Foreign influence and domestic policy∗

In an interconnected world, economic and political interests inevitably reach beyond national borders. Since policy choices generate external economic and political costs, foreign state and non-state actors have an interest in influencing policy actions in other sovereign countries to their advantage. Foreign influence is a strategic choice aimed at internalizing these externalities and takes three principal forms: (i) voluntary agreements, (ii) policy interventions based on rewarding or sanctioning the target country to obtain a specific change in policy and (iii) institution interventions aimed at influencing the political institutions in the target country. We propose a unifying theoretical framework to study when foreign influence is chosen and in which form, and use it to organize and evaluate the new political economics literature on foreign influence along with work in cognate disciplines.


Introduction
In an interconnected world, where one nation's fortunes or misfortunes influence those of others, economic and political interests inevitably reach beyond national borders. The traditional international economics literature, with its focus on the causes and consequences of financial and commercial integration and cooperation, of course, recognizes this. New research in political economics, however, shows that a broader perspective is needed and emphasizes that the fundamental factors that determine a nation's domestic policies, its institutions, or its level of internal conflict, are not exclusively found within the confines of the nation itself. On the contrary, it is necessary to study the different channels through which foreign state and non-state actors seek to influence all these outcomes. Foreign influence is too important to be ignored. • Policy-for-aid deals: International organizations and donor countries routinely attach conditionalities related to specific policies and "good governance" to aid and loan agreements in an explicit attempt to influence policy making in the recipient countries.
"Vote buying" with promises of aid in the United Nations and other international organisations is another example. The Marshall Plan after World War II is perhaps the best example of a successful and mutually beneficial aid-for-policy deal. At a more specific level, the United States "punishing" Argentina for passing a patent law by removing preferential entry status to many imported products in 1997 (Albornoz, Brambilla, and Ornelas 2019) or "linking" bilateral aid to Columbia's drugs and terrorism policy between 1998 and 2012 (Riaño-Rodríguez 2014) show how foreign influence may narrowly target domestic policies.
• Economic sanctions: Since 1945, there have been more than 1400 cases in which one or more countries have threatened and/or imposed economic sanctions on another country in an attempt to force it to change its policy or institutions (Morgan, Bapat, and Krustev 2009). Two recent examples are the sanctions imposed by Western countries on Russia in relation to the conflict in Ukraine or on Iran in relations to its nuclear program. The boycott of economic and social interaction with South Africa orchestrated by a mixture of state actors (such as the African National Congress) and civil society (such as the Anti-Apartheid Movement) undoubtedly contributed to end the apartheid system.
• Coup d'état: Regime change operations aimed at overthrowing foreign leaders or at changing political institutions abroad are not as common as sanctions but still widespread. Examples of US-backed coup d'état include Iran in 1953, Guatemala in 1954, and Chile in 1973(Kinzer 2007), but such operations are, of course, not exclusive to US foreign policy. For example, the 1974 coup d'état in Niger would not have been possible without the support of France (Higgott and Fuglestad 1975) and Britain was heavily involved in deposing Mosaddeq in Iran in 1953 (Gasiorowski 1987).
• Influencing foreign elections: Foreign actors routinely channel campaign funds to help their favorite candidate or party to win election in other countries. One example of this is the American politician, Jay Kim (Republican, CA), who obtained one-third of all donations to his 1992 campaign (illegally) from South Korean sources. Another example is the funds that Russia donated to the incumbent president, Kurmanbek Bakiev, to boost his re-election chances in the 2009 election in Kyrgyzstan (Bader, Grävingholt, and Kästner 2010). Social media have opened up new avenues for meddling in foreign elections. The evidence suggests that Russia sponsored various social media strategies to influence the outcome of the Brexit referendum in the United Kingdom in 2016 and the US presidential election the same year (Gorodnichenko, Pham, and Talavera 2018). Martin, Shapiro, and Nedashkovskaya (2019)  • Interventions in civil wars: Out of the 150 civil wars studied by Regan (2002), as many as 101 experienced some form of intervention from at least one foreign power.
Military or technical aid is central to this, but so are bases or sanctuaries on foreign soil such as those given to the Colombian insurgent group FARC in Venezuela (Martínez 2017).
• Peacekeeping operations: Since 1948, the United Nations (UN) has been involved in more than 71 peacekeeping operations. In the past decades, many other organizations, including the North Atlantic Treaty Organization, the African Union, and the Economic Community of West African States, have participated in such operations (Sandler 2017). Some of these operations, such as the one in Sierra Leone between 1999 and 2005, have been successful in establishing lasting peace agreements and building state capacity. Others, such as the attempt to create peace in Somalia ending in 1995 with the UN withdrawing all peacekeeping troops, have failed.
• Foreign lobbying and bribery: Lobby groups, multi-national companies and other non-state actors are also involved in foreign influence activities. Lobbying of foreign governments by special interest groups and firms is common. The Foreign Agents Registration Act (FARA) gives a snap shot of these activities in the USA: in 2007 there were approximately 1,700 lobbyists representing more than 100 countries before Congress, the White House and the federal government. 1 Another widespread activity is outright bribery. A recent OECD report, OECD (2014), documents how foreign firms often pay bribes to obtain public procurement contracts and to clear customs procedures. The report estimates that, on average, bribes equalled 10.9 percent of the total transaction value and 34.5 percent of the profits.
These examples clearly show that economic and political interests are interconnected. Even essentially economic issues, such as international trade or foreign investment, can have political effects and might be politically motivated (e.g., Martin, Mayer, and Thoenig 2012).
Similarly, interventions with a clear political motive can have economic effects such as when CIA operations abroad benefit US exporters (Berger, Easterly, Nunn, andSatyanath 2013, Bove, Elia, andSekeris 2014). In other words, foreign influence has a political as well as an economic dimension. The examples also demonstrate that foreign influence operates through multiple channels; it is, in fact, common that a target country is subject to many types of interventions simultaneously. 2 The most important lesson to take from these examples is that diverse policy domains, ranging from international development, trade and foreign investment, and international security to environment protection and drugs policy, cannot be fully understood with exclusive reference to domestic political economy considerations. Instead, they must be viewed through the lens of foreign influence. Conversely, to fully understand foreign influence, its multiplicity and common elements, the phenomenon needs to be treated within a unified framework that makes these interconnections clear.
This survey takes stock of the new political economics literature on foreign influence and develops a unifying framework within which to conceptualize foreign influence. We emphasize the methodological and theoretical contributions that the recent literature makes towards identifying the causes and consequences of different forms of foreign influence and towards specifying the associated mechanisms. The importance of foreign influence has long been recognized in related social sciences 3 and we relate the new political economics literature to discussions in the fields of international relations, international political economy, conflict studies, and political science. The new political economics literature on foreign influence consists of various scattered contributions that deal with different aspects of a common, although not always explicitly stated, broader issue: how, why, and with what consequences do some nations, supra-national institutions or non-state actors seek to influence policies, institutions, and the level of conflict in other nations? An important aim of this survey is to organize these contributions within a unifying theoretical framework and to incorporate them into a common narrative.
The survey is structured as follows. Section 2 presents trends in the different types of foreign influence strategies. Section 3 defines foreign influence and presents a new typology of the phenomenon. The typology highlights three intervention types: agreement interventions, policy interventions, and institution interventions. Section 4 briefly discusses the challenges facing empirical work on foreign influence. Section 5 presents the unifying model of foreign influence that we use to structure the literature related to the three intervention types.
Section 6 discusses agreement interventions. Section 7 discusses policy interventions. Section 8 discusses institution interventions with and without conflict. Section 9 uses the unifying model to derive optimal intervention strategies. Section 10 identifies challenges for future research and concludes. The online appendix contains an overview of many of the data sources that are available for research on foreign influence and some mathematical details related to the unifying model.

Some trends in foreign intervention
While many foreign interventions are clouded in secrecy, some are directly observable or become public after formerly secret files are declassified and can be traced over time and space. Figure 1 displays trends in the prevalence of four different forms of foreign influence for the period after World War II. The upper left panel displays the number of CIA and KGB interventions per year during the Cold War , as revealed by declassified secret files (Berger, Easterly, Nunn, andSatyanath 2013, Berger, Corvalan, Easterly, and. We estimate that, in an average year, about 12 percent of the world's population live in a country that was subject to a CIA or KGB intervention, with a peak of 25 percent in the late 1960s. 4 The upper right panel shows the number of external (hostile) military interventions per year , as recorded in the International Military Intervention (IMI) dataset (Pearson andBaumann 1993, Pickering andKisangani 2009). 5 The lower left panel displays the number of imposed and threatened sanctions per year , respectively, as reported in the Threat and Imposition of Sanctions (TIES,version 4.0) dataset (Morgan, Bapat, and Kobayashi 2014). We estimate that, on average, around 40 percent of the world's population live in a country affected by sanctions, with a peak of 60 percent in 1960. 6 Finally, the lower right panel shows three forms of "non-coercive economic interventions" aimed at inducing a policy change in the target country in a non-coercive manner. First, we plot the number of outstanding IMF loan agreements that are conditional on the borrower adopting policy reforms prescribed or negotiated with the IMF . 7 Second, we plot, for each year, the number of countries that benefit from preferential market access (PMA) (such as the Generalized System of Preferences (GSP), the African Growth and Opportunity Act (AGOA), or the "Everything But Arms" program (EBA)) to either the US or the EU. 8 Third, we plot, for each year, the average number of preferential trade agreement (PTA) partners per country. 9 4 The online web appendix to Berger, Easterly, Nunn, and Satyanath (2013) discusses data construction and sources. 5 As in Abu-Bader and Ianchovichina (2019), we code a dummy variable that takes the value of one if there was at least one non-neutral or non-humanitarian (hostile) intervention in a target country during the four years preceding the current year. We, then, count (and plot) the number of these interventions per year. 6 The TIES dataset defines sanctions as actions that one or more countries take to limit or end their economic relations with a target country as a tool to influence policy in that country. 7 The source is the IMF Conditionality Dataset (Kentikelenis, Stubbs, and King 2016). The conditions imposed vary across different agreements. Quantitative conditions refer to macroeconomic variables under the control of state authorities, such as monetary and credit aggregates, international reserves, fiscal balances, and external borrowing. For example, a program might require a state to maintain a minimum level of net international reserves. Structural conditions refer to reform requirements fundamental to achieving program goals. Examples include deregulation of the financial sector, fiscal adjustment, or privatization programs. 8 Since we focus on PMA granted by the EU or US, our estimate gives a lower bound for PMA incidence: many other industrialized nations and even some emerging economies have PMA programs. For example, Chile started its own program in 2014 with 49 beneficiaries and Turkey has offered PMA to 176 countries since 2002 (Ornelas 2016). Ornelas (2016) discusses the literature on preferential market access for developing countries emphasizing whether program participation encourages the target country to adopt more liberal trade policies. 9 This variable is more informative than the simple count of active PTAs because the latter does not distinguish bilateral from multilateral PTAs. The source is the Database on Economic Integration Agreements constructed by Scott Baier and Jeffrey Bergstrand.  1940 1950 1960 1970 1980 1990 2000 2010 Year    Finally, preferential market access (PMA) is generally not correlated with any of the other intervention forms. These correlations suggest that the different forms of foreign intervention are governed by their own internal logic, that they may be substitute or complementary tools, and that they are used in response to different restrictions or opportunities. The rest of the paper is devoted to uncovering the underlying logic.

Definitions
Foreign influence necessarily involves at least two actors: the actor that seeks to influence (the foreign power ), and the actor towards which these efforts are directed (the target country).
The foreign power is, typically, a single nation state, a group of states, or an international organization, but can also be a non-state actor (e.g., a foreign special interest group or multinational firm). Neither the foreign power nor the target country need to be a monolithic actor sharing a common interest. In fact, the political economics literature on foreign influence emphasizes the role played by internal conflict of interest (e.g., between different social groups or different parts of the government apparatus), as well as the conflicts of interest that cross national borders. We define foreign influence as follows: Definition 1 (Foreign influence) A foreign power (a state or a non-state actor) seeks to affect a policy outcome in a (often less powerful) target country that is de jure outside of its jurisdiction.
We stress two important points about this definition. First, a necessary condition for a foreign power to seek foreign influence is that the policy choice of the target country affects its "welfare". That is, there must be a transnational policy externality. Examples of economic policies that involve such externalities abound: trade policy, environmental regulation, rules for foreign direct investment, tax policy, labor standards, fiscal and monetary policy, etc.
But the externalities can also derive from broader geopolitical objectives. Second, the foreign power may use different strategies to influence the target country's policy choices. We make a distinction between three intervention strategies: 1. Agreement interventions: The foreign power seeks to influence the policy choice in the target country through a negotiated bilateral agreement.

Policy interventions:
The foreign power seeks to change the policy choice in the target country through strategically chosen rewards or sanctions, but without seeking to change the target country's institutions.

Institution interventions:
The foreign power seeks to change the institutions that govern policy-making in the target country in order to influence its future policy choices.
We further distinguish two subcategories: regime interventions that do not result in (long-lasting) violent conflict and conflict interventions, which cause, intensify, or end a violent conflict.
This scheme is different from the classification used in the international organization literature, which is organized around the concepts of contracting, coercion, and imposition (see, e.g., Krasner and Weinstein 2014). 11 Contracting involves a voluntary agreement between the parties. Agreement and policy interventions based on rewards fall into this category.
Coercion occurs when the foreign power can credibly threaten to make the target country worse off without relying on the use of force. Policy and institution interventions that involve 11 Drezner (2003) adds a fourth category -persuasion -where the foreign power seeks to influence the internal values of the target country. sanctions fall into this category. Imposition involves the use of force or the threat thereof.
Regime and conflict interventions fall into this category. 12 The advantage of our new classification scheme is that it emphasizes that the ultimate goal of all foreign intervention is to change the policy choice of the target country, but that this can be achieved through three fundamentally different strategies. We can rank these from less to more intrusive. In Section 5, we nest them within a unifying theoretical framework where each intervention strategy represents a particular deviation from a "nointervention" baseline. Before doing so, however, we briefly discuss some challenges facing the empirical literature on foreign influence and how these are reflected in the review.

Empirical challenges for research on foreign influence
Empirical research on foreign influence faces two primary challenges: (i) measurement and (ii) causal inference. Measurement is a challenge because many types of foreign influence are covert and even when an intervention -e.g., economic sanctions or conditional foreign aid -is observed, it is difficult to quantify the subtle details needed for fully understanding its consequences. Causal inference is a challenge because the targets of foreign influence are not randomly selected and because the foreign powers strategically select which "tools" to use in a non-random way. Moreover, policy externalities invalidates statistical inference from cross-national panel or gravity regressions often used in comparative politics, international political economy and international trade if the (unobserved) dependency that they create between the countries are not taken into account.
Researchers have devoted significant effort to create data on different types of foreign intervention. 13 This has spurred important research into the correlates of foreign intervention which, in turn, has inspired theoretical modelling of causal mechanisms. Yet, for many aspects of foreign intervention, especially related to those that are covert, measurement continues to be a major challenge.
The recent literature engages more seriously with causal inference, but progress is slow.
The primary problem is that cross-national natural experiments are rare. Consequently, 12 Waltz (1979) uses three images to categorize how international relations influence a country's foreign policy. The first image relates to the individual leader's characteristics, including emotional and psychological aspects. The second image relates to the impact of domestic factors on international politics. The third image relates to the systemic conditions that govern international interactions. Our approach shares features with the so-called "second image reversed" literature (Gourevitch 1978), which argues, as we do, that the causality implied by the "second image" is, in fact, reversed and that it is external factors that influence domestic policy. 13 The data appendix lists the datasets used by the literature we survey.
researchers have adopted a number of other strategies to deal with the twin problem of selection and unobserved confounders. First, it is sometimes possible to model the selection process underlying the foreign power's choice of where to intervene directly through a Heckman selection model (see, e.g., Escribà-Folch and Wright (2010)). The success of this strategy, however, hinges on whether it can be underpinned by a convincing theory of how foreign powers select their targets independently of what is otherwise happening in the target country. This is problematic if there is selection on many margins (where, when and why to intervene). Second, many researchers use instrumental variables to induce quasirandom variation in foreign intervention. 14 The success of this strategy hinges on finding convincing instruments that are neither weak nor invalid. Third, research, in particular in the conflict economics literature, has demonstrated the value of studying individual countries (e.g., Hyde (2007), Dell andQuerubin (2017), Enikolopov, Korovkin, Petrova, Sonin, andZakharov (2013)) where, unlike at the cross-national level, it often is possible to find credible natural experiments. Finally, in cases where foreign intervention is covert, a theory-based identification strategy can overcome both the measurement and the selection problem. The theory explains why a foreign power wants to intervene and quasi-random variation in these "reasons" for intervention is, then, related to policy changes or other outcomes in the target countries (e.g., Albornoz and Hauk (2014)). 15 In our discussion of the empirical literature, we emphasize those papers that are most successful in dealing with these empirical challenges.

