The Unforeseen Consequences of Extended Deterrence: Moral Hazard in a Nuclear Client State

Abstract

Do “nuclear umbrellas” create a moral hazard that can increase the risk of war? In this article, we investigate whether situations of extended deterrence in which a nuclear patron makes a defensive commitment to a nonnuclear client state can inadvertently increase the likelihood that a client will initiate a crisis with another state. Using data on the crisis behavior of states from 1950 to 2000, we estimate the impact of a nuclear umbrella on various crisis outcomes, including the initiation and escalation of militarized conflict. Interestingly, we find no evidence that such commitments increase the risk of war or even two-sided violence at lower levels. However, consistent with both the moral hazard logic and bargaining theories of war, we show that this appears to be because potential target states offer increased policy concessions to client states to avoid costly fighting. Thus, the link between nuclear umbrellas and moral hazard appears to be real, but it is reflected in the division of benefits rather than a greater likelihood of war. The results have important policy implications as the US contemplates extending its nuclear umbrella.

Keywords

nuclear weapons nuclear proliferation bargaining international alliance

The ongoing dispute in the East China Sea over the Diaoyu/Senkaku Islands has rekindled tensions in United States–Japan–China relations. In particular, recent public affirmations of the US security guarantee to protect Japan in the event of a war with China have raised the specter of conflict in East Asia. Indeed, journalists in China have increasingly viewed the US alliance with Japan (and the Philippines) as both threatening to regional stability and its own rise in East Asia. For example, one recent editorial stated, “…it is increasingly obvious that Washington is taking Beijing as an opponent.”¹ Another editorial went one step further, suggesting that Japan may be using its relationship with the United States to aggressively further its own objectives: “Japan is taking advantage of American greed to cause trouble with its neighbors (i.e., China) in the Asia-Pacific region. China’s peaceful rise will not be constrained by any other country…”

In response to perceptions of Japanese revisionism, Chinese strategists have increasingly called on the United States to “publicly limit extended nuclear deterrence” out of fear that such commitments may embolden Washington’s allies (Li Bin and He Yun 2012). Similarly, Rapp Hooper (2015) argues that the United States would be unwise in deepening its commitments to extended nuclear deterrence, because:

…doing so may create a moral hazard problem, encouraging allies to press their claims with more confidence. Knowing that they have guaranteed backing, Tokyo or Manila may grow more assertive in disputes with Beijing…This, in turn, could cause crisis escalation or conflict that might otherwise have been avoided. (p. 139)

The crisis between China and its rivals in East Asia raises important questions about the US nuclear security guarantees in the region and about the inadvertent consequences of extended deterrence more generally. Has the US commitment to defend its allies in East Asia actually encouraged its clients to press their claims where they wouldn’t otherwise in the absence of the US “nuclear umbrella”? More generally, is it possible that commitments to extended deterrence create a moral hazard problem, whereby client states protected under a nuclear umbrella are emboldened to become more revisionary—pressing their demands in anticipation that a patron will intervene, and thereby perversely increasing the risk of a crisis?

In this article, we explore the relationship between nuclear umbrellas, militarized conflict, and crisis bargaining. Drawing on existing bargaining theories of war, we argue that, because war is costly, both parties in a crisis have an incentive to avoid fighting. This implies that—in equilibrium—the impact of a nuclear umbrella on the risk of war between a client state protected under a nuclear umbrella and a potential target should generally be zero, assuming information is complete, commitments are credible, and the stakes are divisible. However, this does not mean that such commitments are benign, or that they pose no risk to potential targets and nuclear patrons. Instead, we argue that a client state’s expectation that its power will be augmented in the event of war (by that of its nuclear patron) will make it more likely to expand the scope of its demands and seek to revise the status quo. Because war is generally ex post inefficient, leaders of target states are likely to offer concessions in the amount that reflects the changed balance of power, rather than fight a costly war. Thus, we argue that the risk of moral hazard from nuclear umbrellas should be observable in the bargaining outcomes short of war, if not in the observable patterns of militarized conflict.

We begin by investigating whether nuclear umbrellas generate a risk of moral hazard by increasing the risk of militarized interstate disputes (MIDs). We find evidence that protection under a nuclear umbrella slightly increases the risk that a client state protected under a nuclear umbrella will initiate an MID compared to a state that lacks this protection. However, we find that this overall effect is driven entirely by one-sided use of force initiated by the client state protected under a nuclear umbrella that never escalates to the reciprocal use of force by the target state. At the same time that targets appear to avoid the reciprocal use of force, we find strong evidence that a client state’s protection under a nuclear umbrella is positively associated with the likelihood that a crisis will include a peaceful settlement attempt and an increased likelihood that a target will offer policy concessions to the client state. Together, the results along both dimensions—conflict and bargaining outcomes—are consistent with the observable implications of the theory.

The remainder of this article proceeds as follows. We begin by examining some of the extant research on alliances and entrapment or moral hazard. We then develop our theory for why, despite the conventional wisdom that security guarantees increase the likelihood of war, we should expect that—if a risk of moral hazard exists—the consequences should be observable in the terms of negotiated settlements or concessions short of war. Next, we introduce the research design and data we use to test our hypotheses. We then present our results and discuss our main findings. Following the large-n results, we examine an illustrative case of the hypothesized mechanism in the United States-Republic of China (ROC)/Taiwan Mutual Defense Treaty (MDT). Finally, we conclude with a discussion of the policy implications.

Alliances, Entrapment, and the Risk of War

The existing literature on the causes and consequences of military alliances in international relations makes a compelling case for the general risk of moral hazard in the behavior of states protected under defensive security commitments. According to the conventional logic, alliances can increase the combined bargaining power of allied states by augmenting the military capabilities of each state with that of the other (Morrow 1994, 2000; Lake 2001; Leeds 2000, 2003). Two benefits are thought to follow: first, assuming sides are unable to settle their disputes, the formation of an alliance shifts the likely outcome of war in favor of the allied states; second, the prospect that a state will intervene on behalf of an alliance partner may deter a potential challenger from initiating a crisis in the first place (Huth 1988, 1990; Leeds 2003; Johnson and Leeds 2011).

