International Systems and Domestic Politics: LinkingComplex Theories with Empirical Models in International

Relations

Stephen Chaudoin, Helen V. Milner, Xun Pang∗

February 6, 2012

Abstract

Outcomes of interest to IR scholars are the product of complex relationships. Domesticand international variables influence the outcome of interest, as well as each other. Outcomesfor one unit in the international system influence outcomes in other units. As their theorieshave become more complex, IR scholars face a potentially daunting task of choose from awide range of empirical models (“regular,” hierarchical, spatial, etc.) to account for the com-plexity being considered. We provide a road map for navigating this choice. We outline anextensive set of theoretical interactions often considered in IR, and then describe the processof choosing the best empirical model for that theory. Just as theorists face a parsimony vs.complexity tradeoff, empiricists face a tradeoff between the desire for generality, i.e. empiri-cal models that do not make restrictive assumptions about the data-generating process, andthe additional complexity and data requirements that accompany more general models. Weshow the assumptions entailed in each approach and ways to adjudicate between models.Additionally, we develop an empirical model that advances current spatial econometric ap-proaches. Our model allows for the estimation of a time-varying connectivity parameter in ahierarchical structure. This not only allows us to describe how the level of interdependenceamong units has evolved over time, but also considers two complex types of interaction atthe same time. We demonstrate the usefulness of our road map and new model, by revisitingthe recent IPE debate between Milner and Kubota (2005) and Oatley (2011) over the rela-tionship between trade policy and regime type for LDC’s. Contrary to Oatley’s suggestionthat IR scholars de-emphasize the search for law-like empirical regularities, we show that awealth of empirical models exist that, when applied correctly, can elucidate even the mostcomplicated relationships.

1 Introduction

International relations scholars have long debated the relative importance of systemic versus do-mestic influences in world politics. Waltz (1979) and Jervis (1997), for example, clearly givepriority to the international system. Others like Moravcsik (1997); Milner (1997) and much of theliterature on the democratic peace (Doyle, 1986; Oneal and Russet, 1997; Reiter and Stam III,

∗[thanks]

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1998; Small and Singer, 1976) prioritize domestic factors, like the preferences of political actorsor the structure of political institutions. Most scholars, however, agree that the phenomena ofinterest in international relations are often outcomes resulting from complex interactions betweendomestic and systemic factors. As Gourevitch (1978, p.882) claimed over thirty years ago, “Weall know about interaction; we all understand that international politics and domestic structuresaffect each other.”

The increasing globalization of the world economy has led scholars to posit more complex theo-retical relationships between domestic and systemic variables. The goal of this paper is categorizethe potential relationships between domestic and systemic factors and then provide researcherswith a road map linking these different theoretical relationships with the appropriate empiricalapproaches. We explore five possible sets of interactions between systemic and domestic variables.We discuss each type of interaction and connect each with a set of empirical models designed tocapture that particular relationship. For a researcher who has developed a complex theory, choos-ing the appropriate empirical model can be a daunting task. We aim to clarify the theoreticalinteractions possible between systemic and domestic forces and to provide practical guidance onthe question of empirical strategies for assessing these relationships.

These contributions are especially important in light of a recent and sweeping critique ofexisting work in international political economy (IPE). Thomas Oatley (2011) argues that theliterature frequently ignores how international and domestic factors interrelate, instead engagingin a “reductionist gamble” that focuses on domestic variables to the exclusion of systemic ones.Given globalization and the other forces that make the world complex, this focus, he contends,is more misleading than ever. As a result of their gamble, researchers employing reductionistapproaches have often generated incorrect inferences. This challenge is potentially very serious.Oatley limits his analysis to IPE, concluding that significant errors have been made in each ofIPE’s core issue areas (p.334). Put simply, by using empirical models that oversimplify the complexrelationships present in IR, IPE scholars have come up with the wrong answers to the questionsthey have asked.

Oatley casts the challenge facing IR researchers as a stark choice: given the inherent complexityof the international system, researchers can continue to engage in a reductionist, quantitativesearch for law-like empirical regularities, or researchers can adopt a problem-based approach that“recognizes that the phenomena scholars study emerge from the complex interaction between themicro and the macro.” Oatley emphasizes the latter, arguing that we should “[strive to produce]useful knowledge rather than to identify law-like relationships” (p.335). Oatley concludes with acall for “a common overarching framework, [that] would substantially advance our understandingof how the interaction between domestic politics and macro processes shapes developments in theglobal political economy” (p.336).

Our paper does exactly that. However, we depart with Oatley on one major issue: quan-titative analysis and the search for empirical regularities are not hindrances to specifying andunderstanding complex relationships between international and domestic variables. Rather, awealth of empirical models exist that can elucidate even the most complicated IR relationships.With precisely theorized relationships between systemic and domestic factors and with properattention to choosing the appropriate empirical model, researchers need not despair in the face ofIR’s complexity.

We illustrate our argument by revisiting a recent debate and one that Oatley argues hasbeen incorrectly assessed by reductionist methods: the relationship between regime type and

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trade policy. A number of scholars have focused on the relationship between democracy andglobalization, especially the link to trade.1 Milner and Kubota (2005), in particular, arguedthat increased democratization among LDC’s caused those countries to lower their trade barriers.Democratization empowered workers in these labor-rich countries, curtailing the ability of capitalowners to use their political power to erect protectionist barriers. Oatley claims this relationshipis misspecified and that once the moderating effect of the global trading system, especially theGATT/WTO, is taken into account this relationship disappears. We use this debate to explore thefive different types of systemic-domestic interactions, demonstrating how these potential systemic-domestic relationships might theoretically operate in the context of regime type and trade policy,and then apply the appropriate empirical model to examine those relationships. The finding thatdemocracy is associated with lower tariffs is not an artifact of a reductionist approach. Rather, weshow that this relationship is robust to a broad array of potential interactions between systemicand domestic factors.

In demonstrating our guide in a substantive context, we also advance the frontier of empiricalmodeling in IR. We demonstrate how multilevel modeling is an under-utilized tool in IR that canaddress many of the complexities that IR scholars are interested in. We also advance empiricalmethods for modeling spatial interdependence by showing how interdependencies can change overtime. Additionally, we show how these two methods can be combined to model even the mostcomplex IR relationships.

In the sections that follow, we first provide a categorization of the different relationships be-tween systemic and domestic factors that arise in IR. We classify each relationship into one offive categories: independence, direct system effects, indirect system effects, moderation, and in-terdependence. We show examples of each from existing literature and discuss how the theoreticalmodels in IR have evolved over time. In section 3, we describe the appropriate empirical modelfor each of these relationships and demonstrate their implementation in the context of the debateabout democracy and trade liberalization. Section 4 concludes.

2 Categorizing Theoretical Interactions

International relations often are characterized as a set of units–often states–interacting in a par-ticular system. Systems theorists highlight the homogeneity of these units, while those focused ondomestic politics underline their heterogeneity.2 We will describe possible relationships betweenthree types of variables: domestic, systemic, and outcome variables. The outcome variable is theoutcome of interest to the researcher. We refer to variables representing the outcome of interestas Yit, with potential subscripts for a particular unit, i and time period t. In IPE, the outcome ofinterest is often the particular policy or economic conditions of a particular country at a particu-lar time. Did country i have a fixed or floating exchange rate in year t? Did country i in year texperience a banking sector crisis? How high were country i’s import tariffs in year t?

International relations is often concerned with the effects of two types of explanatory variables,domestic and systemic, on the outcome of interest. Domestic variables describe a property orattribute of the unit (Waltz, 1979, p.39). These variables tend to vary both across countries and

1See: (Milner and Kubota, 2005; Milner and Mukherjee, 2009; Eichengreen and Leblang, 2008; Adsera and Boix,2002; Ahlquist and Wibbels, 2012).

2In international relations, despite repeated calls for the inclusion of other units, states remain the frequentfocus of attention. For simplicity, we will refer to “states” and “units” interchangeably from here forward.

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over time, though some country-specific characteristics may change slowly or invariant for quitea long time. The most popular example of a domestic variable is a state’s regime type or level ofdemocracy. We denote domestic variables as Dit.

In contrast, systemic variables describe features of the world or the international system thatapply to all units, not just one particular unit. Systemic variables characterize the entire systemand are not dependent on a particular state’s characteristics. They describe the context in whichstates operate. They may be aggregations of many states’ characteristics or a result of states’behaviors and interactions, but they must describe the system as a whole and not its componentparts.3 They tend to vary over time, often very slowly however, and they do not vary acrosscountries at any one point in time. Technological advances are one example, since once a tech-nology has been discovered, it cannot be un-discovered. The advent of cheaper shipping methodsirrevocably changed the environment in which countries exchanged goods. While the impact ofthis change may differ across countries–e.g., some countries may be better able to take advantageof new shipping methods–every country now inhibits a world with different shipping methods thanin previous years.

Systemic variables can also describe the distribution of other variables, like military power,amongst nations. For instance, classifications of the polarity of the system, e.g., unipolar, bipolar,multipolar, are systemic factors that are emphasized in the Realist tradition. In order to evaluatethe effect of an independent variable on a dependent variable, the independent variable mustactually vary. Systemic factors, by definition, cannot vary cross-nationally, and can only varytemporally. For any single time interval, the researcher can only observe one system, and thatsystem is the same for each of the countries inhabiting it. It may have different effects on differentstates but it is a single system. We denote systemic variables as St.

2.1 The Evolution of IR Theory on the Interaction of Domestic andInternational Factors

What types of theories have IR scholars developed to link systemic and domestic variables withoutcomes of interest? In the 1970s and early 1980s, IR theory emphasized systemic factors heav-ily. In Waltz’s theory of IR, the most important explanatory variables to consider were systemic.This stemmed logically from his assumption that units within the system can safely be treatedas homogeneous: if there is no variation across units (i.e., states), then they could be ignored forthe purposes of explaining variation in the outcomes of interest. The Realist tradition4 empha-

3As Fearon (1998) notes, this distinction between system and unit-level variables is not always an easy orconsensual one. Fearon further distinguishes two meanings, one minimalist and one maximalist, of system-levelfactors and two corresponding ones for unit-level. A minimalist definition of systemic variables implies any factorthat describes a system where unitary, purposive states are interacting and choosing actions based on their beliefsabout what other states will do. This focuses attention on the strategic interaction among states. A second, moremaximalist and restrictive definition of systemic variables is more similar to Waltz’s definition. In this case, a factoris systemic only if it does not include any information about characteristics of individual states. Corresponding tothe first definition of systemic variables is a minimalist definition of unit-level variables; here they must imply thatat least one state in the system acts in a non-unitary way and that this produces behavior that is different from(usually worse than) what would happen if it were unitary. Corresponding to the second definition of systemic, adomestic factor may be must more broadly construed as any variable that does not describe the system; hence anyinteraction among states, except perhaps the balance of capabilities, is not systemic.

4Of course, there is no single Realist tradition. We simplify broad approaches here to demonstrate how Oatley’sargument views the progression of IR research, and to contrast it with how we view IR research.

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sizes systemic variables like polarity: whether the system is unipolar, bipolar, or multipolar. In aunipolar system, every country inhabits a world in which the distribution of military capabilitiesis concentrated in one country, compared to bipolar or multipolar systems where the distributionof power is more dispersed. The polarity of the system affects important variables of interest,like whether countries will choose to balance against a hegemon. In IPE, arguments like hege-monic stability theory (Keohane, 1980; Krasner, 1976; Kindleberger, 1981; Lake, 1988)emphasizedthe importance of systemic variables: the stability brought on by unipolarity facilitated greatereconomic openness and international trade.

As the pendulum swung away from a Realist focus on systemic variables in the 1980s and1990s, IR scholars began to explore the role of domestic variables in several ways. Some scholarsemphasized the “second image reversed” concept (Gourevitch, 1978). This concept argued thatsystemic variables affect domestic variables, which in turn, can affect the outcome of interest.Another strand of research, Liberalism, built off of (and even more frequently criticized) the Realistmodel. Liberalism as a general theory for IR emphasized domestic variables like the preferences ofsubnational actors and the institutions within which they influenced political behavior (Moravcsik,1997). Other scholars emphasized domestic politics as a way to provide “micro-foundations” forthe assumptions made in earlier research (Oatley, 2011, pp. 312).

According to Oatley, the pendulum has now swung too far in the domestic direction to the ex-clusion of systemic variables and has developed into a reductionist approach that ignores importantand complex roles for systemic variables. The reductionist approach ignores “macro processes”like international bargaining, coercion, contagion, network externalities, and diffusion. Surveying102 articles from International Organization and the American Political Science Review, Oatleydetermines that more than three quarters of these articles “study domestic politics in isolationfrom international politics” (p.314).

He claims that this oversimplification of the complex processes that generate outcomes of in-terest resulted in incorrect inferences about the effects of domestic variables on outcome variables:“The neglect of macro processes generates biased inferences about the domestic political relation-ships under investigation” (p.319). IR scholars gambled on reductionism as an appropriate wayto model the world, and all too often, they lost.

