Peace and Enforcement Problems

Fearon summarizes succinctly three rationalist explanations for conflict: commitment problems, uncertainty and incentives to misrepresent, and divisibility problems.⁴

Even if the belligerents are able to agree to stop fighting, the implementation of the agreement is often mired by similar commitment problems. Former belligerents fear that the other side may not reciprocate their compliance with the provisions of the agreement. Distrust is high, and monitoring compliance is often difficult. Peace may break down not because either side prefers a renewed war to peace, but because they fear that their compliance with the provisions of the agreement leaves them vulnerable to exploitation or to a surprise attack from the opposing side. Strong agreements that improve monitoring capabilities, build trust, and raise the costs of defections can overcome these fears and provide the parties with the confidence to take the measures necessary to secure peace.⁸

These explanations for the failure of peace focus primarily on the inability of the belligerents to credibly commit to implementing the terms of the agreement under conditions of first-strike advantages⁹

Peace and Distribution Issues

Although commitment problems are one explanation for the failure of peace, an alternative (but not contradictory) explanation focuses on problems related to distribution and uncertainty. Several formal models that take issues of distribution and uncertainty as their point of departure have recently been published.¹¹

Although the bargaining and war models differ in many details, they all highlight a common dynamic. If wars are costly and the belligerents are able to negotiate a settlement (divisibility or enforcement issues are not acute), then the belligerents should reach an agreement based broadly on their common beliefs about the likely military outcome if fighting were to continue (or start). Negotiations fail, in contrast, if the belligerents' beliefs regarding the consequences of continued fighting diverge sufficiently such that they cannot agree as to which side needs to make concessions or how large the concessions need to be. In these instances, the belligerents' divergent beliefs about the consequences of continuing the war ensure that there is no contract zone, or set of agreements that both sides prefer to continuing the war. In Figure 1, for instance, no contract zone exists because both sides believe that they are likely to win the war and therefore are unwilling to make the concessions the other side demands. Through the course of the war, however, the belligerents' expectations about the consequences of continued fighting converge as a result of the information provided by the war itself. At this point, a contract zone emerges based on these common-enough expectations and the belligerents are able to negotiate terms of settlement that both sides prefer to continuing the war (see Figure 2). Critically, these models suggest that wars end because both sides believe that they can gain nothing more from continuing the war than they have gained from the terms of settlement specified in the agreement. Fighting is costly and the terms of settlement reflect the common expectations of what would have happened if the war were to have continued.

Divergent expectations regarding outcomes of war eliminates contract zone, where a and b indicate A's and B's expected costs of fighting, respectively

Converging expectations regarding outcome of war creates contract zone, where a and b indicate A's and B's costs of fighting, respectively

Several implications regarding the durability of peace and the recurrence of war can be inferred from this general dynamic. Note first that settlements should generally be robust. If the terms of the settlement reflect the belligerents' convergent expectations regarding the consequences of continued fighting, then neither belligerent should have an obvious incentive to return to war because neither should expect to receive a better deal if the war were to resume.¹²

Although the bargaining and war models suggest that settlements generally should be robust and that no particular distributional agreement should be inherently superior to another, certain settlements are expected to be more prone to failure than others. This expectation may seem contrary to the two previous expectations. Recall that a settlement will only be reached if both sides believe that the benefits from accepting the terms exceed the expected benefits from continuing to fight. The fact that the war ended suggests that a contract zone existed and the agreement, regardless of its terms, was contained within this contract zone. Any informational or distributional problems that remained at the time of the settlement were clearly not sufficient to thwart an agreement.

However, conditions and expectations can change. It is possible that an agreement that was initially acceptable to both sides may subsequently fall outside of the set of mutually acceptable agreements as the contract zone either shrinks or shifts. This “obsolete agreement” then is subject to challenge because at least one belligerent no longer prefers peace on the terms initially negotiated to a renewed war. If the changes subsequent to the agreement eliminate the contract zone altogether, then efforts to renegotiate the obsolete agreement peacefully will be unsuccessful, and war will resume. We maintain that certain settlements or settlements negotiated under certain conditions are more vulnerable to obsolescence than others. We also maintain that the same reasons that make these settlements prone to obsolescence ensure that these settlements will be more difficult than others to renegotiate peacefully.