The unifying model
The aim of the model is to offer a unified framework that brings together different strands of literature on foreign intervention. It stresses that foreign powers select their optimal intervention strategy from a menu of possible strategies and that this choice is systematically related to conditions in the target country and in the foreign power itself. The model builds on two fundamental assumptions. The first assumption is that policy choices are associated with cross-national policy externalities, so that the foreign power is directly affected by the target country's policy choice and vice versa. The second assumption is that the foreign power's preferences over the target country's policy choice are more closely aligned to the 14 Examples include Galiani, Knack, Xu, and Zou (2017) and Dube and Naidu (2015). 15 Matching is often used to make the assumption of conditional independence that underlies standard regression analysis more tenable but without solving the endogeneity problem. The idea is to mimic randomization by creating a sample of units that received the "treatment", say sanctions, that is comparable on all observed covariates to a sample of units that did not receive the treatment (e.g., Levin (2016), Nielsen, Findley, Davis, Candland, and Nielson (2011) or Gilligan and Sergenti (2008)).
preferences of one group within the target country than to another. The first assumption implies that the foreign power has a stake in what the policy choice in the target country is; the second assumption implies that the foreign power has a stake in who in the target country controls the policy choice. Together, they give the foreign power an instrumental, economic reason to intervene in the decision making process in the target country.
This framework combines ideas from the two main schools of thought in international relations: realism and liberalism. 16 Realists view international relations as a struggle for power between self-interested and rational unitary state actors in an anarchic international system (e.g., Waltz 1979, Grieco 1988. Relations between states are determined by their relative power and are conceptualized either as zero-sum or prisoner's dilemma games. In our model, the power asymmetry between the foreign power and the target country, on the one hand, and the policy externality, which leads to a prisoner's dilemma, on the other, are central to understanding the logic of foreign intervention. For liberalists, international relations are not just about security and power ("high politics"), they are also about economics and culture ("low politics"). As a consequence, absolute gains can be realized through cooperation and international institutions and non-state actors can shape a state's policy choices (e.g., Moravcsik 1997, Keohane 1984. Our focus is also on "low politics" and it is critical to our theory that the target country is not a unitary actor and that some groups are more aligned with the interests of the foreign power than others. Institutional factors internal to the foreign power, to the target country, and to the international system shape, in our theory, the opportunities and incentives for a foreign power to intervene in a target country's internal affairs.

Structure
We consider a two-country world with a target country (D) and a foreign power (F ). Each country controls one policy instrument denoted t D and t F , respectively. The policy choices are associated with cross-national policy externalities. Examples include policies related to trade, taxation, investment, natural resources, the environmental, capital import restrictions, 17 etc. or to geopolitical politics, strategic alliances, and security. The target country is inhabited by two social groups (i ∈ {1, 2}) with conflicting policy preferences. The objective 16 Fearon (2018) contains an excellent overview and develops a game theoretical model that reconciles the two schools.
17 Lucas (1990) shows how a foreign power with monopoly control over trade in capital goods can influence wages in a target country.

function of the target country is
where W D,i (.) is the policy preference function of group i ∈ {1, 2}, which is a function of the policy choice at home and abroad. The institutions of the target country are represented by a reduced form bargaining game where β ∈ [0, 1] is the relative bargaining power of group 1. We interpret extreme values of β as autocratic institutions and intermediate values as democratic institutions that facilitate a compromise between the two groups.
The foreign power is the dominant actor and it can devise strategies to influence the policy choice of the target country. The source of this fundamental asymmetry is partly geopolitical, and partly related to economic dominance and to differences in military, legal and technocratic resources and capacities. We assume that the preferences of the foreign power are aligned with the preferences of group 1 in the target country. We refer to this group as the "aligned group". It is, therefore, in the interest of the foreign power that β is as large as possible. The objective function of the foreign power is where γ F ≥ 0 captures the degree of alignment with group 1 and v F (t F , t D ) is the social welfare or political support function of country F itself. We assume that W D and W F are strictly concave functions. The shape of the function W D captures the target country's (marginal) cost of adjusting its policy in the face of foreign influence. Variation in the shape reflects that different policies are associated with different adjustment costs: some policies are relatively easy to adjust (e.g., a trade tax), others are not (e.g., property protection laws). Policy externalities are present whenever the policy choice in the other country has a direct effect on W D or v F , respectively. Importantly, the foreign power cares about the policy choice of the target country even in the absence of a policy externality (operating through v F ) because of its alignment with group 1. Policy externalities and alignment are fundamental for understanding the foreign power's incentive to intervene: externalities offer a rationale for seeking influence on the policy, while alignment provides a rationale for seeking influence on the target country's institutions.

The no-intervention benchmark without ongoing conflict
The benchmark is a situation without any intervention. Without ongoing conflict in the target country, in the no-intervention benchmark, the two countries independently decide their optimal policy. This is sub-optimal from a global perspective because the policy externalities are not internalized. It is straightforward to show that there is a Nash equilibrium with optimal policies, t U D and t U F , which yield payoffs Figure 2 illustrates the Nash equilibrium policy outcome under the assumption that the policy variables are strategic complements. The reaction functions of the two countries are the two dotted upwards sloping (blue) curves and the Nash equilibrium is at point U where the two curves intercept. The policy indifference curves for the two countries associated with W D (U ) and W F (U ), respectively define a cone of policy outcomes that Pareto dominate the nointervention equilibrium: due to the policy externalities, the two countries would be better off if they both "increased" their policy variable. Examples of this include environmental policy (if we interpret a "higher" choice of t i as more protection), trade policy (if we interpret a "higher" choice of t i to mean lower tariffs), and commitments to mutual security cooperation. With ongoing conflict in the target country, the no-intervention benchmark is the ongoing internal conflict. We return to this in Section 8.2.
Notes: The dotted (blue) lines labeled F F and DD are the reaction functions of the two countries and the policy indifference curves are indicated in red and blue, respectively. The welfare of country F increases towards south-east and the welfare of country D increases towards north-west (because policies are strategic complements). U is the policy outcome of the non-cooperative game in the absence of any active intervention.
IA is the policy outcome with an international agreement. It is located on the contract curve labelled P P .

Intervention strategies
Within this framework, we operationalize the three intervention strategies from Section 3 as follows: • Agreement interventions (IA): The two countries negotiate a bilateral policy agreement to facilitate policy coordination.
• Policy interventions (PI): The foreign power seeks to change the target country's policy choice for a given set of institutions (captured by β). This can happen through Strategic rewards (SR) or Strategic sanctions (SS).
• Institution interventions (II): The foreign power seeks to change the target country's institutions (increase β so that the aligned group gets more influence on policy), in order to change the policy choice in its favor. This can happen through a -Regime intervention (RI): The intervention increases β without violent conflict in the target country.
-Conflict intervention (CI): The intervention may increase β by triggering, intensifying, or stopping a violent conflict in the target country.
The policy externality is necessary to motivate agreement and policy interventions, with preference alignment playing no essential role. In contrast, the combination of preference alignment and the policy externality is necessary to motivate institution interventions. In the following sections, we use this framework to develop the logic of each intervention strategy and to structure the discussion of the literature related to each of them.

Agreement interventions
Since the no-intervention benchmark is inefficient, the foreign power may adopt a Coasian approach and seek to influence the policy choice of the target country by offering a bilateral agreement that internalizes the externality. In the absence of side payments, however, any deviation from the no-intervention benchmark must benefit both countries. This has two implications. First, agreement interventions are consensual and voluntary: the target country cannot be worse off by accepting the agreement. Second, an agreement intervention requires either that the policy externality itself is bi-directional (i.e., the policy choice in one country affects the welfare in the other and vice versa) or, if not, that it is bundled up with other policies that are.
Within our model, it is natural to assume that the foreign power is sufficiently powerful that it can make a "take-it-or-leave-it" bilateral offer to the target country. In Figure 2, this assumption pins the agreement down to the point labeled IA on the contract curve (labeled P P ) at the edge of the Pareto set defined relative to the no-intervention benchmark (U ).
We denote the policies associated with this agreement t IA D and t IA F and the associated payoffs . This agreement allocates all the gains from trade to the foreign power and leaves the target country no better off than in the benchmark.
In practice, however, the foreign power may not be able to commit to this (and it has a strict incentive, in the example in Figure 2, to deviate to the policy located on its reaction function). Assuming that the agreement is credible only with some probability q IA < 1, the foreign power's expected payoff is It follows that W e F (IA) ≥ W F (U ), but by how much depends on q IA , i.e., on how credible the agreement is. 18 The lack of commitment rules out a political Coase Theorem (Acemoglu 2003). In the following sub-sections, we utilize the model to address two central questions about bilateral international agreements interpreted as manifestations of foreign influence: (a) what is the rationale for the two countries to enter them, and (b) why do countries fail to reach agreement? 19

Why do countries enter bilateral international agreements?
There are three main rationales for why a foreign power wants to offer a bilateral agreement to a target country and why the target country would accept it. The first rationale is, as in our model, that the agreement internalizes bi-directional policy externalities. This eliminates beggar-my-neighbor-policies in situations featuring a prisoner's dilemma, with policies that are unilaterally attractive, but mutually destructive, and are (weakly) beneficial to all parties. This can explain, for example, bilateral free trade agreements, foreign investment protection agreements, and tax treaties between pairs of countries. It can also explain why countries enter agreements to internalize uni-directional externalities if we interpret the policy variables as bundles of policies, some of which are associated with bi-directional externalities (Ederington 2010).
The second rationale is that bilateral agreements can serve as a commitment device against future beggar-myself-policies. There is a rich theoretical literature illustrating how.
FTAs, for example, can neutralize pressure from protectionist lobby groups (Maggi and Rodriguez-Clare 1998; or destroy protectionist rents (Ornelas 2005), can lock domestic reform policies in (Chauffour andMaur 2010, Baccini andUrpelainen 2014), can signal a politician's achievements to voters (Mansfield, Milner, and Rosendorff 2002), or consolidate 18 Credibility depends on whether the bilateral agreement is formal or informal (Lipson 1991). A formal agreement, like a treaty, is more credible than an informal agreement because the political costs of noncompliance are higher.
19 Surveying the general literature on international agreements is beyond our scope and multilateral agreements such as UN protocols, the World Trade Organization (WTO), etc. should not be considered foreign influence in the sense we define it. For discussions of multilateral agreements, see, e.g., Grossman (2016) and Allee and Elsig (2017) for trade agreements, Bagwell and Staiger (1999) on the foundations of GATT or WTO, Nordhaus (2015) and Marrouch and Chaudhuri (2016) for environmental treaties, and Hollyer and Rosendorff (2012) and Dancy (2013) for human rights agreements. democracy by destroying future protectionist rents, thereby lowering the risk of autocratic backlash (Liu and Ornelas 2014). Empirical evidence lends some support to these theories. Baccini and Urpelainen (2014) show, using structural breaks analysis, that accepting a preferential trade agreement (PTA) with a foreign power can help a developing country eliminate domestic political pressures and to lock in policy reforms. Estevadeordal, Freund, and Ornelas (2008) present robust evidence from ten Latin American countries that bilateral trade agreements beget subsequent unilateral trade liberalization. Liu and Ornelas (2014) study the impact of FTAs on the likelihood that democratic countries remain democratic.
Since unstable democracies are, arguably, more likely to accept free trade offers than stable ones, the direction of causality is unclear. To mitigate this problem, Liu and Ornelas (2014) argue that there is "contagion" in FTA formation at the regional level: a country is more likely to enter a FTA if its neighbors do. Using regional participation in FTAs as an instrument, they show that FTAs facilitate democratic consolidation. Other forms of bilateral agreements may, however, have the opposite effect. For example, Arias, Hollyer, and Rosendorff (2018) show that bilateral investment treaties (BITs) keep autocratic leaders in power. 20 They argue that this is because such agreements improve the domestic investment climate, which reduces the likelihood that an autocratic leader is removed from office due to poor economic performance.
The third rationale for entering bilateral international agreements -in particular on international trade -is to avoid interstate conflict. The argument is that countries with a free trade agreement are less likely to go to war with each other. 21 Importantly, Martin, Mayer, and Thoenig (2008) show, using an instrumental variables approach, that this is true only for bilateral agreements between pairs of countries and not for multilateral agreements.
The reason is that bilateral conflict increases bilateral trade costs, but not necessarily the cost of trading with other countries not directly affected by the bilateral conflict. An unintended consequence of this type of "consensual" foreign intervention aimed at influencing the target country's policy choice (say, on trade), therefore, is to maintain peace.
These various strategic reasons for bilateral agreements, however, operate differently for the (dominant) foreign power and the (economically and politically weaker) target country.
The former tends to weigh economic gains against political factors and to pick the politically most important target countries (Hinz 2017). Moreover, non-trade factors related to the 20 Arias, Hollyer, and Rosendorff (2018) adopt an instrumental variables approach to deal with reverse causality. Their instrument for BIT accession is the cumulative number of non-economic UNESCO conventions that a country has signed. 21 For studies of this relationship, see Martin, Mayer, and Thoenig (2012), Vicard (2012) and Hegre, Oneal, and Russett (2010). geopolitical importance of the target country are important for the foreign power's incentive to offer bilateral trade deals (Limão 2007). Target countries, on the other hand, often sign bilateral agreements for defensive reasons. For example, the case studies in Wesley (2008) suggest that many target countries accept bilateral deals because they fear exclusion or becoming too dependent on one foreign power. 22 6.2 Why do countries fail to reach an agreement?
As our model highlights, the fundamental threat to bilateral agreements is that each country prefers to free-ride and let the other country adopt the agreed policy to reduce the externality.
Moreover, domestic politics interacts with international politics to support or undermine the agreement's credibility. Putnam (1988) conceptualizes these domestic-international interactions as a two-level game. At level I, representatives of the two countries bargain and reach a tentative agreement. This agreement has to be ratified at level II by national parliaments.
This highlights a serious agency problem: the representatives who negotiate on behalf of a country might misrepresent national or foreign interests to advance their own agenda.
Moreover, the fact that any agreement has to be ratified, opens the door to a host of other strategic considerations. First, domestic veto players -whose approval is necessary for change -must be satisfied. Allee and Elsig (2017) argue that veto players are decisive, not only for ratifying an agreement but also for its content. They provide correlational evidence from the analysis of 350 bilateral PTAs between 1947 and 2009 in support of this. Second, in democratic societies, electoral considerations play a crucial role for at least three reasons.
Firstly, Battaglini and Harstad (2020) argue that a non-binding international agreement allows political parties to differentiate their political campaigns by either promising to implement an agreement or to withdraw from it. This encourages an incumbent government to negotiate a treaty that is simultaneously overambitious and weak in the sense of being only partially implementable. They present regression-based evidence that is consistent with this. Secondly, if a bilateral agreement is negotiated prior to an election, but ratification occurs afterwards, the negotiators' ex ante expectations of how the agreement will play with domestic political interests influence its content (Brown and Urpelainen 2015). The details of the agreement can, in particular, induce or discourage interest group mobilization which, in turn, affects domestic support for or opposition to it. Thirdly, an international agreement, typically, leads to a loss of sovereignty (McLaren 1997, Bagwell andStaiger 2018, Rodrik 22 Baldwin and Jaimovich (2012) develop a FTA contagion index and show empirically that defensive FTAs, signed to reduce discrimination created by third-nation FTAs, are important. See Chen and Joshi (2010) for a model of this mechanism. 2000). This restriction on future sovereignty is itself an act of sovereignty and, hence, can be rescinded. Accordingly, even if an agreement is ratified now, new information may come to light later. This can trigger renegotiation (Buisseret and Bernhardt 2018) even if this possibility was taken into account in the design of the initial agreement (Maggi and Staiger 2015). The model developed by Richardson and Stähler (2018) shows that the possibility of future exit from an agreement makes it harder to achieve cooperation in the present and that exit can be an equilibrium outcome. Ex post exit is, therefore, not necessarily a sign of failed ex ante negotiations.
In our model, agreement interventions are attractive to a foreign power because it extracts all the surplus. However, the lack of enforceability, the lack of bargaining power, or the inability to bundle uni-directional policy externalities may motivate a foreign power to consider other intervention strategies. We discuss these alternatives in the next sections, but note that these alternatives, in particular those that influence the institutional framework that governs policy choices in the target country (institution interventions), are often combined with an agreement intervention strategy (e.g., Bonfatti 2017, Antràs and Padró i Miquel 2011).