2.2 What Has Happened

What has happened (and continues to happen) is very different from the reductionist approachthat Oatley criticizes. As IR scholars began to focus less on the appropriate “-ism” to describephenomena of interest, they began to develop and analyze theories that were tailored to theirparticular area of inquiry. The emphasis was less on finding a particular mapping of systemic anddomestic variables that explained many phenomena, but rather on developing nuanced theoriesthat best explained important outcomes. Research became in a sense more problem driven: whyare countries around the world liberalizing their trade? Why are countries adopting independentcentral banks? Why do some countries develop when others do not? Why do some countriesexperience financial and/or exchange rate crises? Why are some regions and countries morepeaceful than others?

In reality, very little contemporary IR work is reductionist in the way that Oatley describes.The degree of emphasis on systemic factors and the way that they are integrated into IR scholarshipvaries, but very rarely do IR scholars focus exclusively on the effects of domestic variables. Weresurveyed the articles mentioned by Oatley and found that the majority of IPE research did not

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consider domestic effects independently of systemic effects. Of the 34 articles we resurveyed, 56%(19) explicitly linked their domestic variables with a theory of international politics.5

Even among the remaining articles that Oatley labels reductionist, many analyses examinedone country in one particular time period, thus making systemic effects impossible to assess.Since systemic variables cannot vary when considering one country-year, it is impossible in sucha research design to assess their impact. For instance, Alt et al. (1999), which is one of thearticles Oatley calls out as reductionist, survey Norwegian firms that are under pressure frominternational competition and find that firms with high asset specificity lobby harder than firmswith mobile assets. Apart from the fact that this article’s premise explicitly considers the role ofinternational competition, the argument is only about Norwegian firms’ activity in a narrow timeperiod (∼1988), so explicit incorporation of systemic effects would have been difficult since thesystem was constant during the window of their analysis. Since the system did not vary, it wouldnot have been possible to assess its effects.

IR research incorporates a wide range of possible relationships between domestic, systemic,and outcome variables. Some research considers the effects of domestic or systemic variables inisolation. Some research considers them jointly. Other research considers complicated relationshipsbetween systemic and domestic factors to explain outcomes. Virtually all of this research falls intoone of five categories of relationships: independence, direct system effects, indirect system effects,moderation, and interdependence. We illustrate each of these categories and describe examplesfrom existing literature.

2.2.1 Independence

Some IR research considers the effects of domestic variables independently from any effects ofsystemic variables. This is the canonical reductionist approach that Oatley describes and isdepicted in Figure 1. These theories link domestic variables with outcomes of interest and donot capture any role for systemic variables. For example, the argument in Leblang and Bernhard(2000) focuses on domestic variables. When government cabinets are likely to dissolve and whenthe new government is likely to be more Liberal, the probability of speculative attacks is higher(pp 293). Their theoretical and empirical focus is on two domestic explanatory variables: cabinetdissolution and the likely direction of party change.6 That this approach is focused on domesticvariables independent of systemic variables is not a criticism. In fact, we will show below howthis approach is perfectly appropriate in many instances. It is simply one way to think about howdomestic and systemic variables do (or in this case, do not) interrelate to produce outcomes ofinterest.

2.2.2 Direct Systemic Effects

Many arguments in IR explicitly consider the direct effects of systemic variables on the outcomeof interest. These arguments theorize about the potential impact of systemic variables on the

5We asked him for his data and got no response, so we surveyed the articles that he mentions in footnotes 14-18,which are a list of articles that he thinks consider the impact of domestic variables on domestic outcomes. Weexcluded one article from his list because it was only about theory, and not empirics, so Oatley’s argument did notapply here.

6Note that even this argument is not completely reductionist. Leblang and Bernhard (2000) include controlvariables that measure whether or not an observation occurred during the European Monetary System, which is asystemic variable. We were hard pressed to find any arguments that were one hundred percent reductionist.

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Figure 1: “Reductionist” Model

D Y

outcome of interest, and they include systemic variables in their empirical analysis, as depicted inFigure 2. But the system in this case has only a direct effect on the outcome and does not affectdomestic politics otherwise. Many of the articles that Oatley alleges to be reductionist fall intothis category; they include discussions of international politics in their theoretical arguments andsystemic variables in their empirical analysis. But these international factors are seen as havingtheir only impact directly on the outcome.

Figure 2: Direct System Effects

D SY

Lawrence Broz (1999)’s article explaining the U.S. Federal Reserve system is one example.The theoretical and empirical arguments are explicitly about a direct role for systemic variables.According to Broz, “students of the Federal Reserve have not paid sufficient attention to interna-tional factors” (pp. 40). A key component of the creation of the Federal Reserve Bank was thedesire of the New York financial elite to have the U.S. dollar achieve international currency status.This desire was not driven by some innate domestic preference of New York bankers for the dollarto hold international currency status, but rather because of the advantages that internationalcurrency status would afford them given the complex international financial interactions takingplace at the time.7

Other arguments that are more heavily focused on cross-national empirical analysis includesystemic variables to account for their direct effects. For example, Li and Resnick (2003)’s em-pirical analysis of FDI inflows incorporates a systemic variable, the amount of world FDI inflowsfor a particular year, that they consider theoretically important. Still other articles incorporatesystemic effects, even though they do not discuss them in theoretical terms. Many articles usecontrols for unobserved system-wide heterogeneity that varies across years but are common to eachcountry–e.g., year fixed effects, such as those used by Bearce (2003). This empirical approach isdesigned to exploit within-year, i.e. within system, variation to make arguments about the ef-fects of domestic variables. Even though this approach may not be accompanied by a theoreticaldiscussion of system effects, it is designed to account for concerns about omitting direct systemiceffects.

All three of these articles are named by Oatley as being reductionist. According to our catego-rization, these articles are not reductionist; they consider direct system effects in different ways.Oatley’s inclusion of Li and Resnick (2003) on the list of reductionist articles is particularly puz-zling since their approach (including systemic variables in a regression) is the exact approach thatOatley criticizes Leblang and Bernhard (2000) for not using. Oatley argues that Leblang andBernhard’s omission of a key systemic variable–the worldwide occurrence of speculative attacks-

7For other works that emphasize systemic factors in the context of international finance, see: (Frieden, 1991;Andrews, 1994).

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biases their findings. The point is that inclusion of systemic variables, including year fixed effects,in empirical models implies that the scholar believes systemic factors may have an important,direct effect on the outcome. According to our categorization of the recent literature, most schol-ars in IPE include such systemic factors and hence are not assuming that domestic forces alonecondition outcomes.

2.2.3 Indirect System Effects

Other IR research considers indirect system effects, as depicted in Figure 3. In this type ofrelationship, systemic variables influence the value of domestic variables, which in turn, affect theoutcome variable. In other words, systemic variables can affect the outcome of interest directly (asin the previous category) as well as indirectly via their influence on domestic variables.8 Gourevitch(1978) had this type of theoretical relationship in mind with his classic “second image reversed”analysis. He argues for a causal chain in which the international system affects domestic politics,which in turn, affect the foreign policy choices of nations.

“Two aspects of the international system have powerful effects upon the character of domesticregimes: the distribution of power among states, or the international state system; and the distri-bution of economic activity and wealth, or the international economy. Put more simply, politicaldevelopment is shaped by war and trade” (882-3). And then he notes that domestic politicalstructures, of course, have large effects on foreign policy choices. He thus emphasizes the indirectway that the international system can alter domestic political structures and coalitions, which inturn shape foreign policy.

Figure 3: Indirect System Effects

Y

D S

These types of relationships are a mainstay of theory in IR and IPE. Frieden 1991 arguesthat increased capital mobility and trade have changed domestic groups’ preferences and thusled to changes in foreign economic policies. Andrews 1994 claims that global capital mobility isnow a systemic condition that indirectly affects monetary policy through its impact on domesticpolitics and directly shapes interactions among states. Frieden and Rogowski (1996) study avariety of ways in which increasing benefits and decreasing costs of international transactionsin trade and finance affect the preferences of societal actors over government policy, which inturn, shape the policies chosen once political institutions aggregate those preferences in variousways. As Gourevitch presaged, Comparative Politics (CP) and Comparative Political Economy(CPE) have been particularly attentive to the direct and indirect effects of the international

8Note that nothing precludes analysis of a similar relationship in which domestic variables influence the valueof systemic variables. Since systemic variables describe features of the world that are common to all units, it istheoretically unlikely that the value of one particular country’s domestic variable would significantly influence thevalue of a systemic variable, especially for “small” countries. As a result, we focus on how systemic variables mightaffect the value of domestic variables, and not the reverse case.

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system on outcomes of interest. Recently, Kalyvas and Balcells (2010) argues that changes in theinternational system (i.e., systemic factors) have affected the capacity of both insurgent groupsand governments(i.e., domestic variables) which have, in turn, affected the way that civil wars arefought (outcome variable). Their theoretical argument entails a nuanced consideration of boththe direct and indirect effects of systemic variables:

By specifying three distinct technologies of rebelion and by identifying a major andoverlooked process of transformation of civil wars, we are able to theorize the link be-tween system polarity, the Cold War, and internal conflict, as well as provide empiricalsupport for it. The way in which civil wars are waged turns out to be clearly related tothe international system in ways that are more obvious (e.g., superpower interference)or less (e.g., the decline of irregular war). (427)

These types of relationships are often referred to as “mediating” relationships.9 In the contextof interactions between domestic and systemic factors, a domestic variable may mediate the effectsof a systemic variable if the systemic variable affects the value of the domestic variable. Thisgenerates two interesting effects to estimate: the direct effect of systemic variables on the outcomevariable, and the indirect effects of systemic variables through their effect on domestic variables.In section 3 below, we describe ways to model these relationships as well as how to test for thepresence of mediating effects.

2.2.4 Moderation

Another category of interactions between systemic and domestic factors concerns the moderatingrole of systemic variables. In this category, which is depicted in Figure 4, systemic variables alterthe way in which domestic variables affect the outcome of interest. “Conceptually, a moderator isa variable that modifies the effect of a predictor on a response” (Tang et al., 2009). According to(Baron and Kenny, 1986, p.1174), “moderator variables specify when certain effects will hold...themoderator function of third variables, which partitions a focal independent variable into subgroupsthat establish its domains of maximal effectiveness in regard to a given dependent variable.” Theindirect systemic effects discussed above, which are often terms mediating relationships, differfrom moderating ones, although they appear very similar. In our case, a moderator is a systemicvariable that affects the direction and/or strength of the relationship between an independentdomestic variable and the dependent outcome variable. A moderator is represented often as aninteraction between the independent variable and the systemic factor that specifies the appropriateconditions for its operation. In contrast, a systemic variable acts as a mediator to the extent thatit counts for the relation between the independent domestic variable and the dependent variable.Mediators show the causal chain from the independent variable to the dependent one. Whereasmoderator variables specify when certain effects will hold, mediators show how or why such effectsoccur.

9Direct and indirect effects are often associated with causal analysis of mediating variables. We include thisaspect of their relations but also non-causal effects. “We define a causal mechanism as a process whereby onevariable T causally affects another Y through an intermediate variable or a mediator M that operationalizes thehypothesized mechanism.” “Thus, an inferential goal is to decompose the causal effect of a treatment into theindirect effect, which represents the hypothesized causal mechanism, and the direct effect, which represents all theother mechanisms. Figure 1a graphically illustrates this simple idea and the assumed causal ordering. The indirecteffect combines two arrows going from the treatment T to the outcome Y through the mediator M, whereas thedirect effect is represented by a single arrow from T to Y” (Imai et al., 2011, pp. 768).

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Figure 4: Moderating Effect of Systemic Variable

Y

D S

!D !S

Y

D S

!D

(a) (b)

One of the most well-known IPE articles, Rogowski (1987), considers a moderating role forsystemic variables. He argues that decreases in the costs of trade will induce different politicalcleavages in a country, depending on that country’s land-labor ratios and level of development.Developed countries that are labor-abundant and less-developed countries that are land-abundantshould experience urban-rural political conflict. Developed countries that are land-abundant andless-developed countries that are labor-abundant should experience class conflict. The systemicvariable is the costs of trade and the domestic variables are factor endowment ratios. The out-come of interest is the nature of resulting political cleavages. The value of the systemic variableconditions the effects of the value of the domestic variables on the outcome of interest.

Boix (2011) develops a theory that is also based on systemic variables moderating the effectsof domestic variables. Boix argues that the relationship between a country’s level of development(domestic variable) and the country’s level of democratization (outcome variable) depends onthe structure of the international system (systemic variable). In his words, “The relationshipbetween income and democracy varies also with factors that are ‘exogenous’ to development. Inparticular, great powers tend to deal with (and interfere in) the domestic politics of their allies(and, if possible, of the allies of their enemies) as a further means of advancing their interests inthe international arena” (pp. 814).

