Wa, Uncetainty, and Leade Tenue Badley C. Smith William Spaniel Octobe 7, 2016 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 a cisis involving new leades is 25.3% moe likely to last one month than a cisis involving leades with fou yeas of tenue. Moeove, such conflicts ae moe likely to esult in geate fatalities. These esults futhe indicate that leade tenue is a useful poxy fo uncetainty. We ae gateful to Phil Aena fo helpful discussion. Comments and suggestions ae welcome. Depatment of Political Science, Univesity of Rocheste, Hakness Hall 333, Rocheste, NY 14627 (badley.cal.smith@gmail.com, http://badleycalsmith.com). Depatment of Political Science, Univesity of Pittsbugh, Pittsbugh, PA 15260. (williamspaniel@gmail.com, http://williamspaniel.com).
1 INTRODUCTION 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. But 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). Howeve, 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 1979. 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. Infomation poblems coespondingly an deepe. 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 consequently 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. Thus, we develop a simple game of bagaining and fighting, which boows heavily 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 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 lagen empiical analysis of all militaized intestate disputes between 1816 and 2007. Dawing fom the compaative static, we hypothesize that moe uncetainty leads to longe and moe 1 Indeed, Weisige (2013, 152-158) and Hio (1989, 36-37) ague that Iaq sought to exploit a tempoay weakness in Ianian militay powe following the evolution. While lage-n quantitative analysis cannot disciminate causal mechanisms fo a single case, we investigate this potential confounde in the empiical discussion. 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) allows fo uncetainty ove esolve in his model. It 1
1 INTRODUCTION violent conflicts. Boowing fom Thyne (2012), Ride (2013), Spaniel and Smith (2015) and Uzonyi and Wells (2015), 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, while 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. While 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. Pehaps newe leades, having not yet consolidated powe, face geate political constaints which pevent them fom cedibly committing to conflict and make them moe attactive tagets of aggession (Gelpi and Gieco, 2001). Altenatively, if divesionay incentives (Chiozza and Goemans, 2003) ae moe pevalent at the beginning of a leade s tenue, then initiations may esult fom this mechanism instead. Unde yet anothe mechanism, new leades may be peceived as especially weak tagets (Bak and Palme, 2010), again leading to the expectation that shote tenue duations to be coelated with cisis initiation. As this suvey of ecent wok indicates, egadless of the causal mechanism specified, a negative elationship between the tenue of a leade and the likelihood of conflict initiation is expected. Thus, when the outcome of inteest is the initiation of conflict, existing wok has not povided evidence diffeentiating the infomational, divesionay, leade-vulneability, and othe mechanisms that each pedict this elationship. Because analyzing these mechanisms in the context of initiation esults in a lack of claity as to whethe one of these mechanisms dominates, we shift focus to analyze the duation of disputes to allow fo such a test. By focusing on the duation and intensity of conflict, athe than its initiation, we help 3 Oigins of theoetical mechanism date back futhe to connections between new leades and incentives to build eputations fo toughness (Dallek, 2003, 413-414). 2
1 INTRODUCTION distinguish among these mechanisms. This is because with espect to conflict duation, the infomational mechanism implies a diffeent effect of leade tenue than each of the altenative mechanisms outlined above. Ou theoetical esults, pesented in section 2, indicate that as uncetainty deceases, the duation of a conflict deceases. In contast, if leade tenue influenced conflict duation because new leades ae militay weake, we might expect the enfeebled paty to lose moe quickly than an aveage state. Similaly, if newe leades divesionay incentives ende the bagaining ange empty, we would expect the paties to settle once the leade captues the pivate benefit; futhe fighting isks evealing the domestic conflict of inteest (Weisige, 2013, 48-51). Moeove, if commitment poblems with new leades caused cises, such a conflict should end once that leade consolidates his o he powe, the commitment poblem subsides, and the states can stike a deal within the