Along with these benefits, however, comes at least one important consequence. At the same time that alliances can deter potential challenges, states protected under the alliance may become emboldened to expand the scope of their demands or to become intransigent in ongoing negotiations with other states. In this way, a conventional wisdom holds that alliance commitments can actually increase the risk of war by emboldening an alliance partner to demand more from other states and run a greater risk of war in expectation of an ally coming to its aid (Snyder 1984; Jervis 1994; Smith 1995; Leeds 2003; Zagare and Kilgour 2003; Yuen 2009; Benson 2011, 2012; Kim 2011; Benson, Bentley, and Ray 2013; Benson, Meirowitz, and Ramsay 2014). According to Snyder (1984), this classic moral hazard problem is one reason why states attempt to leave their security commitments purposely ambiguous to avoid the risk of “entrapment.”²

Despite the large volume of research on alliances, this logic of moral hazard and entrapment has yet to be investigated with respect to the specific case of nuclear umbrellas—a type of alliance in which a state with nuclear weapons makes a commitment to defend a nonnuclear alliance partner in the event of an attack.³ In particular, researchers have yet to systematically analyze whether nuclear umbrellas, otherwise known as “nuclear security assurances” or “commitments to extended deterrence” have the unintended side effect of increasing the risk of conflict.⁴ This is surprising, given that such assurances have long been a centerpiece of defense policy for major powers like the United States and Soviet Union (Lay 1953).

The lack of empirical evidence notwithstanding, the logic of moral hazard has led many scholars to warn against the potentially perverse side effects of nuclear umbrellas (Knopf 2012). Although nuclear umbrellas vary in important ways from conventional alliances—possibly including the requirement that a crisis escalate to the use of nonconventional capabilities (V. Narang 2013) —nuclear security guarantees are analogous to conventional alliances in that they require a patron to defend nonnuclear alliance partners in the event of an attack. Thus, nuclear umbrellas may inadvertently enhance the risk of war by dramatically shifting the likely outcome of war in favor of a client state, thereby emboldening a client state to expand the scope of its demands by targeting new states or to become intransigent in ongoing negotiations. In doing so, client states may expect to entrap their nuclear patrons into undertaking costly actions—often risking the initiation of militarized conflict—to defend them against aggressors (Snyder 1984, 1997; Christensen and Snyder 1990; Yuen 2009; Fearon 1997; Crawford 2003, 2005).

This conventional logic—and its application to nuclear umbrellas by security strategists—leads to the following hypotheses about the relationship between nuclear umbrellas and crisis initiation and escalation through moral hazard:

Hypothesis 1: Nonnuclear client states protected in an alliance by a nuclear-weapon state are more likely than states that lack a nuclear patron to initiate a conventional militarized dispute (MID).

Hypothesis 2: Nonnuclear client states protected in an alliance by a nuclear-weapon state are more likely than states that lack a nuclear patron to escalate a conventional militarized dispute (MID).

Nuclear Umbrellas, Moral Hazard, and Crisis Bargaining

In contrast to the conventional expectations above, we argue that it is unlikely that a client state protected under a nuclear umbrella will exhibit a greater propensity to engage in violent conflict. This is not because nuclear weapons have no impact on crises, nor is it because the logic of moral hazard in alliance politics does not apply in the specific domain of extended nuclear deterrence. Rather, we follow Gartzke and Jo (2009) in positing that the perverse consequence of moral hazard from nuclear security assurances will be observable in the crisis bargaining and subsequent distribution of benefits within negotiated settlements, if not the likelihood of violent conflict.

Consider the simplest model of crisis bargaining. Fearon (1995) suggests that coherent rationalist explanations for war will fall into one of two categories: actors can fail to find a settlement because they have private information with incentives to misrepresent or because they are unable to credibly commit to the agreement. According to the first explanation, sides have asymmetric information about their own capabilities and resolve and they often have an incentive to misrepresent their ability on these dimensions to secure a better settlement. As a result, while the costs of fighting open a range of settlements both sides should prefer to war, sides also have the incentive to bluff in order to shift the bargaining range in their favor (N. Narang 2015). The second explanation is that sides may prefer to fight now if their opponent is unlikely to honor a settlement in the future (Fearon 1998; Fortna 2003; Leeds 2000; Narang 2014; Walter 1997).

The bargaining logic of war has important observable implications for the impact of nuclear weapons and—by extension—nuclear umbrellas on crisis outcomes. Historically, states that have acquired nuclear weapons have generally been quick to reveal their newfound capability, so the risk of bargaining failure from private information about these capabilities is relatively remote.⁵ Furthermore, doubts about the credibility of a nuclear rival’s commitment to a negotiated settlement are unlikely to be sufficient to motivate a game-ending nuclear war. Together, the conditions under which crisis bargaining occurs between nuclear states—or asymmetrically between nuclear states and nonnuclear states—highly incentivizes a negotiated settlement. As Jervis (1976, 96) notes, “no country could win an all-out nuclear war, not only in the sense of coming out of the war better than it went in, but in the sense of being better off fighting than making the concessions needed to avoid the conflict.”

However, it also follows that, even if nuclear weapons may reduce the danger of war in some circumstances, they should nonetheless influence shared beliefs about the distribution of power among states. A state whose power increases through the acquisition of nuclear weapons may be emboldened to revise the status quo in its favor by threatening war to extract concessions—a threat that would be credible if the status quo distribution of benefits falls outside of an expanded and shifted range of mutually acceptable agreements. Thus, while nuclear weapons may have no effect on the observable incidence of militarized conflict, they should increase the bargaining power of the nuclear capable state, which could in turn lead to substantial effects on other policy dimensions.

As Gartzke and Jo (2009, 209) explain, “Diplomatic bargains tend to dampen the observable impact of nuclear weapons…. To the degree that nuclear weapons influence the concessions proliferators are likely to obtain in lieu of force, proliferation does much less to account for behavioral conflict.” One clear source of evidence that leaders “err in equilibrium” toward negotiated settlements is that war is rare (and nuclear war even more rare). Another source of evidence is a state’s level of diplomatic influence, which Gartzke and Jo show to increase significantly for nuclear-capable states.

This same logic may extend beyond a state’s own nuclear capability to that of a client state protected under a nuclear umbrella. Recall that the intended purpose of a nuclear security assurance is to reduce the utility of nuclear weapons in coercive bargaining by deterring potential adversaries from threatening war, including nuclear war, against an ally (Fuhrmann and Sechser 2014b).⁶ However, in joining the military capabilities of a nonnuclear state with the capabilities of a nuclear state, the alliance increases the combined bargaining power of the allied states relative to a third party. This may, in turn, embolden a nuclear client to spark a crisis and demand more policy concessions from other states in expectation of an ally coming to its aid. When potential target states believe the nuclear umbrella to be credible, they are likely to offer concessions sufficient to deter the initiation and escalation of a crisis. Thus, we hypothesize that although nuclear umbrellas may not create a moral hazard problem with respect to observable patterns in militarized conflict, they may nevertheless create a moral hazard with respect to client states’ willingness and ability to either spark a crisis in order to actively extract or passively receive, greater policy concessions from potential target states. We investigate the following observable implications that uniquely follow from our argument.