Empirically, moderating relationships are often modeled using multiplicative interaction terms.Bernhard and Leblang (2002) analyze how fixed exchange rates and central bank independenceaffect cabinet durability. They interact their key independent variables with a dummy variablefor whether the observation is from the pre- or post-Maastricht treaty time period, which is asystemic variable. In other words, they allow the effects of their key domestic variables on cabinetdurability to vary based on a theoretically important systemic variable.10

Most studies of moderating relationships employ interaction terms. We argue that there arebetter ways to empirically model this type of relationship. Below, we show how multilevel modeling(MLM) can be a powerful tool for understanding these types of moderating relationships. Thisapproach, which is rarely used in IR, affords several advantages over the traditional interactionterm approach. First, multilevel modeling captures the nature of the hierarchical influence of theinternational system on states. It enables empirical models to explore how this overarching contextcan affect individual state behavior. Unlike interaction terms which assume “mutual moderation”where a systemic variable moderates a domestic one and vice versa, MLM’s allow researchers todesign empirical models that allow for one- or two-way moderation. MLM also avoids making

10Ironically, Bernhard and Leblang (2002) is another article from Oatley’s reductionist list. Furthermore, as withthe above Li and Resnick (2003) example, Bernhard and Leblang (2002) use the exact approach (interaction terms)that Oatley advocates in his criticism of Milner and Kubota (2005).

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the assumption of “deterministic moderation,” in which there is no uncertainty in moderatingrelationships. Finally, MLM allows researchers to specify much richer moderating relationshipsin which many variables, not just one, can affect or moderate the role of another variable. Wedescribe each of these advantages in greater detail below and compare the different approaches tomodeling moderation.

2.2.5 Interdependence

Our final category of systemic effects considers interdependence, which is how the units within theinternational system interact with one another. Such relationships are depicted in Figure 5 andare often the focus of the existing literature that utilizes network theory and spatial econometrics.Both network theory and spatial econometrics are concerned with the possibility that the outcomein one unit, Yi, affects the outcome in another unit, Yj . In network analysis, researchers modelfeatures of the entire network of units, i.e. how interconnected or dense the network is. Forexample, Kim and Shin (2002) find that global trade networks have become more dense over time.Researchers also focus on describing characteristics of a particular unit in the system relativeto the characteristics of other units. For instance, network analysis often focuses on whether aparticular node is a hub, with many connections to other nodes. Charli Carpenter (2011) arguesthat advocacy groups that are hubs within the network of advocacy groups have greater influenceover weapons norm agenda choices than do advocacy groups on the periphery.11

Figure 5: Direct System Effects

Y2

D1 D2

S

Y1

Spatial econometrics has become an often-used tool, particularly in the study of the diffusionof national policies across countries.12 Spatial econometrics explicitly incorporates the notionthat one country’s policy can be correlated across space and time with another country’s policies.These models generally include a “connectivity matrix” that takes advantage of the researcher’sknowledge to construct a matrix that measures the degree of connectivity between each pair ofunits in the system. One country’s policy choice is allowed to be influenced by spatially and/ortemporally lagged outcome variables from other countries. Like network analysis, spatial econo-metrics is interested in estimating a parameter describing the degree to which outcomes in othercountries or time periods affect a particular country’s choice. Much of this research concerns issuesof policy diffusion (Simmons, Dobbin and Garrett, 2006).

A significant and growing body of research has used spatial econometric tools to investigateinteresting questions. Searching for IPE articles in International Organization alone, it is hard

11For other examples of network analysis being using in IR, see: Hafner-Burton, Kahler and Montgomery (2009).12Graham, Shipan and Volden (N.d.) estimate that over 400 articles have been written in social science over the

last decade that consider the diffusion of policies from one government to another.

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not to encounter analyses using these tools in virtually every context.13 Mukherjee and Singer(2008), for example, explicitly test the explanatory power of domestic interests versus diffusionin explaining inflation policies. Existing applications of spatial tools go far beyond IPE, coveringdiverse topics ranging from refugee spreads (Salehyan and Gleditsch, 2006) to military expendi-tures (Flores, 2011). The econometric tools themselves continue to be refined by social scientistsstudying international relations and comparative politics (Spatial Effects in Dyadic Data, 2010;Hoff and Ward, 2004; Beck, Gleditsch and Beardsley, 2006; Poast, 2010; Plumper and Nuemayer,2010).

Like network analysis, spatial econometrics is often interested in estimating a parameter thatdescribes the overall level of connectivity among units. In other words, both approaches seek toestimate the degree to which spatially- and temporally-related units influence one another. Inspatial econometrics, this parameter is often called “rho,” ρ. When ρ is positive and greater inmagnitude, the outcome variable in spatially- and temporally-linked units more closely resembleone another. For example, if the outcome of interest is trade barriers in a country, then a positiverho means that as those countries that are more closely linked to the country raise their barriersthe country also raises its barriers. When ρ is zero, the value of the outcome variable in one unitdoes not affect the value for another unit. And when ρ is negative, the values can be inverselyrelated.

Below, we show how spatial econometric models can be a powerful tool for modeling thetypes of interdependence across units that arises from processes like bargaining and diffusion. Wealso extend the frontier of these models by allowing interdependence across units to be dynamic.Existing spatial models constrain the degree of interdependence between units to be fixed, i.e. theρ parameter is time-invariant. These models therefore assume that the intensity of correlationacross units does not vary over time. We develop and demonstrate a model that relaxes thisassumption and accounts for time-varying ρ’s. It is not hard to imagine theoretical reasons whyinterdependence among states might increase or decrease over time, or be positive at some timesand negative at others. For instance, interdependence as a result of international bargaining maybecome more intense as more and more countries join a particular international institution. If thedegree of interdependence across units is changing over time, then this reflects important changesin the international system that researchers might be interested in.

Finally, we also note that nothing precludes researchers from considering combinations of thecategories of interactions described above. Researchers could develop and test theories in whichany combination of direct, indirect, interdependent, or moderating relationships are present. Forexample, Ahlquist and Wibbels (2012) develop a theory and accompanying empirical approach thatconsiders moderation and interdependence. They argue that changes in the world trade openness(systemic variable) affect the relationship between factor endowments (domestic variable) anddemocratization (outcome variable), which is a moderating relationship. They also argue that thespatial and temporal clustering of factor endowments is an important phenomenon that wouldmake democratization outcomes interdependent across similar countries. They incorporate boththese features into their empirical approach. At the conclusion of the following section, we estimateand evaluate such a complicated model- i.e., one that includes all of these potential relationships.

13For a far from exhaustive list, see: (Karol, 2000; Jahn, 2006) on trade and globalization; (Elkins, Guzmanand Simmons, 2006; Spatial Effects in Dyadic Data, 2010) on investment; (Money, 1997) on immigration; (Swank,2006) on tax policy. For an extensive list of studies using these approaches in CPE and more general survey ofthese methods, see: (Franzese and Hays, 2008).

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3 Models of Interactions

Having described a set of theoretical relationships between systemic, domestic, and outcome vari-ables, we now turn towards empirical models designed to test predictions derived from suchrelationships. Most importantly, for each category outlined above, one or more empirical modelsexist that capture the exact type of relationship described. As we consider the empirical modelsassociated with increasingly complex theoretical relationships, the empirical models will simul-taneously become more complex and more general. The simplest model (independence) can bethought of as a model that implicitly assumes that other types of relationships (direct effects, in-direct effects, interdependence, and moderation) are not present. As the empirical models becomemore complex, they also become more general, i.e., they relax more assumptions and allows moretypes of relationships between the three types of variables.

For each category of relationship, we do two things. First, we describe the execution of anappropriate model in greater detail, the assumptions entailed in choosing a particular approachover its alternatives, and also the conditions under which a more complex model is needed. Thisallows us to describe in more general terms how a researcher might navigate the task of choosingan appropriate model. It is important to note that there may be other appropriate models andmethods than those we discuss for each types of interaction, but our goal is not to exhaust allexisting models. Instead, this paper is intended to demonstrate the availability of empirical modelsto appropriately analyze all important types of interactions in the simple-to-complex spectrum.In addition, although we are aware of other important methodological issues associated with time-series cross-section data (Beck and Katz, 1996; Beck, Katz and Tucker, 1998; Beck and Katz,2007), our discussion will focus only on those issues directly related to interactions.

Second, we demonstrate these concepts by re-analyzing the debate over the relationship be-tween democratization and trade policy. We choose work on trade liberalization and regime typeas our particular empirical application because it is substantively important and because of therich possibilities for systemic-domestic interactions. In addition, Oatley focuses on this topic as anexample of the problematic omission of systemic forces; therefore, our re-analysis of it addressesthis concern and allows us to demonstrate the usefulness of systematically considering differentpossible relationships between domestic and systemic factors.

We also advance the frontier of these models. We show the usefulness of multilevel or hierarchi-cal modeling as a tool for assessing moderation dynamics between domestic and systemic variables.It also has one important advantage over the fixed-effects estimator on panel data (TSCS data) toinclude both observed and unobserved systemic effects in analysis. We also advance the literatureon spatial econometrics by developing a model that can account for time-varying levels of con-nectivity. In other words, rather than assuming that the degree of connectivity between units isconstant over time, we allow this parameter to vary. As a result, we can trace whether particulardynamics like contagion or diffusion have likely become more or less important over certain timeperiods. At the same time, the model is also able to capture even more complex picture whenputting all those important types of interaction together.

3.1 Brief Background on Trade Policy and Regime Type

An analysis of trade policy and democratization in LDC’s is originally the focus of work by HelenMilner and Keiko Kubota (2005). Milner and Kubota hypothesize that as labor-rich developingcountries become more democratic, they are less likely to turn towards protectionist tariffs to

13

garner political support. They analyze data on the outcome variable, tariff rates, for approximately101 LDC’s for the years 1970-1999. Their central explanatory variable is domestic. They use PolityIII and Polity IV scores to measure the regime type of country i in year t. They also collect data ona set of covariates, some domestic and some systemic. Using a series of models, they consistentlyfind that democracy is negatively related with tariff rates.

Oatley criticizes the Milner and Kubota analysis for its omission of a moderating effect forsystemic variables.14 He argues in favor of a “macro theory” that accounts for possible bargainingamong countries in the WTO forum. To link “macro theory” with the empirical evidence, heargues for a conditional hypothesis, that accounts for the possibility that “the impact of regimetype on tariffs is mediated by participation in the WTO,” which he considers to be a systemicvariable, and re-estimates certain models from Milner and Kubota, including an interaction termbetween a dummy variable indicating a country’s membership in the WTO and the regime typevariable. He finds that democracy decreases tariffs only for WTO members and concludes that thisis evidence of the biased inferences drawn from Milner and Kubota’s analysis, as a result of theiromission of international bargaining from the empirical analysis. Because Milner and Kubota didnot consider a possible moderating role of systemic variables, Oatley argues that their conclusionswere incorrect.

While Oatley’s analysis is potentially insightful for the topic of regime type and tariff levels, itdemonstrates the difficulty of evaluating interrelationships between domestic and systemic factorsin practice. Puzzlingly, to account for systemic processes, he focuses on a country’s WTO mem-bership in a given year, which is a domestic variable by definition. Whether a country belongsto the WTO describes a particular characteristic of one country, not the system as a whole. The“macro theory” that he advances also does not match his subsequent choice of empirical model.His description of “macro theory”’s implications for analyzing tariff rates is one of a direct effect forthe WTO. Countries in the WTO should be more willing to lower tariffs because they can securereciprocal promises from other WTO members. He concludes that democracy, therefore, shouldonly affect tariff rates for those in the WTO and have no effect for non-members. Just becausethe WTO provides a bargaining forum for members, does not imply that democracy should haveno effect on non-member tariffs, since they are not logically contradictory and can be two differentcausal chains, intertwined or not. To account for possible bargaining between countries, whichsuggests an interest in the relationship between outcome variables–the tariffs chosen in country iand those chosen in country j–he interacts two explanatory variables. 15

To remedy this problem, we systematically re-evaluate the relationship between regime typeand trade policy, describing and accounting for possible interrelationships between systemic vari-ables and forces and outcomes of interest. We will take the original Milner and Kubota analysisas a starting point, and begin with a purely “reductionist” model (we will call it “independence”model). This is actually a slight injustice since the Milner and Kubota models did include anddiscuss systemic variables, but we will organize our analysis in this way for illustrative purposes.

14Oatley actually uses the term mediation for this effect, but we will remain consistent with the existing literatureand refer to this as moderation instead of mediation.

15The same could be said of Oatley’s other applications, where at times, he advocates split samples, additionalcontrol variables, or network analysis as appropriate solutions without any guidance for using these tools beyondthe applications he considers.

14

3.2 Dataset

The data we use in our empirical application are identical to that of Milner and Kubota andOatley’s analysis, with a few exceptions. First, we significantly extend the time period coveredby either analysis. The original analyses covered the years 1970-1999, which unfortunately, onlyincludes four years of the post-WTO period. We extend the analysis to 2008, which triples theamount of WTO-period years under consideration. We also standardize a set of variables to beused in each analysis. Since we are concerned with modeling approaches, rather than variableselection, we focus on a set of 12 explanatory variables, across models. The 12 variables are listedin Table 1, among which 7 are domestic variables and 5 are systemic. The resulting dataset covers39 years for 85 countries. We use the multiple imputation method to fill in the missing data inorder to more efficiently use data information (Rubin, 1987; King et al., 2001; Honaker and King,2010).

