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The origins and evolution of the U.S. alliance network: how military allies transform and transact

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The origins and evolution of the U.S. alliance network: how military allies transform and transact

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Content THE ORIGINS AND EVOLUTION OF THE U.S. ALLIANCE NETWORK: HOW MILITARY ALLIES TRANSFORM AND TRANSACT by Stephanie Nayoung Kang A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (POLITICAL SCIENCE AND INTERNATIONAL RELATIONS) August 2020 Copyright 2020 Stephanie N. Kang Acknowledgements There are so many individuals to thank in this long, and often what could have been a soli- tary, journey towards receiving a Ph.D. The encouragement and help from many people made the process of formulating and writing a dissertation both tolerable and, at times, even enjoyable. First I would like to thank my committee members, David Kang, Andrew Coe, Robert Trager, and Odilon Camara for their constant guidance, sound mentorship, and unwa- vering support for my research. I’m especially thankful to have an adviser who not only challenges me to think for myself, but also deeply cares for his students’ well-being and success. Thank you Shifu for your many pearls of wisdom. The only way to make it through the arduous Ph.D. grind is to have a community that supports. I’m grateful for the USC community, both the staff and the students that came before and after me. Special thanks to Veri Chavarin for being an understanding, efficient, and empathetic grad advisor who has (and will continue) to guide many students in the program. I’m also thankful to be a part of the KSI family and all the support it has given me throughout the years. I consider myself very lucky to have entered the program with the GOAT Cohort — Ada, Brian, Jenn, Shiming, Suzie, Victoria, Whitney, and Yu-Ting — the greatest of all time cohort mates. I’m honored to call them my colleagues and couldn’t have asked for a more diverse, fun, and strange group of people to share this unique experience with. The friendships that I have formed and maintained are even more meaningful in the demanding and critical academic environment. I’m grateful to the friends I have made during my graduate studies and to those that have been with me since I was young. Mao, Mingmin, and Xinru are like cohort mates and have made the Ph.D. so enjoyable (i.e. in- troduced me to great food). Carolyn and Jonathon (and Mr. Bobos!) helped me finish my dissertation by sharing in the experience in my final year and leading by example. Crystal, Dolly, Hana, Hyereon, and the ChYangs have supported me from early on and I can always rely on them to cheer me up. And my best friend, Sarah Lee: you know how important you are to me and that I can’t function like a normal human without you. I thank my family who has been with me since the beginning (literally). I’m thankful for the Kangs and Lees, especially my grandma who helped raise me and would have been so proud. I couldn’t ask for a more caring and encouraging family. To Dad, Mom, Carol, Josh, Kaylee, and Jameson: thank you for your unwavering love and continued support. You always inspire me to be better and to think of others. I would not be where I am now without all of you and this dissertation is dedicated to you all. Above all, I thank Him for His grace and unfailing plan for me. ii Contents Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii 1 Introduction 1 The Puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Explaining Variation in Military Commitments . . . . . . . . . . . . . . . . . . . . 6 Extended Deterrence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Target Restraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Deterrence-Restraint Dilemma . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Going Beyond Formal Alliances: Treaty and Material Commitments . . . . . . . . 10 Challenging common assumptions about third-party commitments . . . . . 11 The Argument in Brief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Implications for Alliance Studies and American Grand Strategy . . . . . . . . . . 15 Outline of the Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Variation in Third-Party Military Commitments 18 Definitions and Scope: Treaty and Material Commitments . . . . . . . . . . . . . 20 Spatial and Temporal Variation in Military Commitments . . . . . . . . . . . . . . 22 How Do We Measure Military Commitment? . . . . . . . . . . . . . . . . . . . . . 24 Why Alliances Alone Are Not Enough . . . . . . . . . . . . . . . . . . . . . . 28 Theoretical Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 A Measurement Model of Military Commitment . . . . . . . . . . . . . . . . . . . 33 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Model Specification: Bayesian Mixed Data Factor Analysis . . . . . . . . . . 37 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Factor Loadings and Error Variance . . . . . . . . . . . . . . . . . . . . . . . 41 Substantive Country Comparisons . . . . . . . . . . . . . . . . . . . . . . . . 43 A New Typology of Third-Party Military Commitments . . . . . . . . . . . . . . . 49 Effect on Strategic Environment and State Behavior . . . . . . . . . . . . . . 50 Dimensions of Military Cooperation . . . . . . . . . . . . . . . . . . . . . . . 53 Institutional Design and Costs . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Military Effect and Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 iii 3 A Theory of Military Commitments 63 A Model of Material Commitments . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Key feature of model: variation in material commitments . . . . . . . . . . . 69 No material commitments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Material commitments to improve joint capabilities . . . . . . . . . . . . . . 73 Material commitments to improve target unilateral capabilities . . . . . . . 75 All material commitments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Variation in third-party military commitments . . . . . . . . . . . . . . . . . 78 Entrapment and abandonment: why third-party commitments don’t always tie hands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Empirical Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Third-party defender intervention . . . . . . . . . . . . . . . . . . . . . . . . 83 Third-party defender commitment strategy . . . . . . . . . . . . . . . . . . . 84 Model Extension: War under Complete Information . . . . . . . . . . . . . . . . . 87 War equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Model Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Proof of equilibrium with no material commitments . . . . . . . . . . . . . . 93 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Proof of equilibrium with all material commitments . . . . . . . . . . . . . . 100 Model Extension: War under Complete Information . . . . . . . . . . . . . . . . . 102 4 US Commitments to East Asia 105 Case Selection and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Cross-Country Comparison: South Korea and Taiwan . . . . . . . . . . . . . 106 Historical Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Reorientation of US Foreign Policy: Truman Doctrine and Containment . . . 108 The Korean War and Mutual Defense Treaty . . . . . . . . . . . . . . . . . . 109 Maintaining US Commitments while Scaling Back: The Nixon Doctrine . . . 110 South Korea: joint capabilities after the Korean War . . . . . . . . . . . . . . . . . 111 Moving towards modernization . . . . . . . . . . . . . . . . . . . . . . . . . 113 Taiwan: unilateral capabilities and Sino-US relations . . . . . . . . . . . . . . . . 115 Alternative explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Limitations and Potential Model Extensions . . . . . . . . . . . . . . . . . . . . . 121 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 iv 5 Conclusion 133 Importance of Variation in Military Commitments . . . . . . . . . . . . . . . . . . 133 Peacetime Costs and Resource Constraints . . . . . . . . . . . . . . . . . . . 133 Military Effect of Commitments . . . . . . . . . . . . . . . . . . . . . . . . . 134 Reducing Entrapment Risks . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Future of Alliances and Other Third-Party Commitments . . . . . . . . . . . . . . 137 Changing Commitments: From Transformation to Transaction . . . . . . . . . . . 138 References 140 v List of Tables 2.1 US Military Commitments to Formal Allies vs. Non-Formal Allies . . . . . . 31 2.2 Dataset and Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3 Descriptive Statistics for Manifest Variables . . . . . . . . . . . . . . . . . . 37 2.4 Correlation Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.5 Summary of Posterior Density (2000) . . . . . . . . . . . . . . . . . . . . . 42 2.6 Variation in Design and Implementation of Third-Party Military Commit- ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.1 Model Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2 Summary of Expected Utilities . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3 Summary of Expected Utilities . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.4 Summary of Defender’s Strategies . . . . . . . . . . . . . . . . . . . . . . . . 92 4.1 South Korea and Taiwan Comparison . . . . . . . . . . . . . . . . . . . . . . 118 vi List of Figures 1.1 US Arms Transfers to Key Countries (1950-2014) . . . . . . . . . . . . . . . 4 1.2 US Military Aid to Key Countries (1950-2014) . . . . . . . . . . . . . . . . . 5 1.3 US Troop Deployments to Key Countries (1950-2014) . . . . . . . . . . . . . 6 1.4 Outline of Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1 US Troop Deployments to NATO Countries, 1950-2014 . . . . . . . . . . . . 29 2.2 US Arms Transfers to Formal and Non-formal Allies . . . . . . . . . . . . . . 31 2.3 Distributions of Manifest Variables . . . . . . . . . . . . . . . . . . . . . . . 37 2.4 Latent variable model of military commitment . . . . . . . . . . . . . . . . . 39 2.5 Posterior Means for East Asian Countries in 2000 . . . . . . . . . . . . . . . 44 2.6 Posterior Means for NATO Members in 2000 . . . . . . . . . . . . . . . . . . 45 2.7 Posterior Means for Allies and Non-Allies in 2000 . . . . . . . . . . . . . . . 47 2.8 Typology of Military Commitments . . . . . . . . . . . . . . . . . . . . . . . 54 2.9 Trace Plots for Factor Loadings and Error Variance . . . . . . . . . . . . . . . 60 2.10 Posterior Mean Distributions for Factor Loadings and Error Variances . . . . 61 2.11 Autocorrelation Plot for Observed Indicators . . . . . . . . . . . . . . . . . . 62 4.1 Dispute Outcome Expectations among Great Powers (US, China, Russia) . . 127 4.2 Dispute Outcome Expectations for North and South Korea . . . . . . . . . . 128 4.3 Dispute Outcome Expectations for China and Taiwan . . . . . . . . . . . . . 129 4.4 US Troop Deployments to South Korea and Taiwan (1950-2014) . . . . . . . 130 4.5 US Arms Transfers to South Korea and Taiwan (1950-2014) . . . . . . . . . 131 4.6 US Military Aid to South Korea and Taiwan (1950-2014) . . . . . . . . . . . 132 vii Abstract This dissertation examines the puzzle of why military cooperation between countries is changing over time despite the static nature of treaty alliances or written, legal obligations to militarily support a state in conflict. The project explores three important research ar- eas, using diverse methods, to address enduring questions in the alliance and international security literatures. First, I contend that US military commitments, or promises to provide military support in the event of conflict, are changing significantly over time despite rela- tively few changes to the actual agreements made under treaty alliances. Second, I develop a novel theory of commitment design and implementation using both game theory and his- torical case studies to unpack the complex strategic interactions between states involved in international disputes. Finally, I use qualitative methods and in-depth historical case studies to explain why post-WWII US military commitments to South Korea and Taiwan differed so significantly despite common security threats. The project contributes to the study of military cooperation by challenging the idea that external military support is best represented by formal military alliances. My research addresses this gap by conceptualiz- ing US military commitments both in the context of alliances and beyond, and provides theoretical underpinnings for explaining security relationships that evolve substantially over time. The US alliance network is a key component of American grand strategy and the United States is deeply invested in the security of its allies, particularly in Western Eu- rope and East Asia despite recent skepticism and debate over American engagement versus retrenchment. This project provides a better understanding of how the maintenance of al- liances is changing and why that is not necessarily a sign of US withdrawal or declining US support for allies abroad. viii Chapter 1 Introduction The Puzzle The United States is committed to defend over fifty unique countries from armed attack under the obligations of seven formal, or treaty, alliances. 1 Yet the United States has not signed onto a new collective defense agreement since 1960. In addition, the legal obligations and provisions outlined in US alliance treaties have changed very little over time. 2 Despite not forming new military alliances nor changing them significantly, the United States is very much actively engaged in cooperating militarily with its current allies and many other states of strategic importance. The US continues to pour military aid into countries with aligned security interests in the Middle East, like Israel and Saudi Arabia, and maintains a dense network of military relations with both formal and non-formal allies abroad in the form of arms transfers, foreign military bases, nuclear deployments, and joint 1 The seven collective defense agreements that the US is party to are: the North Atlantic Treaty Or- ganization (NATO), Agreement between the United States and Australia and New Zealand (ANZUS), the US-Philippine Treaty, the Southeast Asian Treaty Organization (SEATO), the US-Republic of Korea Treaty, the US-Japan Treaty, and the Rio Treaty (or Inter-American Treaty of Reciprocal Assistance). For a complete list of US defense agreements and members, see https://2009-2017.state.gov/s/l/treaty/collectivedefense/ /index.htm. 2 There were some revisions to US collective security agreements over time, but few changed the actual content of the treaties themselves. In 1954, the US added an “Understanding of the United States" to the US- South Korea Mutual Defense Treaty to specify when US commitment to defend South Korea was activated. Originally signed in 1951, the Treaty of Mutual Cooperation and Security betweeen the US and Japan was revised in 1960 to include provisions for US basing rights and a commitment to defend in the case of an armed attack. 1 military exercises. 3 Beyond the United States, the annual number of new alliances formed between states is stagnant, at best, while the number of defense cooperation agreements (DCAs), or “formal bilateral agreements that establish institutional frameworks for routine defense cooperation," has been increasing rapidly since the early 1990s. 4 Thus the puzzle arises: why do military commitments between states differ despite the static nature of alliances? Third-party states to an international dispute (hereafter, “third- party defender") often pledge their willingness to support one of the disputants (hereafter, “target state") in various ways. 5 States with aligned interests will often cooperate militarily in preparation for potential militarized conflict. Military cooperation takes on many forms for different purposes, is employed in various means that entail a wide range of costs for its implementation, and involves different types of military actions that have varying effects on the strategic environment of states in disputes. US military commitments to its allies in Western Europe and the Asia-Pacific are not only encapsulated in its treaty alliances with member states in these regions, but are also backed by strong military measures, such as permanent overseas bases, foreign troop deployments, and integrated military commands. A related set of questions addresses the decision-making processes and consequent for- eign policy behaviors that follow from the design and implementation of different types of military commitments. How do national leaders strategically choose which forms of military cooperation to engage in to address external threats to countries of aligned in- 3 Formal allies refer to states in military alliances under the operational definition of alliances from the ATOP dataset, whereas non-formal allies are states with aligned interests but no treaty alliance. For how alliances are defined by the ATOP dataset, see Leeds et al. (2002). This reference to formality simply dis- tinguishes between states that are in an alliance and those that are not, and differs from actual measures of formality (Leeds and Anac 2005; Morrow 1994). 4 For the definition of a DCA, see Kinne (2018, 803). Also refer to Kinne (2019) for a detailed account of DCAs. 5 The literature on extended deterrence uses multiple terms interchangeably to refer to the actors of interest. A third-party defender is also referenced as: the patron, the third-party intervener, the third-party ally, the third-party, etc. A state that receives actual or potential military support from a third party and is involved in an international dispute is often referred to as: the protégé, the client, the target state (i.e. target of a conflict), etc. Last, the other party to the dispute that makes a threat against the target state is often labeled as: the challenger, the adversary, the rival/opponent etc. In this project, I use the following titles for consistency: the third-party defender (or just “defender"), the target state (or simply “target"), and the challenger. 2 terest? What effect does the variation in military commitments have on the behavior of states in international disputes? How do the actual military measures taken in peacetime interact with the legal obligations and provisions laid out in alliance treaties? A powerful patron, like the United States, is still limited in the resources it can expend on providing security for its allies and other states of strategic importance. Figures 1.1, 1.2, 1.3 show that the distribution of US military resources to key countries – such as arms transfers, military aid, and troop deployments – is changing over time, with the US investing in the military capabilities of certain states over others. Clearly, the decision of which states to make military commitments to, how much to commit, and what form of commitment to make are all strategic in nature. This project develops a comprehensive theory of military commitment design and implementation that accounts for, not only the strategic choice of commitment, but the effect such commitment strategies have on crisis bargaining behavior and the likelihood of conflict. 3 Figure 1.1: US Arms Transfers to Key Countries (1950-2014) 0.00 0.25 0.50 0.75 1.00 1950 1960 1970 1980 1990 2000 2010 Y ear Proportion of US Arms Transfers Germany Israel Italy Japan Saudi Arabia South Korea Taiwan United Kingdom Source: SIPRI Arms Transfers Database. According to SIPRI, the volume or “TIV is based on the known unit production costs of a core set of weapons and is intended to represent the transfer of military resources rather than the financial value of the transfer." 4 Figure 1.2: US Military Aid to Key Countries (1950-2014) 0.00 0.25 0.50 0.75 1.00 1950 1960 1970 1980 1990 2000 2010 Y ear Proportion of US Military Aid Germany Israel Italy Japan Saudi Arabia South Korea Taiwan United Kingdom Source: USAID Greenbook. 5 Figure 1.3: US Troop Deployments to Key Countries (1950-2014) 0.00 0.25 0.50 0.75 1.00 1950 1960 1970 1980 1990 2000 2010 Y ear Proportion of US Deployed Troops Germany Israel Italy Japan Saudi Arabia South Korea Taiwan United Kingdom Data missing for years 2007 and 2008. Source: Kane (2004) and US DoD Defense Manpower Data Center. Explaining Variation in Military Commitments A relevant third-party actor (defender) often has incentives to influence the outcomes of international disputes by committing to militarily support its preferred side (target). Mil- itary commitments take on many forms for different purposes, are employed in various means that entail a wide range of costs for their implementation, and involve different types of military actions that have varying effects on the strategic environment of states in dispute. As a result, states with aligned security interests will often cooperate militarily in preparation for potential militarized conflict. Traditionally, most scholars measure third- party involvement in disputes using military alliances, or “formal agreement[s] among 6 independent states to cooperate militarily in the face of potential or realized military con- flict" (Leeds et al. 2002, 6). 6 Alliances can be powerful, costly signals of a third-party de- fender’s resolve to militarily support its ally in war (Fearon 1997; Fuhrmann and Sechser 2014; Trager 2015; McManus and Yarhi-Milo 2017) and alliances can effectively deter challengers from initiating conflict (Snyder 1997; Smith 1996; Huth 1988; Leeds 2003b; Werner 2000; Yuen 2009; Leeds and Johnson 2016). 7 Yet, empirically, third-party military commitments extend well beyond the obligations and provisions laid out in alliances. More often than not, formal alliances are complemented or substituted by other mil- itary actions to increase the target state’s security against a challenger. Notably, some scholars have examined the choice between entering alliances versus investing in arms (Morrow 1993; Yarhi-Milo, Lanoszka and Cooper 2016; Digiuseppe and Poast 2018). Even then, third-party commitments are not limited to a series of binary choices: whether to ally or not, or whether to invest in arms or alliances. Instead, a defender has a diverse set of military options to choose from – such as arms transfers, military aid, foreign basing, inte- gration of military commands, and/or joint military exercises – that shape both the degree and manner in which it would support a state in conflict. We currently do not have a clear understanding of how different forms of military cooperation conceptually and em- pirically differ from treaty alliances, and how such variation in commitments influences crisis bargaining behavior in related but distinct ways. The variation in third-party mil- itary commitments is largely explained through three main facets of research: extended deterrence, target restraint, and the deterrence-restraint dilemma. 6 In this paper, I define formal allies as states in military alliances under the ATOP dataset’s operational definition of alliances, whereas non-formal allies are states with aligned interests but no treaty alliance. For how alliances are defined by the ATOP dataset, see Leeds et al. (2002, 238). This reference to formality simply distinguishes between states that are in an alliance and those that are not, and differs from actual measures of formality (Leeds and Anac 2005; Morrow 1994). 7 Trager (2015) offers another signaling mechanism in which third-party commitments to intervene are made credible even without costly signals. This project characterizes certain military commitments as having both sunk costs and hands-tying effects that are more in line with Slantchev (2005). 7 Extended Deterrence Most research on alliances points to alliances as maximizing deterrence. If the only goal of military alliances was to increase extended deterrence, then we should not observe such variation in third-party military commitments. In fact, we would expect to see the most aggressive alliances or offensive pacts (Benson, Meirowitz and Ramsay 2013), uncondi- tional obligations to defend an ally (Benson 2012), and/or the costliest forms of military cooperation, such as foreign nuclear deployments and permanent overseas military bases. The logic is that if military commitments are only aimed at maximizing extended deter- rence, then a third-party defender would want to make the most credible commitments it could to deter a challenger from making large demands on the target state. In line with the costly signaling literature and arguments put forth by Fearon (1997), a defender that wishes to maximize deterrence through its alliance should make the costliest commitments that can signal its willingness to intervene in conflict for its ally and distinguish itself from those that would not. Empirically, however, these types of third-party commitments are not dominant. The rising number of less institutionalized forms of military cooperation, such as DCAs, and the general ambiguity of most alliance commitments show that there are multiple goals that are in play when actors design their military commitments. Target Restraint Some scholars argue that alliances, in addition to providing extended deterrence, are also used to restrain potentially aggressive target states. Fang, Johnson and Leeds (2014) find that an alliance can restrain an emboldened target if the target values the alliance highly. Cha (2016) develops the “powerplay" theory in which tight, bilateral alliances that exerted political, military, and economic control over key countries in East Asia were designed to restrain national leaders from instigating and dragging the US into unwanted conflicts (South Korea and Taiwan) or ensure that the region’s major power evolved in a 8 direction in line with US interests (Japan). 8 While historical evidence does offer support for the powerplay argument, the theory does not explain variation in military commitments over time. US military cooperation with South Korea has changed significantly over time, including the introduction and removal of tactical nuclear weapons in South Korea, large troop reductions under the Nixon Doctrine, and changes in military aid to South Korea after the Cold War period. It is also unclear under what conditions alliances or certain forms of third-party military commitments are used to restrain target states and when they are not. A comparison between the multilateral collective defense agreements under NATO and the Rio Pact, on one hand, and the US hub-and-spokes system of bilateral alliances in East Asia, on the other, show that entrapment concerns are not universal. In fact, another puzzling empirical observation is the relative rarity of entrapment (Beckley 2015; Kim 2011). Third-party defenders are not actually dragged into their targets’ conflicts as often as conventional wisdom would suggest. Deterrence-Restraint Dilemma To balance concerns faced by the deterrence-restraint dilemma, scholars argue that states maintain strategic ambiguity by making their obligations intentionally vague and flexible so that they are not entrapped but can also deter challengers from making large threats. This research points to the incentive for leaders to design their alliances in a way that allows them flexibility to renege on commitments without facing significant political costs (Mattes 2012a; Chiba, Johnson and Leeds 2016) or to make probabilistic commitments to simultaneously deter challengers while preventing emboldened target states from initiat- ing or escalating crises (Snyder 1984; Zagare and Kilgour 2006; Benson 2011, 2012). As a result, third-party military commitments are couched in purposefully vague language that allow defenders to avoid providing unconditional military support in the event of conflict. 8 See Cha (2009), especially chapters 1 and 2 for an explanation of the powerplay theory. 9 Yet the notion of strategic ambiguity does not address the empirical observation that there are many forms of military cooperation that states engage in that are made upfront, are extremely costly, and are even unambiguous. For example, the stationing of troops in for- eign military bases or the integration of two or more states’ military command structures are commitments that are easily observed, impose high costs for their maintenance and institutionalization, and are constantly being employed even in peacetime. Going Beyond Formal Alliances: Treaty and Material Com- mitments Scholarly research aimed at explaining variation in third-party military commitments has led to burgeoning studies on alliance design, especially how the military commitments laid out in alliance treaties vary (Leeds et al. 2002; Benson 2012; Benson and Clinton 2016). As a result, the literature focuses almost exclusively on the obligations and provisions spelled out in alliance treaties. The conventional argument is that military alliances, or treaty commitments, increase the risk of war by raising the defender’s costs from abandoning the target state in conflict. 9 Thus military alliances are seen as hands-tying commitment mechanisms that also signal the defender’s willingness to intervene and support the target in conflict against the challenger (Morrow 2000). Yet third-party defenders can, and often do, employ a wide range of military measures to extend security to target states that go beyond what is written in alliance treaties: what I refer to as material commitments. Material commitments are physical actions taken in peacetime to bolster a target’s defense or improve military coordination between a de- fender and target state. Such military measures include (but are not limited to): the pro- vision of conventional arms or military aid, the deployment of troops or nuclear weapons 9 Most often the costs from reneging on one’s alliance are reputational in nature. This includes domestic audience costs for backing down, costs for violating a legally-binding agreement, hurting one’s credibility to make commitments in the future, etc. See Fearon (1997, 7) and Fearon (1994a). 10 abroad, and joint military exercises. Unlike treaty commitments which simply tie hands, material commitments both sink costs and tie hands. In an international dispute with two actors, Slantchev (2005) argues that “one can hardly wage war without preparing for it, and the primary role of mobilization is not to incur costs but rather to prepare for fighting by increasing the chances of victory" [534]. 10 This logic applies much in the same way in a multi-actor context: states do not simply enter into costly alliances without preparing for a potential conflict that involves members of the alliance. Material commitments impose sunk costs for their employment in peace- time, but they also directly influence the probability of the target state winning a war alone and the probability of allies winning a war together. As a result, material commitments go beyond being just signals of the defender’s willingness to support or abandon the target in conflict. Such military actions change the strategic environment by dynamically shifting the status quo local balance of power among actors in dispute in ways that alliances alone do not. While alliances make a third-party defender’s threat to intervene more credible, material commitments not only signal costly commitment but also directly influence the actual military capabilities of states. Challenging common assumptions about third-party commitments When we adopt a conceptualization of military commitments that goes beyond formal al- liances, we can begin to challenge and revise a common set of assumptions that limits current alliance studies. First, most models of extended deterrence assume that there is no ex ante or peacetime cost to forming an alliance. The cost, and thus costly signaling effect, from alliances arises when alliances are actually tested in war and a defender reneges on its commitments. This assumption is limiting because the cost of coordinating and main- taining military cooperation in peacetime has a direct effect on the third-party defender’s choice of commitment strategy. When the cost of implementing certain military measures, 10 See also Fearon (1997), footnote 27. 11 or material commitments, is too high, then the defender cannot make such commitments even if it would be willing to intervene in war to defend its ally. In reality, national leaders are constantly faced with budget and resource constraints that may limit their ability to make military commitments to states. In addition to sunk costs, the focus of models of extended deterrence has been on alliance formation and hands-tying, but the dynamics and strategic interaction from third- party commitments can also be applied to actors that are not formally allied. In other words, most theories examine a discrete, often binary, set of options for the third-party actor – namely, the decision to enter into an alliance or not. The commitment strategy of the third-party defender influences expected war payoffs, but in a uniform way, that is limited to formal allies. For example, while a third-party actor can still choose to support or abandon a target state that is not an ally, the cost of reneging on one’s commitment is zero. The underlying assumption is that if a commitment, such as an alliance, is not made upfront, then there are no costs to backing down or not supporting a state with aligned interests in war. Yet political and even material costs from abandonment are not limited to members of an alliance. For example, if the US were to renege on its commitments to Israel or Taiwan, both non-formal allies, then the US would face significant costs for “abandoning" or not supporting these states in disputes. A final common assumption that underlies alliance theories is that the target state is inherently aggressive and desires conflict more than the third-party actor to a dispute. Mil- itary commitments, arguably, increase the risk of entrapment by emboldening the target to reject a greater range of offers made in bargaining under the shadow of the defender’s sup- port in war. While there is both historical and empirical evidence of target emboldenment (Benson 2012; Cha 2016), the empirical record of actual entrapment is less conclusive (Kim 2011; Beckley 2015). When we account for the variation in third-party military com- mitments, we can examine the conditions under which entrapment is an actual risk for security-providers. Because various military measures can be adopted to address different 12 security concerns, it is not clear that emboldenment will always lead to a greater likelihood of entrapment for a third-party defender. The Argument in Brief This project develops a theory of commitment design and implementation that derives the conditions under which a third-party defender will choose one form of military cooperation over another, and the effect such a commitment strategy will have on crisis bargaining be- havior. A relevant external actor, or third-party defender, often has incentives to influence the outcomes of international disputes by committing to militarily support its preferred side. Most studies on military commitments focus primarily on the formation and design of formal alliances. Yet current explanations only provide a snapshot of different military commitments at a fixed point in time when alliances are formed. When making military commitments to states, national leaders are not constrained to simply enter into a military alliance or not. Instead, leaders have a large selection of tools, or military actions, from a toolkit of various commitment strategies. The US can militarily support another state in many ways apart from alliances, from exporting arms to deploying troops and integrating its mil- itary under a central command structure. Using an original cross-national, time-series dataset, I show that there are meaningful differences in US military commitments to states in the same collective security agreement, such as the North Atlantic Treaty Organization (NATO), and to countries that are formal allies (e.g. South Korea, Japan, NATO) and those that are not (e.g. Taiwan, Israel, Saudi Arabia). This principled approach to measuring US military commitments allows scholars to essentially rank which countries receive more or less American military support based on observed military measures taken during peace- time, and which countries (allies or not) are prioritized for defense at different points in time. 13 To understand why a third-party defender makes such varied military commitments to different states, I introduce a novel theory about how military cooperation is devised and how it influences the strategic environment of states in dispute. I argue that national leaders design and implement different military commitments based on the direct effect they have on states’ military capabilities and the local balance of power. A certain class of military support – arms exports, military bases, foreign deployed nuclear weapons, an integrated military command – directly influences the military capabilities of states in dis- pute. While alliances only take effect when obligations are tested and external actors are brought into conflict, different material commitments, or military actions taken in prepa- ration for potential war, have varying and immediate effects on states’ military capabilities. As a result, the US designs and implements diverse forms of military cooperation that are not necessarily tied to promises made under alliances. Contrary to conventional expectation, entrapment is only a concern under certain con- ditions. I find that a powerful patron can directly influence states’ military capabilities without ever fighting. By providing a country with the tools to fight alone, such as arms transfers or military aid, the US can shift the local balance of military power in its favor without making guarantees to intervene in conflict. My theoretical model explains why US military commitments to South Korea and Taiwan diverged during the Cold War despite common threats and a common hub-and-spokes system of defense. This counterintuitive finding also explains why the United States made costly, upfront military commitments to Taiwan despite abrogating its treaty alliance in favor of normalizing diplomatic relations with China. Figure 1.4 shows the overarching logic that guides my theory of commitment design and implementation. A third-party defender’s choice of commitment strategy is the result of its expectations about how other actors will behave in crisis bargaining which, in turn, is conditioned by underlying structural constraints such as the local balance of power and the costs of implementing different peacetime military measures. To understand how external 14 military support influences extended deterrence and the likelihood of war, we need to consider that the design of military commitments is affected by actors’ expectations about how others will behave under certain constraining factors. Figure 1.4: Outline of Theory Implications for Alliance Studies and American Grand Strat- egy My research and findings make significant contributions to both the theoretical and em- pirical study of military cooperation and alliance politics. First, my project contributes to the study of military cooperation by challenging the idea that external military support is best represented by formal military alliances. In the next chapter, I show that there is significant variation in the form and function of military commitments between states that extend well beyond alliance obligations and provisions. I also argue that this variation is a result of strategic design and implementation choices by national leaders, which have a direct effect on states’ military capabilities and their behavior in international disputes. The consequences of not accounting for the variation that exists in military commitments outside of formal alliances is significant: we do not have a principled way to compare US military commitments to different countries over time, and our analysis of military sup- 15 port is often restricted to cooperation between allies. My research addresses this gap by conceptualizing US military commitments both in the context of alliances and beyond, and provides theoretical underpinnings for explaining alliances as dynamic forms of military cooperation that evolve substantially over time. Second, my research has direct implications for American grand strategy and whether the formation of military alliances is becoming increasingly obsolete in the face of more transactional forms of military cooperation. The form and function of US alliances at the time of their signing differ greatly from how ally relations are managed today. By adopting a dynamic conceptualization of military commitments and accounting – both theoretically and empirically – for variation in US military support to countries over time, we can ex- plain not only changes in US alliances but also how US grand strategy in the post-war era has evolved as well. The US alliance network is a key component of American grand strategy and the United States is deeply invested in the security of its allies, particularly in Western Europe and East Asia. Yet there is also skepticism and debate over American engagement versus retrenchment (Gholz, Press and Sapolsky 1997; Brooks, Ikenberry and Wohlforth 2012), especially as the Trump administration makes greater demands for in- creased burden sharing among allies and a policy of “America First." By explaining the changes in US military cooperation and strategy with rigorous empirical data and in-depth case studies, my research provides a better understanding of how the maintenance of al- liances is changing and why that is not necessarily a sign of US withdrawal or declining US support for allies abroad. Outline of the Project This chapter addresses the puzzle of why military commitments between states vary and the effect such variation has on the strategic behavior of states in dispute. Chapter 2 introduces a new way of conceptualizing military commitments that goes beyond the obli- 16 gations and provisions outlined in formal alliance treaties. The novel typology of military commitments allows researchers to account for both spatial and temporal variation in third-party military commitments. Additionally, I employ a statistical measurement model that allows for a principled comparison of military commitments between members of the same alliance, between formal allies and non-formal allies, and changes over time. Chap- ter 3 presents a formal, theoretical model that generates novel predictions about which types of commitment strategies states will adopt to provide for another state’s security. The design of third-party military commitments are driven by expectations of strategic in- teraction between states in dispute and the implementation are conditioned by structural constraints such as the local balance of power between disputants and the cost of carrying out different military measures. In Chapter 4, I examine the dynamic evolution of US mili- tary commitments to South Korea and Taiwan over time. Chapter 5 concludes with further avenues of study for alliance politics and draws implications for American foreign policy, especially the formulation of US grand strategy and how the US global alliance network is managed. 