Policy interventions
This section studies the strategies other than bilateral international agreements that foreign powers use to influence policy decisions in other countries. While international agreements involve state actors, some of these other strategies are open also to non-state actors, such as multinational corporations and foreign special interest groups. Examples of policy interventions include: conditional trade agreements, aid and concessional loans, foreign lobbying, and economic sanctions and boycotts.
We consider two categories of policy interventions. In both cases, the foreign power makes a strategic policy demand. First, strategic rewards involve a voluntary transaction between the foreign power and the target country, and the target country can refuse to accept the reward. Second, strategic sanctions involve coercion and the foreign power unilaterally threatens to harm the target country if it does not adjust its policy. We organize the literature according to these categories and use our model to illustrate their logic.

Strategic rewards (SR)
We conceptualize the relationship between the foreign power and the target country as a principal-agent relationship. The foreign power (the principal) offers the target country (the agent) a reward in exchange for adjusting its policy. This strategy is non-coercive and the target country is free to refuse the offer. The foreign power offers the target country a reward function C(t D ; t F ), which specifies the reward as a function of the target country's policy choice t D . The objective functions of the two countries, respectively, are where W F (.) and W D (.) are defined in equations (1) and (2), respectively. Incentive compatibility requires compensating the target country for any deviation from the no-intervention where the target country is exactly "compensated" for the welfare loss of moving away from the uncoordinated policy choice (see Grossman and Helpman 2001;Chapter 7). Due to the externality, the policy choice of the foreign power affects indirectly the cost of rewarding the target country for adjusting its policy. Bearing equations (4) to (6) in mind, the foreign power's "ideal" policy vector maximizes the aggregate welfare of the two countries: Notes: The basic structure is similar to Figure 2. SR is the policy outcome with strategic rewards. SSη SS < 1 is an example of an equilibrium policy outcome with strategic sanctions and positive transaction costs. For comparison, the figure also shows U which is the policy outcome in the no-intervention benchmark and IA which is the policy outcome with an international agreement. As illustrated in Figure 3, this equilibrium policy outcome is outside the Pareto set defined relative to U . That is, in pure policy terms, the target country is worse off. This is possible because the foreign power "compensates" it with the reward and, at equilibrium, where the incentive compatibility constraint binds, the target country gets W D (t SR D , t SR F )+C(t SR D ; t SR F ) = W D (U ), i.e., the same welfare as without any intervention. The equilibrium policy maximizes the aggregate welfare of the two countries and so, in Figure 3, the equilibrium is located on the contract curve P P at point SR. The foreign power is (weakly) better off than under an agreement intervention if the strategic rewards strategy is fully credible. 23 However, in practice, the foreign power may not keep its reward promise. To capture this, we assume that the reward is, in fact, paid with probability q SR only. Thus, with probability (1 − q SR ), both countries revert to the no-intervention equilibrium. 24 The foreign power's expected 23 This follows because the foreign power can obtain W F (IA) without paying a reward. If it pays the prescribed reward -which it must do to obtain a policy outside the Pareto set -it is because its welfare inclusive of the reward cost is higher.
24 This formulation neglects two additional commitment problems: (i) the reward is paid, but there is no policy shift (Dunning 2004) and (ii) the reward is not paid, but policy shifts anyway (Hudson 2013). We payoff, therefore, is The expected value of the reward strategy increases with the foreign power's ability to commit to pay the reward. If commitment is impossible, this strategy is no better than the no-intervention equilibrium. The literature documents many ways in which a foreign power can reward a target country for a policy change. We draw an important distinction between state and non-state actors. Non-state actors include foreign or international special interest groups, such as trade or industry organizations, unions, or environmental groups and large multinational corporations. For these actors, the "reward instruments" include contributions to political campaigns, information lobbying, as well as outright bribery. For state actors, the "reward instruments" include different forms of foreign aid and subsidized loans among others. State actors may act openly or covertly through international organizations. 25

Non-state actors
Non-state actors often lobby to influence policy outcomes in other countries, but are subject to many legal restrictions. According to the International Institute for Democracy and Electoral Assistance's Political Finance Database, 41 countries, including the USA, the UK, France, and Brazil, ban or restrict foreign donations to political parties. Still, many loopholes exist. Other countries, including Australia, Denmark, and Colombia, do not impose such bans. Rather than seeking to influence election outcomes or to use political contributions to "buy" post-election access to key politicians, foreign lobby groups can hire professional lobbyists from the lobbying industry in the target country to get their point of view across to the relevant policy makers (Blanes i Vidal, Draca, and Fons-Rosen 2012).
In our model, foreign lobby groups are willing to pay to influence the target country's policy because of the policy externality. The empirical literature provides many examples of this behavior. Desbordes and Vauday (2007) study lobbying by foreign firms in 48 developing countries. They report correlational evidence based on survey data that foreign lobbying is associated with substantial fiscal and regulatory benefits, deriving, in particular, from could capture these possibilities by reinterpreting the objective functions of the two countries in expected terms and require the reward to be ex ante incentive compatible. Hence, ex post outcome (i) and (ii) can occur. 25 Influence via an international organization may proceed through formal channels (e.g. through voting power) or informal procedures related to information disclosure, hiring practices, or the location of the institution's headquarters. the foreign firms' ability to negotiate superior entry conditions. Foreign lobbying is also important in developed countries. Gawande, Krishna, and Robbins (2006) find a correlation between foreign lobbying activities and changes in US trade policy. Kee, Olarreaga, and Silva (2007) report structural estimates that suggest that the weight given by the US government in its objective function to foreign lobby contributions offered in exchange for market access is five times higher than the weight given to tariff revenue forgone. 26 A potential benefit of foreign lobbying is that it can internalize cross-national externalities (Antràs and Padró i Miquel 2011). In fact, if all parties affected by a policy choice can lobby and all governments are equally receptive to the rewards offered by foreign and domestic lobby groups, then foreign lobbying can fully internalize the policy externality (Conconi 2003, Aidt andHwang 2008;. It is, perhaps, more relevant to evaluate whether the target country wants to ban foreign lobbying to insulate itself from this type of foreign influence. The answer depends critically on whether the foreign lobby groups have objectives that are aligned with unorganized domestic groups that are under-represented in the political calculus of the target country. If this is the case, allowing foreign lobbying can increase the target country's social welfare because it corrects a pre-existing political distortion (Aidt and Hwang 2014). In other words, foreign lobbying can be second-best optimal for the target country. This benefit arguably has to be traded off against the real or perceived loss of democratic legitimacy.
Foreign special interests can also "buy" influence on the the target country's policy choices through bribery (Rose-Ackerman 1999, Aidt 2003). Since bribery is illegal, its extent is not directly observed, but survey evidence from, for example, the World Bank's Doing Business survey, suggests that it is widespread in many places and multinational companies in the arms trade, the pharmaceutical industry, and in resource extraction are regularly caught in corruption scandals (OECD 2014, Zhu 2017. In contrast to lobbying for, say, low import tariffs, which benefit all foreign exporters in an industry (at the expense of domestic producers), bribes are used to buy private benefits, such as a government procurement contract and may contribute to rent creation (Zhu 2017). It is, therefore, doubtful if the externality argument that can be advanced in support of foreign lobbying is applicable here. 27 26 The effect of foreign lobbying goes beyond trade policy and information provided by foreign special interests groups can, for example, enhance tourism (Gawande, Maloney, and Montes Rojas 2009).
27 Van Long and Stähler (2009), however, argue that foreign participation in contests for government procurement contracts can reduce wasteful domestic rent-seeking.

State actors
State actors -governments acting alone, in groups or through international organizationsoften use conditional aid and loans to reward target countries for changing their policy, but can also adopt more indirect reward forms, such as preferential market access for exports from the target country. 28 Such aid-for-policy deals reflect the strategic considerations of the foreign power, including the prospect of economic and commercial benefits and geopolitical considerations. 29 Colonial past and political alliances are also important correlates of aidfor-policy deals (Alesina and Dollar 2000).
From a foreign influence perspective, the key question is: how does the foreign power benefit from giving aid? The evidence points to three specific benefits -votes in international organizations, policy concessions, and electoral advantage -and to a set of more diffuse and hard to quantify (potential) benefits coming from the effect that aid has on the target country's economy more generally. First, foreign powers often channel their foreign influence activities through international agencies -like the United Nations (UN), the World Bank, and the International Monetary Fund (IMF) -and use aid-for-vote deals to "buy" the support of target countries in critical roll call votes within these organizations. To establish this, researchers exploit the fact that the internal decision making procedures of international institutions induce exogenous variation in how much the support of a particular target country is worth. For example, countries outside the group of permanent members are rotated onto the UN security council by lottery. This gives a country temporary voting power and the major donor countries can use aid to buy the votes of temporary members in need of it. The evidence is clear: an aid-receiving country temporarily serving on the UN security council receives greater inflows of aid and financial assistance than when it is not on the council if it votes in line with the donor country's interest. 30 Similar aid-for-vote deals take place in the UN general assembly. 31 Aid-for-votes deals are commonly used to signal "political friendship" between new leaders in the recipient or the donor country (Rommel and Schaudt 28 In fact, non-reciprocal preferential market access (PMA) is frequently used as "foreign aid", and granted to more than 120 developing countries. Although the proclaimed goal is to foster export-led growth in the target countries, PMA to, for example, the EU involves many policy conditionalities (Ornelas 2016). The same is true, although less explicit, for countries that gain access to the US market through the Generalized System of Preferences (GSP).
29 See, e.g., Stone (2004), Barro and Lee (2005) and Dreher, Nunnenkamp, and Schmaljohann (2015). 30 See, e.g., Kuziemko and Werker (2006) for evidence that temporary members get more US and UN aid, Dreher, Sturm, and Vreeland (2009) for evidence that access to World Bank programs is also affected, and Vreeland (2011) for evidence that other donor countries than the USA engage in such vote buying. 31 See, e.g., Barro and Lee (2005), Dreher and Jensen (2007), Carter and Stone (2015), Andersen, Harr, and Tarp (2006). 2019). Furthermore, Gassebner and Gnutzmann-Mkrtchyan (2018) show that countries with access to the US market under the Generalized System of Preference that align with the USA in the United Nations General Assembly votes are less likely to lose their preferential market access following eligibility reviews regarding workers' rights violations. Unfortunately, for target countries that receive such politically motivated aid, it tends to be less effective in promoting growth than other forms of aid (Dreher, Eichenauer, andGehring 2018, Bearce andTirone 2010).
Second, the foreign power can use aid-for-policy deals to obtain policy concessions from the target country. One strategy is for the foreign power to attach bilateral aid to issues that it wants on top of the target country's policy agenda. The target country is willing to give these issues priority because the aid reduces the cost of addressing them. Riaño-Rodríguez (2014) uses content analysis of presidential speeches to demonstrate how the US used this strategy to influence Colombian's drugs and terrorism agenda between 1998 and 2012. Aid-for-policy deals can also operate via non-reciprocal market access programs. Ozden and Reinhardt (2005) study 154 countries with access to the US market via the Generalized System of Preference and show that they adopted a more liberal trade policy after being granted preferential access. Removal of Generalized System Preference access to the US market can also induce policy changes in the target country (with a view to regain access), as the case of disputes over Argentinian patent laws in 1997 demonstrates (Albornoz, Brambilla, and Ornelas 2019). Andersen, Harr, and Tarp (2006) and Dreher and Jensen (2007) argue that aid-for-policy deals can be intermediated by international organizations. Andersen, Harr, and Tarp (2006) develop a principal-agent model to show how this logic works. In the model, one dominant country (the US) can influence the decision making of an international lender (the IMF). This forces borrowing countries to give concessions that benefit the dominant country in exchange for loans. Empirically, they find that the probability that a target country obtains an IMF loan is increasing in the political concessions the country makes to the US. Along similar lines, Dreher and Jensen (2007) show that the number of conditions imposed by the IMF on its loans are positively associated with the borrowing country's alignment with the US in United Nations General Assembly votes.
Third, although aid-for-policy deals may not explicitly aim at entrenching or replacing political leaders, the deals often do. The selectorate model of political survival captures the logic (Bueno de Mesquita and Smith 2009). To stay in power, a politician needs to retain sufficient support (forming a winning coalition) from the subset of the population with the power to oust him (the selectorate). In the target country, the politician will, therefore, strategically use some of the "reward" received from the foreign power directly 32 or by claiming undeserved credit 33 to maintain the required level of support. More surprisingly, aidfor-policy deals can also enhance the re-election chances of the foreign power's government. Carter and Stone (2015), for example, show that the US government can win votes at home by using aid-for-policy deals to get a democratic target country to vote in line with its interest in United Nations Assembly. Aid-for-policy deals can, therefore, improve the chance of political survival for the leaders in both countries.
Finally, aid or concessional lending have a range of economic and social consequences that are often caused by or at least mediated by the policies that the target country adopts in response to aid and loans. Some of these consequences may have been intended by the foreign power, but many of them were probably "unintended". The difficulty arises because the literature, in general, struggles to identify the economic consequences of aid for at least two reasons. 34 First, the benefits of aid-for-policy deals are often very specific and studies that focus on aggregate measures of aid will, as Qian (2015) points out, confound a bundle of different and potentially offsetting effects. This makes it difficult to develop credible identification strategies even for specific aid policies. Second, it is hard to distinguish the economic effects of aid or loans from the fact that poor economic conditions push countries to self-select into being potential recipients of aid and loans. A credible identification strategy, therefore, requires finding (exogenous) non-economic factors that affect the foreign power's incentive to offer aid-for-policy deals, but which are not related to economic conditions in the target countries. Barro and Lee (2005) take a step in this direction by exploiting the details of the IMF's internal procedures for approving financial assistance to find such factors.
Using (i) the target country's share of IMF quotas, (ii) its share of professional economists working at the IMF, and (iii) its proximity to the major shareholders, as expressed, for example, in voting behavior in the United Nations General Assembly, as instruments for 32 For example, in his study on electoral politics in Kenya, Jablonski (2014) finds a strong bias in the allocation of aid toward constituencies with high vote shares for the incumbent government. 33 Cruz and Schneider (2017) show -with a regression discontinuity design -how local politicians in the Philippines increased their re-election prospect by claiming credit for the World Bank funded KALAHI-CIDSS project despite the fact that their municipality had been selected for the program by chance. Guiteras and Mobarak (2015) show -based on a natural experiment in Bangladesh -that uncertainty about the identity of the donor is crucial for citizens to give undeserved credit to local politicians for an aid program.
34 See Qian (2015) for an overview of the aid effectiveness literature and Doucouliagos and Paldam (2008) for a meta study of the effect of aid on economic growth. Galiani, Knack, Xu, and Zou (2017) critically evaluate the various identification strategies used in this literature and exploit the fact that since 1987 the International Development Association has used a threshold rule for per capita income to determine eligibility for aid to identify (a positive) causal effect of aid on growth.
IMF loan programs, they find that agreements with the IMF, not only have a negative effect on economic growth, but also have negative effects on the quality of democracy and on the income distribution. This type of identification strategy has the potential to produce new insights into the economic and political logic of aid-for-policy deals.

