Event Sequences in Disputed Issues*

Shawna K. Metzger College of William and Mary

skmetzger@wm.edu

Emily U. Schilling University of Tennessee, Knoxville

eschill2@utk.edu

July 10, 2018

Prepared for the Annual Meeting of the Society for Political Methodology Provo, UT

July 19-21, 2018

** Some simulations still in progress, circulate further at own risk **

Abstract: Do event sequences matter in territorial disputes between states? Existing work focuses on events’ shorter-term impact, both theoretically and empirically, but does not consider the events’ possible longer-term effects. Building from the literature on critical junctures, we articulate two conceptual requirements any argument must satisfy to make a compelling case for longer-term effects. We then argue the first settlement attempt’s type (peaceful or militarized) has the potential to meet these conditions by affecting disputant states’ propensity to use different types of settlement attempts in the future. We analyze Huth and Allee’s (2002) and the Issue Correlates of War’s (Hensel 2001) territorial dispute datasets to assess our hypothesis. We innovate by considering the entire event sequence in our analysis, instead of examining the individual events composing the sequence, as current work does. We find suggestive evidence of longer-term first-event effects, contributing to our understanding of territorial disputes.

* We thank Justin Esarey, Dean Knox, Sara Mitchell, Paul Poast, and the University of Tennessee’s Faculty Research Workshop participants for feedback on earlier drafts. We bear sole responsibility for any remaining errors and shortcomings. All analyses are performed using Stata 14.2.

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“…the negotiations in Paris had been progressing so well when they ended on 29 August [1958] that, if only the British trawlers and warships had stayed away for a few extra days, an agreement would have been achieved. But now, [Anderson1] maintained, ‘events’ had made a solution impossible.” – Jóhannesson (2004, 570)

The order in which events occur can matter. The epigraph refers to the 1958 Cod War between

Britain and Iceland, precipitated by Iceland unilaterally extending its territorial limit at sea from 4 miles

to 12 miles in June 1958 (Jóhannesson 2004, 556). The extension encompassed fishing grounds

historically frequented by British fishermen; the announcement was not received well. The British

government formally protested Iceland’s actions, noting it was “their duty to prevent any unlawful

attempt to interfere with British fishing vessels on the High Seas…” (quoted in Jónsson 1982, 85). In an

effort to stave off the impending crisis, a group of NATO countries, including Britain and Iceland, tried

another round of negotiations to address fishing quotas and the recognized mile limit in early August

(Jóhannesson 2004, 564). However, as the August negotiations were going on, British fishermen setting

sail for Icelandic waters were accompanied by warships. When Iceland began enforcing the 12-mile limit

on September 1, non-lethal skirmishes between the Icelandic coast guard and the British warships ensued.

Public outcry in Iceland was strong enough that any negotiated settlement in the near future amounted to

political suicide for the tenuously situated Icelandic government (Jóhannesson 2004, 565–66).

Anderson’s claim in the opening epigraph is simple: had the British refrained from deploying warships,

the militarized clashes would not have occurred, and negotiations would have been able to continue.2

Asking whether order matters is fundamentally a question about event sequencing. Above, the

key question is a counterfactual: would the Cod War’s pattern of settlement attempts have been different,

had the naval skirmishes not occurred? The primary events of interest within a disputed issue are whether

a peaceful, a militarized, or no settlement attempt occurs. Current work argues past events matter because

they either reveal information about the bargaining environment (Fearon 1995; Hensel 2001; Powell

1 Hans G. Anderson, Iceland’s permanent delegate at NATO (Jóhannesson 2004, 553). 2 Instead, the disagreement continued until 1961, three years later. Underscoring Anderson’s point: the 1961 agreement was nearly identical to Iceland’s final proposal during the August 1958 negotiations (Jóhannesson 2004, 562–63; Jónsson 1982, 105).

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2004; Slantchev 2011) or they alter payoffs in some way, which includes subjective emotional buildup as

a possible mechanism (Colaresi, Rasler, and Thompson 2007; Hensel 2001; Hensel et al. 2008; Metzger

2017; Vasquez and Mansbach 1984). Either story produces a potential effect influencing which events

occur later, and existing evidence indeed suggests the likelihood of peaceful settlement attempts and

militarized attempts is dependent on the history of settlement attempts (Hensel 2001; Hensel et al.

2008).3,4

However, while current studies do focus on whether different types of settlement attempts occur,

they do not speak to questions of sequence, more broadly. We do not know whether a different number

of peaceful and militarized settlement attempts occur after some critical event, such as the skirmishes in

the opening illustration. Work on historical institutionalism and path dependence describe critical events

that fundamentally alter the subsequent number and type of events we observe in a process (Bennett and

Elman 2006; Page 2006; Pierson 2004; Thelen 1999). Instead, all the current disputed issues studies

conceive of the past in a short-term way, focusing on a single event immediately following the prior one

(or a set of prior events falling within some time range). While doing so has certainly advanced our

knowledge about resolving disputed issues, we are left with questions about the longer-term ramifications

of the dispute’s past settlement attempts.

Our interest is in a very specific type of sequencing effect: first-event effects.5 We investigate

whether a dispute’s first settlement attempt being militarized or peaceful has an impact on the number of

subsequent militarizations we observe.6,7 We recognize sequencing could matter in other ways, but we

3 We focus on disputed issues to make the paper’s scope manageable. However, within international security more generally, many arguments feature past events affecting future ones. Examples include action-reaction/rational expectations arguments (Axelrod 1984; Goldstein and Freeman 1990; Williams and McGinnis 1988), evolutionary approaches to interstate rivalry (Hensel 1999), arguments regarding past settlement strategies’ success during disagreements (Leng 1983; Wiegand and Powell 2011), game-theoretic approaches to crisis bargaining (Filson and Werner 2002), and the steps-to-war theory (Vasquez 2009). 4 Casper and Wilson (2015) and D’Orazio and Yonamine (2015) also examine sequences for national crises and pre-intrastate conflict events, respectively. Both articles use sequence analysis (Abbott and Tsay 2000; Mills 2011, chap. 11), which is different than the approach we take here. We discuss the differences further in a later section. That aside, neither study evaluates what makes certain sequences more or less likely than others. 5 We discuss “history matters” more thoroughly, with an organizational typology, in Appendix A. 6 We synonymously refer to militarized settlement attempts as militarizations, and peaceful settlement attempts as negotiations.

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think our decision reasonable for two reasons important to state upfront. First, it allows us to parse out

the relative importance of disputants’ first move. If no differences exist between disputes whose first

settlement attempt is militarization vs. negotiation, it would suggest the dispute is memoryless at its

outset. However, if we do find differences, it suggests first settlement attempts matter more than we

currently realize. They set the stage for everything that subsequently occurs. As a consequence, decision

makers may elect to be more deliberative at a dispute’s outset by choosing the settlement type that best

forwards their country’s goals. Second, whether or not the type of first attempt matters has ramifications

for where future research should focus. If type does matter, scholars can more carefully think about how

first attempts are exerting this effect. If type does not matter, the question becomes what aspects of

history do, and thinking about how we can assess whether these different aspects of history matter.

Conceptually, we articulate two conditions that any argument must meet to make a convincing

case that past events affect subsequent ones in the longer term. Existing theories regarding past

settlement attempts in disputed issues, and our empirical evaluations of them, only partially satisfy one of

these two conditions, underscoring our point about these studies’ limitations. We then argue the first

settlement attempt’s type can meet both our conditions by altering states’ incentives. The initial attempt

can impose different costs (and/or benefits) on some but not all future settlement attempt types. This

some-but-not-all conditionality ultimately produces a different number of subsequent militarized and

peaceful settlement attempts within the dispute, providing us with a testable implication.

We assess our hypotheses using two different territorial dispute datasets: Huth and Allee’s global

sample of territorial disputes between 1919 and 1995 (Huth and Allee 2002), and the Issue Correlates of

War project’s territorial dispute data for the Western Hemisphere and Western Europe between 1816 and

2001 (Hensel 2001; Hensel and Mitchell 2007). Our major innovation is our new dataset structure, in

7 Additional examples abound of historical conditions affecting how subsequent behavior evolves. For instance, Acemoglu, Johnson, and Robinson (2001) argue the way in which former colonizers governed their former colonies affect those former colonies’ development levels in the present day. As another, Maoz (1989) argues the manner in which a state became independent has effects on its subsequent conflict patterns, and Lemke and Carter (2016) similarly argue how a state became independent affects its propensity to both wage and win interstate and intrastate wars.

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which each row represents a possible event sequence for a disputed issue instead of a disputed issue-dyad-

year. Our setup includes both observed and unobserved event sequences, meaning we can easily assess

whether the event sequences we observe deviate from the sequences true randomness would produce.

Using true randomness as baseline for comparison is important because it gives us an absolute benchmark

to which we can compare observed sequences with different characteristics, instead of comparing the

different observed sequences to one another, in relative terms. More simply put: our setup allows us to

examine both the dogs that bark (our observed event sequences) and the dogs that do not (our potential

event sequences, if the sequence of events was truly random), and whether barking dogs have

significantly different characteristics than non-barking ones.

We find evidence broadly consistent with a first-event effect. Like behavior begets like behavior:

whatever type of settlement attempt we observe first, we become increasingly likely to see disputes with

sequences as the subsequent number of that settlement type increases. For instance, we are more likely to

observe sequences that do not begin with militarization, and we become increasingly more likely to

observe such sequences as the number of subsequent negotiation attempts increase. We also find partial

support for a ‘deterring opposites’ effect: for disputes not beginning with militarizations, we become less

likely to observe sequences with higher numbers of subsequent militarization attempts. We find a similar

effect for militarizations first and subsequent negotiations, but only in the Huth and Allee dataset.

By looking at the entire sequence in this way, we make important contributions to our

understanding of events within territorial disputes. We show dispute sequences beginning with a

militarized settlement attempt have a different combination of subsequent militarizations and negotiations

compared to dispute sequences beginning with a peaceful settlement attempt. By contrast, current

studies’ empirics focus on the pieces composing the sequence—individual peaceful or militarized

settlement attempts—meaning it can speak to what makes an event more or less likely to happen, but

cannot speak to the sequence’s overall composition like we can.

The paper has four sections. First, we discuss how events occurring earlier in a territorial dispute

could affect the subsequent sequence of events we observe. We begin by talking in the abstract, drawing

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on the path dependence literature, before moving to territorial disputes more specifically. Second, we lay

out our research design, particularly the unique features that permit us to assess hypotheses about

sequencing in a new way. Third, we discuss the results from our analysis. We conclude with some

summarizing remarks.

I. Theory

A. History: The Effect of Past Events

We discuss territorial disputes in terms of each dispute’s event sequence—the pattern of

militarized and peaceful settlement attempts that occur until the dispute is resolved.8 We use a simplified

sequence with two different event types in Figure 1 to help concretize what follows. Figure 1’s α’s

represent the probability of an event occurring after another, with the subscripts denoting the current and

future event. Let k denote the different events composing a sequence, with subscripts denoting the event’s

type, of which there are K total.

