Nuclear Superiority or Minimum Deterrence - Nuclear Force Posture ...

Nuclear Superiority or Minimum Deterrence - Nuclear Force Posture ...

Date: March 13, 2011Word count: 11,289Nuclear Superiority or Minimum Deterrence?Nuclear Force Posture, Deterrence, and Militarized Interstate DisputesMatthew Kroenig 1Assistant ProfessorDepartment of GovernmentGeorgetown UniversityMichael WeintraubPh.D. StudentDepartment of GovernmentGeorgetown UniversityAbstractWhat is the relationship between nuclear force posture and deterrence outcomes?Scholars have long debated whether a minimum deterrent is sufficient to deter potentialchallengers, or whether nuclear superiority over potential rivals provides a more effectivenuclear deterrent. Scholars have not, however, articulated a clear logic linkingsuperiority to improved deterrence outcomes, nor have they systematically analyzed thesearguments against the entire universe of empirical cases. Using a new dataset on nuclearforce posture, which includes information on nuclear arsenal size and delivery vehicles,this article analyzes the determinants of deterrence success. We argue that nuclearsuperiority, by increasing the expected costs of conflict, improves a state’s ability to deterpotential adversaries. We then show that states that enjoy nuclear superiority over theiropponents are less likely to be the targets of militarized challenges. Arguments thatcontend that a minimum deterrent posture is sufficient to deter militarized challenges findonly qualified support in the data. This paper presents a new theoretical explanation andthe first comprehensive empirical examination of the relationship between nuclearsuperiority and deterrence outcomes.1 For helpful comments on earlier drafts of this paper, we thank participants at theGeorgetown University International Theory and Research Seminar (GUITARS), the

The relationship between nuclear force posture and deterrence outcomes is an issue ofextreme real-world importance. Policymakers, strategists, and academics in nuclearweapon states debate the requirements for successful deterrence as they size their ownnuclear arsenals. For example, in the 2010 Nuclear Posture Review (NPR), U.S.Secretary of Defense Robert Gates (2010, v) declared that U.S. “nuclear forces willcontinue to play an essential role in deterring potential adversaries,” and that thefundamental role of the US nuclear arsenal “is to deter nuclear attack on the UnitedStates, our allies, and partners.” In order to achieve deterrence, Secretary Gatesprescribed a nuclear posture consisting of thousands of nuclear weapons, nuclear-armedbombers, intercontinental ballistic missiles (ICBMs), submarine-launched ballisticmissiles (SLBMs), and forward-deployed tactical nuclear weapons. While the 2010 NPRreceived widespread bipartisan support, it was also criticized by many. Some argued thatsuch a large arsenal was overkill in the present security environment and that the UnitedStates could make deeper cuts and still deter adversaries. Others argued that by drawingdown the size of its strategic forces from previous levels, the United States wasweakening its nuclear deterrent and inviting potential challengers. This debate raises animportant question about the relationship between nuclear force posture and deterrence:what type of nuclear force posture is necessary to deter military challenges?A large theoretical literature has examined the relationship between nuclear forceposture and deterrence outcomes. Many international relations scholars (e.g., Waltz1995) hold that a minimum deterrent is sufficient to deter any rational adversary. Theyclaim that because nuclear weapons portend such destructive power, leaders will bedeterred from engaging in aggression if there is a remote possibility that they could be2

attacked by even a small number of nuclear weapons in response. These scholarscontend that nuclear-armed states, regardless of the size and sophistication of theirarsenals, can deter potential adversaries. Other scholars and policymakers (e.g., Nitze1976-77) maintain that states can gain a deterrent advantage by possessing nuclearsuperiority over potential challengers. However, these analysts have not articulated aclear logic by which nuclear superiority translates into improved deterrence outcomes. 2Moreover, these competing theoretical claims have not been subjected to systematicempirical investigation against the entire universe of cases.To examine the relationship between nuclear superiority and nuclear deterrence,we propose an argument, grounded in a nuclear deterrence theory framework, which linksnuclear superiority to the frequency of militarized challenges. We argue that nuclearsuperiority – defined as an advantage in the size of a state’s nuclear arsenal relative tothat of its opponent – increases the expected costs that a state can impose on a challengerin the event of a conflict and, therefore, decreases the probability that a country willbecome the target of militarized interstate disputes. A militarized challenge against anuclear-armed state is not an unavoidable leap into nuclear war, but is rather “a threat thatleaves something to chance” (Schelling 1960, 187). The payoff of challenging a nucleararmedstate is a function of a number of factors, including the expected cost of a nuclear2 Analysts have explained how a splendid first-strike capability, the ability to completelydisarm an opponent’s nuclear arsenal by launching a nuclear attack, can provide a statewith strategic advantages, but have not articulated how a nuclear advantage translatesinto diplomatic influence once an opponent can absorb a first strike and launch aretaliatory nuclear strike.3

exchange. While the expected cost of any nuclear war is high, not all nuclear wars areequally devastating. Countries that possess nuclear superiority can inflict greater levelsof damage on their adversaries, raising the expected costs of war. For this reason, statesthat enjoy nuclear superiority are, on average, less likely to become the targets ofmilitarized challenges.Drawing on a new data set of nuclear force posture, we examine the impact ofnuclear superiority on the probability of becoming the target of a militarized interstatedispute. We find a powerful, negative relationship between nuclear superiority and thefrequency of militarized challenges. Countries that enjoy nuclear superiority over theiropponents are less likely to be targeted in militarized disputes. These findings hold aftercontrolling for conventional military capabilities, the possession of a secure-second strikecapability, and other confounding factors. They even hold in tests performed in asubsample of nuclear-armed states. In addition, the results are robust to the exclusion ofeach individual country, alleviating concerns that the results are being driven by anysingle state.We find qualified support for the idea that a minimum nuclear posture detersmilitary challenges. Countries that possess nuclear weapons or a secure second-strikecapability are less likely to be the targets of military challenges, but this effect disappearswhen one controls for the nuclear balance between states. This suggests that thepossession of a minimum nuclear deterrent reduces the probability of being challenged bynonnuclear weapons states or by nuclear weapon states with smaller nuclear arsenals, butthat it does not decrease one’s chances of being challenged by nuclear weapon states withlarger nuclear arsenals. If one wishes to explain the probability of militarized challenges,4

therefore, one must look to the nuclear balance between states, not simply the nuclearcapabilities of the target state.This article presents a new approach to the scholarly study of nuclear deterrence,focusing on the relationship between the nuclear balance between states and deterrenceoutcomes. The systematic, empirical literature on nuclear deterrence has treated nuclearweapons as a dichotomous variable (e.g., Gartzke and Jo 2009). Analysts measuredsimply whether countries possessed nuclear weapons or not. These studies are useful forexamining the differences in conflict behavior between nuclear and nonnuclear states, butdo not shed light on how various types of nuclear force postures might influencedeterrence outcomes. Recently, scholars (Narang 2010, Lieber and Press n.d.) haveincorporated more sophisticated understandings of nuclear posture into studies of nucleardeterrence, but these scholars focus on the defender’s nuclear posture only and not on thenuclear balance between states. In addition, these recent studies are limited in bothhistorical timeframe and geographical scope. Many scholars and policy analysts haveadvocated that the United States maintain nuclear superiority over its adversaries (e.g.,Nitze 1956, 190-191), but the pathways through which nuclear superiority might translateinto improved deterrence outcomes were not clearly articulated. This article provides anew theoretical explanation, and the first systematic empirical test, of the relationshipbetween nuclear superiority and deterrence success.Explaining Nuclear DeterrenceThe vast nuclear deterrence theory literature has thoroughly hypothesized the types ofnuclear force posture necessary to deter rivals from initiating military challenges.5