stable bagaining ange. These cases would all suggest that newe leades unde some conditions ought to fight shote was. Thus, the infomational mechanism caies a diffeent implication than competing mechanisms, allowing fo an evaluation of the elative meits of these explanations. Focusing on conflict duation also allows us to daw theoetical expectations about the destuctiveness of conflict. Ou theoetical esults indicate that as uncetainty diminishes, the numbe of costly battles also diminishes. Dawing upon 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 would be unable to 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 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 (2015) 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 commit- 4 Thyne (2012) finds this effect fo tenue but does not check fo inteactive effects with institutional constaints. 3
2 THEORY ment 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 in ode to fomalize the logic tying 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. 2 Theoy The game consists of two states, A and B, engaged in a cisis 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 state B s type as unesolved with pobability q and esolved with pobability 1 q. State B sees its own type but state 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 state A eceiving x 1 and state B eceiving 1 x 1. If state B ejects, the paties fight a battle. The battle costs state A c A > 0 and state B c B > 0. To model the uncetainty ove esolve, the two types of B intenalize this cost diffeently. 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. Following the liteatue on esolve and leades, such diffeences in costs might be because one type of leade (compaed to the othe) has a constituency that is moe insulated fom the costs of wa (Bueno De Mesquita 4
2.1 Equilibium 2 THEORY et al., 2005), pesonally finds violence to be a useful altenative to diplomacy (Goemans, 2000; Chiozza and Goemans, 2003; Hoowitz and Stam, 2014), feas the consequences of a foeign policy failue to a geate extent (Goemans, 2008; Debs and Goemans, 2010; Coco, 2011; Weeks, 2012), o places geate value on the good at stake due to pivate benefits fom wa (Chiozza and Goemans, 2011). 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. Poposition 1 states that one of thee outcomes occu depending on state A s pio belief that state B is the unesolved type: Poposition 1. The duation of wa depends on A s pio belief about B s type: If state B is sufficiently unlikely to be the unesolved type, state A demands a small amount in the fist stage. Both types accept, and they fight no battles. If the pobability state B is the unesolved type falls in a middle ange, state A demands a modeate amount in the fist stage. Only the unesolved type accepts. State A then demands an amount in the second stage, and the esolved type accepts. The states fight only one battle and only if A is facing the esolved type. If state B is sufficiently likely to be the esolved type, state A demands a lage amount in the fist stage. The unesolved type sometimes accepts and sometimes ejects, while the esolved type always ejects. State A then 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. 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
2.1 Equilibium 2 THEORY The appendix contains a full poof and deivation of the cutpoints on q. Howeve, the intuition is as follows. State A faces a isk-etun tadeoff. Smalle demands induce geate ates of acceptance but geneate wose tems fo state A. In contast, lage demands lead to highe peaceful payoffs but geate ates of ejection. In the pocess, state A must woy about the unesolved type s incentive to eject an initial demand, bluff stength by fighting a battle, and attempt to obtain a geate shae of the good in the second peiod. Howeve, because the unesolved type pays a geate cost to fight, well-calculated offes fom state A can induce the unesolved type to sepaate although bluffing will lead to a geate offe, the diffeentially geate battle cost outweighs the potential gain. This pemits infomation evelation despite the appaent incentives to misepesent. Whethe state A wishes to sceen types in this manne depends on its pio belief about state B s type. If state A believes state B is sufficiently likely to be the esolved type, sceening out the unesolved type with high demands is too costly. Indeed, any attempt to sceen esults in battles against the moe abundant esolved type. Because wa is costly and state B is likely the esolved type in this case, state A pefes buying off both types immediately and guaanteeing itself some amount of the suplus. As such, no battles occu hee. Now conside situations whee the likelihoods of the esolved and unesolved types ae elatively balanced. Hee, the fequency of unesolved types is high enough that state A pefes gambling to making the safe demand. That said, state A must be caeful in its demand stategy. As peviewed above, the unesolved type could eject an initial offe, mimic the esolved type by fighting, and achieve geate concessions in the second peiod. Nevetheless, state A can develop a demand stategy that cedibly sepaates the unesolved fom the esolved types. 