Strategic Sanctions (SS)
Instead of "rewards", a foreign power can use sanctions to influence a target country's policy choice. Sanctions take many forms: trade sanctions (tariffs, export and import restrictions, or embargoes), financial sanctions (freezing assets, cutting off financial aid and bank lending and services), or stopping aid and preferential market access programs. 35 Often the threat of a sanction is sufficient to induce the target country to acquiesce.
As in Section 7.1, we conceptualize strategic sanctions within a principal-agent relationship where the foreign power -the principal -seeks to induce the target country -the agent -to adopt a particular policy. It does this by threatening to impose a costly sanction should the target country deviate from the foreign power's policy demand, denoted t SS D . The sanction is a function of the target country's policy choice t D and is represented by is the foreign power's best (uncoordinated) response to the target country's policy choice. The objective functions of the two countries are where η SS ∈ (0, 1] is a transaction cost. Sanctions are costly for both parties. For the target country, this reflects the direct economic cost, which depends on how easy it is to "bust" the sanctions. How much the sanction "hurts" is inversely proportional to the transaction cost parameter η SS . For the foreign power, the sanction cost is associated with enforcement and the loss of trade. W D captures the target country's "benefit" from violating the "demands" of the foreign power; W F captures the corresponding "violation cost" for the foreign power. Clearly, the sanction policy must be incentive compatible to be effective. Unlike the case of strategic rewards, the target country cannot opt out of the sanction altogether, but it 35 While sanctions are mostly used by state actors, they can sometimes be used by non-state actors. Dal Bó, Dal Bó, and Di Tella (2006) develop a model of this in which domestic non-state actors (special interest groups) can use rewards (bribes) and private coercion (sanctions) in the forms of media smear campaigns, legal harassment and violence in influencing a target country. Unlike in our model, they treat the stick and the carrot as complements: private coercion is used to save on bribes. How important private coercion is for foreign influence is an open question.
can decide which policy to implement and, thus, which sanction to incur. Given the policy demand, t SS D , and the foreign power's own matching policy t SS for all t D . Since sanctions are costly to everyone, the sanction associated with the foreign power's policy demand must be zero. The least costly sanction that gets {t SS The foreign power's policy demand, therefore, is As with strategic rewards (see equation (7)), the equilibrium policy maximizes a weighted average of the two country's welfare, with the target country's weight being the inverse of the transaction cost parameter η SS . Furthermore, if there were no transaction cost (η SS = 1), then the policy choice would be the same as with strategic rewards and located at the point labeled SR in Figure 3. With transaction costs η SS < 1, the sanction threat has less bite, and the policy choice moves up the contract curve (P P ) to a point like the one labeled SS| η SS . Since the threat of a credible sanction is sufficient to induce the target country to acquiesce, it is clear that sanctions (with low transaction costs) dominate both IA and SR as the preferred intervention strategy. The logic is that the foreign power must pay a positive reward to get its desired policy, while the sanction is a threat and, at equilibrium, the foreign power pays nothing. In this sense, the "stick" is better for the foreign power than the "carrot". However, the threat has to be credible to work. Denoting the probability that the sanction policy is credible by q SS and assuming that the two countries play the nointervention equilibrium (see Section 5.2) if the sanctions fail, the foreign power's expected payoff is where c a ≥ 0 is the audience cost that the foreign power incurs when it fails to issue a credible threat or to carry through with it. It reflects the negative effect on the foreign power's ability to sanction other target countries in the future. Sanctions often lack credibility because they require coordination among many countries and it is hard to get third parties to respect and enforce them. 36 In short, a sanction works best when there is a credible international framework for its enforcement (q SS is high) and when the transaction cost η SS is low and it is hard for the target country to reduce the harm suffered.

Theoretical models of sanctions
Our theoretical framework nests many existing models in the literature on sanctions, which conceptualize sanctions as sender-receiver games. The foreign power (the sender) "sends" a sanction threat. If the target country (the receiver) does not acquiesce, then the sender decides whether or not to implement the sanction. Under complete information, sanctions are, as in our model, never imposed in equilibrium: if the target country is too weak to withstand a sanction, it acquiesces to the sanction threat; and if it is strong enough to endure a sanction, then the foreign power knowing this never imposes one (Spaniel and Smith 2015).
In practice, however, sanctions are imposed. There are two main theoretical reasons for this. The first is asymmetric information, either about the target country's or the foreign power's type. Spaniel and Smith (2015) study the situation with private information about the target country's type. Some leaders are too weak to survive a sanction politically and respond to a sanction threat by adjusting policy to please the foreign power. Others are politically strong and can survive a sanction. They never acquiesce to a threat. 37 Weak leaders, clearly, have an incentive to bluff strength by not backing down in the face of a threat and pretend to be strong and will, in equilibrium, do so with some probability.
The foreign power knows this, but is unable to separate weak from strong leaders. In a semi-pooling (perfect Bayesian) equilibrium, it is optimal for the foreign power to impose sanctions with positive probability in order to incentivize weak leaders to bluff strength less often. Since strong leaders are more likely to ignore sanction threats than weak leaders, the foreign power often ends up imposing sanctions against leaders who will not give in. This makes both the sanction threat and the sanction itself ineffective in achieving the desired policy change.
Hovi, Huseby, and Sprinz (2005) (2015) considers two ways a third party can "bust" a sanction. It can give aid, which is costly, or it can allow for trade with the sanctioned target country, which may be profitable. 37 This would correspond to η SS → 0 in our model.
faces. If the target country underestimates the foreign power's willingness to impose the sanction, it will take the chance and ignore the threat. The foreign power, in turn, will only implement the sanction if its sanction threat was serious to begin with. In a separating (perfect Bayesian) equilibrium, therefore, sanctions get implemented when the foreign power is willing to go through with the threat; and in response to this, the target country ex post adjusts its policy and the sanctions, having proved effective, are lifted. 38 The second reason why sanctions may be imposed in equilibrium, explored by Hovi, Huseby, and Sprinz (2005), is that sanction policies are "lumpy" and, unlike in our model, cannot be fine-tuned perfectly. They argue that rather than not imposing any sanction or imposing a tough one that works, the foreign power can impose lenient sanctions that are less costly to both parties, but will not induce the target country to adjust its policy.
Despite this, the foreign power may nevertheless pick this option. This is because the foreign power may incur considerably bigger audience costs by doing nothing than by imposing an ineffective sanction, and because it may be too costly to enforce an effective sanction.
In our model, the probability q SS captures the credibility of the sanction strategy. Credibility is directly related to whether or not sanctions can be enforced. Bapat and Kwon (2015) model the enforcement problem associated with a sanction policy that prohibits firms in the foreign power trading with the target country. They emphasize that firms with business interests in the target country have an incentive to unlawfully undermine the sanction, and if insufficient resources are allocated to monitor and check such behavior, the sanction will be ineffective. This is likely to happen in two cases. First, if the foreign firms have little economic interaction with the target country, then sanctions, even if enforced, are ineffective because they do not hurt the target country sufficiently. Second, at the other extreme, if the foreign firms have a major economic interest in the target country, then sanctions are unenforceable because the incentive to undermine them is too strong. The implication is that sanctions are most likely to be successful (as a threat) in situations in which firms from the foreign power have a moderate economic interest in the target country. 39 The "power to hurt" is central to many theoretical models of sanctions and is captured by the transaction cost parameter η SS in our model. The power to hurt is related to how easy it is for the target country to replace sanctioned trade with trade from other countries (Kavakli, Chatagnier, and Hatipoglu 2019). Importantly, since the actual cost of a sanction also depends on the power to resist, it can be manipulated strategically. For example, if the target country enhances its power to resist by strategically stockpiling to-be-sanctioned 38 Whang, McLean, and Kuberski (2013) consider the case with two-sided private information. 39 Bapat and Kwon (2015) report evidence consistent with this.
goods prior to the actual implementation of the sanction, the threat of a sanction, in fact, undermines the effectiveness of the sanction once it is imposed (Afesorgbor 2019). Beladi and Oladi (2015) distinguish between "smart sanctions" that hurt only the politicians in the target country and "dumb sanctions" that hurt the entire population. "Smart sanctions" are likely to be more effective at inducing policy changes than "dumb sanctions" because they operate directly on the incentives of the politicians with the authority to give in to the foreign power's demand. The power to hurt will also depend on whether sanctions are unilateral or multilateral. Ultimately, sanctions are a network phenomenon and, therefore, most effective within a multilateral framework (Cranmer, Heinrich, and Desmarais 2014).

Empirical evidence on sanctions
Empirical research on sanctions is particularly challenging. As discussed above, sanctions do not need to be implemented to affect the target country, and sanction threats, even if they could be observed, require credible commitment, the presence of which is hard to assess.
Moreover, sanctions that are actually imposed may fail because those that would have been successful are never imposed -the threat is enough -and are thus not observed. Therefore, of what constitutes a sanction or a sanction threat. 40 As a consequence, to improve our understanding of how sanctions work, when they are used and why, there is a real need for better, consistent and more detailed data.
The theoretical work highlights that non-random selection of target countries is a major obstacle to causal inference and may bias estimates of sanction effectiveness. Theory-based quantification methods offer a potential remedy. For example, Whang, McLean, and Kuber-ski (2013) use a structural trade model to estimate the "coercive power of sanction threats".
They conjecture that sanction threats are more likely to be effective if the target country is more vulnerable to the disruption of bilateral trade with the foreign power than the foreign power itself. Applying this logic, they find that the likelihood that a target country concedes to a sanction threat is higher when the foreign power can leverage the target country's economic dependency. 41 As discussed above, asymmetric information about the target country's willingness to acquiesce and the foreign power's commitment to impose sanctions is one reason why sanction threats lead to actual sanctions. Typically, the uninformed party can learn about the other party's type over time by observing its actions. Exploring this logic, Spaniel and Smith (2015) argue that a foreign power knows more about how a target country will respond to a sanction, the longer its leader has been in office. It follows that a foreign power is more likely to follow through with a sanction threat against a new (unknown) leader in a target country.
Empirically, they show, while carefully addressing the selection problem, that the longer the leader of a potential target country has been in power, the lower is the probability that a sanction is imposed on that country. When a sanction is imposed, the question becomes for how long. Krustev and Morgan (2011)  and Kwon (2015) use the foreign power's market share in the target country to measure the capacity of sanctions to hurt. This is also problematic because it does not capture the target country's power to resist being hurt. However, this can, in principle, be proxied by how important a trading partner the foreign power is to the target country. In the end, what matters both for the power to hurt and for the power to resist is the cost of finding alternative trade partners. Based on this logic, Kavakli, Chatagnier, and Hatipoglu (2019) estimate the cost of sanctions through a revealed comparative advantage calculation that, for each commodity category, takes into account the number of unique goods exported by the target country and the distribution of the value of these goods within the target country's export portfolio. This measures the target country's ability to adapt domestically and to raise the foreign power's cost of maintaining the sanction, respectively. Their empirical analysis indicates that sanctions are more likely to succeed (in getting the target country to adjust its policy) when the foreign power has a comparative advantage in its exports to the target country. On the other hand, they are more likely to fail if the target country's export portfolio is diversified or if the target country has a comparative advantage in the goods that it exports to the foreign power. 43 The empirical literature also uncovers many potentially adverse consequences of sanctions on economic growth and the poverty gap (Neuenkirch and Neumeier 2015), on income distribution (Afesorgbor and Mahadevan 2016), and on the likelihood of currency crises (Peksen and Son 2015). It remains an open question whether the foreign power internalizes any of these adverse effects when deciding whether or not to impose sanctions, or they are ignored in the strategic calculation. In that case, these effects are "unintended consequences" of the sanction policy. 44

Institution Intervention (II)
Rather than influencing the policies of the target country directly, a foreign power can seek to influence them indirectly through a change in the target country's institutional framework.
These institution interventions take many forms. Some involve covert operations to overthrow leaders and provoke regime transitions (from democracy to autocracy or vice versa); others involve meddling in elections or making aid and trade deals contingent on reforms of 43 Crozet and Hinz (2016) use a general equilibrium trade model to quantify the costs that 37 Western countries inflicted upon themselves in 2014-15 when they imposed sanctions on Russia in relation to the conflict in Ukraine. They report that the cost was 0.3 percent of their total exports (US$ 42 billion). 44 Wood (2008) (2010), Lo, Hashimoto, and Reiter (2008), Pickering and Peceny (2006) and many others provide examples. 46 Aidt, Albornoz, and Gassebner (2018) use regional histories of post-regime transition loans to quantify these expectations, arguing that neighbor effects are plausibly exogenous to the political process of a particular country.
47 This might be a reason for the association between the adoption of IMF programs and civil war onset reported in Hartzell, Hoddie, and Bauer (2010). 48 An important literature, starting with Acemoglu, Johnson, and Robinson (2001), shows that European colonization spread different types of institutions -extractive or inclusive -across the rest of the world with significant implications for long-run economic and political development (Dell 2010, Michalopoulos and Papaioannou 2016, Dell and Olken 2019. Arguably, colonialism is a primordial form of foreign institution intervention. However, colonizers ruled their colonies directly, albeit often with collaboration from local elite groups. This is a critical difference with respect to the forms of foreign influence we survey, where the target country retains its sovereignty as a nation. For this reason, the literature on the economic effects of colonialism (e.g., Heldring and Robinson 2018) is beyond the scope of this survey.

Regime interventions (RI)
In a regime intervention, the foreign power supports a political regime transition in the target country that empowers the social group with the strongest alignment with its (economic or geopolitical) interest. If the induced regime change ensures that the aligned group attains long-lasting control over the policy decision making process in the target country (Acemoglu and Robinson 2000;, then a regime intervention circumvents, to some extent, the credibility problem associated with policy interventions (discussed in Section 7). Yet, this advantage comes at a cost: regime change operations require significant resources; even when they are successful, policy decisions remain uncoordinated and policy externalities will not be internalized; and the strategy can only be successful if there is a viable social group in the target country with sufficiently aligned interests to those of the foreign power.
To develop the logic of regime interventions, we return to the unifying model. Recall that the policy preferences of the foreign power are aligned with those of group 1 in the target country (the aligned group). A regime intervention is, therefore, aimed at increasing the power of group 1, i.e., to increase β from its initial value to a higher post-intervention value β RI > β. This is costly for the foreign power, but the regime transition itself does not result in a direct output loss in the target country. This is the main difference between a regime intervention and a conflict intervention. Examples of regime interventions include a coup d'état that is concluded in a matter of days, interventions that facilitate a peaceful transition to democracy, and interference in elections. The cost to the foreign power reflects direct costs (e.g., the cost of a covert operation) and indirect reputation costs. Specifically, we model the post-intervention bargaining power of group 1 as where the foreign power chooses the regime intervention cost, I F , it is willing to incur. If it is willing to incur a cost that is higher than the lower threshold I F , then a minor regime intervention succeeds in increasing the aligned group's bargaining power from β to β; if it is willing to incur a cost higher than the upper thresholdĪ F , then a major intervention succeeds in increasing the aligned group's power from β to β > β. The more costly major intervention represents a fundamental change in the institutions that govern policy making in the target country, such as overthrowing a democracy and replacing it with a dictatorship or vice versa. The less costly minor regime intervention has less significant effects on the target country's institutions and captures regime interventions such as those aimed at meddling in the electoral process, or at assisting the target country with monitoring elections.
Notes: The basic structure is similar to Figure 2. RI(β) shows the equilibrium policy outcome, which is located along the foreign power's reaction function, of a minor (β) and a major (β) regime intervention, respectively. CI(β = i) for i ∈ {0, 1} represents the two possible policy outcomes after a violent conflict. For comparison, the figure also shows U , which is the policy outcome of the no-intervention benchmark; IA, which is the policy outcome with an international agreement; SR, which is the policy outcome with strategic rewards, and SSη SS < 1, which is an example of a policy outcome with strategic sanctions and a positive transaction cost.