Scholars in the minimum deterrence school (e.g. Waltz 1995; Lewis 2007) argue thatcountries will be extremely unlikely to initiate a militarized dispute against a nucleararmedstate because any nuclear exchange would carry unacceptable costs. Therefore,they argue, the mere possibility that a country might possess nuclear weapons issufficient to deter a potential military challenger. Other scholars in the same basictradition (e.g., Jervis 1984; Glaser 1990), place the bar for successful nuclear deterrenceslightly higher. They argue that a country can successfully deter military challenges onceit possesses a secure, second-strike capability – the ability to absorb a nuclear attack froman opponent and maintain enough survivable nuclear forces to launch a devastatingcounterattack. Again, the logic is similar. No country would choose to initiate a militaryconflict that could potentially result in unacceptable nuclear retaliation.On the other hand, scholars in the nuclear war-fighting school (e.g., Kahn 1960;Nitze 1976-77; Gray 1979) argue that the strategic nuclear balance between states iscritical to maintaining a credible deterrent. These scholars claim that if one state wouldsuffer significantly less damage in the event of nuclear war than its adversary, it mightnot be deterred. However, these scholars have not articulated a clear logic by whichnuclear superiority should affect deterrence effectiveness. As Charles Glaser argues(1990, 38-39), “the logical case” for the argument that nuclear superiority enhancesdeterrence “is weak, proponents have done little to support their claims, and efforts to fillin the logical gaps in their arguments encounter overwhelming difficulties.” Similarly,Robert Jervis (1984, 127) claims that in a world of mutually assured destruction, “if onetries to argue…that denying the Russians any [nuclear] advantage contributes strongly todeterrence and may even be necessary for it—problems abound.”6

Moreover, neither set of theoretical claims has been subjected to systematicempirical investigation. The existing scholarship (e.g., Jervis 1984; Glaser 1990) hasconsisted largely of theoretical postulations supplemented by illustrative case evidencefrom the United States and the Soviet Union during the Cold War, but has notsystematically examined the entire case universe.Other scholars have examined the effect of nuclear weapons possession onconflict onset, but these scholars have not examined the nuclear balance between states.In the “optimism-pessimism” debate (e.g, Sagan and Waltz 1995), analysts argue whetherthe presence of nuclear weapons increases or decreases the likelihood of internationalconflict, but do not specifically analyze how various types of nuclear postures affectdeterrence outcomes. Researchers (e.g., Gartzke and Kroenig 2009) have also conductedstatistical analyses to find that nuclear weapon states are, in the aggregate, neither morenor less conflict prone than similar nonnuclear states (Gartzke and Jo 2009), but that theconflicts in which they are involved tend to occur shortly after they acquire nuclearweapons (Horowitz 2009), are less intense (Rauchhaus 2009), and that nuclear-armedstates tend to emerge victorious from them (Beardsley and Asal 2009). The aboveliterature, however, both quantitative and qualitative, treats nuclear weapons possessionessentially as a dichotomous variable. It does not carefully explore how varieties ofnuclear force posture affect deterrence outcomes.Recently scholars have begun to incorporate more sophisticated understandings ofnuclear posture into studies of deterrence. Vipin Narang (2010), for example, hasanalyzed how Pakistan’s nuclear doctrine affects South Asian stability and Keir Lieberand Daryl Press (n.d.) have tracked how developments in the Soviet nuclear arsenal7

affected U.S. nuclear war planning. These studies focus on the unilateral nuclear forceposture of the defending state only, however, and do not examine the nuclear balancebetween states.Theory: Nuclear Superiority and DeterrenceIn this section we develop a theoretical framework linking nuclear superiority todeterrence success. We argue that countries will be less likely, on average, to challengestates that possess nuclear superiority because the expected costs of a full-scale war witha nuclear superior state are greater than the expected costs of a major war against otherstates.We begin from the basic insight that a state’s expected utility to initiating amilitary challenge is in part a function of the expected cost of fighting a full-scale war ifthe dispute escalates. There are, of course, a number of possible outcomes of amilitarized dispute: the targeted state might back down, resulting in a victory for theinitiator; the initiating state might itself submit and suffer a political defeat; the targetedstate might reciprocate the dispute, leading to the imposition of costs on the initiatingstate in the form of economic sanctions or limited military conflict; or, finally, the disputemight escalate into a full-scale war. As a state considers the initiation of a militarychallenge, therefore, it calculates the payoffs from, and the probabilities of arriving at, allof these possible outcomes. As the expected utility to be derived from initiating amilitarized challenge decreases, countries will be less likely to choose dispute initiation.Of course, the greater the expected costs of a full-scale war, holding other factorsconstant, the lower a state’s expected payoff to initiating a militarized challenge. The8

greater the costs of war against a particular state, therefore, the less likely other states willbe to challenge it.We argue that states will be less likely, on average, to challenge nuclear superiorstates because wars against nuclear superior states carry greater expected costs. To aid inthis task, we draw on two insights well developed in the nuclear strategy literature. 3First, nuclear strategists recognize that not all nuclear wars would be equally devastating.To calculate the varying effects of nuclear war, analysts (see e.g., Khan 1960; Kaplan1991; Freedman 2003; Huntington 1982, 38-42) consider factors such as total number ofdeaths and casualties, economic destruction, expected length of time for society torecover from war, and all of these factors relative to an opponent. As Herman Kahn(1960, 20) argued, “Few people differentiate between having 10 million dead, 50 milliondead, or 100 million dead. It all seems too horrible. However, it does not take muchimagination to see that there is a difference.” For Kahn, nuclear war scenarios in which acountry suffers 10 million deaths and requires 5 years to regain prewar levels ofeconomic output versus one with 80 million deaths and 50 years of economicrecuperation are “tragic, but distinguishable” outcomes. Nuclear strategists also drawdistinctions between postwar outcomes often considered to be in the realm of mutuallyassured destruction. For example, at the height of the Cold War, defense analysts (seee.g., Glaser 1990, 211-212) argued that even if the Soviet Union could destroy all majorU.S. cities in a nuclear attack, it might be prevented from killing U.S. citizens living in3 For a thorough review of this literature, see Glaser (1990); Kaplan (1991); Sagan (1989,10-57); and Freedman (2003).9