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. Consequently, state A can demand just enough that the unesolved type pefes accepting that to fighting and obtaining the esolved type s shae in the second stage. Meanwhile, the esolved type ejects; it eans stictly moe because its wa cost is smalle. As such, state A fights a battle against just the esolved type in the fist stage and settles with cetainty in the second stage. Lastly, conside situations whee the unesolved type is sufficiently likely. If state A pusues a demand stategy that induces sepaation, it must pay a pemium to the unesolved type in the fist stage so as to disincentivize bluffing. While that pemium is acceptable when the unesolved type is not paticulaly likely, it becomes futhe unacceptable as state A becomes inceasingly cetain that it is facing the unesolved type. State A s altenative involves offeing an amount in the fist stage equal to the unesolved type s payoff fo wa. Yet the unesolved type cannot accept with cetainty hee if it did, state A would demand 6
2.2 Empiical Implication 2 THEORY 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. Then, in the second stage, state A again tailos its demand to appease only the unesolved type. The esolved type ejects thoughout. Although state 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. 2.2 Empiical Implication While Poposition 1 explains the outcome of the game, it lacks empiical claity. 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. 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. 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 why, 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 7
3 EMPIRICAL ANALYSIS (1 q) ( ca + c B c B ( 1 1 ) Note that this value is stictly deceasing in q. Indeed, as q goes to 1, the pobability of obseving one battle goes to 0. 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. 6 All told, the key takeaway fom Poposition 2 is that we ought to expect the duation of fighting to decease when uncetainty about a state s esolve disappeas. empiical implications of this compaative static below. ) We test two 3 Empiical Analysis Befoe tuning to the data, we must fist efomulate 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. Wheneve a new leade entes office, opposing intelligence oganizations must discad thei files on the pevious leadeship and begin thei eseach pocess again. Meanwhile, as a leade pogesses in tenue, she cannot help but make publicly obsevable actions. Put togethe, these two factos indicate that opposing states should 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 6 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 (Spaniel and Smith, 2015, 740). 8
3.1 Data 3 EMPIRICAL ANALYSIS 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 leade tenue. While 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. 7 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. 3.1 Data To test ou hypothesis, we investigate the duation of militaized intestate disputes (MIDs). Thus, ou units of obsevation ae all dyadic MIDs fom 1816 to 2010. 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 7 See Ramsay (2011), Satoi (2002), and Tage (2010) fo exceptions. 9
3.1 Data 3 EMPIRICAL ANALYSIS descibe the data used in this study. 8 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. 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, this data contains 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. 9 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. 3.1.2 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. 10 8 We utilize the EUGene data geneating softwae to obtain all elevant COW data (Bennett and Stam, 2000) 9 Note that 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. 10 See (Weisige, 2015) fo an analysis of leadeship tunove duing a conflict. 10