The domestic variable that we focus on describes a country’s regime type, REGIME TYPE, and ismeasured with the standard combined Polity IV scores. We also include domestic control variablesmeasuring the log of a country’s population, LN POP, and its per capita GDP, GDP PC. We includea dummy variable that equals 1 in years when a country experienced an economic crisis, meaningthe country experienced a severe inflation or negative income shock, or a balance of payment crisis,which occurs when a country’s currency reserves fall to dangerously low levels, EC/BP CRISIS. Weinclude a control for the number of years that the current government has been in office, OFFICE.Lastly we include a dummy variable indicating membership in the GATT or WTO, GATT.16

We also focus on five systemic variables. Three are from the original Milner and Kubotaanalysis. We measure the percent of world trade that is accounted for by U.S. imports andexports, to capture the degree of U.S. hegemony in the international market, US HEGEMONY. Wealso measure the openness of capital markets in the 8 largest countries in the world, 8 OPEN.17

For country i in year t, we calculate the average tariff level for countries other than country i,AV. TARIFF.18 Lastly, we include systemic variables that measure the degree of WTO influence inthe system. We choose these two variables because, unlike a country’s GATT/WTO membership,which Oatley emphasizes, these are systemic variables and not domestic variables. We measure thepercentage of countries in the world that are members of the GATT/WTO in that year, GLOBALWTO MEM. (more often labeled as WTOM in the tables and figures). We also measure the percentof world trade that takes place in mutual-GATT/WTO member dyads in a given year, GLOBALWTO TRADE.19 These systemic variables capture variation in the overall importance of the WTOto world trade. These variables are not binary, which allows us to consider richer variation.

16The exact coding and theoretical reasons for including these variables, as well as the systemic variables, arecovered in the original Milner and Kubota article. For brevity’s sake, we do not repeat them here.

17We thank Quinn, [xx cite] for generously sharing his updated data on this variable. This is a similar variableto the “5 Open” variable used in Milner and Kubota.

18Since the calculation excludes country i’s tariff in order to avoid endogeneity, this variable does vary slightlyacross countries within a particular year. However, this is essentially systemic variation since no sample countryinfluences the average very strongly.

19We summed the exports from i to j and from j to i for dyads where i and j were both WTO members, anddivided this by the sum of exports across all dyads.

15

Table 1: Domestic and Systemic Variables

Domestic Variable Definition Systemic Variable DefinitionREGIME Polity IV Score AV TARIFF Average Sample Tariff Level (t)

LN POP Population US HEGEMONY The degree of U.S. hegemony inthe international market

GDP PC GDP per capita 8 OPEN the openness of capital marketsin the 8 largest countries in theworld

EC CRISIS Economic Crisis GLOBAL WTO MEM. The percent of countries in theworld that are members of theGATT/WTO

BP CRISIS Balance of Payment Crisis GLOBAL WTO TRADE The percent of world tradethat takes place in mutual-GATT/WTO member dyads

OFFICE Number of Years in Office

GATT GATT/WTO Member State

3.2.1 Category 1: Independence Model

The point of departure for our description of models for the five types of domestic-systemic in-terrelationships described above is what we call the “independence model.” This model is thearchetype that Oatley criticizes for being reductionist. This model only considers the effects ofdomestic variables on the outcome of interest, and it ascribes no role for systemic variables. Thismodel assumes that the effects of domestic variables, namely regime type, take place indepen-dently from any systemic effects, and implicitly assumes that the other four roles for systemicvariables–i.e., direct, indirect, interdependent, and moderating– are not present. Table 2 showseach of these assumptions.

Figure 6: Independence Model

D Y!D

Figure 6 demonstrates the assumption that the systemic variable has no role to play whenanalyzing the relationship between the domestic variable and the outcome, because the systemicvariable does not have any effect on the outcome, or because, whatever effect the systemic variablemay have on the outcome, the effect is absolutely irrelevant to the relationship between thedomestic and outcome variable. Accordingly, the empirical model that produces an unbiasedestimate of the parameter of interest, namely the effect of the domestic variable on the outcome,

16

βD, is simple and familiar.20 The model is a multivariate regression of the outcome variable onthe domestic variables, and the country-fixed effects term, αi, controls for the unobserved time-invariant effect for country i.21

Yit = β0 + βDDit + αi + εit (1)

The ability of Model 1 to produce unbiased estimates of βD requires several strong assumptionsabout the relationships between the systemic, domestic, and outcome variables as presented inTable 2.22 In each of the models that follow, we relax one or more of these assumptions.

Table 2: Assumptions Made (or Relaxed) in Models

Assumption Independence Direct Indirect Moderation Interdep. All-in-One

A1 No Direct Effect xS 9 Y

A2 No Indirect Effect x xS 9 D → Y

A3 No Moderation on D x x x xE(βD|S) = E(βD)

A4 No Interdependence x x x xcor(Yi, Yj |D,S) = 0

Assumptions Made Strong & Many −−−−−−−−−−−−−−−−− → Weak & FewComplexity of Stats. Model Simple & Parsimonious −−−−−−−−−− → Complex & Accurate

In the context of our tariff data, such a model would represent a theory that only domesticvariables affected the tariff level of a country. Table 3, column 1, shows the results from estimatingModel 1 using our tariff data. The model only includes the seven domestic variables as covariates.Regime type, the primary domestic variable of interest, has a negative and significant coefficient,as in the original Milner and Kubota argument. Higher levels of democracy decrease tariff levels.

3.2.2 Category 2: Direct System Effects

One of the most immediately apparent assumptions made by the independence model is thatsystemic variables have no direct effect on the outcome of interest; this is Assumption 1. Thedirect effects model relaxes this assumption, as shown in Figure 7.

20As above, the index i denotes country i and t denotes year t.21We include country specific intercepts in each of the models as a way to control for unobserved unit level

heterogeneity. Their inclusion or exclusion is not important to our arguments about the relationship betweendomestic and systemic variables. We include them for the sake of thoroughness. No year-fixed effects are includedin the model, because the model will not be a “independence” model with year-fixed effects, which we will discussin more detail in next subsection.

22In reality, there are other assumptions needed for unbiasedness, for example, the assumption of linearity andno omitted domestic variables. With panel data, additional assumptions are required depending on the estimatorwe choose (see Wooldridge (2001)). We focus on the assumptions related to systemic variables that are needed.

17

Figure 7: Direct System Effects

!S

Y

D S

!D

cor(D, S)

The appropriate model for direct system effects is again familiar and simple. When theoreticallyimportant variation in systemic variables is observed and measured by St, multivariate regressionthat includes these variables produces unbiased estimates of βD, as in Model 2.

Yit = β0 + βDDit + βSSt + αi + εit (2)

Since it is impossible to know with certainty whether Assumption 1 holds, when is the in-dependence model appropriate and when is the model that accounts for direct systemic ef-fects needed? When A1 holds, the independence model is sufficient because A1 implies thatE(Y |D,S) = E(Y |D). When A1 does not hold, the independence model produces biased esti-mates when the systemic variable is correlated with the domestic variable, cor(Dit, St) 6= 0.

In the presence of direct systemic effects, the intuition behind the choice between the inde-pendence model and another model is akin to the familiar conditions of omitted variable bias. Amodel that omits a particular explanatory variable will produce biased estimates for the effect ofthe explanatory variable of interest when the omitted variable does in fact affect the outcome ofinterest and also is correlated with the explanatory variable of interest. In the domestic/systemiccontext, the omission of systemic variables is worrying when those systemic variables affect theoutcome and also are correlated with the domestic variable of interest.

If either of those two conditions are not met, then choosing a simpler model that does notprovide for any direct systemic role will still produce unbiased estimates of the effects of domesticvariables. When the systemic variable is not correlated with the domestic variable, omitting it willnot confound the relationship between the domestic variable and the outcome. If βD is what isinteresting in a research, the independence model is still applicable, though it may perform poorlyin prediction. But if the systemic variable is correlated with the domestic variable, we have tocontrol for the effect of the systemic variable in order to unbiasedly estimate βD.

When the researcher is concerned about important unobserved system variation, then a modelthat includes year fixed effects produces unbiased estimated of βD, as in Model 3.

Yit = β0 + βDDit + αi + δt + εit (3)

Unfortunately, the fixed effects model, using either within-differencing or first-differencing estima-tor, cannot include the observed and unobserved systemic effects at the same time, because nocross-sectionally invariant variables can be included together with year-fixed effects. This meansthat when using the fixed effects model, we have to face the difficult choice between modeling theeffects of the observed and unobserved systemic variables. This is not a problem for some othermodels, such as the random effects panel model or multilevel model. For comparability, we stick

18

to the fixed effects model to analyze our tariff data, and will discuss and apply other methods inlater sections to include both observed and unobserved systemic variables.

In the context of our tariff data, Model 2 is more appropriate when the researcher observes allthe systemic variables that she thinks are theoretically important and that also are actually allthat empirically matters. For instance, if there were theoretical reasons to think that the averageglobal tariff level of all the countries under examination (AV. TARIFF, which is observable, affectedindividual countries’ tariff levels, then the researcher would want to include this in her model. Ifthe researcher was worried about unobserved variation in the system across years, and was notparticularly interested in estimating the direct effects of systemic variables, then she might chooseModel 3 and let the year-fixed effects to include all those potentially effective systemic variables.

Table 3, Columns 5 and 6, show the results from estimating the equation in Model 2. Thecoefficient on regime type is [-0.238] compared with [-0.329] from the independence model inColumns 1 and 2. The difference in estimates arises because some systemic variables appear todirectly affect the outcome of interest in Model 2 and because some systemic variables are at leastweakly correlated with regime type. The coefficients on AV. TARIFF, 8 OPEN, and GLOBAL WTO

MEM. are all significant. Higher average global tariffs unsurprisingly increase individual countries’tariffs, and the openness of the eight largest countries tends to decrease tariffs. Surprisingly,increased global WTO membership is associated with increased tariffs.

Table 4 shows the pairwise correlation coefficients for each of the variables in the dataset.Looking at the first column, some of the systemic variables are correlated with the measureof regime type. And since some of the systemic variables are also correlated with tariff levels,the estimated coefficient for REGIME TYPE differs depending on whether systemic variables areincluded.

Table 3, Columns 3 and 4 show the results from estimating the equation in Model 3. Theresults are very similar to the results from Model 2. The coefficient on regime type is now [-0.212]. Whether a researcher should prefer Model 2 or Model 3 depends on her goal. If she is onlyinterested in estimating the effect of the domestic variable, REGIME TYPE, on the outcome variable,then Model 3 is appealing since it accounts for all types of unobserved system heterogeneitythrough the use of year fixed effects. If, on the other hand, the researcher is explicitly interestedin knowing the direct effects of particular systemic variables, then Model 2 is more appealing sinceit actually estimates those effects. Notably, however, the relationship between regime type andand tariffs remains negative and significant even when accounting for direct system effects.

3.2.3 Category 3: Indirect Effects

The independence model also assumes that systemic variables have no indirect effects on theoutcome of interest, as assumed in A2. Recall that systemic variables have indirect effects whentheir value influences the value of domestic variables, which in turn, affect the outcome of interest.This is also sometimes called a mediating relationship. This type of relationship is depicted inFigure 8.23

Note that in the graph, we consider the situation that the systemic variable has both direct andindirect effects, because if the systemic variable has no direct effect at all, this type of interaction

23Note that nothing precludes systemic variables from mediating the effects of domestic variables. It is possibleto think of a relationship where domestic variables influence the value of systemic variables, which in turn, affectthe outcome of interest. Such examples are unlikely to be supported by theory in most instances, since one countrydoes not often influence the overall system.

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Table 3: Independence and Direct Effects

Independence Direct Effect of SystemM1 M3 (Year-Fixed Effects) M2 (Observed St)

Covariate Estimate SE Estimate SE Estimate SE

Domestic

REGIME −0.329 (0.042)∗ −0.212 (0.045)∗ −0.238 (0.042)∗LN POP −1.743 (0.884)∗ 2.620 (1.733)∗ 1.572 (0.905)GDP PC −2.364 (0.470)∗ −1.842 (0.488)∗ −1.754 (0.463)∗BP CRISIS 1.719 (0.450)∗ 0.721 (0.445)∗ 0.918 (0.444)∗EC CRISIS 3.268 (0.942)∗ 1.737 (0.927)∗ 1.842 (0.925)∗OFFICE 0.001 (0.001) 0.002 (0.001) 0.002 (0.001)GATT 0.214 (0.714) 1.864 (0.705)∗ 1.508 (0.706)∗

Systemic

US HEG −10.539 (18.195)AV TARIFF 0.853 (0.066)∗8 Open −0.309 (0.144)∗WTOM 47.706 (23.877)∗WTOT 218.609 (197.140)

Country FE Y Y YYear FE N Y N

∗ Significant at 95% level.