Hypothesis 3: Nonnuclear client states protected in an alliance by a nuclear-weapon state are more likely to obtain preferred policies peacefully compared to nonnuclear-weapon states without protection under a nuclear umbrella.

Gartzke and Jo (2009, 216) explain the straightforward logic behind this hypothesis clearly: the bargaining model of conflicts suggests that “nuclear nations and competitors will benefit most if they adjust diplomatic bargains in response to evolving strategic conditions rather than choosing to fight costly and unnecessary battles.” Consistent with this, Hypothesis 3 seeks to determine whether Issue Correlates of War (ICOW) settlements flow in favor of the nuclear client.

Importantly, the hypotheses above all directly follow from an important ongoing policy debate in outlined above, wherein analysts specifically identify extended nuclear deterrence as uniquely emboldening (Li Bin and He Yun 2012; Rapp Hooper 2015). However, these hypotheses imply an untreated comparison group that includes both states that have a purely conventional defensive pact and states that have no military alliances. Thus, popular claims leave ambiguous whether nuclear guarantees might uniquely cause moral hazard compared to conventional military guarantees or whether nuclear guarantees only cause moral hazard compared to having no guarantee at all.⁷ Therefore, it is instructive to explicitly theorize about the differential risk of moral hazard when client states have access to nuclear capabilities versus when client states only have access to conventional capabilities through an alliance.

Existing theory remains ambiguous about what differences one should reasonably expect across the two types of alliances with respect to the risk of moral hazard. On one hand, one might suppose that the nuclear element might amplify the risk of moral hazard when compared to conventional alliances, since a client state might be even more emboldened to seek expanded objectives. After all, if alliances facilitate capability aggregation, there is perhaps no greater military capability than nuclear weapons. On the other hand, the opposite may also be true: nuclear umbrellas run little to no additional risk of moral hazard when compared to conventional alliances. This is because threats to use nuclear may be inherently incredible (Paul 2009; Tannenwald 2007; V. Narang 2015; Avey 2015). After all, there is compelling logic to suggest an emerging norm against the use of nuclear weapons (Tannenwald 2007; Paul 2009) and to suggest that the use of nuclear weapons could undermine regional and global strategic stability (Lee 2007), including by increasing the potential for a retaliatory strike against the nuclear patron state itself (Avey 2015; Rapp Hooper 2015; Lanoszka 2014). These factors may combine to explain why nuclear weapons have not been used in combat since World War II.

Since theory generates no strong priors about the differential effects of nuclear versus conventional alliances on the risk of moral hazard, we investigate whether there is any significant difference—either positive or negative—between the risk of moral hazard across client states that have access to nuclear weapons through an alliance versus client states that only have access conventional capabilities through an alliance.

Hypothesis 4: Nonnuclear client states protected in an alliance by a nuclear-weapon state exhibit a different likelihood of obtaining preferred policies peacefully compared to states that have only a conventional defensive pact.

Finally, for all hypotheses the logic implies that client states generally believe alliances to be credible. However, uncertainty over the likelihood of compliance is ubiquitous to all international agreements, including alliances (Morrow 1994, 2000; Fearon 1994, 1997; N. Narang and LeVeck 2011; LeVeck and N. Narang 2016). Nevertheless, we make a more modest assumption that a formal alliance commitment—while certainly incomplete—increases the probability that the patron will honor the commitment sometime in the future by some nonzero and positive amount. Resolution of this uncertainty is perhaps the primary reason states sign formal alliance commitments at the outset: they seek to influence the beliefs of their alliance partners and any prospective challengers by publically signaling their intention to intervene in the event of a war (Morrow 1994; Smith 1995; Fearon 1997). Nonetheless, it is almost certainly the case that the impact of a nuclear umbrella and conventional alliance on the risk of moral hazard is partly mediated by factors that make the agreement more or less credible. Based on a time-series cross-sectional analysis of all nuclear umbrellas from 1950 to 2001, N. Narang (2017) provides systematic evidence that there is not only a positive average treatment effect from nuclear umbrellas on the assurance of client states, but that clients appear to behave in a way that is increasingly assured as nuclear umbrellas become more institutionalized. The finding is ascribed to the costs of negotiating and implementing more intricate and costly alliances, which serve as costly signals of more reliable commitments.⁸

Research Design and Data

We employ a directed-dyad unit of analysis on a data set that includes all countries in the international system from 1950 to 2000 to test our hypotheses. Specifically, we begin with data from V. Narang (2013) to create a data set with an observation for each state as a potential initiator of a crisis with every other relevant state in the international system.⁹ Directed dyads make it possible to differentiate between the behavior of the challenger and the target state, which provides more information with which to test the causal process implied by the moral hazard logic. Specifically, each hypothesis links the protection provided under a nuclear security assurance, to the crisis behavior of a client state as a potential initiator. A directed-dyad structure also allows us to investigate whether settlements flow from targeted states without protection under a nuclear umbrella to client states protected under a nuclear umbrella.

Following previous work (Gartzke and Jo 2009; Bell and Miller 2013), we use probit, rare events logit, and ordinal probit to analyze the effect of our independent variables on the dependent variables, and we use Huber–White standard errors to correct for spatial dependence. We also cluster on the dyad to address heteroskedastic error variance, in addition to correcting for temporal dependence using “peace years” and splines (Beck, Katz, and Tucker 1998).