3.1 Data 3 EMPIRICAL ANALYSIS Note that 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. 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. The pimay difficulty aises because each conflict included in the data we utilize includes a numbe of 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 based on 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 ules out many altenative measues. One such option would be to simply sum the tenue of all leades involved in a conflict (o all oiginatos of a conflict). We believe that this is 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. 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: To contol fo egime type, we include the POLITY scoe of the leade coesponding to ou measue of minimum tenue. This allows fo us to contol fo the possibility that egime type might influence a leade s incentives fo standing fim vesus backing down duing a conflict, as Debs and Goemans (2010) ague. 11
3.1 Data 3 EMPIRICAL ANALYSIS 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, summing 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 diffeent 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. 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. 12
3.1 Data 3 EMPIRICAL ANALYSIS Scatteplot of Leade Tenue and Duation 300 Duation in Weeks 200 100 polity 10 5 0 5 10 0 0 2500 5000 7500 10000 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. 13
3.2 Results 3 EMPIRICAL ANALYSIS Scatteplot of Tenue and Fatality Level 6 MID Fatality Level 4 2 0 0 2500 5000 7500 10000 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. 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. 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. 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 14
3.2 Results 3 EMPIRICAL ANALYSIS 300 Duation 200 100 0 10 5 0 5 10 Polity 300 Duation 200 100 0 0.5 0.6 0.7 0.8 0.9 1.0 Cap. Ratio Figue 3: Scatteplot of contol vaiables and conflict duation. 15
3.2 Results 3 EMPIRICAL ANALYSIS Dependent vaiable: Conflict Duation (Weeks) (1) (2) (3) (4) (5) Tenue (Logged) 0.177 0.196 0.176 0.146 0.153 (0.034) (0.038) (0.035) (0.035) (0.039) Polity 0.005 0.004 (0.003) (0.003) Cap. Ratio 0.098 0.264 (0.145) (0.157) Teitoy 0.660 0.742 (0.064) (0.071) Policy 0.255 0.299 (0.055) (0.062) Regime 0.829 0.861 (0.112) (0.125) Obsevations 2,101 1,823 2,034 2,101 1,766 Log Likelihood 13,962.930 11,855.150 13,451.850 13,893.150 11,362.810 Note: p<0.1; p<0.05; p<0.01 Table 1: Cox Popotional Hazads Model Results 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. 16
3.2 Results 3 EMPIRICAL ANALYSIS 2.00 Hazad Ratio with 95% CI 1.75 Relative Hazad 1.50 1.25 1.00 2.4 2.6 2.8 3.0 3.2 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. Altenatively, we can intepet the esults using pedicted suvival pobabilities based on 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 0.475 fo the new leade, while it is only 0.355 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. 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. Upon fist glance, 17
3.2 Results 3 EMPIRICAL ANALYSIS Dependent vaiable: Fatality (1) (2) (3) (4) (5) Tenue (Logged) 0.222 0.252 0.222 0.181 0.206 (0.044) (0.047) (0.045) (0.042) (0.047) Polity 0.015 0.010 (0.004) (0.004) Cap. Ratio 0.577 0.395 (0.185) (0.191) Teitoy 0.780 0.678 (0.077) (0.086) Policy 0.017 0.012 (0.067) (0.074) Regime 0.896 0.921 (0.148) (0.168) Constant 1.077 1.186 1.541 0.736 1.161 (0.122) (0.134) (0.196) (0.127) (0.212) Obsevations 1,978 1,733 1,911 1,978 1,676 R 2 0.013 0.021 0.017 0.092 0.089 Adjusted R 2 0.012 0.020 0.016 0.090 0.086 Note: p<0.1; p<0.05; p<0.01 Table 2: OLS Results fo Fatality Level 18
3.3 Robustness 3 EMPIRICAL ANALYSIS ou use of this statistical appoach may appea inappopiate given the odinal natue of ou outcome vaiable. Often when using odeed categoical data, analysts use a model designed to uncove the latent dimension fom which the categoies wee geneated. Howeve, in this case we do not believe that the use of such a model is appopiate given ou knowledge of the data collection pocess. Specifically, models such as odeed pobit posit that the obseved outcome vaiable y is the esult of some undelying but unobseved continuous measue y. As such, odeed pobit estimates, along with egession coefficients, a seies of cutpoints that descibes the elationship between y and y. Fo ou data, howeve, the undelying dimension used to geneate y is known. To be pecise, each fatality categoy is associated with a specified ange of battle deaths as outlined in the Coelates of Wa coding manual. As such, we believe that a statistical technique that would estimate these cutpoints when they ae known is inappopiate. This leads us to ou use of standad OLS egession. Tuning to the esults pesented in Table 2, we see that acoss all models, ou measue of leade tenue has a negative and statistically significant elationship with fatality level. This finding is consistent with Hypothesis 2. We also note that this finding caies substantive weight. In paticula, holding all othe vaiables at thei median values, a shift fom a bandnew leade to one that has held office fo fou yeas is sufficient to shift the expected numbe of fatalities down a full categoy unde the MID coding scheme. In addition to ou esults on leade tenue, the esults on the contol vaiables acoss the models deseve some attention. Ou duation esults suggest that democacy does not have a significant effect on the duation of conflict. Howeve, consistent with Valentino, Huth and Coco (2010), we find that democatic states incu significantly fewe casualties duing peiods of intestate conflict. The effect of democacy depends upon whethe the outcome vaiable is conflict duation o fatality level. A simila patten emeges with espect to the elative capability of states. We find that asymmetic was tend to be longe, but esult in fewe fatalities. Depending upon whethe the outcome vaiable is duation o fatality level, we find dispaate effects. In contast, the influence of leade tenue is consistent acoss the two outcome measues. This povides a futhe justification fo ou focus on both duation and fatality level. Consistent with ou theoy, the influence of tenue is consistent acoss the two outcome measues. 3.3 Robustness While the esults pesented above povide evidence in favo of ou hypothesis, it is still impotant to conside how sensitive these esults ae to altenative specifications of the model. In this section, we descibe the findings obtained fom vaious obustness checks. In the esults epoted in Table 1, we contol fo the issue unde dispute in each obsevation 19
3.3 Robustness 3 EMPIRICAL ANALYSIS using dummy vaiables. Howeve, this scheme only allows us to detemine how these issue aeas compae to the base categoy, as descibed in the data section. One concen aising fom this is that the elationship between leade tenue and conflict duation might only be elevant to some types of conflicts. Accodingly, we dig deepe into how the issue unde dispute influences the elationship between leade tenue and conflict duation by subsetting the data by issue, then unning sepaate egessions with all othe contols included. We find that in each of these egessions, ou findings fom Table 1 emain unchanged both substantively and statistically. Weisige (2013) agues that paticulaly chaotic leade tunoves lead to a shifting powe commitment poblem (Feaon, 1995; Powell, 2006) in which ivals fight was to captue bagaining goods befoe the new leade can eestablish thei militay postue. Because these commitment poblems ae not easily solved shot of complete militay defeat of one side, this mechanism would geneate the same empiical implication. We thus an two seies of subsetted models to diffeentiate the mechanism. Fist, the commitment poblem suggests that such was must stat paticulaly ealy in a leade s tenue to foestall the powe shift. We thus an models subsetting out leades with up to 90, up to 180, and up to 365 days in office. Consistent with the infomational stoy, longe tenues ae associated with shote fights. Second, because democatic tunoves ought to have compaatively smooth bueaucatic tansitions, we looked at conflicts whee the new leade s county has a Polity scoe of at least 1, 6, and 8. Again, in each of these subsetted models, the infomational mechanism held up. Anothe potential concen is that outlies in the data, involving leades of autocatic states who ae involved in vey shot, low-level conflicts might be diving the esults. To account fo this possibility, we discad all obsevations fo which eithe the duation of the conflict o ou measuement of leade tenue is an outlie. 11 esults emain unchanged. When we emove these obsevations, the Uzonyi and Wells (2015) find that the effect of leade tenue on civil was depends on constaining institutions of the executive. In paticula, they theoize that constained leades can ovecome commitment poblems that plague civil was (Walte (1997)), allowing the infomational mechanism to wok. Because these domestic commitment issues do not affect intestate conflicts, we would not expect a conditional effect hee. To test this, we inteacted tenue with the W scoe of that state (Bueno De Mesquita et al. (2005)). 12 Both duation and fatalities models fail to eject the null hypothesis. Even though ou pape is on intestate 11 Hee, we deem any obsevation that lies moe than thee times the distance spanned by the intequatile ange above the 75th pecentile as an outlie. 12 W is a five-point scale coded fom Polity that inceases when the state has a non-militay egime, competitive and open executive ecuitment, competitive political paticipation, and competitive paty systems. 20