17 Chapter 2 Variation in Third-Party Military Commitments This chapter shows that there is significant variation in military cooperation between states, and this variation has real implications for the unobserved level of military com- mitment from one state to another. US military commitments to states, both formal allies and not, have changed substantially over time. A static measure of alliances does not fully account for this variation. I show that US peacetime military cooperation with states is changing, develop a statistical measurement model to make comparisons between dyads in a principled manner, and redefine how we conceptualize military commitments between states. Alliances are “written agreements, signed by official representatives of at least two in- dependent states, that include promises to aid a partner in the event of military conflict, to remain neutral in the event of conflict, to refrain from military conflict with one an- other, or to consult/cooperate in the event of international crises that create a potential for military conflict." (Leeds et al. 2002, 6). The literature on why states form alliances (Morrow 2000; Snyder 1997; Walt 1987) and the military effect of alliances on deter- rence is extensive (Snyder 1997; Smith 1996; Huth 1988; Leeds 2003b; Werner 2000; Yuen 2009; Kenwick, Vasquez and Powers 2015; Leeds and Johnson 2016; Kenwick and Vasquez 2016; Morrow 2016). More recently, scholars have begun to focus on measuring variation among alliances to explain important behaviors and outcomes related to conflict. 18 Current studies on alliances show there is variation in what states promise they will do on behalf of their allies. There is wide variation in what states outline in their alliance treaties (Leeds et al. 2002), variation in the firmness of commitments laid out in alliances (Benson 2012, 2011), and variation in the scope of the obligations, depth of commitments, and potential military strength of formal alliances (Benson and Clinton 2016). Yet all of these measures are based on treaty commitments, or what states pledge to do in the event of conflict. How, then, do we account for the variation in military commitments between both formally allied countries and non-formal allies? How do we explain changing global trends in military cooperation, and how third-party commitments vary over time that do not follow the static nature of alliances? The Correlates of War (COW) Formal Alliances data records all formal military alliances between states, including mutual defense pacts, non-aggression treaties, and ententes (Gibler 2009). Building off the COW data, Leeds et al. (2002) have compiled the most comprehensive dataset on formal military alliances that not only captures defense, offense, neutrality, and non-aggression pacts, but also the specific obligations and provisions agreed upon between states at the time of signing. For example, the Alliance Treaty Obligations and Provisions (ATOP) dataset includes measures for whether obligations are applicable under certain conditions, whether a specific threat or location is mentioned, and whether the alliance calls for provisions among members, such as military aid, military contact, basing rights, and/or an integrated military command. Other scholarship has further categorized alliance commitments based on their objec- tive (deterrence or compellence) and trigger (specific or none) (Benson 2011, 2012). Ben- son and Clinton (2016) employ Bayesian factor analysis to estimate the scope, depth, and potential military capacity of formal military alliances based on the observable obligations and provisions laid out in treaties. Yet few studies have looked beyond treaty alliances as a measure of third-party alliance commitments. Kinne (2019) examines defense cooperation agreements (DCAs) as an alternative measure for routine defense cooperation rather than 19 just military support in conflict. Definitions and Scope: Treaty and Material Commitments Military cooperation between states extends beyond the obligations and provisions laid out in legal, written agreements, or what I refer to as “treaty commitments." More often than not, formal alliances are accompanied by military actions taken by a third-party defender to increase the security of the target state against its challenger. Yet these military actions are not unique to alliances – aligned states that are not formally allied also militarily cooperate to improve security against a common adversary. In an effort to understand a broader range of military commitments that are not encapsulated in military alliances, this project examines what I define as “material commitments" or physical military actions taken by an independent state in peacetime to bolster another state’s security or improve joint military coordination against a common threat arising from an international dispute. Material commitments are defined by several key components. First, material commitments are the actual military measures that a state employs to improve another state’s security against a common threat. Improving another state’s de- fense can entail: increasing its ability to fight effectively (offensive capabilities), increas- ing its ability to withstand attacks (defensive capabilities), and/or increasing joint military cooperation to coordinate combined war-fighting efforts. The ATOP dataset includes vari- ables that measure the institutionalization of an alliance or the “arrangements the part- ners make to organize collaboration," which are coded from the text of legal documents or treaties. 1 Yet states do not always uphold their international agreements, choose to act be- yond the conditions specified, or make military commitments outside of alliances. Studies on alliances find that states do, indeed, violate their treaty commitments (Berkemeier and Fuhrmann 2018). Allied states may also employ military actions that go beyond what is 1 See Leeds et al. (2002, 243), section on ATOP coding of alliance design. 20 specified in their alliance. For example, the US-South Korean mutual defense treaty does not include provisions for military contact between the two countries, military aid, or sub- ordination of South Korean forces to US command during conflict. Yet the US and South Korea maintain consistent contact between defense officials and the two militaries, South Korea was a major recipient of US military aid during the Cold War, and the US still retains wartime operational control under the Combined Forces Command (CFC). Finally, military commitments are not limited to formal alliances and states make material commitments to non-formal allies too, such as arms transfers, troop deployments, and military aid. It is important to note that material commitments are distinct from, but not exclusive of, writ- ten or verbal promises to undertake certain military actions; they are the actual actions themselves. In other words, material commitments may be outlined in or carried out from alliances but they need not be as well. Second, material commitments are military actions taken in preparation for potential conflict. In other words, material commitments are made in peacetime preceding any militarized conflict. This definition excludes military measures taken when both states are at war against a common opponent because such forms of military cooperation, while having a large effect on the battlefield, have less of an impact on the strategic behavior of states in dispute that are deciding whether to go to war or not. Put differently, military transfers or actions between a third-party defender and a target state during war against a challenger are not included in the definition of material commitments. For example, we should expect there to be significant differences in troops mobilized and deployed for an ongoing war (World War II) versus troops deployed to permanent overseas bases in anticipation of and to prevent a potential conflict (NATO). This project is mainly concerned with examining extended deterrence and the likelihood of militarized conflict under the shadow of a third-party actor’s military commitments. Thus, the study of ad-hoc military coalitions established for the purpose of waging war are reserved for other studies outside 21 of the scope of this project. 2 Last, material commitments should be aimed at improving a state’s security against a known and common adversary that is involved in a dispute between independent states. Because this project focuses on questions pertaining to alliances, third-party involvement in international disputes, and state behavior in crisis bargaining, material commitments are limited to military actions in preparation for a potential conflict among states. As a result, this definition does not include military cooperation between states aimed at ad- dressing threats from non-state actors or bolstering security for general purposes, such as countering terrorism and piracy, enhancing cybersecurity, quelling internal unrest, or increasing intelligence-sharing. 3 Material commitments are made between independent states which means military “cooperation" that occurs under colonization or forced occu- pation of another state is also not included under this definition. Spatial and Temporal Variation in Military Commitments Military commitments vary between states (spatial) and over time (temporal). First, we observe significant variation in the types of military commitments made between states. States are not confined to a binary choice between entering into an alliance or not (one type of military commitment). Instead, states can choose from a broad toolbox of different military strategies that incorporate either or both treaty and material commitments. Even among material commitments, there is wide variation in the types of military actions a state can employ on behalf of another state’s security, and each type of military measure has a unique effect on the strategic environment of actors in dispute. For example, arms 2 For more on military coalitions aimed at war see Wolford (2015). 3 It may be the case that alliances or material commitments are used for military purposes outside their original intended purpose. For example, member states of the Warsaw Pact invaded Czechoslovakia in 1968 to crush liberalization reforms and strengthen the Communist Party of Czechoslovakia. In 2011, members of the Gulf Cooperation Council deployed the Peninsula Shield Forces in response to civil unrest in Bahrain. While these instances saw the use of material commitments to address threats by non-state actors or inter- vene in internal affairs, if the main purpose of material commitments is to increase the security of member states against threats from other states, then such cases are included. 22 transfers will have a different effect on the balance of power than integrating two (or more) states’ militaries. In Chapter 3, I specifically examine each of these unique effects and how different military commitments have varying impacts on states’ behaviors and conflict outcomes. Clearly, not all military commitments between states are created equal. Because there is inherent variation in the types of military actions states can take and their effects on the strategic environment, we see stark differences between the military commitments that formal and non-formal allies receive as a result. Just as the decision to form an alliance is not random, the decision to invest in material commitments, or phys- ical military measures, to improve another state’s security is made strategically, and this includes non-formal allies. In addition, the types of military commitments that non-formal allies receive from third-party defenders are substantial. The top importers of US arms and the top recipients of US military aid are not formal allies. 4 While the ATOP dataset does not include arms sales agreements and military aid agreements in its working definition of alliances, I argue that these types of military commitments (i.e. material commitments) do, in fact, have a significant influence on the strategic behaviors and calculi of states in dispute because they can alter the balance of power in ways comparable to the effect alliances have on conflict behavior. Not only is there spatial variation in military com- mitments between formal and non-formal allies, but we see wide variation in material commitments among even members of the same alliance. For instance, US troop deploy- ments to Germany versus Belgium – despite both being significant NATO allies – illustrate the wide variation in military commitments under even a common military alliance. 5 Second, military commitments can change over time. ATOP provides substantial in- formation on the negotiated agreements between states at the time of signing. Although the ATOP dataset accounts for renewals or amendments in alliances over time by mea- suring different phases of an alliance (i.e. if agreements change), the dataset only notes 4 See https://www.sipri.org/media/press-release/2020/usa-and-france-dramatically-increase-major- arms-exports-saudi-arabia-largest-arms-importer-says 5 From 1950-2015, the peak level of permanently stationed US military personnel in Germany was 274,000 compared to 3,500 in Belgium (Kane 2016, 7). 23 changes to alliances when they are renegotiated by both states, if applicable. 6 As a re- sult, our current measures of treaty commitments only provide a brief snapshot of military commitments at the time the alliance was agreed upon or revised. Empirically, military commitments vary significantly across different states (even those in the same alliance) and evolve substantially over time to meet new security challenges and enhance military coordination. In particular, alliances signed shortly after a war may invoke different types of material commitments to meet the security needs of that time. For instance, one might expect that the goal and design of military commitments made during the Cold War differ from the military commitments made afterwards. A stationary measure of military com- mitments – or a measure of only treaty commitments – is limited in explaining changing trends in military cooperation between states and whether material commitments follow from the obligations and provisions laid out in alliances. In the following sections, I outline several dimensions on which military commitments vary. How Do We Measure Military Commitment? While formal alliances do not change significantly from the time of their formation, mili- tary cooperation between states constantly changes in meaningful ways that has implica- tions for important outcomes of interest, like how states behave in disputes and whether alliances actually deter conflict. A related, but often overlooked, question is: what exactly do formal military alliances represent? When researchers use alliances as an explanatory variable to predict outcomes related to conflict, what do alliances actually measure? To answer enduring questions about the role of military alliances in international relations and security, we must first consider whether alliances are appropriate measures. Alliances are only one of many types of observed means of military support from one state to another. Formal military alliances, along with other military actions such as arms 6 For more on how ATOP codes different alliance phases, see ATOP codebook p. 13. 24 transfers, troop deployments, or military aid, are all observable indicators of an underlying latent variable: third-party military commitment. A third-party military commitment is the unobserved extent to which an external actor (third party to a dispute) is willing to militarily support, or commit itself to, its preferred side in a conflict (target of a demand in a dispute). When war occurs and military commitments are put to the test, we may observe a third party’s level of military support by seeing if it honors its alliances (Leeds, Long and Mitchell 2000; Leeds 2003a; Berkemeier and Fuhrmann 2018). Yet military measures on behalf of another state’s defense are often taken in peacetime as a means to prevent conflict from occurring. Thus we do not directly observe the latent level of external military commitment unless deterrence has already failed. 7 Current scholarship that examines variation in military commitments is limited to ex- plaining differences between formal alliances (Leeds et al. 2002; Benson 2011, 2012; Ben- son and Clinton 2016). But a latent construct of third-party military commitments goes well beyond military alliances at the time of their formation. If we only use variation in al- liances as a measure for third-party military commitments, we would consider all members of the North Atlantic Treaty Organization (NATO) to receive the same amount of military support from the United States. Empirically, this is not the case. 8 Similarly, a measure of military commitments that only looks at alliances will not capture variation over time nor commitments to non-formal allies. How, then, do we characterize and distinguish dif- ferent levels of military commitment from one state to another? In other words, how do we compare US military cooperation with each individual member of the same alliance like NATO? How do we compare US military support over time, such as during and after the Cold War? And how do we compare US defense commitments to formal allies (NATO, South Korea, Japan) and non-formal allies (Taiwan and Israel)? 7 This points to the difficulty of determining whether deterrence is successful or not because we can only observe the cases in which it fails, but the observed absence of conflict is not necessarily evidence that deterrence has succeeded. See Fearon (1994b). 8 On average, the United States deploys around 70,000 troops to Germany compared to 22,000 to the United Kingdom and only about 1,500 to Belgium. Numbers are compiled from Kane (2016) and the US Department of Defense, Defense Manpower Data Center (DMDC). 25 This chapter uses a statistical measurement model to estimate the latent level of US military commitment to states over time. I employ Bayesian factor analysis for mixed or- dinal and continuous responses, as specified in Quinn (2004), to provide a novel way of comparing military commitments across country pairs, whether formally allied or not, and at different points in time. I show that military measures that increase joint capabilities, or military support for improving military cooperation between states, should be associated with higher levels of third-party military commitment, than those that increase a target’s unilateral capabilities, or its independent fighting ability. 9 An external actor to a dispute can either improve its ability to fight with the target state against a common threat (joint capabilities) or transfer the tools needed for the target to fight alone (unilateral capa- bilities). I find that military actions that increase joint capabilities are indeed positively associated with higher values of the latent factor of third-party military commitment than those that increase a target’s unilateral fighting capability. Target countries that receive improvements in joint capabilities – such as foreign nuclear deployments, foreign military installations, and defense pacts – score higher on the scale of US military commitment than countries that do not get these measures. Unilateral transfers, such as military aid, are associated with low values of military commitment. There are several significant implications that arise from measuring third-party military commitment as a latent variable. First, a statistical approach to measuring military com- mitments provides a method for comparing different forms of military cooperation that variation in alliances alone cannot account for. The main goal is to create a principled way of aggregating different observed indicators of military cooperation between states over time using theoretically informed measures of third-party military commitment. The re- sults support the argument that there is significant variation among members of the same alliance that measures of military commitment that use only alliances cannot account for. While US formal allies indeed score higher on the latent factor of US military commitment, 9 For more details, see my working paper “Arms, Alliances, and Everything Else: Variation in Third-Party Military Commitments." 26 we currently do not have a systematic method to make this comparison with our current measures. The Bayesian latent variable approach presented in this paper produces a set of rules for comparing military commitments across individual states, across time periods, and across regions. Essentially, we can “rank" or compare US military commitments to different countries in a given year based on a common scale. This allows scholars to make important comparisons and conduct analyses for enduring questions in international re- lations, such as whether there are meaningful differences between multilateral (NATO) versus bilateral (hub and spokes in East Asia) security structures, the effects of the advent of nuclear weapons and the end of the Cold War on security relations, and the use of power projection as a means of achieving foreign policy goals. Measuring military commitments as a latent variable also has important implications for the empirical study of alliances and conflict. Do military alliances reduce or raise the likelihood of interstate conflict? This question is central to understanding the role alliances play in international relations and security, but the empirical record remains divided on whether military alliances deter or provoke conflict. Traditionally, formal alliances repre- sent external military support that influences the likelihood of conflict through a number of different mechanisms, such as costly signaling to deter adversaries (Fearon 1997), em- boldening recipients of military support (Benson 2012), or even restraining them (Cha 2009; Fang, Johnson and Leeds 2014). Some studies point to defensive alliances as reduc- ing conflict due to their deterrent effect (Leeds 2003b; Johnson and Leeds 2011; Benson 2012; Leeds and Johnson 2016). Others argue that forming alliances do not effectively de- ter adversaries and can even raise the likelihood of militarized conflict (Kenwick, Vasquez and Powers 2015; Kenwick and Vasquez 2016). 10 Most models of conflict use a binary measure of alliances as an explanatory variable or as a standard control to account for whether a state in a dispute has an outside ally or not. Yet this oversimplified measure can bias predictions about conflict because states that 10 See also Morrow (2016) for an assessment of the conditions under which alliances reduce or raise the likelihood of conflict. 27 receive significant military support from external actors, like Taiwan and Israel, will be coded as zero while states that receive significantly varied support, such as Belgium versus Germany, will both be coded the same. The consequences of measurement error in regres- sion analysis are substantial. “Estimated slopes are biased and inconsistent. With only one poorly measured variable... the coefficient on that variable is attenuated, while the others are biased and inconsistent in unknown direction and magnitude" (Treier and Jackman 2008, 203). Thus we must recognize that observed indicators of military cooperation be- tween states, especially alliances, are imperfect measures of a state’s underlying (latent) military commitment and that error in measurement should be accounted for (Treier and Jackman 2008, 202-203). Why Alliances Alone Are Not Enough What are the limitations of measuring variation in third-party military commitments as formal alliances? If formal alliances are perfect complements of other forms of military actions, then they can account for all the variation in military cooperation between states. Clearly, this is not the case. Military commitments are not restricted to states in alliances nor the obligations and provisions agreed upon at the time of formation. In fact, military commitments between members of even the same alliance can differ significantly across states and over time. US troop deployments to individual members of NATO drastically vary (Figure 2.1). A measure of third-party military commitments that only uses alliances will code Germany, Turkey, and Luxembourg as receiving the same level of military support from the United States. 11 Yet, empirically, this comparison is misleading. In addition, states often design strategically ambiguous alliances to allow for greater flexibility (Benson 2012; Chiba, Johnson and Leeds 2016; Mattes 2012b) and there are real differences between what states promise to do (words) and what they actually do (deeds) (Leeds and Anac 2005; Fuhrmann and Sechser 2014). 11 Luxembourg is actually one of the founding members of NATO. 28 Figure 2.1: US Troop Deployments to NATO Countries, 1950-2014 Spain Turkey United Kingdom Norway Poland Portugal Romania Slovakia Slovenia Iceland Italy Latvia Lithuania Luxembourg Netherlands Denmark Estonia France Germany Greece Hungary Albania Belgium Bulgaria Canada Croatia Czech Republic 1960 1980 2000 1960 1980 2000 1960 1980 2000 1960 1980 2000 1960 1980 2000 1960 1980 2000 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 Y ear Troops (in thousands) US troop deployments to individual members of NATO. Data missing for years 2007 and 2008. Source: Kane (2004) and US DoD Defense Manpower Data Center. Comparisons across members of the same alliance are diffcult and so are comparisons over time. Current measures of military commitments that rely on alliances only pro- vide a snapshot of external military support at the time of alliance formation. Benson and Clinton (2016) provide factor scores for the breadth of legal obligations (scope), the peacetime costs that an alliance imposes on its members (depth), and the total adjusted potential military strength (military capacity) of each unique alliance coded in the ATOP dataset, but their measure only captures the latent construct at a fixed point in time (i.e. time of alliance formation). 12 Put simply, observed indicators of US support to South Korea are measured by the mutual defense pact signed in 1953. But US-South Korean military 12 The ATOP dataset assigns a unique identifier to each alliance based on the time of formation, with higher numbers representing more recent alliances. For example, NATO is coded 3180 and the US-South Korea alliance is coded 3240. 29 cooperation has fluctuated significantly over time, such as the removal of thousands of US troops under the Nixon Doctrine and both the deployment and withdrawal of US nuclear weapons from South Korean soil. A measure of formal alliances will not capture tempo- ral variation which is important because military commitments and cooperation between states evolves over time in response to changes in both structural constraints and states’ internal preferences. Beyond alliances, how should we compare third-party military commitments between allies and non-formal allies? Table 2.1 contains descriptive statistics for different indica- tors of military commitment across US formal allies and non-allies. Figures 2.1 and 2.2 show that there are important differences between military commitments made to allies versus non-allies. On average, the United States deploys troops to allied countries consis- tently over time whereas troop deployments to non-allies are mostly contained to US wars abroad. Clearly, US allies receive more external military support from the United States; but certain types of commitments (like arms transfers) are not limited to formal allies and we observe an upward trend in US arms exports to non-allies in recent years. Again, a measure of variation in alliances will not capture these important differences in the actual implementation of military commitments. Put together, this means that alliances are only one type of military commitment that a state can make on behalf of another state’s security. In other words, there is meaningful variation across not only alliances but other forms of military cooperation as well. 30 Figure 2.2: US Arms Transfers to Formal and Non-formal Allies 0 5 10 1950 1960 1970 1980 1990 2000 2010 Y ear Volume (in hundreds of thousands) Formal Allies Non−Formal Allies According to SIPRI, the volume or “TIV is based on the known unit production costs of a core set of weapons and is intended to represent the transfer of military resources rather than the financial value of the transfer." Source: SIPRI Arms Transfers Database. Table 2.1: US Military Commitments to Formal Allies vs. Non-Formal Allies Observed Military Commitment Years Formal Allies Average Non-Allies Average Total Average Conventional arms transfers 1950-2014 211.01 mil 142.92 mil 184.57 mil Military aid 1945-2014 161.43 mil 130.28 mil 143.78 mil Troops (in thousands) 1950-2014 5.21 1.42 3.08 Value of Foreign Military Installations 1999-2014 1113.29 231.34 817.64 (USD millions) N = 3; 391 N = 6; 271 N = 9; 662 Theoretical Expectations In the following chapter, I examine a formal model that shows why and when states make different types of military commitments and how variation in military cooperation influ- 31 ences state behavior in international disputes. 13 I argue that different types of military commitments have varying effects on states’ abilities to fight (or their military capabili- ties). As a result, an external actor, like the United States, has incentives to make certain types of military commitments to some states, but not others. I find that a third party to a dispute will invest in external military support that improves states’ joint military capa- bilities only if it would intervene on behalf of its preferred side (the target state). Military commitments that increase joint capabilities require active cooperation between states and cannot be employed without coordination between both the defender and target. For ex- ample, US-South Korea joint capabilities include an integrated military command under the CFC, annual joint military exercises that facilitate military coordination during a con- tingency, and permanent US bases on Korean soil that house US troops stationed abroad. In my model, I also show that a third-party defender only forms an alliance with a target (i.e. defense pact) when it would indeed defend it in war. In contrast, a third-party defender can also invest in improving a target state’s unilateral military capabilities or the target’s ability to fight alone. In other words, the United States can transfer military technologies or financial support – such as arms transfers and military aid – that increase a country’s ability to wage war on its own. Unilateral capabilities do not necessarily require joint cooperation between states for their effectiveness. States can transfer the military tools and means for other states to fight on their own. For instance, the US F-35 Joint Strike Fighter (JSF) Program exports advanced US fighter jets to countries that can be used for their independent military capabilities. 14 I expect to find that observed indicators that represent improvements to joint capabil- ities (troop deployments, nuclear weapons, military installations, and defense pacts) are 13 Working paper available upon request. 14 “So the Brits, who will fly their F-35s from carriers, have just gained that ability to do on their own a lot of the fancy stuff that they could do until now only with the Americans. If they want to carry out a deep stealth strike against, say, Argentina, they don’t need the US to hold their hand to do it. Likewise, their contributions will become more important in any coalition, including one involving the US military. So a whole bunch of countries can now operate at a much higher level, with greater strategic impact, independent of the US." https://www.vice.com/en_us/article/d39eyv/what-does-the-f-35-mean. Accessed November 11, 2019. 32 stronger measures of latent military commitment than those that improve unilateral ca- pabilities (conventional arms transfers, military aid). In terms of an item response theory (IRT) model, joint capabilities should have higher difficulty (more costly military action to engage in) and higher discrimination (costly actions are more informative of military commitment) than unilateral capabilties. A Measurement Model of Military Commitment Data I use an original dataset of US military cooperation with countries from 1950 to 2014. The unit of analysis is the directed dyad-year, or US-country X pairs in which the United States provides some type of military support to country X in year t. At present, the dataset only includes US military measures due to the availability of data but, because the United States maintains a large network of military alliances (with over 50 unique countries) and provides some sort of military support to over 200 countries, there is no shortage of observations. 15 In the following section, I describe the data and manifest variables in detail. I identify six different manifest variables to estimate the latent level of military com- mitment and compile indicators for each variable from several different data sources. US troop deployments, foreign nuclear deployments, and foreign military installations all rep- resent military measures that improve joint capabilities. Without active US military fa- cilitation, coordination, and cooperation, these military measures cannot be used by the target state alone. In other words, the movement of deployed forces requires close co- ordination between states to utilize in war. This stands in contrast to improvements in 15 There are a total of 9,819 observations in the dataset (from 1950-2014). I used the COW Trade Data (Barbieri and Keshk 2016) as the base data and merged in data on US military cooperation from other sources. The COW Trade Data has a total of 13,584 observations for the US from 1870 to 2014. I chose a dataset that would be comprehensive enough to capture most – if not all – US relations with other states in the international system over time, both allies and non-allies. 33 the target’s unilateral capabilities, such as military aid and arms transfers, because these military “tools" can be used by the target to bolster its own military and ability to fight. For example, foreign aid that contributes to military training and financing for defense sales does not require active cooperation between states after aid has been received. 16 In this section, I describe each manifest variable in detail. The data sources and variables are summarized in Table 2.2. Table 2.2: Dataset and Variables Data Source Variable Measure Years Joint capabilities Kane (2016) and Defense Manpower and Data Center Troop deployments Total number of troops deployed to host country 1950-2016 Fuhrmann and Sechser (2014) Foreign nuclear deployment Coded 1 if nuclear deployment present; 0 otherwise 1945-2000 US Base Structure Report Foreign military installation Calculated cost (USD mil) to replace DoD property 1999-2017 Unilateral capabilities Stockholm International Peace Research Institute (SIPRI 2020) Arms exports/transfers Total volume of transfers to host country (TIV) 1950-2018 USAID Greenbook (USAID 2017) Military aid Total foreign military aid (in constant USD) 1945-2018 Treaty commitments Alliance Treaty Obligations and Provisions (Leeds et al. 2002) Defense Pact Coded 1 if formal defense treaty; 0 otherwise 1815-2014 TROOP DEPLOYMENTS. This variable measures US troop deployments to foreign coun- tries. Data on troop deployments from 2008-2016 were collected from the US Department of Defense (DoD), Defense Manpower and Data Center (DMDC) and used to extend the original dataset developed by Kane (2004), which covered the time period from 1950- 2005. 17 The data represent a snapshot of military personnel stationed abroad at a given point in time, annually. The separate branches of the military – Army, Air Force, Navy, and Marines – are aggregated by country and year. FOREIGN NUCLEAR DEPLOYMENTS. This variable codes whether the United States de- ployed a nuclear weapon to another country. Because the movement of nuclear weapons abroad is often kept confidential, Fuhrmann and Sechser (2014) use a high bar for entry into the dataset and consult three independent sources for verification. 18 FOREIGN MILITARY INSTALLATIONS. This variable measures military installations owned 16 While it is true that recipients of US military aid tend to receive aid over long periods of time, the point here is that military aid can be used by the target state to bolster its own military without constant consultation with or approval from the United States. 17 Data for US troop deployments from fiscal years 2006 and 2007 are missing. 18 See the appendix in Fuhrmann and Sechser (2014) for a brief description of the types of nuclear weapons deployed. Sender states are three countries: the United States, Great Britain, and the Soviet Union. 34 and leased by the US government in foreign territories. The data are provided by the US Base Structure Reports (BSR), which account for DoD sites, or “physical (geographic) location[s]... owned by, leased to, or otherwise possessed by a DoD Component" (DoD 2014). 