Unfair fights: Power asymmetry,nascent nuclear capability,and preventive conflict

Studies of preventive war

A sizable shift in relative power is arguably the most often invoked cause of war. Taylor (1954: 166) claims, “Every war between Great Powers [in the 1848–1914 period] started as a preventive war, not a war of conquest.” ⁴ It is thus unsurprising that a vast literature on international conflict addresses the role of looming changes in power distributions in promoting conflict. The bargaining theory of war demonstrates that even with complete information, rational states can fail to achieve an accord if there is an impending shift in relative power (Fearon, 1995; Powell, 1999, 2006). ⁵ Recent contributions further this research agenda by making power shifts endogenous. Considerations include shifts generally (Chadefaux, 2011), probabilistic diffusion of new technologies such as nuclear weapons (Bas and Coe, 2012), fighting itself as a means to forestall power changes (Powell, 2012), or imperfect observability of nuclear proliferation (Debs and Monteiro, 2014).

In contrast to the substantial literature addressing the magnitude and timing of power shifts, little work considers what other factors may influence the likelihood of intractable commitment problems occurring. A few exceptions suggest preventive war is more likely when the offense–defense balance favors offense (Van Evera, 1999), the declining state is non-democratic (Schweller, 1992), or when the future is highly valued relative to the present (Tingley, 2011).

I argue another factor matters; preventive war is more likely when initial power asymmetries are greater. Consequences of the pre-shift power balance have received fleeting attention. Gilpin (1981) argues that radical revision to the status quo is most probable when transitions occur—that is, when a hegemon is overtaken. Rather than delaying conflict until equality is achieved, the declining state opts to eliminate the rising challenger while it maintains a military advantage. Levy (1987) suggests that the preventive motive can arise without the prospect of a power transition, noting that the size and speed of change are critical, not transition itself. However, this conjecture stipulates that if the declining state’s initial advantage is enormous, war is unlikely unless there is a stark and discontinuous shift in the dyadic balance of power, such as a rising state’s procurement of weapons of mass destruction. ⁶ In the bargaining theory of war, the symmetry of initial capability endowments and the possibility of a power transition are immaterial to commitment problems emerging. Debs and Monteiro (2014) are partial exceptions, positing that preventive war is more likely the larger the net effect of a shift in power on the relative balance of capabilities and the smaller the costs of preventive war. Both of these conditions, though not directly modeled in Debs and Monteiro (2014), are associated with asymmetric dyads. I reach a complementary conclusion while elaborating upon the cost argument and developing an alternative underpinning for the relationship between asymmetry and preventive war.

A litany of quantitative tests have generated little consensus regarding the effect of power shifts on conflict onset (Organski and Kugler, 1980; Kim and Morrow, 1992; Bennett and Stam, 2004). Furthermore, studies often operationalize power shifts in a retrospective manner that provides a test of power transition theories but not of preventive reasoning. That is, the quantity identified reflects whether past shifts, not anticipated shifts, induce conflict. The logic of conflict in this formulation is one of revision, not prevention. The dearth of quantitative testing of preventive war stems from the difficulties of operationalizing when a shift is approaching. Lemke (2003) and Weisiger (2013) provide rigorous expositions of these empirical hurdles and suggest a measure of past shifts can proxy for the presence of a preventive motivation. This proposition requires the assumption that states extrapolate past changes in relative capabilities into the future. Empirical specifications in this paper do not rely on this assumption, which I address in later sections.

Studies of asymmetric war

This study also speaks to the literature on asymmetric war which is perhaps most associated with deterrence failures. Facing challenges by more powerful rivals, weak states cannot credibly threaten to impose heavy costs in the case of attack. As a result, stronger actors pursue territorial aggrandizement or other self-enriching actions at the expense of weaker states by first making demands and then using force if the target does not capitulate. ⁷ While theories of deterrence provide a compelling account of why stronger states make onerous demands of weaker states, it is unclear why the latter do not simply concede. That is, why does bargaining break down into conflict? In bargaining accounts of war, the power balance of a dyad is immaterial to the likelihood of bargaining failures. It is not the distribution of power that matters, but how this distribution relates to the distribution of benefits—for example, territory or wealth (Powell, 1999). Novel theories make strides toward explaining how asymmetries may generate conflict. For instance, a powerful state’s inability to signal that it will not threaten a weaker state again in the future, coupled with the weaker state’s reputational concerns, may lead to asymmetric war (Sechser, 2010). Alternatively, a powerful state’s threats may lack credibility or its demands might be too onerous for the weaker state to meet, both of which lead the overmatched state to resist (Allen and Fordham, 2011). This paper contributes another explanation; asymmetric conflict can occur because strong states with large power advantages have a low threshold for initiating preventive conflict.