Figure 4: The policy outcomes associated with regime and conflict interventions
After an intervention, the two governments adopt the uncoordinated policy, which reflects the new allocation of bargaining power in the target country. In Figure 4, a minor regime intervention shifts the target country's reaction function outwards (not shown in the figure) and the equilibrium policy moves along the foreign power's reaction function to the point labeled RI(β). A major intervention shifts the equilibrium further towards the north-east, say, to the point labeled RI(β). We denote these policy choices by t D (β RI ) and t F (β RI ), respectively. We index the equilibrium payoffs (gross of the cost of intervention, I F ) by β RI and write the foreign power's payoff as W F (RI, β RI ) ≡ W F (t F (β RI ), t D (β RI )). It is clear from the figure that W F (RI, β) > W F (RI, β) > W F (RI, β) = W F (U ) because the foreign power is better off playing the uncoordinated policy game with the target country when group 1 has more power. Moreover, viewed purely in policy terms (i.e., ignoring the intervention cost (I F ) and the potential lack of credibility associated with the policy and agreement interventions), in the example drawn, the foreign power prefers the major regime intervention to the agreement intervention, and might, if the equilibrium were shifted even further along its reaction function than drawn, prefer, purely in policy terms, the major regime intervention to strategic sanctions and rewards. This highlights a trade off between policy and agreement interventions that directly aim at internalizing the policy externality and regime interventions that aim at empowering the aligned group without any direct attempt at internalizing the externality. The regime intervention strategy works best in environments with modest policy externalities and a strongly aligned social group in the target country.
Taking the cost of intervention (I F ) into account, a major regime intervention pays off for the foreign power relative to no intervention if and a minor intervention is better than no intervention if If both of these inequalities hold, then the optimal regime intervention strategy is the one with the greatest net payoff. A major intervention is the best choice when it is possible to increase β a lot at relatively low cost.

The theoretical literature on regime interventions
The theoretical literature on regime interventions distinguishes between three regime intervention types, reflecting different degrees of change in the target country's political institutions (different shifts in β). First, the foreign intervention can be aimed at influencing election outcomes in the target country. Antràs and Padró i Miquel (2011) develop a twocountry probabilistic voting model in which the foreign power can influence, at a cost, how voters in the target country perceive their politicians. This affects the platform choices of the politicians running for office, which helps internalize (trade) policy externalities to the foreign power's advantage. At equilibrium, the incumbent and the opposition in the target country commit to a common policy platform that maximizes a weighted sum of domestic and foreign welfare. It is the threat itself that sustains these platforms. No foreign intervention -meddling in the election process -actually occurs in equilibrium. This is an example of a regime intervention that does not aim at a fundamental institutional change, but at changing who gets elected and on which platform. 49 Second, foreign intervention can be aimed at triggering a political regime transition or at stabilizing a threatened regime. Aidt and Albornoz (2011) show how this works, using the theory of political transitions developed by Acemoglu and Robinson (2000;2005). In their model, the aim of the regime intervention is to protect foreign direct investments (FDI) in the target country. Both the foreign investors and the target country's economic elite, who controls policy if the target country is an autocracy, want low taxes on foreign investments.
Therefore, a regime intervention is aimed at strengthening the power of the target country's economic elite (corresponding to a high value of β in our model). In equilibrium, the foreign intervention either stabilizes an existing autocracy or sponsors a coup d'état against a vulnerable democracy. These pro-autocracy interventions require a foreign power with a substantial pro-investor bias and high income inequalities in a target country with profitable if the target country is relatively small compared to the hegemonic power that leads the coalition. Interestingly, the analysis shows that the cost of intervention is disproportionally borne by the hegemonic power.
Third, a regime intervention can be aimed at promoting democratization (pushing β 49 Ellman and Wantchekon (2000) show that another way to induce such power shifts is to sponsor political unrest or strikes in the target country.
50 Bonfatti (2017) argues that geopolitical motives play an important role for this type of foreign intervention. In his framework, two foreign powers with different geopolitical interests aim at improving a trade agreement with the target country by sponsoring a regime transition that empowers aligned social groups. Typically, only the foreign power with the most significant geopolitical and economic interest intervenes, and when it does, it is always in favor of the social group in the target country that is most pro-trade. towards the middle range). One mechanism is sanctions against an autocratic regime. Oechslin (2014) highlights that the success of pro-democracy sanctions hinges on how resistant the political elite of the target country is to sanctions that cause scarcity of foreign inputs. Democracy can be established by a costly revolt or by voluntary exit of the elite. The incumbent political elite can respond to sanctions by strategically making internal revolt more costly, but at the cost of lower economic output. The autocratic elite may, therefore, look for exile opportunities as an alternative. If the payoff from exile is relatively high, sanctions may be successful in inducing a voluntary exit of the autocratic elite. If the value of exile is relatively low, the elite will resist and sanctions will eventually be lifted before any transition to democracy takes place. 51 Another mechanism through which a foreign power can strengthen democracy in a semiautocratic target country is to support fair and free elections through election monitoring.
Such efforts are, however, often undermined by the strategic behavior of autocrats. For example, an autocratic leader fearing a revolution might be willing to call an election and pretend to democratize because elections are informative about the strength of the opposition (Little 2012). This signal is especially valuable for moderately insecure autocrats, who would stand a fair chance of doing well in an election and, in that way, consolidating their power. Importantly, any electoral fraud will naturally be discounted by voters, which would make elections less effective as a way to reduce the risk of revolution. For this reason, electoral monitoring becomes valuable to autocrats as a commitment devise: monitoring ties their hands and reduces the possibility of fraud. Thus, monitoring increases the autocrat's interest in democratic elections but, rather than strengthening democracy, it consolidates the autocracy. Another consideration, highlighted by Chernykh and Svolik (2015), is that incumbent autocrats may, in fact, be better informed about their popular support than opposition groups. Ill-informed opposition groups can use election results to infer their strength, knowing that the incumbent autocrat has incentives to misrepresent the election result. In case the autocrat claims victory, the opposition can either accept or attempt to unseat the incumbent in a costly post-election uprising. In this context, foreign election monitors, who can publicly certify the election result, might induce self-enforcing compliance with the result. In this sense, electoral certification may help the opposition to (correctly) infer the level of opposition to the incumbent regime since it reduces the incumbent autocrat's incentives 51 Wright (2009) models the effect of conditioning foreign aid on democratic reform. He shows that the success of such aid in triggering a transition to democracy depends on whether or not the incumbent autocratic leader expects to remain in office after the transition. A weakness of this paper, which is shared by many others in this literature, is that the foreign power is not a strategic player. to misreport. While these results are insightful, existing models of election monitoring do not treat the decision to monitor an election as strategic. This important limitation needs to be addressed by future research.

The empirical literature on regime interventions
A major challenge for empirical research on regime interventions is to measure these interventions. Interventions that are overt and readily observable can be quantified with relative ease. It is much harder to obtain information on covert interventions that the foreign power wants to keep secret. We organize the evaluation of the empirical literature along an overtcovert axis.
Interventions that are aimed at promoting democracy are, typically, overt and include electoral assistance and monitoring, aid conditional on holding elections or sanctions for the failure to do so. Firstly, the foreign power can offer technical election assistance and monitoring to strengthen democratic accountability in target countries with weak electoral institutions. By helping with the organization of free and fair elections, democratic values may be disseminated and politicians' incentives to conform with basic democratic principles may be enhanced (Finkel, Pérez-Liñán, and Seligson 2007). Consequently, in elections that are subject to international monitoring, the win probability of opposition candidates should increase and electoral fraud should diminish, while protest after fraudulent elections should increase. To document such effects empirically, researchers face the challenge that an incumbent government's willingness to accept external monitoring is systematically related to its prospect of winning the election to be monitored or to its intentions with regard to manipulating it. Roussias and Ruiz-Rufino (2018) adopt an instrumental variables strategy to engage with this selection problem. 52 They combine information on international election monitoring with election outcomes in newly established democracies with multi-party elections. They report that the presence of monitors substantially reduces the incumbent's margin of victory and facilitates power transitions when the incumbent loses. 53 Hyde (2007) deals with the selection problem by exploiting that international election monitors were randomly assigned to polling stations in the 2003 presidential election in Armenia. She reports a reduction in the vote share for the incumbent at polling stations that were (randomly) 52 Their first instrument is a dummy variable for the period before and after the collapse of the communist bloc. After the collapse, election monitoring became a norm, while before it was not. The second is a variable that captures the prevalence of election monitoring in the region around a country in the two years preceding an election. 53 Kelley (2012b) reports that election monitoring correlates with higher government turnover.
monitored. Moreover, the presence of monitors reduced election day fraud considerably.
Along similar lines, Enikolopov, Korovkin, Petrova, Sonin, and Zakharov (2013) explore that independent election monitors were randomly assigned to 156 of 3,164 polling stations in the city of Moscow in the 2011 Russian parliamentary election. They report that the vote share of the incumbent (the United Russia Party) at polling stations with randomly assigned independent election monitors compared to those without was at least 11 percent lower than the official count and that recorded turnout decreased by 6.5 percent where election monitors were present. This is strong, causal evidence that the presence of international election monitors reduces election fraud. However, the evidence does not address whether or not public denouncement of election fraud by international monitors reduces fraud in future elections. To begin addressing this question, Donno (2010)  Wright (2009) uses an instrumental variable strategy 55 to establish that autocrats, who are supported by a broad-based coalition and, therefore, have a good chance of winning a free and fair election, tend to respond to conditional aid by democratizing. In contrast, conditional aid is counter-productive and helps autocrats hang on to power when they are supported by a narrow coalition. This is consistent with selectorate theory (Bueno de Mesquita and Smith 2009) and suggests that the effectiveness of making aid conditional on holding elections or undertaking other democratic reforms depends critically on the preexisting autocratic institutions in the target country. It also depends on the geopolitical context. Bermeo (2016) shows that the negative correlation between aid and democratic reform is confined to the Cold War period, except for autocracies of particular geopolitical importance, and Dunning (2004) shows that aid to sub-Saharan Africa made contingent on democratic reform promoted democracy only after, but not during, the Cold War. Generally, autocrats use a combination of repression and public funds to buy loyalty to stay in power (Wintrobe 2000). Escribà-Folch (2012) and Escribà-Folch and Wright (2010) study how autocratic leaders adjust public spending in the presence of sanctions. Using a Heckman model, they report that sanctions increase the likelihood of democratic change in so-called personalist autocracies only, and that they have no effect in single-party and military dictatorships. The likely reason is that personalist autocracies, where power is centered around one individual, are particularly sensitive to the loss of external revenue to fund patronage. To summarize the findings on overt regime interventions, an increasing body of evidence suggests that election 54 They find that if a country's former colonizer holds the presidency of the Council, then the country receives considerably more foreign aid than other aid-receiving countries. 55 Aid is instrumented by past aid, by life expectancy, by log(population), and by a dummy for the recipient of the largest amount of aid in the sample (Guinea-Bissau). monitoring can foster democratic accountability, at least in the short run, but conditional aid or sanctions imposed openly in the name of democracy exhibit a mixed record and their effectiveness is conditional on a battery of inter-mediating factors.
Many regime interventions are secretive and covert. This is a real obstacle to empirical research on their causes and consequences. The recent declassification of CIA and KGB files from the Cold War era has, however, created opportunities for new empirical research on USand Soviet-sponsored covert regime interventions. Berger, Corvalan, Easterly, and Satyanath (2013) create new panel data with information on CIA and KGB interventions during the Cold War. These interventions often resulted in substantive anti-democratic regime change, exemplified by the CIA's role in the coup in Chile in 1973 (a major regime change in our model). More broadly, they report that covert CIA interventions abroad are correlated with significant short and medium term declines in the quality of democratic institutions in the target countries, but have no long run effect. Using the same dataset, Berger, Easterly, Nunn, and Satyanath (2013) argue that economic factors motivated these covert interventions. They estimate gravity models of international trade and show that "successful" CIA interventions, which triggered regime change, gave US exporters a larger market share in the target countries in industries in which the US had a comparative disadvantage. These interventions can, therefore, be interpreted as a form of commercial imperialism: they helped US firms and harmed firms in the target country. Further evidence indicates that the benefits of US regime interventions were not confined to trade, and the operations were often directed at target countries where US companies were under threat of expropriation. Using the augmented Fama-French four-factor model and their own newly developed distributionfree small sample tests, Dube, Kaplan, and Naidu (2011) show that the asset prices of US firms under threat in the target countries increased abnormally the day the CIA operations were approved, i.e., before they actually took place. This suggests that the US firms that benefited from these interventions and their investors knew about them in advance, and that they expected to benefit commercially from them. Some (covert) regime interventions are not aimed at overthrowing political leaders or at triggering a fundamental change in the target country's political institutions but at meddling in other countries' elections (a minor regime intervention in our model). 56 Levin (2016) defines an election intervention "as a situation in which one or more sovereign countries intentionally undertakes specific actions to influence an upcoming election in another sovereign country in an overt or covert manner that they believe will favor or hurt one of the sides contesting that election and which incurs, or may incur, significant costs to the intervener(s) or the intervened country (p. 192)". The methods used include financing the preferred candidate's or party's campaign and sabotaging the campaign of unwanted candidates or parties. It also includes making threats and promises prior to the elections to cut-off or give aid depending on who wins the election (Faye and Niehaus 2012). Based on declassified secret US files and files from the USSR smuggled out by a deserter, Levin (2019a) has constructed a detailed record of the two superpowers' "election interventions" in other countries (the PEIG dataset). Strikingly, this happened in as many as one-ninth of all competitive national executive elections held around the globe between 1946 and 2000. Most of these interventions were covert, meaning that the average voter would not have been aware of them, but some were open. Using matching techniques, Levin (2016) estimates that these electoral interventions significantly increased the election chance of the aided candidate or party and that overt interventions were more effective than covert ones. This type of intervention serves to undermine democratic legitimacy and makes the target country more susceptible to democratic breakdown (Levin 2019b). 57

Conflict Interventions (CI)
Regime transitions or leader replacement often happen through violent conflict. Foreign powers, therefore, have a stake in conflicts abroad and may provoke a conflict, take side in an ongoing conflict, or try to terminate one that is ongoing. To organize the literature, we distinguish three types of conflict interventions: those that aim at starting a conflict (conflict-creating interventions), those that aim at supporting one side in an already ongoing conflict (conflict-intensifying interventions), and those that aim at stopping an ongoing conflict (peace-keeping interventions). While they all share the same goal of empowering the aligned group in the target country, the underlying logic differs, as so does the normative implications.

Conflict-creating (CCI) and conflict-intensifying (CII) interventions
These two strategies involve the foreign power in a violent and costly conflict in the target country that destroys part of the target country's economic output. To develop the logic, we assume, in our model, that the two groups in the target country may engage in a violent conflict. The winner of the conflict takes power: β CI = 1 if group 1 wins and β CI = 0 otherwise. The winner selects the policy without any international policy coordination (as in Section 5.2). The two points on the foreign power's reaction function (F F ) labeled CI(β = 0) and CI(β = 1), respectively, in Figure 4 illustrate possible policy outcomes. The associated policy-related payoffs are W D,1 (β CI ), W D,2 (β CI ) and W F (β CI ). In the absence of conflict, the status quo institutional arrangement with β ∈ (0, 1) determines the political power of each group, and the payoffs are W D,1 (U ), W D,2 (U ) and W F (U ). For the foreign power, the "conflict outcome" with group 1 (2) as the winner is better (worse) than the "peace outcome".
Without a foreign intervention, the probability that group 1 wins a conflict is p. A conflict breaks out if at least one of the groups starts it. Before the groups decide on this, the foreign power can make a promise, which it will honor with probability q CI , to support the aligned group 1 in an eventual conflict. 58 Foreign intervention (say, military aid or technical assistance) increases the win probability of group 1, as perceived ex ante by the two groups and the foreign power, to p CI = p + q CI ε < 1, where ε measures the foreign power's conflict intervention capacity. 59 Group i ∈ {1, 2} starts a conflict if where c is the welfare cost of a conflict, which is shared by everyone in the target country.
We can write the foreign power's expected policy-related conflict payoff for a given win probability of group 1 (p ) as The foreign power partly internalizes the cost of the conflict (γ F c) as long as it cares about the welfare of group 1 (γ F > 0). Additionally, the foreign power must pay its own direct intervention cost c F > 0, so that its expected payoff from a conflict-creating or a conflictintensifying intervention is: 58 One interpretation is that the foreign government in power at the time the promise is made cannot bind the hands of future governments. 59 To insure that group 1's win probability is below 1, we assume that < 1−p q CI .
The foreign power's incentive to support the aligned group depends on whether the intervention triggers a new conflict or intensifies an already ongoing conflict. The reason is that the no-intervention status quo is different in the two cases: peace in the former and conflict in the latter.
First, consider the foreign power's incentive to start a conflict (CCI). This is a relevant choice if equation (18), evaluated at p CI = p, fails for both groups but holds for group 1 at The condition shows that the foreign intervention can trigger a (new) conflict if the foreign power's conflict intervention capacity (ε) is sufficiently large, if the promise of support is credible (q CI is close to 1), or if the cost of fighting (c) is not too large. We note that expectations of a foreign intervention can trigger conflict.
A conflict-creating intervention is better than no intervention for the foreign power if , which we can express as Interestingly, the ability to make a credible promise of support (a higher q CI ) may not increase the likelihood of a conflict-creating intervention. There are two countervailing effects.
On the one hand, a higher q CI increases the expected cost of the intervention; on the other, it increases the expected win probability of group 1.
Second, consider the case where a conflict starts even without a foreign interventionequation (18), evaluated at p CI = p, holds for at least one of the groups -and the foreign power, therefore, has to decide whether or not to intervene in favor of group 1 in an ongoing