What types of settlements are particularly prone to obsolescence? First, settlements negotiated when considerable uncertainty regarding the consequences of continued fighting remains are more likely to become obsolete than settlements negotiated when the consequences of continuing to fight are more evident.¹⁴

We test this expectation by considering the effect of the pattern of conflict on the durability of peace. Battle outcomes are a key source of information regarding the capabilities and the resolve of the opponent; trends in battle outcomes can tell a lot about the amount of uncertainty regarding the consequences of continuing to fight that may remain at the end of the war. On the one hand, consistent battle outcomes provide consistent information and encourage the belligerents' expectations about the future of the war to converge. Wars in which one side consistently defeats the other in battle, for instance, demonstrate clearly and with little room for conflicting interpretations the relative superiority of the first belligerent over the second.¹⁵

On the other hand, inconsistent battle outcomes can ensure that considerable uncertainty remains and increase the chance that the agreement becomes obsolete and the contract zone eliminated. First, inconsistent battle outcomes can provide conflicting information to the belligerents and can thereby sustain a considerable amount of “observer uncertainty” about the consequences of continuing the war or renewing the war at a later date. A war in which the tide of war turns often, for instance, could easily be subject to alternative interpretations and could sustain divergent beliefs regarding the consequences of renewing the war. Although the uncertainty regarding the consequences of continuing this war may be sufficient to create a contract zone and allow the belligerents to negotiate a settlement, the fact that both sides can find evidence of success in the war may ultimately create considerable uncertainty about the consequences of renewing the war. Under these conditions, the belligerents can successfully agree to end the war but subsequently choose to challenge the negotiated agreement and renew the war with the expectation that the war will turn out differently.

Second, inconsistent battle outcomes may in some instances also encourage the belief that the probability of victory for either side is equal and can thereby create considerable “inherent risk.” Although the belligerents may share common expectations about the expected value of continuing or renewing the war, the variance over the belligerents' beliefs regarding the capabilities or resolve of their opponent is likely higher if the belligerents appear evenly matched than if the distribution of power is more skewed.¹⁶

These arguments lead us to expect that the more consistent the battle trend at the time of the ceasefire, the more durable that settlement will be. These expectations are summarized in Hypothesis 1.

Hypothesis 1: Ceasefires that follow a war with a consistent pattern of battle outcomes are at a decreased risk of failure.

A second type of settlement that is prone to obsolescence are agreements that specify terms that do not correspond well with the expected military outcome of renewed fighting. The divergence between the political and the expected military outcome provides an incentive for at least one side to challenge the settlement to secure better terms. In contrast, if the political and expected military outcomes were similar, neither side would expect to be able to secure better terms by returning to war. How could such a divergence exist or be created? As the bargaining and war model highlights, the belligerents should only accept the settlement in the first place if the terms at least roughly reflect the expected military outcome of continuing the war. If the terms did not, at least one side would have an incentive to continue fighting. Although changes in power or resolve after the settlement may be one reason for the emergence of a divergence between the terms of settlement specified in the agreement and the expected military outcome of renewed fighting,²⁰

Motivated in some instances by humanitarian concerns and in other instances by selfish, strategic concerns, pressure by third parties to ceasefire is increasingly commonplace. Although third parties occasionally become active belligerents in the dispute, more common is for third parties to place heavy diplomatic pressure on the disputants to stop fighting by threatening one or both sides with economic, military, or political repercussions. Such pressure has the immediate and seemingly positive effect of enlarging the contract zone for the belligerents. Because failing to agree will evoke the displeasure of outside actors (often quite powerful states), a wider range of settlements becomes preferable to the belligerents than nonagreement. Given enough pressure, a contract zone can emerge where none previously existed. In Figure 3, for instance, the belligerents were initially unable to reach a mutually acceptable agreement because they had different expectations about the military outcome of the war. Nonagreement becomes more costly and the range of acceptable agreements increases, however, when third parties pressure the disputants to stop fighting. In the bottom half of Figure 3, the expected costs of invoking the displeasure of a third party is sufficient to create a contract zone that allows the belligerents to reach an agreement even though the belligerents' expectations about the outcome of the war have not changed.

The impact of third-party intervention on the contract zone, where a and b indicate A's and B's costs of fighting, respectively

Over the longer run, however, such “unnatural settlements” are unlikely to last. Significantly, the agreement is only acceptable to both belligerents because they believe that failure to accept the agreement will result in penalties imposed by the third party. In the absence of third-party pressure, no agreement existed that was acceptable to both sides. If and when third-party attention wanes, not only is the agreement likely to become obsolete, but efforts to renegotiate the agreement are unlikely to be successful as well because considerable uncertainty remains regarding the consequences of continuing the war.

Further, third parties may also pressure the disputants to accept a settlement that differs from the terms that the belligerents themselves would have ultimately negotiated. In some instances, the desire of outside actors to end the fighting ensures that the de facto settlement in such “unnatural” ceasefires is simply the military status quo at that particular time. Although the expected repercussions of failing to accept the military status quo as the de facto settlement may encourage the belligerents to accept such terms initially, the ceasefire line may not reflect well one or both of the belligerents' expectations of where the ultimate line would have been if fighting were to have continued. In this case, the agreement is even more likely to become obsolete as third-party attention wanes because the terms of the agreement as initially agreed to do not correspond well with the belligerents' expectations of what the “natural” settlement would have been. In other instances, third parties do not simply pressure for a ceasefire along current battle lines, but instead pressure the belligerents to return either to the antebellum status quo or to accept a compromise agreement that meets current perceptions of fairness or justice. Given that third parties often intervene when one side is decisively defeating the other,²¹