Model structure

Consider a bargaining model entailing a two-player infinitely repeated game with complete information and a take-it-or-leave-it bargaining protocol (Fearon, 1995). Players A and B contest the division of a resource standardized such that R = 1, where A’s ideal outcome is 1 while B’s is 0. Play commences with A proposing a split of the resource whereby it retains x_1A and B receives 1 − x_1A. B decides whether to accept this proposal, in which case each player receives payoffs in accordance with A’s proposal, or rejects the offer. If B rejects, a costly lottery (war) ensues with the winner retaining the entirety of the contested resource and each side bearing the costs of war, respectively c_A and c_B. A’s probability of victory is given by p₁, which is a function of the relative capabilities held by each state and is common knowledge. The winner of the resource receives a payoff of 1 in all subsequent rounds (discounted by δ), the loser earns nothing, and bargaining terminates. In contrast, if the proposal is accepted the game is repeated with the key difference that relative power, reflected by p, is dynamic between the first and second round of negotiation—that is, p₁≠p₂—and fixed thereafter. This shift, which favors A by assumption, arises exogenously and is also common knowledge (Fearon, 1995; Powell, 2006). That is, A is rising and B is declining. As before, A makes a proposal to retain x_2A of the resource in period two, which B can accept or reject with identical repercussions to those of period one. Play continues in this fashion. I opt for the simplest bargaining protocol for expositional clarity. In the Supporting Information, I consider an alternative framework in which the game tree allows each state, not only the declining state, to initiate conflict. My central theoretical propositions also hold for this bargaining protocol, albeit in a more limited portion of the parameter space.

I propose two extensions to the above framework linking initial capability endowments to bargaining outcomes. Each is a distinct and separate addition relating the dyadic power balance to preventive war onset. Either extension is sufficient to generate the hypothesized relationship.

The first concerns preferences for certainty. Clausewitz suggested that “war is the province of chance,” ⁸ an intuition the model incorporates with probabilistic outcomes for war. This is the sole source of uncertainty in the complete information bargaining framework. ⁹ The magnitude of this uncertainty will fluctuate depending on either side’s probability of victory. Consider the extreme cases. Leaders of a state with a probability of victory equal to 1 have no uncertainty over conflict’s outcome while state leaders with 50–50 chances have great uncertainty. With lottery outcome values fixed for victory and defeat, expected utility theory’s independence axiom stipulates a state’s utility function is linear in the probabilities (Von Neumann and Morgenstern, 1948). Substantively, this implies the lottery’s uncertainty itself has no effect on utility except through affecting the likelihood of realizing the two potential outcomes.

Many empirical findings refute the independence assumption. The Allais Paradox is a famous example (Allais, 1953). According to the paradox, altering the prospects of a choice problem in an identical fashion reveals that individuals find it more desirable when the alteration shifts a prospect from a probable gain to a certain one, than when the alteration shifts a prospect from a probable gain to an even more probable gain. The finding contradicts expected utility theory which predicts neither change should be more desirable than the other. Subsequent studies similarly find that individuals overweight prospects that are certain versus those that are probable (for example, Tversky and Kahneman, 1979; Andreoni and Spenger, 2012), which Tversky and Kahneman (1979) dubbed the certainty effect.