small and medium-sized cities and in rural and outlying areas and that the United Stateshad both a strategic incentive and a moral responsibility to protect these lives.Second, nuclear strategists recognize that nuclear superiority reduces the expectedcosts that a country would incur in the event of nuclear war. As Charles Glaser (1990,133) elaborates in his study of U.S. nuclear strategy, analysts in the “damage limitationschool” maintain that U.S. nuclear “superiority would reduce the cost to the United Statesin an all-out nuclear war.” States plan for counterforce nuclear targeting, i.e., usingnuclear weapons to destroy the nuclear weapons of an opponent, in an attempt to limit thedamage that the opponent could impose in a nuclear attack. 4According to then U.S.Secretary of Defense Harold Brown (1980, 66), “we have always considered it important,in the event of war, to be able to attack the forces that could do damage to the UnitedStates and its allies.” States that enjoy nuclear superiority are expected to perform betterin counterforce exchanges because they have more firepower with which to blunt theretaliatory capability of their opponents (see e.g., Kaplan 1991, 201-219; Freedman 2003,117-130; Glaser 1990, 133-165).In sum, strategic nuclear analysts and defense planners assess that some nuclearwars might be more devastating than others, and that nuclear superiority limits theexpected damage that a country would incur in the event of a nuclear exchange.Incorporating these insights into the expected utility framework of militarizedchallenges elucidated above, we should expect that the costs of challenging a nuclearsuperior state are greater than the expected costs of challenging other states for two4 On the damage limitation approach to nuclear war, see also Kaplan (1991 201-219) andFreedman (2003, 117-130).10

There is strong evidence that throughout the Cold War, U.S. policymakersbelieved that some nuclear wars would be worse than others, that a nuclear advantagetranslated into an ability to inflict greater levels of damage on one’s adversary, and thatmaintaining nuclear superiority was, therefore, critical to deterring the Soviet Union. Forexample, a secret White House memorandum from 1972 claimed that Washington mustmaintain a large enough nuclear arsenal “to ensure that the United States would emergefrom a nuclear war in discernibly better shape than the Soviet Union” (Herken 1987,266). Similarly, then Secretary of Defense Melvin Laird (1972, 65) argued that avoidinga position of nuclear inferiority vis-à-vis Moscow was necessary for “preventing theSoviet Union from gaining the ability to cause considerable greater urban/industrialdestruction than the United States would in a nuclear war.” In addition, in 1977, thenSecretary of Defense Donald Rumsfeld (1977, 68) testified, “if the Soviet Union couldemerge [from a nuclear war] with superior military power, and could recuperate from theeffects more rapidly than the United States, the U.S. capability for assured retaliationwould be considered inadequate.” Moreover, Paul Nitze (1956, 190-191), a defense andarms control official in many U.S. administrations, argued that one could determine thewinner of a nuclear war through a “comparison between the postwar position of the victorand the defeated.” Nitze claimed, therefore, that it was “of the utmost importance that theWest maintain a sufficient margin of superior capability so that if general war occurredwe could ‘win’ in this sense. The greater the margin (and the more clearly thecommunists understand that we have a margin), the less likely it is that nuclear war willever occur.” Finally, then Secretary of the Air force Harold Brown (1968, 186) claimed12

that “even 25% casualties might not be enough for deterrence if U.S. casualties weredisproportionately higher—if the Soviets thought they would be able to recover in someperiod of time while the U.S. would take three or four times as long, or would neverrecover, then the Soviets might not be deterred.”In sum, deductive logic and illustrative historical evidence suggest that countrieswith nuclear superiority over their opponents possess a more effective nuclear deterrentand will be less likely to be challenged militarily.The strongest counterargument to these claims is that a minimum deterrentposture, or a secure second-strike capability, is sufficient to deter militarized challenges.According to this perspective, nuclear-armed states should rarely become the targets ofmilitarized challenges, regardless of whether they possess a nuclear advantage over theiropponents. There are, however, reasons to be skeptical that a minimum nuclear posturealone provides an effective deterrent. While nuclear weapons raise the costs of war, theydo not eliminate political competition among states (e.g., Schelling 1966, 1-34; Powell1990, 1-32). States still seek to coerce nuclear-armed adversaries. While they cannotthreaten to launch a suicidal nuclear war, they can “make a threat that leaves somethingto chance” (Schelling 1960, 187). States can initiate a process, the nuclear crisis, in anattempt to force a less resolved opponent to back down. These games of nuclearbrinkmanship become “competitions in risk taking” (e.g., Schelling 1966, 92-125; Jervis1984, 126-146; Powell 1990, 33-109) in which the state that is willing to run the greatestrisk of nuclear war will prevail. States, therefore, will be willing to challenge nucleararmedstates if they believe that the nuclear-armed target will capitulate rather than fighta nuclear war over the contested issue. States may, therefore, be just as likely, if not13

more likely, to challenge nuclear-armed states over which they enjoy nuclear superioritybecause they might assess that they will be more likely to win the dispute. Nuclearsuperior states can push harder in a game of nuclear brinkmanship, increasing thelikelihood that they will prevail, because, for them, the costs of a nuclear exchange arerelatively lower (Kroenig 2010). Approaching nuclear deterrence from a brinkmanshipframework casts doubt on claims that a minimum nuclear posture provides a robustnuclear deterrent.Nevertheless, to test these ideas, we control for both a minimum deterrent postureand a secure second-strike capability in the empirical analysis. There are a number ofother factors that have been identified as potential causes of interstate conflict. Wediscuss these variables in the next sections, in which we describe the data and examinethe evidence for the previous hypotheses.Nuclear Force Posture DataTo examine the effect of nuclear posture on deterrence outcomes, we construct anoriginal nuclear force posture data set. The data set contains yearly information onnuclear-weapon status, nuclear arsenal size, and second-strike capabilities for every statein the international system from 1945 to 2001. 5 A list of nuclear-armed states from 1945to the present is available in Table 1. The unit of analysis is the directed-dyad year.Directed dyads make it possible to distinguish between the behavior of the initiator andthe target, providing additional information about causal processes (Bennett and Stam5 The final year for which data are available on the dependent variable, MilitarizedInterstate Disputes, is 2001.14