Independent Variable: Nuclear Umbrellas

In both the academic and policy literature, the term “nuclear umbrella” is used to refer to the protection provided by a nuclear patron state to a nonnuclear client state generally under a formal defense pact (Knopf 2012, 2). In all previous research, the consensus has been to operationalize a nuclear umbrella by observing whether a state has a defensive alliance with a nuclear-weapon state (Singh and Way 2004; Jo and Gartzke 2007; Verdier 2008; Fuhrmann 2009; Kroenig 2009a, 2009b; Horowitz and Narang 2014; V. Narang 2015; Horowitz and N. Narang 2014; N. Narang, Gartzke and Kroenig 2015). This measure is imperfect in many ways. It is possible that the nuclear-weapon state in the alliance has not made an explicit commitment to use nuclear weapons. This ambiguity is oftentimes deliberate (Knopf 2012; Rapp Hooper 2015). However, it is important to note that analysts can only observe the same public declarations of commitment—with all their attendant ambiguities—that leaders observed when deciding whether to resist a challenge or offer concessions. In this way, public declarations influence the beliefs of potential challengers similarly to the retrospective coding of analysts.¹⁰

To operationalize nuclear umbrellas, we used the Alliance Treat Obligations and Provisions (ATOP) data set to identify observations in which states in a dyad received a defensive commitment from a nuclear-weapon state (Leeds et al. 2002). The variable is coded dichotomously, where an observation coded “1” has a defensive commitment from a nuclear-weapon state and “0” otherwise. According to this data, 67 of the 152 defensive pacts active from 1950 to 2001 included an alliance member that was a nuclear-weapon state, protecting sixty-four different client states.¹¹ Directed dyads allow us to distinguish which states in a dyad are client states protected under a nuclear umbrella and which states may have lacked this protection as both the challenger and the target. In total, 26,373 observations of 192,018 include a potential challenger protected under a nuclear umbrella (13.7 percent).

Dependent Variables: Conflict Behavior and Crisis Bargaining Outcomes

We use two categories of dependent variables to test the expectations outlined above. In the first category, we measure conflict behavior in two ways. The first is the initiation of a MID by a challenger as recorded in the Correlates of War (COW) data (Gochman and Maoz 1984; Jones, Bremer, and Singer 1996; Ghosn, Palmer, and Bremer 2004). Specifically, we use data on MID initiation coded “1” if the challenger initiates an MID against its counterpart in a dyad in a given year and “0” otherwise. The second measure is the level of MID escalation coded ordinally from 0 to 4 for how high in intensity a dispute escalated (Bennett and Stam 2004, 63).

In the second category, we use data from the ICOW project on settlement attempts of contentious issues. The ICOW data codes information on settlement attempts and the distribution of stakes in a conflict over issues on which nations disagree. We focus on whether any attempt is made to resolve an ICOW in a given year (attone), whether the attempts are peaceful (attanyp), and which side obtains concessions (resolved).

Control Variables

Our analyses also include several covariates that mirror Gartzke and Jo (2009) and Bell and Miller (2013). First, to control for the security environment, we include a measure for enduring rivalries to identify dyads with security challenges (Bennett 1996; Diehl and Goertz 2000). We include a dyadic rivalry coded “1” if the members of the dyad have a rivalry with each other and separate monadic rivalry status. Second, we measure military power of each county using the COW Composite Index of National Capability. Third, we measure whether dyad members share an alliance, since states that share an alliance can be more (Morrow 2000; Kimball 2006) or less (Bueno de Mesquita 1981) dispute prone. Fourth, we control for the level of democracy, constructed by Gartzke and Jo (2009) using the Polity IV data (Marshall et al. 2002) to measure monadic regime type and joint democracy (Doyle 1997; Russett 1993; Russett and Oneal 2001). Finally, because neighboring states fight more (Boulding 1962; Bremer 1992; Gleditsch 2003), we include an ordinal measure of contiguity based on the six-point COW variable and a continuous metric measure of geographic distance based on the log-transformed distance between capital cities of countries.

Results

We present the results of our statistical tests in three parts, evaluating Hypotheses 1 and 2 on conflict behavior, followed by Hypothesis 3 on policy concessions, and then ending with Hypothesis 4 comparing nuclear umbrellas against conventional military alliances. For each hypothesis, we display the main coefficients along with the 95 percent confidence intervals in box plots, and we relegate the regression tables to the Appendix of the article.

Nuclear Umbrellas and Conflict Initiation and Escalation

Figure 1 shows the estimated relationship between protection under a nuclear umbrella and MID initiation (Hypothesis 1) as well as MID escalation in ongoing militarized disputes (Hypothesis 2).¹² The full regression results with all covariates are shown in Appendix Table A1. In model 1, which estimates the impact on the likelihood that a state will initiate an MID of any type, the coefficient estimate on nuclear umbrella A indicates some support for Hypothesis 1: protection under a nuclear umbrella appears to be positively associated with the likelihood that a client state will initiate an MID against a target state (substantively, a 2.5 percent increase in the likelihood of any MID). At first glance, this finding appears to run counter to the logic of the bargaining model and our expectation that—if a moral hazard exists as a result of a nuclear umbrella—the effect should not be observable with respect to conflict initiation. However, following recent work by Bell and Miller (2013), which showed that nuclear dyads can be more prone to low levels of conflict but not higher levels of war, we probed these results to determine at which levels in the MID escalation ladder that nuclear umbrellas appear to have the strongest influence on the behavior of a client state.

Figure 1.

Impact of nuclear umbrella on probability client will initiate a militarized interstate disputes (MID) (by MID type/MID escalation).

Models 2–4 estimate the impact of a nuclear umbrella on the likelihood a client state will initiate an MID against a target state that escalates to war, the reciprocated use of force, and the one-sided use of force, respectively. Surveying the coefficient estimates on nuclear umbrella A across the escalation ladder, we find no evidence that protection under a nuclear umbrella causes a client state to initiate an MID that leads to war (model 2) or even the reciprocated use of force (model 3) at a higher rate, compared to states that lack a nuclear umbrella. However, we find strong evidence for a positive association between a nuclear umbrella and the likelihood that a client state will initiate an MID through the one-sided use of force that is never reciprocated by the target state (model 4). This finding is consistent with our initial expectation that client states protected under a nuclear umbrella are likely to expand the scope of their demands by challenging other states (substantively, a 15 percent increase in the likelihood of one-sided use of force), but that leaders of targets are more likely to settle than reciprocate fighting.

This interpretation mirrors that of Bell and Miller (2013) who find that asymmetric nuclear dyads are more likely to experience low-level conflict that never escalates to war. They interpret the finding that nuclear capable states are more likely to “initiate disputes against new opponents…” to be “…consistent with the idea that nuclear weapons lead states to expand their interests in world politics.” (p. 75) It is also consistent with the bargaining model of war, which—in assuming war is costly and thus generally ex post inefficient—treats by definition any credible threat or use of force as a rational attempt to alter the distribution of benefits to match a sufficiently changed distribution of power to satisfy the expanded demands of the challenger (Powell 1999).