Any substantive argument about sequencing must meet two criteria. First, the argument must

describe the mechanism by which earlier events influence later ones (Thelen 1999, 400). To meet this

criterion, it is not enough to argue Figure 1 α’s are non-zero.9 Instead, we must make an argument about

change. Define Δ𝑚𝑚 = 𝛼𝑚𝑚 − 𝛼𝑚𝑚′ , where we use 𝛼′ as a notational convenience to denote the

probabilities associated with an immediately prior set of events offscreen in the figure.10 Criterion #1

requires we have a causal mechanism explaining why Δ𝑚𝑚 ≠ 0. For fn. 9’s example, we would need a

mechanism explaining why Δ11 = 1 − 0.5 = 0.5.

8 A territorial dispute is broadly defined as one state “claiming sovereignty over a piece of territory that is claimed or administered by another state” (Hensel 2001, 90). The statements challenging the current status quo must be explicit, and must also be made by official representatives of the state’s government. 9 Imagine a situation in which k1 and k2 have a 50/50 chance of occurring at the outset, but if k1 occurs first, k2 never will again (α11 = 1, α12 = 0). α12 is now zero, but k1 did indeed exert an influence, since k2 began with a 50% chance of occurring. 10 If we wanted to represent fn. 9’s toy example properly using Figure 1, we would need to temporarily define 𝛼11′ and 𝛼22′ as representing the two events’ initial probability of occurrence (denoted with a “0” subscript), instead of the probabilities from an “even earlier” set of events. We would also need to temporarily remove 𝛼12′ and 𝛼21′ , as these quantities would now have no meaning. If we do these things, 𝛼11′ 0 = 𝛼22′ 0 = 0.5.

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Second, the argument cannot simply state how one event type (continue calling this k1, for

convenience) makes subsequent events more or less likely. It must also discuss why all the sequence’s

other possible event types (k¬i, where {i ∈ ℤ | 1 < i ≤ K}) do not produce the same effect as k1 on

subsequent events (Page 2006, 99). Abstractly, there are two non-exclusive ways k1 could have an effect

on future events. First, k1 could affect its own probability of future occurrence, similar to positive or

negative autocorrelation in the time series context (α11).11 The quintessential examples in politics are

processes producing either increasing or decreasing returns (Pierson 2004). Second, k1 could affect the

probability of other events’ future occurrence (k¬1, Figure 1’s α12).12 The key becomes, whatever effect k1

ultimately has on future events (α12, e.g.), it must be different than all other events’ effect on the same

future event (α22, to continue the example). If α12 and α22 were identical, the net effect on future-k2 would

be zero, since it has the same probability of occurring after k1 or k2.

FIGURE 1. Sequencing Criteria

αmn = probability of observing a transition from km to kn, where m = earlier event, n = later event.

Summarized, the two criteria become:

1. MECHANISM. Must articulate a mechanism by which earlier events causally influence later ones,

broadly speaking. In Figure 1, this amounts to (1) a causal explanation for (2) Δ11 ≠ 0, Δ12 ≠ 0,

Δ21 ≠ 0, and/or Δ22 ≠ 0.

11 Situations in which k1 increases the probability of future k1-occurrence is consistent with Bennett and Elman’s discussion of “constraints” (2006, 256–59). 12 Situations in which k1 decreases the probability of future k¬i-occurrence is consistent with Bennett and Elman’s discussion of “closure” (2006, 252).

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2. HETEROGENEOUS ANTECEDENT EFFECTS. Must articulate why sequence’s other possible event

types (k¬i, where {i ∈ ℤ | 1 < i ≤ K}) do not produce the same effect as k1 on future events’ rate of

occurrence. In Figure 1, this amounts to α11 ≠ α21 and/or α12 ≠ α22.

The two criteria are similar, but are nonetheless distinct, both mathematically and substantively.

Mathematically, meeting Criterion #1 is insufficient to guarantee #2,13 and meeting #2 is insufficient to

guarantee #1 for K > 2.14 Substantively, the first criterion emphasizes a mechanism must exist explaining

change across periods, while the second criterion emphasizes the same mechanism must also explain any

change within the same period, across events.

B. Territorial Disputes

1. CURRENT EXPLANATIONS

Existing work on territorial dispute management addresses parts of Criterion #1 alone. From

these studies, we broadly know the past matters. The probability of a settlement attempt within a dispute

can be influenced by (a) disputant states’ past attempts to settle the dispute, (b) the type of past settlement

attempts (peaceful vs. militarized), (c) the success of those attempts, and (d) the type of disputed issue in

question (Hensel 2001; Hensel et al. 2008; Hensel and Mitchell 2005; Powell and Wiegand 2014;

Wiegand and Powell 2011).15 For territorial disputes, like produces like: past militarizations (Figure 1’s

k1, for convenience) make future ones more likely, and past failed peaceful attempts (k2) make future

peaceful attempts more likely, corresponding to increases in Figure 1’s α11 and α22, respectively, yielding

Δ11 ≠ 0 and Δ22 ≠ 0. Additionally, past militarizations make peaceful attempts more likely (increased α12;

Δ12 ≠ 0), and past failed peaceful attempts make militarizations more likely (increased α21; Δ21 ≠ 0). On

13 For an example: say there is a 50/50 chance of k1 vs. k2. If k1 occurs, say there is subsequently a 60/40 chance of k1 vs. k2, satisfying Criterion #1. However, if k2 occurs, say there is also subsequently a 60/40 chance of k1 vs. k2. The example fails to satisfy Criterion #2, since k1’s effect and k2’s effect on future k1 is identical (60%), as are their respective effects on future k2 (40%). 14 See Appendix F for proof. 15 The probability of a settlement attempt is also influenced by a number of other factors, which Mitchell and Hensel (2010) summarize. We focus exclusively on past events’ effect because of our paper’s interest in event sequences.

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the whole, for ongoing territorial disputes, any past settlement attempts increase the probability of

present-day settlement attempts of any type occurring. All of Figure 1’s Δs are non-zero.

How past settlement attempts specifically exert these effects is undertheorized, and devoid of

Criterion #2.16 Hensel (2001) and Hensel et al. (2008) argue past settlement attempts help resolve

information asymmetries regarding some aspects of the disputants’ resolve, by providing information

about “actions the other side is willing to take in pursuit of its issue goals” (Hensel 2001, 86). However,

both pieces go on to suggest only past peaceful settlement attempts have a beneficial informative effect,

with the strong implication being an increase in α22 (Δ22 > 0). Similarly, past peaceful attempts should

make militarized ones less likely, meaning a decrease in α21 (Δ21 < 0), but Hensel (2001, 87), Hensel et al.

(2008, 126–27), and Wiegand and Powell (2011) all suggest the informative effect should manifest only

when past peaceful attempts are successful.

Militarized attempts, by contrast, exert a more pernicious emotive, subjective effect. Each

militarized attempt “typically increase[es] hostility and distrust between the adversaries and mak[es]

future confrontations increasingly likely” (2001, 88), implying an increase in α11, at minimum (Δ11 > 0).

This conflict-begetting-conflict mechanism appears most frequently in the interstate rivalry literature

(Colaresi, Rasler, and Thompson 2007; Vasquez 2009; Vasquez and Mansbach 1984), with Hensel

elsewhere offering domestic politics as one possible explanation for the pattern (Hensel 1999). Hensel

(2001, 88) further argues increased hostility and distrust decrease the probability of peaceful settlement

attempts, implying a decrease in α12 (Δ12 < 0). While Hensel does not foreclose the possibility that

militarized attempts could also play an informative role, the implication is the emotive aspect is stronger

than the informational aspect. Put differently, we have arguments about why the Δ’s should be non-zero

(Criterion #1), but the arguments are not specific enough to speak to the αs’ relative magnitude (Criterion

#2).

16 Empirically, we also do not know whether the second criteria have support at all, as we discuss further in Appendix D.

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2. PROXY VS. CAUSAL

How information produces a beneficial effect for peaceful attempts, but a pernicious effect for

militarized attempts, is unclear. However, both can be situated within a single game-theoretic framework,

using Slantchev’s categorization scheme (2011).17 Seeing these two stories as part of the same

framework helps make clear which could serve as a compelling mechanism for sequencing effects.

Slantchev distinguishes the two explanations based on the different game-theoretic model

structures they imply, yielding two categories. He labels the first “a purely informational approach,”

which corresponds to Hensel’s (2001; Hensel et al. 2008) beneficial effect story. States use their actions

to “manipulate the information available to the opponent to one’s advantage” (2011, 19). Costly

signaling models fall here, with Slantchev’s two specific examples being (1) actions that create sunk

costs, to be paid regardless of how the disagreement is resolved, and (2) actions that create a risk of

militarization beyond the states’ direct control. In both examples, the key defining characteristic is any

cost (or risk) is incurred unconditionally, regardless of what outcome transpires—the action creates

deadweight losses. In terms of Figure 1,18 an informational approach suggests k1 occurring in the past

will result in no net observable change in α11 or α12 from the previous period (Δ11 = 0, Δ12 = 0), since the

same cost is associated with future-k1 and future-k2. Criterion #1 may therefore not be met.

By contrast, costs are not unconditional for Slantchev’s second class of models, which he labels

“manipulating incentives.” Here, states’ actions alter payoffs for only some of the possible outcomes, but

not others. k1’s occurrence changes the α’s by different amounts (Δα11 ≠ 0 or Δα12 ≠ 0), satisfying

Criterion #1. The best-known example is audience cost models, with the costs coming from either the

domestic or international level (or both).19 A state incurs costs if it makes a threat and fails to carry

17 Slantchev assumes all commitments are credible, for streamlining purposes. 18 Figure 1 is in terms of probabilities, but Slantchev’s models are discussed in terms of expected utilities. Because we are using Figure 1 as a way to help organize our discussion, we translate a higher expected utility for an outcome into a higher probability of the outcome occurring. We treat two expected utilities increasing in equal amounts as producing no observable effect on the α’s. Clearly, though, expected utilities and probabilities may not perfectly map in this way. 19 Audience costs are usually framed in punitive terms, but there is no reason why this must be so, as both Carter (2010, 972) and Slantchev (2011, 37–42) discuss.

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through, but incurs no cost if it carries through.20 Because the payoffs for some (but not all) of the

outcomes can change, state actions can alter states’ preferences over actions. Importantly, models of this

form are also consistent with past militarized settlement attempts producing more militarized attempts in

the future (Δ11 ≠ 0)—the pattern Hensel explains with an emotive story.21

Altering disputants’ incentives corresponds to the causal effect we imply when making statements

like “history matters.” It is capable of meeting at least one of our two necessary criteria for a sequencing

effect. For the first criterion, earlier events have a non-zero net effect on later events (Criterion #1) by

changing the expected utility of some future outcomes (which we use here as a shorthand for “future

event”) but not all outcomes.22 The second criterion is less self-evident from Slantchev’s discussion and

other, similar game-theoretic work. There is surprisingly little written on the general characteristics

distinguishing militarized and peaceful settlement attempts from a theoretical perspective, which is what

we would need to articulate Criterion #2. The explanation would need to state why militarization’s effect

on future militarizations (α11) should be different than negotiations’ effect on future militarizations (α21),

for instance.