In short, settlements that are viable in the face of heavy third-party pressure are unlikely to remain so absent such pressure. Ironically, if such agreements had been acceptable to both sides absent third-party pressure, intervention by third parties would not have been needed. If the agreement is based on criteria (such as fairness or precedent) that has little to do with the military balance between the belligerents, then at least one side will believe that better terms may be realized through renewed military action. Efforts to renegotiate the settlement short of war, however, are unlikely to be successful. If a contract zone only emerged because of third-party pressure, then considerable uncertainty regarding the capabilities or resolve likely still remains. Such settlements, then, are particularly precarious, because the imposed peace may not reflect either side's expectation of what gains they could or should have received from the war. Additionally, because belligerents' expectations still differ, postwar attempts to revise the settlement may be particularly difficult.

We thus expect that “unnatural” ceasefires that come about as a consequence of third-party pressure are particularly likely to fail. Note that this negative assessment of the consequences of third-party involvement does not contradict the positive expectations about third-party involvement put forward by Walter or Hartzell, Hoddie, and Rothchild.²²

Hypothesis 2: Ceasefires that follow wars “interrupted” by third-party pressure are at increased risk of failure.

Enforcement issues clearly affect the durability of peace. As such, efforts to enhance the belligerents' ability to credibly commit to enforcing the terms of settlement will enhance peace efforts. An exclusive focus on enforcement issues, however, may be overly optimistic. The enforcement dilemma assumes that the belligerents prefer peace to war but are caught in something like a prisoner's dilemma. We suggest, in contrast, that in some instances, war resumes because the belligerents actually prefer a renewed war to peace. False settlements or a failure to reconcile past uncertainty completely can create conditions in which one or both parties believe that a renewed war will lead to a better settlement than currently exists. In the following section, we evaluate these expectations to determine whether distributional arguments, such as enforcement arguments, can help to explain why some ceasefires last while others do not.

Empirical Evaluation

Measurement

To test the two additional hypotheses derived from distributional arguments, we operationalize two variables: interrupted war and battle consistency. The variable interrupted war identifies ceasefires that occurred only as a consequence of third-party pressure to do so; without such pressure, the war would have continued. Of course, one cannot know for certain what would have happened in the counterfactual case of no third-party pressure. Instead, we consider ceasefires to be “interrupted wars” when (1) there is clear evidence of significant third-party pressure to ceasefire, and (2) the ceasefire is invoked before the parties negotiate the final settlement. Evidence of significant third-party pressure indicates first that such pressure existed. We also verify with the historical record that the belligerents were aware of such pressure and that it mattered to them. This pressure, coupled with evidence that the ceasefire preceded a final settlement, suggests that the ceasefire occurred not because the belligerents were ready and able to settle on a compromise to end the war, but as a consequence of outside pressure to stop fighting.²⁹

As Pillar 1983 demonstrates, the timing between ceasefires and settlements can vary. Ceasefires have preceded settlements in some instances and followed settlement in others. In still other instances, the settlement and the ceasefire occur simultaneously.

We focus on third-party pressure and ceasefire timing together as an indicator of interrupted war because, as Pillar argues, ceasefires are inherently intertwined with the final political settlement.³⁰

Pillar 1983.

If a third-party pressures the belligerents to ceasefire without an accompanying settlement, the ceasefire line becomes the basis for final settlement negotiations. If the ceasefire emerged because of third-party pressure, the ceasefire line likely reflects only the immediate circumstances on the battlefield or even the arbitrary conditions designed to get the belligerents to agree to immediate peace. Any final settlement, then, likely has far more to do with the ceasefire lines mandated by the third party instead of convergent military expectations about the consequences of continuing the war. Ceasefires that are brought about in large part as a consequence of third-party pressure and that precede (and ultimately influence) any final settlement indicate well our theoretical ideas regarding the dangers of “interrupted wars.”

The variable battle consistency identifies whether or not the war revealed consistent information to the belligerents. We measure battle consistency as the duration of the last tide of the war before the ceasefire as a proportion of the total duration of the war. By “tide” we mean a period in which one side is consistently winning battles. The “tide turns” or ends, when and if the other side enjoys a period of victory. To determine the duration of the last tide of the war, we measured from the last known date of a new offensive to the end of the war. In cases in which an organized offensive was not used, we assessed the outcomes of the final battles of the war to determine the duration of the last tide of the war. Zeros denote wars that reached a stalemate, meaning neither side was making significant progress in battle. An example would be the Korean War, which eventually reached a stalemate so long-lived that the status quo battle line has prevailed, even to the present day. Wars coded 1 mean that one side consistently won battles from the beginning to the end of the war, such as in the first Gulf War in which the United States successfully expelled Iraq from Kuwait. Values of battle consistency that are between 0 and 1 suggest that some change in battle conditions (for example, military strategy, capability, leadership, and so on) led one side to gain an advantage and begin winning battles consistently enough to precipitate negotiations. For example, in the Yom Kippur War (coded 0.645), Israel, after a surprise attack, managed to turn the tide of battle in its favor, forcing Egypt, Syria, and Jordan to settle. If the duration of the last tide as a proportion of the total duration of the war was long, then both “observer uncertainty” and “inherent risk” are low. Not only is it less likely for two observers to come away from the war with different conclusions regarding its ultimate outcome, but the perception of the probability of ultimate victory is also heavily skewed toward one side avoiding the inherent risk associated with perceptions of power parity and the greater variance over possible outcomes. The coding for the interrupted war and battle consistency variables for each case are provided in Appendix 1.³¹