19 This variable represents an inventory of the real property of the US Federal Government, both domestically and abroad. Overseas military assets aim to measure the cost of maintaining military facilities (including bases, training facilities, storage, etc.) overseas and the monetary value placed on each site. In particular, the plant replacement value (PRV) is a calculated value for all DoD facilities that represents the cost to replace a physical facility and supporting infrastructure using current construction costs (labor and materials) and standards (methods and codes). 20 Data for each military installation abroad are provided and are aggregated at the country level to match the unit of analysis (dyad-year). 21 CONVENTIONAL ARMS TRANSFERS. This variable measures the actual deliveries of major conventional weapons from one state to another, or US arms exports to a country. The data are sourced from the SIPRI Arms Transfers Database, using the unique trend-indicator value (TIV) as a common unit for comparison across different types of weapons systems. According to SIPRI, the “TIV is based on the known unit production costs of a core set of weapons and is intended to represent the transfer of military resources rather than the financial value of the transfer." 22 Thus this variable represents the volume of conventional arms transfers rather than their actual financial value (i.e. sales prices). MILITARY AID. This variable measures US military aid to foreign countries in constant 19 See p. 3 in BSR for Fiscal Year 2015. Each site is within an installation: “a military base, camp, post, station, yard, center, homeport facility for any ship, or other activity under the jurisdiction of the Department of Defense, including leased space, that is controlled by, or primarily supports DoD’s activities." 20 The PRV is calculated by: PRV = facility quantity x construction cost factor x area cost factor x historical records adjustment x planning and design factor x supervision inspection and overhead factor x contingency factor. For a measure of each variable, see p. 5 in BSR Fiscal Year 2015. 21 For example, there is a unique entry for each military installation per country such as Camp Humphreys and Yongsan in South Korea. I aggregated the individual property values into a single observation per country and year. 22 See https://www.sipri.org/databases/armstransfers/sources-and-methods. Accessed November 4, 2019. 35 US dollars. The data are collected from USAID’s annual publication on foreign assistance, “U.S. Overseas Loans and Grants" or the “Greenbook." The Greenbook reports on both eco- nomic and military assistance. Military assistance is defined as “foreign aid for programs primarily for the benefit of recipient government armed forces, or aid which subsidizes or substantially enhances military capability. Military assistance excludes humanitarian and non-military development programs funded by the U.S. Department of Defense" (US- AID 2017, 7). Military assistance programs include: cooperative threat reduction, foreign military financing, and international military education and training. DEFENSE PACT. This variable measures whether two countries have a formal defense pact or not. I adopt the coding scheme in the ATOP codebook which defines a defense pact as the following: “Dummy variable coded 1 if the alliance member promises to provide active military support in the event of attack on the sovereignty or territorial integrity of one or more alliance partners. A promise to treat such an attack on one alliance member as an attack on all alliance members qualifies as a promise of defensive support" (Leeds et al. 2002, 22). I chose defense pacts instead of the existence of an alliance or not because defensive support should be a stronger measure of latent third-party military commitment than other types of alliances, such as consultation, neutrality, or non-aggression pacts. Another potentially strong indicator of external military support would be offense treaties, or obligations of active military support without conditions on a precipitated attack, but there are no offense alliances in the present dataset. Summary statistics of the six observable indicators are provided in Table 2.3 and their distributions are presented in Figure 2.3. 36 Table 2.3: Descriptive Statistics for Manifest Variables Manifest Variable Type Mean SD Min Max Observations Troop deployments (thousands) Continuous 3.08 18.38 0 537.38 6738 Foreign nuclear deployment Binary 0 1 7036 Plant Replacement Value (PRV) Continuous 817.64 3881.26 0 41684.7 352 Conventional arms transfers Continuous 184.57 mil 346.39 mil 0 4452 mil 3193 Military aid Continuous 143.78 mil 683.49 mil 0.001 mil 14563.53 mil 5377 Defense Pact Binary 0 1 9662 Figure 2.3: Distributions of Manifest Variables 0 2000 4000 6000 0 1 Defense Pact Count 0.0 0.1 0.2 0 5 10 Log of Troops Density 0.00 0.05 0.10 0.15 10 15 20 Log of Military Aid Density 0 2000 4000 6000 0 1 Foreign Nuclear Deployment Count 0.00 0.05 0.10 0.15 0 2 4 6 8 Log of Arms Transfers Density 0.00 0.05 0.10 0.15 0.20 0 4 8 Log of Plant Replacement Value (PRV) Density Distributions for continuous variables are logged. Model Specification: Bayesian Mixed Data Factor Analysis The basic intuition of Bayesian analysis is that we have a set of beliefs, or priors, about the state of the world before looking at data. A likelihood distribution informs us of what the data means by estimating the parameter values that would make it most likely to observe 37 the data that we see. By combining the prior and likelihood distributions, the posterior distribution tells us which parameter values maximize the chance of observing the data that we do given the priors we had. This is analogous to information updating under Bayes’ Rule. Using sampling methods, such as Markov chain Monte Carlo (MCMC), we can approximate the posterior distribution by repeatedly drawing samples (or iterations) from it. 23 In the latent variable context, the aim is to specify a statistical measurement model that can identify patterns of association between different observed variables that arise from a common underlying unobserved variable – in this case, third-party military commitment (Quinn 2004, 339). Latent variable models assume local independence among observed variables, such that the observed indicators should not have causal relationships with each other. Instead, the predicted associations between observed variables are due to their com- mon relationship with the underlying, unobserved variable. 24 Figure 2.4 illustrates the ba- sic intuition of the measurement model estimated. There is an underlying level of military commitment between states, whether they are allies or not. The “responses" or values of observed indicators are used to estimate a measure of latent military commitment, with some degree of error since we can only imperfectly measure unobserved traits. In Bayesian factor analysis, the factor loadings (correlation coefficient for observed indicator and latent variable), factor scores (estimated numerical value on scale of latent variable), and error variance (how much variation is explained in latent variable by observed variables) are calculated from estimates of the posterior distribution. Table 2.4 reports the correlation matrix of the observed indicators. 23 For a basic explanation of MCMC, see https://towardsdatascience.com/a-zero-math-introduction-to- markov-chain-monte-carlo-methods-dcba889e0c50 24 See also Huddleston (2019, 12). 38 Figure 2.4: Latent variable model of military commitment Credit to Huddleston (2019) for inspiration for this visual Table 2.4: Correlation Matrix Defense Pact Troop Deployments Arms Exports Military Aid PRV Nuclear Deployment Defense Pact 1 0:028 0:139 0:028 0:195 0:408 Troop Deployments 0:028 1 0:657 0:007 0:909 0:512 Arms Exports 0:139 0:657 1 0:301 0:573 0:615 Military Aid 0:028 0:007 0:301 1 0:154 0:102 PRV 0:195 0:909 0:573 0:154 1 0:461 Nuclear Deployment 0:408 0:512 0:615 0:102 0:461 1 I conduct Bayesian factor analysis for mixed ordinal and continuous responses to esti- mate the latent trait,x i , for each uniti = 1;:::;N that corresponds toj = 1;:::;K response variables for each observation (Quinn 2004). 25 Third-party military commitment is mod- eled as a latent variable, x i , for each observation i (US-country X dyad) with j values of the observed indicators of military cooperation. An observed variable, x ij , can be ei- 25 The function, MCMCmixfactanal, is used from the package MCMCpack inR https://cran.r-project.org/ web/packages/MCMCpack/MCMCpack.pdf, pp. 87-91. 39 ther ordinal with C j categories or continuous. The distribution of X is determined by a NK matrix of latent variables, X , and cutpoints at . 26 The Bayesian factor analytic model generates patterns of association between the observed variables in X to estimate the latent variableX according to: x i = i + i (2.1) where x i is the k-vector of latent variables for observation i, is the kd matrix of factor loadings, and i is the d-vector of latent factor scores. The first element of i is assumed to be equal to 1 for all i. 27 The error term is a vector of disturbances that is normally distributed with mean 0 and variance such that: i N (0; ) (2.2) A mixed data factor analysis is appropriate given that the data contain both continuous and binary (or ordinal) manifest variables. I treat the two binary variables, NUCLEAR DEPLOYMENT and DEFENSE PACT, as ordinal variables. MCMC is used to fit the model by simulating from the posterior distribution using a Metropolis-Hastings within Gibbs sampling algorithm. 28 To measure latent US military commitment,x i , I take the posterior means for every US-Country X dyad per year with 100,000 iterations and 1,000 burn- ins. 29 Trace plots for the factor loadings and error variance of each manifest variable can be found in the Appendix, Figure 2.9. 26 The cutpoint isx ij if variablej is continuous andc ifx ij 2 ( j(c1) ; jc ] and variablej is ordinal. 27 This assumption ensures that “the elements in the first column of function as negative item diffi- culty parameters for the ordinal response variables. The elements in first column of that correspond to continuous responses represent the mean of these continuous variables" (Quinn 2004, 340). 28 SeeR package MCMCpack. 29 Burn-ins are essentially “warmup draws" that help the model converge and estimates are thrown out. 40 Results Factor Loadings and Error Variance In this section, I turn to a discussion of the estimated measures of US military commitment to states. The goal of this paper is to develop a principled way to aggregate observed indicators of military cooperation to measure unobserved US military commitments to countries and to be able to compare different country pairs along a common scale. Table 2.5 summarizes the posterior distributions of the factor loadings for each indicator () and the error variance ( ) for observations in year 2000. 30 The factor loading, , indicates the correlation coefficient for the observed variable and the latent factor, or how much variation in the observed variables is being explained by a shared association with the latent variable. Put simply, factor loadings describe the strength of the link between latent third-party military commitment and each observed indicator of military cooperation. The error variance, , indicates how much variation in the observed variables are explained by other underlying factors. The continuous variables were logged and standardized to normal distributions with mean 0 and standard deviation 1 in the model. The factor loadings for troop deployments and military aid are in line with my theoretical expectations: military cooperation that improves joint capabilities (like troop deployments) load positively on the latent factor of third-party (here, US) military commitment. Military aid, a transfer that increases the target’s unilateral capabilities, has a negative factor loading of -0.16 which implies that states that receive more military aid are less correlated with firm external military support. Again, this is in line with my theory which argues that transfers of military tools imply 30 I present the summary of the posterior distribution for a single year instead of the full time-series dataset due to computing challenges and missing data. The full dataset includes over 9000 observations for which many values of certain indicators, namely the PRV, are missing. This means that, for the model to store factor scores, a lot of memory (and time) is required. Additionally, missing data issues mean there are not many complete cases (i.e. when all indicators have a value) which makes estimation difficult. I report and in Figure 2.10 in the appendix. Because I did not constrain the parameters, the factor loadings are all negative. 41 lower levels of latent military commitment because the third-party defender is strategically avoiding tying its hands to another state’s defense. Conversely, conventional arms transfers are positive and load higher than troop deployments (a form of joint capabilities). A potential explanation for this result is that troop deployments may have some noise in terms of improving joint capabilities between the defender and target. It may be the case that US troop deployments abroad are being used for purposes other than the defense of a country, such as peacekeeping operations, contingency operations or even wars. Foreign nuclear deployments and foreign military installations (as measured by the PRV) also score positively on the latent factor with relatively high loadings of 0.61 and 0.78 respectively. In expectation, countries receiving higher levels of military commitment should be more associated with being hosts of US military bases/DoD property and/or house US tactical nuclear weapons. Defense pacts, or formal alliances that include obli- gations for the defense of a country under unprovoked attack, also have positive factor loadings of 0.56 and explain a high amount of variation in the latent variable. While al- liances and military commitment have positive association, the factor loadings show that alliances are not complete complements for other forms of military cooperation like foreign deployed nuclear weapons or military bases. Not all formal allies receive these extremely costly forms of external military support and this variation is reflected in the latent factor. Table 2.5: Summary of Posterior Density (2000) Observed Indicator Factor Loading () Error Variance ( ) Troop deployments (thousands) 0.37 0.87 Foreign nuclear deployment 0.61 0.65 Plant Replacement Value (PRV) 0.78 0.41 Conventional arms transfers 0.57 0.69 Military aid -0.16 0.98 Defense Pact 0.56 0.70 42 Substantive Country Comparisons To understand the real empirical value of the latent variable measurement model, I present several substantive country comparisons that are made possible with the estimated factor scores. There are two points to first note: 1) the marginal credible intervals in the plots indicate that the mean estimates of latent US military commitment contain uncertainty given that we are measuring an unobserved variable and, 2) to determine whether one ob- servation (a) has a higher value of the latent factor than another (b), we need to calculate the posterior probability that a is greater than b (Quinn 2004, 348). 31 Regional Variation: East Asia Figure 2.5 shows the posterior means of i , or the factor scores, for different countries in East Asia in 2000. I chose this particular year because it contains a good amount of com- plete cases, especially since the overlap between the PRV and foreign nuclear deployment data is limited to only two years (1999 and 2000). In East Asia, Japan and South Korea are on the higher end of the scale, meaning that US military commitments are stronger for these countries than others like the Philippines and Taiwan. Even though we would not expect the US to militarily commit itself to defend a country like North Korea, I include it as a check of face validity: it scores lowest on the scale, with Vietnam, which indicates that US commitment is weakest for these countries. Taiwan is also an interesting case in that the United States maintains close security relations with Taiwan and exports de- fensive, unilateral military articles under the provisions of the Taiwan Relations Act; yet Taiwan scores relatively low on the scale of US military commitment. In line with my theoretical expectations, this puzzling behavior – that the United States would continue to pour costly military investments into bolstering Taiwan’s unilateral military capabilities – is explained by the US’ relatively low level of commitment, or coming to Taiwan’s defense 31 Calculating the posterior probability is relatively straightforward. One can take the MCMC output from the model and calculate the fraction of draws where a > b . 43 in war, despite its costly military measures. Instead, as my theoretical model shows, the United States is willing to make costly, upfront military investments to increase the target state’s unilateral fighting ability even if it would not support it in war because this gives the target a better bargaining position in disputes. 32 Figure 2.5: Posterior Means for East Asian Countries in 2000 North Korea Vietnam Taiwan Philippines South Korea Japan −1 0 1 2 3 Latent Factor Score Plot of estimates of latent US military commitment to East Asian countries in 2000. The dots are posterior means and the lines show central 95% credible intervals for each US-Country X dyad. Model was run with 100,000 MCMC iterations and 1000 burn-ins. Variation within Alliance: NATO One of the biggest limitations of current measures of third-party commitments is that they cannot account for variation within alliances. Figure 2.6 shows that this is precisely the case: that US military commitments to members of even the same alliance can vary signif- icantly. This has significant implications for how we code and empirically test the relation- 32 Formal model not presented in this paper but summarized briefly in section 2. 44 ship between external military support and conflict. A measure of formal alliances would code the individual countries in Figure 2.6 the same despite the meaningful differences that exist among them. For example, Poland and the Czech Republic are at the low end of the scale, indicating that US military commitments to these countries is weakest compared to other NATO members like Germany and the United Kingdom. As former members of the Warsaw Pact and more recent signatories of NATO, this result is not surprising. The main implication is that a measure of third-party commitment that uses alliances would treat US military support to Poland and the Czech Republic as indistinguishable from US support to Germany. The consequences of measurement error are substantial as improperly measured explanatory variables can bias estimates of outcome variables. Figure 2.6: Posterior Means for NATO Members in 2000 Czech Republic Poland Luxembourg Spain Greece Turkey United Kingdom Italy Belgium Germany −1 0 1 2 3 4 Latent Factor Score Plot of estimates of latent US military commitment to NATO members in 2000. The dots are posterior means and the lines show central 95% credible intervals for each US-Country X dyad. Model was run with 100,000 MCMC iterations and 1000 burn-ins. 45 Variation between Allies and Non-Allies How does one compare military commitments to formal allies versus non-allies? Is it always true that military commitments between allied countries are stronger than those between non-allies? Using alliances as a measure of third-party military commitments does not provide a systematic way to make these comparisons. With a binary measure of external military support – alliance exists (1) or not (0) – scholars cannot account for the fact that non-allies also receive significant military benefits from third-party defenders like the United States. Benson and Clinton (2016) report the factor scores for the scope, depth, and potential military capacity of all alliances identified in the ATOP dataset. While the scores are informative for comparing alliances, there is no way to compare military commitments to Japan versus Israel versus Thailand. Figure 2.7 shows comparisons be- tween US allies and non-allies. Even though US non-allies have lower numerical values on the latent factor, indicating lower levels of US military commitment, the results of the measurement model allow researchers to make direct comparisons of US military support to different states at the same point in time (and across time). Figure 2.7 indicates that US military commitments to NATO allies are relatively higher than its commitment to bilateral allies in East Asia. At the same time, US commitments to East Asian allies are greater than members of the multilateral Latin American defense alliance, the Rio Pact. On face value, it is interesting to note that a country like Mexico – a non-ally – has a relatively higher value of US military commitment given that it shares a direct border with the United States. The measurement model presented here provides scholars with a systematic and principled way of making these comparisons among different states, whether they are formally allied or not. 46 Figure 2.7: Posterior Means for Allies and Non-Allies in 2000 Taiwan India Israel Saudi Arabia Mexico Thailand Brazil South Korea Australia Japan United Kingdom Germany 0 2 4 Latent Factor Score Plot of estimates of latent US military commitment to both formal and non-formal allies in 2000. The dots are posterior means and the lines show central 95% credible intervals for each US-Country X dyad. Model was run with 100,000 MCMC iterations and 1000 burn-ins. Temporal Variation Finally, a latent variable approach allows researchers to identify trends or changes in la- tent military commitment over time. Formal alliances are formed at a fixed point in time and do not change much, both in their legal agreements and actual provisions. While I present single year country-dyad comparisons in this paper, the measurement model can be applied broadly to time-series data. I plan to use a robust dynamic model as presented in Reuning, Kenwick and Fariss (2019). The authors state that “Robust models, broadly defined, weaken the parametric assumptions common to standard statistical models as a means of accommodating unique data structures and the potential for influential outlying observations" (Reuning, Kenwick and Fariss 2019, 4). They show that a robust dynamic 47 model performs better than the static and the standard dynamic models in capturing the latent factor, especially when it is subject to volatility or rapid change. While there is concern that the assumption of temporal independence in the latent variable model, that observations are independent across time t, is violated, I find that there is low autocorre- lation across all observed indicators (Figure 2.11). Robustness Checks One potential limitation of the present study is that military actions taken on behalf of one state can also be used to militarily support another state. Put simply, US forces and military bases in Germany are also used to protect other members of NATO, and the measurement model may not account for this. As a robustness check, I ran the model recoding the observed indicators as a proportion of total military investments rather than actual values. For the continuous variables – troop deployments, military aid, arms exports, and base values – I created individual variables that represent ratios: the amount the US invested in country X in year t divided by the total amount invested in all foreign countries in the same year t. 33 The results of the measurement model are consistent and US military commitments to states are ranked in the same manner and degree as the original model run with absolute values. Another potential limitation is that the observed indicators may be capturing another, related latent variable: common threat. While it is true that military commitments could be highly correlated to a common military threat facing multiple countries, the model shows that there is variation within the same alliance and regions, which means military commitments to states that share a military threat still differ. For example, in East Asia, the common military threat facing the US and other countries is China and North Korea. Yet 33 For example, I summed the total number of US troops deployed in a given year and aggregated them to the year level. Then I divided the number of US troops deployed to each country in that same year by the total. This provides a proportion of troops deployed to one country out of all troops deployed abroad in a given year. 48 we observe significant variation in US military commitments to South Korea, Japan, the Philippines, Vietnam, and Taiwan (Figure 2.5). For both political and military reasons, US military commitments to these countries differ despite sharing a common threat. Similarly, in Europe, there are significant differences between US commitments to NATO members. In fact, US military commitments to Eastern European countries, like Poland and the Czech Republic, which arguably face the greatest threat from Russia, receive the lowest levels of commitment (Figure 2.6). The substantive results from the measurement model lend support for the argument that the model is correctly identifying and measuring the latent variable of third-party military commitment. A New Typology of Third-Party Military Commitments In the previous section, I showed that military commitments – particularly those of the United States – vary significantly across states and over time. The measurement model provides a principled way to compare US commitments to states, both formally allied and not. In the following section, I introduce a new typology of military commitments that draws from the dimensions summarized in previous sections: effect on the strategic environment of states in dispute, institutional design, and implementation and costs. I argue that these dimensions are interrelated and together determine strategic behavior in bargaining which, in turn, influence a third-party defender’s choice of commitment strategy. Based on the purpose/goal of military commitments (intended effect) and their actual impact on states’ behaviors (expected effect), a defender will decide on the most appropriate means to achieve its goals. The means are outlined in the institutional design of military cooperation and are, then, implemented at a cost for the defender. The actual implementation of military commitments and their associated costs also affect what form of commitment design is ideal. In other words, for material commitments to be credible, they must be realistic to enact based on how much the third-party is willing to invest in 49 the target state’s security. In sum, it is essential to recognize the importance of strategic interaction: how a third-party state expects a target and challenger to act in equilibrium will determine its own commitment strategy and its commitment strategy will influence how other states choose to act. Chapter 3 outlines a formal theory that accounts for this strategic interaction among actors and derives testable implications for third-party military commitments. Effect on Strategic Environment and State Behavior To understand why a third-party defender designs and implements varying military com- mitments for different target states, we must first consider for what purpose and goal military commitments are made. I examine both the intended effect and the expected ef- fect of third-party commitments on the strategic behavior of and the strategic environment surrounding states in dispute. Intended effect As outlined in Chapter 1, the common underlying assumption that drives nearly all re- search on alliances is that third-party military commitments are aimed at maximizing ex- tended deterrence. A third-party defender – that has aligned interests with a target – has incentive to invest in improving the target state’s security. Thus when maximizing extended deterrence is the main goal of third-party military commitments, the cost of entrapment is relatively low for the defender given its high valuation of the target or the disputed good (in which its preferences are more aligned with the target state). A third-party defender may also prefer to maximize authority over another state to restrain an overaggressive ally from entrapping it in an unwanted conflict. Even though I assume the defender and target have more aligned preferences than the defender does with a potential challenger, this assumption does not imply that the defender and tar- get’s policy preferences are identical. The risk of entrapment for third-party defenders is 50 real given that costly and credible military commitments can embolden target states to be more aggressive in international disputes (Benson 2012). As a result, the goal of third- party commitments can also be to restrain target states by making them overdependent on the defender’s provision of security and restricting their ability to take unilateral military actions (Fang, Johnson and Leeds 2014; Cha 2016). When the main goal of third-party military commitments is to maximize extended deterrence or restraint of another state, we would expect to observe similar types of commitments from a defender despite the different goals it wishes to achieve. We should see such a third-party defender making costly military commitments that credibly tie its hands to a target state, such as entering into a formal military alliance, maintaining permanent bases in the target’s territory, and establishing high levels of military coordination. To address the dual problem of increas- ing deterrence against threats from potential challengers and restraining one’s ally from instigating conflicts (emboldenment), the third-party defender may intend to maintain strategic ambiguity, or uncertainty about the firmness of its military commitments. By aim- ing for strategic ambiguity, the third party may enter into a formal alliance but condition its involvement in conflict (Benson 2012). Apart from (or in addition to) trying to resolve the deterrence-restraint dilemma, a third-party actor may also make military commitments to a state in dispute if: 1) the state is key to the stability of a region or 2) the state faces a risk of collapse. On the one hand, it could be in a third-party defender’s interest to improve the security of a state that has strategic importance in a region and allows the defender to maintain its influence in that region. The US maintains close military ties with non-formal allies in the Middle East, namely Israel, Saudi Arabia, and the United Arab Emirates, which are often accompanied by costly military commitments. On the other hand, a third-party actor may prefer to prevent another state’s regime from collapsing due to weaknesses in its security or loss in an international dispute. The internal regime stability of another state can be of significant strategic importance for a defender if the target state’s security is connected to 51 the defender’s own security or national interests. This is especially true when the third- party defender shares borders with the target and, thus, may want a physical buffer against a larger external threat or desire to protect its borders from an influx of refugees following a war in its neighbor. Arguably, the Sino-North Korean military alliance is aimed, in part, at preserving North Korea’s regime as a buffer against American and South Korean political and military influence in the region. The goals of third-party military commitments can, and do, change over time. It is also difficult to pinpoint what the original purpose of certain military commitments is given that policymakers may adapt their rhetoric to their changing needs. Yet, at the same time, understanding the intended effect of military cooperation can shed light on the design and implementation of third-party commitments. These original design choices have enduring effects on the implementation and any subsequent changes in military cooperation over time and across states. In particular, a third-party actor’s decision to make (or not) treaty commitments to an ally have lasting impacts on how the two states’ security relationship evolves. In the following section, I examine the expected effect of military commitments, which may differ from their intended goal. Expected effect The expected effect of third-party commitments is more in line with the actual effect mil- itary commitments have on the strategic environment surrounding states in dispute, in- cluding their calculated behavior. Depending on the purpose of different forms of military cooperation, there can be diverse effects on the strategic behavior of states in dispute and outcomes related to conflict. Arguably, the expected effect of military commitments is closely related to their intended effect. Yet the original purpose of third-party commit- ments may not always match with the actual effect realized; thus these effects can be intended or unintended. First, military commitments from third-party states have a direct effect on the likelihood 52 of conflict. The risk of militarized conflict can be reduced if third-party military commit- ments successfully deter challengers from initiating conflict or making demands that are too large to be accepted in crisis bargaining. Yet military commitments can also increase the likelihood of conflict when the target state is emboldened to act more aggressively in international disputes if it is backed by a powerful patron. By rejecting a greater set of bargains with the challenger, the risk of war is increased. Second, third-party commitments can also influence the size of militarized conflicts, namely the risk of entrapment or dragging third-party states into wars. When a third- party defender pledges military support for one side in a dispute, the defender increases its risk of being entrapped in a conflict that it does not actually wish to fight in. As a result, bilateral conflicts can quickly escalate into multilateral conflicts that involve more actors and are far costlier. Last, in a world of uncertainty and private information, military commitments from a third party can also act as signaling mechanisms that convey willingness to fight and make a third-party defender’s threats to intervene credible. These signals of intent, or what Fearon (1997) refers to as “costly signals," also aim to improve extended deterrence by making potential challengers wary of provoking allied states. Dimensions of Military Cooperation Given that third-party actors have different expectations – both intended and unintended – from their provision of military commitments, third-party defenders design their com- mitments in a variety of ways to shape the strategic environment. Taking into account the intended and expected effects of their military commitments, third-party states to a dis- pute can choose from a wide range of commitment strategies to employ. Although military commitments vary on a wide range of dimensions, I focus on two main dimensions that capture most forms of military cooperation between states: the level of institutionalization and the effect on states’ military capabilities. Along these two dimensions, most forms of 53 military cooperation can be mapped onto four different quadrants. Figure 2.8 provides a visual representation of the typology of military commitments. I examine each dimension in detail with several empirical examples. Figure 2.8: Typology of Military Commitments Institutionalization and Costs The first dimension is a measure of institutionalization, or the formality of military coop- eration between states. The institutional design of third-party commitments outlines how a defender defines its military cooperation with a target state. The more institutionalized military commitments between states are, the more likely the defender is to become in- volved in a potential conflict. Intuitively, the tighter military cooperation between states is, the more credible military commitments are. Highly institutionalized military cooperation 54 involves consistent interaction over a long period of time, is enmeshed into an organiza- tion or legal institutions, and imposes governance costs on actors. 34 The conditions under which military commitments apply, the processes in which obligations are made, and the relational arrangement of military cooperation fall under this dimension. The conditions under which third-party involvement in conflict apply – the “trigger" or casus belli – can also vary depending on the obligations outlined in a treaty. Not only do third-party states make promises to defend their allies in war, they may also bind them- selves to more proactive measures under offensive alliances or loosen their commitments by simply entering into non-aggression or neutrality pacts. The process or set of obligations made can indicate the strategic weight given to certain allies, formal and non-formal alike. If military cooperation is made public and formally ratified by domestic political bodies in the third-party state, then the defender signals that it is willing to incur political costs if it reneges on its obligations to the target state. Finally, the arrangement of the relationship between the third-party defender and target state can influence how military cooperation between the two states is defined. States can determine how many members are accepted and, as a result, we observe significant differences in bilateral versus multilateral alliances, where the former may be more effective for restraining rogue allies when that is the goal of military commitments (Cha 2016). In addition, the structure of the relationship, namely whether it is hierarchical or symmetric, also varies across states. On the one hand, the US hub-and-spokes alliance system in East Asia has generally been led by a “benign" hegemon at the center of smaller states. On the other hand, Russia exercised authoritative force to influence the military policies and actions of other Soviet states under the Warsaw Pact. Investing in institutionalized forms of military cooperation incurs costs for the third- party defender, both political and/or material. For more institutionalized military com- mitments, such as an integrated military command and foreign basing, the financial costs 34 Leeds and Anac (2005, 186) state that “states are willing to incur greater governance costs in managing their joint projects when doing so makes profitable joint action possible where it would otherwise have been considered too risky." 55 and political costs are high, as governments require close consultation and coordination to negotiate and manage burden sharing agreements (i.e. Special Measures Agreement or SMA) and status of forces agreements (SOFA). Even for less institutionalized third-party commitments, there may be costs outside of alliances, such as passing domestic laws to approve of strategic partnerships or providing loans for the export of military technology and arms. Despite the costs, institutionalized military cooperation also entails varying benefits for both third-party defenders and target states. For example, the Major Non-NATO Ally status that the US designates to certain key target states comes with significant material benefits that not all US allies receive, such as priority deliveries of US military surplus, war reserve stocks, and American financing for the purchase of defense equipment. Target states are not the only ones to benefit from highly institutionalized forms of military cooperation; third-party defenders may also receive special domestic rights in the territory of the target state, such as military basing rights, tax breaks, and/or exclusive contracts to access a target’s defense market. Military Effect and Costs The second dimension is the military effect that material commitments have on states’ war-fighting capabilities. Once states have defined their security relationship through an institutional design of military commitments, they may proceed to implement tangible forms of military cooperation, or material commitments. 