2000). Because militarized conflict is extremely unlikely between many states in theinternational system, we focus our analysis on politically-relevant dyads (e.g., Lemke2001). 6 (Insert Table 1 here)The dichotomous dependent variable is Militarized challenge. 7Drawing from theCorrelates of War (COW) Militarized Interstate Disputes (MID) dataset (Gochman andMaoz 1984; Jones, Bremer, and Singer 1996; Ghosn, Palmer, and Bremer 2004), thisvariable is coded 1 if a country is the target of MID initiation from a potential challengerstate, and 0 otherwise. MIDs include threats to use force, shows of force, uses of force,and war. A total of 1,534 MIDs were initiated between 1945 and 2001.We construct independent variables to test the hypotheses explicated previously.To assess whether countries that enjoy nuclear superiority over their opponents are lesslikely to become the targets of militarized disputes, we generate Nuclear superiority.This dichotomous variable indicates whether a potential target state possessed a largernumber of nuclear warheads than a potential challenger state. To begin the constructionof this variable, we gathered detailed information on the size of nuclear arsenals in eachnuclear weapon state in every year from 1945 to 2001. Appendix A provides informationon the coding rules and sources used to calculate nuclear arsenal sizes. Among those6 Robustness tests performed on the universe of all states in the international systemproduced nearly identical results.7 The dependent variable is lagged, in line with the recommendations of Beck (2001).15

states possessing nuclear weapons, the size of nuclear arsenals ranges from a low of one(e.g., South Africa in 1979) to a high of 40,723 (Soviet Union in 1986). Using thisinformation, we code a binary variable to indicate whether a potential target state hadmore nuclear weapons than a potential challenger state in each dyad-year.These data aim to provide an objective assessment of the number of nuclearweapons that a country possessed at any given time. In the realm of deterrence, however,what is most important is not the actual nuclear balance, but an adversary’s perception ofthe nuclear balance. Fortunately for researchers interested in the relationship betweennuclear force size and deterrence, there is very good reason to believe that there is a tightcorrespondence between the actual and the perceived nuclear balance. Even during thenow notorious Cold War debates about a possible “bomber gap” and a “missile gap” withthe Soviet Union, U.S. policymakers possessed fairly accurate information about theactual nuclear balance (Kaplan 1991, 155-175). Fears of a gap, which later turned out tobe incorrect, were based on projections of the future, not the contemporary, nuclearbalance and were the result of faculty assessments about the rate at which the SovietUnion was expanding its strategic forces. In sum, an objective count of nuclear arsenalsize and thus the strategic nuclear balance provides a reasonable measure of how state’sperceived the nuclear balance at any given time.Nuclear analysts often consider additional factors when calculating the nuclearbalance between states including: total megatonnage of the nuclear arsenal, numbers ofdelivery vehicles, accuracy of delivery vehicles, and the ability of command and controlsystems to execute war plans in a crisis. Aggregating these factors into a nuclearsuperiority index might be desirable, but detailed information on these variables is not16

available for every nuclear weapon state in every year. Moreover, nuclear force size, thevariable measured in this study, is generally regarded as the most important element ofany country’s nuclear force posture. Finally, there is good reason to believe that simplewarhead counts and more complicated assessments of nuclear capabilities are highlycorrelated. For example, according to almost any measure, the United States enjoyednuclear superiority over the Soviet Union from 1945 until the mid-1970s, at which pointMoscow achieved parity with, and arguably gained a strategic edge over, Washington(e.g., Nitze 1976-77, 201-203; Betts 1987, 89; Freedman 2003, 342-354).To examine the idea that the greater the level of nuclear superiority a countrypossesses over its opponent, the less likely it will be challenged, we construct Nuclearratio. Nuclear ratio is calculated as the number of nuclear weapons possessed by thepotential target divided by the total number of nuclear weapons in the combined arsenalsof the potential target and the potential challenger. The theoretical and empirical range ofthis variable is from 0 to 1.To test the alternative hypotheses that a minimum nuclear deterrent, or a secure,second-strike capability, will be sufficient to deter military challenges, we create twovariables. The first, Nuclear possession, is a dichotomous variable gauging whether acountry possesses nuclear weapons. Drawing on nuclear proliferation dates from Gartzkeand Kroenig (2009), we code this variable 1 for each year in which a potential target statepossesses at least one deliverable nuclear weapon, and 0 otherwise.To give the minimum deterrence argument its fullest possible test, we create asecond variable. Second strike is a dichotomous variable assessing whether a country hasthe ability to absorb a nuclear attack from an opponent and maintain enough reserve17

nuclear forces to respond with a devastating nuclear counterattack. We code a country aspossessing a secure, second-strike capability if it possesses either submarine launchedballistic missiles (SLBMs), mobile missiles with ranges capable of reaching the territoryof an “enduring rival,” or maintains nuclear-armed aircraft on continuous airborne alert. 8To code this variable, information was taken from a variety of sources, including TheBulletin of the Atomic Scientists, the Federation of American Scientists, the NationalResources Defense Council, and the Nuclear Threat Initiative. Countries to havedeveloped a secure, second-strike capability between 1945 and 2001, according to thisdefinition, include: the Soviet Union, 1956; 9 the United States, 1960; 10 Great Britain,1968; 11 Israel, 1970; 12 France, 1973; 13 China 1986; 14 Pakistan, 1995; 15 and India 1995. 168 On enduring rivalries, see Paul. F. Diehl, The Dynamics of Enduring Rivalries (Urbana:University of Illinois Press, 1998).9 The Soviet Union’s R-5 missile reached initial operational capability (IOC) in 1956. Itwas road mobile and capable of reaching strategic targets in Western Europe. The SovietUnion first developed SLBMs in 1958.10 The United States first developed SLBMs in 1960. The Pershing I, the U.S.’s firstmobile missiles capable of reaching the Soviet Union when deployed in West Germany,reached IOC in 1962. The United States, from 1961 to 1968, was the only country tohave ever maintained a continuous airborne alert.11 Great Britain developed SLBMs in 1968. It never developed mobile missiles capableof reaching an enduring rival.12 The Jericho I is a mobile missile with a range capable of reaching several enduringrivals in the Middle East, including Egypt. It first reached IOC in 1970. It is possible18