Importantly, the finding is not restricted to choices with complete—that is, 100%—certainty. Wu and Gonzalez (1996) show similar effects when choices approach, but do not reach, certainty. That is, the preference for greater certainty holds even when shifting a prospect such that the more certain prospect still entails risk that the adverse outcome occurs. Put differently, the Allais result indicates individuals find it more desirable to shift the probability of receiving nothing (the adverse outcome) from, say, 66% to 0% versus from 67% to 1%. Wu and Gonzalez (1996) indicate this result is not unique to eliminating all risk of the adverse outcome. Reducing the probability of the adverse outcome from 63% to 3% is more desirable than reducing it from 65% to 5%.

In the context of conflict, if state leaders have a preference for certainty, less favorable bargaining outcomes will suffice to avoid war and its attendant uncertainty. Granting the possibility that decisions by state leaders exhibit such non-linearity in the probabilities, I incorporate a preference for certainty into the bargaining framework. Existing choice models introduce non-linearity in the probabilities by incorporating decision weights on the probabilities themselves (Tversky and Kahneman, 1979, 1992; Wu and Gonzalez, 1996). ¹⁰

To highlight the extension to the base model, I directly parameterize uncertainty premiums rather than use decision weights. To begin, consider a proxy for uncertainty. War is modeled as a binary event, or Bernoulli trial, with probability p that A wins. The variance of a Bernoulli trial, given by p(1 − p), measures the magnitude of uncertainty about war’s outcome and is a function of a dyad’s power parity or asymmetry. This variance dictates the size of the uncertainty premium. Accordingly, I introduce an uncertainty premium parameter r(p _t ), which is a strictly concave function of p _t such that r(p _t ) = p _t (1 − p_t) and amounts to an additional cost parameter in the lottery. This captures certainty effects by imposing a small cost when war’s outcome is relatively certain and a larger cost as war’s outcome becomes increasingly ambiguous with the sharpest marginal changes occurring when victory is nearly certain. Incorporating decision weights into the utility function as opposed to using an uncertainty premium parameter yields similar results. ¹¹

A second, and simpler, addition concerns each side’s costs of war which are typically modeled as fixed and exogenous. However, we might expect that a state’s costs are, at least in part, a function of the dyad’s relative capability endowments. Specifically, a declining state with a large initial power advantage would anticipate lower costs of war, c_B, than a declining state facing a roughly equal foe. We can conceive of war costs (or the utility loss of conflict) as a function of both a state’s resolve and dyadic material conditions. The latter factor is of importance here. Following prior work, I anticipate a state’s war costs are inversely related to the favorability of the dyadic balance of power (Powell, 1999: 161). Intuitively, we expect a war against China today to be more costly for the US than one against Iraq in 2003. Formally, let c _B (c _A ) be a function of p_t that is monotonically increasing (decreasing) and weakly concave, with t indicating the bargaining round. The weakly concave functional form captures a state’s diminishing sensitivity to the marginal losses associated with fighting stronger opponents. For concreteness, this implies the marginal cost (utility loss) resulting from the 18 US fatalities in the Battle of Mogadishu was greater than the marginal cost of the final 18 US fatalities suffered at the Battle of the Bulge. The concavity assumption recognizes that costs may approach a maximum at which point a state being even more overpowered than it already is will have negligible effects on that state’s war costs. ¹²

Note that the costs of war within the bargaining model reflect a state’s utility loss relative to the resource’s value. If the stakes of war are trivial, costs in the model will be relatively substantial even if the absolute material losses associated with war are small (Fearon, 1995: 387). For the theory and subsequent empirical tests, I am primarily interested in dyads with meaningful stakes such that war costs are not prohibitively high so as to preclude the possibility of conflict. The notion of dyadic rivalry—dyads in which states compete over meaningful stakes and view the use of force as a viable option—offers a fruitful conception of the cases of greatest interest.