35 I separate the different types of material commitments into two main categories: 1) those that entail active military coor- dination between the target and defender and 2) those that involve transactions, mostly in the form of military transfers from the defender to target. In the next chapter, I examine the actual expected effect each type of material commitment has on the local balance of 35 It is important to note here that the decision to implement material commitments is strategic and is a choice for the third-party defender to make. The same goes for the institutional design of military commit- ments. 56 power between states in dispute. The main distinction between the two general classes of material commitments is that the former requires close, joint military coordination between a third-party defender and a target state. Put simply, the third-party defender must actively participate in maintaining its military commitments to the target through close consultation, exchange, and third- party direct involvement. Military measures that fall under this category are (but not limited to): foreign troop deployments, permanent overseas military bases, joint military exercises, a common defense policy, an integratd military command, and foreign deployed nuclear weapons. 36 In contrast, transfers do not require as much joint coordination or the defender’s direct involvement beyond the negotiation of contracts and sales/deliveries. Foreign military sales, aid, and military financing are included in this form of material commitment that improves a target state’s unilateral or independent capabilities. Sometimes the transfer of advanced military technology does entail close consultation with a third party (the seller/provider), such as missile defense technology or training. Yet this still differs signifi- cantly from military cooperation that actively requires the third-party defender’s consistent involvement in order to properly function, like an integrated military command. It is unclear whether costs that improve joint military capabilities are necessarily more costly than those that improve a target’s unilateral capabilities through transfers. The over- all trend towards more transactional forms of military cooperation, namely in the form of military aid and arms exports, may indicate that third-party actors are trying to minimize their involvement in other states’ conflicts, but there are still costs to doing so. Given that budget and resource constraints determine how much and where states can invest in pro- viding security, the cost of implementing military measures in peacetime is an important consideration in the design choices of commitment strategies. I examine the different costs associated with varying types of military cooperation in detail in Chapter 3 where I develop 36 Foreign deployed nuclear weapons call for close coordination because the deploying country rarely, if ever, transfers the ability to use nuclear weapons to the host country. 57 a theory of commitment design and implementation. Table 2.6 summarizes the variation we observe in third-party military commitments along the dimensions examined here. Table 2.6: Variation in Design and Implementation of Third-Party Military Commitments Dimension Measure Characteristics Examples Strategic Effect Goal Maximize extended deterrence Maximize authority over target Strategic ambiguity Regional stability Regime survival/stability Balance of power Improve joint capabilities Improve target unilateral capabilities Target behavior Embolden Restrain Design Members Multilateral Rio Pact Bilateral U.S.-Philippines Structure Symmetric Asymmetric with benign hegemon U.S. hub and spokes in Asia Asymmetric with authoritative hegemon Warsaw Pact Obligation Offensive Poland-Hungary (1948) Defensive Allies of WWII Non-aggression Molotov-Ribbentrop Pact Neutrality Soviet-Japanese Neutrality Pact Consultation SEATO Ratification Executive/legislative agreement Formal ratification by domestic political bodies Transparency Public Secret Reinsurance Treaty Implementation Coordination (Joint) Integrated military command Warsaw Pact Military contact ANZUS Treaty Common defense policy Overseas military installations (i.e. bases) NATO Troops U.S.-Japan Foreign nuclear deployment Soviet Union-Czechoslovakia Transfers (Unilateral) Arms U.S.-Saudi Arabia Military aid/loans U.S.-Israel Missile defense or military technology U.S.-South Korea Economic aid Chapter Summary The study of alliances is central to understanding how military cooperation is formulated, carried out, and used by states to reduce international conflict. Often, military alliances are taken for granted as a proxy or measure of underlying military commitments between states. While alliances do, indeed, have positive associations with latent military support, other forms of military cooperation implemented in peacetime do as well; in some cases, 58 to an even greater degree than alliances such as nuclear weapons deployments and foreign bases. I presented a Bayesian latent variable approach to show that potential measurement error in our constructs of external military support may be a reason scholars draw differ- ent conclusions about the effect of alliances on conflict. In addition, treating third-party military commitment as a latent variable allows researchers to generate a measure of an unobserved trait and account for the error that goes into that measure. As a result, we can make comparisons across a wider set of dimensions – such as within regions, within alliances, between allies and non-allies, and over time – of latent military commitment in a principled way. I introduce a method to aggregate different observed indicators of military coopera- tion to measure the unobserved level of military commitment between states. US military commitments to other countries of national security interest are not equal. Instead, la- tent military commitment drives third-party defenders to make strategic decisions about which types of military cooperation to engage in and which forms of military measures to implement on behalf of another state’s security. The results from the measurement model presented have implications for US foreign policy in that a lot of facilitation and cooper- ation is required to maintain and improve third-party military commitments, even in the presence of a formal alliance. Additionally, the novel typology of third-party commitments presented in this chap- ter highlights the importance of accounting for variation in military cooperation between states. While the measurement model empirically shows there is variation in US underly- ing commitments to different states, the conceptualization of third-party commitments as being a multi-dimensional continuum allows scholars to better understand the design and implementation choicse that are available to national leaders in security-providing states. This chapter emphasizes the need to move beyond the study of alliances, or treaty commit- ments, and towards a more comprehensive understanding of the various tools that leaders strategically choose from to pursue different foreign policy objectives. 59 Appendix Figure 2.9: Trace Plots for Factor Loadings and Error Variance Psi.arms_log Psi.milaid_log Psi.nuclear_deployment Psi.prv_log Lambdanuclear_deployment.2 Lambdaprv_log.2 Psi.defense Psi.troops_log Lambdadefense.2 Lambdatroops_log.2 Lambdaarms_log.2 Lambdamilaid_log.2 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 −0.350 −0.325 −0.300 −0.275 0.675 0.700 0.725 0.750 0.93 0.96 0.99 1.02 −0.700 −0.675 −0.650 −0.625 0.60 0.63 0.66 0.69 0.72 0.94 0.96 0.98 1.00 1.02 1.04 1.06 −0.58 −0.56 −0.54 −0.52 −0.50 −0.225 −0.200 −0.175 −0.150 0.875 0.900 0.925 0.950 −0.625 −0.600 −0.575 −0.550 −0.525 −0.06 −0.04 −0.02 0.00 0.02 0.04 0.500 0.525 0.550 0.575 0.600 Model was run with 100,000 MCMC iterations and 1000 burn-ins. 60 Figure 2.10: Posterior Mean Distributions for Factor Loadings and Error Variances Psi.prv_log Psi.nuclear_deployment Psi.milaid_log Psi.arms_log Psi.troops_log Psi.defense Lambdaprv_log.2 Lambdanuclear_deployment.2 Lambdamilaid_log.2 Lambdaarms_log.2 Lambdatroops_log.2 Lambdadefense.2 −0.5 0.0 0.5 1.0 Model was run with 100,000 MCMC iterations and 1000 burn-ins. 61 Figure 2.11: Autocorrelation Plot for Observed Indicators Psi.arms_log Psi.milaid_log Psi.nuclear_deployment Psi.prv_log Lambdanuclear_deployment.2 Lambdaprv_log.2 Psi.defense Psi.troops_log Lambdadefense.2 Lambdatroops_log.2 Lambdaarms_log.2 Lambdamilaid_log.2 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 Lag Autocorrelation With chain run for 100,000 MCMC iterations and 1000 burn-ins. 62 Chapter 3 A Theory of Military Commitments In the previous chapter, I showed that military cooperation aimed at providing defense for another country varies significantly and that one can measure these differences across members of the same alliance, between formal allies and non-formal allies, and over time. In this chapter, I develop a formal model that shows that it is precisely this variation in military commitments between states that drives important security dynamics, such as the decision to invest in certain forms of military cooperation over others, the conditions un- der which entrapment is a real risk for allies, and the effectiveness of extended deterrence in multi-actor conflict settings. The model shows that a third party to a dispute can make credible threats to intervene in conflict even without alliances, and that alliances have a much smaller influence on crisis bargaining behavior when signaling is not involved. Al- liances matter for international security, not so much for the legal obligations they impose, but for the actual military cooperation that comes along with the formation and mainte- nance of alliances. First, the model shows that a third-party defender is more likely to intervene in conflict the greater its ability to shift the local balance of power is. A defender implements costly commitments that improve the defender and target state’s joint military capabilities when it prefers to intervene in war. Yet the third party’s investment in joint capabilities is con- ditioned by its cost-effectiveness, or the cost of making a military commitment weighed by its effect on war-fighting capabilities. In fact, as the third party becomes increasingly 63 stronger (relative to the target and challenger), it has less incentive to make costly ma- terial commitments because its mere intervention in war is enough to raise its chances of victory. This finding can help explain why the United States may be less willing to invest in improving its joint military capabilities with its allies over time as it becomes more mil- itarily powerful. Additionally, the size of the effect that a third-party actor will have on shifting the chances of war victory in its favor also explains why most US military relaton- ships are asymmetric. The disparity in power between the target and defender increases the incentive for the third-party defender to militarily support the target. When the defender and target share interests over the issue in dispute, material com- mitments that increase joint capabilities make the target state more aggressive in bargain- ing, thus, extracting better settlement offers from the challenger. While this finding is consistent with existing theories of alliances and their emboldening effect, the mechanism differs. Alliances are typically understood to be costly signals of a defender’s threat to inter- vene in war, but the results of the model show that material commitments have real effects on the peacetime strategic environment that do not rely on asymmetric information or signaling dynamics. 1 The strategic effect of military cooperation and the cost-effectiveness of implementation also influence the third party’s decision to commit or not, rather than just uncertainty about the defender’s costs of war and abandoning its ally. Second, I find that a third-party defender can also influence the strategic behaviors of states in dispute even if it would abandon its preferred side in conflict. Unlike military alliances, certain forms of military cooperation – such as the transfer of arms or provision of missile defense systems – can directly affect the peacetime balance of power by improving the target state’s unilateral military capabilities. In other words, third-party involvement in conflict is not put to the test only when war occurs and alliances are activated. Under certain conditions, a third-party actor can employ military measures that shift the local balance of power in its favor without ever entering war and directly fighting. 1 For another complete information model related to alliances and third-party intervention in conflict, see Smith (2019), “Committing to Neutrality." 64 If a defender prefers to abandon the target state in conflict, it can make a material commitment that improves the target’s individual fighting capabilities, in turn, improving the target’s leverage in bargaining. By giving a target state the tools it needs to improve its own military capabilities, the defender can extract greater settlements from adversaries than it would in the absence of any military commitments. This provides an explanation for why a defender would be willing to make a costly, upfront security commitment to a target that it would actually not support in war. Empirically, this counterintuitive finding explains why states of high strategic interest, like Israel and Taiwan, often receive costly, peacetime military commitments from a third-party actor (the United States) without being formally allied. The results of the model can be extended to empirical studies of alliances and conflict behavior/outcomes. The empirical record suggests mixed evidence as to whether alliances deter or provoke militarized conflict (Leeds 2003b; Kenwick, Vasquez and Powers 2015; Leeds and Johnson 2016; Kenwick and Vasquez 2016; Morrow 2016). 2 Because treaty and material commitments often go hand-in-hand, the mixed empirical findings on whether alliances increase or decrease conflict may be driven by the variation in military commit- ments between states and their different effects on actors’ behaviors in disputes. Current empirical studies treat alliances as substitutes for all or most forms of military support, but my theoretical model shows that material commitments are complementary but unique to treaty commtiments. Before we begin to test the effect alliances have on the likelihood of conflict, we should first aim to understand how different military commitments influence crisis bargaining behavior in distinct ways from alliances alone. Thus it is important to theoretically unpack the variation in military cooperation between states, both between formal treaty allies and non-formal allies. In this chapter, I analyze a complete information model that expands the types of mili- 2 Refer to the Scholarly Dialogue in volume 79, issue 1 of the Journal of Politics for an extensive debate on this question. See also Benson and Smith’s (2019) working paper titled “Do Alliances Cause Commitment Problems and War?" 65 tary commitments that a third-party actor to a dispute can make and discuss the results. I present a set of testable empirical implications derived from the model and provide a plau- sible alternative explanation for why US military commitments to South Korea and Taiwan during the Cold War differed so greatly. I conclude with the theoretical and empirical implications of the model for the study of alliances. A Model of Material Commitments Model Setup The model begins with three actors: a third-party defender (D) aligned with a target state (T) that has a conflict of interests over some good with a challenger (C). In bargaining, C makes a demandx2X = [0; 1], which T can accept or reject. If T accepts C’s demand, all actors reach a settlement in which D and T receive 1x and C receivesx. For simplicity, I assume that the defender and target value the disputed good equally so that both share identical ideal points over its division. If T rejects C’s demand, war occurs. In war, D decides whether to intervene and support T or abandon it with cost k a > 0, where a2 fL;Hg. 3 D faces a cost for abandoning T in war, with a higher cost for abandoning a formal ally (k H ) over a non-formal ally (k L ), such thatk H >k L . 4 War is costly for all actors involved, such that they payc i fori2fC;T;Dg, wherec i > 0. The probability of war victory for T against C is p w 2 (0; 1) and q w 2 (0; 1) for T and D against C, where w2fB;Hg. Suppose T’s baseline probability of unilaterally winning war against C (without D’s support) is p B and the baseline probability of D and T jointly 3 The term “abandon" is used here to mean that D does not intervene to militarily support T in war. The term does not necessarily imply that D made any prior promise to defend T in war. 4 Intuitively, states may pay costs for looking weak in crises, for reneging on allies, and/or face material costs, such as the loss of soldiers’ lives outside of war. This assumption simply states that, while D may incur various costs from abandoning T, it is costlier for D to abandon T when it has made an upfront commitment to defend T in war (most often through the signing of a defense pact). The logic is similar to that of domestic audience costs and backing down (Fearon 1994a). Even if k L = 0 for non-formal allies (i.e. no cost for abandoning a non-ally) andk H > 0 for formal allies, the results of the model are consistent. 66 winning war (with D’s support) is q B . Consistent with previous models of alliances, I assume that q B > p B such that the baseline probability of D and T winning together is always greater than T winning alone. Prior to bargaining, D can choose to make a peace- time material commitment that directly affects the local balance of power but at a cost for implementation of j for j2fp;q;pqg. D can choose to either improve T’s unilateral capabilities, improve joint capabilities, both, or make no ex ante material contribution. 5 In addition to the choice of material commitment, D also decides whether or not to enter into a formal treaty alliance with T, which is accounted for in its cost of abandonment (i.e. entering into a military alliance with T raises D’s cost of abandonment from k L to k H ). I assume that if D is indifferent between entering into a formal treaty with T or not, D will choose to do so. 6 Table 3.1 outlines the notation of the model. Table 3.1: Model Notation x; 1x Challenger and target/defender shares of good, respectively p w Target’s probability of winning war alone q w Target and defender’s probability of winning war together c i Actori’s cost of war j Defender’s cost for making material commitment k a Defender’s cost for abandoning target in war The novel feature of this model that differs from other models of third-party commit- ments is that D has a set of diverse choices over its peacetime military support to T, which have varying effects on the status quo balance of power. D can increase T’s baseline prob- ability of winning from p B to p H by making an upfront military transfer. Put simply, by providing T with advanced weaponry, D can improve T’s unilateral military capabilities and shift the balance of power in T’s favor. I use the probability of winning war and military capabilities interchangeably. An improvement in military capabilities tips the local 5 Here, I treat D’s decision over its material commitment as a set of discrete choices rather than continuous. While we can also treat the probabilities of winning in war as functions of D’s initial military contribution, it complicates the model. The results of the model should be consistent even if we make D’s commitment strategy a continuous space. 6 Consistent with the alliance literature, making a treaty commitment imposes no sunk costs for D. 67 balance of power in favor of one (or two) actor(s) over the opposing side, which also shifts the chances of winning in war. D can also choose to raise the chances of victory when both D and T fight together in war by making a costly military investment in joint capabilities that increase q B to q H . I assume that material commitments increase subsequent proba- bilities of winning in war such that q H > q B > p H > p B . 7 Substantively, this implies that the baseline probability of winning war with D’s support is always higher than any level of material commitments that can be transferred to T to improve its unilateral capabilities. In other words, T’s chances of winning war are strictly better with D’s intervention than any possible increase in its individual chances. D could transfer arms/aid to T and enter war on its behalf (q B ), which yields a strictly higher probability of victory than transferring arms/aid and abandoning T (p H ). 8 For each type of peacetime material commitment, D pays a sunk cost for its implemen- tation. Intuitively, we can assume that different military measures entail varying costs for D such that material commitments that improve T’s unilateral military capabilities cost p 0 for D and those that improve joint capabilities cost q 0. These sunk costs can be understood as training an ally’s military forces, institutional costs for integrating military command structures, or conducting joint exercises in preparation for potential conflict. If D chooses to invest in improving both joint and T’s unilateral capabilities, it pays even higher costs where pq > q and pq > p . Making no material commitment imposes zero costs on D (i.e. = 0). This yields a total of eight possible commitment mechanisms that D can choose from at the onset of the game. 9 Table 3.2 outlines the actors’ expected utilities from settlement, war with D’s involve- ment, and war without D’s involvement. D’s expected utility from war and settlement is conditioned on the its military commitment to T. For example, if D prefers to support T in 7 Here,p H andq H represent a higher probability of war victory for T fighting alone and D and T fighting together, respectively, after D has made some material commitment upfront. In the absence of a material commitment (i.e. just treaty commitment or nothing at all), the probabilities of winning remain baseline probabilities. 8 This does not occur in equilibrium and is discussed in later sections of this paper. 9 For a summary of D’s strategies, see table 3.4 in appendix. 68 war and chooses to improve joint capabilities to raise the probability of D and T winning war, then the actors’ expected utilities from multilateral war are: 1q H c C for the chal- lenger,q H c T for the target, andq H c D q for the defender. If D decides to not invest in peacetime military cooperation nor form an alliance such thatp B ;q B ;k L , but still prefers to support T in war, then the actors expect to receive 1q B c C ;q B c T ;q B c D as their war payoffs. If D abandons T in war without making any commitment, the actors expect 1p B c C ;p B c T ;p B k L c D in war. Table 3.2: Summary of Expected Utilities Settlement War (with D’s support) War (without D’s support) Challenger x 1q w c C 1p w c C Target 1x q w c T p w c T Defender 1x j q w c D j p w k a j Key feature of model: variation in material commitments Different types of material commitments The addition of different material commitments to a standard crisis bargaining model with multiple actors has direct effects on the strategic environment of states in dispute and, as a result, produces new equilibrium behaviors. The key feature of my model that differs from extant models is that the defender can invest in an upfront material commitment at some cost that directly increases the target’s unilateral capabilities and/or the allies’ joint military capabilities. In other words, D and/or T’s preparation for potential conflict has a direct effect on their/its ability to fight and win, depending on the type of material commitment made by D in peacetime. Different commitment mechanisms have varying effects on the local balance of power among states in a dispute. For simplicity, I argue that D can make two types of material commitments to T: military measures that improve T’s 69 unilateral capabilities or those that improve both D and T’s joint military capabilities. 10 Improving military capabilities increases the probability of winning war against C. Ma- terial commitments that improve T’s unilateral capabilities increase the baseline probabil- ity of T winning a bilateral war against C such thatp H >p B . Some military contributions of this nature include: military or economic aid and conventional arms transfers. For exam- ple, advanced military technologies – such as tanks, fighter jets, missile defense systems, short or long-range missiles, stealth technology, etc. – and the money to acquire or develop them increase T’s unilateral ability to fight and win war even without D’s direct interven- tion. Put simply, D can provide T with the tools to wage war effectively without involving itself in the actual fighting (since material commitments are made prior to conflict). Another type of material commitment is one that improves D and T’s joint war-fighting capabilities or raises the baseline probability of winning war together such that q H > q B . These material commitments include: a common defense policy that entails close consultation and coordination, an integrated military command that creates a structure of command for multiple states’ militaries, permanent bases that house foreign deployed troops, and the deployment of nuclear weapons to another state’s territory. 11 Material commitments that improve joint capabilities represent military measures that require D and T to actively coordinate and cooperate in peacetime in preparation for potential war. The key difference between material commitments that improve T’s unilateral capabili- ties versus joint capabilities is that the latter is only effective when D is directly involved in conflict. In other words, material commitments that improve joint capabilities cannot be used by T without D’s active participation or involvement in conflict. T would not be able to command D’s troops on its own, implement military tactics that require the combined forces of D and T, nor use nuclear weapons that are controlled by D. As a result, because material commitments that improve joint capabilities require close military coordination 10 As mentioned in the model setup, D’s choices over which material commitments to make are discrete: it can improve T’s unilateral capabilities, improve joint capabilities, neither, or both. 11 In most cases, foreign deployed nuclear weapons remain under the control of the deploying state despite being housed in another state’s territory. 70 between D and T, they have less of an effect on T’s unilateral capabilities. To provide an illustration, imagine preparing a soldier for war: one can devise a team-coordinated plan of attack (joint capabilities) or give the soldier a rifle to fend for herself (unilateral capa- bilities). Both provisions increase the soldier’s fighting ability and chances of survival, but with different probabilities and by different means. Different costs of material commitments Just as different material commitments have varying effects on the strategic environment and states’ abilities to fight war, the two types of material commitments carry differ- ent costs as well. Military measures that require physical transfers or active coordina- tion/institutionalization are inherently costly for the security-providing state, D. Different types of material commitments impose varying costs on D, depending on the form of mil- itary cooperation being implemented, the degree to which T can offset D’s costs, and do- mestic factors within D. For material commitments that improve T’s unilateral capabilities, there is a direct monetary cost for D in providing military aid or arms to T. 12 For material commitments that improve joint capabilities, the costs for D may be those associated with policy coordination, such as efforts to establish institutions to oversee military cooperation between D and T. D may also face costs from stationing troops abroad, maintaining bases or defense structures, or even domestic political costs. 13 In the model presented here, it is important to note that p and q are unique sunk costs associated with the two types of material commitments and that investing in both types simultaneously incurs the highest cost for D, or pq . 12 Arguably, arms exports entail material profits for a third-party defender that may reduce the cost of transfers. Yet, oftentimes, a third party provides military financing or loans/aid to purchase the arms it exports, as seen by the United States and Israel. The cost for improving T’s unilateral capabilities can also be domestic or political, such as Chinese backlash against the US deployment of THAAD to South Korea. This is just to say that arms transfers are not necessarily costless and do not always include large profits for the exporter. 13 Domestic political costs may include domestic opposition to stationing troops abroad, debates over al- liance burden-sharing (especially if D is paying the bulk for defense), and political backlash for certain military measures. An example of political backlash would be the US public punishing its leaders for paying too much for the defense of foreign allies, such as NATO and South Korea. 71 I examine four separate cases in which material commitments are: 1) never cost- effective, 2) material commitments that improve joint capabilities are cost-effective, 3) material commitments that improve T’s unilateral capabilities are cost-effective, and 4) all material commitments are cost-effective for D to make. Here, cost-effectiveness simply means that D’s active improvement of military capabilities outweighs the cost of imple- mentation. For example, if an arms transfer from D to T does not shift the local balance of power relative to D’s cost of making such a transfer, then the action is not cost-effective. If D only makes a treaty commitment to T, it faces no upfront costs. 14 Because war does not occur with positive probability in equilibrium (under complete information), D’s deci- sion over its military commitment is determined by comparing its utility from settlement with or without the cost of making a material commitment. Material commitments that improve joint capabilities are cost-effective when: 1x q 1x 0 1 (1q H +c T ) q 1 (1q B +c T ) , q q H q B (3.1) Material commitments that improve T’s unilateral capabilities are cost-effective when: 1x p 1x 0 1 (1p H +c T ) q 1 (1p B +c T ) , p p H p B (3.2) 14 As with other extended deterrence models, treaty commitments have a hands-tying effect in which D faces costs only if it backs down/abandons in war. 72 No material commitments First, consider the case when material commitments are too costly for the third-party actor to make and thus, in equilibrium, we observe no material commitments. When p >p H p B and q >q H q B , material commitments are not cost-effective for D. In the absence of material commitments, the model is consistent with existing extended deterrence models in which D’s only choice of commitment to T is whether to form an alliance or not (i.e. treaty commitment). This case follows the same logic as alliances serving as hands tying mechanisms. Military alliances tie D’s hands to ensure that D would support T in war by imposing costs for abandonment and, consequently, raising D’s expected utility from war. D and T can extract a better settlement offer from C in bargaining and D would always prefer to commit if it can credibly do so (see lemma 1). Similar to other models of alliances, there is no upfront or sunk cost for making a treaty commitment. The full proof is in the appendix. Material commitments to improve joint capabilities I begin the analysis of subgame perfect equilibria in which D can make material commit- ments to show how adding material commitments produces new equilibrium behaviors. I start by examining the case where only material commitments that improve joint capabili- ties are cost-effective. Proposition 1 The defender will make a material commitment to improve joint capabilities if and only if it would support the target in war and such a material commitment is cost-effective, such that q q H q B . Let HB = q H p B . Under proposition 1, if and only if D prefers to support T in war, it will make a material commitment to improve joint capabilities. When c D k L < HB , D is indifferent between entering into a military alliance or not because D’s cost of war is sufficiently low that it would unconditionally support T in war, regardless of 73 its commitment strategy. Given D’s unconditional support in war, D prefers to raise its chances of war victory. In other words, if D would intervene in conflict and expects its material commitment to increase its odds of winning against C, then it would choose to do so. D can essentially best prepare for a war it is already willing to fight. Material commitments that improve joint capabilities are cost-effective when q q H q B , and D only makes a material commitment if this inequality holds. If the marginal impact of D’s material commitment on war victory is less than the cost of making it, then D will not invest in military actions even if it would support T in war. As material commitments that improve joint capabilities become more cost-effective, D is more likely to make them. For middling costs of war or c D k H < HB < c D k L , the presence of a treaty commitment determines D’s support in war. If D is in an alliance with T, then D always prefers to support T in war and, given its support, D makes a material commitment that only improves joint capabilities. Again, material commitments that improve joint capabil- ities are cost-effective and D would prefer to implement them when its support in war is guaranteed. As a result of the first two conditions, T is emboldened to reject a larger set of C’s demands as its utility from war increases with D’s involvement and the added prepa- ration for conflict from D’s material commitment. In equilibrium, C makes the smallest demand, x 1 , which T accepts. D pays a peacetime cost, q , for implementing a material commitment that improves only joint capabilities but improves its settlement utility as a result (compared to the absence of such a material commitment). Finally, when the cost of war is too high for D orc D k H > HB , D strictly prefers to abandon T in war and is indifferent between entering into a treaty alliance or not. Because D would always abandon T whenc D k H > HB , investing in improving joint capabilities is not in D’s interest. Substantively, D does not invest in military actions that increase the ability of D and T to fight together against C if D would never intervene in war in the first place. Since material commitments that improve only T’s unilateral capabilities are not cost-effective, or p > p H p B , D makes no material commitment to T in equilibrium. As 74 a result, C makes the largest demand in settlement,x 4 , which T accepts. The full proof of proposition 1 is in the appendix. Material commitments to improve target unilateral capabilities Now I turn to the case where only material commitment that improve T’s unilateral ca- pabilities are cost-effective. Depending on the type of material commitment, equilibrium behavior changes accordingly. Proposition 2 The defender will make a material commitment to improve the target’s uni- lateral capabilities if and only if it would abandon the target state in war and such a material commitment is cost-effective, such that p p H p B . Let BB =q B p B . From proposition 2, D always supports T in war whenc D k L < BB and is indifferent between entering into an alliance or not. If D prefers to support T but improving joint capabilities is not cost-effective, then D will make no material commitment to T. From lemma 1, we know that D’s support in war increases the probability of war victory over any improvement that D can make to T’s unilateral capabilities, such thatq B > p H . If D would support T in war, then it has no incentive to make a material commitment that only improves T’s unilateral capabilities, even if it is cost-effective. This is because D’s guaranteed support in war is strictly better for improving war-fighting capabilities than increasing T’s individual fighting ability alone. Thus D has no incentive to deviate when c D k L < BB : D still prefers to support T in war than to abandon T and provide material commitments that only improve T’s capabilities. Likewise, ifc D k H < BB <c D k L , then D’s decision over allying or not determines whether it supports or abandons T in war. Because supporting T in war yields a strictly higher utility for D than making a material commitment that only improves T’s military capabilities, D would always prefer to enter into a treaty alliance with T to guarantee its support in war. Again, because material commitments that improve joint capabilities are 75 not cost-effective, or q >q H q B , D does not make any material commitments under this condition but would still support T in war. For high costs of war, such thatc D k H > BB , D always abandons T in conflict and is indifferent between forming an alliance or not. Because material commitments that improve T’s unilateral capabilities are cost-effective, D will initiate military transfers to T but abandon it in war. D’s material commitment to improve T’s individual capabilities decreases C’s demand in bargaining because now C faces a militarily stronger T in war. An important and unique equilibrium result arises from this proposition. Through D’s peacetime material commitment, D is able to effectively shift the status quo balance of power in its favor without its direct intervention. As a result, D and T can extract a better settlement offer from C in equilibrium under the shadow of D’s material commitment to T, even though D would still abandon T in war. 15 Unlike previous alliance models, D can make a costly, upfront commitment to help T in war that does not tie its hands. In effect, D is willing to make a costly material commitment (given it is cost-effective) even if it would strictly prefer to abandon T in war. All material commitments Last, briefly consider the case in which both types of material commitments are cost- effective such that p <p H p B and q <q H q B . 16 Equilibrium behavior follows directly from propositions 1 and 2. If, and only if, D would support T in war, it makes a material commitment that improves joint capabilities and is indifferent between making a treaty commitment or not. If D would, instead, abandon T in war, it makes a material commit- ment to improve T’s unilateral capabilities. In equilibrium, D never chooses to increase both joint capabilities and T’s unilateral capabilities simultaneously. The cost of doing so leaves D worse off than if it were to only invest in one type of material commitment. Be- 15 In equilibrium, T receives its war payoff in settlement where x 3 = p H c T and x 4 = p B c T and p H >p B . 16 Full proof in appendix. 