4 DISCUSSION AND CONCLUSION was, these esults incease ou confidence in Uzonyi and Wells mechanism egading civil was, as thei theoy would pedict the null findings hee. Finally, in studying sanctions, Spaniel and Smith (2015) find an inteaction effect between tenue and democacy. We tested this by inteacting ou a leade s tenue with the polity scoe of his o he state and found null esults. Howeve, this is not supising given the diffeences between the cases. Wheeas sanctions often taget specific leades and thei suppotes, states cannot taget egimes in this manne as easily duing was. As such, uncetainty about a winning coalition s toleance to bea costs which Spaniel and Smith ague is citical to explain sanctions does not apply as stongly hee. Indeed, fo many was, individuals outside the coalition suffe the costs of fighting while those inside enjoy the benefits of victoy (Bueno De Mesquita et al., 2005; Goemans, 2000). 4 Discussion and Conclusion Ou main contibution connects leade tenue to the duation of intestate cises. If a state is elatively cetain of an opponent s esolve, we fomally showed that the duation of a cisis should be shot; the popose ought to make consevative demands o will aely be wong when it chooses an aggessive amount. The pape then investigated whethe this connection held boadly. Sue enough, we estimated that going fom a newly enteed leade to a leade with fou yeas of tenue leads to a 25.3% decease in the chances that a conflict sustains past one month. Additionally, we dew upon ou theoetical expectations about duation to deive an additional empiical implication; as uncetainty vanishes, so too should the numbe of casualties esulting fom conflict. Ou use of leade tenue as a poxy fo uncetainty again allowed us to evaluate this finding. We find boad suppot fo this expectation, noting that a shift fom one to fou yeas in office can esult in a substantial eduction in the expected numbe of fatalities. These esults help disciminate among the many theoies of leade tenue. Multiple mechanisms explain why states ae moe likely to ente conflict ealie in a leade s tenue. The infomation hypothesis pedicts that uncetainty will linge though fighting, causing was to last longe and be moe deadly fo newe leades. This matches the empiical esults. In contast, the othe mechanisms ae ambiguous about duation expectations o imply the opposite esult. All told, this gives us futhe confidence that leade tenue is an effective poxy fo uncetainty as othe scholas have used it. We conclude with seveal implications of ou esults. Fist, longe tenued leades povide positive extenalities to othe states; because it is easie to undestand thei motivations, ivals 21
5 APPENDIX can moe easily make the coect demands and avoid wa. In contast, long-tem leades may find themselves in a toughe situation. With moe publicly known about them, thei ability to bluff diminishes. In tun, they lose thei ability to secue concessions exceeding what they would expect to win though conflict. Next, fom a policy pespective, ou esults indicate that states ought to be especially caeful when negotiating with newe leades. Geate uncetainty implies that poposing states will have to spend moe time soting though thei opposition. Given that wa is costly, they may wish to instead buy off thei opposition immediately o decease thei demands to acceleate the negotiation pocess. This implication is especially impotant in light of ou findings on fatalities. By ignoing the infomational consequences of leade tenue, policymakes isk not only engaging in wasteful and lengthy diplomatic disputes, but also in the loss of human life. 5 Appendix 5.1 Poof of Popositions 1 Conside the game in its two stages. Let s be state A s posteio belief at the beginning of stage 2 that B is the unesolved type. Futhe, let s = c A+ c B c A + c B. The following lemma about stage 2 will pove useful thoughout: Lemma 1. In stage 2, state A s optimal demand stategy is: x p A + c B 2 = p A + c B if s s if s s Aftewad, the unesolved type accepts iff x 2 p A + c B x p A + c B. and the esolved type accepts iff We poceed backwad. Conside the accept/eject decision of state 2 in the second stage. This is the teminal node of the game egadless of its decision. Thus, it simply maximizes its payoff egadless of what type of signal a decision sends. If the esolved type ejects, it eans 1 p A c B. Theefoe, it is willing to accept any demand such that 1 x 1 p A c B, o x p A + c B. Analogously, the unesolved type eans 1 p A c B if it ejects. As such, it is willing to accept any demand such that 1 x 1 p A c B, o x p A + c B. 13 13 Fo convenience, we assume that state 2 accepts when indiffeent hee. Due to the standad easons, no othe equilibia exist hee if we pemit ejection in the case of indiffeence hee. 22