The source list for each war used to code the interrupted war and battle consistency variables is available from the authors on request.

We also include a variable that marks the change in relative capabilities between the belligerents during the peace.³²

See Werner 1999.

Changes in relative capabilities are a particularly potent reason why the belligerents may no longer prefer the settlement they had previously accepted to war. As relative power shifts, at least one side can expect that a renewed war could result in a better settlement. We use the composite capabilities index from the COW data set to measure changes in relative capabilities.³³

change in capabilities at time

. In future analyses, we intend to formulate alternative measures of power in order to address more directly the concern expressed by Fortna 2003 that the war may be creating the change in capabilities, rather than vice versa.

In order to evaluate and compare the importance of agreement strength to the durability of peace, we also include Fortna's index of agreement strength variable. Her index of agreement strength measures the number of mechanisms incorporated into the peace agreement to facilitate enforcement. The index varies from 0, which indicates that no agreement was in place at that time, to 10, which indicates that all of the following mechanisms were incorporated into the agreement: provisions for a demilitarized zone, arms control agreements, peacekeeping forces, confidence building measures, dispute resolution mechanisms, a formal agreement, specific provisions, provisions for internal control, external involvement, and withdrawal of forces.³⁴

See Fortna 2003 for specific details and sources.

Following Fortna, we also include several variables identified by others as important to the durability of peace to control for the degree of difficulty of the case.³⁵

Ibid.

These control variables include whether or not the war ended in a tie, the costs of the war, the history of conflict between the belligerents, whether one side's existence was threatened during the war, and whether the belligerents were contiguous. The tie variable is a dummy coded as 1 when the war ended in a tie, and 0 otherwise. The cost of war variable is operationalized as the natural log of the combined battle deaths of the belligerents during the war. The history of conflict variable equals the proportion of years during the life of the dyad in which they experienced a militarized dispute. The existence at stake variable is a dummy coded 1 when one side's existence was at stake during the war, and 0 otherwise. Finally, the variable contiguous is a dummy coded as 1 when the belligerents were contiguous by land or were separated by less than 150 miles by sea. Descriptive statistics and a correlation matrix for all variables are available in Appendix 2.

Results

Weibull Analysis

Note first that in the Weibull analyses that follow positive coefficients suggest that the variable increases the risk that peace fails with a renewed war, while negative coefficients suggest that the variable decreases the risk that peace fails. To ensure consistency with Fortna's analysis,³⁶

Ibid.

we first replicate her results and then evaluate the additional hypotheses generated from distributional arguments. Column 1 of Table 1 replicates Fortna's results.³⁷

Ibid. See tab. 2, col. 2.

In column 2 of Table 1, we reanalyze the same model but in this case do not drop, as Fortna did in her analysis,³⁸

Ibid.

the cases of joint democracy. We were unsure of the logic for dropping these cases and would prefer not to do so without a compelling reason. As one can see, the results from column 1 and column 2 are similar, suggesting that the decision to include or exclude these cases does not affect the results. In all analyses that follow, we retain the joint democracy cases.

Hazard analysis of risk that ceasefire ends with a new war, Weibull distribution

As one can see from these results, the strength of the agreement significantly reduces the risk that ceasefires fail. One can well imagine that in a time rife with distrust, mechanisms that help secure the agreement by reducing incentives to defect and fears of duplicity would be extremely important. These results are consistent with results presented by Hartzell, Hoddie, and Rothchild.³⁹

Hartzell, Hoddie, and Rothchild 2001.

They find, in a study of civil conflict, that third-party enforcement and territorial autonomy increase the durability of peace by mitigating the former belligerents' security fears.

The results also replicate Werner's result that changes in relative capabilities after the ceasefire increase the risk that the agreement fails.⁴⁰

Werner 1999.

Note that here we did not include the lag of change in relative capabilities, as Fortna does.⁴¹

Fortna 2003.