Defining second-strike capability according to whether a country possesses SLBMs onlyand repeating the analysis produced virtually identical results.We also include a number of control variables. To control for differences in scaleand possible aggregation biases (Signorino and Xiang n.d.), we include a lower-orderterm, Total nuclear weapons, that counts the total number of nuclear weapons within adyad. 17 Countries with a conventional military advantage might be better able to determilitarized challenges (Mearsheimer 1985). To gauge the conventional military balancebetween states, we generate Capabilities. We employ a power ratio variable that assessesthe capabilities of the potential target state, divided by the total combined capabilities ofthat Israel deployed nuclear-armed cruise missiles on its Dolphin-class submarinesbeginning in 2000. Israel does not possess SLBMs.13 France developed SLBMs in 1973. It never developed mobile missiles capable ofreaching an enduring rival.14 The DF-21 can be launched from a transporter-erector-launcher (TEL). It reached IOCin 1986. China deployed SLBMs on a single submarine in 1986, but there is somequestion as to whether the missiles are fully operational. The Pentagon characterizesChina’s SLBMs as experimental.15 The Hatf-III is a mobile missile capable of reaching Indian territory. It entered IOC in1995.16 The Prithvi I is a road-mobile missile capable of reaching Pakistani territory. Itreached IOC in 1995. India is in the process of testing, but has not yet deployed, SLBMs.17 We divide this variable by 100,000 when reporting our results to make the coefficientsmore legible.19

oth the potential target and the potential challenger. 18 Capabilities is a composite indexcontaining information on total population, urban population, energy consumption, ironand steel production, military manpower, and military expenditures. Data for thisvariable are drawn from the Correlates of War composite capabilities index, version 3.02(Singer, Bremer, and Stuckey 1972) and extracted using EUGene (Bennett and Stam2000).Countries in threatening security environments may be more likely to experiencemilitarized disputes. To control for the severity of a state’s security environment and tocorrect for potential autocorrelation in the dependent variable (Beck, Katz and Tucker1998, 1272), we generate Security. This variable provides a running average of thenumber of MIDs (Ghosn, Palmer, and Bremer 2004) a state experiences per year.The democratic peace hypothesis holds that the presence of joint democracydrastically reduces the probability of conflict (e.g., Doyle 1986; Oneal and Russett 1997).To measure Joint democracy, we use Polity scores, drawn from the Polity IV data set(Jaggers and Gurr 1995). The binary variable codes whether both states in a given dyadpossess a Polity score of seven or greater. 19States in close geographic proximity are more likely to fight with one another(Boulding 1962; Bremer 1992; Gleditsch 2003). To control for the confounding effectthat geography may have on the likelihood of MID initiation, we create Contiguity, a18 The correlation between Capabilities and Superiority is 0.226.19 We follow previous scholarship (e.g. Pevehouse and Russett 2006) in definingdemocratic states as those that receive a Polity score of seven or greater. Using six as thethreshold for democracy does not change the core results reported below.20

dichotomous variable that gauges whether states in a given dyad share a common border.In line with the Correlates of War standard, Contiguity is an ordinal variable identifyingnational proximity based on a six-point scale. 20 We also code a Distance variable, whichmeasures the distance between capital cities of countries in a directed-dyad year.The commercial peace literature contends that dyadic trade dependence has anegative, deterrent effect on the onset of conflict (e.g. Russett and Oneal 2001). Tocapture this confounding factor, we include in our models Economic dependence, withdata taken from Gleditsch (2003). This variable measures the sum of a potentialchallenger’s exports and imports with a potential target, divided by the potentialchallenger’s GDP.Some scholars argue that states that are economically open to the internationalsystem are less likely to fight (Barbieri and Peters 2003; Lee and Pyun 2009), whileothers hold that global trade can increase conflict (Martin et al. 2008). We generateEconomic openness to gauge the potential challenger’s openness to the internationaleconomic system. The variable measures total trade (imports plus exports) of thepotential challenger divided by gross domestic product (GDP) (Heston, Summers, andAten 2002). Summary statistics are presented in Table 2.(Insert Table 2 here)20 Using a dichotomous measure of contiguity did not affect the core results reportedbelow.21

Data AnalysisWe employ probit models to test claims about the correlates of militarized challenges. 21Robust standard errors are adjusted for clustering by dyad to correct for interdependenceof observations. We estimate each model after including cubic polynomials to accountfor temporal dependence in the dependent variable (Carter and Signorino 2010). Table 3presents the results.First, we explore the hypothesis that states that enjoy nuclear superiority overtheir opponents are less likely to be the targets of militarized challenges. Turning toTable 3, we find strong support for this hypothesis. We see that Nuclear superiority isnegative and statistically significant in a fully-specified (model 3), when nested in amodel that includes Nuclear possession and Second strike (models 4 and 5, respectively),and in a trimmed model (model 6). The analysis reveals a strong empirical link betweennuclear superiority and militarized challenges. Countries that enjoy nuclear superiorityover their potential opponents are less likely to be the targets of militarized disputes.(Insert Table 3 here)Assessing the effect of a nuclear advantage over an opponent, however, is onlythe first step. Next we explore the hypothesis that the greater the degree of nuclearsuperiority that a country possesses over its opponent, the less likely it is to face21 Using Rare-events Logit (King and Zeng 2001) did not significantly alter the coreresults.22

militarized challenges. Turning to Table 4, we find strong support for this idea. Thecoefficient on Nuclear ratio is negative and statistically significant when included in afully-specified model (7) alongside Nuclear possession, when nested in models withNuclear possession and Second strike (models 8 and 9, respectively), and in a trimmedmodel (model 10). These findings demonstrate that as one’s share of nuclear weaponswithin a dyad increases, one becomes increasingly less likely to be the target of amilitarized challenge.(Insert Table 4 here)Using Clarify, we assess the substantive effect of shifting from a position ofnuclear disadvantage to a nuclear advantage on the expected probability of being targetedin a MID, after controlling for other factors. 22Figure 1 plots the conditional effects of thenuclear balance on the expected probability that a state will be challenged. At the lefthandside of the figure, we can see that the expected probability of being the target of aMID in a given directed-dyad year for a state that possesses 5% of the total number ofnuclear weapons held by both states in the dyad is 0.0045843. 23 As we move to the rightof the figure, however, we see that an increase in the proportion of nuclear weapons that astate possesses within a dyad results in a corresponding decrease in the likelihood ofbeing challenged in a MID. Indeed, at the far right-hand side of the figure, we can seethat a country that possesses 95% of the total number of nuclear weapons held by both22 The conditional probabilities that follow are drawn from model 10.23 The 95% confidence interval is 0.0034538 to 0.0058405.23

states in the dyad has an expected probability of 0.0018533 of having a MID initiatedagainst it. 24 Therefore, states that possess only 5% of the total number of nuclear weaponsheld by both states in the dyad are nearly two and a half times more likely to bechallenged in a MID than those states that possess 95%. 25There is strong support for thehypothesis that countries with greater levels of nuclear superiority over their opponentspossess a more effective nuclear deterrent.(Insert Figure 1 here)The idea that states that possess a minimum nuclear posture are less likely to bechallenged finds only qualified support in the data. In models 1 and 2, we see thatNuclear possession and Second strike are negative and statistically significant. Thisfinding suggests that the possession of a minimum nuclear capability reduces theprobability that a country will be challenged militarily. Turning to the other models,however, we see that this finding washes away when one takes into account the nuclearbalance between states. Second strike is no longer statistically significant in models 5and 9. Nuclear possession is statistically significant in models 4 and 8, but the sign onthe coefficient is positive, suggesting that after the nuclear balance between states istaken into account, nuclear weapon states are more not less dispute prone. Takentogether, these findings suggests that a minimum nuclear posture is sufficient for24 The 95% confidence interval is 0.0009666 to 0.0032352.25 The odds ratio is 2.47. The first difference is -0.002731, with a 95% confidenceinterval of -0.0043767 to -0.000877.24

deterring militarized challenges from nonnuclear weapon states, or from nuclear-armedstates with smaller nuclear arsenals, but that they do not reduce the probability that acountry will be challenged by nuclear-armed states with larger nuclear arsenals. 26We briefly comment on the control variables. A state’s security environment altersthe probability of being challenged militarily. Security is statistically significant andpositive in every model in which it is included, suggesting that states in dangerousneighborhoods are more likely to become the targets of militarized disputes. Jointdemocracy is negative and statistically significant in each and every model. In support ofthe democratic peace hypothesis, we find that dyads in which both states are democraciesare less likely to see conflict than dyads that include at least one non-democratic state.Contiguity is significant and positive in every model, providing support for the idea thatterritorially contiguous dyads are more conflict prone. Economic openness is alsosignificant and positive in every model, suggesting that states with greater ties to theworld economy are more likely to be the targets of militarized disputes. None of the othercontrol variables reaches statistical significance. The total number of nuclear weapons inthe dyad, the conventional military balance, and economic dependence do not appear toshape a state’s likelihood of becoming the target of a militarized challenge.The analysis of the relationship between nuclear superiority and militarizedchallenges performed on the entire universe of empirical cases represents only one part ofour findings, however. Next, we conduct a similar analysis on the subset of cases in26 As alternate measures of second-strike capability, we tried dummy variables indicatingwhether a country possessed at least 50, 100, and 150 nuclear warheads, respectively.The results were nearly identical.25

which both countries in the dyad possess nuclear weapons. These tests will allow us tofurther examine the central hypotheses of this paper. If nuclear superiority providesstates with a deterrent advantage, we should expect that this finding holds against nuclearas well as nonnuclear states. This set of tests also permits us to explore the idea that aminimum nuclear posture provides a sufficient deterrent. If additional increases to thesize of a state’s nuclear arsenal above and beyond a minimum deterrent are simplyoverkill, then we should expect to find no relationship between nuclear superiority andthe probability of militarized challenges among a subset of nuclear-armed states.Because every state in the sample already possesses a minimum nuclear deterrent, anymeasures of nuclear capability to distinguish among the states in this group should notreach statistical significance if the minimum deterrence hypotheses are correct. To testthese ideas, we repeated the above analysis on a subsample of the 1,028 dyad years from1945 to 2001 in which both states in the dyad possessed at least one nuclear weapon.As we can see in Table 5, Nuclear ratio is negative and statistically significant inthe subsample of nuclear-nuclear dyads. Among nuclear weapon states, the greater thelevel of nuclear superiority over a potential opponent, the less likely a country is to bechallenged militarily. This finding provides strong support for the central hypothesis ofthis paper. Nuclear superiority provides a deterrent advantage against nuclear as well asnonnuclear opponents. In contrast, this finding undermines the claims of those in theminimum deterrence school. Rather, the results indicate that increases in the size of astate’s nuclear arsenal above and beyond a minimum nuclear posture continue to reducethe probability that they are challenged militarily by other nuclear-armed states.26

Robustness TestsThis section presents the results of a number of robustness tests. First, we examinedwhether our results depended on the definition of the universe of cases. We performedthe above analysis on a sample of politically-relevant dyads only, but to assess whetherthe results were contingent on this choice, we repeated the above analysis using the entireuniverse of all dyad-years. As might be expected, the negative relationship betweennuclear superiority and the probability of a militarized challenge was even stronger in thetests among this broader sample of data.Second, we tested whether our results were robust to the measurement of thedependent variable. The above tests examined the deterrent effect of nuclear weapons onthe initiation of all MIDs, ranging from threats to use force to full-scale war. But, onecould argue that the threat of nuclear war might be most relevant in higher-level militarychallenges. To examine this idea, we repeated the above analysis after defining amilitarized challenge to include uses of force or full-scale war only. In all tests, the signon the coefficient for Nuclear superiority and Nuclear ratio remained negative andstatistically significant and, as might be expected, the substantive effect of these variableswas even stronger in this subset of tests, indicating that a country with a nuclearadvantage over an opponent is even less likely to experience higher-level militarychallenges. Using Clarify, we can assess the substantive effect of shifting from nuclearinferiority to nuclear superiority on the expected probability of becoming the target of a27

higher-level militarized challenge, after controlling for other confounding factors. 27 Theexpected probability of being challenged in a higher-level MID in a given directed-dyadyear for a state possessing 5% of the nuclear weapons in a dyad is 0.0123129. 28 Acountry that possess 95% of the nuclear weapons in a dyad, by contrast, faces anexpected probability of 0.0036005 of having a higher-level MID initiated against it in agiven directed-dyad year. 29 Therefore, states in a position of extreme nuclear inferiorityare nearly three and a half times more likely to be challenged in a higher-level MID thanstates in a position of nuclear superiority. 30Nuclear superiority has a substantivelyimportant effect on deterring higher-level militarized challenges.Third, to assess whether the results were contingent on the inclusion or coding ofany particular country, we removed each country in turn from the first position of thedirected dyad, the challenger position, and reran the analysis. We then removed eachcountry from the second position, the target position, and reran the analysis. Next, wesequentially removed each state from the data set completely, from both the challengerand target positions, and reestimated the statistical models. Finally, to assess whetherthe results were being driven by the superpowers, we removed all the United States and27 The conditional probabilities that follow are drawn from model 10, substituting in ahigher-level MID onset lagged dependent variable and newly-constructed cubicpolynomials.28 The 95% confidence interval is 0.0102176 to 0.0144776.29 The 95% confidence interval is 0.0021515 to 0.0054265.30 The odds ratio is 3.42. The first difference is -0.0087124, with a 95% confidenceinterval of -0.011458 to -0.0058772.28

the Soviet Union from the dataset and reestimated the models using only the observationsamong nonsuperpowers. In all of the above tests, the core results were unaltered.Nuclear superiority and Nuclear ratio were negative and statistically significant in eachand every model. The core results are not being driven by any single country observation.Discussion and ConclusionThis article examined the relationship between nuclear posture and militarizedchallenges. We found that states that enjoy nuclear superiority over their opponents areless likely to be the targets of militarized disputes. This finding held under a variety ofmodel specifications and robustness tests. We derived a new theoretical implication ofnuclear deterrence theory to account for the observed relationship between nuclearsuperiority and deterrence success. We argued that a nuclear exchange with a nuclearsuperior state is potentially more devastating than a major war with other states, raisingthe expected costs of challenging a nuclear superior state. On average, states withnuclear superiority over their rivals are less likely to be challenged. In other words,nuclear superiority over potential opponents enhances the efficacy of a state’s nucleardeterrent.We find some support for the idea that a minimum nuclear posture deters militarychallenges, but this effect disappears when one controls for the nuclear balance betweenstates. This indicates that the possession of a minimum nuclear deterrent reduces theprobability of being challenged by nonnuclear weapons states or by nuclear weaponstates with smaller nuclear arsenals, but that it does not decrease one’s chances of beingchallenged by nuclear weapon states with larger nuclear arsenals. The findings suggest29

