy fo leade tenue (Gelpi and Gieco, 2001). Finally, and pehaps most elevant fo ou study, Eyeman and Hat J 14

16 (1996) find a obust negative elationship between joint democacy and the duation of conflict. These factos all point to some measue of democacy being a necessay contol in ou study. We theefoe include the POLITY scoe of the leade coesponding to ou measue of minimum tenue. As anticipated, Logged Tenue and Polity ae negatively coelated (-0.208). Capability Ratio. Following existing wok on powe pepondeance and the duation of conflict, we expect that the distibution of capabilities among each side in a militaized intestate dispute should be elated to its duation (Slantchev, 2004; Reed, 2003). To contol fo this, we include a capability atio measue that indicates whethe thee is elative paity o a pepondeance of powe between each side in a conflict. We use the Coelates of Wa s Composite Index of National Capability (CINC) scoes to constuct this measue. To deal with the pevalence of multilatealism, we sum these scoes within each side of a dispute as identified by the MID data. Then, the measue is constucted by taking the maximum of these scoes and dividing by the sum. As such, this vaiable takes on values between 0.5 and 1, with lowe values indicating powe paity and highe values indicating a pepondeance of powe on one side. Issue Dummies. Pehaps the issue unde dispute is elated to the willingness of states to incu the costs of conflict. If this is tue, then ou estimation must account fo these diffeences. Accodingly, we include a set of dummy vaiables indicating the pimay issue unde dispute in each militaized intestate dispute contained in ou data. The base case that we omit ae the set of disputes classified as othe by the Coelates of Wa coding ules. The indicatos we include ae as follows: Teitoy. Indicato fo teitoial disputes. Policy. Indicato fo intenational policy disputes. Regime. Indicato fo disputes ove issues elated to a taget s egime. To establish the plausibility of ou esults, Figue 1 pesents a scatteplot of leade tenue measued in days against the duation of conflict as measued in weeks. The plot colos points by the Polity scoe of the leade with minimum tenue. We include this to obtain a fist-pass idea of whethe the influence of leade tenue might be distibuted diffeently fo vaious egime types. Looking to Figue 1, we find initial suppot fo ou theoetical expectation. This scatteplot demonstates that the elationship that we expect is plausible. In paticula, no data points lie in the uppe-ight quadant (long tenue/long length) of the gaph. This is consistent with ou expectation that the duation of conflicts should be deceasing in leade tenue. 15

17 Scatteplot of Leade Tenue and Duation 300 Duation in Weeks polity Minimum Tenue in Days Figue 1: Scatteplot of leade tenue and conflict duation. This plot povides initial evidence in favo of ou theoetical expectations. In paticula, no points inhabit the uppe-ight aea of the plot, indicating that the duation of conflicts initiated against leades who have been in office fo a long peiod of time tends to be shote than conflicts involving new leades. 16

18 Scatteplot of Tenue and Fatality Level 6 MID Fatality Level Tenue in Days Figue 2: Scatteplot of leade tenue and fatality level. No points inhabit the uppe-ight quadant. This is suggestive of a negative elationship between tenue and fatality level. Note that the y-axis is jitteed to aid in visual intepetation of the data. Futhe, the scatteplot does not eveal any clea elationship between egime type and this influence. With the exception of extemely long tenues, egime types appea to be distibuted thoughout the obsevations faily evenly. Nevetheless, this only povides initial evidence in favo of ou claims, and so we will tun to egession analysis to futhe solidify ou empiical findings. Next, we pefom a simila execise fo ou fatality vaiable. Figue 2 pesents a scatteplot of leade tenue and fatality. The distibution appeas simila to that of duation: the uppe-ight quadant (long tenue/high fatalities) is empty. Again, at fist pass, this gives us confidence that the expected elationship exists. Befoe moving on to any analysis, we also pesent scatteplots of ou contol vaiables against duation to get a bette feel fo the elationships in the data. These gaphics ae pesented in Figue 3. As the figue demonstates, neithe Polity no capability atios appea to have a stong elationship with duation. Additionally, each of these scatteplots demonstate that ou contols ae well distibuted acoss the ange of possible values. 17

19 300 Duation Polity 300 Duation Cap. Ratio Figue 3: Scatteplot of contol vaiables and conflict duation. 18