76 cause all actors know whether D would support or abandon T in war, D and T can prepare for conflict accordingly and, as a result, C makes an offer equal to T’s war payoff that T will always accept. Yet, empirically, we observe that third-party defenders indeed invest in both joint and unilateral capabilities. This observation might be explained if we introduce differing ideal points between D and T over the contested good and/or private information about D’s preference for war. When D has an ideal point that is closer to C’s, then embold- ening T to be more aggressive in bargaining with material commitments may be too costly. If private information is introduced, D might combine different types of material commit- ments to create strategic uncertainty about its preference over the good and its cost of war. If actors are uncertain if D will intervene in conflict or not, D’s material commitment may not be a perfect signal of its resolve to fight. Discussion The results of the model have broad theoretical and empirical implications for important alliance dynamics: the design of military commitments as a strategic choice; the relation- ship between the cost and effect of military actions taken in peacetime to prepare coun- tries for potential conflict; how willing a defender is to intervene in war; and extended deterrence in crisis bargaining. Even though war never occurs in equilibrium, the model presented here highlights the varying effects that different types of military commitments have on the balance of power of actors in dispute. When we simply account for the fact that material commitments both sink costs and raise the defender’s utility from war (Slantchev 2005), we can uncover new equilibrium behavior that models of alliances or arms alone cannot explain. An examination of the baseline model without material commitments – when material commitments are too costly for a defender to make – yields expectations and results that are consistent with and closely resemble dynamics from costly signaling and existing models of extended deterrence. Yet, when a third-party defender is given a 77 choice over a larger range of commitment strategies, the model explains puzzling state behavior in crises and generates new testable empirical implications. Variation in third-party military commitments The model produces novel predictions for third-party commitment design, even in the absence of uncertainty and private information. Most scholars of alliances argue that military commitments laid out in the obligations and provisions of treaties rely on strategic ambiguity to resolve the dilemma of emboldening one’s target versus deterring challengers. Even with the analysis of a complete information game in which all parameters are known, I find that the addition of material commitments has significantly different results from models of treaty commitments alone. I argue that a defender can both embolden its target and deter challengers (i.e. reduce the size of demands) even with unambiguous and easily observable military measures in peacetime. In fact, the actual military effect of alliances is never directly observed in peacetime: treaty commitments, or those made under alliances, are only tested when war occurs and casus foederis is activated. The strategic effect of alliances on international disputes is limited to the ability of a third-party defender to credibly signal its threat to intervene. Material commitments, in contrast, are easily observable as states often engage in many forms of public military cooperation prior to conflict, such as arms transfers, military inte- gration and deployments. Arguably, the importance of alliances for international security is attributed to the military effect of different military actions that often accompany al- liances and not just the presence or absence of an alliance itself. The results of the model are not driven by asymmetric information or signaling but, rather, by the different effects that various types of material commitments have on the balance of power among actors in dispute. As a result, the model presented here is not limited to explaining only formal treaty alliances, but offers an alternative explanation for how third-party defenders can influence multistate crisis bargaining behavior that involves non-formal allies as well. 78 Scholars’ efforts to explain a broader range of military cooperation that go beyond formal treaty alliances are, again, limited by the restrictions placed on a third-party de- fender’s strategic choices over its military commitments. A key feature of my model is that a defender’s choice over its material commitments directly influences the strategic envi- ronment, endogenizing the probabilities of winning war. Propositions 1 and 2 show that in the shadow of a third-party defender’s material commitments to its target, the allied parties can extract better settlement offers in crisis bargaining. In addition, my theory accounts for the fact that treaty and material commitments can be made alongside each other. Current theories of arms versus alliances do not take these different types of military commitments into account and how they have varying effects on crisis bargaining behav- ior. Extant models cannot explain why defenders implement costly military measures, such as an integrated military command or troop deployments, on top of alliances. The deci- sion for a defender is not simply whether to form a military alliance or provide arms to its target. Instead, a third-party defender strategically selects which package of military com- mitments to make to certain states. Thus alliances are not merely substitutes for physical, military actions taken in peacetime to deter adversaries; instead, treaty commitments are complements to material commitments and have each type has distinct effects on actors’ strategic behaviors in bargaining. My model also considers that the costs to implement peacetime military measures on behalf of allies differ and that these differences matter. It is important to account for the varying costs that different types of military actions entail for states and how such costs influence which commitment strategies are optimal for defender states. When we take into consideration the broad range of material commitments that exist and their different effects on war outcomes, we can begin to empirically test under which conditions a de- fender would prefer to choose one type of military commitment over another. The model presented in this paper provides a better explanation for why we observe significant varia- tion across formal military alliances, variation among states under the same alliance, and 79 variation in third-party commitments to even non-formal allies. Entrapment and abandonment: why third-party commitments don’t always tie hands One of the most interesting equilibrium results from the model arises from proposition 2: when a defender and target share preferences over the disputed good, the defender might actually prefer to embolden its target and make a costly material commitment even if it would abandon its target in war. This result has important implications for the deterrence- restraint dilemma and defender intervention in conflict. Propositions 1 and 2 show that material contributions from a defender embolden a target to reject a greater range of de- mands from its adversary. In other words, the target requires more to be satisfied with the challenger’s offer when its chances of winning war – either jointly or unilaterally – in- crease. As a result, we should expect material commitments that improve joint capabilities to make a target most aggressive in bargaining because it expects its defender’s support in war. The target can extract more from a challenger with the threat of the defender’s involvement. This logic is consistent with the idea that overcommitment from a powerful patron creates a moral hazard effect in which the target is emboldened to act more aggres- sively. In terms of the model, overcommitment is equivalent to material commitments that improve joint capabilities because the defender only employs such commitment strategies when it would unconditionally support its target in conflict (proposition 1). While target emboldenment occurs through material commitments, they do not al- ways entrap a third-party defender as conventional wisdom suggests. In fact, material commitments that only improve a target’s unilateral capabilities do not tie the defender’s hands because the defender can make a costly material commitment to increase the target’s chances of winning without directly fighting itself. Put simply, a third-party defender can directly influence the balance of power among states in dispute without its involvement in conflict. This side option for the defender becomes available only when we consider a 80 larger range of commitment strategies that go beyond forming alliances or not. When we consider different forms of military cooperation, especially those that improve the target’s unilateral capabilities, the defender can both shift the balance of power in its favor (ex- tended deterrence) and allay fears of entrapment (restraint) without ever abandoning or reneging on its commitments. This new finding departs from the conventional wisdom that costly commitments are a signal of a defender’s resolve to intervene in conflict on behalf of its target. My model shows that, even if the defender would abandon the target in war, it can deter the chal- lenger from making larger demands by transferring military technologies to the target that improve its unilateral war-fighting capabilities. Despite costly military actions, a third- party defender is not always entrapped by the target’s emboldenment in crisis bargaining. This result explains why a defender would make a costly, upfront material commitment to another state even if it would abandon it in war, and why entanglement is not as com- mon as most scholars expect (Beckley 2015; Kim 2011; Leeds 2003a). While an alliance may serve as a hands-tying mechanism to make a third party’s threat of intervention more credible, not all forms of third-party commitments influence the strategic environment of states in dispute this way. Entrapment is a real concern for third-party defenders, but only under certain condi- tions. In the present model, D and T have identical preferences over the disputed good so entrapment is not a risk for D. On the one hand, D only makes material commitments to T that improve joint capabilities if it would intervene on T’s behalf in war. Thus D is already resolved to fight and does not face a fear of being entrapped in an undesirable conflict. On the other hand, if D is not willing to fight for T, then it may choose to make a commitment that improves T’s unilateral military capabilities instead. By transferring war- fighting technologies and not forming an alliance, D is not tied to militarily support T in war and, thus, is not dragged into conflict if it were to occur. When D and T have different preferences over the contested issue, then entrapment can occur, especially when D’s ideal 81 point gets farther from T’s. The focus of this paper is to show that even a baseline model of extended deterrence that incorporates material commitments can produce new testable results that differ from existing models. The model identifies the conditions under which entrapment is not a concern for a third-party defender. This implication is significant given that most models of alliances assume entrapment fears are an underlying motivation that drives important defender behaviors in dispute (to avoid it), such as making ambiguous commitments (Benson 2012) or strong commitments used to control overaggressive target states (Cha 2016). Empirical Implications The model presented in this paper examines the conditions under which a third-party de- fender will decide to make a treaty and/or material commitment to a target and, if so, the type of military support it will employ. The defender’s choice over its commitment strategy has a significant effect on actors’ behaviors, including whether the target is emboldened to reject a larger range of settlement offers and how big a demand the challenger is willing to make in bargaining. In this section, I present a set of testable hypotheses derived from the theoretical model that creates novel predictions about which commitment strategy the defender will adopt and the effect such commitments have on actors’ behaviors. From propositions 1 and 2, we can generate observable implications for 1) what type of material commitments D will make to T in peacetime and 2) D’s intervention in war (i.e. whether it is more likely to support or abandon T). While the current model does not predict war in equilibrium, it provides a foundation for understanding how different types of third-party military com- mitments have varying effects on the strategic environment, which can be extended in future research to understand the impact such commitment strategies have on the likeli- hood of militarized conflict. 82 In the next chapter, the general model is then evaluated in the context of US military commitments to South Korea and Taiwan during the Cold War. By looking at historical cases, we can examine changes in the model’s parameters, such as the defender’s willing- ness to support or abandon its target in conflict (i.e. utility from war) and the choice of third-party commitments. The cases of South Korea and Taiwan lend support for the setup and applicability of the model to the real design of military commitments. Third-party defender intervention When does a third-party defender intervene in conflict to militarily support a target? Ex- isting models of third-party commitments mainly compare the defender’s cost of war and cost of abandoning the target to determine the conditions under which a defender would intervene or not. 17 My model shows that the actual military effect of different types of third-party commitments also influence the defender’s decision to intervene or not. Hypothesis 1 The more a third-party defender can shift the local balance of power in its favor, the more likely it is to intervene in conflict, all else equal. From the theoretical model, I show that as the difference between the defender and target’s baseline military capabilities increases (or for increasing values of BB ), the more likely the defender is to support the target in war. Put differently, when the third-party defender is much stronger than the target, the defender’s support in war has a greater marginal effect on improving the chances of war victory, which makes fighting more at- tractive for the defender. The greater the defender’s ability to shift the balance of power in its favor is, the more incentive it has to do so. 18 As a result, the status quo balance of power among states in dispute has a significant effect on the third party’s decision to fight or not. 17 Some studies include other costs such as costs to the alliance relationship if policies diverge (Fang, Johnson and Leeds 2014). 18 Refer to proposition 2 and the conditions on BB . 83 Third-party defender commitment strategy Under what conditions does a third-party defender make military commitments to improve another state’s security? Even if a powerful patron would support its target in war, invest- ing in material commitments is not always optimal. Material commitments carry peacetime costs for their implementation. While a bulk of the alliance literature focuses on the effect treaty commitments have on the likelihood of conflict, there is scant attention paid to how actors strategically choose among a diverse set of military actions. The model provides new testable implications about the type of military commitment a defender is more or less likely to make based on its military effect and conditioned by its cost-effectiveness. Hypothesis 2 The militarily stronger a target is relative to its adversary, material commit- ments that improve the target’s unilateral capabilities become less cost-effective, all else equal. Hypothesis 3 The militarily stronger a third-party defender is relative to its adversary, ma- terial commitments that improve joint capabilities become less cost-effective, all else equal. The assumption that underpins hypotheses 2 and 3 is that the defender does not make a material commitment if it is not cost-effective to do so. This implies that the less cost- effective a material commitment is, the less likely the defender is to make it in the first place. For hypothesis 2, if a target is already much stronger than its opponent, then the third-party defender – holding its military capabilities constant – will have a small marginal effect on shifting the local balance of power in favor of itself and its target. In other words, the target is more than capable of fighting (and winning) a war against its adversary without the aid of its ally. Given a limited ability to change the balance of power among disputants, the defender is less likely to intervene in conflict. At the same time, material commitments that improve the target’s unilateral capabil- ities are also less cost-effective because the target already has the tools to fight and win against the challenger. The defender need not pay extra costs to implement costly mili- tary measures in peacetime if the probability of the target winning in war is already high 84 in the absence of material commitments. In terms of the model parameters, this can be understood as shrinking the difference p H p B , where p H is T’s increased probability of war victory with D’s material commitment andp B is the baseline probability of war victory without material commitments. As a result, if a target is much stronger than its oppo- nent, the third-party defender is less likely to make a material commitment that improves its target’s unilateral capabilities because of its decreasing cost-effectiveness. This empiri- cal implication may explain why American allies do not have great incentives to invest in or significantly improve their own military capabilities despite their growing wealth and potential military power. US allies, particularly in East Asia, continue to rely on US re- assurances for defense because, if they were to become too powerful compared to their adversaries, then the United States would actually have less incentive to militarily support them in conflict. Similarly, the defender is less likely to make a material commitment that improves joint capabilities when it is much stronger than its adversary. According to lemma 1, the defender always prefers to support its target in conflict if it can credibly do so. This is because a defender can extract a better settlement offer from a challenger if the defender can ensure it would indeed intervene in war. Given this logic, if a third-party defender is significantly stronger than its opponent, then all it needs is to guarantee its support in war to have a large effect on shifting the local balance of power in its favor. Material commitments that improve joint capabilities simply become added costs for the defender with small benefits. In terms of the model’s parameters, for a high baseline probability of war victory with the defender’s support (q B ), the difference a material commitment can make in improving the chances of victory is reduced, shrinking q H q B . Thus material commitments that improve joint capabilities become less cost-effective when the defender is already much stronger than its opponent. The logic behind hypothesis 3 is a bit counterintuitive: the more powerful a third-party defender is relative to the target and challenger, the more capable it is of making material 85 commitments, but it is also less likely to do so because such commitments are not as cost- effective as its mere support in war. This may partially explain why the United States is limiting its investment in joint capabilities with its allies despite the fact that it remains a powerful hegemon with the military and economic means to do so. As a result, we observe a reduction in foreign troop deployments, a consolidation of military bases, and increased calls for burden sharing among NATO and East Asian allies. 19 Now consider the case when a defender and challenger are evenly matched while the target is significantly weaker. Under this case, the defender has a large marginal effect on shifting the local balance of power in its favor because the target is weak. Thus the de- fender has greater incentive to support the target in war and material commitments that improve joint capabilities become more cost-effective. This is because when a defender and challenger are evenly matched in military strength, any military advantage that the defender can take to increase its chances of winning in war is substantial. If the local balance of power is heavily skewed to one side, incremental improvements to military ca- pabilties are less meaningful. Yet if the balance of power is relatively even, then increasing one’s chances of victory is significant and one would have increasing incentive to do so (i.e. invest in material commitments). US military commitments to key European and East Asian allies during the Cold War suggest this dynamic is plausible. The United States was relatively evenly matched with the Soviet Union during the height of the Cold War and, as a result, we observe significant material commitments to strategically valuable US allies within NATO and South Korea. The material commitments the United States made to its allies during this period were those that improved joint capabilities, such as the integration of military commands, the expansion of foreign bases, and maintenance of substantial troop deployments. 19 This is not to say that domestic political considerations can be ignored. I simply argue that this result is in line with US strategic behavior and can help explain this phenomenon. 86 Model Extension: war under complete information In the baseline model, war never occurs in equilibrium under complete information be- cause war is inefficient and costly, and the challenger knows exactly how much to demand in bargaining to obtain a peaceful settlement. Now consider when the target receives ad- ditional utility, 0, from going to war. Empirically, a state in a dispute can gain from winning conflict such as the acquisition of territory, control over a policy, or a boost in nationalism and domestic support. The payoffs of actors are summarized in Table 3.3. Table 3.3: Summary of Expected Utilities Settlement War (with D’s support) War (without D’s support) Challenger x 1q w c C 1p w c C Target 1x q w c T + p w c T + Defender 1x j q w c D j p w k a j The propositions derived from the baseline model essentially treat the target’s war utility as = 0, such that there is no additional gain from going to war for the target state. When c T < < 1q H +c T , or the target receives a higher war payoff, war becomes possible in equilibrium because the target will accept a smaller set of demands from the challenger. 20 When the target requires too much to be satisfied with peace, the challenger may prefer war over settlement. The analysis of the complete information model follows from the baseline model. Yet the addition of to the model generates conditions under which war occurs in equilibrium and limits how the defender’s commitment can shape bargaining outcomes. In the follow- ing sections, I examine the conditions under which the defender can influence strategic behavior in bargaining and the likelihood of war. The proofs are outlined in the appendix. 20 This is a stricter condition than> 0 given thatc i > 0. The condition on ensures that the inequalities hold such thatc C is greater than 0 andx is also strictly positive. 87 War equilibrium Proposition 3 War occurs in equilibrium under complete information whenc C <c T and c T < < 1q H +c T . The challenger makes a demand so high that the target would never accept. All actors go to war and receive respective war payoffs, and the third-party defender makes material commitments if they are cost-effective. When the target receives additional positive utility from going to war, war becomes possible in equilibrium even under complete information. The parameter increases T’s preference for war, which also drives down the demands that C can make in bargaining that T will accept. For small enough demands, C will always prefer war over settlement regardless of D’s threat of intervention. In other words, when C expects to receive so little in bargaining, it instead makes a demand so high that T would not accept in equilibrium. This is because C strictly prefers war over anything it can get in settlement. As a result, D cannot influence strategic behavior and the likelihood of war when C is sufficiently resolved to go to war. When C makes demands that it does not expect T to accept, war occurs in equilibrium and D’s ability to shape the strategic environment is limited. D’s decision to support or abandon T in conflict does not influence the size of demands in bargaining. Discussion The model extension finds that war is possible in equiibrium, but only when the chal- lenger’s utility from settlement is sufficiently low that war is always preferable. This means that, regardless of the third-party defender’s decision to intervene or not, war will occur if the challenger is sufficiently resolved. It is interesting to note that as or the utility that the target state receives from war increases, the cost of war for the challenger increases as well (see proof in appendix). While it may seem counterintuitive that an increasing cost of war would make the challenger more willing to enter conflict, this results can also 88 be interpreted as the challenger being so resolved to fight that even rising costs of war are not enough to deter it. When the demand the challenger can make in settlement is sufficiently small, then the challenger would prefer to go to war instead. This is in line with the other finding that the third-party defender’s decision to intervene or not does not influence bargaining behavior. Even if the defender is willing to support the target in war, the challenger still cannot be deterred under certain conditions. The war equilibrium shows the conditions under which war can occur and when the defender’s involvement in war becomes constrained (i.e. cannot influence bargaining be- havior and states’ decision to go to war). Yet proposition 3 lends support to the argument that a third-party defender’s ex ante commitment can still influence outcomes; in this case, material commitments affect each actor’s war payoffs. If material commitments are cost- effective, then a defender can properly prepare for the war it is willing to fight. The third party’s commitments shift the balance of power in the defender and target’s favor, as in- vesting in joint capabilities can improve the chances of victory in a multilateral war while improving only the target’s unilateral capabilities still increases chances of victory in a bilateral war as well. Chapter Summary Recognizing the significance of variation in third-party commitments has broad theoreti- cal and empirical implications for the study of military alliances. The theoretical model developed in this chapter provides a first cut at understanding why military commitments between states differ and how the variation influences crisis bargaining behavior that mil- itary alliances alone cannot explain. I find that a state’s decision to intervene in conflict on behalf of its ally is driven by its ability to shift the balance of power in its favor. The degree to which a third-party defender can influence the strategic environment is conditioned by its ability to make a material commitment that bolsters either a target’s unilateral capabili- 89 ties or the allies’ joint capabilities. 21 By expanding the set of tools or commitment strategies that states can employ to protect their allies, the model uncovers new equilibrium behav- iors that are driven by the variation in military commitments and actors’ expectations of their different effects. In particular, entrapment fears are ameliorated when a defender can influence the strategic environment of actors in dispute even without its intervention in war. This novel prediction challenges the conventional wisdom that powerful patrons are overly concerned with restraining emboldened target states and explains why certain states also receive substantial military support from non-formal allies. The model also produces new empirical implications about which types of military commitments are made between states. These predictions about commitment design can then be tested with observational data on military cooperation over time. There is also more empirical purchase from this study given that third-party commitments are not only made through alliances but other military means as well. By not restricting the analysis to states already in formal military alliances, we can expand the number of cases to examine. Before we can fully understand how military alliances affect the likelihood of conflict, we must first examine how state leaders design and implement military commitments to other states. Clearly, military cooperation between states is not bound to the obligations and provisions laid out in treaties. Instead, there exists a broad range of commitment tools that each have unique military effects on the strategic environment of actors in dispute. The findings from the theory have significant implications for foreign policy and the maintenance of global military cooperation. Alliances are important for international se- curity because of the actual military actions that often accompany them. National leaders design and implement military support for other states in various ways, but are constrained by different structural factors, such as the balance of power between states and the costs of maintaining military cooperation. These strategic considerations are important for policy debates between deep engagement versus retrenchment, or how involved powerful pa- 21 Here, again, the term “allies" can be formal allies (treaty) or not. 90 trons should be in providing security for others (Gholz, Press and Sapolsky 1997; Brooks, Ikenberry and Wohlforth 2012). 91 Appendix Model Setup Table 3.4: Summary of Defender’s Strategies D’s commitment strategy D’s commitment mechanism D’s cost of making commitment k L ;p B ;q B No material commitment (MC), no alliance 0 k L ;p H ;q B MC that improves only T’s unilateral capabilities, but no alliance p k L ;p B ;q H MC that improves only D and T’s joint capabilities, but no alliance q k L ;p H ;q H MC that improves both joint and unilateral capabilities, but no alliance pq k H ;p B ;q B No MC, but formal alliance 0 k H ;p H ;q B MC that improves only T’s unilateral capabilities, with alliance p k H ;p B ;q H MC that improves only D and T’s joint capabilities, with alliance q k H ;p H ;q H MC that improves both joint and unilateral capabilities, with alliance pq Model Solution I solve the model under complete information (all parameters known to actors) using a subgame perfect Nash equilibrium solution. Using backwards induction, we start with determining the conditions under which D would support T in war. EU D (WarjSupport)EU D (WarjAbandon) q w c D j p w k a j ,q w p w c D k a (3.3) T’s decision to accept or reject C’s demand is conditioned on what war it expects to fight, namely whether it expects D’s support or not. Thus T will accept settlement over war if: EU T (Settlement)EU T (WarjSupport=Abandon) (3.4) T’s war payoff with D’s support is its probability of winning (q w ) minus its cost of war (c T ). Without D’s support, T faces a bilateral war with C alone such that (p w c T ). Here, T’s probability of winning is conditioned on D’s ex ante material commitment (both the type of military contribution that is made and whether it is made at all). If D supports T in war, then T accepts C’s demand when: EU T (Settlement)EU T (WarjSupport) 1xq w c T ,x 1q w +c T (3.5) C maximizes its utility by demanding just enough to get T to accept in equilibrium or, in other words, offering T its expected value from war. Given there is no private information 92 in the model, the actors always prefer settlement in equilibrium and never go to war because it is inefficient and costly (Fearon 1995). 22 Thus the four possible demands that C will make, in equilibrium, are: 23 x 1 = 1q H +c T x 2 = 1q B +c T x 3 = 1p H +c T x 4 = 1p B +c T (3.6) C’s demands can be ranked from smallest to largest: x 1 < x 2 < x 3 < x 4 , where D and T most prefer a settlement that yieldsx 1 and C most prefersx 4 . D’s choice over its commitment mechanism is driven by the cost-effectiveness of its material commitment. D prefers to maximize its settlement payoff, 1x j , conditioned on how its material commitment influences C’s demand in equilibrium and the relative cost of making such a material commitment. In other words, D will choose the material commitment that has a sufficiently large enough effect on shifting the balance of power in its favor at an acceptable cost. Now I turn to analyzing four cases that detail equilibrium behavior. For each, I identify the conditions under which 1) D will support or abandon T in war, 2) D will enter into an alliance with T or not, and 3) the type of material commitment D will make (i.e. improve T’s unilateral capabilities, improve joint capabilities, or neither). Proof of equilibrium with no material commitments I examine the case where D does not make any material commitments. This case serves as a baseline model for understanding how the inclusion of material commitments can produce new equilibrium results. Under complete information, all actors prefer settlement in equilibrium and D receivesp B c T from abandoning T andq B c T from supporting T in war. D’s utility from settlement is 1x j , or its settlement offer in equilibrium minus the cost of making a material commitment. Here, D never makes a material commitment because it is too costly such that = 0. In equilibrium, D’s utility from settlement when it would support T is strictly greater than if it would abandon it, such thatq B c T >p B c T , where q B > p B . Since D and T share identical ideal points over the disputed good, this implies that D would always receive higher utility in equilibrium if it would support T in war over abandonment. Lemma 1 In equilibrium, D’s utility from settlement is always greater when it would support T in war than when it would abandon T in war. 22 The challenger cannot unilaterally impose war on the other actors in the current model. D’s decision to support or abandon T in war is solely determined by the probability of winning war and its cost of war/cost of abandonment. T can instigate war or not depending on its expectation of D’s involvement (or lack thereof). 23 Note that C’s equilibrium demands are simply T’s war payoffs, depending on D’s decision to support or abandon. C offers T just enough to be satisified with not going to war, while keeping what it demands for itself. 93 Lemma 1 implies that D always supports T in war but only if it can credibly do so. Put differently, D will support T in war for sufficiently low enough costs of war. For high costs of war, D will choose to abandon T even if it would prefer to support it because D cannot credibly commit for high enough costs of war. In the baseline model, we assume that any type of material commitment is too costly for D to make such that p >p H p B and q >q H q B . Material commitments that improve joint capabilities or T’s unilateral capabilities are not cost-effective because their cost for D exceeds the utility D can gain from changing the balance of power in its favor (i.e. for a better chance of war victory against C). As a result, we only need to examine D’s decision to make a treaty commitment or not. Consider the conditions under which D will form an alliance or not with T. If D does not make a treaty commitment to T it receivesp B k L from abandoning it in war andq B c D if it supports T in war. If D makes a treaty commitment to T, it faces a higher cost to abandoning T in war such that p B k H (where k H > k L ) and the same payoff from support,q B c D . Now we analyze the conditions under which D would prefer to support or abandon T in war. Condition 1. If c D k L < BB , then D always supports T in war, regardless of treaty commitment. EU D (War Support )>EU D (TreatyjWar Abandon )>EU D (TreatyjWar Abandon ) q B c D >p B k L >p B k H q B c D >p B k L ,q B p B >c D k L (3.7) Let BB = q B p B . If c D k L < BB , then D would prefer to support T in war and would be indifferent between making a treaty commitment or not. 24 Put simply, under this condition, D always prefers to support T in war regardless of its decision to enter into a military alliance with T or not. Thus D is indifferent between entering into a military al- liance with T or not (i.e. making a treaty commitment). The cost of war is sufficiently low that D would enter war on T’s behalf no matter what. D strictly prefers to support T if it can do so and receives a better settlement offer in equilibrium (1x 2 =q B c T ) as a result. Condition 2. If c D k H > BB , then D always abandons T in war, regardless of treaty commitment. EU D (War Support )<EU D (TreatyjWar Abandon )<EU D (TreatyjWar Abandon ) q B c D p B k L since it is the stricter inequality overq B c D >p B k H . 94 If c D k H > BB , D would prefer to abandon T in war and be indifferent between making a treaty commitment or not. Here, again, D always prefers to abandon T in war whether or not it enters into an alliance with T. In relation to lemma 1, D would get a higher utility from supporting T in war but cannot do so because its cost of war is too high. Thus D unconditionally abandons T in war under this condition and receives the worst settlement offer from C in equilibrium, 1x 4 =p B c T . Condition 3. Ifc D k L > BB >c D k H , then D supports T in war, if and only if, it has made a treaty commitment to T. EU D (TreatyjWar Abandon )>EU D (War Support )>EU D (TreatyjWar Abandon ) p B k L >q B c D >p B k H ,c D k L >q B p B >c D k H (3.9) The last condition we examine is one in which BB takes on a middling value between c D k L andc D k H . Ifc D k L > BB >c D k H , then D prefers to support T in war only if it is in a treaty alliance with T but abandons otherwise. Unlike the first two conditions an- alyzed above, under this condition, D’s utility from supporting T in war is only better than its utility from abandoning a treaty ally, orq B c D >p B k H . Thus entering into a treaty alliance with T determines D’s decision to support or abandon T in war. From lemma 1, D always prefers to support T in war if it could do so (i.e. receives higher settlement offer in equilibrium) and, as a result, D would enter into a military alliance with T to ensure it supports T in war. Thus D receives a higher utility in equilibrium, 1x 2 = q B c T . This condition shows that in the absence of any material commitments to T, D may tie its hands to T by entering into a military alliance in order to extract a better settlement in equilibrium (i.e. logic behind costly signaling and extended deterrence). The following outlines the complete equilibrium when D is limited to making only a treaty commitment and no material commitments: Suppose p >p H p B and q >q H q B . Let BB =q B p B . Ifc D k L < BB , then D always supports T in war and is indifferent between entering into a treaty alliance with T or not. Ifc D k H < BB <c D k L , then D prefers to make a treaty commitment to T and supports T in war. If c D k H > BB , then D always abandons T in war and is indifferent between entering into a treaty alliance with T or not. If D would support T in war, C makes a demand ofx 2 = 1q B +c T and T accepts. Otherwise, D abandons, C demandsx 4 = 1p B +c T and T accepts. All actors receive settlement payoffs. 95 Discussion Under this case, material commitments are too costly for D to make relative to D’s ability to shift the balance of power in its favor. In equilibrium, D does not make any material commitments. If c D k L < BB , D unconditionally supports T in war – regardless of its commitment strategy – because its cost of war is sufficiently low. As a result, D’s expected support raises T’s war payoffs fromp B c T toq B c T and T requires a larger offer from C to be satisfied and not instigate conflict between the actors. Under complete information, C makes a smaller demand in bargaining,x 2 < x 4 , when it expects D to support T in war than if it expects to fight T alone. Here, D is indifferent between entering into a treaty alliance with T or not and will always support T in war, thus, D’s threat of intervention reduces the size of C’s demand in bargaining. Ifc D k H > BB , D would always abandon T in war and is indifferent between making a treaty commitment or not. The cost of war for D is too high such that it strictly prefers to not intervene and abandon T instead. When the cost of war for D is sufficiently high and it prefers to abandon T in war, C will make the largest demand in equilibrium atx 4 , leaving D and T worst off. Finally, ifc D k H < BB <c D k L , then entering into a treaty determines D’s support and D makes a treaty commitment to T if it prefers to support T in war. Under this con- dition, the cost of abandoning T (k H ) is too high for D and it does not make any material commitments in equilibrium. As a result, when forming a military alliance with T guar- antees D’s support in war, D would prefer to do so (lemma 1) in order to extract the best settlement offer from C orx 2 . Proof of Proposition 1 Suppose p > p H p B and q q H q B . Under this case, material commitments that improve D and T’s joint capabilities are cost-effective while material commitments that only improve T’s unilateral capabilities are not. In other words, D can shift the balance of power in its favor with a material contribution to joint capabilities that does not exceed the cost of making the commitment. Following the logic of case 1, we examine the conditions under which D will support or abandon T in war, whether D will make a material commitment that improves joint capabilities, and whether D will make a treaty commitment to T or not. If D does not enter into a treaty alliance with T, D’s utility from supporting T in war isq H c D q and p B k L q from abandon. If D is in a treaty alliance with T, its utility from support is the same (q H c D q ) and p B k H q from abandon. When material commitments that improve joint capabilities are cost-effective, D would choose to make them if and only if it would support T in war. D’s material contribution raises the probability of defeating C in war from q B to q H , but at a cost of q > 0. The probability that T defeats C alone (i.e. without D’s support) remains the baseline probability, orp B , since material commitments that only improve T’s unilateral capabilities are too costly for D ( p > p H p B ). Once again, being treaty allies with T raises D’s costs from abandonment fromk L tok H . 