Figure 8: Indirect System Effects

!

Y

D S

"D "S

reduces to category 1 (Figure 6). In this case, domestic variables mediate the effects of systemicvariables. If a researcher has theoretical reasons to suspect such a relationship, then what empiricalmodel should she choose? The answer depends on her goals. If the goal is to simply estimate theeffect of domestic variables on the outcome of interest, then the multivariate regression modelsused to model direct effects in the section above will suffice. Even in the presence of indirect systemeffects, such a model will provide an unbiased estimate of the effects of the domestic variables.The multivariate regression suffices in this context because it is unconcerned with the reasons forchange in the domestic variables, and is only concerned with their effects.

On the other hand, if the researcher is specifically interested in the direct and indirect effectsof system variables, mediation analysis should be conducted to disaggregate the total effects.Mediation tests can be either parametric or nonparametric. One of the most frequently appliedparametric mediation tests uses steps outlines by Baron and Kenny (1986) and Judd and Kenny(1981), as well as subsequent modifications (Bollen and Stine, 1990; Shrout and Bolger, 2002).The core is a structural equation model, as in Model 4.

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Table 4: Correlation Between Domestic and Systemic Variables

REGIME GDP PC LN POP BP CRISIS EC CRISIS OFFICE GATT

US HEGEMONY 0.043 0.007 −0.031 0.071 0.013 0.035 0.021AV TARIFF −0.262 −0.086 −0.060 0.211 0.108 −0.110 −0.2298 OPEN −0.256 −0.422 0.209 0.011 −0.089 0.082 0.007GLOBAL WTO MEM. −0.064 −0.185 0.275 −0.063 −0.085 0.109 −0.076GLOBAL WTO TRADE 0.182 0.253 −0.210 0.049 0.074 −0.173 0.008

Yit = β′sSt + βX + εit (Total-Effect Model)

Dit = δSt + βX + ζit (Mediation Model)

Yit = βDDit + βsSt + βX + uit, (Direct-Effect Model)

(4)

where X denotes all other control variables. The approach in Model 4 allows the researcher todescribe both the direct and indirect effects of system variables. The direct effect of S is capturedby the estimate of βs in the Direct-Effect Model. The indirect effects are captured either byconsidering δ × βD using the Mediation Model and Direct-Effect Model or β′s − βs based on theTotal-Effect Model and the Direct-Effect Model.

Often, the researcher is interested in testing whether certain variables are or are not mediatorsfor other variables, which requires her to compute the standard errors associated with each effect.The standard error of the mediation effect, which is the effect of one variable “through” its medi-ator, can be calculated in various ways and forms slightly different tests, such as the Sobel Test,the Aroian Test and the Goodman Test (Goodman, 1960; Aroian, 1944; Sobel, 1987; Mackinnonand Dwyer, 1993; Mackinnon et al., 2002). Although those tests are widely applied to analyzemediation effects, their restrictive assumptions, instability, and incoherence have been long noticedand criticized (Baron and Kenny, 1986; Fritz and Mackinnon, 2007; Imai, Keele and Yamamoto,2010; Imai and Keele, 2010; Imai et al., 2011; Glynn, 2012). To improve mediation analysis, moreflexible methods have been proposed, such as bias-corrected bootstrapping tests (Fritz and Mack-innon, 2007; Macho and Ledermann, 2011)and nonparametric methods for identifying mediationeffects (Imai, Keele and Yamamoto, 2010; Imai and Keele, 2010; Imai et al., 2011). It is beyondthe scope of this paper to resolve these debates.

In the context of our tariff data, the researcher might think that a system variable affects tariffsdirectly, and indirectly through its effect on a domestic variable. Global WTO Membership mighthave a direct effect on a country’s tariffs, which we found in the results from previous models.Global WTO membership might also affect a country’s regime type, in which case it would havean indirect effect since regime type was also found to affect tariffs. This is theoretically plausible;Aaronson and Abouharb (2011) argue that WTO membership can increase political participationand a country’s level of democracy. In this case, REGIME TYPE would mediate the relationshipbetween GLOBAL WTO MEM. and tariff levels. The researcher might therefore be interested in thedirect, indirect, and overall effects of GLOBAL WTO MEM..

21

We demonstrate several tests for this type of mediation. Table 5 reports the test results basedon estimating Model 4 using different test statistics. Due to the limitations of the tests, all modelsrequired in mediation testing are simple linear models, without considering the fact that our dataare panel data or in the mediation model the outcome variable, REGIME TYPE, is discrete (orderedcategorical variable). The mediation effect reported in the table is the indirect effect of GLOBAL

WTO MEM. on tariffs through its effect on REGIME TYPE. The tests ask whether this indirect effectof the systemic variable is statistically different from zero, by showing the standard errors, teststatistic, and p-values associated with each test. Across the three tests, we find evidence in supportof a mediating relationship. In this case, the indirect effect of global WTO membership on tariffsis negative and significant: global WTO membership tends to increase a country’s democracyscore, which is associated with decreasing tariffs.

In Table 6, we apply the more flexible nonparametric testing method described in Imai et al.(2011) to test for mediation effects. The table reports the indirect effects of GLOBAL WTO MEM.,through its mediator, REGIME TYPE, the direct effects, and the total effect, which takes into accountboth of the other effects. The 95 percent quasi-Bayesian credibility intervals are reported beloweach effect. Column 1 estimates the effects with the same regressions in Model 4. Column 2estimates the effects, with a correction for clustering within countries. Estimates reported inColumns 3 and 4 are from the same structural equation system as in Model 4 except that theMediation model is a ordered logistic model instead of a linear one, considering that the outcomevariable, REGIME TYPE, is ordered categorical variable. Column 3 does not correct the within-country clustering, but Column 4 does. As in the tests ran in Table 5, we find evidence ofa negative indirect effect and a positive direct effect. However, combining the two effects, theoverall effect is only weakly positive and is not significantly different from zero.

Systemic factors may thus operate indirectly through domestic ones and directly on outcomesof interest. Checking for these effects is important when assessing relationships between domesticand systemic factors. In this particular case, global WTO membership seems to indirectly affecta country’s tariff rates through its impact on a country’s level of democracy. But regime typeremains a stable mediator, always negatively affecting trade barriers.

Table 5: Conventional Mediation Tests for REGIME TYPE and GLOBAL WTO MEM.

Type of Effect Sobel Test Aroian Test Goodman Test

Indirect Effect −3.464 −3.464 −3.464Std. Error 1.767 1.788 1.746Test Statistic −1.960 −1.938 −1.983p-Value 0.050 0.053 0.047

z-Value Formula δ×βD√β2D×se

2δ+δ

2×se2βD

δ×βD√β2D×se

2δ+δ

2×se2βD+se2δ×se2βD

δ×βD√β2D×se

2δ+δ

2×se2βD−se2δ×se

2βD

3.2.4 Category 4: Moderation

The independence model also assumes that systemic variables do not change the effects of domesticvariables, as shown in Assumption 3. Recall that systemic variables can play a moderating role

22

Table 6: Imai et al (2011) Mediation Tests for REGIME TYPE and GLOBAL WTO MEM.

Type of Effect Test 1 Test 2 Test 3 Test 4

Indirect Effect −8.647 −8.702 −3.984 −3.700(−11.228, −6.116) (−14.474, −4.011) (−5.124, −2.865) (−5.594, −2.045)

Direct Effect 13.710 13.950 13.720 13.600( 5.199, 21.821) ( −4.795, 33.888) ( 5.233, 23.266) ( −7.653, 34.247)

Total Effect 5.066 5.248 9.738 9.895( −3.547, 12.765) (−14.32, 25.79) ( 1.220, 18.825) (−10.76, 29.95)

In the parentheses are the 95% quasi-Bayesian credibility intervals.

In Test 1 and Test 2, both the outcome model and the mediation model are linear regression. Test 2 uses robust

standard errors to correct the dependence caused by clustered observations within the same country.

In Test 3 and Test 4, the outcome model is linear regression, but the mediation model is an ordered logistic model.

Test 4 uses robust standard errors to correct the dependence caused by clustered observations within the same

country.

when the effect of domestic variables on the outcome of interest changes, depending on the valueof the systemic variable. Moderating relationships can be “one way,” where the effect of oneexplanatory variable, X1 on the outcome variable depends on the value of another explanatoryvariable, X2, but the effect of X2 does not depend on the value of X1. Moderating relationshipscan also be “two-way,” where the effects of X1 depend on the value of X2, and vice versa. Thesetwo relationships are depicted in Figure 9, with panel (a) showing a “one-way” relationship with asystemic variable moderating the effect of a domestic variable, and panel (b) showing a “two-way”relationship.

Assumption 3 is likely to be violated if changes in systemic level variables affect the way inwhich domestic variables influence the outcome. If the effect of domestic variables is conditionalon the system, then the effect of a domestic variable in one time period may not be the sameas in another time period. Assumption 3 is akin to assuming “constant effects” for the domesticvariables.

Figure 9: Moderating Effect of Systemic Variable

cor(D, S) or !

Y

D S

"D"S

#1

cor(D, S) or !

Y

D S

"D "S

#1$1

(a) (b)

How should the researcher proceed if she is interested in empirically modeling theories thatinclude moderating relationships? The use of multiplicative interaction terms (Baron and Kenny,

23

1986; Aiken and West, 1991; Kutner et al., 2004) is by far the most common approach in IR.However, to better model moderating relationships we can take advantage of the recent develop-ment of multilevel analysis. Multilevel modeling takes advantage of the researcher’s knowledgethat individual observations in the data are often part of larger groups. A classic, frequently usedexample is to consider data on individual students. The students are grouped into classes; classesare grouped into schools; schools are grouped into districts, etc. Multilevel modeling is designed totake advantage of this structure to describe individual and group level similarities and differences.

International relations scholars often consider data with similar structure. States or countriesare like individual units, that could be grouped regionally or temporally. For our application, itis natural to think about groupings based on the international system. The individuals (coun-tries) belong to different groups based on features of the international system. For instance, ifwe had data describing characteristics of countries, it might make further sense to think aboutcountries operating under a multipolar international system or a unipolar system. Changes in theinternational system can affect country-level coefficients.

Model 5 describes a multilevel model that allows for one-way moderation.

Yit = β0 + β0t + αi + βD,tDit + εit (Individual-Level Model)

β0t = βSSt + ct (System-Level Model)

βD,t = γ0 + γ1St + ζt (System-Level Model)

(5)

The individual level of Model 5 describes relationships between individual-level explanatoryvariables and the outcome of interest. In this level, both the outcome variable, Yit, and theexplanatory variables Dit vary across countries and over time, and values of these variables aremeasured at the country-year level or individual level. At this level, β0 is the global intercept forall observations, and is similar to the intercept in more familiar single-level regression models. β0tis the year-specific intercept that essentially capture the overall direct effect of the internationalsystem. αi is the country-specific intercept, which is equivalent to the familiar country fixed effects.Combining αi and βDtDit, we can see that αi + βDtDit is the total effect of domestic factors onthe outcome in country i in year t, including the observed time-varying domestic factors D andthe unobserved country-specific characteristics whose effects are in αi.

Distinct from ordinary linear regression, we allow the effect of D to vary over time, i.e., tohave a varying effect with the changes occurring in the international system. There is no observedsystemic variable at the individual level, because systemic variables are macro-level variables andshould enter into the system-level regressions. In the first system-level regression, the overalleffect of the international system is further explained by the direct effect of the observed systemicvariables St and the unobserved ones left into the error term ct. While this equation modelsthe direct effects of the international system, the second line is about the moderating effect ofthe international system. The coefficient of D is now the outcome variable in this system-levelregression, and the variation of βD,t is explained by the observed systemic variables St and theunobserved ones left in the error term ζt, along with an intercept γ0. Now it is easy to see that inModel 5, systemic variables affect the outcome in two ways: directly and through their moderatingeffect. For identification, the errors at different levels are assumed to be normally distributed andcentered at zero: εit ∼ N (0, σ2

ε ), et ∼ N (0, σ2e), and ζt ∼ N (0, σ2

ζ ).

24

The error term, ct, is similar to the year-fixed effects in the more familiar fixed effects panelmodel, but the year-fixed effects cannot be included together with St because neither of themhave cross-sectional variation. However, in this multilevel model, they can be included in themodel at the same time at the system level, because multilevel models are not estimated usingany differencing methods. In this section, we will use functions in the lme4 R package to estimatethe multilevel models, which mainly use Maximum Likelihood estimators.

If a two-way moderation relationship is suggested by the theory between S and D, then amultilevel model like Model 6 can accommodate this situation by letting the coefficient of St varyacross different levels of D, assuming that D is categorical, as is in our tariff data.