3. TESTABLE IMPLICATIONS

The difficulty lies in distinguishing between a proxy vs. causal mechanism. Both militarized and

peaceful attempts can both reveal existing information and alter incentives, meaning we cannot leverage

different event types to assess claims about sequencing mechanisms. For militarized settlements,

militarized behavior reveals information (by acting as a sunk cost, for instance), but can also alter states’

incentives (e.g., if it induces audience costs) (Slantchev 2005, 2011). Yet, peaceful settlement attempts

20 Game-theoretic models also falling under this header include those where actions can manipulate fighting’s benefits (Slantchev 2011, 45–47). 21 Slantchev (2011, 31) goes on to argue militarized actions have “both signaling and incentive-rearranging features.” 22 Admittedly, levying costs is a somewhat vague mechanism in its own right. Further, some recent work has begun pointing out audience costs’ heterogeneous nature by investigating the costs’ microfoundations while also laying out theoretical refinements (e.g., Brutger and Kertzer 2018; Kertzer and Brutger 2016). Rather than wade into this debate, we opt to place our theoretical concerns elsewhere for justifiable reasons we discuss in the next section.

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may have the same duality. For a purely informational approach, IOs’ information brokerage roles appear

frequently in the literature (Abbott and Snidal 1998; Boehmer, Gartzke, and Nordstrom 2004; Garrett and

Weingast 1993; Keohane 1984). From an altering incentives perspective, interventionist IOs with the

ability to arbitrate, adjudicate, send peacekeepers, and/or otherwise sanction states, can impose audience

costs on disputant states (Shannon, Morey, and Boehmke 2010; Thompson 2006). Importantly, these

costs will only materialize if states fail to comply with any agreement. Certain IOs can also level

reputational costs, with arguments about IOs’ socialization abilities as a prime example (Bearce and

Bondanella 2007; Checkel 2005; Finnemore 1996; Johnston 2001). In short: both attempt types can

operate through either mechanism.

Our existing theories are also not so specific as to produce fine-grained predictions about when

and where an effect is causal vs. a proxy for another factor. Issue salience is a good illustration, where

salience refers to the importance of the issue to disputant states (Mansbach and Vasquez 1981; Randle

1987; Rosenau 1971). At first, salience would appear to be a good representation of a proxy effect.

Salience changes little across time, and is also a characteristic intrinsic to the sequence itself. We know

more salient issues have a higher probability of both militarized and peaceful settlement attempts (Hensel

2001; Hensel et al. 2008; Hensel and Mitchell 2005). Because salience is relatively invariant within a

dispute (and, therefore, within the sequence), we could say any detected first-event effects are a proxy for

salience’s effect, and could use salience to begin disentangling whether the detected effects are causal or a

proxy. However, this assertion only works if salience’s effect is homogenous. It must exert the same

effect on militarized settlement attempts as it does peaceful attempts, since a proxy mechanism requires

disputants to pay a sunk cost, regardless of what type of settlement attempt subsequently transpires

(Δα11 = 0, Δα12 = 0).23 Whether this assertion has merit is debatable, making it a shaky foundation for

theory-building purposes.24

23 As a weaker condition for a proxy effect, salience could have different effects on peaceful vs. militarized effects, so long as those effects do not alter states’ preferences over actions. 24 For instance, while higher salience issues are more likely to experience a settlement attempt of any type than lower salience issues in absolute terms, perhaps they are more likely to see a militarized settlement attempt than

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Our point, in talking about settlement attempts in this way, is that we have no ex ante predictions

from the interstate literature as to how militarized or peaceful settlement attempts might either reveal

information or alter states’ interests. We also lack ex ante predictions about the factors potentially

associated with one of the mechanisms, but not the other. We are open to any number of possibilities, as

far as potential stories (and the different empirical patterns they imply). The key for us, though, is that if

first-event effects exist—regardless of whether they are causal or a proxy—the first settlement attempt’s

type will produce divergent effects on the number of subsequent events of each type:

General Hypothesis: The distribution of militarized-to-peaceful settlement attempts in a sequence is

affected by the first settlement attempt’s type.

II. Research Design

In order to test this proposition, we utilize two different territorial dispute datasets: Huth and

Allee’s (2002) dataset (H&A) and the Issue Correlates of War (ICOW) project’s dataset. The H&A

dataset contains 396 territorial disputes worldwide from 1919 to 1995, involving 399 dispute-directed

dyads. The ICOW dataset contains 122 territorial disputes in the Western Hemisphere and Western

Europe from 1816 to 2000, with 191 unique dispute-dyad pairings.25 The observation level for both

datasets is claim-dyad-year but for our purposes we collapse each disputed issue into an event sequence.26

Our event sequences are composed of four possible events: Challenge (C), Military (M),

Negotiation (N), Resolved (R).

peaceful settlement attempts, in relative terms. If so, it would suggest the costs associated with salience are heterogeneous, with the costs’ magnitude being conditional on settlement type, implying the causal mechanism is at work. We have no evidence to say one way or the other whether salience levies unconditional or conditional costs, because current analyses examine peaceful attempts in one model and militarized attempts in another, precluding us from assessing relative effects (e.g., Hensel et al. 2008; Hensel and Mitchell 2005). 25 For our broad definition of territorial dispute, see fn. 8. 26 The two datasets have other organizational differences. Huth and Allee’s dataset also records whether a target state actively challenges the initial claim made by another state (coded as “dual” disputes), whereas ICOW does not. Further, H&A only record challenger-initiated settlement attempts over the issue, while ICOW records all settlement attempts over the issue, regardless of who initiates them. Finally, H&A do not record simultaneous settlement attempts over an issue, whereas ICOW does. For more details on the last two, see Jones and Metzger (2018, Supplemental Appendix A, 31).

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• Challenge (C) means a territorial dispute exists between two states, but neither is taking action

to resolve the dispute (Huth and Allee 2002, 36, 45).

• Militarized settlement attempts (M) are defined as Militarized Interstate Disputes (MIDs),

which are threats, displays, or uses of military force by one state against another state (Ghosn,

Palmer, and Bremer 2004). To appear in either the H&A or ICOW datasets, the MID must be,

in part, related to a territorial dispute in the dataset.

• Peaceful settlement attempts (N) are “bilateral negotiations, …nonbinding third-party

assistance (inquiry, conciliation, good offices, or mediation), or…binding arbitration or

adjudication” (Hensel 2001, 95–96) between two disputant states convened specifically to

address the issue under dispute. Huth and Allee’s definition is less clear, but cross-referencing

H&A with ICOW, while being mindful of the coding differences in fn. 26, suggests H&A use a

similar definition.

• Resolved (R) denotes the disputants have concluded their disagreement. For Huth and Allee, a

dispute is considered resolved if “(1) negotiations yield an agreed-upon settlement, (2) a MID

yields a victory, in that one side receives the territory, (3) the dispute-dyad is between a

colonizing power and another state, and becomes moot once the colony becomes independent”

(Jones and Metzger 2018, 827). ICOW employs a similar definition of “resolved” (Hensel and

Mitchell 2007, 9–10).

Each row of our dataset is filled with a possible event sequence for a dispute. This dataset

structure permits us to problematize sequence length and the sequences’ composition, whereas network

analyses (e.g., Cranmer et al. 2017; Cranmer and Desmarais 2011; Hafner-Burton, Kahler, and

Montgomery 2009; Maoz 2012) and path analyses (Knox 2016) force us to fix (and exhaustively

elucidate) the number of times a dispute can militarize, negotiate, and revert to no active settlement

attempt. Further, because each row contains a possible event sequence, all of our dataset’s rows are

independent of one another, removing a perennial source of concern in dyad-year-based analyses of

14

disputed issues (Cranmer and Desmarais 2016; Erikson, Pinto, and Rader 2014). Importantly, we include

sequences that did occur and generate sequences that did not to assess our hypothesis—our barking and

non-barking dogs—which we discuss in more detail in Appendix B.27

We adapt the data structure from Poast’s (2010) k-ad analysis. Poast’s interest is which

combinations of states form treaties. Accordingly, his dataset’s rows are filled with different possible

combinations of states. By contrast, our interest is which combinations of events we observe in a disputed

issue. Further, unlike Poast, we are also interested in not just the combination of settlement attempts, but

the order in which they occur (i.e., permutations, not combinations). As a result, our data structure falls

more in line with Knox’s (2016) path analysis, which he uses to investigate walking routes in Baghdad.

TABLE 1. Reshaped H&A Dataset Excerpt Observed? Event 1 Event 2 Event 3 Event 4 Event 5

1 C M C N R

0 C N R

0 C N M C R

0 C N M N R

0 C N C N R

0 C

We include all observed event sequences in our dataset and pull a random sample of non-

observed event sequences. Our non-observed sequences represent the patterns we would see if C, M, N,

and R had a 25% chance of appearing in each position in the sequence—i.e., the events are all truly

independent of one another. Table 1 displays an arbitrary excerpt from our H&A dataset, making it clear

how we reshaped the original claim-directed dyad-year data into a single row containing the entire

sequence. Table 1’s example observed sequence (light shading) is the 1941-1947 Russo-Finnish dispute 27 We make several simplifying assumptions worth mentioning. First, we weight all stages equally, regardless of the stages’ length. This is for analytical tractability, and in future work, we intend to relax this assumption. Second, we make a homogenizing assumption for all militarized attempts and for all peaceful settlement attempts. Specifically, we treat all militarized attempts the same, regardless of their severity and the attempts’ number of participants. We similarly treat all peaceful attempts the same, regardless of whether the attempts were bilateral negotiations, non-binding third-party attempts (e.g., mediation), or binding third-party attempts (e.g., arbitration).

15

over Russia’s territorial gains from the Winter War, with Finland being the status quo challenger (H&A

dispute B23). After the challenge (C), the dispute militarizes (M, the Continuation War), then reverts

back to a challenge with no active settlement attempts (C). Negotiations (N) ensue, and the dispute is

ultimately resolved (R) in the 1947 Paris Peace Treaty. Our dataset reshape permits us to account for the

whole history of a dispute.

Table 1 also shows some of our randomly generated unobserved sequences, discussed further in

Appendix B. Importantly, any observed dispute sequence also has the possibility of being sampled again

as an unobserved sequence. Heuristically using Table 1’s CMCNR sequence helps illustrate why, via a

counterfactual. While we did observe a dispute with this event sequence, any dispute with a different

event sequence *of any length* in truth could have also conceivably had CMCNR as its sequence. To

investigate whether we see more or fewer disputes with CMCNR than pure randomness would dictate,

where sequence does not matter, we need to see how many times CMCNR would appear if all sequences

had an equal chance of appearing. Our unobserved sequences constitute this sample. We weight all

unobserved sequences equally using inverse probability weights, regardless of the sequence’s length or

whether it also appears in the observed sample. The strategy is most similar (but not identical) to

sampling random graph null models28 in network analysis, to generate an ensemble of possible networks

(Fosdick et al. 2018; Newman 2010).