conflict. The foreign power prefers a conflict-intensifying intervention to no intervention if
, which we can express as where W F (1)−W F (0) is the difference between the foreign power's policy-related payoff with group 1 (β = 1) and group 2 (β = 0) in power, respectively. In contrast to the decision to trigger a conflict, the decision to intervene in an ongoing conflict is independent of the cost of 60 If the condition fails for group 2 at p CI = p, then it will also fail at p CI = p + qε.
conflict (c) and of the probability that the support will materialize (q CI ). It depends solely on the foreign power's conflict intervention capacity (ε) and on the direct intervention cost (c F ). The fact that a civil war may be very costly, therefore, only affects the foreign power's incentive to start one (and then only if it cares about at least a subset of the population in the target country (γ F > 0)), not the incentive to intervene in an ongoing conflict.
8.2.1.1 Theories of conflict intervention In our model, violent conflict breaks out when (with or without foreign intervention) the expected benefit exceeds the expected cost for at least one of the two social groups in the target country. While from a rationalist perspective, this is a necessary condition for conflict, it is not sufficient because the parties, in principle, could avoid conflict through bargaining (Fearon 1995). The theoretical literature on conflict studies two main reasons why bargaining does not prevent conflict in practice: commitment problems and asymmetric information (Fearon 1995, Powell 20042006).
The literature emphasizes two particular commitment problems (see, e.g., Fearon 1995): firstly, a conflict might be started preventively to gain offensive advantage and, secondly, neither side can commit not to use resources gained through bargaining to enhance its fighting capacity. A different commitment problem arises when a foreign power is involved. Albornoz and Hauk (2014) argue that any commitment to foreign intervention is transient.
One important reason is government turnover in the foreign power: some governments are more willing to intervene abroad than others. For the opposing groups in a target country, a promise of support from the foreign power is, therefore, equivalent to a temporary shift in their relative fighting strength. Since the advantage is transient, the group strengthened by the promise of foreign intervention may prefer conflict to peace to capitalize on the support while it can.
The second main reason for conflict is asymmetric information. The "spoils politics model" illustrates the logic for a conflict between an incumbent government and a rebel group (Dal Bó and Powell 2009). If the incumbent government has private information about the value of the contested "spoils" and can misrepresent it, the rebel group's optimal response to the government's announcement of "low spoils" is to start a conflict with positive probability. Otherwise, the government would always claim that the spoils are low to keep more of the share. In a stable environment, conflict should eventually stop because the fighting parties learn the truth about their opponent's strength over time (Fearon 2004).
However, the presence of a foreign power can destabilize the environment. First, the side offered foreign assistance will be better informed about its value than the opposition. For example, humanitarian aid changes the cost of fighting (Narang 2015), but the incumbent government knows the value of such aid better than the opposition (Nielsen, Findley, Davis, Candland, and Nielson 2011). This exacerbates information asymmetries. Second, rebel groups are empowered by being offered external sanctuaries where they can hide and regroup in relative safety (Salehyan 2007). The willingness of a foreign power to provide sanctuary depends on (changing) political factors, which are external to the conflict in the target country and often unpredictable, leading to persistent information asymmetries. Third, expectations of foreign intervention might lead the target country's government to offer less of the spoils to the rebels, which increases the likelihood of conflict onset. Woo (2017) argues this is especially relevant for politically unstable oil-producing countries. When their market power increases, oil-importing foreign powers have a strong incentive to intervene to avoid interruption of oil import-export ties. This gives the government of an oil-producing country less reason to share the "spoils" with opposition groups, which, in turn, increases the risk of conflict onset. 61 In these different ways, foreign interventions generate persistent uncertainty and tend to prolong or trigger conflicts by exacerbating information problems.
Our theoretical model abstracts from the principal-agent problem that arises because the foreign power and its "agent" in the target country (group 1) may have different priorities (Ladwig 2016). Additionally, the "agent" -whether the incumbent government or a rebel group -is often not a unified group (there can be several rebel groups or the government might work with paramilitary groups). This makes it hard for the foreign power to control its allies. Salehyan, Gleditsch, and Cunningham (2011) model this principal-agent relationship to understand when rebels are offered and accept foreign support. Their model predicts that the strongest and weakest rebel organizations, relative to their opponent, are least likely to receive external support. Foreign powers tend, on the one hand, not to support weak rebel groups unlikely to pose a significant threat to the target regime. Strong rebel groups tend, on the other hand, to reject offered support because they prefer to retain their autonomy. 62 Another aspect of this principal-agent problem is rivalry within a rebel group between leaders or factions. The foreign power can, through a divide-and-rule strategy, affect the distribution of power within such a group by allocating external resources strategically (Tamm 2016). 61 This suggests that the foreign intervention in oil-producing countries by oil-dependent foreign powers induces a variant of the "institutional natural resource curse" (Robinson, Torvik, and Verdier 2006) leading to civil war onset (Woo 2017) or to a regime change (Sarr, Ravetti, and Swanson 2015). However, natural resources do not induce a "curse" via the "voracity effect" and weak domestic institutions; rather, natural resources encourage a foreign intervention that destabilizes politics and institutions in the target country. This variant of the "institutional natural resource curse" is an important topic for future research.
62 Using newly created post-war data with information on rebel organizations, Salehyan, Gleditsch, and Cunningham (2011) report correlational evidence that is consistent with this.

Motives for conflict interventions
In our model, the foreign power's ultimate motive is to help its ally to win the conflict in order to obtain a favorable shift in the target country's policy, but, in general, political economy motives internal to the foreign power and wider geopolitical motives also play a role. First, Bove, Elia, and Sekeris (2014) present evidence that is consistent with the first motive. They use an augmented gravity model of international trade and an instrumental variable strategy to show that US security interventions abroad increase post-intervention trade flows between the USA and the target country. Second, Albornoz and Hauk (2014) present a theoretical framework in which political economy considerations in the foreign power is the key determinant of its willingness to intervene in conflicts abroad. In particular, a foreign government whose domestic popularity falls may adopt a "gambling for resurrection strategy" that involves covert conflict interventions abroad in a bid to regain popularity. 63 The causal mechanism of this theory can be tested without data on the actual foreign interventions by relating swings in the foreign government's popularity to civil war incidence in other countries. Using this theory-based identification strategy, Albornoz and Hauk (2014) report that the incidence of civil war around the world decreases with US presidential approval rates. Using plausibly exogenous variation in world oil market prices, Ahmed and Werker (2015) show that a similar logic applies to oil-rich autocracies. 64 When oil prices are high, oil-rich (Muslim) autocrats tend to give aid to oil-poor (Muslim) countries. This allows an oil-rich autocrat to consolidate his power at home because the cost of the intervention eliminates excess resources that the opposition might otherwise attempt to appropriate through a challenge to his regime. This, in turn, lowers the likelihood of civil war.
Third, the wider geopolitical environment shapes the motives underlying many conflict interventions. Each foreign power acts alongside other powers with similar or opposing interests. Findley and Teo (2006) argue that many conflict interventions are themselves reactions to earlier instances of third-party intervention. Especially during the Cold War, the superpowers often got involved in conflicts without appearing to be directly involved (proxy wars) to protect their geopolitical interest (Yoon 1997, Huth 1998, Mullenbach and Matthews 2008 or to promote foreign policy objectives (Alesina andDollar 2000, Palmer andMorgan 2010). Changes in the geopolitical situation that "weaken" one superpower relative to the other can lead to civil war in other countries. This happens because opposition groups 63 Unlike such covert interventions, Enterline, Garrison, and Aubone (2008) argue that for democracies the political cost of overt conflict interventions often outweighs the potential benefits and show that the correlation between overt foreign interventions and support in subsequent elections is negative.
64 They build on Besley and Persson (2011)'s model of state capacity and political violence.
gain relative power in countries where the incumbent regime previously enjoyed protection by the "weakened" superpower (McCormack 2019). 65 In addition to its influence on conflict onset and duration, the international geopolitical situation also affects the way in which civil wars are fought and the strategies that rebels employ (Kalyvas and Balcells 2010).
8.2.1.3 Empirical evidence on conflict interventions Unlike our unifying model, the theoretical literature on foreign intervention in civil war does not make a clear distinction between conflict-creating and conflict-intensifying interventions. Yet, this distinction is conceptually important because the "no-intervention" status quo is fundamentally different.
Fortunately, considerable effort has gone into creating datasets on pre-conflict foreign intervention in politically unstable states 66 (Regan and Meachum 2014) and on intervention into ongoing civil war (Uexkull and Pettersson 2018). Below, we discuss the evidence on three important types of conflict interventions: rebel sanctuaries, sanctions, and foreign aid, and we distinguish their effects on conflict onset and duration whenever we can.
Rebel sanctuaries Rebel sanctuaries are a common form of foreign support to rebel groups. In fact, since 1945, a majority of rebel groups have used external bases and safe havens (Salehyan 2007) as a base of operation and to escape the repression capabilities of their own state. Sanctuaries significantly lower a rebel group's cost of fighting and make civil war, triggered by asymmetric information or commitment problems, more likely. Salehyan (2007) reports that a promise of a sanctuary from a geographic neighbor is positively correlated with conflict onset. The correlation between extraterritorial rebel sanctuaries and conflict duration also appears to be positive, significant, and substantial. 67 However, the offer of a rebel sanctuary is related to many other causes of conflict. To establish the causal effect of sanctuaries, if any, some researchers study changes in a foreign power's policy towards rebel sanctuaries that are unrelated to the actual civil conflict to which the sanctuary is related. One example is the sanctuary given to the Colombian insurgent group FARC after Hugo Chávez became president of Venezuela. Martínez (2017) uses this plausibly exogenous 65 Empirically, McCormack (2019) uses economic shocks to the US or USSR economies to proxy for movements in their relative strength and shows that such shocks correlate negatively with the likelihood of conflict in countries within their orbit of influence. 66 To classify states that are unstable, Goldstone, Bates, Epstein, Gurr, Lustik, Marshall, Ulfelder, and Woodward (2010) estimate a risk score that indicates the likelihood that a country will experience a civil war onset two years in the future and classify a state as politically unstable if it falls into the top quartile of all states included in their dataset.
67 Some rebel sanctuaries are created by refugees (Lebson 2013). Camarena (2015) studies the strategic choice of a refugee recipient country with respect to how much support to offer to such (refugee) rebels. event in his difference-in-difference research design to provide causal evidence that proximity to cross-border sanctuary increases the intensity of violence. Withdrawal of rebel support triggered by events exogenous to a conflict also affects fighting intensity. For example, in Uganda the government launched a military crackdown on the rebel movement (the Lord's Resistance Army) after it was declared a terrorist organization by the USA in 2001, as part of the Patriot Act, and it lost its external sanctuaries in Sudan. Rohner, Thoenig, and Zilibotti (2013) exploit the exogenous shock induced by the Patriot Act to study the causal effect of war on inter-ethnic trust. Identifying such exogenous policy shocks is an important avenue for future research into the causal link between rebel sanctuaries and civil war.
Sanctions The effect of sanctions on civil war depends on their type and on whether they remain a threat or are actually implemented. The theoretical arguments are clear: on the one hand, a sanction threat can be used to signal foreign discontent with a target country's political regime or its leaders and might thereby encourage internal dissent (Grauvogel, Licht, and von Soest 2017). On the other hand, imposed sanctions cause economic hardship, which may influence conflict by fueling existing dissent against the target country's government (Wallensteen 2000, Weiss 1999 or spurring opposition to the regime by mobilizing dissatisfied -but previously uncommitted and passive -members of society (Blanchard andRipsman 1999, Kaempfer andLowenberg 1999). The empirical evidence is less clear and the literature has hardly gone beyond case studies (e.g., Grauvogel, Licht, and von Soest (2017)) and correlations. Hultman and Peksen (2017) study the correlations between the threat and imposition of sanctions and the intensity of civil conflict in Africa between 1989 and 2005. Threats of economic sanctions and of arms embargoes are both positively correlated with an increase in conflict intensity. However, only actual economic sanctions tend to contribute to conflict escalation while implemented arms embargoes have the opposite effect. Grauvogel, Licht, and von Soest (2017) argue that sanction threats work as an international stamp of approval for would-be rebels and they present correlational evidence that sanction threats increase the probability of anti-government protest. Clearly, more empirical research is needed on this topic to establish the causal links between sanctions and conflict.
Foreign aid The category of aid most directly related to conflict is arms support and technical training of military personnel in the target country. Duration models suggest that neutral third-party military interventions tend to lengthen conflicts, while a biased intervention in favor of one of the fighting parties can serve to end a conflict more quickly (Regan 2002). In politically unstable countries, external military interventions increase the likelihood of civil war onset (Regan and Meachum 2014). Jones (2017) creates new data distinguishing between military aid aimed at bolstering the fighting power of the supported side and aid aimed at degrading the capabilities of the opposition. The data show that the timing of the foreign intervention is critical for its effect. Military support for rebel organizations is likely to be most effective during a short window early in a civil war, while military assistance to the government is likely to increase its chance of victory only after a civil war has become protracted. Along similar lines, direct commercial sales of weapons by the USA to foreign governments tend to increase the risk of civil war onset, but is not correlated with its duration (Magesan and Swee 2018). 68 Evaluation of the causal effects of military aid or interventions on conflict is complicated by the fact that these interventions tend to be non-random. Recent research overcomes this problem by moving away from comparative cross-national studies to within-country studies where fine-grained spatial differences in exposure to foreign intervention can be explored. Dube and Naidu (2015) use this strategy to provide convincing causal evidence on the impact of US military aid to Colombia on violent conflict between left-wing guerrillas, the Colombian state, and right-wing paramilitary groups (unofficially supporting the government) between 1988 and 2005. The US military aid was allocated to preexisting military bases located in a subset of 900 Colombian municipalities. Using this fact along with general shocks to US military spending around the world (excluding Latin America) as inputs to an instrumental variable strategy, they establish that US military aid had an asymmetric impact on the conflict. While it increased paramilitary violence differentially in aided areas with government military bases, it had no significant effect on the intensity of guerilla warfare. Military aid does not only affect the intensity of violent conflict (and its short-run economic costs), it also has the potential to influence longer term development outcomes.
Miguel and Roland (2011) study within-country spatial variation in US bombing during the Vietnam war to demonstrate this, exploiting the fact that the most heavily bombed areas were located near the 17th parallel north. Using the distance to the 17th parallel as an instrument for the intensity of bombing, they can isolate plausibly exogenous variation in bombing and estimate the effect on long-run development. They show that heavy bombing neither increased local poverty rates nor lowered consumption or literacy (as measured in 2002). While it is possible that the long-term consequences of foreign military intervention of this type are minor, there clearly is a need for more research to fully understand the long-run effects of foreign interventions. 68 Magesan and Swee (2018) tackle the causality problem by instrumenting contemporaneous weapon sales by an interaction between a country's historical frequency of weapon purchases and past US price inflation.
Foreign powers can influence the outcome of an ongoing conflict by using aid to win over non-combatants. Non-combatants may stay neutral, protect insurgents, or collaborate with counter-insurgency forces, and foreign aid can potentially influence their choice. Dell and Querubin (2017) evaluate the effectiveness of development programs sponsored by the US military during the Vietnam war in winning over the hearts-and-minds of the population and compare this to the military strategy of using overwhelming fire-power in air strikes.
Since the two different strategies were deployed in separate regions and by separate military corps, Dell and Querubin (2017) can exploit a spatial discontinuity design, which compares nearby hamlets on either side of the "corps border", to estimate the causal effect of the two intervention strategies. While the use of overwhelming fire-power led to more support for the Viet Cong, the winning the hearts-and-minds strategy made non-combatants more likely to side with the Americans. Another example is the aftermath of the Iraq war: Berman, Shapiro, and Felter (2011) provide correlational evidence, based on new panel data from Iraq on violence against Coalition and Iraqi forces, that reconstruction spending, conditional on community characteristics (sectarian status, socio-economic grievances, and natural resource endowments) reduced insurgent violence.
Clearly, insurgents and rebel groups have a strong incentive to counter any hearts-andminds strategy by sabotaging development projects and retaliating against civilian informants. This can lead to an increase in violence and undermine the strategy. Khanna and Zimmermann (2017), for example, show that the world's largest anti-poverty program, the National Rural Employment Guarantee Act in India, intensified the conflict between Maoist insurgents and the government of Indian. 69 Along similar lines, Crost, Felter, and Johnston (2014) show that insurgents sabotaged a large community-driven development program (KALAHI-CIDSS) in the Philippines. Finally, Sexton (2016) argues that the ability of insurgents to carry out such sabotage is, in part, related to who controls the territory. His evaluation of civilian development aid deployed by the US military to counter the Taliban insurgency in Afghanistan suggests that it can only reduce insurgent violence in places already under pro-government control. In contested areas, aid provokes insurgents to carry out more bombings and more direct attacks against pro-government forces. 70 Taken together, the evidence suggests that an important determinant of the effectiveness of development aid to win over non-combatants is the ability of insurgents to react. 69 Khanna and Zimmermann (2017) can use a regression-discontinuity design to obtain causal estimates because the program was rolled out (non-randomly) in three implementation phases and poorer districts were treated earlier. 70 Sexton (2016) uses geo-located incidents of violence to examine these correlations.
Unlike military support and aid used to win over hearts-and-minds, aid given for purely humanitarian reasons is not designed strategically to influence the level of conflict. Nevertheless, it may have the (unintended) effect of prolonging an ongoing conflict. This can happen through a number of channels: humanitarian aid can, if sufficiently fungible, free up resources for fighting; it can create protected demilitarized spaces; or it can reduce the political cost of sustaining a costly conflict (Narang 2015). An example of this is US food aid. Nunn and Qian (2014) exploit a combination of exogenous variations in US food aid shipments caused by weather-related shocks to the US wheat production and the recipient country's general tendency to receive US food aid to show that such aid causes an increase in the duration of civil wars, but has no effect on civil war onset. Bluhm, Gassebner, Langlotz, and Schaudt (2016) argue that the (unintended) effect of development aid on conflict depends critically on the preexisting levels of conflict. They create a new ordinal measure of conflict with four "grades of conflict", including low intensity conflicts, which have previously been neglected by the literature. To isolate exogenous variation in aid at the donor-recipient level, they interact a time-varying index of political fractionalization in the donor country with the probability that the recipient receives aid from that donor, comparing regular and occasional aid recipients. They show that aid has no effect on conflict if the recipient (target) country is either peaceful or already in the midst of a full-blown civil war. However, for target countries with ongoing, low-intensity conflict, aid can trigger conflict escalation.
It is not only the level of aid inflow that affects conflict; fluctuations in these flows are also important. Arcand and Chauvet (2001) present a model that demonstrates that fluctuations in aid revenues increase the risk of civil war, firstly, by increasing the payoff to a successful rebellion and, secondly, by varying the level of fungible funds the recipient government has for repression. Empirically, Nielsen, Findley, Davis, Candland, and Nielson (2011) find, in a rare-event logit analysis supplemented with a matching strategy, that negative aid shocks significantly increase the probability of conflict onset, while positive aid shocks have no effect.
This suggests that withdrawal of aid shifts the bargaining power towards rebels because it becomes harder for the government to meet the rebels' appeasement demands.