Yit = β0 + β0t + αi + βD,tDit + εit (Individual-Level Model)

β0t = βS,jSt + ct (System-Level Model)

βD,t = γ0 + γ1St + ζt (System-Level Model)

βS,j = α0 + α1Dit + εj (Regime-Level Model)

(6)

The model is similar to the one-way moderation model (Model 5), except that it lets the directeffect of S to be different at different level of D. Assume that D can take J unique values, and theindex j = 1, 2, ..., J denotes the increasing order of the J unique values. To model the moderatingeffect of D on S, we can group the observations indexed by it’s into J groups according the valueof Dit. In the third regression above, the domestic variable Dit take a value at the jth level, whichmeans the observation it belongs to the jth group. However, the moderation effects α1 and γ1cannot be identified in Model 6, but only the aggregate moderation effect α1+γ1 can be estimated.This means that, like the interaction model, when two-way moderation is modeled, the effect inneither direction can be identified even with the multilevel model.

There are at least four advantages of using multilevel modeling (MLM) to analyze cross-levelmoderation relationship, as opposed to conventional interaction term methods. First, MLM allowsthe researcher to better approximate the hierarchical structure of the international system, withstates being considered in the context of a larger system. It thus allows theoretical knowledge ofthe data-generating process to improve estimation of the relationships of interest. The researchercan tailor the structure of her empirical model to the theoretical relationships that she thinks areat work. Second, multilevel modeling has a clear interpretation of the moderation relationship. Inthe interaction term model, there is no way to tell which component term in the interaction termis the moderator, and therefore, moderation relationship is assumed to be a mutual relationship.But when one’s theory clearly suggests that the systemic variable moderates the domestic variable,not the other way around, only multilevel models can describe such a one-direction moderationrelationship.

The third advantage is that MLM more easily accommodates a richer set of moderators. Unlikethe conventional interaction term approach, nothing in the multilevel model requires that therebe only one moderator, because the system level regression can be either simple or multipleregression. In fact, the model can accommodate situations where multiple factors can moderatethe effect of one of the explanatory variables. For instance, if there were multiple systemic factorsthat moderated the effect of a particular domestic variable, then this setup can easily be capturedby including more variables in the system-level regressions. Conventional interaction models canapproach this type of richness by including triple (or worse) interaction terms, but conventional

25

interaction models can be difficult enough to interpret (Brambor, Clark and Golder, Winter 2006)even without this additional complication.

The fourth advantage is that multilevel modeling allows probabilistic instead of deterministicmoderation. In the interaction term model, the change in the effect of the domestic variable isa deterministic function of the moderator (i.e., the systemic variable), βD = f(St) = γ0 + γ1St.But if there is an omitted systemic variable then the model is biased. Multilevel modeling cancontrol for any bias caused by omitted moderators, because, of the inclusion of an error term, asin Model 5, βD,t = γ0 + γ1St + ζt. The error term ζt is a stochastic term, and the unobservedmoderators are left into this error term. In fact, the interaction term approach is a special caseof the multilevel model when we impose an additional restriction ζt = 0, i.e., that there are no noomitted moderators and no random shocks to this moderation relationship. To see more clearly,first consider a reduced form of Model 5, which is expressed in the first equation below. Thisequation substitutes the lower lines of Model 5 into the top line and simplifies.

Yit = β0 + β0t + αi + βD,tDit + εit

= β0 + βSSt + αi + (γ0 + γ1St + ζt)Dit + εit

= β0 + γ0Dit + βSSt + γ1DitSt + αi + ct + (ζtDit + εit)

= β0 + γ0Dit + βSSt + γ1DitSt + αi + ct + uit

where uit = (ζtDit + εit)

We will compare this to the equation below, which is the conventional multiplicative interactionterm model (with country- and year-fixed effects).

Yit = β0 + γ0Dit + βSSt + γ1StDit + αi + ct + εit

It is straightforward to see that the multiplicative interaction term model is a special caseof the multilevel model with the restriction, ζt = 0. The interaction model makes an implicitassumption that variation in the effect of D is completely determined by St, i.e. that no error ispresent. The estimates produced by the interaction term model will be biased if ζt 6= 0 becausethe error term uit, which contains Dit, is correlated with the observed covariate Dit. IR scholarsshould recognize concerns of this type: they are the all-too-familiar problem of endogeneity thatoften troubles researchers.

In the context of our tariff data, we can imagine theoretical reasons why moderating relation-ships might be present. For instance, the degree of global WTO membership might moderatethe effect of regime type. If GATT/WTO members use those organizations as fora in which tocollectively bargain over mutual tariff reductions, then we might expect the effect of regime typeto be strongest when more countries are members of the GATT/WTO. When fewer countries aremembers, the effect of regime type might be dampened. It could also be the case that all, none, orsome combination of our system variables moderate the effect of regime type in particular ways.

We will consider all three types of models: conventional interaction term, one-way moderation,and mutual moderation models. For the conventional interaction models , we will include themultiplicative interaction between REGIME TYPE and GLOBAL WTO MEM.. As the more generalspecification of the interaction model, the mutual moderation multilevel model allows REGIME TYPE

and GLOBAL WTO MEM percentage to moderate one another. Based on our theory, we actually wantto analyze one-way moderation relationship: the international system changes the relationship

26

between REGIME TYPE and TARIFF. Therefore, in the one-way moderation multilevel models, weallow combinations of the systemic variables to moderate the effect of regime type. The results fromthese models are presented in Table 7. The first column shows the results from the conventionalinteraction term model. The coefficient on the constituent term for REGIME TYPE is positive, butthe coefficient on the interaction term is negative. The easiest way to see the substantive effectsof regime type on tariffs is by looking at Figure 10, the top two pictures. The left pane shows themarginal effect of GLOBAL WTO MEM. as REGIME TYPE varies. The right pane shows how the effectof REGIME TYPE changes as GLOBAL WTO MEM. varies. For the application at hand, the right panelis the most relevant. It shows two things. First, the effect of REGIME TYPE is always negative.Contrary to Oatley’s description of his findings, REGIME TYPE decreases tariff levels, regardlessof the extent of WTO membership. However, the effect of REGIME TYPE is most pronouncedas GLOBAL WTO MEM. increases. As more and more countries have joined the WTO, democracyhas had an increasingly liberalizing effect. Because the model cannot tell which one of the twovariables is actually moderating the other’s effect, we have to look at the left panel to completethe interpretation of the interaction term. The graph shows that when polity score is below −1,GLOBAL WTO MEM generally have a positive effect on tariff and the effect decreases with an increasein the polity score. When the polity score is higher than −1, GLOBAL WTO MEM no longer hasany reliable effect on the tariff at the 0.05 significance level. We do not think this moderationrelationship from polity score to GLOBAL WTO MEM is substantively sensible.

Column 2 of Table 7 shows the results from the mutual moderation model. Figure 10 shows theeffects of these variables in the bottom panel, in the same way as for the multiplicative interactionmodels before. These conditional effects are expected values, because the residual effects, ζ̂t andε̂j, are not presented in the graph. The results of the mutual moderation model are very similarto those of the conventional interaction term model. In the mutual moderation models, RegimeType still has a negative effect on tariffs, and this effect becomes more pronounced as GlobalWTO Membership increases. This similarity of the results between the interaction model and thetwo-way multilevel model is not surprising, since, again, the former is a special case of the latter.When the possible omitted moderators and random shocks are not important, the two shouldproduce similar results.

The reasons for the similarity of results become more apparent when considering Columns3-5 of Table 7. These are the one-way moderation models, in which different combinations ofsystemic variables are allowed to moderate the effects of regime type. Starting with Column 5, wesee that very few of the systemic variables appear to moderate the relationship between REGIME

TYPE and tariffs, with only AV. TARIFF reaching a conventional level of significance. Column4 restricts the set of moderators to only include GLOBAL WTO MEM. and AV. TARIFF, and Col-umn 4 only considers the moderating effects of GLOBAL WTO MEM.. The general weakness of themoderators, specifically, U.S. HEGEMONY, 8 OPEN, and GLOBAL WTO TRADE, explains why omit-ting these moderators resulted in similar results for the interaction term and mutual moderationmodels.

The effects of REGIME TYPE from the one-way moderation model in Column 5 are presentedin Figure 11. The upper-left panel shows the effect of REGIME TYPE as GLOBAL WTO MEM. variesholding AV.TARIFF constant at its sample mean, which is similar to the results above. The upper-right panel shows the effect of REGIME TYPE as AV. TARIFF varies, holding GLOBAL WTO MEM.

constant at its sample mean. REGIME TYPE has the strongest negative effect on tariffs, whenAV. TARIFF are low, and a weaker effect when AV. TARIFF are high. The lower panel shows

27

Figure 10: Mutual Moderating Effects of GLOBAL WTO MEM and REGIME TYPE

Marginal Effects (Interaction Term Model)

-10 -5 0 5 10

020

4060

80100

Polity Score

Mar

gina

l Effe

ct o

f WTO

M

0.55 0.60 0.65 0.70 0.75 0.80

-0.5

-0.4

-0.3

-0.2

-0.1

WTOM

Mar

gina

l Effe

ct o

f Reg

ime

Varying Effects (Two-Way MLM: Model 6)

-10 -5 0 5 10

-10

010

2030

4050

Polity Score

Effe

ct o

f WTO

M

0.55 0.60 0.65 0.70 0.75 0.80

-0.5

-0.4

-0.3

-0.2

-0.1

WTOM

Mar

gina

l Effe

ct o

f Reg

ime

The upper-left and lower-left panels present how the effect of WTOM varies with the change of polity score with the

mean and the 95% confidence interval. The upper-right and lower-right panels are about how WTOM moderates the

effect of REGIME TYPE on tariff, with the mean and the 95% confidence interval. The upper panels are based on

the conventional interaction term model, and the lower panels are based on its multilevel counterpart.

28

the expected effect of REGIME TYPE on tariff levels in a particular year. This effect is calculatedbased on the values of the moderating systemic variables (GLOBAL WTO MEM./AV. TARIFF) fromthat year: E(βt) = γ0 + γ1GLOBAL WTO MEM.t + γ2AV. TARIFFt. REGIME TYPE has a consistentlynegative effect on tariff levels, though this effect is insignificant for a few years in the late 1980’s.The overall effect of REGIME TYPE, when accounting for moderation from these two systemicvariables, is strongest in later time periods, especially after the early 1990’s. The timing of thiseffect is unlikely to be accidental: the GATT regime officially transitioned to the WTO regimein January of 1994. Since the WTO regime is thought to be stronger in many ways than itspredecessor, it is possible that the new regime magnified the tariff-dampening effects of REGIME

TYPE.Overall, we find evidence of a moderating relationship between systemic variables and regime

type. As in previous sections, a country’s regime type is negatively correlated with tariffs, acrossa variety of specifications, but we learned that this relationship is stronger as the number ofGATT/WTO members globally increases, which is consistent with theories of bargaining at thesemultilateral fora. The similarity between the mutual moderation models and the one-way mod-eration models suggests that the moderating effect of global WTO membership is likely to beone-way. Global WTO membership moderates the effect of regime type, but not vice versa.

3.2.5 Category 5: Interdependence

The independence model also assumes that there is no interdependence of the outcome variableacross units, as maintained in Assumption 4. In other words, the independence model assumesthat the outcome in country i does not directly affect the outcome in country j, conditional onthe covariates. Assumption 4 is likely to be violated when there are strong theoretical reasons tosuspect that outcome variables are correlated across units and the correlation is not fully explainedby the covariates. If there is strategic interdependence among countries, then maintaining thisassumption is problematic. As described above, there are a variety of theoretical types of strategicinterdependence: diffusion, coercion, bargaining, etc..

An appropriate model for this type of interaction should account for spatial interdependenceamong the units. The concept of the international system takes on an additional dimension inthis context. Rather than simply being a variable whose effects need to be modeled, the systemnow also describes the ways in which units interact and directly influence one another. This typeof relationship, together with the relationships we discussed in the previous sections, is depictedin Figure 12 and can be estimated using Model 7.

Yit = ρtWitYt + βDDit + βSSt + αi + ct + εit (7)

This empirical model allows us to estimate the effects of the domestic and systemic variables,as well as to account for the possibility of interdependence across the units. It does so by includingthree terms: ρt, Wit and Yt. Yt is often called the “spatial lag.”24 Yt is an n dimensional vectorthat includes the outcome variable, Y , in year t, where n is the number of countries.

W is often called the “weighting matrix.” It is an n× n matrix where each entry describes ameasurement of the connectivity between two units. Wit is the ith row of this matrix for year t,

24Here, we only focus on spatial lags, but often, works using these methods consider spatial and temporal lagstogether.