Poast (2010, 410) recommends generating at least 2-5 unobserved sequences for every one

observed, but notes more 0s are preferable to fewer, if possible. We use an unobserved-to-observed ratio

of 20-1. We generate separate samples of unobserved sequences for both datasets (ICOW and H&A),

with the restrictions we discuss in Appendix B. When we add these sampled unobserved sequences to

our observed sequences, our final ICOW dataset expands to 4,202 observations and the H&A dataset to

8,712.29 Our dependent variable is coded 1 if the observation corresponds to one of our observed dispute-

28 These are synonymously called “configuration networks” by some (Fosdick et al. 2018). 29 Appendix C’s Figures 6 and 7 graphically display the distribution of our observed sequences’ lengths.

16

dyads and 0 otherwise. This means we have 399 1’s in our H&A dataset, corresponding to H&A’s 399

dispute-directed dyads, and 191 1’s in our ICOW dataset, corresponding to ICOW’s 191 dispute-dyads.

Our key independent variables derive from the possible sequence’s characteristics, similar to how

network models’ regressors can pertain to characteristics of the possible network (Cranmer and

Desmarais 2011). To test our hypothesis about first-order effects, our first independent variable is

MIL1ST, a dichotomous variable coded 1 if the sequence’s first settlement attempt is a MID and 0 if the

first settlement attempt is a negotiation or if no settlement attempt has yet occurred, for sequences with

length 1. Six (1 in H&A and 5 in ICOW) of our 587 observed sequences contain at least one settlement

attempt, meaning we do not introduce a sample selection problem by including this variable. We argue

the initial settlement attempt will affect how many subsequent militarizations or negotiations occur in the

sequence, Accordingly, we include two count variables—one counting the number of subsequent

militarizations (COUNTM) in the sequence, and the other counting the number of subsequent negotiations

(COUNTN).30 Finally, in order to properly assess the conditioning effects of the first settlement attempt’s

type on the subsequent sequence, we interact MIL1ST with COUNTM and MIL1ST with COUNTN.

III. Results

In Table 2, we report our generalized linear models (GLM) analysis of both the reshaped H&A

and ICOW data. We use a logit link with our GLM, and use an iterative reweighting process during

estimation to help with an otherwise-difficult optimization problem (McCullagh and Nelder 1989),

complements of our data’s sparseness and our probability weights. To prevent any sensitivity to a single

unobserved sequence draw, we devise a simple Monte Carlo simulation in which we pull 1000 samples of

unobserved sequences, add our observed sequences to each, run our GLM on each sample, and report the

average coefficient estimate across all the samples in Table 2.31 Recall our dependent variable is whether

30 We do not count the first settlement attempt when we define these variables, to prevent double-counting with MIL1ST. 31 With the difficulty of optimization, we do lose a few simulations because of nonconvergence (2 observations with H&A and 21 observations with ICOW).

17

or not the sequence is observed, meaning the model estimates indicate which factors affect the probability

of a sequence being observed. Signage has the same general meaning as any binary DV model: positive

signs mean higher covariate values increase the probability of observing a sequence; negative signs, a

decreased probability.

TABLE 2. MC Analysis of H&A and ICOW on MIL1ST Effects Huth & Allee Data ICOW Data

MILITARIZATION 1ST? -2.304** (-2.352, -2.256)

-6.551** (-6.629, -6.473)

# OF SUBSEQUENT NEGOTIATIONS

1.289** (1.266, 1.313)

1.321** (1.298,1.345)

# OF SUBSEQUENT MILITARIZATIONS

-3.288** (-3.339, -3.237)

-3.091** (-3.215, -2.967)

MIL1ST * SUBSQ. NEG. -0.691** (-0.723, -0.658)

0.544** (0.507, 0.581)

MIL1ST * SUBSQ. MIL. 1.686*** (1.485, 1.887)

1.385** (1.243, 1.527)

CONSTANT -6.684** (-6.708, -6.660)

-6.567** (-6.593, -6.541)

Note: *p < 0.05, **p < 0.01. Average coefficient value across 1000 simulations reported. 95% confidence intervals in parentheses.32

The results across both datasets are generally consistent with one another, in terms of significance

and direction. The exception is the interaction between the count of subsequent negotiations and the first

settlement being militarized (MIL1ST * SUBSQ. NEG), which switches signs. The negative sign on MIL1ST

shows we are unlikely to observe a sequence where the first settlement attempt is militarization and there

are no further settlement attempts in the dispute (i.e., the only transition would be the first one). In

addition, the positive sign on the COUNTN indicates a sequence is more likely to be observed as the

number of subsequent negotiations increases, provided the first settlement attempt was not militarization.

On the other hand, the negative sign COUNTM indicates sequences starting with negotiations are less

likely to be observed as the number of subsequent militarizations increases. This lends itself to our

hypothesis: disputes starting with negotiation tend to lead to more negotiation attempts rather than more

militarizations. These are the types of disputes we are more likely to observe.

32 For a closer look at the distribution of results from the simulations, Appendix C contains the k-density plots for each estimate.

18

Our hypothesis is more specifically about the conditioning effects of the first settlement attempt

type, which our interaction terms tap into.33 For both interaction terms, we find that the relationship is

statistically significant, on average, indicating differences exist in the distribution of observed sequences’

subsequent event types vs. the unobserved sequences. Further, this difference is conditional on the first

event. Beginning with subsequent militarizations, we find that if a dispute starts with militarization, we

are more likely to observe the sequence as the number of militarization attempts increases, in both

datasets.

Next, we move to subsequent negotiations’ effect in disputes beginning with a militarization.

Here, the two datasets’ results are radically different. With the ICOW dataset, if the first settlement

attempt was militarization, we are more likely to observe the sequence as the number of subsequent

negotiations increases. The H&A results indicate the exact opposite: if the dispute starts with

militarization, we are less likely to observe the sequence as the number of negotiations increases. The

difference’s source is yet unclear. The ICOW dataset has a relatively small number of disputes that begin

with a militarization (20 out of the 191 conflicts in the dataset), and 16 of the 20 have at least two

subsequent negotiation attempts. The H&A dataset has more balance to it with respect to both the

number of disputes starting with militarization and the distribution of those that have subsequent

negotiation attempts vs. subsequent militarization attempts.

IV. Conclusion

Does the type of first settlement attempt in a territorial dispute matter? We investigate this

question about sequencing by using a new approach, involving datasets filled of possible event sequences.

We then evaluate whether certain characteristics appear more frequently among observed sequences,

compared to a random sample of unobserved sequences. We find sequences are more likely to occur if

they begin with non-militarization. From there, we are more likely to see sequences with higher numbers

33 PolMeth 2018 note: predicted probability simulations still running.

19

of subsequent negotiation attempts, and are more likely to see sequences with fewer subsequent

militarizations.

Our results expand upon existing findings in a few ways. Existing work looks at the effect of

militarized and peaceful settlement attempts in the short term, counting the number of each event type

occurring within the last 10 or 15 years (Hensel 2001; Hensel et al. 2008). By contrast, we look at the

effect of past events from a different angle by examining whether the first settlement’s attempt type

matters, regardless of how long ago that settlement attempt occurred. Our results suggest the type of first

settlement attempt matters. These results are important because they give us some of the first evidence

regarding whether first-event effects exist in any way for territorial disputes between states.

Our approach also provides broader insight into the composition of territorial disputes’ event

sequences. From current work, we know more past settlement attempts (of either type) increase the

probability of more settlement attempts (again, of either type) in territorial disputes (Hensel et al. 2008).

However, current research cannot speak to what these increased or decreased probabilities mean for the

dispute’s overall sequence of events—do we see more militarizations compared to negotiations? Equal

numbers of both? We cannot address these questions about sequence composition because current

studies’ empirical tests are not constructed around the sequence. Instead, they are based around claim-

dyad-years, and the tests also do not assess whether the various event types’ antecedent effects are

different. Our analysis can speak to these types of questions by casting our unit of analysis as the

potential sequence, which permits us to investigate the likelihood of observing sequences with different

numbers of militarizations and negotiations. Formulating our unit of analysis in this way also means (a)

we have both observed and unobserved sequences (barking vs. non-barking dogs) and (b) our

observations are guaranteed to be independent of one another without even conditioning on our

covariates, permitting us to sidestep the current debate about dyad-years within the IR literature.

20

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Appendix A: On “History Mattering”

Defining what “history matters” means is an important first step. Current work tends to use

“history matters” informally, to broadly describe an argument’s gist before moving into specifics, with

these specifics varying across studies. We conceptualize history mattering on a continuum (Figure 2),

which we roughly divide into three segments for discussion purposes. We map Page’s (2006) discussion

of history mattering to our three segments, because Page’s formalization adds some much needed clarity.

FIGURE 2. History’s Effects

Anchoring the left end of the spectrum is a situation in which history is irrelevant. The classical

example is a memoryless process, such as flipping a fair coin multiple times or rolling fair dice multiple

times. Nothing about past events affects the probability of observing future ones, including the specific

times at which the past events occurred.

For the rest of Figure 2, history is relevant, but varies as to how it is relevant.35 In the middle of

the spectrum, we have situations where past events affect future ones in the short-term only. Page terms

these “outcome-dependent processes” (2006, 92). Markov processes are a good example: the previous

outcome (usually notated yt – 1) affects the next, future outcome (y). Time-homogenous processes also fall

here, in which the probability of one event following another is the same, regardless of event type or the

event’s position in the sequence (Page’s “stationarity,” 2006, 95).36 Additionally, all ergodic processes

are outcome-dependent, where it is possible (though not necessarily probable) for one event type to occur

35 Page calls this “history-dependence” (2006, 94). 36 Page’s distinction between independence and outcome-dependence is subtle. To amplify the differences: for independence, nothing about past events—both event type and timing—affect the probability of a current event. For something arbitrary, but concrete: Pr(yt = 1) = α + βxt, say. By contrast, for outcome-dependence, time (e.g.) can affect the event’s probability. Time homogeneity means time’s effect is constant for all t, but time nonetheless has a non-zero effect. It is equivalent to moving the intercept up or down by some constant (call this λ, where λ ≠ 0): Pr(yt = 1) = (α + λ) + βxt. A similar logic holds if past events matter—at minimum, the intercept will shift by some λ. Either way, the independence and outcome-dependence expressions are not equal.

No effect

Memoryless process, time independent

Long-Term Effect

Equilibrium Dependence, Path/Equil.-Phat

Dependence

Short-Term Effect

Outcome Dependence, Outcome-Phat Dep.

Intermediate- Term Effect

Distribution of Events within Sequence

25

sometime after any other event does. As Page succinctly states: outcome-dependent processes must be

time-homogeneous, have a finite set of possible event histories, and be ergodic (2006, 96), meaning all

history-as-short-term-effects processes must possess these characteristics, too.

Finally, anchoring the right hand of the spectrum, we have situations in which past events have a

longer-term influence on future ones. Making the distinction between short- and long-term effects is

difficult. We find it helpful to conceptualize the difference in econometric terms: short-term effects

amount to an estimator’s finite-sample properties, whereas long-term effects are more in line with an

estimator’s asymptotic properties. These situations are Page’s “equilibrium-dependent processes.”37

Here, if we could sample an infinite number of sequences, and we recorded the sequence’s last observed

event type, our samples from an equilibrium-dependent process would not all converge to the same event

type. As Page says, with equilibrium dependence, “the long-run distribution over outcomes depends on

past outcomes” (2006, 92). There are a number of ways past outcomes could exert this effect, with time-

inhomogeneous processes and non-ergodic processes being two large examples. In English: the

probability of eventually seeing some events after others is different (time-inhomogeneous), or it is

outright impossible to see some events after others (non-ergodic).

While we discuss our substantive example later in detail, our discussion already raises an

important point for territorial disputes. It is impossible for territorial disputes to exhibit equilibrium

dependence, if we take it to mean “the final event we observe in the sequence,” as Page does. Territorial

disputes constitute a challenge to the status quo. These challenges are, eventually, resolved. This

assumption underlies all formal models of interstate conflict, and also underlies all econometric models.

Ergo, all territorial dispute sequences will end in resolved, regardless of what happens along the way.

There is no long-term distribution over outcomes, because there is no distribution.

37 Page notes all equilibrium-dependent outcomes are automatically also outcome-dependent, since “if the equilibrium distribution over outcomes depends on the past, then so must the outcomes in individual time periods” (2006, 92). In our discussion, we have been implicitly using the terms in a more mutually exclusive way for explication purposes. Our outcome-dependent processes are those with Page’s outcome-dependence but not equilibrium-dependence, and “equilibrium-dependent processes” are those with both Page’s outcome- and equilibrium-dependence.

26

However, we can adopt a modified notion of “long-term effects,” which we term “intermediate-

term effects.” These effects fall somewhere between “short” and “long” on the spectrum.38 In these

cases, certain past events affect the number and type of events that subsequently occur within the process.

However, the past events still produce a unique long-term distribution over outcomes, distinguishing

intermediate-term effects from long-term effects. The refinement is important for us, since territorial

disputes could show signs of intermediate-term effects.

38 We have picked an arbitrary location in Figure 2 to insert intermediate-term effects for illustrative purposes.

27

Appendix B: Simulation Information

We claim we can test hypotheses about how first actions affect the probability of observing

certain sequences by modifying Poast’s (2010) k-ad structure, yielding a dataset congruent with Knox’s

(2016) definition of “path data.” However, do our empirical tests actually assess what we say? Can our

setup detect when the first event has an impact on the subsequent sequence and when it has no effect?

We run Monte Carlo simulations to demonstrate that our setup can indeed detect “first event” effects.

I. Simulation Details

A. The Procedure

To test, we need code that (a) produces an entire sequence of events, and (b) allows us to make

some sequences more likely than others, given the first event’s type. We generate our simulated data in

two parts, depicted in Figure 3.

FIGURE 3. Dataset for Simulations.

Observed Sequences (M&J code)

Candidate Paths: all permissible

Unobserved Sequences (IPW sample)

Candidate Paths: all permissible

NOTE: within each cell, same path may appear multiple times; same path may also appear across each cell.

1. GENERATE OBSERVED SEQUENCES

We modify Metzger and Jones’ (forthcoming) simulations for multistate survival models to our

application.39 Their Stata code generates an interpretable post-estimation quantity (transition

probabilities) by simulating how a group of subjects moves through a set of discrete stages across time.

39 For an introduction to multistate survival models, see Metzger and Jones (2016).

28

Utilizing Metzger and Jones’ code yields a dataset composed of event sequences for hypothetical disputed

issues. We treat these as our observedsequences.

To generate our observed sequences, Metzger and Jones’ code requires three things:

1. A list of all possible stages a subject could occupy, and the possible transitions between these

stages

2. The probability of each transition occurring

3. The times at which the transitions occur

Regarding the first requirement, “stages” in our application amount to the different events a disputed issue

can experience: Challenge (C), Negotiations (N), Military (M), or Resolved (R). For the third

requirement, the key for us is, first, to conceive of “time” as “position in the sequence,” and second, to

have an event (“transition,” in multistate parlance) occur at every (integer) time point. For instance, if a

disputed issue is in the Challenge stage to begin (first event in the sequence), it then must transition to

either N, M, or R for the second event in the sequence. If it transitions to, e.g., Negotiations for the

second event in the sequence, then the third event must be C, M, or R. This procedure continues—the

dispute is ongoing—until the dispute transitions into the Resolved stage, at which point it drops from our

dataset, satisfying our overarching simulation code criterion (a). If the dispute does not transition—e.g.,

we pull another Negotiations, and we are already in Negotiations—we treat the dispute as ongoing in the

right-censored sense, which also satisfies (a).

Above, we alluded to the fact that we have restrictions on which events can appear where in the

sequence, to mimic the constraints of our actual dataset. No dispute can have two of the same stage in a

row (by virtue of how the source data are coded). Additionally, Resolved is an absorbing state, and

therefore can only appear at the end of a sequence. We enforce these patterns when we specify our

transition probability matrix, which will define the probability of transitioning from one particular stage to

another, for each sequence position. For simplification purposes in the simulation, we treat this

probability as constant within the sequence for each transition: e.g., the probability of going from C → M

29

is the same regardless of whether the transition appears at the middle or end of the sequence (“time-

homogenous,” in the multistate literature, equivalent to an exponential duration model).

We use the transition probability matrix to enforce the two constraints we mentioned in the

previous paragraph. Additionally, we use the transition probability matrix to produce some sequences

being more likely than others, satisfying our overarching criterion (b). The exact structure of the

transition probability matrix will depend on the scenario of interest for that particular set of simulations;

we discuss the specifics below in Section II. Finally, the same sequence may appear multiple times in the

dataset, which is substantively equivalent to multiple disputes having the same sequence of events.

2. GENERATE UNOBSERVED SEQUENCES

Next, we must generate unobserved sequences. These represent sequences that our simulations in

I.1 could have generated with a non-zero probability, but did not. We term these “permissible”

sequences, more formally defined as sequences adhering to the transition rules we have defined—the

same event cannot be experienced twice in a row, and Resolved may only occur at the end of a sequence.

While our general approach is motivated by Poast’s (2010) k-ad setup, the logic we apply here is more

reminiscent of Knox (2016), since Poast is interested in combinations (of states, in his application), while

Knox is interested in permutations (e.g., of geographic parcels in the context of road construction, in one

of his applications), the same as us.

Regardless of whether we take Poast’s or Knox’s view, both procedures start in the same place:

recognizing there are many permissible sequences we can observe. The two views begin diverging when

they define the rules for selecting these sequences: combinations for Poast (2010) and permutations for

Knox (2016), as we mentioned. For those needing a refresher on the distinction between the two:40 as a

running toy example, imagine assigning students to a hypothetical project group, where the group’s size

can vary from one person to the entire class. Poast (2010) is interested in combinations: the number of

unique groups that can occur, given the set of objects. For the student groups, we are interested in the 40 Those in no need of a refresher can skip to the paragraph after next without an issue.

30

group’s final roster—specifically, the number of possible rosters (i.e., combinations) we could generate

from our set of students. It does not matter which student was assigned to the group first, second, third,

…, or last. Group membership is all that matters, which aligns with Poast’s substantive interest in

investigating why some groups of states form alliances and others do not.

By contrast, Knox (2016) is interested in permutations: not just whether the objects belong to a

certain group, but the order in which they were selected. Here, it does matter who entered the group first,

second, third, and so on. For our application, this is a crucially important distinction, since we are

arguing that settlement attempt order matters. Similarly for Knox, his applications focus on geographic

routes—for instance, the different routes a new proposed road could take to reach some destination.

Where the next portion of the road can be built depends on what portions have already been built, and

where these portions are located.

Either selection rule implies a large number of permissible sequences. However, the difference in

permissible sequences generated for combinations vs. permutations creates an even larger amount. IR

scholars are familiar with this difference already, as it amounts to the difference between undirected

dyads (combinations) and directed dyads (permutations). Our application also has an additional wrinkle,

since our disputes can experience the same stage multiple times, amounting to sampling elements with

replacement. In the project group example, sampling elements with replacement would hypothetically

mean being able to pick the same student again to assign to a group, even if s/he has already been

assigned a group.

To see the number of possible sequences this implies: imagine we have an observed sequence of

length 10, composed of three different types of potentially recurrent elements: A, B, and C. Let the only

restriction be that the same element cannot occur twice in a row. The number of permissible sequences

would be:

31

• Combinations

o Without replacement: 0 41

o With replacement: 66

• Permutations

o Without replacement: 0 41

o With replacement: 59049

If we refine our scenario by saying we have an observed sequence of at least length 10 with the same

candidate elements, we now have to keep a running tally of the above quantities for all lengths between 1

and L (=10). We must do the calculations for length 1 and three candidate elements, for length 2 and

three elements, all the way through length 10 and three elements. Our dispute application has the same

“at least length L” property. The resultant numbers:

• Combinations

o Without replacement: 7

o With replacement: 285

• Permutations

o Without replacement: 15

o With replacement: 88572

To put these numbers in context: some of our observed dispute sequences are 66 elements long. In short:

the number of permissible sequences quickly increases when using permutations instead of combinations,

and increases even further when using permutations with element replacement vs. no replacement.

Fortunately, we do not need to create an exhaustive list of all possible sequences. We can

sample, implement the appropriate adjustments, and estimate our model. Our interest in permutations is

important, because it dictates our sampling strategy. The strategy is most similar (but not identical) to

sampling random graph null models42 in network analysis, to generate an ensemble of possible networks

41 Since it is impossible to have three elements fill a sequence 10 elements long, if the elements cannot be replaced. 42 These are synonymously called “configuration networks” by some (Fosdick et al. 2018).

32

(Fosdick et al. 2018; Newman 2010). The key idea is all the sampled permissible sequences must have

equal weight in the final sample, regardless of the sequence’s length and regardless of whether or not it is

also in the observed sample (see Figure 3’s caption).43 Once we sample these permissible sequences, we

treat them as our “unobserved sequences.” We then use inverse probability weights to ensure each

unobserved sequence is equally weighted in the estimation sample, giving us our target uniform

distribution.44 For every 1 observed sequence, we pull 50 unobserved sequences.

We combine the “observed” and “unobserved” samples into one, producing our simulated dataset.

We run our logit model on this dataset, with the adjustment to ensure equal probability for all permissible

sequences (pweights in Stata). In total, we pull 1000 simulated datasets.

B. The Datasets

We run two different simulation scenarios:

1. “NO EFFECT” DATA

In the first set of simulations, we investigate whether we can detect null effects. This implies the

first event has no effect on the subsequent event sequence that transpires. In Figure 4, the Negotiation

and the Militarization transition probabilities—both to enter and to exit each respective stage—are

identical. It does not matter which of these events occurs first. In either case, a hypothetical disputed

issue will have a 45 percent chance of transitioning back to Challenge, a 45% chance of transitioning to

the other active settlement attempt stage, and a 10% chance of being Resolved, all for the next event in

43 Formally, the sample of permissible sequences must be uniformly distributed (Knox 2016, 12). 44 For instance, for our three element case, when we sample paths: Pr(A) = 1/3, Pr(AA) = 1/9, Pr(AAA) = 1/27. However, because the probability we select a given path is not identical, we need to weight the paths so they occur with equal frequency in our estimation sample. Here, the path weights would be 3, 9, and 27, respectively. In our sample from Section I.A.1, each observed sequence receives a weight of 1.

33

the sequence.45 The implication is either active settlement attempt (N or M) is equally as effective at

resolving disputes.

Figure 4. “No Effect” Stage Diagram

NOTE: arrows represent possible transitions. Numbers = transition’s probability of occurring. All outward transition probabilities from a stage must sum to 1.

2. “EFFECT” DATA

In our second simulation scenario, the first attempt matters. We could have chosen any number

of scenarios with this property. Arbitrarily, we selected a scenario in which subsequent negotiations are

very effective at resolution if the first settlement attempt was a negotiation, but are very ineffective if the

first settlement attempt was a militarization. We induce this property by permitting different exit and

entrance transitions for ‘subsequent’ settlement attempts, depending on whether the dispute experienced a

negotiation or militarization first.46 The stage diagram (Figure 5) is considerably more complex looking

as a result. A hypothetical disputed issue can transition into the top cluster of stages only if its first

settlement attempt is a negotiation. Likewise, a disputed issue can transition into the bottom cluster of

stages only if the first settlement attempt is a militarization.

45 We also ran a scenario in which all stages except Resolved were literally identical with a 45 percent chance of transitioning to the two other non-Resolved stages and a 10% chance of being Resolved. 46 Repeated event duration models use the same general logic (Box-Steffensmeier and Zorn 2002).

34

We induce “negotiations being effective if first attempt is negotiations” by giving “subsequent

negotiations” (top cluster) a 55 percent chance of resolving the dispute—the best resolution probability

within the entire stage diagram. We further reinforce this dynamic by (1) making the top cluster’s

“subsequent militarizations” extremely ineffective at resolving the dispute with a 0.5 percent chance, (2)

giving subsequent negotiations a 75 percent of occurring from the “challenge exists, but no active

settlement” (Challenge) stage following the first negotiation, and (3) making subsequent militarizations

unlikely to occur from the “challenge exists, but no active settlement” (Challenge) stage with a 2 percent

chance.

To create a situation in which “negotiations are ineffective if the first attempt is a militarization,”

we use a similar logic. We primarily generate this effect through the bottom cluster’s “subsequent

negotiations,” where we give these negotiations only a 5 percent chance of resolving the dispute. We also

give disputes an 85 percent chance of returning to the bottom cluster’s Challenge stage from subsequent

negotiations. As before, we keep subsequent militarization’s probability of resolving the dispute in the

bottom cluster somewhat low, with a 20 percent chance of resolution.

35

FIGURE 5. “Effect” Stage Diagram

NOTE: arrows represent possible transitions. Numbers = transition’s probability of occurring. All outward transition probabilities from a stage must sum to 1. Some 0% transitions drawn in for parallel’s sake.

36

II. Results

Preliminary results. For each simulation draw, we pull one sample of unobserved sequences, add in our

observed sequences, and then perform the GLM. The results are generally supportive, though some

anomalies exist. These preliminary results led us to estimating our main models with 1000 samples of

unobserved sequences, instead of just one. We are currently rerunning this appendix’s simulations, in

which we are taking 1000 samples of unobserved sequences and performing the same procedure as the

main text, for every one of the simulations’ 1000 draws. Since the simulations are being rerun, we report

the raw tables for the current, preliminary results.

For quick reference:

n

Scenario 1 {NE}: All fail

Scenario 2 {E}:

All fail

Scenario 3 {NE}:

Some RC

Scenario 4 {E}:

Some RC

Scenario 5 {E}:

𝛼11′ ≠ 𝛼22′ 𝛼11 = 𝛼21 𝛼12 = 𝛼22

Scenario 6 {E}:

𝛼11′ = 𝛼22′ 𝛼11 ≠ 𝛼21 𝛼12 ≠ 𝛼22

100 A D G J M P

250 B E H K N Q

500 C F I L O R

{NE}: no sequencing effect, {E}: effect, RC: right censoring (not all disputes are resolved).

37

b_cons -8.47752 -6.83406b_mil1st_countM -.82683 1.19851b_mil1st_countN -.994896 1.02852 b_countM -1.13617 .108846 b_countN -1.29181 .083033 b_mil1st -2.29867 1.07318 Variable 2.5 97.5

se_cons 1,000 154365.5 4881458 .1000388 1.54e+08se_mil1st_~M 1,000 40348.8 1275932 .1872361 4.03e+07 se_mil1st_~N 1,000 84371.41 2668049 .1954471 8.44e+07 se_countM 1,000 33308.85 1053313 .1107338 3.33e+07 se_countN 1,000 78728.37 2489603 .1221415 7.87e+07 se_mil1st 1,000 173533.8 5487601 .2422867 1.74e+08 b_cons 1,000 -175247.8 5541583 -1.75e+08 -5.80057 b_mil1st_c~M 1,000 31412.73 993353.4 -12.66597 3.14e+07b_mil1st_c~N 1,000 -77654.06 2455638 -7.77e+07 12.07184 b_countM 1,000 -42988.88 1359412 -4.30e+07 .4515872 b_countN 1,000 75227.39 2378917 -12.55105 7.52e+07 b_mil1st 1,000 -1.52e+08 4.82e+09 -1.52e+11 1.641317 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 1C.dta

b_cons -10.3016 -7.00347b_mil1st_countM -1.31566 2.01274b_mil1st_countN -1.35824 2.06423 b_countM -1.43062 .486057 b_countN -1.19161 .826352 b_mil1st -5.62541 1.6295 Variable 2.5 97.5

se_cons 1,000 .793164 .3973674 .1588702 2.574092se_mil1st_~M 1,000 .4831732 .2168608 .2709288 5.766223 se_mil1st_~N 1,000 .4991665 .1509414 .2549111 1.720489 se_countM 1,000 .2907988 .0818917 .1311678 .7917121 se_countN 1,000 .3057381 .0917186 .1548464 .7822834 se_mil1st 1,000 1.60871 .7667145 .3598524 11.17392 b_cons 1,000 -8.430769 .8792109 -10.88296 -6.042647 b_mil1st_c~M 1,000 .3051466 1.93396 -39.85816 14.90841b_mil1st_c~N 1,000 .3350881 1.316355 -16.75372 20.9205 b_countM 1,000 -.4681052 1.017535 -14.56909 1.109979 b_countN 1,000 -.2063687 .7412082 -12.64361 1.464594 b_mil1st 1,000 -2.033003 2.295644 -40.29963 3.498911 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 1B.dta

b_cons -8.47675 -6.49767b_mil1st_countM -.983904 1.98128b_mil1st_countN -1.44186 1.50967 b_countM -1.3558 .181037 b_countN -1.24762 .586657 b_mil1st -3.61812 .759726 Variable 2.5 97.5

se_cons 1,000 .5703896 .2572589 .1726248 1.895733se_mil1st_~M 1,000 .5300227 .1585412 .2841795 1.5642 se_mil1st_~N 1,000 .5146846 .1501815 .2996218 1.408258 se_countM 1,000 .3115888 .0840056 .1588624 1.141633 se_countN 1,000 .3246008 .0992975 .1739066 1.120298 se_mil1st 1,000 1.329909 .6088236 .4269401 4.567114 b_cons 1,000 -7.330759 .5094545 -9.472591 -5.597753 b_mil1st_c~M 1,000 .4166923 1.245703 -11.73167 13.33949b_mil1st_c~N 1,000 .0008223 1.075972 -12.82398 12.72982 b_countM 1,000 -.6181431 .8681766 -13.10058 .8449724 b_countN 1,000 -.3717743 .823497 -13.18264 1.163482 b_mil1st 1,000 -1.215235 1.155813 -4.917342 2.126432 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 1A.dta

b_cons -5.75956 -5.44842b_mil1st_countM -.142684 12.4833b_mil1st_countN .530395 2.88578 b_countM -13.186 -2.85753 b_countN -.47309 .548082 b_mil1st -14.7854 -8.40953 Variable 2.5 97.5

se_cons 1,000 473670.7 7171240 0 1.54e+08se_mil1st_~M 1,000 260158.2 3465336 0 6.29e+07 se_mil1st_~N 1,000 313044.6 4275687 0 8.44e+07 se_countM 1,000 174698.4 2634437 0 5.64e+07 se_countN 1,000 194789.1 3163504 0 7.87e+07 se_mil1st 1,000 824533.5 1.07e+07 0 1.74e+08 b_cons 1,000 -660655.5 9736265 -1.86e+08 -5.313262 b_mil1st_c~M 1,000 5189.888 1903162 -3.80e+07 4.34e+07b_mil1st_c~N 1,000 83385.95 1804729 -1.76e+07 4.14e+07 b_countM 1,000 -19317.02 472809.8 -1.43e+07 -2.54773 b_countN 1,000 -5171.765 115100.6 -2729108 .8676803 b_mil1st 1,000 -1.06e+09 1.98e+10 -5.40e+11 -7.478807 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 2F.dta

b_cons -5.7362 -5.43266b_mil1st_countM .167874 11.8126b_mil1st_countN .446348 2.82121 b_countM -13.3482 -2.84523 b_countN -.481537 .662197 b_mil1st -15.6297 -8.23692 Variable 2.5 97.5

se_cons 1,000 217787.4 3521983 0 7.42e+07se_mil1st_~M 1,000 248340 3580276 0 6.11e+07 se_mil1st_~N 1,000 302941.9 4531597 0 8.95e+07 se_countM 1,000 128349.6 2077886 0 4.39e+07 se_countN 1,000 128583.6 2041615 0 3.57e+07 se_mil1st 1,000 989462.7 1.54e+07 0 3.83e+08 b_cons 1,000 -6.25e+07 1.96e+09 -6.21e+10 -5.302769 b_mil1st_c~M 1,000 -15437.18 1182800 -1.89e+07 1.94e+07b_mil1st_c~N 1,000 82944.23 1171041 -623834.9 2.27e+07 b_countM 1,000 -86487.03 1481674 -3.67e+07 -2.56012 b_countN 1,000 234.8925 150779.9 -2213113 3947553 b_mil1st 1,000 -8.24e+08 1.73e+10 -4.08e+11 6.19e+10 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 2E.dta

b_cons -5.98412 -5.50706b_mil1st_countM -.429548 6.98633b_mil1st_countN .063608 3.00949 b_countM -5.81234 -2.47277 b_countN -.579497 1.23403 b_mil1st -13.9364 -7.08542 Variable 2.5 97.5

se_cons 1,000 .1662366 .0195411 .1265257 .2499784se_mil1st_~M 1,000 145661.1 2667302 .367864 5.47e+07 se_mil1st_~N 1,000 122881.7 2277186 .368121 4.88e+07 se_countM 1,000 .5628116 .238109 .1935169 3.041656 se_countN 1,000 .2927964 .0501384 .1791654 .5999196 se_mil1st 1,000 294540 6145611 1.003181 1.75e+08 b_cons 1,000 -5.744241 .1191333 -6.178115 -5.327908 b_mil1st_c~M 1,000 90116.03 2012278 -69.22684 4.80e+07b_mil1st_c~N 1,000 -71799.29 1727644 -5.05e+07 42.80052 b_countM 1,000 -3.790879 1.440149 -17.11044 -2.125337 b_countN 1,000 .3224966 .4449846 -1.09713 1.797908 b_mil1st 1,000 -909649.8 1.86e+07 -5.21e+08 -3.743343 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 2D.dta

38

b_cons -6.80387 -6.25369b_mil1st_countM -.404633 .985961b_mil1st_countN -.630204 .705479 b_countM -1.31319 -.538008 b_countN -1.15707 -.284675 b_mil1st -1.5965 -.039596 Variable 2.5 97.5

se_cons 1,000 .131617 .0140726 .0771134 .1799524se_mil1st_~M 1,000 .220328 .0351915 .1566223 .5705318 se_mil1st_~N 1,000 .2203636 .0362556 .15412 .6457834 se_countM 1,000 .1316848 .0332895 .0867402 .5485918 se_countN 1,000 .1454634 .035324 .0984577 .6294572 se_mil1st 1,000 .2907008 .0509725 .1818112 .5632181 b_cons 1,000 -6.551541 .1546231 -6.955937 -5.596667 b_mil1st_c~M 1,000 .2895882 1.162479 -11.94422 12.60279b_mil1st_c~N 1,000 .0414612 .928698 -12.2108 12.45277 b_countM 1,000 -.9203877 .8700735 -13.06039 -.317589 b_countN 1,000 -.7127364 .7108385 -13.12005 -.110299 b_mil1st 1,000 -.8014249 .3910471 -2.177459 .7183682 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 3I.dta

b_cons -7.04991 -6.26278b_mil1st_countM -.484946 1.11857b_mil1st_countN -1.07128 .472178 b_countM -1.39573 -.403548 b_countN -1.18789 -.099072 b_mil1st -.906643 .409488 Variable 2.5 97.5

se_cons 1,000 .1866572 .0303482 .1031682 .3095061se_mil1st_~M 1,000 .2840398 .3788107 .1882347 10.79715 se_mil1st_~N 1,000 .2874408 .3781642 .2010679 10.77744 se_countM 1,000 .168269 .041701 .1154181 .753407 se_countN 1,000 .1837363 .0443844 .1168219 .7643714 se_mil1st 1,000 .324543 .0465552 .2050553 .7700146 b_cons 1,000 -6.662757 .217275 -7.315224 -5.63065 b_mil1st_c~M 1,000 .3553072 1.758697 -16.05466 15.14052b_mil1st_c~N 1,000 -.3846347 2.415878 -63.41343 12.27359 b_countM 1,000 -.9538356 1.290714 -15.4908 -.0336685 b_countN 1,000 -.6565826 .9828061 -13.11342 .8346023 b_mil1st 1,000 -.2442075 .3483035 -1.600083 1.478713 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 3H.dta

b_cons -8.55925 -6.62273b_mil1st_countM -1.09829 1.54178b_mil1st_countN -1.27645 1.49769 b_countM -1.14096 .431951 b_countN -1.44243 .339701 b_mil1st -2.67406 1.18554 Variable 2.5 97.5

se_cons 1,000 .6133262 .261848 .1973595 2.093532se_mil1st_~M 1,000 .5332795 .3210685 .2881529 9.32818 se_mil1st_~N 1,000 .4807863 .3687836 .2929014 11.14712 se_countM 1,000 .346235 .3105202 .1603834 9.3198 se_countN 1,000 .3299459 .367161 .1712665 11.14233 se_mil1st 1,000 1.1137 .4636244 .4138927 3.309407 b_cons 1,000 -7.433745 .5020546 -9.243074 -5.739936 b_mil1st_c~M 1,000 .1141972 .9390552 -11.97438 2.726811b_mil1st_c~N 1,000 .0967442 1.277641 -12.61042 13.0296 b_countM 1,000 -.3745166 .4049767 -3.321607 .9838978 b_countN 1,000 -.6258224 1.121267 -13.64047 .8572422 b_mil1st 1,000 -.5331099 .9630727 -3.974131 2.388194 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 3G.dta

b_cons -5.73418 -5.42648b_mil1st_countM .600946 11.751b_mil1st_countN -.532657 2.07046 b_countM -13.2064 -3.10831 b_countN -.449898 .596064 b_mil1st -7.75795 -3.2142 Variable 2.5 97.5

se_cons 1,000 87290.57 2760368 0 8.73e+07se_mil1st_~M 1,000 34096.1 1078197 0 3.41e+07 se_mil1st_~N 1,000 60640.37 1917601 0 6.06e+07 se_countM 1,000 22586.12 714225.5 0 2.26e+07 se_countN 1,000 25648.73 811078.9 0 2.56e+07 se_mil1st 1,000 270011.5 8538466 0 2.70e+08 b_cons 1,000 -1.94e+08 6.14e+09 -1.94e+11 -5.293769 b_mil1st_c~M 1,000 -5982.914 532092.2 -1.45e+07 8517432b_mil1st_c~N 1,000 4503.794 348706.9 -5210446 9713209 b_countM 1,000 -19740.11 624100.4 -1.97e+07 -2.789423 b_countN 1,000 -5779.742 182774.6 -5779842 .9221462 b_mil1st 1,000 3.93e+07 7.85e+09 -1.55e+11 1.94e+11 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 4L.dta

b_cons -5.79676 -5.45115b_mil1st_countM .431628 11.8832b_mil1st_countN -.260093 2.14892 b_countM -13.7129 -2.88125 b_countN -.418265 .788679 b_mil1st -10.0785 -3.86414 Variable 2.5 97.5

se_cons 1,000 334645.8 5108374 .0829542 1.16e+08se_mil1st_~M 1,000 312756.7 3879864 .2906136 6.11e+07 se_mil1st_~N 1,000 332832 4165176 .2438621 8.29e+07 se_countM 1,000 176490.8 2555302 .1247854 4.39e+07 se_countN 1,000 155650.5 2224350 .1475082 3.57e+07 se_mil1st 1,000 770650.2 9737164 .4477373 1.53e+08 b_cons 1,000 -4.96e+07 1.55e+09 -4.90e+10 -5.319007 b_mil1st_c~M 1,000 -72864.79 1969777 -5.10e+07 1.65e+07b_mil1st_c~N 1,000 -34885.15 3094505 -5.59e+07 4.61e+07 b_countM 1,000 -104878.5 1760933 -4.52e+07 -2.584064 b_countN 1,000 48123.11 1378593 -6014976 4.18e+07 b_mil1st 1,000 -9.35e+08 1.65e+10 -3.68e+11 4.88e+10 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 4K.dta

b_cons -6.33533 -5.66363b_mil1st_countM -.338176 7.16154b_mil1st_countN -.000906 2.97531 b_countM -6.43182 -2.32511 b_countN -.429884 1.61754 b_mil1st -16.4283 -7.23349 Variable 2.5 97.5

se_cons 1,000 .2172257 .0326971 0 .3216265se_mil1st_~M 1,000 305065.7 3792637 0 7.32e+07 se_mil1st_~N 1,000 229716.4 2790005 0 4.69e+07 se_countM 1,000 .5867022 .263218 0 3.379527 se_countN 1,000 .3172005 .0523422 0 .6621652 se_mil1st 1,000 987533.3 1.30e+07 0 2.63e+08 b_cons 1,000 -6.010116 .1721784 -6.636388 -5.434521 b_mil1st_c~M 1,000 -272948.4 7867275 -1.76e+08 9.01e+07b_mil1st_c~N 1,000 -73597.88 2471859 -4.97e+07 3.56e+07 b_countM 1,000 -3.928799 1.760466 -20.93523 -1.912721 b_countN 1,000 .6051478 .506186 -1.01494 2.18416 b_mil1st 1,000 -6.94e+07 1.86e+09 -5.85e+10 -4.960928 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 4J.dta

39

b_cons -7.67982 -6.85741b_mil1st_countM -.168351 1.65389b_mil1st_countN -1.15083 .528891 b_countM -1.41853 -.483131 b_countN -1.05307 -.003124 b_mil1st -1.44338 .976349 Variable 2.5 97.5

se_cons 1,000 70176.41 2219166 .0828259 7.02e+07se_mil1st_~M 1,000 44052.54 1393041 .1830145 4.41e+07 se_mil1st_~N 1,000 41733.51 1319707 .2094438 4.17e+07 se_countM 1,000 37232.7 1177382 .1105353 3.72e+07 se_countN 1,000 25852.87 817519.7 .1363067 2.59e+07 se_mil1st 1,000 120262.7 3803026 .2174176 1.20e+08 b_cons 1,000 -1.10e+09 3.47e+10 -1.10e+12 -6.067601 b_mil1st_c~M 1,000 7962.871 251784.8 -12.59516 7962135b_mil1st_c~N 1,000 8264.462 261355.6 -14.57993 8264790 b_countM 1,000 -8273.291 261593.6 -8272317 -.2121927 b_countN 1,000 -8927.785 282305.6 -8927288 .4081808 b_mil1st 1,000 1.10e+09 3.47e+10 -2.322013 1.10e+12 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 5O.dta

b_cons -7.84171 -6.90201b_mil1st_countM -.647585 1.36082b_mil1st_countN -.85667 .934629 b_countM -1.17784 -.142072 b_countN -1.40808 -.261086 b_mil1st -.972452 1.27028 Variable 2.5 97.5

se_cons 1,000 .2878795 .0602333 .1374917 .583928se_mil1st_~M 1,000 .3510761 .2378272 .2135975 4.984414 se_mil1st_~N 1,000 .3629423 .2937582 .2385885 6.247744 se_countM 1,000 .2340513 .2427688 .1360415 4.981077 se_countN 1,000 .2534018 .2984323 .143236 6.242309 se_mil1st 1,000 .5078932 .1321038 .266895 2.306129 b_cons 1,000 -7.398633 .2531086 -8.19561 -6.09995 b_mil1st_c~M 1,000 .3238156 2.392681 -58.68581 14.23277b_mil1st_c~N 1,000 .1069933 1.486717 -16.6461 23.78741 b_countM 1,000 -.7065008 1.188263 -14.3171 .2371342 b_countN 1,000 -.8557307 1.11689 -12.73919 .6362683 b_mil1st 1,000 .2327299 1.477693 -42.9306 2.438129 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 5N.dta