Peace-keeping interventions (PKI)
Conflict is costly, not only to the groups fighting and the civilians caught up, but also for the foreign power. The latter, typically, loses trade opportunities (Martin, Mayer, andThoenig 2008, Magee andMassoud 2011) or access to valuable resources and sees its geopolitical interest threatened (e.g., through large-scale refugee movements). It can, therefore, be in the interest of the foreign power to stop a conflict.

Theories of peace-keeping interventions
In our model, we conceptualize a peace-keeping foreign intervention (PKI) as an attempt to stop an ongoing conflict and to reestablish the pre-conflict institutional arrangement where group 1's bargaining power is β. To succeed, the intervention must deliver a peace dividend b that is sufficient to stop the fighting. This is costly for the foreign power. We denote the cost by c P KI = α F b where α F > 0. To be effective, the peace dividend must appease the group that started the conflict.
If group 1 was the instigator, then the peace dividend must satisfy 71 where group 1 gets W D,1 (U ) + b if the intervention creates peace. The higher group 1's win probability, the harder it is to create peace and the larger must the peace dividend be. The foreign power wants to sponsor a peace-keeping intervention if where equation (19) defines the foreign power's expected payoff with conflict, W F (p). The foreign power benefits indirectly from peace because group 1 does. We assume α F > γ F so that its net intervention cost is (α F − γ F )b > 0. Condition (25) can be rewritten as where W D,1 (CI) is defined in equation (18) and is positive (since group 1 by assumption started the conflict). 72 A necessary condition for a peace-keeping intervention is that the foreign power prefers the "peace outcome" to gambling on the "conflict outcome". This is more likely if the win probability of group 1 (p) is low and the cost of the conflict (c) is high.
These arguments are applicable to situations with ongoing conflict. However, if the "peace dividend" is "delivered" prior to the outbreak of a civil war that would start in its absence, 71 The case in which group 2 is the instigator is similar. 72 To see that there exists values of b > 0 that will satisfy conditions ( 24) and (26), evaluate equation (26) at the minimum b for which equation (24) holds: which may hold. then our model can also rationalize "preemptive" peace-keeping interventions. Most of the limited existing theoretical work on foreign influence and peace-keeping is precisely focused on this situation. Its starting point is that conflict is caused by a commitment problem resulting from shifts in the relative bargaining power of the opposing parties (Walter 2009).
Within this framework, two types of preemptive foreign peace-keeping interventions can prevent a conflict. First, the strategic use of sanctions can smooth shifts in the relative power of the opposing parties, thereby eliminating the commitment problem that would otherwise result in conflict. 73 Second, the threat of a large-scale, international military intervention in support of the target country's government can also prevent conflict (Cunningham 2016). This is because if such an intervention were to become a reality, the rebels cannot expect any gain from fighting. Anticipating this, the rebels will not fight in the first place. 74 Meirowitz, Morelli, Ramsay, and Squintani (2019) examine theoretically whether international conflict resolution institutions can prevent conflict. They show that a neutral mediator, who does not favor any side and collects confidential information from the conflicting parties (a so-called Myerson mediator), might be successful because the incentive to arm is reduced.

Empirical evidence on peace-keeping interventions
In practice, most peacekeeping interventions are aimed at stopping an ongoing conflict. They are, typically, multilateral and organized through the United Nations (UN). However, after the end of the Cold War there have been many non-UN peace-keeping operations led by the North Atlantic Treaty Organization, the African Union, the Economic Community of West African States, and individual countries. Doyle and Sambanis (2000) make a distinction between traditional UN peace-keeping interventions that deploy military units and civilian officials in the target country to facilitate a negotiated peace and multi-dimensional peace-keeping operations which, in addition to traditional peace-keeping, involve economic reconstruction and institutional transformation (e.g., reform of the police, army, and judicial system; elections; and civil society rebuilding). They report correlational evidence that multi-dimensional peacekeeping operations are most successful in establishing peace in target countries with relatively high pre-intervention institutional capacities. The success of traditional peace-keeping, on the other hand, is more dependent on the scale of the intervention and on low hostility levels 73 McCormack and Pascoe (2017) make this argument for interstate wars; clearly, it also applies to civil wars.
74 Empirically, Cunningham (2016) proxies the rebels' expectations of a US intervention in a potential civil war by the country's place as a subordinate in the international security hierarchy relative to the USA (as measured by Lake's security hierarchy index (Lake 2013)). Using the natural log of the distance between each country's capital and Washington DC as an instrument for a country's place in the security hierarchy, he finds that countries in a more hierarchical relationship with the US are less likely to experience civil war. than on the target country's institutional capacities.
The primary challenge for empirical research on peace-keeping interventions is that they are not random. As pointed out by Gilligan and Sergenti (2008), there are three selection processes at play: where, when and why to intervene. This makes it hard to use standard tools to deal with selection, such as a Heckman selection model or an instrumental variable approach, and few studies rise to this serious empirical challenge. First, the countries that are targets for intervention are systematically selected on factors that also relate to the difficulty of maintaining internal peace. Fortna (2004), for example, finds that peace-keeping interventions are, typically, not targeted at conflict-prone countries with strong governments and armies. Rather, they are targeted at long-lasting conflicts with many casualties Elia 2011, Gilligan andStedman 2003). This tends to bias estimates of their success downwards, although Fortna (2004), after controlling for factors that might explain why a country was selected for a peace-keeping intervention, finds that post-conflict peace-keeping interventions help maintaining peace. Second, the timing of a peace-keeping intervention is important for its success. Gilligan and Sergenti (2008) study the success of UN peacekeeping interventions in post-Cold-War conflicts. Using a matching approach, they find that post-conflict peace-keeping interventions are effective in reducing the risk of conflict reoccurrence, while interventions in an ongoing civil war are ineffective. Third, foreign powers get involved in peace-keeping interventions for a variety of reasons. Security concerns is one important driver. Kathman and Melin (2016) find that deployment of troops to peacekeeping operations abroad can attenuate the risk of a coup d'état at home and shield domestic politics from interference by the country's own military. Pure economic interest is another important driver. Stojek and Tir (2015) report correlational evidence that conflict-prone countries that are economically more connected to the five permanent members of the UN security council are more likely to receive UN peace-keeping assistance. Interest in oil is another important driver for unilateral military interventions aimed at ending a civil war. Bove, Gleditsch, and Sekeris (2016) argue that an oil-importing foreign power's incentive to intervene to end a civil war in an oil-producing target country is stronger the higher the oil endowments of the target country and the bigger the foreign power's oil-dependency is.
They report correlational evidence that is consistent with this. 75 Another challenge for empirical research is that the effectiveness of a peace-keeping intervention depends on the willingness of the conflicting parties to cooperate with the peacekeepers. Using newly created event data on UN peace-keeping missions from 1989 to 2005, 75 The existence of oil fields can also cause conflict (Caselli, Morelli, and Rohner 2015). Ruggeri, Gizelis, and Dorussen (2013) report correlational evidence that the size of a peacekeeping operation and the distribution of military power between rebel and government forces are important for its success. Only relatively weak rebel groups that face a strong government and the prospect of a large-scale foreign intervention are willing to cooperate with UN peace-keepers. Dorussen and Gizelis (2013) point out that multi-dimensional peacekeeping interventions that involve state-building have significant effects on the distribution of power between rebels and the government. This creates uneven incentives for collaborating.
Empirically, they report that government authorities tend to respond more cooperatively to multi-dimensional UN peace-keeping operations than rebels. Moreover, policies aimed at strengthening state capacity tend to go uncontested, while policies related to human rights tend to be contested by all parties. In sum, it is clear from this discussion that further research on peace-keeping foreign interventions is needed and that researchers must find new ways to deal with the non-randomness of these interventions to make progress.

On the optimal choice of intervention strategy
The previously discussed research mostly focuses on one single intervention strategy in isolation. It develops theories of particular forms of foreign intervention, constructs empirical measurements, and provides evidence on the specific consequences and motivations. Clearly, these efforts constitute essential first steps towards understanding the role of foreign influence in shaping domestic policy.
However, a piecemeal approach is necessarily incomplete, primarily because the foreign power makes calculated choices about whether, where and how to intervene. To complete the picture, a general theory of foreign influence is needed. Our theoretical framework provides a starting point. By modeling the menu of possible intervention strategies within a unified framework, it becomes possible to study the welfare effects of the different strategies and thereby to address the questions of "when", "where" and "how" a foreign power seeks to influence a target country's policy. Furthermore, a better theoretical understanding of the intervention choice is essential to inform empirical strategies that can deal with the omnipresent selection problem.
Our framework highlights factors that are fundamental to understanding the foreign intervention choice. This include factors 1. Internal to the foreign power: Examples include the foreign power's ability to commit to international agreements, to impose sanctions, to grant rewards, or to use its military capacity to intervene in a conflict.
2. Internal to the target country: Examples include the target country's political system or the conflict technology of different social groups.
3. Specific to the bilateral relationship between the foreign power and the target country: Examples include the nature of the policy externalities and the degree of alignment between the interests of the foreign power and various social groups in the target country.
4. Related to the international system: Examples include frameworks for coordinating sanctions, international organizations as indirect channels of foreign influence, or the geopolitical situation.
Our model provides insights into the interplay between these factors and enables a systematic comparative analysis of the choice between the different intervention strategies from the perspective of the foreign power. For this purpose, we need to distinguish between the "no-intervention" status quo with and without ongoing conflict. The status quo without ongoing conflict, where the two countries independently decide their optimal policy (see section 5.2), is relevant for agreement, policy, regime and conflict-creating interventions. The status quo with ongoing conflict is relevant for conflict-intensifying and peace-keeping interventions, which can, therefore, only be compared to each other.

Interventions without ongoing conflict
In a target country without ongoing conflict, the intervention menu is agreement interventions (IA), strategic rewards (SR), strategic sanctions (SS), regime interventions (RI) and conflict-creating interventions (CCI). While the first three strategies aim at changing policy directly, the last two do so indirectly via an institutional change. We first compare the three strategies that directly aim at influencing policy.

The choice among strategy IA, SR and SS
Strategic rewards (SR) and sanctions (SS) can induce policy outcomes that the target country would never accept under a voluntary agreement since they give the target country a policy-related pay-off that is less that W D (U ) (see Figure 4). In terms of implementation The optimal choices are labeled and highlighted with separate patterns. The lines indicates combinations of parameter values for which the foreign power is indifferent between two strategies. Panel A ranks intervention strategies IA, SS and SR in (q SS , q IA ) space. Panel B shows how this ranking is affected by a reduction in η SS -the (inverse) transaction cost associated with strategic sanctions. Panel C assumes that IA, SS and SR are fully credible (q SS = q SR = q IA = 1) and compares the best of these, which is SS, to the regime intervention strategy RI and the conflict-creating strategy CCI for different combinations ofβ and . Panel D ranks intervention strategies CII and P KI in (p, ) space. The dotted line indicates the combinations of p and such that group 1 wins the conflict for sure, and only combinations below this line are feasible. The panel is drawn under the assumptions (i) that group 1 starts a conflict in the absence of foreign intervention and (ii) that the peace dividend b is such that if the foreign power decides to intervene, then it will be sufficient to make the two parties stop fighting. The online appendix contains the mathematical analysis underlying the graphical illustration. The relative merit of the three strategies depends critically on their credibility (i.e., on q IA , q SS , and q SR ) and on how much sanctions hurt (η SS ). The latter depends both on 76 While all three strategies are available to state actors, non-state actors can neither enter international agreements nor impose sanctions against other countries (although they can put pressure on their own governments to do so or engage in consumer boycotts). factors specific to the relationship between the target country and the foreign power (e.g., the economic and geopolitical importance of the target country), and to the configuration of the international system, which influences the ease of imposing and avoiding sanctions.
The credibility of the three strategies is also affected by politics in the foreign power. If, for example, government turnover in the foreign power is frequent and there is no consensus about the appropriate intervention strategy, then all three strategies lack credibility. For these reasons, their relative credibility vary systematically with circumstances. Panel A of Figure 5 illustrates the trade off between the three strategies as a function of q SS and q IA for fixed values of q SR and η SS . The black vertical (horizontal) line defines the critical valuê q SS (q IA ) for the foreign power to be indifferent between strategies SS and SR (SR and IA), respectively. The upward sloping line defines the combinations of q SS and q IA for which strategy SS and IA are equivalent. Strategy IA is "best" in the region with high q IA and low q SS . A less than fully credible sanction strategy may dominate a fully credible international bilateral agreement for low transaction cost (η SS close to 1) because a sanction threat can induce a policy outcome that is impossible under a voluntary agreement. Strategy SS is generally dominant when sanctions are credible (q SS is high), while strategy SR, which is costly to implement as the "reward" must be paid, is preferred for low values of q SS and q IA .
Panel B illustrates what happens if the transaction cost associated with the sanction strategy goes up (η SS falls), reflecting, for example, a situation where the international support for a sanction breaks down. Unsurprisingly, this reduces the appeal of strategy SS.
For high values of q IA , strategy IA dominates strategy SS for a wider range of q SS , while strategy SR dominates for a wider range of q SS for low values of q IA .
In sum, the foreign power's optimal choice among these three policy intervention strategies depends critically on their relative credibility and on the "pain" sanctions inflict on the target country. If it is "easy" for the target country to avoid the economic and social consequences of sanctions, then sanctions are less likely to be chosen even if they are fully credible. However, a foreign power with regular government turnover and polarized views on the merits of bilateral agreements or aid-for-policy deals will either not try to influence policy in the target country at all or do so via sanctions (if there is consensus to carry through with them).