She argues that it is possible that the positive association between changes in relative capabilities and the renewal of war may be because the renewed war caused the change in relative capabilities rather than the reverse. Although we appreciate this argument, we are not entirely persuaded. First, we are not convinced that lagging the change variable is appropriate. Analyzing the lagged variable prevents one from considering large shocks to a relationship that may fundamentally alter the belligerents' assessment of the value of the peace agreement relative to war. The war between India and Pakistan in 1971, for example, was a direct result of an attempted revolt and secession of East Pakistan. West Pakistan used military force against the secessionists, and India entered the conflict in part because the domestic chaos within Pakistan created a strategic opportunity for India to further weaken Pakistan.⁴²

Arnold 1991.

Lagging the change variable assumes that belligerents typically wait a year when an opportunity arises to take advantage of a newly vulnerable opponent.

Further, lagging the change variable creates some data issues as it ensures that the first year of every new peace agreement is dropped from the analysis. Given that there are only forty-eight cases in the data set and several agreements die in the first year, this loss is not insignificant. In fact, when the relative capabilities variable is lagged, eight cases are dropped from the analysis. Significantly, when we include a lagged relative capabilities variable in the data set created by Werner⁴³

Werner 1999.

that spans a longer time period (1816–1992 rather than 1945–97), the lagged variable is positive and statistically significant, albeit at p = 0.08 in a two-tailed test.⁴⁴

Analysis available from the authors on request.

This result is consistent with Werner's original result that changes in capabilities after the settlement increase the risk of a renewed conflict.⁴⁵

Werner 1999.

Although we cannot resolve this issue definitively at this time and appreciate the need to explore further the direction of causality, current analyses suggest that changes in relative capabilities increase the risks that the ceasefire will fail and war will recur.

With regard to the control variables, the results show that ceasefires that follow ties are more likely to fail, as are ceasefires between belligerents that share a conflict-ridden history. Ceasefires that follow wars in which a belligerent's existence was threatened are also more likely to fail. In contrast, ceasefires that follow particularly costly wars are less likely to fail and more likely to endure. These results replicate those produced by Fortna and are largely consistent with those reported by Werner,⁴⁶

Werner 1999.

who also finds that costly wars are less likely to be repeated.

In column 3 of Table 1, we duplicate this analysis but add the interrupted war and battle consistency variables. The results provide strong support for both hypotheses one and two. First, the results show that battle consistency significantly decreases the risks of another war. When the war sends a consistent and incontrovertible message regarding the relative superiority of one side over another, then the peace is much more likely to last than if the information from the war is more subject to interpretation.⁴⁷

Note that this variable is significant despite a relatively strong, negative correlation with the variable tie. As expected, as the consistently of the battle outcomes in the war increase, it becomes less likely that the war ends in a tie. If we drop the tie variable from the analysis, the coefficient of the battle consistency variable becomes larger and more significant, but several other variables including the index of agreement strength become statistically insignificant at conventional levels.

In order to interpret the magnitude of the effect of this variable, hazard ratios are included next to the coefficient. A hazard ratio of 1.0 means that the risk of a new war when the variable increases by one unit is equivalent to the risk of a new war when the variable assumes its original value. Hazard ratios greater than 1.0 imply that the risk of war is increasing as the value of the variable of interest increases. Hazard ratios less than 1.0 imply that the risk of a new war is decreasing as the value of the variable of interest increases. The hazard ratio of 0.004 for battle consistency suggests that the effects of battle consistency on the duration of peace are huge. Ceasefires that follow a war in which there is a single tide throughout the war are only 0.4 percent as likely to fail as ceasefires that follow a war in which there is no discernable tide at the end of the war. This result is robust to a number of different specifications of the model, although the magnitude of the effect varies to some degree, depending on the other variables included.

Second, the results show that ceasefires that come about under intense third-party pressure before any agreement being reached were significantly more likely to fail than ceasefires that occurred at what, one might argue, would be the “natural” end of the war. The ceasefires that follow these “interrupted wars” took place without the belligerents necessarily agreeing on the likely future course of the war. As a result, there is no reason to expect that the de facto settlement—often the ceasefire line or antebellum division—resembled in any fashion the settlement either party expected they would or could have received if the war had continued. Once third-party pressure wanes, it is unsurprising that at least one side would prefer to renew the war rather than maintain the ceasefire and the de facto settlement it represents. This failure does not come about because the belligerents cannot enforce a mutually desirable settlement. Instead, at least one belligerent wants war because it believes that it will lead to a better settlement than previously realized.⁴⁸

See Toft 2002/03 for a discussion of this logic in terms of territorial issues.

Further, attempts to renegotiate the terms of settlement peacefully may be particularly difficult if the belligerents' expectations about the consequences of renewed fighting had not yet converged when the ceasefire was called. The hazard ratio, noted beside the coefficient, reflects the magnitude of the effect of this variable. As with the battle consistency variable, the effects are huge. Ceasefires that follow “interrupted wars” are sixty-five times more likely to fail than ceasefires that occur at the “natural” end of the war. Although third parties may be able to coerce the belligerents into a ceasefire, they appear quite incapable of ensuring that it lasts.