29

Figure 11: Varying-Effect of Regime Type Moderated by GLOBAL WTO MEM. and AV TAR

0.55 0.60 0.65 0.70 0.75 0.80

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

WTOM

Var

ying

Effe

ct o

f Reg

ime

Type

12 14 16 18 20 22 24

-0.6

-0.4

-0.2

0.0

AVE TAR

Var

ying

Effe

ct o

f Reg

ime

Type

1970 1980 1990 2000

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Year

Var

ying

Effe

ct o

f Reg

ime

Type

30

Figure 12: Interdependence

! ! w21

D1 D2

S

Y1 Y2

"D "D

or #1

"S "S

cor(D2, S)or #2

! ! w12

cor(D1, S)

where the entry in cell i, j is a measure of how connected the researcher expects units i and j tobe in year t. Conventionally, the matrix Wt is row-standardized and all the diagonal elements arezero (Banerjee, Gelfand and Carlin, 2003; S.Bivand, Pebesma and Gomez-Robio, 2008), thoughsee (Plumper and Nuemayer, 2010) for a discussion of the implications of row-standardization.Several features of this matrix are worth highlighting. First, it is a matrix of measurementschosen by the researcher, using prior theoretical information. The researcher must choose someproxy, e.g. distance, amount of bilateral trade, mutual organization membership, etc. that shethinks describes the degree of connectivity between the units, Yit and Yjt. Since W is a matrixof measurements of the connectedness of the units chosen by the researcher, results for the modelwill differ depending on the particular W chosen.

Second, the matrix can be time-varying or time-invariant. A time-invariant W matrix mightbe something like geographical distance, which is unchanged in the timespans considered by socialscience. The W matrix can also be time-varying, accounting for the possibility that the units, iand j, are expected to be more or less intensely connected at different times. For instance, if W ,cell i, j, measured the amount of bilateral trade between countries i and j, then the entries canchance over time.

The ρt parameter describes the overall degree of connectivity among units. Unlike W , ρ isa parameter to be estimated by the model. ρ captures the notion of the system as not just anexplanatory variable, but as a description of the environment in which units interact. When allthe elements in Wt are non-negative, positive values of ρ imply that the value of the outcomevariable is generally positively correlated across units, and vice versa. Higher absolute values of ρdenote higher degrees of positive or negative connectivity, given the same W matrix.

The model described in Equation 7 does two important things. First, it produces unbiasedestimates of the effects of domestic and systemic variables on the outcome of interest, even if wehave theoretical reasons to suspect interdependence across units. Taken together, ρtWitYt is likean additional variable that we include in the model; albeit a variable that we have constructedin a particular way. Thinking of ρtWitYt as a variable allows us to see why failing to account forspatial dependence will produce biased estimates if Assumption 4 is violated. Recall our discussionof omitted variable bias from above: omitted variables produce biased estimates when they arecorrelated with other explanatory variables and when they have an effect on the outcome. Both ofthese conditions are likely to be met (thus producing bias) in any situation where an explanatoryvariable is spatially correlated. For instance, if a particular a unit-level characteristic (i.e. adomestic variable) has an effect on the outcome variable and is also correlated in a particular wayacross units, then omitting the term ρtWitYt will produce omitted variable bias for the effects ofthat unit-level characteristic.25

25Franzese and Hays (2008), in the accompanying technical appendix, derive an explicit representation for the

31

Second, the model allows the researcher to estimate another quantity of interest: the intensityof interdependence across units. Specifically, the model estimates the value of ρ which enabling theresearcher to describe the nature of interdependence across units. In models in which ρ is time-invariant, this is an important quantity to estimate since it tells the researcher how connectedunits are, on average, across the years in the sample.

The model we estimate here has an additional benefit. Our model allows us to estimate ρnot just as an across-year average, but year-by-year. We can recover estimates of the intensity ofinterdependence for each particular year, which enables us to describe how important features ofthe international system change over time. As mentioned in the previous sections, even thoughsystemic variables cannot vary across countries, they can potentially evolve and change over time.The same could theoretically be true of systemic relationships that describe interdependenciesamong units. The degree of connectivity across units might be positive for some years, or negativefor others, and can change in magnitude as well.

In the context of our tariff data, we again return to the possibility that WTO membershipplays an important role in tariff levels. Theoretically, a researcher might worry that countries whoare both WTO members might negotiate mutual tariff reductions. This would make tariff levelscorrelated across units: if one WTO member lowered their tariffs, then another WTO membermight be more inclined to do the same. In Oatley’s criticism of Milner and Kubota, he arguesthat the GATT/WTO “provides a forum in which each government can exchange domestic tariffreductions for foreign tariff reductions” (320). This is exactly the type of relationship that spatialmodeling is intended to capture.

To model this relationship, we code two connectivity matrices, one that is time-invariant andone that is time-varying. In the time-invariant W matrix, the entry in cell i, j measures thegeographical distance between countries i and j. This captures the notion that tariffs are geo-graphically correlated, perhaps because factor endowments or technologies are also geographicallycorrelated. In this context, ρ measures the degree to which the tariff levels of geographic neigh-bors affect one another. If ρ is positive, then tariffs tend to move together along geographic lines.When tariffs increase in one country, that country’s neighbors’ tariffs also tend to increase, andvice versa.

We also code a time-varying connectivity matrix that describes whether two countries are bothGATT/WTO members. Specifically, we construct Wt, where entry i, j for the year t equals 1 ifcountries i and j are both members of the WTO in year t and is zero otherwise. The matrix variesover time, since countries may join the GATT/WTO in different years in our sample. This matrixthus captures the specific interdependence mechanism- bargaining among WTO members- thatour theory generates. If bargaining processes are indeed at work, and countries’ tariff levels affectone another when both countries are WTO members, then we should expect ρ to be positive andsignificant. A positive ρ means that tariff levels are positively correlated across WTO members:when one WTO member lowers their tariffs, other WTO members tend to lower theirs as well.A negative ρ would suggest negative correlation across WTO members: when one WTO memberlowers their tariffs, other WTO members tend to raise theirs.

For each of the two W matrices, we estimate a model in which ρ is time-invariant and anotherin which ρ is allowed to be time-varying. This generates a total of four models. As mentioned be-fore, multilevel modeling has the advantages of accommodating the hierarchical structure of paneldata and analyzing the direct effects of observed and unobserved systemic variables. Therefore,

degree of omitted variable bias that arises from omitting spatial or temporal lags.

32

we conduct spatial modeling in the multilevel modeling framework. Model 8 is more complexthan ordinary multilevel model or standard spatial models, and we estimate this model in theBayesian way using Markov Chain Monte Carlo simulation techniques, though Conditional Maxi-mum Likelihood or Quasi Maximum Likelihood are usually used to estimate spatial models (Liangand Zeger, 1986; Frees, 2004; Skrondal and Rabe-Hesketh, 2008). Markov Chain Monte Carlo usesstochastic simulation techniques to make inferences based on the simulated distributions of theparameters given the observed data (Chib and Carlin, 1998; Gelman and Hill, 2006; Shor et al.,2007; Greenberg, 2007). It is especially powerful for estimating complex and parameter-rich mod-els. Using a Markov Chain Monte Carlo approach requires us to specify prior distributions of theparameters, and normally the researcher does not want the inferences are sensitive to the choicesof priors. We use uninformative priors, and show their influences are trivial.

Yit = β0 + β0t + αi + ρtWitYt + βDDit + εit (Individual-Level Model)

β0t = βSSt + ct (System-Level Model)

(8)

These results are reported in Table 8. First consider the top row in each column, which showsthe estimated coefficient for Regime Type. The coefficients are negative and significant acrossall the four model, and they are similar in magnitude to previous regressions. In this case, ouroriginal results for Regime Type were robust to including spatial correlation effects in our model.Contrary to Oatley’s claim, even accounting for “macro processes” like WTO bargaining, higherlevels of democracy are associated with lower tariffs.

Our results for some of the system variables, however, do change. Interestingly, after theinterdependence is modeled, AVE TARIFF is no longer statistically significant, but GLOBAL WTO

MEM. still has a direct effect on TARIFF. Using different W and allowing ρ to vary over time causesome differences in estimates, such as the coefficients of GATT and BP CRISIS, but over all, thefindings are fairly consistent across the four different specifications.

What about the results for ρ? The last row in Table 8 reports the mean and standard error forthe ρ term in each model. For the last two columns, the numbers reported are the average ρ overthe 39 years covered by our sample. In the two models with time-invariant ρ the results are as weexpected: ρ is positive and significant, meaning that tariff levels are positively correlated acrossunits. On average, as one country raises their tariffs, geographically proximate countries and itsfellow WTO members tend to do the same. Additionally, the estimates of the time-invariant ρsuggest very strong connectivity. Since ρ is bounded between −1 and 1 by design, the estimatesare close to 1 in both model and the standard errors are small.

In columns 3 and 4, which included time-varying ρ, the results are different. The average ρ ismuch smaller and is statistically indistinguishable from zero. The reason for the different resultsacross the two sets of models (time-invariant and time-varying ρ’s) becomes apparent when weexamine how ρ has changed over time, using the results from the time-varying ρ models. Theseresults are shown in Figure 13.

The left panel of Figure 13 shows the estimates of ρ across years using the geographic distanceW matrix and the right pane shows the same thing using the mutual WTO membership W matrix.Looking at the left pane, for the first years in the sample, until approximately 1999, ρ is positivesuggesting a positive correlation across geographically proximate countries. But after 2000, ρ isnegative, suggesting a negative correlation across geographically proximate countries. Looking atthe right pane, the overall time trend in ρ is similar, though ρ is statistically indistinguishable from

33

Figure 13: Time-Varying ρ: Geographical Distance and Mutual WTO Membership

Model 6 Model 7

-1.0 -0.5 0.0 0.5 1.0

1970

1980

1990

2000

ρ

Year

-1.0 -0.5 0.0 0.51970

1980

1990

2000

ρ

Year

zero for many of the early years, and ρ becomes negative earlier on. These results are puzzling,since we are unaware of a theoretical reason to expect a negative correlation among countries’tariffs. But the results do uncover an interesting phenomenon–the way that countries’ tariff levelsare related to one another changes over time, perhaps because of changes to the system in whichthey operate.

3.2.6 Category 6: Combination of All of the Above

Nothing about the modifications described in the models above requires that they be used in isola-tion of one another. We can imagine theoretical reasons to suspect violations of any combinationof the assumptions made by the independence model. Within the classes of models describedabove (direct effects, indirect effects, moderation, and interdependence), we can imagine furthertheoretically-informed refinements (specific types of mediation, one-way vs. mutual moderation,time-varying vs. time-invariant W or ρ, etc.), which generates a large number of possible models.In fact, it is possible to construct a model that relaxes all of the assumptions described above.The most “non-reductionist” model possible could account for direct and indirect system effects,interdependence among units, and moderation. Such a relationship is depicted in Figure 14.

Once such multi-headed hydra might look like the following model, Model 9.

Yit = β0 + β0t + β0i + ρtWitYt + βDtDit + εit (Individual-Level Model)

β0t = βSSt + ct (System-Level Model)

βDt = γ0 + γ1St + ζt (System-Level Model)

(9)

34

Figure 14: Combination of Direct, Indirect, Moderating Effects and Interdependence

! ! w21

D1 D2

S

Y1 Y2

"D "D

or #1

"S "S

cor(D2, S)or #2

! ! w12

$1 $1

cor(D1, S)

For the purposes of illustration in the context of our tariff data, we will use the insights gleanedfrom the previous models to estimate two particular models. First, we estimate a model like Model9. In this model, we allow the two moderators previously found to be significant, GLOBAL WTO

MEM. and AV. TARIFF, to moderate the effects of REGIME TYPEin a one-way relationship. Forinterdependence, we use the time-varying W matrix measuring mutual WTO membership andwe allow for time-varying ρ’s. The results from this model are presented in Table 9, Columns 1and 2. Surprisingly, and for the first time, we find negative effects for REGIME TYPE, but they areinsignificant. Why is this the case? The answer lies in the poor performance of the moderatingrelationships specified. Unlike in the previous moderating models, when we now account forinterdependence across units, the moderators are no longer significant. GLOBAL WTO MEM. andAV. TARIFF are no longer particularly good predictors of the effect of REGIME TYPE on tariffs.Both estimates have relatively huge standard errors, which is not only because that the two arefalsely chosen “moderators” but also because 39 years data cannot provide much information tomore precisely locate the coefficients of the poorly chosen system-level predictors. As a result,the model’s predictions for the effect of REGIME TYPE on tariffs are very imprecise, as shownin Figure 15 the left panel, preventing us from concluding anything about the effect of REGIME

TYPE. Another sign that this model is a bad specification is that according to the model neithermoderating effects of the two systemic variables nor interdependence is evident. In Table 9 thegraphical summary of the year-specific ρ is given at the bottom. It shows that only two years outof thirty nine sample years, ρ is significant. This model actually finds very little of significance:only two domestic variables are influential on the tariff level. For all these reasons, we need toeliminate the unimportant systemic variables as moderators.

The second model we estimate takes advantage of this knowledge and excludes the falselyspecified moderators, GLOBAL WTO MEM./AV. TARIFF and REGIME TYPE. However, because thetwo observed systemic variables no longer have moderating effects on the influence of REGIME

TYPE does not enable us to conclude that the international system does not affect the relationshipbetween REGIME TYPE and TARIFF. There may be some unobserved moderators in the system,which can be accommodated by specifying a system-specific (i.e. year-specific) coefficients forREGIME TYPE. However we do not include systemic observed predictors, as described in Model 10.