Analysis

This section proceeds by first identifying when preventive war occurs in the unaltered model, then considers how uncertainty premiums and variable costs change the preventive constraint. When is initiating a preventive war rational? Within the standard framework there exists a series of parameter values for which B rationally rejects the round one offer and opts for preventive war. A discussion of the game’s equilibria is provided in the Appendix. Here I focus on the conditions under which an intractable commitment problem exists because the central concern of this paper is not the exact size of offers a rising state must make to avoid war, but whether any such offer exists at all. To begin, evaluate when no possible round one proposal satisfies B. That is, even if B gets the entire resource (x_1A = 0), it still prefers the costly lottery of war over acceptance. Formally, B opts for preventive war if

1 − p 1 1 − δ − c B > 1 + δ ( 1 − [ p 2 + c B ( 1 − δ ) ] ) 1 − δ ,

(1)

where δ is the common discount factor, the left-hand side gives the expected war payoff, and the right-hand side the bargaining payoff. The above inequality reduces to the preventive war constraint

δ p 2 − p 1 > c B ( 1 − δ ) 2 .

(2)

Preventive war is preferred when this inequality holds.

In previous studies, the comparative static of interest is that as the quantity δp₂ − p₁ increases, preventive war becomes more likely. ¹³ This is self-evident from Equation 2. In this framework, variation in the initial power asymmetry represented by p₁ is not theoretically linked to the size of the shift in power necessary for the constraint to hold.

Certainty effects

Consider how introducing certainty effects impacts the relationship between initial power asymmetries and the likelihood of preventive conflict. Uncertainty premiums amount to an additional cost of war arising from uncertainty over conflict’s outcome. As demonstrated in the Appendix, introducing the new parameter r(p _t ) yields a preventive war constraint of

δ p 2 − p 1 > [ r ( p 1 ) − δ r ( p 2 ) ] + c B ( 1 − δ ) 2 .

(3)

Calculating the comparative static for initial power balance reveals that the constraint becomes less binding as p₁ increases. ¹⁴ Commitment problems are most likely when the state in relative decline initially enjoys a great preponderance of power. When asymmetry is greatest (p₁ is small), a broad set of conditions can make preventive conflict rational.

US military preponderance and the Bush administration’s consequent certainty of a victory in Iraq in 2003 illustrate the underlying logic. Though there are multiple potential causes for the Iraq War, numerous accounts argue that a perceived power shift in favor of Iraq was central to US reasoning. ¹⁵ Unsaddled by doubts over the conflict’s outcome, US leaders opted for preventive war rather than tolerate an adverse power shift resulting from purported Iraqi weapons programs that would make future military interactions less certain. The intuition is that the utility loss from greater uncertainty is most pronounced when losing a position of high certainty of victory. Consequently, state leaders with relatively high initial certainty of victory are less willing to tolerate unfavorable power shifts.

Variable war costs

Variable costs of war cause the range of conditions necessary to preclude peaceful outcomes to vary across levels of the initial power disparity. This result is straightforward and begins by substituting the weakly concave function c _B (p _t ) for c_B in the analysis. As shown in the Appendix, I solve for the new preventive war constraint and calculate comparative statics for initial power asymmetry. With variable costs, the preventive war constraint is

δ p 2 − p 1 > [ c B ( p 1 ) − δ c B ( p 2 ) ] ( 1 − δ ) .

(4)

The war constraint is less likely to hold as p₁ increases. Binding commitment problems are more likely in asymmetric dyads than in dyads near parity. The intuition is that adverse power shifts increase a declining state’s war costs in future interactions. Marginal increases in costs are greatest for preponderant powers in asymmetric dyads. These large cost increases make subsequent bargaining less attractive for declining states that enjoy initial power advantages, increasing the relative appeal of war. Incorporating variable war costs yields the same prediction as incorporating certainty effects. Note that the effect of increasing costs for the declining state is not offset by decreasing costs for the rising state because the latter’s costs are not part of the war constraint. Even if the rising state’s costs do factor into the constraint, as in the alternative model in the Supporting Information, this offset is not exact due to the non-linearity of the cost function.

For an extreme example of the effect of asymmetries and war costs on preventive conflict, consider the Eisenhower administration’s debates regarding a preventive strike against the nascent USSR nuclear arsenal. In 1953 the US enjoyed an asymmetric advantage following the implementation of NSC-68 and the subsequent boom in defense spending. As a result, officials still believed nuclear war was in some sense winnable given its acceptable expected costs. ¹⁶ The mere contemplation of a preventive strike, as exhibited by the recommendations of Project Solarium’s Task Force C, illustrates the effect of capability asymmetries on war costs and commitment problems. As the Soviet nuclear capability approached and surpassed parity in subsequent decades, the anticipated costs of war rose and a preventive strike against the USSR was no longer taken seriously. In sum, greater power asymmetries decrease the costs of war for the declining state which makes the preventive war constraint more likely to hold.