It is also interesting to note that there is a positive correlation (0.61) between the battle consistency variable and the interrupted war variable. In fact, of the fifteen cases where the third party pressured for ceasefire without an agreement in hand, eleven occurred when the battle consistency variable exceeded 0.5.⁴⁹

These cases include the Second Palestine War, the Football War, the Yom Kippur War, the First Turco-Cypriot War, and the Lebanon War. There are a total of eleven cases because each war is broken into its respective dyads.

This suggests that third parties do not place heavy pressure on the belligerents to ceasefire randomly but are instead far more likely to do so when a clear winner is developing on the battlefield. If the third parties then pressure the belligerents to return the antebellum status quo or simply to stop the fighting while one side is making clear gains, the de facto settlement is unlikely to correspond well with the belligerents' expectations about what settlement they could have received if fighting had continued. For the side whose gains were wrest away, the settlement is only temporary—a strategic move to placate powerful third parties until their attention turns in other directions.

In column 4 of Table 1, we reanalyze the same model but drop Fortna's index of agreement strength variable. Interestingly, although this change does not affect the sign or statistical significance of either the battle consistency or the interrupted war variable, the hazard ratio for the interrupted war variable falls considerably. When agreement strength is not controlled for, the hazard ratio drops from 65.14 to 18.82. Although this effect is still quite considerable, suggesting that ceasefires following “interrupted wars” are eighteen times more likely to fail than otherwise, its magnitude is much lower than suggested in the full model.

We interpret this change in the following way. In the analysis where we control for strength of the agreement (column 3), we may in some ways be controlling for continued third-party interest and engagement in the conflict and ensuing peace. If the third parties pressure the belligerents to ceasefire but then follow up that pressure with a strong agreement that defends and enforces the ceasefire, the ceasefire is at less, albeit still considerable, risk. Much more dangerous, however, are instances where third parties put considerable pressure on the belligerents to ceasefire but then neither help the parties to institutionalize the agreement nor maintain sufficient pressure to ensure that the parties do so themselves. As Luttwak argues, “partial interventions” are particularly dangerous.⁵⁰

Luttwak 1999.

The humanitarian impulse to stop the fighting without the commitment to enforce the peace may have the paradoxical consequence of prolonging rather than shortening the conflict.

We also consider the substantive effects of the variables by considering the change in the log likelihoods. Because our model simply adds two additional variables, we can compare the fit of our model to any model that is “nested” within it to see which model fits better.⁵¹

See Clarke 2001 for more on nested and nonnested models.

All results are reported in Table 2. We begin by comparing the fit of a base model that includes only the control variables with Fortna's model, which includes the control variables plus her index of agreement strength variable. The results suggest that the addition of the index of agreement strength variable does not significantly improve on the fit of the base model, performing at a significance level of only 0.1269.⁵²

Tests were done with and without robust standard errors and clustering to ensure that the results were not affected by variance controls.

Thus, while the index of agreement strength variable is statistically significant, its substantive effect is relatively minor and does not significantly improve the fit of the model. To see whether our variables perform any better, we then compared the fit of the base model that includes only the control variables with a model that includes the control variables plus the interrupted war and battle consistency variables. The model including these two additional variables does in fact fit better than the base model at a significance level of 0.0037. The importance of the distributional variables are also apparent when one contrasts the fit of the full model that includes the control variables, the index of agreement strength variable, and the interrupted war and battle consistency variables with the fit of Fortna's model, which includes only the control variables and the index of agreement strength variable. The full model including our variables fits the data much better than Fortna's model at a significance level of 0.001.

Likelihood ratio tests for nested models

Although these initial results suggest that the inclusion of our two distributional variables improve the fit of the model more so than does the inclusion of the index of agreement strength variable, the results do not suggest that Fortna's focus on agreement strength is misplaced. As can be seen in Table 2, if one compares the fit of the model that only includes the control variables and the interrupted war and battle consistency variables with the full model that includes these variables plus Fortna's index of agreement strength variable, the inclusion of Fortna's agreement variable significantly improves the fit of that model, at a significance level of 0.0271. This suggests that once the distributional issues are controlled for, the strength of the agreement is particularly important. Further, if one compares the fit of the full model that includes all of the variables with the base model that only includes the control variables, it is obvious that recognition of both distributional and enforcement problems is critical. The full model improves on the fit of the base model at a significance level just shy of 0.001.

Alternative Model Specifications

The analysis to this point follows Fortna's lead and makes use of a Weibull model. This model, however, assumes that the hazard rate is monotonic, either always increasing or always decreasing. To ensure that our results were not affected by this assumption, we also employed a Cox model and recovered the baseline hazard rate. The results for Fortna's index model and for the full model that includes the battle consistency and interrupted war variables are presented in columns 1 and 2 of Table 3. Positive coefficients should again be interpreted as increasing the risk that peace fails, while negative coefficients suggest that the variable reduces the risk that peace fails. Note first that the index of agreement strength variable is no longer statistically significant in either column 1 or 2 of Table 3. In contrast, the battle consistency and interrupted war variables do retain their significance, albeit at a lower level of confidence.⁵³

As noted in fn. 47, the battle consistency variable and the tie variable are highly correlated as one might expect. When the tie variable is dropped from this analysis, the battle consistency variable is significant at the 0.005 level.

The control variables also retain the same sign and significance as they did in the Weibull analyses. Figure 4 reveals why some of the results differ between the Weibull and Cox models. Rather than a monotonic hazard rate as assumed by the Weibull model, Figure 4 shows that the hazard rate is nonlinear, increasing dramatically for the first seven years and then falling precipitously after that point until it flattens out around the fourteenth year. Figure 4 demonstrates how misleading the p parameters in the Weibull models of Table 1 are. Although the results in Table 1 suggest little duration dependence as the p parameter approaches 1.0 in most models, time since the agreement clearly matters. The Weibull cannot accommodate the increasing and then decreasing hazard rate seen in Figure 1 so it conflates the two patterns and suggests that time has little impact.

Hazard analysis of risk that ceasefire ends with a new war, Cox and log-logistic

Estimated hazard for the full model

Given the nonlinear shape of the hazard function, a Weibull model appears inappropriate. Although the Cox model has the advantage of not imposing any restriction on the shape of the hazard function, because it does not do so it is also not efficient and can overestimate the standard errors. In order to ensure that we have not falsely rejected the hypothesis that the strength of peace agreements matters, we also analyzed the data using a log-logistic model that assumes an increasing and then decreasing hazard rate, similar to what is seen in Figure 4. These results are available in columns 3 and 4 of Table 3. In the log-logistic model, interpretation of the coefficients differs as the coefficients are reported in the accelerated-failure time metric. Positive coefficients thus suggest that the variable increases the time until failure while negative coefficients suggest that the variable decreases the time until failure or that the variable makes peace more precarious.

The results from the log-logistic models also cast some doubts on the importance of the strength of the peace agreement for the durability of peace. Although the strength of the peace agreement is significant in column 3, it is not significant when the full model is specified in column 4. In contrast, the interrupted war variable retains its significance in all cases, as does the battle consistency variable albeit at lower levels than first seen in the Weibull models. Note also that if the index of agreement strength variable is dropped from the analysis (not shown), the statistical significance of the battle consistency variable improves to the 0.01 level.

Substantive Effects

We can also provide a better perspective on the substantive effects of the interrupted war, battle consistency, and agreement strength variables by graphing the hazard function under different scenarios.⁵⁴

To estimate the hazard functions under different parameter values for the variables of interest, we must hold the other variables at constant values. In the estimates that follow, we set the conflict history, existence at stake, contiguity, and tie variables at 1.0, and the war costs, agreement strength, and change in relative capabilities variables at their mean values. This represents a fairly typical dyad within the data set. We varied these values for all estimates to ensure that the relationships between hazard estimates remained stable across different scenarios. While the estimated hazards were higher when we changed the values such that the dyad became more dangerous (that is, existence at stake = 1 rather than 0), the relationships between the hazard functions in each graph remained the same.

In each of the following graphs, we maintain a consistent scale so that the magnitude of the substantive effects can be compared across the different figures. In Figure 5, we present the estimated hazard functions over time for settlements that emerged as a consequence of third-party pressure and for those that emerged in the absence of such pressure. The differences are stark. Although the hazard rates ultimately converge, during the first postwar decade, ceasefires brought about by third-party pressure are much more likely to fail than ceasefires that arise absent such pressure. The increasing hazard function over the initial years of the postwar peace also suggests that agreements following interrupted wars are most robust immediately after the conflict, when third-party attention is still strong, but become more vulnerable as the years go on and the attention of the third party fades.

Estimated hazard functions for interrupted war and uninterrupted war

In Figure 6, we present the estimated hazard functions for settlements of uninterrupted wars that emerged when battle consistency was high, low, and at mean (0.42) levels. Recall that high levels of battle consistency suggest that there was one dominant battle trend in the war—one side won consistently throughout the war. Low levels imply that the war ended without a clear tide emerging for either side. Mean levels suggest that at the war's end, one side had secured consistent victories for more than half of the total duration of the war. For the uninterrupted wars portrayed in Figure 6, the possibility of a recurrent conflict is significantly higher for wars with short battle consistency than for those where a clear battle trend existed at the end of the war. There appears to be little difference, however, between the hazard rates for wars where the battle consistency variable was at mean or high levels. Although the substantive effects of battle consistency appear smaller than the effects for third-party intervention, an ambiguous military ending seems particularly dangerous, leaving open the possibility of different lessons from the war and the particular risks associated with perceptions of power parity.