The results of model 5 provide additional support for this inference. It estimates the relationship between protection under a nuclear umbrella and the likelihood that a client state will escalate an MID. This dependent variable has the added advantage of determining whether a nuclear umbrella is associated with client states becoming more aggressive within ongoing MIDs. We find no evidence of such an effect, as indicated by the lack of significance on nuclear umbrella A. However, in Appendix Table A2, we demonstrate a separate finding with respect to escalation that is nevertheless consistent with our theory. Despite having no effect on the escalation of militarized conflict, client states protected under a nuclear umbrella do appear more intransigent within the underlying negotiations of a crisis based on the International Crisis Behavior (ICB) data set.¹³ Specifically, in models 3 and 4 of Appendix Table A2, we show that client states protected under a nuclear umbrella are less likely to end an underlying crisis sooner by backing down in negotiations when facing a state that lacks protection under a nuclear umbrella, and that a state is simultaneously more likely to back down within the underlying crisis negotiations sooner against an opponent that benefits from protection under a nuclear umbrella.

Our findings—that protection under a nuclear umbrella does not increase the likelihood that a client state will initiate a war or two-sided violence, or that a client state will escalate an ongoing military conflict—are also consistent with those of Fuhrmann and Sescher (2014). They find no evidence of moral hazard with respect to militarized conflict using a monadic research design of all states from 1950 to 2000 and the COW Formal Alliance data set. We also find little to no evidence that protection under a nuclear umbrella influences the propensity for a client state to initiate an MID that escalates to higher levels of conflict. Although—consistent with our theory and results for Hypothesis 3—our findings in Appendix Table A2 suggest that states do become more intransigent within the underlying negotiations of a crisis.

The results of the other variables in Appendix Table A1 are also instructive. In contrast to the expectations of extended nuclear deterrence, we find no evidence that a target state’s protection under a nuclear umbrella has any effect on the likelihood that a challenger will initiate an MID, as indicated by the coefficient estimate for nuclear umbrella B. This result is similar to findings by Gartzke and Jo (2009): there appears to be no significant dampening effect on the likelihood of a challenge against nuclear capable actors.

Nuclear Umbrellas and Moral Hazard through Bargaining Concessions

If nuclear umbrellas generate a risk of moral hazard by the client state, it is reasonable to expect that this risk will be observable in the results of crisis bargaining, if not the risk of militarized conflict. Figure 2 presents the results investigating the impact of a nuclear umbrella on the bargaining behavior of client states and their target. The full regression results are shown in Appendix Table A3. Model 1 evaluates whether protection under a nuclear umbrella is associated with any attempt to settle an ICOW in a given year. Note that the variable is coded inversely, with “1” indicating no attempt to settle the issue in a given year, and “0” indicating a settlement attempt was made. If our theory is correct, we expect that when state A targets state B, and state A is protected under a nuclear umbrella, the coefficient on nuclear umbrella A will be positive (because “1” indicates no settlement attempt made by the challenger) or insignificant, since the protection provided to state A should make it no more likely to offer a settlement. Consistent with our expectations, we find that targets protected under a nuclear umbrella are significantly more likely to receive settlement attempts initiated from challengers (negative coefficient on nuclear umbrella B). At the same time, we find that challengers are no more likely to initiate settlements attempts when they are protected under a nuclear umbrella themselves compared to states that lack protection under a nuclear umbrella, and—if anything—they are less likely to extend settlement attempts (positive but insignificant coefficient on nuclear umbrella A).

Figure 2.

Impact of nuclear umbrella on probability challenger will make no settlement attempt, comparing challenger versus target covered under nuclear umbrella.

Figure 3 displays the results of model 2 in Appendix Table A3, which estimates the relationship between a nuclear umbrella and peaceful settlement attempts. This variable is coded inversely to any settlement attempt in Figure 2: “1” for peaceful settlement attempt made and “0” if no peaceful settlement attempt. We expect the nuclear umbrella A to be negative and nuclear umbrella B to be positive. The results are as expected and similar to Figure 2: challengers are no more likely to pursue peaceful settlements when they are protected under a nuclear umbrella themselves compared to states that lack protection under a nuclear umbrella, but targets protected under a nuclear umbrella are significantly more likely to receive peaceful settlements (substantively, a 5 percent increase in the likelihood of receiving a peaceful settlement offer).

Figure 3.

Impact of nuclear umbrella on probability challenger will make a peaceful settlement attempt, comparing challenger versus target covered under nuclear umbrella.

The insignificant coefficients on nuclear umbrella A across models 1–4 in Appendix Table 3 are not inconsistent with our expectations, since our theory primarily yields implications about whether states protected under a nuclear umbrella are likely to receive settlement attempts, whereas nuclear umbrella A estimates the tendency for a client state protected under a nuclear umbrella to initiate a settlement. It is plausible that states protected under a nuclear umbrella may be both more likely to receive settlement offers and also more likely to initiate settlement offers in an ongoing bargaining exchange. However, our data only allow us to observe the settlement offers initiated from challengers, which means the only way we can observe whether states protected under a nuclear umbrella are recipients of settlement attempts initiated by the other states is to reverse the positions of states as we do using a directed-dyad structure. This is what we show in our estimation of nuclear client B. Furthermore, if states are more likely to receive and initiate settlement offers in an ongoing bargaining exchange, it is not clear what the theoretically expected direction of the coefficient on nuclear client A should be. Nevertheless, the coefficient on nuclear umbrella A suggests that—if anything—challengers protected under a nuclear umbrella may be less likely to make settlement offers to targets.

Finally, in Figure 4, we explore whether nuclear umbrellas make target states easier to influence in crisis bargaining. The full regression results are shown in Appendix Table A4. We use two different portions of the ICOW resolved variable. In model 1 of Appendix Table A4, the dependent variable is coded “1” if the issue was renounced by the challenger, while in model 2 the dependent variable is coded “1” if the issue was renounced by the target. The results are consistent with our expectations. Figure 4 shows the results of model 1, where the challenger’s status as a client state protected under a nuclear umbrella does not appear to be a significant determinant of whether it concedes. The target’s status as a client state protected under a nuclear umbrella does appear to be a significant determinant of whether a challenger concedes.

Figure 4.

Impact of nuclear umbrella on probability challenger renounces issue under dispute, comparing challenger versus target covered under nuclear umbrella.

While not shown in Figure 4, in model 2 in Appendix Table A4, the results for whether the issue was renounced by the target are also supportive. When it is the target that concedes, the challenger’s status as a client state protected under a nuclear umbrella predicts concessions perfectly and drops out of the regression. This result and the previous one are both in line with our theoretical expectations: states with nuclear patrons appear systematically more likely to gain concessions from their opponent compared to states that lack protection under a nuclear umbrella.