96 Condition 1. If c D k L < HB , then D always supports T in war, regardless of treaty commitment. D makes a material commitment that only improves joint capabilities. EU D (War Support )>EU D (TreatyjWar Abandon )>EU D (TreatyjWar Abandon ) q H c D q >p B k L q >p B k H q q H c D >p B k L ,q H p B >c D k L (3.10) Let HB = q H p B . If c D k L < HB , D unconditionally supports T in war and is indifferent between making a treaty commitment or not. D’s material commitment to T increases the probability of war victory and, as a result, D and T can extract the highest settlement offer in equilibrium or 1x 1 q =q H c T q . Condition 2. If c D k H > HB , then D always abandons T in war, regardless of treaty commitment. D does not make a material commitment to T. Under this condition, if and only ifc D k H > HB , D always abandons T in war and is indifferent between making a treaty commitment or not. Since D would abandon T no matter what, D does not make a material commitment in equilibrium that improves joint or T’s unilateral capabilities. In other words, if D would abandon T in war, it does not make any material commitment because improving joint capabilities is only cost-effective when D would support T in war and it is never cost-effective for D to improve T’s unilateral capabilities (by assumption). As a result, D receives the worst settlement in equilibrium or 1x 4 =p B c T . Condition 3. If c D k H < HB < c D k L , then D supports T in war, if and only if, it has made a treaty commitment to T. If D prefers to support T in war, D makes a material commitment that only improves joint capabilities. Following from the baseline model, if c D k H < HB < c D k L , then the presence of a military treaty determines D’s willingness to support T in war or not. If D has a treaty with T, then D would support T in war and, given its support, D would make a material commitment that improves joint capabilities. Whenever D would support T in war (i.e. D’s involvement is guaranteed), D always prefers to improve joint capabilities and raise the joint probability of war victory as long as such material commitments are cost-effective ( q < q H q B ). Thus D’s support yields the highest utility in equilibrium with the cost of investing in a material commitment that improves joint capabilities, or 1x 1 q =q H c T q . The full equilibrium can be stated as follows: Suppose p >p H p B and q q H q B . Let HB =q H p B . 97 If c D k L < HB , then D always supports T in war and is indifferent between entering into a treaty alliance or not. D makes a material commitment that only improves joint capabilities. If c D k H < HB < c D k L , then D prefers to make a treaty commitment to T and supports T in war. D makes a material commitment that only improves joint capabilities. If c D k H > HB , then D always abandons T in war and is indifferent between entering into a treaty alliance or not. D does not make a material commitment to T. If D would support T in war, C makes a demand ofx 1 = 1q H +c T and T accepts. Otherwise, D abandons, C demandsx 4 = 1p B +c T and T accepts. All actors receive settlement payoffs. Proof of Proposition 2 Now we examine the case when material commitments to improve joint capabilities are too costly, but improving T’s unilateral capabilities is cost-effective or p q H q B . Again, the conditions analyzed below follow from the baseline model and proposition 1. Under this case, D’s material commitment improves T’s individual military capabilities against C, such thatp B is raised top H , and the cost to D of implementing such a commitment does not exceed the improvement in T and C’s balance of power (in T’s favor). Yet material commitments that improve joint capabilities are no longer cost-effective. If D makes a treaty commitment to T (i.e D and T are formal treaty allies), D’s utility from supporting T in war isq B c D p and abandoning isp H k H p . If D does not make a treaty commitment to T, D receivesq B c D p from supporting andp H k L p from abandoning T in war. Similar to proposition 1, D pays a sunk cost for making a material commitment to T that improves T’s unilateral capabilities or p . Condition 1. If c D k L < BB , then D always supports T in war, regardless of treaty commitment. D does not make a material commitment to T. EU D (War Support )>EU D (TreatyjWar Abandon )>EU D (TreatyjWar Abandon ) q B c D p >p H k L p >p H k H p q B c D >p H k L ,q B p H >c D k L (3.11) Let BH =q B p H . If BH >c D k L , then D supports T in war no matter what and is indifferent between making a treaty commitment or not. Because material commitments that only improve joint capabilities are too costly, or q > q H q B , D does not make any material commitment in equilibrium but still improves its utility by extending its support to T (lemma 1). Yet if D unconditionally supports T in war, then D does not have to pay the added cost of making a material commitment that only improves T’s unilateral capabilities. In other words, if D would always prefer to support T in war and D’s support 98 in war is strictly better for the odds of war victory than improving T’s capabilities (i.e. q B > p H ), then D would not need to make a material commitment to T’s unilateral capabilities. Improvements to joint capabilities are too costly for D to make, and even improving T’s unilateral capabilities is not as good as directly supporting T in war. This statement is true even if it is still cost-effective to make material commitments that improve T’s unilateral capabilities (i.e. p c D k L , then D always supports T in war, is indifferent between signing a treaty, but makes no material com- mitment in equilibrium. Here, since BB > BH , we can use the stricter condition on improvements in war fighting capabilities such that BB > BH > c D k L . 25 Thus D and T improve their settlement utilities in equilibrium with D’s unconditional support, or 1x 2 =q B c T . Condition 2. If c D k H > BB , then D always abandons T in war, regardless of treaty commitment. D makes a material commitment that only improves T’s unilateral capabili- ties. Under this condition, ifc D k H > BB , then D strictly prefers to abandon T in war and is indifferent between entering into a military alliance or not. Here, we again adopt the stricter condition such that if c D k H > BB > BH , then D always abandons T in war. This stricter condition ensures that D will not deviate to making a material commitment that only improves T’s unilateral capabilities in order to abandon T in war. In other words, this condition guarantees that D will not choose to make a material commitment that only improves T’s unilateral capabilities just so that it can abandon rather than support T in war. The condition is also in line with lemma 1 in that D prefers to support T if it can but, if D cannot get itself to support T in war, then it would prefer to improve T’s unilateral capabil- ities as long as it is cost-effective to do so. Because material commitments that improve T’s unilateral capabilities are cost-effective under this case, D will choose to make them and receive a higher utility in equilibrium than if D did not make the material commitment. In equilibrium, D receives 1x 3 p =p H c T p which is strictly better than its expected utility in the absence of any material commitment (i.e. p B c T ). Condition 3. Ifc D k H < BB <c D k L , then D always supports T in war, if and only if, it has made a treaty commitment to T. D does not make a material commitment to T. Last, ifc D k H < BB <c D k L , then D supports T in war if it has made a treaty com- mitment to T, but does not make any material commitment. The logic for this condition follows from the first, where D’s support in war is strictly better than any improvement it can make to T’s unilateral capabilities. Since increasing joint capabilities is too costly for D, it will choose to make no material commitment to T but support in war under the pres- ence of a military treaty. Entering into a military alliance with T determines D’s decision to support or abandon T in war. From lemma 1, D strictly prefers the settlement outcome from its support and so would prefer to tie its hands into doing so to receive 1x 2 . 25 Since BB =q B p B and BH =q B p H , andp H >p B , then it must be true that BB > BH . 99 The full equilibrium for proposition 2 is: Suppose p p H p B and q >q H q B . Let BB =q B p B . Ifc D k L < BB , then D always supports T in war and is indifferent between entering into a treaty alliance or not. D does not make a material commitment to T. Ifc D k H < BB <c D k L , then D prefers to make a treaty commitment to T and supports T in war. D does not make a material commitment to T. If c D k H > BB , then D always abandons T in war and is indifferent between entering into a treaty alliance or not. D makes a material commitment that only improves T’s unilateral capabilities. If D would support T in war, C makes a demand ofx 2 = 1q B +c T . Otherwise, D abandons, C demandsx 3 = 1p H +c T and T accepts. All actors receive settlement payoffs. Proof of equilibrium with all material commitments Finally, we examine the case in which both types of material commitments – those that improve joint capabilities or improve T’s unilateral capabilities – are cost-effective for D such that p 0. If D is in a treaty alliance with T, then its expected war payoffs areq H c D q from support andp H k H p from abandon. If D is not in an alliance with T, then D receives q H c D q from supporting T in war andp H k L p from abandon. Because both types of material commitments are cost-effective, D can choose to invest in either type and pay its associated costs. Condition 1. If c D k L < HB , then D always supports T in war, regardless of treaty commitment. D makes a material commitment to T that only improves joint capabilities. EU D (War Support )>EU D (TreatyjWar Abandon )>EU D (TreatyjWar Abandon ) q H c D j >p H k L j >p H k H j q H c D >p H k L ,q H p H >c D k L (3.12) Let HH =q H p H . If HH >c D k L , then D unconditionally supports T in war, is in- different between making a treaty commitment or not, and makes a material commitment that improves joint capabilities. Yet, like proposition 2, we can impose an even stricter 100 condition to ensure D does not deviate to abandoning T and only improving its unilateral capabilities. Compare the best utility D can expect to receive in war versus its worst: EU D (War Support )>EU D (TreatyjWar Abandon )>EU D (TreatyjWar Abandon ) q H c D >p B k L >p B k H q H c D >p B k H ,q H p B >c D k H (3.13) Here, D’s expected war payoff from supporting T with a material commitment that im- proves joint capabilities isq H c D . 26 D’s worst utility from war is if D abandons T under the presence of a military alliance and makes no material commitment at all, orp B k H . Not only is the probability of war victory the smallest, but D also pays the higher cost of abandoning a treaty ally. Thus if HB > c D k H , where HB = q H p B , then D always supports T in war and increases its settlement offer in equilibrium by making a material commitment that only improves joint capabilities. Put simply, D receives its highest utility in equilibrium when it prefers to support T in war and, knowing which war it expects to fight, increases its chances of war victory if it is cost-effective to do so. As a result, D and T receive their best settlement offer 1x 1 in equilibrium and D pays q for improving joint capabilities. Condition 2. If c D k H > HB , then D always abandons T in war, regardless of treaty commitment. D makes a material commitment that only improves T’s unilateral capabili- ties. Under this condition, if c D k H > HB , then D abandons T no matter what and is indifferent to entering into a treaty alliance or not. Following from proposition 2, D makes a material commitment that only improves T’s unilateral capabilities because it raises its settlement offer from C in equilibrium and is cost-effective enough to do so. Again, D receives a higher payoff in settlement by increasing T’s individual war-fighting capabilities than in the absence of such material commitments, such thatp H c T p >p B c T . Condition 3. Ifc D k H < HB <c D k L , then D always supports T in war, if and only if, it has a made treaty commiment to T. D makes a material commitment that only improves joint capabilities. Ifc D k H < HB <c D k L , then D’s treaty commitment to T determines its decision to support or abandon T in war. From lemma 1, D always prefers to support T in war if it could and, as a result, D will support and make a material commitment that improves joint capabilities under this condition. Given q <q H q B , it is cost-effective for D to invest in joint capabilities if and only if D would support T in war. As examined in the propositions above, D prefers tie its hands with a treaty commitment to ensure its support in war and 26 Since j is a sunk cost, it does not factor into D’s decision to support or abandon T in war. The comparison in expected war payoffs is used to determine the strictest condition for D’s support. 101 increase its chances of war victory with a peacetime military action (i.e. better prepare for multilateral war). Observing D’s material commitment, C makes the smallest demand in equilibrium (x 1 ). When both types of material commitments are cost-effective, the following is an equilib- rium: Suppose p p H p B and q q H q B . Ifc D k L < HB , then D always supports T in war and is indifferent between entering into a treaty alliance or not. D makes a material commitment to T that improves joint capabilities. If c D k H < HB < c D k L , then D prefers to make a treaty commitment to T and supports T in war. D makes a material commitment to T that improves joint capabilities. If c D k H > HB , then D always abandons T in war and is indifferent between entering into a treaty alliance or not. D makes a material commitment that only improves T’s unilateral capabilities. If D would support T in war, C makes a demand ofx 1 = 1q H +c T and T accepts. Otherwise, D abandons, C demandsx 3 = 1p H +c T , and T accepts. All actors receive settlement payoffs. Discussion Following from propositions 1 and 2, D always makes a material commitment that opti- mizes its utility based on its decision to support or abandon. If D would unconditionally support T in war, it is indifferent between making a treaty commitment to T but improves only joint capabilities. If D strictly prefers to abandon T in war, it is, again, indifferent to entering into an alliance but improves only T’s unilateral capabilities. For middling costs of war where the presence of a treaty determines D’s decision to support or aban- don, D prefers to make a treaty commitment to T to ensure its support in war and makes a material commitment to increase joint capabilities because it is cost-effective to do so. Equilibrium behavior follows from propositions 1 and 2, depending on D’s decision to support or abandon. Model Extension: War under Complete Information D’s decision to support or abandon T in war remains the same as the baseline model, such that: 102 EU D (WarjSupport)EU D (WarjAbandon) q w c D j p w k a j ,q w p w c D k a (3.14) T decides whether to accept or reject C’s demand, but now it receives extra utility from going to war such that> 0. T will accept C’s demand with D’s support in war if: EU T (Settlement)EU T (WarjSupport) 1xq w c T + ,x 1q w +c T (3.15) The set of demands that C is willing to make in equilibrium to satisfy T are as follows: x 1 = 1q H +c T x 2 = 1q B +c T x 3 = 1p H +c T x 4 = 1p B +c T (3.16) Unlike in the baseline model when = 0, C prefers war over a peaceful bargain under certain conditions. Because T requires more in bargaining to be satisfied with settlement, C will not make demands that are so small and would, instead, prefer fighting. Thus C prefers war over settlement if its cost of war,c C , is sufficiently low enough such that: EU C (WarjSupport)>EU C (Settlement) 1q w c C >x ,c C <c T (3.17) This condition on C’s cost of war holds true regardless of if D supports or abandons T in war. As increases, C’s cost of war increases as well. Arguably, this is because as T becomes more “resolved" or receives greater utility from war, the cost of fighting becomes higher for C. Fighting a resolved opponent is costlier and the cost from losing may also be greater. This may not seem intuitive that a rising cost of war for C would increase its willingness to go to war, but this result can be interpreted as a C that prefers war so much that nothing can deter it. To ensure that constraints onc i are consistent with values of, it must also hold true that > c T and < 1q w +c T . This condition makes sure that c i > 0 and thatx 0. If< 1q w +c T , then this is true for all values ofq w andp w since q w >p w . Whenc C <c T , then D’s decision of intervention or not does not influence bargain- ing. Instead, C demands more than 1p B +c T , which is the highest demand it can make and have T accept (if D did not support T in war). T rejects anything overx 4 so war 103 occurs in equilibrium and all actors receive their respective war payoffs. Since all payoffs and costs are known to the actors under complete information, D knows when war will occur in equilibrium and will prepare accordingly. If D prefers to support T in war, such thatq w p w c D k a , then D will make a material commitment to T that improves joint capabilities as long as q q H q B and p <p H p B if it would abandon T instead. The full war equilibrium under complete information is (proposition 3): Supposec T << 1q H +c T andc C <c T . If c D k L < HB , then D always supports T in war and is indifferent between entering into a treaty alliance or not. D makes a material commitment that only improves joint capabilities if q <q H q B . If c D k H < HB < c D k L , then D prefers to make a treaty commitment to T and supports T in war. D makes a material commitment that only improves joint capabilities if q <q H q B . If c D k H > BB , then D always abandons T in war and is indifferent between entering into a treaty alliance or not. D makes a material commitment that only improves T’s unilateral capabilities if p 1p B + c T and T always rejects. All actors go to war and receive their war payoffs. 104 Chapter 4 US Commitments to East Asia The theory developed in Chapter 3 generates a set of testable hypotheses about the design and implementation of third-party military commitments. This chapter uses historical case studies to unpack the causal mechanisms identified in the theoretical model. In particular, I examine changing US commitments to South Korea and Taiwan during the Cold War. Consistent with the theory, I argue that US commitments (as a third-party defender) to South Korea and Taiwan (target states) were largely driven by three main factors: 1) the local balance of power among states in dispute, 2) the cost of investing in commitment strategies, and 3) the varying military effect that material commitments had on states’ capabilities. The three parameters are inter-related as outlined in the model. First, the local bal- ance of power influences both the size of the military effect of different commitments and the third-party actor’s willingness to intervene to support the target in war. Sec- ond, the costs of implementing different commitments condition the defender’s choice of commitment strategy. As outlined in the previous chapter, different forms of military co- operation impose varying costs for the third-party defender, and the cost-effectiveness of investments determines which commitments the defender is credibly willing (or able) to make in equilibrium. Last, material commitments, or physical military measures adopted in peacetime, have different exogenous effects on states’ military capabilities that influ- ence how states behave in bargaining. Material commitments can either improve the third 105 party and target’s joint military capabilities or the target’s unilateral capabilities. In the following sections, I examine these three explanatory variables to explain why and how US commitments to South Korea and Taiwan evolved over time in line with changes in the model parameters. Case Selection and Analysis In this chapter, I examine the empirical implications of the theory and evaluate the hy- potheses derived from the model. While the historical case studies do not provide a test of causal relationships between the explanatory variables (model parameters) and outcome (US commitment strategy), they are useful in unpacking the strategic logic of national leaders when they make decisions about which military commitments to make to which states of aligned interest. Cross-Country Comparison: South Korea and Taiwan A comparison of US military commitments to South Korea and Taiwan during the Cold War is chosen because the commitment strategies to the two countries present interesting research puzzles. For the South Korean case, why did the United States make substantially costly commitments to defend South Korea despite its desire to avoid a second Korean War? For the Taiwanese case, why did the United States continue to export defensive arms to Taiwan despite American efforts to normalize diplomatic relations with China and the abrogation of the US-Taiwan mutual defense pact? Other scholars have focused on the South Korean and Taiwanese cases to show different security dynamics that arise among military allies (Benson 2012; Cha 2016). The historical cases presented here do not necessarily seek to provide a definitive ex- planation for the different strategic design choices of US commitments to South Korea and Taiwan but, rather, lend empirical support for the theoretical model and provide an 106 alternative and plausible explanation for why military commitments vary between states. There are several advantages to using comparative case studies. First, we have access to declassified documents that show which issues and factors national leaders in the United States took into consideration when devising American foreign policy towards South Korea and Taiwan. 1 Another advantage of the comparative case study is that we can hold several potentially confounding variables constant to isolate the effects of key parameters from the model. I compare the two cases under a set of commonalities: the same US leaderships (Eisen- hower and Nixon administrations), the same region (East Asia), and the same time period (Cold War). Scholars also argue that South Korea and Taiwan had authoritarian leaders with similar revisionist ambitions (Benson 2012; Cha 2016) and the level of threat and adversaries involved remain relatively constant across the two cases (China, North Korea, and the Soviet Union). We can even keep relative capabilities between the US, its allies, and its adversaries constant since the United States made great efforts to maintain a stable balance of power. To evaluate the theory, I examine how changes in the costs of commitments and the different military effects of commitments influenced the US design and implementation of peacetime military cooperation with South Korea and Taiwan. Utilizing temporal varia- tion, I look at US military commitments to South Korea and Taiwan following the Korean War and under the Nixon Doctrine. The comparison between these two time frames is important because we observe renewed US commitments immediately following the Ko- rean War and efforts to contain communism, in addition to a shift in US national interests under “Vietnamization" that led to a large scale down in the US military presence in Asia. Thus the two cases keep confounders constant while varying on important parameters of the model, such as the cost of implementing military commitments and the third-party defender’s willingness to go to war. For each case, I provide a brief description of the his- 1 The main source used for these archived documents are the Foreign Relations of the United States, pub- lished by the US Department of State. See https://history.state.gov/historicaldocuments 107 torical context, examine the US’ preferences for intervention in war and the US’ ability to shift the balance of power in its favor, and explain why the US chose one type of military commitment over another for each country. Historical Overview Post-WWII US Foreign Policy: Truman Doctrine and Containment Following World War II, the United States emerged as a new global power – economically, politically, and militarily – carried by the benefits of wartime production and military vic- tory. The US reoriented its foreign policy approach of isolationism and retrenchment in favor of using its growing political influence, military strength, and economic wealth to assist states of key strategic interest, namely in Western Europe and Asia. The reorienta- tion of US foreign policy started with President Truman’s speech to Congress on March 12, 1947 and the subsequent Truman Doctrine. Due to financial constraints/bankruptcy, the British government could no longer sup- port the Greek government against internal communist threat (Greek Civil War). The US government believed instability in Greek and Soviet support of communist efforts in Greece would spillover to Turkey. Thus the Truman Doctrine was established as a “pol- icy of the United States to support free peoples who are resisting attempted subjugation by armed minorities or by outside pressures." The Truman Doctrine called for massive US aid to Greece and Turkey ($400 million) and the dispatch of civilian and military person- nel and equipment to the region. The Truman Doctrine “committed the United States to actively offering assistance to preserve the political integrity of democratic nations when such an offer was deemed to be in the best interest of the United States." 2 The growing Soviet threat led to increasing US efforts to stop the spread of communism and Soviet influence by increasing US aid/willingness to intervene abroad and large investments in 2 https://history.state.gov/milestones/1945-1952/truman-doctrine 108 military capabilities, such as the Marshall Plan (1948), the creation of NATO (1949), and NSC-68 (1950). The Mutual Defense Assistance Program (October 1949) committed $1.4 billion to building Western European defenses as European states requested aid from the US. The Korean War and Revitalized Commitments The communist threat was not contained to Europe but extended to Asia as well. Right before the outbreak of the Korean War, the US government did not consider South Korea or Taiwan of great strategic interest. From the late 1940s, the Truman administration began to distance itself from Chiang Kaishek and the Nationalists, or Kuomintang (KMT), in China as it realized they were facing a losing civil war against the Chinese Communist Party (CCP) and refused to make US commitments to support it in war (Benson 2012, 152-55). The US began withdrawing troops from the Korean Peninsula in 1948, and the last US armed military unit left South Korea on June 29, 1949, leaving only a 500-man advisory group (Cha 2016, 55). As late as January 1950, the US did not even include the two Asian countries as being under US protection. The lack of US commitment to South Korea and Taiwan is best rep- resented by Secretary of State Dean Acheson’s speech to the National Press Club, where he stated that “[s]o far as the military security of other areas in the Pacific [beyond the Ryukus and Philippine Islands] is concerned, it must be clear that no person can guarantee these areas against military attack. But it must also be clear that such a guarantee is hardly sen- sible or necessary within the realm of practical relationship." 3 The Truman administration made it clear that US military support to South Korea and Taiwan was not guaranteed. The Korean War completely reversed US commitments to East Asia and served as an impetus to solidify or form treaty alliances and defend aligned states against the spread of communism. US leaders realized the serious threat imposed by Soviet and (post-1949) 3 https://web.viu.ca/davies/H102/Acheson.speech1950.htm. Accessed April 14, 2019. 109 Chinese influence under communism and took great efforts to secure its allies in the region. The Nixon Doctrine: “Vietnamization" and Scaling Back On July 25, 1969, at a press conference in Guam, President Nixon introduced the Guam Doctrine, which laid down the central principles that would guide American foreign policy towards Asia under the more formalized Nixon Doctrine and a policy of “Vietnamization." Amidst reaching an impasse in the Vietnam War, increasing anti-war sentiments in the US, and rising costs for maintaining a large American military presence in Asia, the Nixon administration introduced a set of principles to define the US’ role in the security of its Asian allies. The three main guiding principles were: 1) that the US would “keep all of its treaty commitments," 2) “provide a shield if a nuclear power threatens the freedom of a nation allied with us or of a nation whose survival we consider vital to our security," and 3) “shall furnish military and economic assistance when requested in accordance with our treaty commitments. But we shall look to the nation directly threatened to assume the primary responsibility of providing the manpower for its defense." 4 The Nixon Doctrine, while still emphasizing the importance of treaty commitments and alliances, represented a departure from the American policy of maximum control and involvement in Asia under the Truman administration after the Korean War. “Vietnamiza- tion" focused on improving the independent capabilities of South Vietnam to defend itself, but this policy extended to other US allies in the region including South Korea and Taiwan. Although the large scaledown of US military presence in Asia was not intended to abandon allies or encourage adversaries to initiate conflicts, it was a move towards improving the unilateral capabilities of Asian target states and reducing military commitments that could entangle the US in future costly wars. These third-party commitments were mostly in the form of withdrawing US troops deployed abroad in large numbers. As a result, the Nixon 4 Richard Nixon, “Address to the Nation on the War in Vietnam," November 3, 1969. See https: //millercenter.org/the-presidency/presidential-speeches/november-3-1969-address-nation-war-vietnam 110 administration initiated a large reduction in US forces abroad in 1971. South Korea: joint capabilities after the Korean War In terms of the model, the defender (here, the United States) only makes material com- mitments when they are cost-effective: when the marginal effect on improving the likeli- hood of winning war outweighs the cost of making the material commitment. The cost- effectiveness of material commitments is conditioned by the local balance of power among actors in dispute. From hypothesis 3, material commitments that improve joint capabil- ities become less cost-effective when the defender is already significantly stronger than the challenger. Yet, when a defender and challenger are evenly matched (and the tar- get is weak), the defender prefers to invest in joint capabilities rather than just offer its support in war. In the Korean context, the United States was relatively evenly matched against the communist forces: China and a Soviet-backed North Korea (figure 4.1). South Korea was also relatively evenly matched against its Northern counterpart so US mate- rial commitments had a large marginal effect on shifting the balance of power in favor of the United States and South Korea (figure 4.2). Because US intervention in war was likely and the United States faced a strong opponent, it recognized that improving joint capabilities would give US-South Korean forces a military advantage over the relatively evenly matched Chinese-North Korean forces. From the model, a big disparity in power would make third-party commitments less attractive because either the chances of win- ning would not be high enough or the chance of winning would be so high as to make the commitments not cost-effective. According to the model, the United States only invests in improving joint capabilities if it is willing to fight to defend South Korea in war (proposition 3). The Korean War reversed the US leaders’ assessments of South Korea’s strategic importance and their willingness to defend the South in conflict. South Korea became an essential bulwark against commu- 111 nism, and this argument was propelled by the Truman administration’s strong belief in the domino theory and domestic pressures to contain and eliminate communist threats. The North Korean-led attack on the South, coupled with a successful Soviet nuclear test in 1949, further cemented US preferences to defend South Korea and support the anti- communist Rhee Syngman regime. Despite grave concerns of entrapment (Cha 2016), the cost of abandoning South Korea was extremely high for the United States and, as a result, the United States was largely committed to supporting it in war. 5 Since US intervention in conflict was likely – given South Korea’s strategic importance for US national security interests in East Asia – US leaders were willing to make material commitments to improve US-South Korean joint capabilities. As a result, we observe US military commitments to South Korea that were aimed at increasing joint capabilities or military cooperation be- tween the two states. The US-led United Nations Command (UNC) held peacetime and wartime operational control over the UN and South Korean forces, essentially integrating the two countries’ militaries. In 1955, the United States initiated combined military ex- ercises with the US 5th Air Force and South Korean 5th Army Corps (Exercise Chugi). In 1958, the US deployed nuclear weapons to South Korean territory. Debates among US leaders over signing a US-South Korea mutual defense treaty were less about the North Korean threat and more about appeasing Rhee to not reignite hostil- ities and ruin the chances of negotiating an armistice agreement. In a declassified memo from the acting Secretary of State, Smith, writes: “The politically most effective concession that we could make to Rhee would be to inform him of our willingness to negotiate a bi- lateral security pact. Such a security pact has very real political and military disadvantages which would have to be weighed against the need for securing Rhee’s cooperation with an armistice." 6 In line with the model, the defender’s consideration over alliances is not as 5 In fact, it is precisely because US fears of entrapment were so high that implies that US involvement in war was likely. US leaders wanted to avoid being dragged into another costly conflict, but knew abandoning South Korea was even more undesirable. 6 “Memorandum by the Acting Secretary of State to the President," Foreign Relations of the United States, 1952-1954, Korea, Volume XV, Part 1, https://history.state.gov/historicaldocuments/frus1952-54v15p1/ d529. Accessed November 2018. 112 important as traditionally argued. When a third-party defender is willing to support the target state in war, it is indifferent between forming an alliance or not. Thus alliances have more to do with political considerations and less to do with actual military effects that can shift the local balance of power in ways that only material commitments distinctively can. The model presented in this paper provides an alternative explanation for why US mil- itary commitments to South Korea were unambiguous and extremely costly. In line with Cha (2016)’s powerplay theory, the United States was concerned with preventing a war and expected to be involved given South Korea’s strategic importance in the region. As a result, following from the model, the US was willing to fight for South Korea and thus invested in military capabilities that increased the US and South Korea’s joint probability of winning in war (or joint war-fighting capabilities). Unlike Benson (2012)’s model that relies on strategic ambiguity and the unobservable nature of certain actions (i.e. if a target violates a mutual defense pact by taking the first shot) and Cha (2016)’s theory of tight control over rogue allies, my theoretical model shows why the United States decided to adopt a certain, specific portfolio of military commitments and why such commitments changed over time as South Korea became more strategically important and the local bal- ance of power shifted in ways that further incentivized the US to intervene. Because the United States preferred to militarily support the South in war and it faced a relatively equal opponent (Chinese forces and Soviet-backed North Korea), the US adopted peacetime mil- itary measures that improved joint capabilities. Moving towards modernization How did US commitments to South Korea change under the Nixon Doctrine? I argue that the rising cost of US commitments and a decreasing willingness to intervene in a second Korean War led the Nixon administration to reduce commitments aimed at improving joint capabilities (i.e. troop deployments) and, instead, prefer the modernization of South Korea’s own forces or its unilateral capabilities. US forces in Korea made up a significant 113 portion of US troops deployed abroad (over 60,000), and the Nixon administration aimed to withdraw around 20,000 troops. The Nixon Doctrine called for Asian allies to take up the burden of their own defenses, as the US would reduce its physical military presence in Asia while also keeping its treaty commitments to allies. In terms of the model, the US was less willing to support South Korea in war due to the rising costs of war and its involvement in Vietnam. Kimball (2006, 68-9) notes that Nixon “knew he needed to reassure allies and clients, including Thieu, of his administration’s resolve... [but] he also needed to reassure the majority of Americans, as well as other allies... that not only was he withdrawing from Vietnam but also... that US troops should not again become bogged down so massively in an Asian quagmire, especially one that was not to its vital interests." The cost of implementing US commitments that improved US-South Korean joint capa- bilities – in the form of massive troop deployments – was also increasing over time without large shifts in relative capabilities, making them less cost-effective (hypothesis 3). In an NSC meeting, President Nixon reiterated the key factors of a reduction in US forces abroad: We must avoid the impression that we are withdrawing from our responsibili- ties by emphasizing that our drawdown has to be accompanied by ROK mod- ernization... In essence, what we are looking for is not a way to get out of Korea but a way to be able to stay in by means of a long-range, viable posture. We are faced with increasing emphasis on domestic spending here at home. Thus, we have to find a way to continue playing a role by drawing down our strength somewhat or else the Congress will refuse to support anything. 