Estimated hazard functions for low, mean, and high levels of battle consistency (uninterrupted war cases)

We explore the joint effects of battle consistency and third-party intervention in Figure 7. Here, we present the estimated hazard functions for low, mean, and high levels of battle consistency for the cases of interrupted wars. As in Figure 6, the highest risk occurs for those cases where battle consistency is low. Note, however, that high battle consistency cases are also at considerable risk—much higher than those cases at mean levels of battle consistency.⁵⁵

Note that for all of these estimates, the variable tie is set at 1.0. However, as previously noted, there is a strong negative correlation between the variables tie and battle consistency—if battle consistency is high, it is unlikely that the war ends in a tie. Varying the battle consistency variable while holding the variable tie constant is thus somewhat misleading. To ensure that the different patterns that emerge in Figure 7 are not dependent on the value of the tie variable, we also ran estimates where the tie value also changed with the battle consistency variable, assuming a value of 1.0 when battle consistency was low and a value of 0 when battle consistency was high. Although the estimated hazard function for the high battle consistency was not as large in the first postwar decade as in the original scenario, the difference remained stark with interrupted wars with high battle consistency being at significantly greater risk of repeating than uninterrupted wars with high battle consistency.

What might explain the different patterns evident in Figures 6 and 7? For cases without third-party intervention, only cases of low battle consistency were at considerable risk for recurrence (Figure 6). For cases with third-party intervention, high battle consistency cases were also at considerable risk, albeit slightly lower risk than low battle consistency cases (Figure 7). We believe this difference arises because third parties are much more likely to intervene and alter the “natural” settlement in cases where a decisive winner is emerging. For uninterrupted wars, consistent battle trends lead to a settlement that likely reflects the belligerents' shared beliefs about the military reality on the ground. This is unlikely to be the case when third parties intervene. If third parties are often motivated to intervene to stop one side from dominating the other and to encourage a “fairer” settlement than would otherwise arise, then settlements following wars with high battle consistency are particularly unlikely to reflect the belligerents' shared beliefs about the military reality on the ground. These settlements then should be particularly vulnerable even though they follow wars with high battle consistency. The stark differences between Figures 6 and 7 support this logic.

Estimated hazard functions for low, mean, and high levels of battle consistency (interrupted war cases)

Finally, we consider the substantive effects of the agreement strength variable in Figure 8. Two things are readily apparent. First, the substantive effect of the agreement strength variable is significantly less than the substantive effect of the other variables of interest. Second, while weak agreements are at the greatest risk of failure, Figure 8 suggests that agreements with average levels of enforcement mechanisms or confidence-building measures are at the lowest risk of failure, not strong agreements, although the difference is fairly small. This suggests to us that selection effects may continue to plague the analysis of peace duration. As Fortna explains well, strong agreements are likely to be put in place in the very cases where they are needed most.⁵⁶

Fortna 2003.

Unless we are able to control for all of the factors that make certain cases particularly risky, it is difficult to discern the true effects that mechanisms within the agreement may have.

Estimated hazard functions for low, mean, and high levels of agreement strength

Discussion

Although our conclusions are not definitive given the relatively small number of cases, the analysis suggests that peace depends heavily on the distributional consequences of the settlement and convergent expectations that better terms cannot be achieved by renewing the war. If the terms of agreement do not reflect the belligerents' common beliefs of the military consequences of continuing to fight, at least one belligerent will have an incentive to revisit the settlement. In these cases, returning to war may lead to better terms, providing a compelling motive for challenging the peace. If considerable uncertainty remains regarding the consequences of fighting either because the lessons from the previous war were unclear or because third parties intervened and ended the war before the uncertainty was resolved, efforts to renegotiate the settlement are unlikely to succeed. When considerable uncertainty remains and the settlement does not reflect at least one of the belligerents' expectations about what could be achieved via war, the risk of recurrent conflict will be high.

In contrast, mechanisms that increase the costs of renewing the war or that help to build trust between the belligerents seem to have less impact. Although the index of agreement strength variable was significant in the Weibull model, it did not improve the fit of the model over a model that simply contained the control variables except when the interrupted war and battle consistency variables were added. Further, the statistical significance of the index of agreement strength variable fell considerably when more appropriate hazard models were analyzed. The substantive effect of the index of agreement strength variable was also relatively small. Despite these results, we believe that enforcement mechanisms can make a difference. The poor results may in part be a consequence of our inability to appropriately identify the “hard cases” through the control variables. As Fortna notes, if strong agreements are more likely to be put in place in the most difficult cases, it will be hard to demonstrate that such mechanisms matter.⁵⁷

Ibid.

We also believe, however, that even the strongest agreements with multiple mechanisms to build trust and create barriers to renewing the violence will ultimately fail in the face of a determined foe. They can work well if the belligerents want peace but need reassurances that the other side wants it too. Absent such desires, even the strongest enforcement provisions may not be sufficient to keep the belligerents from revisiting the terms of settlement and potentially renewing the war.