The choice between strategy RI, CCI and "best" policy intervention
We now turn to the choice among regime interventions (RI), conflict-creating interventions (CCI) and policy interventions. To limit the number of strategies to be compared, we focus on the case where strategic sanctions are the "best" policy intervention. This would be the case for sure if sanction, reward and agreement interventions all were fully credible, and sanctions had the maximum impact on the target country (η SS = 1).
Panel C of Figure 5  The optimal policy intervention (SS) dominates both the regime and the conflict-creating intervention in situations where a regime intervention cannot induce a substantive institutional change in the target country (β <β c ) and the foreign power's conflict intervention capacity is low ( <˜ ). Regime interventions become optimal when the foreign power can increase the political power of group 1 substantially. This case is represented by the area labeled RI. This area expands if the cost of the intervention (I F ) falls. On the other hand, conflict-creating interventions are optimal when the foreign power's conflict intervention capacity is high, as indicated by the area labeled CCI which increases in p. Therefore, conflict-creating interventions are more likely to be preferred if the aligned group in the target country has a sufficiently high probability of winning the conflict on its own. Sanctions are the optimal choice when the foreign power neither has the power to instigate major institutional changes, nor the capacity to trigger a conflict.

Interventions into an ongoing conflict
If there is an ongoing conflict in the target country, the foreign power faces a choice between two intervention strategies. It can either intensify the conflict (CII) by actively supporting the aligned group in the conflict through, for example, active military or logistic involvement, aid or sanctions aimed at harming the unaligned group, or it can try to restore peace (P KI). The latter results in a compromise between the warring parties and, typically, requires international coordination and peace-keepers on the ground.
The two most important considerations shaping the intervention choice are (i) group 1's 77 We focus on major regime interventions and draw the diagram under the assumption that β = β so that a costly minor intervention is never better than no intervention.
78 Panel C is drawn under the assumption that the conflict intervention capacity that is necessary for group pre-intervention fighting capacity p and (ii) the foreign power's conflict intervention capacity ( ). The trade-off is illustrated in Figure 5, panel D. The vertical (blue) line displays the critical valuep for which the foreign power is indifferent between strategy P KI and an ongoing conflict (no intervention). A peace-keeping intervention is better than ongoing conflict when group 1's pre-intervention fighting capacity p is too low. The horizontal (red) line indicates the critical valueˆ at which the foreign power is indifferent between CII and no intervention in the ongoing conflict. This does not depend on p and the conflict-intensifying intervention is better than no intervention when the foreign power has the capacity to increase the win probability of group 1 considerably, i.e., when is larger than the critical value¯ (p)).
Finally, the downward sloping (green) line represents combinations of p and at which the foreign power is indifferent between a conflict-intensifying and a peace-keeping intervention.
The negative trade-off is due to the fact that neither p nor affects the payoff associated with a peace-keeping intervention, while both factors increase the payoff to a conflict-intensifying intervention.
Combining the previous observations, it becomes clear that the foreign power will not intervene in a conflict in which group 1 is likely to win irrespectively of the intervention, and in cases where its capacity to enhance group 1's war effort is limited (the area marked No).
A peace-keeping intervention is optimal when group 1 is unlikely to win the ongoing conflict (p <p) and the foreign power's conflict intervention capacity is low ( <¯ (p)). This case emerges in the area marked P KI. A reduction in the "peace dividend" required to stop the conflict (b) makes the peace-keeping intervention more appealing and expands area P KI.
An increase in the cost of the conflict c has a similar effect. The downside to peace-keeping interventions is that they provide a public good and, therefore, may be undermined by freerider incentives (Sandler 2017). Finally, the conflict-intensifying intervention is optimal if the foreign power has the capacity to enhance group 1's fighting capacity sufficiently, i.e., for p and in the area marked CII. A decrease in the direct conflict intervention cost (c F ) expands this area.

Conclusion
The principle of sovereignty is a cornerstone of modern international law and stipulates that states have supreme authority within their territories. Foreign interventions often constitute a violation of this principle. The violation is clearest if the intervention involves coercion and is minor in case of a voluntary exchange between the foreign power and the target country.
Transnational externalities are the key motivator of foreign influence: the policy choice in the target country, broadly interpreted to include economic and geopolitical effects, has consequences for the foreign power (and vice versa). Foreign influence seeks to internalize this externality, but in a way that reflects asymmetries in the power relations between the intervening foreign power and the target country.
We categorize foreign interventions into three types: agreement, policy, and institution interventions. We sketch a unifying theoretical framework within which these strategies can be compared. Agreement interventions (e.g., bilateral trade agreements) are voluntary, but require that the foreign power can dictate the terms of the agreement and that both parties can commit to respect them. Policy interventions take two forms. They either reward the target country for a policy change or sanction it. The reward strategy is not only used by foreign governments (e.g., via policy-for-aid deals), but also by non-state actors (e.g., foreign corporations that lobby abroad). Sanctions are primarily a tool available to state actors.
From the point of view of the foreign power, sanctions have an advantage over rewards, which are costly, inasmuch as the threat of a sanction can be enough to induce the desired policy change. However, the threat may not work and, if imposed, sanctions are costly to all parties. In general, the success of these policy intervention strategies depend on their credibility.
In practice, that is a major issue. The institution intervention strategy, which aims at changing the structures that govern policy-making in the target country, is one mechanism through which the foreign power can partly avoid this credibility problem; a change in "the rules of the game" is more durable than a policy concession that the next government can repeal. Institution interventions can sometimes achieve their objective without a costly civil war. In other cases, the foreign power either initiates or takes sides in an ongoing conflict.
Another possibility is to support efforts to stop an ongoing civil war. All these intervention strategies are associated with different costs and benefits. Conflict is costly to all parties, including to the intervening foreign power. Such costs can be avoided through a "clinical" regime intervention (e.g., a coup d'état). Whether the foreign power wants to intervene in a conflict by intensifying it or trying to end it depends, amongst other things, on how expensive it is to "buy" peace, on the underlying military strength of the group supported by the foreign power, or on the cost of intervening in the conflict.
Three general messages emerge from our survey of the literature. First, research in economics, international relations, and political science make it clear that foreign influence is the bread-and-butter of international relations. As shown in Section 2, foreign interven-tions take place more frequently than is usually acknowledged outside the particular areas of research. This has wide-ranging implications, not only for the understanding of the interactions between countries, but also for academic investigations into the determinants of policy, institutional reform, and conflict. Foreign influence matters for all of these. An implication, for example, is that it can be misleading to use cross-country comparisons to study the determinants of trade (as in a gravity model), or policy (as in an event-study of tax policy), or institutions (as in a panel study of the origins of democracy) without taking into account that these outcomes are partly the result of foreign influence.
Second, our theoretical framework emphasizes that the decision to intervene abroad is a choice made by the foreign power and based on a cost-benefit analysis of the different intervention strategies. The foreign power selects the intervention strategy that best fits its specific objectives and the context of the target country. Research that concentrates on one particular intervention strategy can, therefore, never fully reveal the true causes and consequences. The implied selection problem becomes obvious once it is recognized that each particular intervention strategy was chosen from a set of possible strategies and for a reason.
Third, foreign interventions can have far-reaching consequences that go beyond the policy externality they narrowly aim at internalizing. The literature has not developed effective tools to establish which of these consequences are intended and taken into account in the cost-benefit analysis when the intervention is decided and which are unintended. This is especially problematic for empirical research since intended consequences that are treated as unintended undermine attempts at causal identification. It also constitutes a major problem for welfare analysis of foreign influence, as different forms of intervention have different welfare effects in the target country and in the world (e.g., Antràs andPadró i Miquel 2011, Aidt andHwang 2014). More work on this topic is urgently required.
While this survey brings together research from across the social sciences on foreign influence on policies, institutions and conflict, many questions remain unanswered. We already pointed to specific challenges for research on particular intervention strategies. Here, we want to discuss five more general challenges for future research: how to overcome (i) the compartmentalization of the theoretical literature and (ii) data limitations; (iii) how to study interventions as a network phenomenon; (iv) how to gain a better understanding of the unintended consequences of foreign influence; and (v) how to engage with foreign influence in cyberspace.
The theoretical literature on foreign intervention is compartmentalized. The many stud-ies of foreign intervention -bilateral international agreements, conditional aid, sanctions, foreign-sponsored coups, or foreign involvement in conflict and peacekeeping -focus narrowly on one particular intervention strategy. As a consequence, they do not recognize that the foreign power behind the intervention could have chosen a different intervention strategy or that several strategies may complement each other and would, therefore, be used simultaneously. An important task for future theoretical research is to develop models that take the polymorphic nature of foreign influence seriously. We have developed a framework that is one step in that direction. The comparative statics analysis in Section 9 shows how changes in the fundamental parameters of the domestic and international environment affect a foreign power's optimal intervention choice. These theoretical insights can, in turn, provide a narrative for understanding the observed trends in intervention choices and for deriving testable implications. For example, as discussed in Section 2, sanctions and open military interventions became more common after 1990. Arguably, these changes were related to the USA reinforcing its hegemonic power in the aftermath of the fall of the USSR. Viewed through the lens of our model, the emergence of a single superpower facilitated international cooperation and increased the USA's relative military power, which, in turn, enhanced the credibility of sanctions and made direct military intervention in foreign conflicts less costly.
Insofar as the emergence of Russia and China as influential international powers challenges the USA's hegemonic power, the model framework predicts that new combinations of foreign intervention strategies will emerge. These speculations, based on a simple model and highly imperfect data, are far from well-established facts or solid predictions. Nevertheless, they illustrate the benefits of studying the inter-dependencies among the different forms of foreign intervention within a unifying framework, and they frame many new questions for research.
Empirical research in the area of foreign influence is seriously hampered by data limitations. One problem is that some forms of foreign influence cannot be observed directly or only many years later when classified documents become declassified. Another is that some forms, such as sanctions, work through threats, which are difficult to quantify. One way around this data problem is to track the effect of foreign intervention on specific outcomes in the target country from observed variation in the causes driving the intervention. This requires a fully articulated theory of what causes a foreign power to intervene from which a credible identification strategy can be developed. Albornoz and Hauk (2014), for example, propose a theory that shows that the approval rating of the government in the foreign power is a fundamental determinant of its incentive to intervene in conflicts abroad. Based on this theory, it is possible to empirically study the effect of foreign intervention on civil war by linking observed variation in conflict to observed variation in the approval rating of the foreign power's government. 79 Another way to address the data challenge is to collect and record better and more accurate data. In recent years, a lot of progress has been made in this regard. Here, we highlight a few examples. More detailed data on aid and aid conditionality have become available (Kentikelenis, Stubbs, and King 2016) along with data on aid from new donor countries such as China (Strange, Dreher, Fuchs, Parks, and Tierney 2017). Sanction threats have been codified in the Threat of Imposition and Economic Sanctions (TIES) dataset Krustev 2009, Morgan, Bapat, andKobayashi 2014 One of the limitations of our unifying model of foreign influence is that it portraits a bilateral relation between one foreign power and one target country or a situation with many foreign powers that fully coordinate their interventions. In practice, however, many foreign interventions are not coordinated and are, instead, the result of competition between many foreign powers with different objectives and goals. Clearly, more research on multilateral interventions is needed. Foreign influence is a network phenomenon and many of the theoretical advances in network economics could fruitfully be applied to the study of foreign 79 Nunn and Qian (2014) and Martínez (2017) adopt similar identification strategies. 80 See, e.g., Berger, Corvalan, Easterly, and Satyanath (2013). 81 For example, in the Congo people can report conflict events via SMS in real time (Van der Windt and Humphreys 2016). 82 This has been used to study conflict onset (Chadefaux 2014, Mueller andRauh 2018) and conflict duration (Ward, Metternich, Dor, Gallop, Hollenbach, Schultz, and Weschle 2013), and to define conflict events (Brandt, Freeman, and Schrodt 2011). influence in general and to the study of unintended third-party spillovers in particular. 83 The empirical literature on foreign influence shows that foreign interventions have farreaching consequences, many of which, arguably, are "unintended". Theoretical models, including ours, assume that the consequences are fully understood (at least in expected terms) by the parties involved. However, it is an open question how far politicians really go in their reasoning when deciding on a foreign intervention. Do they, for example, take into account that offering a trade-for-policy deal will affect their own chance of staying in power?
New technologies, especially related to the internet, have increased the urgency of finding answers to this question. It is becoming more and more common for politicians, who are expected to react quickly to emerging issues, including policies with negative externalities implemented by other countries, to use Twitter to communicate with the general public.
These immediate reactions are unlikely to reflect careful consideration of all consequences.
Moreover, how does this new possibility for "cheap talk" affect the credibility of foreign interventions announced this way? Does it only affect the personal credibility of the politician who tweets or does it also affect the credibility of the country he or she represents? These are important questions for future research.
Along with the spread of the internet and various social media, new forms of foreign influence have emerged. Martin, Shapiro, and Nedashkovskaya (2019) identify 53 cases, involving Russia, China, Iran and Saudi Arabia, of online foreign influence activities directed at 24 countries between 2013 and 2018. This takes place through multiple social media platforms (e.g., Facebook, Twitter, and Instagram) and targets elections, the political agenda, people's opinions, etc. This raises many important research questions. We highlight three: meddling in elections, spreading false news, and cyber warfare. First, the internet provides a new avenue for meddling in elections abroad. One concern is that hackers might modify election registers or election results directly. Another is that foreign agents may use the internet and social media more generally as a tool to persuade voters in other countries to vote in a particular way by, for example, posting positive information about one candidate and negative information about a rival or by persuading specific groups of voters to abstain. This type of foreign intervention is likely to become increasingly important and there is suggestive evidence that the aggressive use of Twitter bots, coupled with the fragmentation of social media and the role of sentiments, could have contributed to the outcome of the 2016 Brexit referendum in the UK and to Donald Trump's election as US president (Gorodnichenko, Pham, and Talavera 2018). Clearly, more research is required in this field. Second, it is very easy to spread false information on the internet. Agents who stand to gain from a foreign intervention could use this strategy to provoke one. A "false news war" can also be used to alter the bargaining power between the intervening foreign power and the target country or between groups in the target country. Such shifts can have far-reaching consequences and trigger interventions that would not otherwise have taken place. Third, cyber attacks, like the one by Russian hackers on Ukraine's power grid in December 2015 (Kostyuk and Zhukov 2019) is a new form of foreign intervention. Cyber attacks need not be large-scale and "low-intensity" operations are probably far more numerous than recognized. Empirically, little is known about cyber warfare, but there is a small emerging literature. Kostyuk and Zhukov (2019), for example, find that cyber attacks related to the conflicts in Ukraine and Syria did not affect battle field outcomes because they were not sufficiently coordinated.
Obviously, this might change in the future and the importance of cyber warfare is likely to rise. Unlike many of the traditional interventions strategies, cyber attacks can be used both by state and non-state actors with the right skills. An implication of this is that new players with motives which are not necessarily anchored in conventional transnational policy externalities can enter the stage. Moreover, simultaneous interventions by state and non-state actors may occur, making it difficult to establish who is responsible. This hinders deterrence and may create strategic complementarities among those who seek foreign infouence leading to more aggressive attacks (Baliga, Bueno de Mesquita, and Wolitzky 2019). Clearly, the emergence of cyber warfare poses new theoretical and empirical challenges to research on foreign influence.