Interestingly, however, we also find that the target’s status as a client state protected under a nuclear umbrella is also positively associated with it conceding. While our theory only makes predictions about the settlement behavior of opponents of state protected under a nuclear umbrella, this result is nevertheless puzzling. One plausible explanation for this finding follows from the work of Fuhrmann and Sechser (2014a). While a target covered by a nuclear umbrella may be able to achieve some additional gains, it also risks violating the patron’s trust and losing its security guarantees altogether. As a result, client states may actually adopt less aggressive stances toward potential adversaries by pressing more modest/less difficult issues. A second explanation may be that the observation of a challenge against a state protected under a nuclear umbrella is not random, and could potentially be the product of sample selection bias based on unobserved differences in the dyadic ratio of conventional capabilities or resolve that causes targets to renounce the issue despite their nominal protection under a nuclear umbrella. As one illustration, we investigated the dyadic ratio of conventional capabilities between the challenger and target in cases where the target renounced the issue while also being protected under a nuclear umbrella. We found that in these cases, the challenger benefits from a conventional capability ratio that is on average 2.5× greater than that of the target, whereas the median capability ratio in the population is 1.0.

As with our tests of crisis escalation, we also probe the robustness of our findings on bargaining concessions using the ICB data in models 1 and 2 of Appendix Table A2 (as a test of Hypothesis 3). The results confirm that client states protected under a nuclear umbrella are more likely to achieve victory (i.e., a state realizing all of its goals) and less likely to experience defeat in a crisis compared to states that lack a nuclear umbrella, while states that lack protection under a nuclear umbrella are simultaneously less likely to achieve victory and more likely to experience defeat when their opponent is asymmetrically protected under a nuclear umbrella.

Comparing Nuclear Umbrellas versus Conventional Alliances

Do nuclear umbrellas uniquely generate a risk of moral hazard compared to conventional military alliances? In Appendix Table A3, we reestimate the models with ICOW settlements as the dependent variable used to make Figures 2 and 3, but this time we include a measure for the number of conventional defensive military alliances that each potential challenger has based on the ATOP data. In Appendix Table A4, we do the same for the models with ICOW resolutions as the dependent variable used to make Figure 4. The tests allow us to compare the effects of nuclear umbrellas with the effect of strictly conventional alliances to see whether the former is more emboldening than the latter.

When we estimate the effect of a conventional defensive alliance on the bargaining behavior of client states and their target while nuclear umbrella is controlled for, we find no evidence that conventional alliances are more likely to result in concessions for the client state. If anything, we actually find evidence in support of Beckley (2015): conventional alliances appear to have a constraining effect for both ICOW settlement variables in models 3 and 4 of Appendix Table A3. Challengers appear slightly more likely to initiate a settlement to a target as a function of conventional defensive alliances in model 3 and more likely to initiate a peaceful attempt in model 4. Meanwhile, the effect of a nuclear umbrella remains the opposite and consistent with the expectations of our theory: challengers are no more likely to extend settlements attempts of some kind when they are protected under a nuclear umbrella, but targets protected under a nuclear umbrella are much more likely to receive settlement attempts of some kind. Similarly, and also consistent with Beckley (2015), we find no evidence in model 3 of Appendix Table A4 that either nuclear or conventional alliances are more likely to result in concessions for the client state. If anything, conventional alliances may have a slight constraining effect for the ability of client states to gain concessions.

In aggregate, since the average effect of conventional alliances is slightly negative at the same time that the coefficient on nuclear umbrella is generally positive and significant as per our expectations, the combined result suggests that—if anything—the “nuclear component” of the nuclear umbrella is so emboldening as to generate a positive effect on client states despite the generally restraining effect of the concurrent conventional commitment, which is otherwise difficult to control for in our models. It may be useful for future work to theorize about the why we observe different effects across the two types of alliances.

The Taiwan Strait Crises and the United States–ROC MDT

The large-n analyses provide a key piece of the puzzle about the systematic impact of security assurances on the behavior of the client states. Yet, they also suggest a need for closer examination within a case due to the potential for selection and endogeneity bias. Thus, we provide qualitative evidence of the hypothesized mechanism through the illustrative case of the United States–Taiwan MDT, in which the United States formally committed to defending the ROC from an armed attack, specifically by using nuclear weapons.

Before the MDT (i.e., pretreatment), Taiwan was the repeated target of provocations from the People’s Republic of China (PRC) beginning in 1949. These provocations reached a climax with the start of the First Taiwan Straits Crisis in August 1954, when Zhou Enlai, premier of the PRC, issued a declaration that Taiwan must be “liberated.” Soon after, the PRC began shelling ROC installations on the Kinmen and Matsu Islands, triggering a crisis for the United States and Taiwan. On September 12, 1954, the Joint Chiefs of Staff recommended to President Eisenhower that the US intervene militarily, including considering the use of nuclear weapons (Chang 1988). However, in the absence of any formal treaty commitments to the ROC in Taiwan, Eisenhower famously resisted pressure to deploy American troops to the conflict or to use nuclear weapons (Gordon 1988; Rushkoff 1981). In response, the PRC quickly intensified its military actions by bombing other Islands in the Taiwan Strait, including the strategically important Tachen Islands (Dachen Islands). Critically, the ROC—lacking formal military assistance from the United States—ultimately backed down by surrendering its position on the Yijiangshan Islands, only eight miles from the Tachen group. On January 18, 1955, the ROC fully abandoned the Tachen Islands, evacuating approximately 30,000 people in its retreat.

Recognizing that verbal warnings were insufficient to slow the advance of the People’s Liberation Army, the United States and the ROC agreed to the Sino-American MDT in December 1954, which promised military assistance to defend the island of Taiwan (i.e., the treatment). On January 29 1955, only 11 days after the ROC abandoned the Tachen Islands, the US Congress then passed the Formosa Resolution establishing a US commitment to defend Taiwan, offering an even greater dosage of assurance. On February 9, 1995, the US Senate had overwhelmingly ratified the MDT.