b_cons -7.61831 -6.56622b_mil1st_countM -.696925 1.24429b_mil1st_countN -1.25803 .737274 b_countM -1.42569 -.238602 b_countN -1.22428 .230573 b_mil1st -.54288 1.24188 Variable 2.5 97.5

se_cons 1,000 .4469984 .1270891 .2189933 1.147968se_mil1st_~M 1,000 .4890964 .2144847 .2708266 3.963684 se_mil1st_~N 1,000 .5370575 .2184398 .2895378 3.933446 se_countM 1,000 .3716705 .2223274 .1650042 3.95294 se_countN 1,000 .419702 .2285743 .1812189 3.923888 se_mil1st 1,000 .6115625 .1306678 .3368556 1.206746 b_cons 1,000 -7.073872 .274346 -8.044979 -5.869841 b_mil1st_c~M 1,000 .262112 1.118514 -12.24103 12.82191b_mil1st_c~N 1,000 -.2303006 1.114216 -12.59398 12.12381 b_countM 1,000 -.8438735 .8086183 -12.7868 .4042902 b_countN 1,000 -.534162 .9894831 -12.76426 .6741514 b_mil1st 1,000 .378608 .440522 -1.240825 1.844901 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 5M.dta

b_cons -6.31532 -5.97548b_mil1st_countM .752188 12.2392b_mil1st_countN .069122 2.20054 b_countM -12.9045 -3.00946 b_countN -.427628 .653192 b_mil1st -9.85806 -4.607 Variable 2.5 97.5

se_cons 1,000 218970.9 5289900 .0729819 1.54e+08se_mil1st_~M 1,000 88864.42 1994430 .2704224 4.85e+07 se_mil1st_~N 1,000 136783.7 3139592 .1837999 8.44e+07 se_countM 1,000 74876.04 1683563 .1406148 4.16e+07 se_countN 1,000 111299.8 2693498 .1089782 7.87e+07 se_mil1st 1,000 285772.3 6532308 .4455786 1.74e+08 b_cons 1,000 -212688.5 4761896 -1.13e+08 -5.838385 b_mil1st_c~M 1,000 -4207.323 161864.1 -5048677 838056.3b_mil1st_c~N 1,000 24758.74 559852.6 -1.019685 1.43e+07 b_countM 1,000 -37412.31 859198.9 -2.31e+07 -2.679799 b_countN 1,000 5827.423 184745.9 -14856.61 5842145 b_mil1st 1,000 -8.66e+07 2.72e+09 -8.60e+10 -2.433033 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 6R.dta

b_cons -6.3596 -6.0436b_mil1st_countM -.115103 11.8107b_mil1st_countN .351044 2.686 b_countM -13.0392 -2.63476 b_countN -.456608 .67579 b_mil1st -11.0168 -5.75671 Variable 2.5 97.5

se_cons 1,000 188918 5974109 0 1.89e+08se_mil1st_~M 1,000 66839.04 2113616 0 6.68e+07 se_mil1st_~N 1,000 87271.2 2759744 0 8.73e+07 se_countM 1,000 33705.26 1065841 0 3.37e+07 se_countN 1,000 52859.23 1671549 0 5.29e+07 se_mil1st 1,000 217223.1 6869154 0 2.17e+08 b_cons 1,000 -175820.6 5559739 -1.76e+08 -5.898764 b_mil1st_c~M 1,000 -60472.1 1588987 -4.89e+07 15.65624b_mil1st_c~N 1,000 146950.7 4354706 -1.06373 1.37e+08 b_countM 1,000 24625.64 778855.8 -16.00141 2.46e+07 b_countN 1,000 -15394.11 486808.4 -1.54e+07 1.055203 b_mil1st 1,000 -6.41e+08 2.02e+10 -6.38e+11 -2.152506 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 6Q.dta

b_cons -6.3924 -5.87703b_mil1st_countM 1.15369 12.2752b_mil1st_countN -.401224 2.22276 b_countM -12.8391 -3.02791 b_countN -.585265 1.35797 b_mil1st -11.6051 -5.29028 Variable 2.5 97.5

se_cons 1,000 .208062 .0281229 0 .3118798se_mil1st_~M 1,000 .9324937 .3431866 0 3.48916 se_mil1st_~N 1,000 .4876685 .3693931 0 11.3804 se_countM 1,000 .7311259 .3012885 0 3.068928 se_countN 1,000 .3301804 .0567047 0 .5536048 se_mil1st 1,000 1.423053 1.177035 0 34.32603 b_cons 1,000 -6.1257 .1251932 -6.577533 -5.745668 b_mil1st_c~M 1,000 -33071.84 1030448 -3.26e+07 16.6698b_mil1st_c~N 1,000 63141.36 1991730 -1.198864 6.30e+07 b_countM 1,000 -4.607354 1.862561 -16.98247 -2.655432 b_countN 1,000 .3807663 .4739997 -1.11275 1.837542 b_mil1st 1,000 -1.68e+08 5.25e+09 -1.66e+11 -3.714605 Variable Obs Mean Std. Dev. Min Max

output - post, Scenario 6P.dta

40

Appendix C: Observed Sequences - Histograms

FIGURE 6. H&A: Frequency Histogram of Sequence Lengths

FIGURE 7. ICOW: Frequency Histogram of Sequence Lengths

41

FIGURE 8. H&A: Distribution of Beta Estimates from 1,000 MC Simulations

FIGURE 9. ICOW: Distribution of Beta Estimates from 1,000 MC Simulations

42

Appendix D: Empirical Support for Criterion 2

Empirically, we do not know whether the second criterion has support at all. Extant work related

to sequencing effects does not empirically assess whether militarized settlement attempts have

heterogeneous antecedent effects. The same is true for peaceful settlement attempts’ effects. The

empirical tests in these papers typically use two count variables—one of past militarization attempts, and

one of past peaceful settlement attempts—as right-hand side variables in a logit or probit regression

whose DV is whether a militarization attempt begins in a claim-dyad-year.47 Putting aside our earlier

point about the conditional independence assumption inherent in this setup, it is important to recognize

what these models assess: Criterion #1 only, by default. The count variables’ coefficients tell us whether

a greater number of past militarizations affects the probability of seeing another militarization in a claim-

dyad-year (Δ11 = 0?, roughly speaking), and whether a greater number of past peaceful settlement

attempts also affects the probability of another militarization in a claim-dyad-year (Δ21 = 0?, again

roughly speaking).

To assess Criterion #2 (heterogeneous antecedents), we would need to take a further step, and

check whether the number of past militarizations and the number of past peaceful settlement attempts

have the same effect on the probability of another militarization (amounting to α11 = α21). A Wald test can

assess this statement by testing if the two count variables’ coefficients are equal. Importantly, we do not

usually perform this test, even though we could with our standard logit/probit model.

47 We use militarization (k1) as our running example throughout the rest of this paragraph, for simplification purposes. Everything we say applies equally to peaceful settlement attempts (k2).

43

Appendix E: Converting Datasets into Sequences

We convert H&A’s dataset into sequence form using the procedure described by Jones and

Metzger (2018, Supplemental Appendix A). Our procedure for ICOW is similar, but has a few additional

wrinkles:

1. The ICOW dataset includes variables denoting whether the settlement attempt resolves the entire

claim-dyad.48 We use this information to determine whether an extra C should be inserted

between the last settlement attempt and resolution. By contrast, the H&A dataset has no such

variable. There, we use the settlement attempt’s and claim’s ending month to make the

determination. We add a C if the two ending months are not the same.

2. If a settlement attempt begins while another is ongoing (see fn. 26), and the attempts are different

types, we record both attempts without an intervening C. For instance: a militarization starting in

January, and is still ongoing in March when a negotiation begins, would be recorded as M → N.

If the attempts are of the same type, we only record one of them.

48 We use clmendall for peaceful attempts and midendiss for militarized attempts.

44

Appendix F: Proof of Criterion #2’s Sufficiency for #1 when K = 2

We can prove the above by contradiction. Intuitively, #2 is sufficient for #1 because there are

only two possible events. Therefore, changes in one event’s probability necessarily mean changes in the

other event’s probability. We reproduce Figure 1 below, for reference.

αmn = probability of observing a transition from km to kn, where m = earlier event, n = later event.

In order for #2 to be met, but not #1, it would mean

Criterion #1 Criterion #2 𝛼11′ 0 = 𝛼11

AND 𝛼22′ 0 = 𝛼22

AND 𝛼11 ≠ 𝛼21

OR 𝛼12 ≠ 𝛼22

At the same time, three constraints must be true: �𝛼11′ 0 + 𝛼22′ 0 = 1� ∧ (𝛼11 + 𝛼12 = 1) ∧ (𝛼21 + 𝛼22 =

1), since all an event’s exiting probabilities must sum to 1, as must the events’ initial probabilities of

occurrence.

Begin from the premise that 𝛼11 ≠ 𝛼21 is true. If we substitute terms, this would mean 𝛼11′ 0 ≠

𝛼21. We also know 𝛼21 = 1 − 𝛼22, yielding 𝛼11′ 0 ≠ 1 − 𝛼22. If we exploit 𝛼22′

0 = 𝛼22 and substitute

again and rearrange, we obtain 𝛼11′ 0 + 𝛼22′ 0 ≠ 1. However, we know 𝛼11′ 0 + 𝛼22′ 0 = 1—our

contradiction.49 One of the three constraints being false is enough to render the entire constraint

statement false, since ANDs are involved. It thus cannot be true that #2 is met, but #1 is not.

49 If we use 𝛼12 ≠ 𝛼22’s truth as our starting point, we obtain the same contradiction by substituting in for 𝛼12.

45

When K > 2, the situation becomes different. One event’s probability changing does not

automatically guarantee that all other events’ probabilities also change, which was the crux of the K = 2

proof’s intuition. For example, for K = 3, we get an additional AND condition from k3 for Criterion #1

(three total), four additional ORs for Criterion #2 (3 events * 2 k¬i events for every i = 6 total), and an

additional constraint also stemming from k3 (giving us four, in total). If we work through the same

condition we did in K = 2 (𝛼11 ≠ 𝛼21), with the requisite substitutions and simplifications, we get

𝛼11′ 0 + 𝛼22′ 0 + 𝛼23 ≠ 1. If we substitute in for 𝛼11′ 0 using the 𝛼11′ 0 + 𝛼22′ 0 + 𝛼33′ 0 ≠ 1 constraint and

simplify further, we obtain 𝛼23 − 𝛼33′ 0 ≠ 0.

𝛼23 − 𝛼33′ 0 ≠ 0 may be false or may be true. We cannot say one way or the other, with the

constraints and conditions we do have. To see why: 𝛼23 ≠ 𝛼33 is one of the four new OR conditions for

Criterion #2. If true, it implies 𝛼23 ≠ 𝛼33′ 0, making the derived statement above true. However, 𝛼23 ≠

𝛼33 need not be true for Criterion #2 to be met, complements of the logical OR. We need only one of #2’s

six conditions to be violated, which we have via our starting premise of 𝛼11 ≠ 𝛼21. If 𝛼23 = 𝛼33, then

the derived statement is false, and we would have our proof by contradiction.