Hypothesis and discussion

The model’s core prediction is that power shifts within asymmetric dyads are more likely to generate preventive conflict than power shifts in dyads near parity. An additional implication is that the effect extends across the entire range of initial relative power balances. A declining state with an initial asymmetric advantage is more likely to initiate preventive conflict than a declining state near parity, and a declining state near parity is more likely to initiate preventive conflict than a declining state that is already overmatched. The proposed relationship holds after incorporating either certainty effects or variable war costs. While the presence of both mechanisms will yield a sharper relationship between asymmetry and preventive conflict, either mechanism alone is sufficient. The analysis generates the following hypothesis:

A weak state’s rise is most dangerous when facing a far stronger power in relative decline. Whereas past work suggests power shifts at the 50–50 divide are most dangerous (for example, Gilpin, 1981), these results demonstrate the opposite. Recall that diminished bargaining leverage after shifts, not elevated survival concerns, underpin, commitment problems. Losing a position of preeminence is not in itself problematic as bargains can still be achieved that adequately compensate the declining power in the initial period so as to mitigate the preventive war logic.

Under a given set of conditions, such as an anticipated power shift of a fixed magnitude, there is a higher probability of conflict in asymmetric dyads than in those near parity. However, this does not imply that commitment problems cannot arise when near parity and transitions are imminent, but rather that a more restrictive set of conditions must be met to eliminate the bargaining range when near parity. A massive shift in power is one such condition that can make preventive conflict rational in relatively balanced dyads. Japan’s 1904 assault before the imminent completion of a Russian railroad to the Far East might be one such occasion when an anticipated power shift in a dyad near parity produced preventive war. Russia’s call for a 40% increase in troop levels, which induced preventive logic in Wilhelmine Germany, offers another example (Fearon, 1995). My contention is not that looming power transitions cannot generate commitment problems, but that transformative shifts of the requisite scale are rare. Rapprochement between the US and the UK is one example of a power transition in which the rising state’s growth was sufficiently gradual so as to mitigate preventive war motives. In contrast, more modest changes in relative capabilities are sufficient cause for preventive conflict in asymmetric dyads.

The hypothesis implies that for anticipated power shifts of a given size, preventive conflict is more likely in asymmetric dyads than in those at parity. This interpretation holds the type of the power shift roughly constant, which is the approach I adopt in the empirical section by focusing on potential nuclear acquisition by a rival state. An alternative interpretation is to consider an interaction in which smaller shifts are sufficient to generate conflict in asymmetric dyads while larger shifts are needed for conflict in dyads at parity. Testing this interpretation requires variation in terms of initial power balances and the size of power shifts. I leave such tests to future research.

A few points merit clarification. Following most of the literature, I model power shifts in terms of changes in the overall probability of victory as opposed to modeling the underlying capabilities of the states. ¹⁷ An alternative framework could model p using a contest function which takes the state’s capabilities as inputs. For instance, a ratio form contest function models p as the rising state’s share of total dyadic capabilities. My approach is problematic if adding new capabilities to the rising state’s stockpile causes a larger absolute change in p when the states are near parity as opposed to asymmetry. To fix ideas, imagine war outcomes are determined by the number of tanks each side has and the rising state is expected to build one new tank. It would be problematic if the addition of a new tank produces a bigger shift in p at parity versus at asymmetry. There is not a strong theoretical argument either direction and it is easy to construct scenarios that refute the critique. At parity where each side has 10 tanks, adding a new tank to the rising state’s capabilities produces a small shift in its victory probability (a roughly 2% point shift in the probability of victory using the ratio form). The shift is much larger at asymmetry where the rising state initially has a single tank while the declining state has 10 tanks (a roughly 7% point shift in the probability of victory). ¹⁸ While it is possible to construct counter-examples, there is no strong theory pointing in either direction as shown formally in the Supporting Information. Disaggregating p into a contest function adds complexity rather than clarity in this particular model.

Another clarification addresses whether the theory’s larger costs at parity due to certainty effects and variable war costs imply that conflict is always less likely at parity, even when power is static. If so, the hypothesis would challenge the broad empirical finding that conflict is generally most probable when states are at parity. I consider instances where power is static and where it is shifting to illustrate why this is not a concern. With static power, larger costs do not affect the probability of conflict if there is complete information. In models with asymmetric information, the size of costs can matter. However, prior work argues that there is the most asymmetric information in dyads around parity (Reed, 2003). Greater information asymmetry can more than offset the larger costs in static balanced dyads. Now consider cases with shifting power. Shifting power takes two forms in unbalanced dyads. In the first form the declining state has 90% of capabilities and the probability of conflict is high according to the hypothesis. However, this is offset by the low probability of conflict in the second form where the declining state has 10% of capabilities. These two scenarios aggregated together can have a lower overall probability of conflict than dyads at parity where regardless of which side is declining, that state has 50% of capabilities. Hence this paper’s theory where conflict is most likely when declining states have asymmetric power advantages does not inherently clash with existing empirical results.

Finally, this relationship taken to the extreme raises the question: why are there not more wars between strong and weak states? Should the US attack Mauritius if the latter grows faster than the former? Two factors limit this concern about extremely asymmetric cases. First, as noted earlier, war costs in the bargaining model capture a state’s utility loss relative to the value of the stakes. If the stakes are trivial, costs will be sufficiently high to greatly reduce the possibility of preventive conflict. In cases with low stakes and high war costs, such as non-rivalrous dyads like the US and Mauritius, the theory’s implications are less applicable. Second, the discount rate ensures an infinitesimal power shift does not preclude negotiated settlements. Provided the present is worth more than the future, the costs of war serve as a deterrent to conflict. For expositional purposes I adopted a simple relationship tying the war outcome probability to costs. A more realistic framework might include these variable costs plus a fixed cost for even the most lopsided conflict. The hurdle for war is lower for asymmetric dyads, but it still exists.

Explanatory and control variables

Relative Capabilities is the explanatory variable of interest. Capabilities are calculated in three ways. The first is based on annual military expenditures and military personnel, equally weighted, as provided by CINC scores (Singer, 1987). This variable reflects dyadic balance of power, operationalized as the potential initiating state’s percentage share of total dyadic capabilities. Consequently, it is a continuous variable bounded between 0 and 1 with 0.5 indicating dyadic parity. Note that the variable reflects the declining state’s probability of victory and is thus constructed as 1 − p₁ as p₁ is defined in the modeling section. The second capabilities measure is calculated equivalently but uses only military expenditures. I prefer to use only military measures because the equal weighting of all six elements in aggregate CINC scores—which includes total population, urban population, iron and steel production, and energy consumption—makes substantial changes in relative power a historical rarity due to the relatively static nature of population totals. Power shifts occur with far greater historical frequency when calculated with only military indicators (Powell, 1999; Debs and Monteiro, 2014). However, I include the full CINC scores as a third measure of relative capabilities for robustness checks. In the specification using the directed anticipated-shift dyad episode as the unit of analysis, the variable is the average of its yearly values for that episode.

Next, I control for variables commonly associated with conflict. Presence of a common border repeatedly emerges as a pivotal factor in dyadic conflict proclivity (Starr and Thomas, 2005; Vasquez, 2009). Contiguity is a binary variable measuring geographic proximity between two states that takes the value 1 if they share a land border or are separated by less than 400 miles of water and 0 otherwise. Duration reflects how long the weapons program has existed. For the model with episode observations, this variable takes the maximum yearly value. Accounting for duration helps ensure that findings are not driven by the perceived imminence of a power shift, which likely tracks with duration. In the yearly observation specification, I follow Carter and Signorino (2010) and account for temporal dependence in the binary outcome panel data with a series of polynomial terms measuring the duration of dyadic peace since the previous militarized dispute. Thus I include Peace Years, Peace Years², and Peace Years³ in the model. ²⁵ While the dyad episode observation model does not suffer similar dependencies because each dyad is included only once, I control for the duration of dyadic peace at the start of the episode with a Peace Years variable. Summary statistics for all variables, as well as robustness tests incorporating additional control variables such as regime type and alliances, are provided in the Supporting Information.

Robustness tests and limitations

The Supporting Information contains a series of tests offering further confirmation of the results. These demonstrate that the results are robust to alternative control variable specifications, including controlling for alliances, initiator and target regime type, or joint democracy. Results are similarly robust to using a stricter definition of preventive conflict that excludes disputes that only reach lower hostility levels, such as threatening to use force or showing force. Another test drops dyads where both states have nuclear programs at the same time, such as the India–Pakistan dyad between 1972 and 1987, because it may be ambiguous which state is rising. Doing so produces nearly identical statistical and substantive results.

One possible concern is that increasing the relative capabilities of an initiating state is always associated with a greater probability of conflict and is not unique to instances with shifting power. Tests in the Supporting Information use an alternative data set and demonstrate that the effects of power asymmetry are especially pronounced when in the presence of shifting power as compared to when relative power is static. The interaction term between the presence of an anticipated-shift and the dyadic power balance is substantively and statistically significant across multiple specifications. This result accords with that found in Table 3 of Sobek et al. (2012).

Additional checks ensure that the relationship between a declining state’s initial share of dyadic capabilities and the probability of conflict is monotonically increasing across the full range of the explanatory variable. These show that the results are not entirely driven by cases in which an already overmatched state confronts a rival with a nuclear program. The concern might be that the findings are due to already overmatched states being unlikely to attack rather than due to different conflict proclivities between dyads at parity and those in which the declining state is initially powerful. Numerous robustness tests presented in the Supporting Information rule out this possibility. Rather than assume a linear relationship between Relative Capabilities and Conflict, I use models with more flexible functional forms. These include (1) a model with cubic polynomials, (2) a generalized additive model, (3) a model with binary indicators for each quarter of the explanatory variable’s range, and (4) a bootstrapped basis regression with oracle model selection (Kenkel and Signorino, 2012). Across all specifications with power shifts, conflict probability increases monotonically in the declining state’s initial share of dyadic capabilities. The relationship differs in dyads where power is static, which further indicates that asymmetric dyads are particularly prone to conflict when power shifts are anticipated.

Three potential limitations to the analysis merit attention. First, while the results are consistent with the model’s predictions, they cannot adjudicate between the posited mechanisms. Certainty effects, variable war costs, or both may drive results consistent with the hypothesis. Second, the empirics are limited to a dramatic form of power shift and cannot speak to whether the model’s implications hold across other forms of power shifts. Third, selection effects might influence whether observations are included in the sample. Starting a nuclear weapons program is not a random or exogenous event. This non-random sampling is potentially problematic if the explanatory variable (relative capabilities) affects entry into the sample. If it does, then conditioning on the presence of a looming shift amounts to controlling for a post-treatment variable which will bias estimates (King and Zeng, 2006). However, it is ex ante unclear why, or in which direction, dyadic power balances would affect relative capability shift proclivity. Even if such a relationship exists, findings from the analysis will be biased upward only if weak states in asymmetric dyads are less dissuaded from building weapons by the possibility of preventive strikes than proliferating states in dyads approaching parity. Though possible, there is theory and evidence suggesting otherwise. According to Monteiro and Debs (2014), weak states without strong allies but with strong rivals face the most acute threat of preventive strikes and consequently are likely to refrain from investing in proliferation efforts. Thus, it is unlikely that the non-random sampling criteria would inflate results in a manner that validates the hypothesis. ²⁷

Results from multiple specifications lend strong support to the central contention of this paper. The unobservable nature of anticipated shifts in relative power has long posed a difficult empirical challenge for researchers of preventive conflict (Lemke, 2003; Weisiger, 2013: 61). Though the tests employed in this study are admittedly limited in scope, they are a positive step toward capturing the logic of preventive war and offer a path for future work to pursue further.