7 As the model explains, the US began to move towards a commitment strategy that aimed to improve the unilateral capabilities of its Asian allies, including South Korea. In negotiations with President Park Chunghee, the Nixon administration discussed the tim- ing, scale, and coordination of US troop withdrawals with clear reference to modernizing South Korean forces. In NSC assessments, the US claimed that “an ROK force of 12–14 unimproved divisions could probably hold an all-out North Korean attack. With a larger 7 Draft Minutes of a National Security Council Meeting, Foreign Relations of the United States 1969–1976, Vol. XIX, Part 1, KOREA, 1969–1972, March 4, 1970. See https://history.state.gov/historicaldocuments/ frus1969-76v19p1/d55. Accessed March 25, 2020. 114 and improved ROK force now envisaged, the ROKs could defeat the North Koreans and at least attempt a march North... [and] an ROK force of 16–18 improved divisions could hold a combined NK/CPR attack for at least 30 days north of Seoul." 8 President Park was strongly opposed to the withdrawal of troops planned for the end of June 1971 and viewed the reduction as an invitation for North Korea to attack. Yet Park was also accepting of US withdrawals as long as they were done after South Korean forces could modernize simul- taneously. 9 Because South Korea and North Korea were relatively evenly matched, despite significant advances in South Korea’s military technology and a growing economy, US in- vestments in unilateral capabilities were worth it as it improved South Korea’s ability to withstand attacks and obtain better dispute outcomes. With a rising cost of war for the US and decreasing cost-effectiveness of commitments that increase joint capabilities, the Nixon administration chose to pursue South Korean modernization as it withdrew a por- tion of its forces. Taiwan: unilateral capabilities and Sino-US relations US military commitments to Taiwan were consistent with those made to South Korea until the momentous normalization of Sino-US relations in 1979. Following the Korean War, containing the spread of communism in Asia became of utmost priority for US leaders and Taiwan was recognized as an important anti-communist ally in the region. In December 8 Italics in original. “Memorandum From Laurence E. Lynn, Jr., of the National Security Council Staff to the President’s Assistant for National Security Affairs (Kissinger)," Foreign Relations of the United States 1969–1976, Vol. XIX, Part 1, KOREA, 1969–1972, February 26, 1970. See https://history.state.gov/ historicaldocuments/frus1969-76v19p1/d53. Accessed March 25, 2020. 9 “The United States forces in Korea serve as a most effective deterrent against the potential aggressors and also as an indispensable element of the defense posture in the case of an armed attack from the north. Any reduction should, therefore, be accompanied by positive measures of strengthening the Republic of Korea forces to offset the effect of such reduction lest it should result in weakening the deterrent or defense capa- bility. It is to be added that major part, if not all, of such measures should be implemented in advance...the mainstay of the United Nations forces, which constitute an indispensable factor for the maintenance of peace in the Korean Peninsula, consists of the United States forces in Korea." See “Telegram From the Em- bassy in Korea to the Department of State," Foreign Relations of the United States 1969–1976, Vol. XIX, Part 1, KOREA, 1969–1972, June 15, 1970, https://history.state.gov/historicaldocuments/frus1969-76v19p1/d61. Accessed March 25, 2020. 115 1954, the United States signed a defense treaty with Taiwan, which “formalized a defense commitment to Taiwan that eliminated ambiguity about American resolve in China’s eyes. It provided a legal basis for US military use of the island in future military contingencies. The treaty also gave legitimacy to the Chiang regime in Taipei, which enhanced domestic stability" (Cha 2016, 83). Yet, unlike the US-South Korean alliance, US troop deployments to Taiwan were limited (see figure 4.4). The diplomatic normalization of Sino-US rela- tions and US recognition of the “one China" policy completely reversed US commitments to defend Taiwan in war. By revoking political recognition of the Taiwanese government in favor of the mainland, US preferences for war changed drastically. The United States was no longer willing to unconditionally support Taiwan if war between China and Taiwan was to break out. In 1979, the US abrogated its treaty alliance with Taiwan and US mili- tary commitments were then guided by the Taiwan Relations Act (TRA) under the Carter administration and reconfirmed by the “Six Assurances" under the Reagan administration. Why did the United States continue to export arms to Taiwan amidst great efforts to improve political relations wtih China? During negotiations between the US and China over normalization, the issue of arms sales to Taiwan remained a central and thorny topic that essentially hindered efforts to establish stable relations and sign a joint communique between the two countries. In a memorandum to President Carter in 1979, Secretary of State Cyrus Vance notes “Arms sales was the most sensitive issue involved in our normal- ization discussions with Beijing. The Chinese took issue with our announcement that we would continue sales of “selected defense weapons" to Taiwan but agreed nonetheless to proceed with normalization." 10 Yet, even though the US had abrogated its mutual defense treaty with Taiwan in favor of normalizing relations with China, the US also continued to sell defensive arms to Taiwan. Hypothesis 2 is supported by US commitments to Taiwan post-1979. Instead of completely abandoning Taiwan (i.e. get rid of all military commit- ments), the United States chose to invest in improving Taiwan’s ability to defend itself in 10 https://history.state.gov/historicaldocuments/frus1977-80v13/d285. Accessed January 17, 2020. 116 war. Although the United States was not willing to defend Taiwan in war against China, the United States did not cease its military support to Taiwan. In fact, the United States increased material commitments to Taiwan in the form of large-scale military assistance packages and significant arms sales/deliveries. My model explains why America invested in making costly commitments to Taiwan even though such commitments hurt its negoti- ations with China and the US had no preference for fighting in a war on Taiwan’s behalf. While US military support to Taiwan was primarily defensive in nature, such material com- mitments still improved Taiwan’s bargaining leverage with China by increasing its ability to defend itself against attack. Material commitments that improve the target’s unilateral capabilities can shift the local balance of power among actors even if the defender would not directly involve itself in conflict. If a defender is able to increase the target’s unilateral war-fighting capability when it would abandon it, it would always choose to do so if it is cost-effective. This is because, if the defender and target share interests over the division of the disputed good, then improving the chances of reaching better settlement offers in bargaining is always preferrable. In the context of US-Taiwan relations, the United States was not willing to support Taiwan in war at the expense of hindering diplomatic relations with Beijing. Yet the United States also still preferred an independent Taiwanese state and invested in Taiwanese defense to maintain such a status quo. Material commitments that improved Taiwan’s unilateral military capabilities were cost-effective because the United States was relatively evenly matched while Taiwan was weak relative to China (figure 4.3). In other words, the United States could make a larger impact on shifting the balance of power short of direct intervention in war, thereby offsetting the costs of making material commitments. In addition, the United States did not make any material commitments that increased joint US-Taiwanese capabilities as it did for South Korea. Figure 4.4 shows US troop de- ployments to Taiwan and South Korea from 1950 to 2014. By 1979, the United States completely withdrew its forces from Taiwan. In line with the model, when the United 117 States was no longer willing to support Taiwan in war, it did not invest in joint capabili- ties (proposition 3). Table 4.1 compares the South Korean and Taiwanese cases and how changes in the model’s parameters explain differences in the types of military commitments employed by the United States to the two countries. Table 4.1: South Korea and Taiwan Comparison South Korea Taiwan Defender cost of abandonment High Low Defender strength Even Even Target strength Even Weak Treaty commitment Yes No (post-1979) Material commitment Joint cost-effective T unilateral cost-effective Commitment strategies Permanent bases, Defensive weapons, joint military exercises, military aid integrated military command, nuclear weapons Alternative explanations In this section, I address some alternative explanations for variation in the design and implementation of US military commitments to South Korea and Taiwan. Balance of threat One major explanation for the formation of alliances is that states will band together to balance against a common threat (Walt 1987). While balance of threat theory may help explain why the United States formed alliances with East Asian states to address the threat of communism, the theory falls short in explaining variation in US military commitments to South Korea and Taiwan, especially over time. In the case of South Korea, the North Korean threat has remained relatively constant over time (albeit fluctuations in perceived severity), but we observe many changes in US-South Korean military cooperation. Figure 4.5 shows that arms transfers to South Korea vary significantly over time that cannot be 118 explained by changes in the level of the North Korean threat alone. 11 Additionally, balance of threat theory does not fully explain why the United States continued to invest in costly material commitments to Taiwan even after the era of detente and the normalization of Sino-US relations. Even though the perceived threat from China was heavily reduced following normalization, the United States continued to sell arms and pour military aid into Taiwan’s defense. The model presented in this paper provides an explanation for this observed variation by arguing that US investments in joint versus unilateral capabilities are driven by US preferences for war and conditioned by structural factors, such as the balance of power and implementation costs. The perception of a common threat is not enough to explain why third-party actors choose to invest in some states’ defenses but not others. Powerplay and institutional design in East Asia Cha (2016) develops the “powerplay" theory to explain the different institutional design decisions that guided US military commitments to Western Europe and East Asia after WWII: a multilateral, collective security structure in the former and a bilateral, hierarchi- cal hub and spokes system in the latter. He argues that US alliances in East Asia were driven by American concerns of restraining staunch anti-communist leaders, namely Rhee Syngman and Chiang Kaishek, from instigating unwanted conflicts and using highly con- trolled, bilateral alliances to do so. The powerplay theory does not explain the variation in US military commitments within East Asia and over time. Despite the common goal of restraining potentially rogue leaders in South Korea and Taiwan, why did US military cooperation with the two countries differ so significantly? Even when US leaders were most concerned with restraining South Korea and Taiwan after the Korean War, we observe significant differences in the levels and types of US commitments to each country. Perhaps the most striking comparison is US troop 11 For example, we do not see corresponding spikes in arms transfers to South Korea following missile and nuclear developments/crises in North Korea, such as in 1992-94 and 2002. 119 deployments to South Korea and Taiwan (figure 4.4). After Sino-US normalization in the late 1970s, US military commitments to South Korea and Taiwan began to diverge even further. Why did the United States continue to station troops and even establish an integrated military command in South Korea while it abrogated its mutual defense treaty with Taiwan in favor of exporting arms? 12 If the bilateral alliances in East Asia are instruments of US control over smaller allies, it is unclear why the United States expanded its bilateral military cooperation with South Korea despite less incentive to restrain its leaders and why the United States terminated its control mechanism over Taiwan altogether. Following the establishment of diplomatic relations between the United States and China, the risk of entrapment from Taiwan should have been significant because the United States had a lot to lose from war with China (i.e. high cost of war). According to a strategy of powerplay, the United States should have exerted greater control over Taiwanese leaders to restrain them from any potentially risky behavior. The United States chose to abrogate its bilateral alliance and transfer arms instead. The theory developed in this paper better explains these variations: the United States invested in improving US-South Korean joint capabilities given the high cost of abandoning the South, whereas the US preferred to increase Taiwan’s unilateral military capabilities given the high cost of war, especially following the normalization of Sino-US relations. Historical artifact Another common explanation for why we observe deep US commitments to certain East Asian states is that they are simply artifacts of US involvement in wars, namely WWII and the Korean War. While high numbers of troops stationed in South Korea are indeed related to the deployment of US forces during the Korean War, this explanation does not account for the strategic decisions by US leaders to establish permanent military bases and an in- 12 The US-South Korea Combined Forces Command (CFC) was officially established in 1978. 120 tegrated military command in South Korea while actively withdrawing forces from Taiwan and, instead, providing defensive arms. The United States entered into formal alliances with both countries (South Korea in 1953 and Taiwan in 1955) with similar obligations and provisions. Yet figure 4.4 shows the stark difference in the sheer number of troops deployed to each country and the near absence of US troops deployed to Taiwan follow- ing the abrogation of the US-Taiwan defense pact (post-1979). If a third-party defender’s decision to provide material commitments or not is path dependent, then we should not expect to see such variation over time. Again, my theory provides a better explanation for why changes in the strategic environment led the United States to choose one form of military cooperation (or commitment strategy) over another. As the military threat from China weakened and the United States became militarily stronger, the cost-effectiveness of investing in US-Taiwan joint capabilities decreased. As a result, the US leaders preferred to improve Taiwan’s unilateral capabilities, at an acceptable cost, without directly involving itself in potential military conflict. Limitations and Potential Model Extensions A potential limitation of the model is in explaining why the United States continued to invest in joint capabilities while also making efforts to improve South Korea’s unilateral capabilities. Because the theoretical model is analyzed under complete information, equi- librium behavior does not support the third-party defender making both types of commit- ments due to the cost. If the defender can properly prepare for the potential conflict it is willing (or not) to intervene in, then it is unnecessary to impose the costs of making mil- itary commitments that both improve joint and target independent capabilities. As men- tioned in previous sections, the introduction of asymmetric information about the third party’s cost of war or its willingness to intervene may explain why a country like the US wants to maintain ambiguity over its preferences for war. In addition, a model extension 121 that allows for differing ideal points between the defender and target may also account for strategic design choices of peacetime commitments that both deter adversaries and re- strain targets. At the very least, the variation and evolution of US military commitments to South Korea under Truman and Nixon show that there is value to understanding how dif- ferent commitment strategies are designed and implemented. Foreign policy decisions are not just binary, such as form an alliance or not, but involve real effects on states’ military capabilities and the local balance of power. The interplay between treaty and material commitments is also an area that requires more examination. In the model, if the third-party defender is willing to support the target in war, then it is indifferent between making a treaty commitment or not. I assume that, in equilibrium, the third-party defender makes a treaty commitment when it would intervene in war for the target state because it makes its threat of intervention that much more cred- ible. The current theoretical model considers a discrete set of treaty commitments, those that carry high or low costs when violated, but it is clear which types of legal obligations fall into each category. Additionally, I find that the third-party actor does not make a treaty commitment when it would not intervene to defend the target in conflict. How, then, do we explain the Nixon administration’s attempts to reassure Park (and other Asian allies) through US treaty commitments while also pursuing material commitments that are in- tended to avoid entrapment (i.e. those that improve target unilateral capabilities)? While the empirical reality does not fully accord with equilibrium behavior, there is evidence that national leaders are thinking of treaty and material commitments as distinct and separate, albeit related, forms of military cooperation. A paper prepared for Nixon and Kissinger by NSC staff highlights this: “Commitment" is a slippery concept. Our actions on specific cases will be guided not by legal phrases but by an assessment of the significance of our interests involved and the nature of the threat. We have said we will “honor” our formal treaty obligations and these are imprecise in the areas where the def- 122 inition of our interests is especially imprecise... Our new Asian approach does not—cannot—instruct us in advance on how we would meet our treaty obli- gations and assist an overwhelmed ally when we have substantially less power than we do now. We would have to explore our options of military assistance, air and naval support, mobilization, tactical and strategic nuclear response. 13 Chapter Summary The cross-country comparison between US military commitments to South Korea and Tai- wan provides preliminary support for the model’s setup and results. The cases lend justifi- cation for a defender’s choice of commitment based on its decision to support or abandon the target in conflict. In addition, the cases highlight the findings that the cost-effectiveness and military effect of commitments conditions which third-party commitments are em- ployed in peacetime. The design and implementation of military cooperation is a strategic decision-making process that involves the consideration of structural constraints, such as the costs of making commitments and the local balance of power, and expectations about how countries will behave in international disputes (i.e. strategic interaction). Following the Korean War, the United States recognized the threat that the spread of communism posed for East Asia and was dedicated to defending target states of impor- tance in war. The Truman administration entered into formal alliances with South Korea and Taiwan to signal to potential adversaries that the US was committed to defend these states if attacked. In South Korea, the US invested heavily in military commitments that improved US-South Korean joint capabilities, such as the maintenance of US forces on the Korean Peninsula, joint military exercises, and close coordination and consultation between the two countries. Similarly in Taiwan, the US deployed its Seventh Fleet as a 13 “The Nixon Doctrine for Asia: Hard Issues," Foreign Relations of the United States, 1969–1976, Vol. I, Foundations of Foreign Policy, 1969–1972, undated, https://history.state.gov/historicaldocuments/ frus1969-76v01/d54 123 costly commitment to defend Taiwan against Chinese aggression. Because the US was relatively evenly matched with its opponents (China and Soviet-backed North Korea), the investments in joint capabilities were cost-effective given that any military advantage was useful. In contrast, starting in the early 1970s, the US adoped a policy of “Vietnamization" or the Nixon Doctrine, which called on America’s allies in Asia to be more independent in their defenses and modernize their domestic forces. The cost of joint capabilities began to rise while the local balance of power remained relatively constant. In fact, the US was arguably stretched thin with its military resources given that it was fighting a long and difficult war in Vietnam. As a result, the Nixon administration chose to invest in South Korea and Taiwan’s unilateral military capabilities instead as it also became increasingly unwilling to support them in wars that were unlikely. This shift in US commitment strategy aligns with the theoretical model in that the United States continued to make costly upfront military commitments to South Korea and Taiwan despite its unwillingness to defend them in war. Although the Nixon government emphasize the unwavering strength of US treaty commitments, there were clear distinctions made between commitments made in alliance treaties and those that involved more physical military measures, such as military aid, troop mobilization, and nuclear umbrellas. In international security scholarship, one of the central aims is to understand whether alliances or military commitments are instruments of peace or conflict (Leeds 2003b; Ken- wick, Vasquez and Powers 2015; Kenwick and Vasquez 2016; Leeds and Johnson 2016; Morrow 2016). To tackle this question, we need to first understand how military commit- ments are designed and under what conditions they are implemented, and to what effect. The historical case studies shed light on the causal mechanisms outlined in the theoretical model and lend support to the argument that scholars need to look beyond formal al- liances as defining third-party military commitments. Peacetime military cooperation that prevents wars is evolving over time and across states, and recognizing these global trends 124 is important for international security. 125 Appendix Figures 4.1 and 4.2 represent the relative military capabilities of the United States, China, and the Soviet Union (during the Cold War), and the two Koreas. Essentially, it is a rough measure of the local balance of power, a key parameter in the theoretical model from Chapter 3. The figures are made based on a new measure of power, developed by Carroll and Kenkel (2019). The authors introduce a standard operationalization of power, as it is typically understood in the bargaining context as “the probability that one state will defeat another in case of militarized conflict, commonly denoted p" (Carroll and Kenkel 2019, 577). Using existing measures taken from the commonly used Correlates of War Composite Index of National Capabilities (CINC) and employing machine learning techniques, Carroll and Kenkel (2019) find that their estimates of power, or Dispute Outcome Expectation (DOE) scores, are a magnitude better than CINC scores in predicting dispite outcomes. The DOE scores are interpreted as probabilities of either side in a dyad winning the war or the dispute resulting in a stalemate. The authors calculate this for every dyad in the international system, presenting both a directed and non-directed version of the dataset in which the former (directed) predicts a higher probability of victory for the initiator whereas the latter (non-directed) takes the average and has the same observations but flipped. 14 14 See the codebook for more details, available at https://dataverse.harvard.edu/dataset.xhtml? persistentId=doi:10.7910/DVN/06A5XJ 126 Figure 4.1: Dispute Outcome Expectations among Great Powers (US, China, Russia) 0.25 0.50 0.75 1860 1875 1890 1905 1920 1935 1950 1965 1980 1995 2010 Dispute Outcome Expectation (DOE) Dispute Outcome China Wins United States Wins Stalemate 0.25 0.50 0.75 1816 1831 1846 1861 1876 1891 1906 1921 1936 1951 1966 1981 1996 2011 Y ear Dispute Outcome Expectation (DOE) Dispute Outcome Russia Wins United States Wins Stalemate Source: DOE scores (Carroll and Kenkel 2019). 127 Figure 4.2: Dispute Outcome Expectations for North and South Korea 0.00 0.25 0.50 0.75 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008 Y ear Dispute Outcome Expectation (DOE) Dispute Outcome North Korea Wins South Korea Wins Stalemate Source: DOE scores (Carroll and Kenkel 2019). 128 Figure 4.3: Dispute Outcome Expectations for China and Taiwan 0.00 0.25 0.50 0.75 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008 Y ear Dispute Outcome Expectation (DOE) Dispute Outcome China Wins Taiwan Wins Stalemate Source: DOE scores (Carroll and Kenkel 2019). 129 Figure 4.4: US Troop Deployments to South Korea and Taiwan (1950-2014) 0 50 100 150 200 250 300 1950 1960 1970 1980 1990 2000 2010 Y ear Troops (in thousands) South Korea Taiwan Source: Kane (2016) and DMDC 130 Figure 4.5: US Arms Transfers to South Korea and Taiwan (1950-2014) 0 500 1000 1500 2000 2500 3000 1950 1960 1970 1980 1990 2000 2010 Y ear Arms Transfers (TIV) South Korea Taiwan Source: SIPRI 131 Figure 4.6: US Military Aid to South Korea and Taiwan (1950-2014) 0 500 1000 1500 2000 2500 3000 3500 1950 1960 1970 1980 1990 2000 2010 Y ear Military Aid (USD mil) South Korea Taiwan Source: USAID Greenbook 132 Chapter 5 Conclusion Importance of Variation in Military Commitments This project represents a systematic approach to examine why and how variation in third- party military commitments is important for understanding the effect that various com- mitment strategies have on state behavior in international crises. Extended deterrence is not limited to alliances. The unique effects of different material commitments on crisis- bargaining behavior and outcomes are not accounted for when scholars only examine treaty commitments, or alliances, alone. The theory of commitment design and implemen- tation presented in this project outlines the conditions under which a third-party defender will select one type of commitment strategy over another, based on the cost of implementa- tion, the particular military effect each type of commitment has on actors’ capabilities, and the local balance of power. In turn, the third-party actor’s commitment strategy in peace- time directly influences deterrence, or the ability to prevent militarized conflict. Several key findings are derived from the theoretical model, which have significant implications for the study of alliances and third-party involvement in international disputes. Peacetime Costs and Resource Constraints First, there are structural constraints on a third-party defender’s ability to invest in mil- itary cooperation or commitments aimed at improving a target state’s (one with aligned 133 interests) security. In most models of alliances, there is almost no ex ante cost to forming an alliance. Instead, the costs arise from backing down or reneging on one’s commitments when alliances are tested in war. In reality, national leaders are faced with limits on re- source allocation and opportunity costs. In other words, a third-party defender’s military commitment to one country comes at another country’s expense. While this is not explic- itly modeled, my theory accounts for the peacetime costs that are imposed when military measures are implemented by third parties. The cost of making a material commitment conditions which commitment strategy can be made in equilibrium. When a defender’s military commitment can improve states’ capabilities – joint or uni- lateral – more than the cost of implementation, then it is cost-effective to do so. Yet, counterintuitively, as the likelihood of winning war increases for the allies (defender and target) or for the target alone, investing in additional capabilities becomes increasingly expensive with diminishing returns (hypotheses 2 and 3). The consideration of military commitments carrying costs is important because it directly conditions which commitment strategies are feasible for third-party defenders. As shown in Chapter 3, most alliance models only account for the case in which all material commitments are not cost-effective and, thus, are not made in equilibrium. 1 Resource constraints on military commitments explain why we observe variation in military cooperation: a third-party actor to a dispute invests in another state’s security up to the level it is credibly able to, and these costs differ for different third-party actors. Military Effect of Commitments Another key finding addresses the puzzle of why a third-party defender would make an upfront, costly commitment to a target state even if it were unwilling to support it in war. Costly signals, such as third-party military support, are used to distinguish credible threats 1 By not incorporating peacetime costs for implementation in their models, current studies essentially treat the cost as being zero. 134 made by resolved states from those that would otherwise try to bluff and misrepresent their commitment. I argue that material commitments are not just costly signals that tie an actor’s hands, but also directly impact the local balance of power in peacetime. Unlike alliances, which only shift the balance of power when an ally actually carries out its threat to intervene in conflict, material commitments influence the local balance of power before conflict ever occurs. In fact, a third-party defender strategically designs its military commitments to extract better bargains in disputes while also deterring war. The defender’s commitment directly shifts the local balance of power in its favor by improving either joint military capabilities or a target state’s unilateral capabilities; in turn, making the chances of war victory more likely (propositions 1 and 2). War can occur in equilibrium under complete information, but only when a challenger strictly prefers war over settlement (proposition 3). In this case, the defender’s decision to intervene or not does not influence bargaining behavior, but its peacetime commitments still affect the local balance of power and outcome of war by shifting the likelihood of victory in its favor. 2 Third-party military commitments have a unique effect on states’ military capabilities, and the military effect varies by commitment type. A defender would only prefer to make a military commitment to a target that improves joint capabilities if it would also support the target in war. When actors know which kind of war they would be fighting, they make peacetime preparations specific to that conflict. Put simply, if the third party expects to get involved, it would want to increase its chances of winning as much as possible, conditioned by how much it can invest ex ante. Thus the variation in third-party commitments is explained by, not only design choices for alliances to condition third-party involvement in wars, but also by the actual and unique military effects that peacetime military cooperation have on crisis-bargaining behavior. 2 This assumes that third-party military commitments are cost-effective to make in the first place. 135 Reducing Entrapment Risks Finally, variation in the design and implementation of military commitments outlines the conditions under which entrapment is a real security concern for national leaders. Stud- ies in extended deterrence have shown, empirically, that revisionist target states (or those receiving security from a third party) are emboldened by stronger, more credible commit- ments from an outside actor (Benson 2012; Fang, Johnson and Leeds 2014; Cha 2016). 3 The conventional wisdom that entrapment is a major risk for third-party actors is so preva- lent that it undergirds studies that examine the deterrence-restraint dilemma and even policy efforts to restrict committing to an ally’s defense. Yet the actual conditions that contribute to entrapment are underdeveloped and empirical evidence has shown that en- trapment is not as common as assumed (Snyder 1997; Kim 2011; Beckley 2015; Lanoszka 2018). When we account for the various military effects different types of military commit- ments have, I find that a third-party defender can make costly commitments that shift the local balance of power in its favor while also avoiding direct intervention in war. In- vestments in the modernization and improvement of a target state’s unilateral capabilities allow aligned states to gain better bargains in settlement than in the absence of such ma- terial commitments. In addition, the explanation provided by my theory is not mutually exclusive, but does not rely on target restraint. A defender may actually want to embolden a target state by improving its unilateral military capabilities to increase deterrence and not face the risks of being entangled in a conflict. Thus a third-party actor to a dispute designs its material commitments in way that aligns with its preferences for war: entrap- ment does not necessarily occur because the defender makes commitments in preparation for the type of war it is already willing to face (whether it intervenes or not). This partially explains why the Nixon administration made great efforts to invest in 3 Here, stronger and more credible commitments refers to third-party commitments that guarantee greater military support and are more likely to be used in conflict (i.e. unconditional commitments). 136 South Korea’s military modernization program amidst a large reduction in US troops de- ployed to the Korean Peninsula. The theory also sheds light on why the United States would continue to invest in Taiwan’s defense, through the sale of arms, despite clear signals that it would not intervene in a war with China. The theoretical model provides insight into why entrapment is relatively rare despite the emboldening effect alliance commit- ments have, and why the US is willing to engage in costly peacetime military cooperation with many states despite not entering into formal alliances. The variation in third-party military commitments allows scholars to better develop the conditions under which en- trapment occurs and how states can design their military commitments in ways to reduce such risks. Alliances and Other Third-Party Commitments The original puzzle this project explores is why military cooperation between states, in the form of third-party military commitments, differs despite the relatively unchanging nature of alliances. Current studies of alliances do not fully develop the conditions under which alliances are complements to or substitutes for other forms of military commitments, such as arms transfers, foreign nuclear deployments, and an integrated military command. In Chapter 2, I show that there is real variation among different US military commitments, which can be measured in a principled way for informative comparison across states and across time. Chapter 3 develops a theoretical model for analyzing the unique military ef- fects of certain classes of military commitments and how they influence crisis-bargaining behavior and outcomes. The model is examined under complete information, which means the signaling effect of alliances – which has received a majority of the focus in extant re- search – is not the only reason for why they matter for international security. Chapter 4 applies the empirical implications generated by the theory to historical cases of US commit- ments to South Korea and Taiwan during the Cold War. The case studies provide prelim- 137 inary support for the theory, but further extensions of the model that include asymmetric information and differing ideal points will make the theory more robust and empirically valid. What does the study of third-party military commitments mean for the future of formal alliances? Are other forms of military cooperation (material commitments) replacing or reinforcing formal alliances (treaty commitments)? The theoretical and empirical impli- cations that arise from this project both challenge but also propel the study of military alliances. The theory presented in this project examines the unique strategic effect that material commitments have states’ decision-making calculi and actions, which are not ac- counted for in current theories of alliances. I find that treaty alliances, while increasing the willingness of a defender to go to war for a target, matter less for strategic behavior in crises when signaling dynamics are taken out. Instead, it is the actual military effect of peacetime commitments that drive important behaviors, such as target emboldenment, third-party intervention in conflict, and the design of commitment strategies. Yet there is more work to be done to examine how treaty and material commitments interact to ex- plain why national leaders often employ both. In future research, the interplay between the level of institutionalization and military effect of different third-party commitments should be explored, especially in terms of opportunity costs and trade-offs. Evolving Commitments: From Transformation to Transac- tion Moving forward, the research agenda for studying variation in third-party military com- mitments is rich and carries significant implications for both alliance theories and foreign policy. A greater amount of attention should be paid to how military cooperation is evolv- ing over time and how it is changing commitments with it, especially in the post-Cold War era. How is the US network of global alliances changing in the face of different security 138 threats and changes in the member states themselves? US alliances originated from Amer- ican incentives to transform and fundamentally shape allies to be in line with US strategic interests but, over time, the US alliance network has moved towards more transaction- based forms of military cooperation that rely on flexible agreements and increased burden sharing between allies. This is evidenced by the rapid growth of DCAs, arguably a less institutionalized substitute for formal alliances, and other security structures that rely on more region-focused issues and broader coalitions of members. US military commitments to its global network of allies are becoming more uniform over time as the United States moves toward more transactional forms of military coop- eration, such as the export of advanced American military technology. While US allies have become extremely wealthy, politically influential, and militarily independent in their own right, they continue to rely on US military commitments and reassurances for their security. How does the United States balance the costs of making military commitments to allies and non-allies abroad while also reducing incentives for states to free-ride on US security provision? Trump’s recent calls for increased burden sharing among allies is an example of this move towards more reciprocal, transaction-based military cooperation. 4 When we develop theories that examine the full range of variation in third-party military commitments, we can begin to account for the strategic design choices of different types of military cooperation between states that drives important security dynamics like deter- rence, foreign intervention, troop and weapons deployments, and the decision to go to war or not. 4 Notably, the American public still supports US engagement and commitments to allies abroad. See https://www.thechicagocouncil.org/publication/lcc/rejecting-retreat. Accessed March 23, 2020. 139 References Barbieri, Katherine and Omar M. G. 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Abstract (if available)