Yit = β0 + β0t + β0i + ρtWitYt + βDtDit + εit

β0t = βSSt + ct

βDt = γ0 + ζt

(10)

35

Figure 15: Time-Varying Effect of Regime Type: Model 12 and Model 13

-6 -4 -2 0 2 4 6

1970

1980

1990

2000

Year-Specific Effect of Regime Type

Year

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

1970

1980

1990

2000

Year-Specific Effect of Regime Type

Year

As shown in Table 9 Columns 3 and 4, REGIME TYPE has a negative and significant coefficient,as it does for the vast majority of preceding models. The year-specific or system-specific effect ofregime type is graphically presented in Figure 15. The right panel shows the effects of unobservedmoderators in the international system considered in the confidence intervals. Looking at theeffect of REGIME TYPE over time, the coefficient is significant or mostly significant, in most of thesample years, and the expected effect of regime time is very similar to the results from previousmodels. In addition, the pattern of the change of ρ over time is similar to what was found in theinterdependence models discussed before, as shown in Table 9 at the bottom.

In general, we find that the effect of regime type on tariffs is relatively stable, negative, andsignificant, as shown in Figure 16. For our interest in the effect of regime type on tariffs, welearned that this relationship is consistent across a broad range of models that are designed tocapture complex relationships between domestic and systemic variables. After all, the results fromeven the most complicated models were similar to those of the simple independence model. Forother variables, we did not find such robust relationships. The effects of some variables dependedon what type of model we were estimating, which suggests that these relationships are less robustoverall. This shows one immediate benefit of considering a broad range of models; we can assesshow robust results are overall to different specifications of the relationship between domestic andsystemic factors. Another benefit of considering a broad range of models is that we learned agreat deal about relationships beyond simply the effect of one variable of interest. We were able todescribe in detail the degree to which the evidence supported or disconfirmed particular theoreticalrelationships, like mediation, moderation, and interdependence. Overall, we were able to analyzean extremely rich set of possible relationships between systemic and domestic variables.

4 Conclusion

This paper makes five contributions. First, it lays out systematically the five possible theoreticalways in which systemic and domestic forces might interact in world politics. We connect each

36

Figure 16: Effect of Regime Type: Different Types of Interaction Considered

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1

All-Considered

Interdependence

Moderation

Indirect Effect

Direct Effect

Independence

Reported above are the means and 95% confidence intervals of the effect of REGIME TYPE estimated from the models

considering different types of interactions. When there are multiple specifications for one type of interaction, we

choose the one that most appropriately captures the interaction and the data structure.

theoretical model to an empirical specification that best tests the theory of interactions employed.Interestingly, we show that more complex interactions actually require empirical models that havefewer restrictive assumptions. We show how the literature in IR and especially IPE has developedover time according to these five categories. We point out that the “reductionist” model, whichwe term one of independence among domestic and international factors, is actually quite rarein the literature recently. More commonly, as we demonstrate, models assume indirect and/ordirect effects (i.e., mediation) of the system on domestic politics as well as moderation, usuallythrough the use of interaction terms. We advocate that scholars consider more complex forms ofinteraction and model them using newer empirical methods. In particular, we urge IPE scholarsto be clearer about the exact form of interaction they expect and to use the most appropriateempirical strategies to examine it. In sum, to analyze the many different ways in which systemicand domestic factors might interact, we can employ quantitative data and empirical models toadvance our knowledge of IPE. The globalization of the world economy and the dense ties ithas created among states do not mean that we cannot study the foreign economic policies in asystematic way. It does, however, call for scholars to think through very carefully the type ofsystemic and domestic interactions that they expect to see.

Second, we show that examining all of these five interaction effects relative to one particularquestion can yield interesting results. The relationship between democracy and globalization, inparticular, trade, has been a topic of much recent interest (Milner and Kubota, 2005; Milner andMukherjee, 2009; Eichengreen and Leblang, 2008; Adsera and Boix, 2002; Ahlquist and Wibbels,2012). We consider this relationship from democratization to trade liberalization using updateddata and employing all five empirical models of the interaction between systemic and domestic fac-tors that might shape this relationship. We show that even accounting for many types of systemiceffects the relationship between democratization and trade liberalization is robust. Democrati-zation in the developing world has had a positive effect on trade liberalization. This suggests

37

that using the most complex models of systemic-domestic interactions is not always the preferredstrategy. One’s theory of the interaction between domestic and systemic forces should guide thechoice of empirical strategy used. More complex empirical models are not always justified by thedata, even in today’s highly globalized world.

We also make a number of methodological contributions. Our third point is that when theoriz-ing about systemic forces that moderate domestic ones, we should focus much more on multilevelmodels and less on the use of interaction terms. Multilevel models are more appropriate for un-derstanding this relationship because of the structure of world politics. States are embedded in aglobal system; logically they all exist within the context of the global system or economy. Thiscontext is important and rarely can be altered by a single state. Even in unipolar moments allcountries may inhabit a world economy that no one of them can overlook; the so called bondmarket vigilantes, for instance, set the context for the US economy just as they do for the rest ofthe world. Multilevel models explicitly take this hierarchical nature of the system and its unitsinto account. The global system sets the context for states’ actions and this is captured by theMLM, and not by the use of interaction terms. Furthermore, MLMs are better at addressing asituation where there are multiple contextual factors that states must take into account. Interac-tion models quickly become overwhelmed when multiple interactions are included, but MLMs caneasily handle this situation. In addition, MLMs treat the system and its effects on countries asprobabilistic and not deterministic, which is the assumption made in interaction models. Hencewhen theory posits that systemic factors moderate domestic ones, we advocate the use of MLMinstead of interaction terms.

Fourth, the use of spatial econometric models has become more common. And this is a goodoutcome. These models create a connectivity matrix positing how states are linked to one anotherin a particular global system. This nicely captures the strategic interaction among states dependingon how they are linked to one another. Most models of this connectivity assume that the systemis static over time. That is, while the connectivity matrix may be changing over time, the effectit has on states (rho) is stable across the years. We however think that this may oversimplifythe interactions among states and they system. The system’s effects may be changing over time.Hence we introduce into the literature a time-varying spatial connectivity model. This allows usto capture changes in the system and how states interact with one another as the system evolves.We believe that this adds further realism into our empirical models.

Finally, we propose the most complex type of interaction of systemic and domestic factors todate. We bring together MLM and spatial connectivity to explore how the conjunction of manyforms of systemic influence on states can be studied. It is not clear that the world system-whetherpolitical or economic-has only one set of effects on states. It may not only set the context for statebehavior but also shape the way in which states strategically interact with one another. Puttingthese multiple forms of interaction together into one model allows us to examine the many formsof influence the international system can have on its units. As we noted above, however, using themost complex empirical model is not always necessary. The level of complexity should depend onthe theory of interactions being proposed.

These five contributions should help scholars better understand the globalized world we livein today. The fear of a “reductionist” approach to international relations espoused by Oatley(2011) has not come to pass. With newer empirical models and with clear thinking about how tomatch theoretical approaches to these models, international relations scholars are well-equippedto explain even those most complex real-world phenomena.

38

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Table 7: Moderation Models: Interaction Terms and MLM

Mutural Moderation One-Way ModerationCovariate Interact. Model 6 Model 5

Domestic

REGIME TYPE 0.263 0.252 0.215 −0.326 0.175(0.248) (0.233) (0.231) (0.288) (0.830)

LN POP 1.677 2.368 2.363 2.367 2.375(0.906)∗ (0.263)∗ (0.268)∗ (0.267)∗ (0.267)∗

GDP PC −1.754 −1.881 −1.830 −1.772 −1.783(0.463)∗ (0.330)∗ (0.332)∗ (0.332)∗ (0.332)∗

BP CRISIS 0.921 0.888 0.860 0.839 0.814(0.444)∗ (0.430)∗ (0.431)∗ (0.430)∗ (0.431)∗

EC CRISIS 1.821 1.699 1.809 1.596 1.620(0.924)∗ (0.915) (0.916)∗ (0.918) (0.918)

OFFICE 0.002 0.002 0.002 0.002 0.002(0.001) (0.001) (0.001) (0.001) (0.001)

GATT 1.488 2.255 2.233 2.375 2.299(0.705)∗ (0.602)∗ (0.601)∗ (0.602)∗ (0.605)∗

Systemic

US HEG −10.421 −4.825 −5.109 −5.931 −13.810(18.186) (21.424) (21.220) (21.432) (23.269)

AV.TARIFF 0.856 0.959 0.934 0.851 0.851(0.066)∗ (0.072)∗ (0.071)∗ (0.076)∗ (0.078)∗

8 OPEN −0.332 −0.058 −0.062 −0.052 −0.047(0.145)∗ (0.053) (0.054) (0.054) (0.054)

GLOBAL WTO MEM. 47.072 17.915 17.312 16.103 15.726(23.867)∗ (8.213)∗ (8.393)∗ (8.360)∗ (8.616)∗

GLOBAL WTO TRADE 189.057 22.776 15.308 28.323 26.429(197.568) (112.083) (114.036) (113.647) (117.805)

Moder.

REG. TYPE× GLOB.WTO MEM. −0.778 −0.760 −0.706 −0.690 −0.397(0.380)∗ (0.359)∗ (0.350)∗ (0.349)∗ (0.822)

REG.TYPE× U.S. HEG. 2.641(3.000)

REG.TYPE× AV.TARIFF 0.030 0.027(0.009)∗ (0.010)∗

REG.TYPE× 8 OPEN −0.005(0.005)

REG.TYPE× GLOB.WTO TRADE −9.063(11.6703)

R2 0.111log Like. -12575 -12579 -12578 -12576BIC 25328 25311 25317 25337

∗ Significant at 95% level.

45

Table 8: Spatial Modeling: From Constant ρ and W to Time-Varying ρ and W

Time-Invariant ρ Time-Varying ρCovariate M4 M5 M6 M7

Domestic

REGIME −0.221 −0.208 −0.207 −0.194(0.038)∗ (0.038)∗ (0.039)∗ (0.039)∗

LN POP 2.338 2.313 2.398 2.306(0.261)∗ (0.261)∗ (0.251)∗ (0.266)∗

GDP PC −1.855 −1.962 −1.702 −1.762(0.321)∗ (0.332)∗ (0.319)∗ (0.318)∗

BP CRISIS 0.744 0.372 0.748 0.546(0.430)∗ (0.437) (0.422)∗ (0.430)

EC CRISIS 1.848 1.730 1.725 1.798(0.903)∗ (0.937)∗ (0.901)∗ (0.914)∗

OFFICE 0.002 0.000 0.002 0.002(0.001) (0.001) (0.001) (0.001)

GATT 2.289 −14.335 2.350 2.096(0.597)∗ (0.972)∗ (0.590)∗ (1.310)

Systemic

US HEG −3.379 6.342 6.987 5.168(13.673) (14.360) (16.360) (16.162)

AV TARIFF −0.030 0.010 −1.731 −0.217(0.069) (0.076) (0.111) (0.151)

Eight Open −0.067 −0.073 −0.041 −0.062(0.047) (0.047) (0.046) (0.047)

WTOM 15.765 16.310 1.089 15.580(7.116)∗ (7.191)∗ (7.012)∗ (7.247)∗

WTOT −0.591 −0.421 0.682 −2.215(19.859) (19.570) (19.673) (19.629)

ρ 0.963 0.949 0.307 −0.142(0.030)∗ (0.043)∗ (0.532) (0.357)

∗ Significant at 95% level.

In M6 and M7, the reported estimates of ρ is the pooled posterior distribution of ρt in 39 years. The distributions

of ρt’s are graphically summarized in Figure 13.

46

Table 9: Moderation and Interdependence: Time-Varying W and ρ

Type of Variable Name M12 M13

Domestic

REGIME −0.539 (11.190) −0.197 (0.050)∗LN POP 2.442 (0.263)∗ 2.308 (0.254)∗GDP PC −1.622 (0.317)∗ −1.775 (0.326)∗BP CRISIS 0.681 (0.429) 0.584 (0.429)EC CRISIS 1.565 (0.920) 1.741 (0.912)∗OFFICE 0.001 (0.001) −0.000 (0.001)GATT 1.965 (1.872) 1.200 (1.601)

Systemic

US HEG 0.578 (16.293) 5.814 (16.221)AV TARIFF 0.417 (0.207) −0.209 (0.158)Eight Open 0.022 (0.029) −0.060 (0.047)WTOM −10.691 (17.288) 15.406 (7.241)∗WTOT −3.664 (19.610) −2.514 (19.664)

ModerationREGIME× WTOM −0.14 (16.675)REGIME× AV TARIFF 0.027 (0.079)

Year-Specific/Time-Varying ρ (1970-2008)

-1.0 -0.5 0.0 0.5

1970

1980

1990

2000

ρ

Year

-1.0 -0.5 0.0 0.5

1970

1980

1990

2000

ρ

Year

∗Significant at 95% level.

47