It would be difficult to overstate the impact of these agreements on the parties to the crisis. As Chang (1988) notes, prior to the ratification of the MDT and passage of the Formosa Resolution, “Eisenhower and Dulles left vague whether the commitment to the Nationalists extended to the offshore islands under their control…to keep Beijing guessing as to U.S. intentions” (p. 100). However, the signing of the MDT “removed any doubt about Washington’s support for the Nationalists.” It all but assured the security and continuity of the ROC government in Taiwan, as Eisenhower had made clear for the first time that the United States was formally committed to defending Taiwan from an attack. With the passage of the Formosa Resolution, the US Congress granted Eisenhower the authority to use military force to defend Taiwan “as he deems necessary,” giving him “a virtual blank check” (Chang 1988, 103). And in perhaps the most dramatic demonstration of commitment to the ROC, Eisenhower and Dulles reaffirmed their commitment to the defense of the islands through “the use of atomic missiles,” with Dulles stating in a nationally televised speech that “the administration considered atomic weapons ‘interchangeable with the conventional weapons’ in the American arsenal” (Chang 1988, 103). This speech was among the first in a campaign of public statements in which “the administration deliberately introduced specific comments about employing tactical nuclear weapons if war broke out in the Taiwan Strait” culminating in a news conference where Eisenhower said he saw no reason “why they shouldn’t be used just exactly as you would use a bullet or anything else” (Chang 1988, 108). Importantly, the ROC leader, Chiang Kai-shek, was well aware of these public affirmations, and certainty not averse to the use of atomic weapons against the Chinese on the mainland. He told Admiral Felix Stump, Commander in Chief, Pacific Command, that he would accept the use of nuclear weapons against the mainland “as a war necessity” (Chang 1988, 107).

Immediately following the US commitment to use nuclear weapons in defense of Taiwan under the MDT, subsequent ROC behavior was consistent with a new sense of assurance (i.e., posttreatment). Knowing that the United States did not want to be drawn into the conflict, but that it nevertheless wanted the ROC to maintain control of the islands (State Department Report 1992), the ROC submitted a request for the US approval to conduct escalatory offensive air strikes on mainland targets in the Spring of 1955 (Chang 1988, 114). Within weeks, a newly emboldened and increasingly intransigent Chiang Kai-shek refused to entertain any idea of drawing down forces deployed on the Jinmen and Mazu Islands, despite repeated requests from the United States (Chang 1988, 116).

At the same time, PRC behavior clearly demonstrated a sudden concessionary shift. According to the US State Department, within weeks of the passage of the MDT and Formosa Resolution, “in April 1955 in Bandung PRC Foreign Minister Zhou Enlai announced a desire to negotiate with the United States…to discuss the question of relaxing tension in the Taiwan area” (https://history.state.gov/milestones/1953-1960/taiwan-strait-crises). State Department accounts suggest that “the PRC’s sudden shift could have stemmed from…the very real possibility of war with the United States.” According to Chang (1988, 11), “the initiative that finally ended the crisis came not from Washington but unexpectedly from the Chinese Communists…On April 23, just before Robertson and Radford talked with Jiang, Chinese Premier Zhou Enlai dramatically announced at the Bandung Conference that his government wanted no war with the United States.”

If the Chiang Kai-shek’s ROC forces were emboldened in the First Taiwan Straits Crisis, they appeared only more emboldened in the Second Taiwan Straits Crisis that began in 1958. Indeed, even in the prelude to the crisis, as Secretary Dulles visited Taiwan in March 1958, Chiang Kai-shek urged efforts to exploit the instability he perceived on the mainland (US Department of State 1992, 6). Once the 1958 Taiwan Crisis erupted over Kinmen, a newly assured ROC this time dug in and returned fire, in contrast to the First Taiwan Straits Crisis where ROC forces conceded the Yijiangshan Islands relatively quickly.

Soon after the Second Taiwan Straits crisis began, the ROC publically evoked the US commitment under the MDT, whereby Eisenhower ordered the reinforcement of the Seventh Fleet to aid the ROC in August 1958. At the same time, Dulles publically reaffirmed that a US intervention might involve nuclear weapons. As Chiang Kai-shek demanded even bolder public statements promising US support for the defense of the offshore islands, Eisenhower reportedly grew frustrated at increasing pressure from Chiang to involve the United States in the conflict (US Department of State 1992, 60).

Primary speeches and memoirs suggest that the sudden emboldenment of Chiang Kai-shek immediately was not coincidental. As Gordon (1985) notes, “The Mutual Defense Treaty…clearly encouraged the Nationalists to take bolder measures against the Communists, despite the defensive character of the pact” (p. 638). According to Gordon, “It was clear in 1956 that the U.S. and Chinese Nationalist views diverged sharply. The U.S. objective was limited to defense of Taiwan and the Penghu (Pescadores) Islands…whereas the Nationalist government sought a military potential that would enable it to recover the mainland” (p. 642). He continues that “…the divergent views on retaliation further strained relations between the U.S. and the Nationalist Chinese” (p. 647). Gordon notes that, as the conflict continued, “the State Department grew increasingly concerned that the Nationalists might exploit the situation and bring the U.S. into a conflict” (p. 655). More recently, Popino (2016) draws on primary sources to explain that while, “the U.S. conducted 145 nuclear test shots” between 1955 and 1957, Chiang not only refused “to at least reduce the number of Nationalist forces stationed on the offshore islands…he increased the Nationalist presence on the island of Quemoy to 85,000 military personnel.”¹⁴ (pp. 68-69)

Equally important, the weight of the evidence suggests that it was specifically the nuclear element of the US commitment and not the long-standing commitment to use conventional forces that appears to have emboldened Chiang Kai-shek. According to Brown (1994), in a key National Security Council meeting, Special Assistant Robert Cutler, recounted that if US intervention became necessary, “it should not do so with conventional weapons,” because “such intervention would not be decisive…the U.S. might have to intervene with atomic weapons” (p. 70). Similarly, Tannenwald (2007) notes that General MacArthur, commander in the field, “argued that the U.S. would be able to restore Chiang Kai-shek to the mainland…only with nuclear weapons” (p. 131). Paul (2009, 53–54) explains that Dulles proclaimed: “If we defend Quemoy and Matsu, we’ll have to use atomic weapons. They alone will be effective…” However, Dulles also acknowledged that “…it would probably lead to initiating the use of atomic weapons.” And indeed, primary statements provide direct evidence in support of the resulting impact on ROC beliefs and behavior. Eisenhower’s advisors openly worried that talk of nuclear weapons would “embolden the Nationalist leader Chiang Kai-shek to engage in his own aggressive moves that could provoke the outbreak of hostilities that Eisenhower was striving to deter” (p. 70).