20 3.2 Results The fist of ou hypotheses elates to the duation of intestate cises. As such, we equie a statistical model designed to handle duation data. To avoid distotions of the undelying hazad ate that may aise fom paametic assumptions, we take a semipaametic appoach, utilizing a Cox popotional hazads model. 14 In Table 1, we epot the esults of ou duation analysis. Note that acoss each of the model specifications, the coefficient on ou measue of leade tenue indicates that an incease in tenue coesponds to an incease in the hazad. Futhemoe, in all of the models, this coefficient obtains statistical significance at at least the 95% level. Thus, the esults of ou estimation povide evidence in favo of ou hypothesis that leade tenue should be associated with shote conflict duations. In Figue 4, we gaphically epesent the influence of shifts in leade tenue on the estimated hazad atio. As this gaphic demonstates, ou model pedicts that an incease in leade tenue is associated with an incease in the estimated hazad atio. Substantively, this means that the pobability of conflict temination at any given point is geate fo conflicts involving longe-tenued leades vesus leades who have only ecently enteed office. As the plot indicates, shifting acoss the intequatile ange esults in a ten pecentage-point shift in the estimated hazad atio. Altenatively, we can intepet the esults using pedicted suvival pobabilities given substantively inteesting values of ou independent vaiables. Holding all othe vaiables at thei medians, we calculate the pobability that a conflict lasts at least one month fo a leade that has only spent one day in office vesus a leade that has held office fo fou full yeas. We find that this pobability is fo the new leade, while it is only fo the leade that has been in office fo fou yeas. Thus, conflicts involving a new leade ae 25.3% moe likely to sustain past one month than a conflict in a dyad with the leade having held office fo fou yeas. This indicates that the influence of leade tenue on the duation of conflict is not only statistically significant, but that it also holds substantive weight. Next, we tun to ou analysis of leade tenue s influence on the fatality level of disputes. 14 The validity of the Cox model depends upon assuming that the effect of coefficients on the undelying hazad ae popotional acoss time. As Box-Steffensmeie, Reite and Zon (2003) point out, a failue to check fo and coect violations of this assumption may lead to invalid infeences. To guad against this possibility, we implement a standad check fo non-popotionality by inspecting the Schoenfeld esiduals poduced fom the model. These tests fail to detect a non-popotional effect of leade tenue on the hazad, and so we pesent standad Cox esults thoughout. Sample selection is anothe elevant concen in ou setting. Unfotunately, the natue of ou independent vaiable of inteest, which is measued in days, endes existing appoaches, e.g. Boehmke, Moey and Shannon (2006) difficult to implement. Fotunately, ou theoetical model indicates that, even given the selection pocess esulting fom the decision to intiate conflict, the elationship between leade tenue and duation still holds. As such, the fomal esults indicate that the expected elationship should hold, even in the pesence of selection into conflict. 19

21 Dependent vaiable: Conflict Duation (Weeks) (1) (2) (3) (4) (5) Tenue (Logged) (0.034) (0.038) (0.035) (0.035) (0.039) Polity (0.003) (0.003) Cap. Ratio (0.145) (0.157) Teitoy (0.064) (0.071) Policy (0.055) (0.062) Regime (0.112) (0.125) Obsevations 2,101 1,823 2,034 2,101 1,766 Log Likelihood 13, , , , , Note: p<0.1; p<0.05; p<0.01 Table 1: Cox Popotional Hazads Model Results 20

22 Hazad Ratio with 95% CI Relative Hazad Leade Tenue (Logged Scale) Figue 4: Estimated hazad atios obtained by vaying leade tenue acoss its intequatile ange. The lowe bound of this ange is 7 months and the uppe bound is 4 yeas and 3 months. 21

23 Dependent vaiable: Fatality (1) (2) (3) (4) (5) Tenue (Logged) (0.044) (0.047) (0.045) (0.042) (0.047) Polity (0.004) (0.004) Cap. Ratio (0.185) (0.191) Teitoy (0.077) (0.086) Policy (0.067) (0.074) Regime (0.148) (0.168) Constant (0.122) (0.134) (0.196) (0.127) (0.212) Obsevations 1,978 1,733 1,911 1,978 1,676 R Adjusted R Note: p<0.1; p<0.05; p<0.01 Table 2: OLS Results fo Fatality Level As discussed in the pevious section, ou measue of fatality level is an odinal value of the estimated numbe of fatalities accoding to the COW poject s coding ule. While this is not a pecise measue, it does allow us to sidestep the poblematic non-andom missingness pesent in the pecise fatality measue included in the COW data. The statistical model we use fo this analysis is standad OLS egession. A potential concen hee is that OLS may not be appopiate given the natue of ou outcome vaiable. In paticula, the diffeent categoies in the COW fatality level vaiable coespond to diffeent magnitudes of obseved fatalities, such that a jump fom a 0 to 1 occus with a single casualty, 22

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