Abstract This dissertation examines the puzzle of why military cooperation between countries is changing over time despite the static nature of treaty alliances or written, legal obligations to militarily support a state in conflict. The project explores three important research areas, using diverse methods, to address enduring questions in the alliance and international security literatures. First, I contend that US military commitments, or promises to provide military support in the event of conflict, are changing significantly over time despite relatively few changes to the actual agreements made under treaty alliances. Second, I develop a novel theory of commitment design and implementation using both game theory and historical case studies to unpack the complex strategic interactions between states involved in international disputes. Finally, I use qualitative methods and in-depth historical case studies to explain why post-WWII US military commitments to South Korea and Taiwan differed so significantly despite common security threats. The project contributes to the study of military cooperation by challenging the idea that external military support is best represented by formal military alliances. My research addresses this gap by conceptualizing US military commitments both in the context of alliances and beyond, and provides theoretical underpinnings for explaining security relationships that evolve substantially over time. The US alliance network is a key component of American grand strategy and the United States is deeply invested in the security of its allies, particularly in Western Europe and East Asia despite recent skepticism and debate over American engagement versus retrenchment. This project provides a better understanding of how the maintenance of alliances is changing and why that is not necessarily a sign of US withdrawal or declining US support for allies abroad.

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Asset Metadata

Creator Kang, Stephanie Nayoung (author)

Core Title The origins and evolution of the U.S. alliance network: how military allies transform and transact

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Political Science and International Relations

Publication Date 08/02/2020

Defense Date 08/01/2020

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag alliances,American foreign policy,East Asian security,International relations,international security,military cooperation,NATO,OAI-PMH Harvest

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Kang, David (committee chair), Camara, Odilon (committee member), Coe, Andrew (committee member), Trager, Robert (committee member)

Creator Email kangsn@usc.edu,stephanienkang@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-357864

Unique identifier UC11666406

Identifier etd-KangStepha-8872.pdf (filename),usctheses-c89-357864 (legacy record id)

Legacy Identifier etd-KangStepha-8872.pdf

Dmrecord 357864

Document Type Dissertation

Rights Kang, Stephanie Nayoung

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA