Alliances and Conflict, or Conflict and Alliances? Appraising the Causal Effect of Alliances on Conflict

Benjamin Campbell

REVIEW 3 major objections 4 minor 9 references

Alliances and Conflict, or Conflict and Alliances? Appraising the Causal Effect of Alliances on Conflict

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper claims that once alliance formation is modeled jointly with conflict, a target's relevant defensive alliance commitment neither deters nor provokes a challenger, with an estimated average treatment effect of -0.016 (95% CI…

desk verdict A serious, readable empirical challenge to the alliance-deterrence consensus, but the null result leans entirely on an unvalidated infant-mortality exclusion restriction and a predictive comparison that does not isolate the endogeneity correction. read the letter →

arxiv 1908.07100 v1 pith:SMWJZ5GB submitted 2019-08-19 stat.AP stat.ML

Benjamin Campbell This is my paper · ORCID

classification stat.APstat.ML

keywords militaryalliancesdeterrenceendogeneitygeneralizedjointregressionmodelsmilitarizedinterstatedisputesinstrumentalvariablescausalinferenceallianceformation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Military alliances are usually studied as if they were randomly assigned, but states form alliances because they expect conflict. This paper re-estimates the effect of a target's defensive alliance commitments on whether a challenger initiates a militarized interstate dispute (a threat, display, or use of force), allowing alliance formation and conflict to be driven by the same unobserved security concerns. When alliance formation is modeled jointly with conflict, the targeted state's defensive commitment has essentially no effect: an average treatment effect of -0.016 with a 95% interval crossing zero. The paper argues that this null means alliances neither deter nor provoke aggression, and that conventional estimates showing deterrence mostly captured selection into alliances. The finding matters because it challenges a central premise of deterrence theory and redirects research toward the conditions under which alliances might work.

What carries the argument

The carrying mechanism is the generalized joint regression model (GJRM): a recursive bivariate probit in which the first equation predicts whether the target has a relevant defensive commitment and the second predicts whether a challenger initiates a dispute. A copula—a function linking the two equations' unobserved errors, chosen here as the 180-degree rotated Clayton—lets the same unmeasured factors influence both alliance formation and conflict, which is the channel that the paper says accounts for the apparent deterrent effect. The alliance equation also includes two instruments: the target's infant mortality rate and its one-year change, both used to satisfy the exclusion restriction.

What would settle it

A credible demonstration that infant mortality or its short-run change has a direct effect on interstate dispute initiation—through, say, state weakness or diversionary incentives—after conditioning on GDP per capita and civil conflict would break the exclusion restriction and leave the null average treatment effect unidentified.

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Extended reading notes

Core claim

The paper's central claim is that, once the endogeneity of alliance formation is accounted for, a target's relevant defensive alliance commitment neither deters nor provokes a challenger. In a bivariate recursive probit model estimated on directed-dyad years 1816-2000, the average treatment effect of the defensive commitment on dispute initiation is -0.016 with a 95% credible interval [-0.053, 0.016], materially smaller than the roughly 20% reduction reported by prior exogenous models. The paper attributes the difference to unobserved confounders—offensive intention, ally reliability, and burden sharing—that make states with high conflict risk more likely to form alliances, so apparent deterrence is selection. It interprets the null as the causal effect of alliance commitments once these confounders are accounted for.

Load-bearing premise

The result stands or falls on the assumption that a target's infant mortality rate affects whether it is attacked only by changing its alliance choices, after taking GDP per capita and civil conflict into account.

Editorial extensions

If this is right

The conventional finding that defensive alliances cut the probability of being attacked by about 20 percent is not reproduced when alliance formation is endogenous; the estimated effect is 1.6 percent and statistically indistinguishable from zero.
The null result is robust across copula choices: 18 of 19 specifications yield null or provocation effects, and only the poorly fitting Student-t copula recovers deterrence.
Models that endogenize alliance formation predict militarized disputes better than the exogenous benchmark, improving out-of-sample precision-recall by 57.4 percent.
Alliance formation and conflict initiation should be modeled as one joint process, since conflict expectations shape alliance choices and alliances may then shape conflict.
Research should shift from asking whether alliances deter to identifying moderating conditions under which particular commitments deter or provoke.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the null is correct, past correlational evidence for deterrence mostly documented selection: threatened states form alliances, and those same threats predict attack; policy claims that alliances reliably buy security need re-examination.
The exclusion-restriction strategy could be stress-tested with different instruments tapping public-goods pressure, such as disease burden or schooling enrollment; a second independent instrument producing the same null would strengthen the case.
A null average effect does not mean alliances are useless; their benefits may appear in non-conflict domains such as autonomy, domestic survival, or postwar management, which are not measured here.
The copula results imply a common unobserved factor raises both alliance formation and conflict; identifying that factor empirically could replace instrumental-variable reliance with direct measurement.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The thing to know: this is a serious, well-written attempt to endogenize alliance formation in models of interstate conflict, and if the identification held it would overturn a well-known result. But the identifying assumption is doing essentially all the work, and the paper does not validate it. I would still send it out—the field should confront this—but I would not take the null as established.

What is actually new is the application: a recursive bivariate probit GJRM where a target's relevant defensive alliance commitment is endogenous, instrumented by the target's infant mortality rate and its year-to-year change, and the conflict equation then estimates an ATE on challenger dispute initiation. The paper engages both the alliance-formation and alliance-conflict literatures, includes controls from both strands, checks every copula in the GJRM package, and reports an ATE of -0.016 with a 95% interval [-0.053, 0.016]. That is a dramatically different conclusion from Johnson and Leeds's 20% deterrent effect. The theoretical story—unobserved threat, ally reliability, and burden sharing drive both alliance formation and attack—is coherent, and the null is not imposed by construction. Citation-wise, it engages the main exchange fairly and credits Braumoeller et al. for the method.

The soft spot, and it is load-bearing, is the exclusion restriction in Section 4.1. The paper argues that infant mortality should influence whether A attacks B only through alliance formation, civil conflict, or capabilities, with civil conflict history and GDP per capita conditioned out. But infant mortality is a broad proxy for state fragility, public health, and demographic stress; a fragile target is plausibly a more attractive target for reasons not captured by GDP and civil conflict history. And those two conditioning variables are themselves potentially endogenous to conflict. The paper's stated defense—'I find no published evidence of a direct relationship'—is an appeal to absence of documentation, not a design-based justification. No amount of copula flexibility or out-of-sample PR-AUC fixes a failed exclusion restriction.

The second issue is the predictive improvement claim. The endogenous model includes extra covariates and a different functional form, so the PR-AUC gain over the Johnson and Leeds baseline does not isolate the effect of endogenizing alliances. A same-covariate non-endogenous baseline would be needed. Minor points: no replication code or data is provided, and the instruments are asserted to be strong in a footnote without reported test statistics.

Who is this for: IR scholars working on alliances and deterrence, and applied methodologists interested in binary endogenous treatments. It deserves a serious referee, but the referee should push hard on the instruments and on the model-comparison design. My recommendation: peer review, with the expectation of major revisions or a substantial weakening of the causal claims.

Referee Report

3 major / 4 minor

Summary. The paper challenges the conventional finding that defensive alliances deter militarized conflict. The author argues that alliance formation is endogenous to the security environment and conflict expectations, and models this with a recursive bivariate probit 'generalized joint regression model' using the target's infant mortality rate and its change as instruments for the target's relevant defensive alliance commitment. The central empirical result is an average treatment effect of -0.016 with a 95% credible interval [-0.053, 0.016], which is interpreted as evidence that alliances neither deter nor provoke aggression. The paper also reports that the joint model outperforms a standard Johnson-Leeds logistic regression in precision-recall AUC and that the null result is robust to alternative copula specifications.

Significance. If the causal identification were credible, the paper would be a significant challenge to a prominent finding in international relations: that explicitly relevant defensive commitments deter attack. The manuscript has genuine strengths: it takes the endogeneity of alliances seriously, uses instruments borrowed from prior published work, reports an ATE with a credible interval, and includes a sensitivity analysis over nineteen copulas. The out-of-sample predictive comparison is useful descriptive evidence. However, the central claim rests on an untestable exclusion restriction, and the predictive comparison does not isolate the role of endogenizing alliances. The significance of the paper is therefore conditional on whether the identification strategy can be defended more convincingly or the claims appropriately weakened.

major comments (3)