Importantly, these same leaders joined Chiang Kai-shek in downplaying the conventional element of the alliance. Indeed, as the pivotal nuclear element to the commitment was being repeatedly affirmed publically, evidence from Chang (1988, 116) and Clubb (1959, 525) suggest that Chiang strongly doubted the credibility of the US conventional military commitment.

As expected by our theory, the conclusion of the Second Taiwan Straits crisis took place at the negotiating table.¹⁵ On September 4, Dulles issued a statement, in which he hinted that Eisenhower would authorize US action to protect the offshore islands under the “Formosa Resolution.” Within two days, in a move that is consistent with our theoretical mechanism, then Chinese Premier Zhou Enlai issued a statement on September 6 declaring the PRC government’s willingness to resume the ambassadorial talks with the United States–ROC alliance, effectively increasing the level of diplomatic recognition. In exchange, China’s Defense Minister, P’eng Te-huai announced that PRC forces would refrain from shelling the offshore islands on even-numbered days, provided that there would continue to be no US escort (US Department of State 1992, 215, 227). These were concessions that the outmatched ROC was unlikely to secure in the absence of the frequently reiterated nuclear threat provided through the MDT. However, even as the talks ended the crisis for the United States on September 30—with Dulles declaring that the United States favored the evacuation of ROC forces form the offshore islands—Taiwan persisted in the crisis bargaining for more than a month (US Department of State 1992), in a move that is consistent with our moral hazard mechanism.

Conclusion

In this article, we address a long-standing question in the academic and policy communities about the role of nuclear umbrellas in broader interstate relations. Specifically, we examine how client states behave under the protection of a nuclear patron by investigating two important dimensions of behavior: the initiation of militarized disputes and bargaining outcomes short of war. We find that, although client states protected under a nuclear umbrella are no more likely to initiate MIDs against a target state that escalate to war or the reciprocated use of force, these states, nevertheless, appear more emboldened to initiate crises. However, these crises tend not to escalate to higher levels of militarized conflict because target states appear to act in equilibrium: preferring to settle disputes peacefully rather than resist militarily through costly fighting. We find that client states protected under a nuclear umbrella are more often the recipients of policy concessions from their targets compared to states that lack protection under a nuclear umbrella. Together, these results provide comprehensive support for our argument that there is some risk of moral hazard in a client state protected under a nuclear umbrella, as clients appear more emboldened and more successful at revising the status quo in expectation of a patron coming to their aid.

The urgency to understand the strategic consequences of nuclear umbrellas is perhaps most real today, as the United States seeks to rebalance its overall security portfolio to the Asia-Pacific in anticipation of a rising China and to provide additional assurances to its allies in the Middle East in light of potential proliferation challenges. And yet, we have surprisingly little evidence that such commitments are effective at reducing the risk of conflict on net, given the widely presumed, but still untested, risk for moral hazard in the client state. Meanwhile, policymakers in the United States and abroad continue to propose expanding the US nuclear umbrella while further reassuring allies covered within it. Our research suggests that the expansion of the nuclear umbrella may perversely exacerbate the concerns of potential targets and inadvertently destabilize the status quo by increasing the risk of a crisis and the opportunity for bargaining to fail.

If client states protected under a nuclear umbrella are encouraged to pursue more aggressive military and diplomatic policies toward other states, this may pose an increased risk of conflict to patrons, particularly as nuclear patrons like the United States seek to strengthen and reaffirm their commitments to their allies. Of course, this risk must be balanced against any risk of moral hazard that might flow from a client state protected under a nuclear umbrella, or any potential nonnuclear state, acquiring its own nuclear weapons in the absence of such commitments (N. Narang 2015). It may very well be the case that nuclear umbrellas cause emboldenment/moral hazard, but that this is nonetheless preferable to the nuclear emboldenment that would result if the state acquired nuclear weapons (Kapur 2007). In so far as the net effect is unclear, it is possible that policymakers might want to persist in offering nuclear umbrellas to states in order to prevent proliferation despite their moral hazard inducing consequences (Mehta 2017).¹⁶

Footnotes

Appendix

Table A4.

Nuclear Umbrellas and ICOW Resolutions (Probit, Directed Dyads, 1945–2000).

DV: ICOW Resolution (State A Targets State B)	Model 1	Model 2	Model 3
DV: ICOW Resolution (State A Targets State B)	DV: Challenger Concedes	DV: Target Concedes	DV: Challenger Concedes
Nuclear umbrella A	0.0201		0.0414
	(0.211)		(0.218)
Nuclear umbrella B	0.427*	0.837**	0.438**
	(0.221)	(0.325)	(0.215)
Conventional alliances A			−0.0529
			(0.0497)
Nuclear weapons A	0.205	2.418***	0.403
	(0.434)	(0.685)	(0.321)
Nuclear weapons B	0.933***	1.207**	0.894***
	(0.257)	(0.580)	(0.256)
Rivalry status A	−0.295	−5.377***	−0.292
	(0.325)	(0.520)	(0.294)
Rivalry status B	−0.0384		0.0291
	(0.303)		(0.314)
Dyadic rivalry	0.293	5.444***	0.261
	(0.379)	(0.404)	(0.379)
CINC A	0.726	−120.5***	6.627
	(3.008)	(31.78)	(6.906)
CINC B	−1.706	−93.85**	−2.028
	(3.940)	(37.62)	(4.230)
CINC A × CINC B	−1,877*	−25,563	−1,953
	(1,022)	(38,201)	(1,264)
Democracy A	0.0886**	0.989*	0.0814*
	(0.0449)	(0.528)	(0.0432)
Democracy B	0.124***	1.182**	0.125***
	(0.0464)	(0.580)	(0.0457)
Dem. A × Dem. B	−0.0226***	−0.117*	−0.0216***
	(0.00622)		(0.00613)
Contiguity	−5.838***		−6.005***
	(1.660)		(1.706)
Distance (ln)	−0.805***		−0.826***
	(0.224)	(0.0626)	(0.227)
Alliance	−0.203	0.238	−0.215
	(0.194)	(0.597)	(0.204)
Intercept	3.072*	−12.37**	3.324*
	(1.720)	(5.178)	(1.762)
N	2,913	2,383	2,913
Log likelihood	−125.53666	−27.718597	−27.718597
χ²	75.62	1,401.11	1,401.11

Note: Robust standard errors are in parentheses. ICOW = Issue Correlates of War; CINC = Composite Index of National Capability; nuclear umbrella A = 0 predicts failure perfectly; DV = dependent variable.

*p < .1.

**p < .05.

***p < .01.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

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