that a nuclear advantage over a rival, and not just the possession of a secure-second strikeadvantage, is necessary to deter military aggression.The argument of this article began with a simple insight, grounded in the nucleardeterrence literature, that nuclear superior states possess a deterrent advantage. Fordecades, leading scholars (e.g., Jervis 1989) have argued that nuclear weaponscompletely and irrevocably altered the nature of international conflict. Unlike inprevious eras, when larger militaries translated into greater political influence, it wasthought that the introduction of nuclear weapons brought about a “nuclear revolution” inmilitary affairs. Once a state had acquired a secure-second strike capability, additionalnuclear weapons were thought to be irrelevant to a state’s ability to deter adversaries(e.g., Jervis 1984). The empirical results of this research advocate for aconventionalization of the study of nuclear weapons. Conflict in the nuclear age is insome ways very similar to competition in earlier eras; the balance of military powerheavily shapes deterrence outcomes.This research suggests a new approach to the study of nuclear deterrence,focusing on the effect of the nuclear balance between states on international politicaloutcomes. In doing so, it contributes to a growing scholarly literature that takes nuclearforce posture seriously (e.g., Narang 2010, Lieber and Press n.d.). The past, systematic,empirical research on the relationship between nuclear weapons and international conflictmeasured whether a country possessed nuclear weapons, but did not analyze therelationship between various types of nuclear postures and international conflict.Defense planners have long operated under the assumption, however, that not only thepossession of nuclear weapons, but also the specific details of nuclear posture, including30

nuclear arsenal size, total megatonnage, survivability, range and accuracy of deliveryvehicles, nuclear doctrine, missile defenses, and civilian defenses, contributed to aneffective deterrence policy. The approach adopted in this article begins to address thereal-world concerns of nuclear strategists. Defense planners in nuclear weapon states donot often debate whether or not to maintain a nuclear arsenal, but they frequentlyconsider what type of nuclear arsenal they should build and maintain. Future researchcan better contribute to these real-world concerns by examining the effect of nuclearpostures and nuclear doctrines on deterrence effectiveness.Given that nuclear superiority improves deterrence effectiveness, it may appearpuzzling that some countries refrain from building large nuclear arsenals. Althoughmany countries, including the United States and the Soviet Union during the Cold War,and India and Pakistan today, arms race in order to avoid falling into a position of nuclearinferiority against a key rival, other countries, such as China, appear to be content with aminimum nuclear posture (Lewis 2007). There are a number of reasons why countriesmight choose a minimum posture over nuclear superiority despite the latter’s deterrentadvantages. Deterrence is only one of many factors that states take into considerationwhen sizing their nuclear forces and there might be some notable advantages to thepossession of smaller nuclear arsenals, including cost savings, reduced likelihood ofsparking a dangerous arms race with a rival, and reduced costs of catastrophe shouldnuclear war occur. In addition, some countries might prefer a larger nuclear arsenal, butsimply lack the ability to produce one. While scholars have long argued that China’sminimum deterrent was rooted in the strategic thinking of Mao Zedong and DengXiaoping, for example, recent research suggests that growth in China’s nuclear arsenal31

was stunted by organizational and political pathologies (Fravel and Medeiros 2010).Future research could explore in more detail the causes, as opposed to the effects, ofnuclear force size.On April 8, 2010, U.S. President Barack Obama and Russian President Dmitri A.Medvedev signed an historic arms control agreement, vowing to reduce the total numberof deployed strategic nuclear warheads in each country to 1,550, down from a previoushigh of 2,200 (Shear 2010). Proponents celebrated the agreement as a step toward a saferworld, while critics argued that the reductions could weaken America’s nuclear deterrent.The findings of this article suggest that cuts in the size of the U.S. nuclear arsenal couldincrease the probability that the United States will become the target of militarizedchallenges from other countries. This does not imply, however, that the United States orany other country should pursue nuclear superiority. While this research suggests oneadvantage to the possession of nuclear superiority, there might be many otherdisadvantages to the maintenance of large nuclear arsenals. When designing a nuclearposture, therefore, policymakers must carefully assesses how the composition of nuclearforces could affect a number of possible outcomes, in addition to deterring militarychallenges, including: nuclear terrorism, nuclear and conventional arms races, nuclearproliferation decisions in other states, the credibility of security guarantees to alliedstates, the outcomes of nuclear exchanges, and the probability of nuclear war. There isgood reason to believe that many of these national security objectives could best be metwith smaller, as opposed to larger, nuclear arsenals.Appendix A: Nuclear Arsenal Size32

To assess a country’s nuclear arsenal size, we measure all nuclear warheads in the state’sarsenal, including both tactical and strategic weapons. 31Data on nuclear arsenal sizewere drawn from a number of sources. Detailed annual information on the arsenals of thefive countries recognized as nuclear weapon states by the Nuclear NonproliferationTreaty (the United States, Russia, Great Britain, France, and China) is available from theNational Resource Defense Council’s online nuclear database (NRDC Nuclear Data).After disabling its nuclear arsenal in 1990, the South African government releaseddetailed information on the size of its nuclear arsenal. Data on the size of South Africa’snuclear arsenal from 1979 to 1990 were gathered from a variety of sources. There is lessinformation available on the size of the nuclear arsenals in Israel, India, and Pakistan.Estimates of Israel’s arsenal size from the mid 1980s until the present vary anywherefrom seventy to four hundred weapons. We used data from the Federation of AmericanScientists that estimates the size of Israel’s arsenal in every year from 1967 to the presentbased on the capacity of Israel’s nuclear facilities to produce weapons-grade fissilematerial (Federation of American Scientists). According to these estimates, Israelcurrently possesses roughly two hundred nuclear weapons. India and Pakistan arethought to maintain nuclear warheads de-mated from delivery systems. Estimates of thesize of these countries arsenals, therefore, are denominated in nuclear weapon equivalents(NWEs). Estimates of India and Pakistan’s NWEs are available from a variety of sources31 We assess that aggregate stockpile counts provide the best indicator of the nuclearbalance between states. Moreover, due to data limitations, we are unable to produceseparate counts of tactical and strategic weapons, or of deployed and non-deployedweapons, for each nuclear weapon state in each year.33

and are based on the weapons-grade fissile material production capacity of the countries’nuclear facilities. When sources provide an estimated range for a given year, or whenmultiple sources provide different point estimates, we take the mean of these estimates asthe size of the countries’ arsenal in that year. For years in which no estimate is available,we assume that the arsenal changed at a steady rate between the years for which pointestimates are available, calculating the difference in arsenal size, divided by the numberof years between estimates. While these estimates may not be exact, they provide a morethan adequate foundation for measuring whether a country has a larger nuclear arsenalthan its opponent for the creation of the Superiority variable and for gauging the roughsize of that advantage for generating the Nuclear ratio variable. We do not code NorthKorea as a nuclear weapon state. Pyongyang possessed enough separated plutonium toproduce one or two nuclear weapons in the early 1990s, but after two inconclusive testsin 2006 and 2009, experts doubt whether North Korea possesses the ability to produce adeliverable nuclear weapon to this day. 3232 See, for example, Thom Shanker and William J. Broad, “Seismic Readings Point to aSmall Nuclear Test,” New York Times, May 26, 2009, A1.34