[Section 4.1, 'Modeling Alliance Formation'] The identification of the alliance ATE rests entirely on the exclusion restriction that the target's infant mortality rate and its change affect the challenger's conflict initiation only through the target's defensive alliance commitments, after conditioning on target GDP per capita and civil conflict history. The support offered in the text — 'I find no published evidence of a direct relationship' — is an appeal to an absence of documentation rather than a design-based or statistical justification. Infant mortality is a broad proxy for state capacity, public health, demographic structure, and fragility; these dimensions are not fully blocked by GDP per capita and civil conflict history, and those two controls are themselves potentially endogenous. If infant mortality directly raises the probability that a challenger attacks a fragile target while also increasing the target's propensity to ally, the estimated alliance coefficient is contaminated by a direct instrument-to-outcome path. Because the recursive bivariate probit is identified by these instruments alone, this concern is load-bearing for the null ATE.
[Section 5, 'Predictive performance' and Figure 4] The claim that endogenizing alliances improves predictive performance is not supported by the reported comparison. The Johnson and Leeds (2011) baseline and the GJRM differ in their covariate sets: the GJRM adds target GDP per capita, target civil-conflict history, challenger trade dependence, and a peace-years spline, among other differences. The 57–59% PR-AUC improvement in Figure 4 therefore cannot be attributed to modeling alliance endogeneity. The conclusion in Section 6 that 'endogenizing... improves our ability to predict' requires either a nested comparison with identical covariate sets or a decomposition of the performance gain.
[Section 5, 'Average treatment effect' and Section 6] The conclusion that alliances 'neither deter nor provoke aggression' is stronger than the evidence. The estimated ATE is -0.016 with 95% credible interval [-0.053, 0.016]; a null result with this interval cannot establish equivalence or the absence of substantively meaningful effects. The paper itself notes in Section 5 that the result is 'not definitive,' but the abstract and conclusion use language of a definitive null. Equivalence testing, a sensitivity analysis to unobserved confounding, or bounds on plausible effect sizes would be needed to support the strong conclusion.

minor comments (4)

[Section 4.1] The phrase 'Infant morality rate' should read 'infant mortality rate.'
[Section 5, 'Copula selection'] The definitions of precision and recall are garbled: precision is TP/(TP+FP) and recall is TP/(TP+FN), but the text appears to reverse or confuse these quantities. This should be corrected because the PR-AUC comparisons rely on these definitions.
[Section 4.1 and Section 5] The instruments are described as strong based on chi-square and likelihood-ratio tests, but no first-stage coefficient table is presented. Including a table with the first-stage estimates and standard errors would clarify the strength and sign of the instrument-alliance relationship.
[Section 5] The predictive comparison between the Johnson-Leeds model and the GJRM may also be affected by differences in estimation samples (e.g., due to missing GDP or trade data). The paper should report the number of observations used in each model and any sample restrictions.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the null ATE is estimated rather than imposed, and no load-bearing claim reduces to its own inputs.

full rationale

The paper's central claim is that a target's relevant defensive alliance commitment has no average causal effect on challenger dispute initiation once alliance formation is treated as endogenous. The claim is not built into the model: the conflict equation includes the defensive-commitment variable as a freely estimated regressor, and the reported ATE of -0.016 with 95% interval [-0.053, 0.016] is a posterior simulation quantity, not a constrained zero. The identifying instruments (infant mortality and its change) are taken from Kimball (2010) and used only in the alliance-formation equation; whether they satisfy the exclusion restriction is an identifying assumption, not a definitional identity. The data-driven copula selection is performed on out-of-sample PR-AUC, but the null result is shown to hold across nearly all of the 19 copulas examined (Figures 5 and 6), so the central inference does not depend on the selected Clayton rotation. The only self-citation, Campbell, Cranmer and Desmarais (2018), is used to justify PR-AUC as a metric for rare events and is not load-bearing for the causal estimate. There is no equation in which the outcome is defined in terms of the treatment, no fitted parameter renamed as a prediction, and no uniqueness claim imported from the author's own prior work. The derivation chain is therefore self-contained in the relevant sense; concerns about instrument validity belong to a robustness or exclusion-restriction critique, not to circularity.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The ledger contains no hand-chosen numeric constants; all regression coefficients are estimated from data. The load-bearing assumptions are the exclusion restriction and the copula error structure, both domain assumptions rather than standard mathematical axioms.

assumptions (5)

domain assumption The infant mortality instruments satisfy the exclusion restriction: after conditioning on target GDP per capita and civil conflict history, they affect conflict only through alliance formation.
Invoked in Section 4.1. No direct falsifiable evidence is provided; the paper notes the absence of published findings of a direct relationship.
domain assumption Unobserved confounders linking alliance formation and conflict are captured by the copula dependence between the two equations' errors.
Section 3.3 and Section 5 rely on this for identification of the null ATE. The copula family is selected by out-of-sample PR-AUC, which does not verify the structural confounder story.
domain assumption The bivariate recursive probit with the selected copula correctly specifies the joint distribution of alliance formation and conflict.
Standard statistical assumption for consistency of the GJRM estimator, assumed throughout Sections 4 and 5.
domain assumption The directed-dyad-year sample is a census, so there is no sample selection bias.
Stated in footnote 2. Needed to interpret the model as estimating causal effects for the full population of directed dyads.
domain assumption Dyad-year observations are independent; alliances or conflicts in one dyad do not directly alter the treatment or outcome in another dyad.
Not discussed in the paper but required by the likelihood used in the GJRM. Violations (network spillovers) could bias the ATE.

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Cite this review

Pith. "Pith review of Alliances and Conflict, or Conflict and Alliances? Appraising the Causal Effect of Alliances on Conflict." pith.science (2026). https://pith.science/paper/SMWJZ5GB

@misc{pith2026190807100,
  author       = {Pith},
  title        = {Pith review of: Alliances and Conflict, or Conflict and Alliances? Appraising the Causal Effect of Alliances on Conflict},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SMWJZ5GB}},
  note         = {Machine review of arXiv:1908.07100}
}

read the original abstract

The deterrent effect of military alliances is well documented and widely accepted. However, such work has typically assumed that alliances are exogenous. This is problematic as alliances may simultaneously influence the probability of conflict and be influenced by the probability of conflict. Failing to account for such endogeneity produces overly simplistic theories of alliance politics and barriers to identifying the causal effect of alliances on conflict. In this manuscript, I propose a solution to this theoretical and empirical modeling challenge. Synthesizing theories of alliance formation and the alliance-conflict relationship, I innovate an endogenous theory of alliances and conflict. I then test this theory using innovative generalized joint regression models that allow me to endogenize alliance formation on the causal path to conflict. Once doing so, I ultimately find that alliances neither deter nor provoke aggression. This has significant implications for our understanding of interstate conflict and alliance politics.

Figures

Figures reproduced from arXiv: 1908.07100 by the authors.

**Figure 2.** Out-of-Sample Area Under the Precision-Recall Curve by Copula Function. [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗

**Figure 3.** Coefficient Plot for Johnson and Leeds (2011) Model and Bivariate Model [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: The in-sample PR AUC for the endogenous alliances model is 0 [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]

**Figure 4.** Figure 4: Precision-Recall Curves for Johnson and Leeds (2011) Model and Bivariate [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]

**Figure 5.** Figure 5: Z Statistics for the Endogenous Relevant Defensive Alliance Commitment [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]

**Figure 6.** Figure 6: Average Treatment Effects for the Endogenous Relevant Defensive Alliance [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

9 extracted references · 9 canonical work pages

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arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [5]

Alliance treaty obligations and provisions, 1815-1944

“Alliance treaty obligations and provisions, 1815-1944.” International Interactions 28(3):237–260. Lemke, Douglas and William Reed

work page 1944

[2] [1972]

Capability distribution, uncertainty, and major power war, 1820-1965

“Capability distribution, uncertainty, and major power war, 1820-1965.” Peace, war, and numbers 19:48. Slantchev, Branislav L

work page 1965

[3] [1976]

Alliances, 1815-1945: Weapons of Power and Tools of Management’, Histor- ical Dimensions of National Security Problems, K

“Alliances, 1815-1945: Weapons of Power and Tools of Management’, Histor- ical Dimensions of National Security Problems, K.” Knorr (ed.),(Lawrence, Kan.,

work page 1945

[4] [1981]

Alliance formation and war behavior: An analysis of the great powers, 1495-1975

“Alliance formation and war behavior: An analysis of the great powers, 1495-1975.” Journal of Conﬂict Resolution pp. 581–613. Liska, George

work page 1975

[5] [1992]

Dangerous dyads: Conditions aﬀecting the likelihood of interstate war, 1816-1965

“Dangerous dyads: Conditions aﬀecting the likelihood of interstate war, 1816-1965.” Journal of Conﬂict Resolution 36(2):309–341. Bueno de Mesquita, Bruce

work page 1965

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Normative and structural causes of democratic peace, 1946–1986

“Normative and structural causes of democratic peace, 1946–1986.” American Political Science Review 87(3):624–638. Marra, Giampiero and Rosalba Radice

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Democracy, political similarity, and international alliances, 1816-1992

“Democracy, political similarity, and international alliances, 1816-1992.” Journal of Conﬂict Resolution 44(2):203–227. Leeds, Brett Ashley. 2003 a. “Alliance reliability in times of war: Explaining state decisions to violate treaties.” International Organization 57(4):801–827. Leeds, Brett Ashley. 2003b. “Do alliances deter aggression? The inﬂuence of mi...

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