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Table 1: Nuclear-Armed States, 1945-PresentCountryDateUnited States 1945-presentSoviet Union/Russia 1949-presentUnited Kingdom 1952-presentFrance1960-presentChina1964-presentIsrael1967-presentIndia1988-presentSouth Africa 1982-1990Pakistan1990-presentBelarusNeverKazakhstan NeverNorth Korea NeverUzbekistan NeverData on nuclear-armed states from Gartzke andKroenig (2009). North Korea tested nuclear devicesin October 2006 and May 2009, but expertsdisagree about whether the tests were successfuland whether North Korea has a functioning nucleardevice.40

Table 2. Summary StatisticsVariableMeanStandarddeviationMinimum Maximum ObservationsDependent VariableMilitarized challenge 0.001 0.038 0 1 1,077,136Explanatory variablesNuclear superiority 0.04 0.197 0 1 1,121,260Nuclear ratio 0.041 0.197 0 1 1,115,618Nuclear possession 0.044 0.205 0 1 1,118,552Second strike 0.031 0.172 0 1 1,121,260Control variablesTotal nuclear weaponsin dyad0.005 0.034 0 0.639 1,115,618Capabilities 0.5 0.369 0 1 1,115,588Security 0.388 0.596 0 3.82 1,115,618Joint democracy 0.155 0.362 0 1 1,115,844Contiguity 5.867 0.757 0 6 1,115,618Distance 4.775 2.761 0 12.347 1,115,618Economic dependence 0.002 0.013 0 1.823 714,092Economic openness 0.339 0.716 0 14.576 976,41041

Table 3. The Advantages of Nuclear SuperiorityModel 1 Model 2 Model 3 Model 4 Model 5 Model 6Nuclear Superiority -0.321** -0.518*** -0.252** -0.325**(0.113) (0.135) (0.105) (0.112)Nuclear RatioNuclear Possession -0.208* 0.235*(0.116) (0.136)Second Strike -0.244** -0.133(0.116) (0.117)Total Nukes in Dyad 0.096 0.292 0.056 -0.002 0.184(0.257) (0.284) (0.252) (0.256) (0.287)Capabilities -0.636*** -0.644*** -0.595*** -0.589*** -0.594*** -0.604***(0.098) (0.096) (0.097) (0.097) (0.098) (0.097)Security 0.363*** 0.356*** 0.381*** 0.370*** 0.388*** 0.383***(0.043) (0.038) (0.042) (0.043) (0.043) (0.040)Joint Democracy -0.200** -0.200** -0.198** -0.202** -0.196** -0.212**(0.079) (0.079) (0.079) (0.079) (0.079) (0.076)Contiguity -0.166*** -0.167*** -0.160*** -0.160*** -0.159*** -0.160***(0.019) (0.019) (0.018) (0.018) (0.019) (0.019)Distance -0.063*** -0.066*** -0.064*** -0.064*** -0.066*** -0.063***(0.019) (0.019) (0.018) (0.018) (0.018) (0.018)Econ. Dependence -0.500 -0.513 -0.423 -0.397 -0.427(0.466) (0.473) (0.452) (0.449) (0.452)Economic Openness 0.048** 0.045** 0.048** 0.048** 0.046** 0.047**(0.021) (0.021) (0.021) (0.021) (0.021) (0.021)Constant -1.012*** -1.008*** -1.046*** -1.045*** -1.052*** -1.043***(0.061) (0.062) (0.061) (0.061) (0.063) (0.062)N 59,876 59,876 59,876 59,876 59,876 59,876Pseudo R-sq 0.234 0.235 0.236 0.236 0.236 0.236* p

Table 4. The Advantages of Increasing Levels of Nuclear SuperiorityModel 7 Model 8 Model 9 Model 10Nuclear Ratio -0.339** -0.639*** -0.271** -0.342**(0.121) (0.171) (0.116) (0.120)Nuclear Possession 0.339**(0.158)Second Strike -0.125(0.118)Total Nukes in Dyad -0.679 -0.025 0.177(0.655) (0.255) (0.286)Capabilities -0.592*** -0.579*** -0.591*** -0.601***(0.097) (0.097) (0.098) (0.097)Security 0.385*** 0.371*** 0.390*** 0.387***(0.043) (0.043) (0.044) (0.042)Joint Democracy -0.197** -0.203** -0.195** -0.211**(0.079) (0.079) (0.079) (0.076)Contiguity -0.159*** -0.159*** -0.159*** -0.159***(0.018) (0.017) (0.018) (0.019)Distance -0.064*** -0.064*** -0.065*** -0.063***(0.018) (0.018) (0.018) (0.018)Econ. Dependence -0.416 -0.371 -0.421(0.450) (0.444) (0.450)Economic Openness 0.048** 0.048** 0.046** 0.047**(0.021) (0.021) (0.021) (0.021)Constant -1.050*** -1.052*** -1.055*** -1.047***(0.061) (0.061) (0.062) (0.062)N 59,876 59,876 59,876 59,876Pseudo R-sq 0.236 0.236 0.236 0.236* p

Table 5. The Advantages of Nuclear Superiority Among Nuclear/Nuclear DyadsModel 11 Model 12Nuclear Ratio -0.460** -0.484**(0.198) (0.231)Total Nukes in Dyad -0.903(0.654)Capabilities -0.390(0.634)Security 0.416** 0.325**(0.179) (0.106)Joint Democracy -0.022(0.377)Contiguity -0.170*** -0.122***(0.045) (0.0355)Distance 0.057(0.039)Econ. Dependence 0.032(3.655)Economic Openness 0.224(1.413)Constant -0.822** -0.916**(0.348) (0.335)N 1,028 1,028Pseudo R-sq 0.399 0.394* p

Figure 1. Conditional effects of the nuclear ratio on the expected probability of beingchallenged in a Militarized Interstate Dispute.Note: Estimates obtained from model 10. Nuclear Ratio is from lowest (0) to highest (1).45

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