Two Stage Modelling of Arms Trade: Applying Inferential Network Analysis on the Cold War Period

Two Stage Modelling of Arms Trade: Applying Inferential Network Analysis on the Cold War Period Eva Ziegler, Michael Lebacher ú, Paul W. Thurner, Göran Kauermann ú Draft version. Do not cite! We demonstrate how a novel two-stage approach for valued networks delivers new insights into the trade of major conventional weapons (MCW) during the Cold War. We follow the concept from international trade literature to explore first the extensive margin of trade relations between sender and receiver and second the intensive margin of the amount stage. On the first stage we rely on the dichotomous arms trade network and use exponential random graph models (ERGMs) allowing us to account for network interdependencies. The second stage consists of analysing continuous positive trade flows conditioned on the given network employing linear mixed models. Applying this approach on the Cold War period we have three main results, firstly, the binary decision to trade is strongly driven by network e ects and indicates a predominance of strategic considerations in contrast to economic ones. Secondly, the e ects on the second stage are di erent insofar that the receiver s economic prowess now plays a role for the decision of how much to trade. Thirdly, it seems that flows from the Eastern Bloc are more strongly correlated among each other than in the Western Bloc. The advantage of our two stage model is therefore that we can disentangle between di erent considerations on the extensive and intensive margin. Overall, we can show that the political economy of international arms trade (IAT) during the Cold War is characterised and can be distinguished in the Western Bloc by it s market economy and the planned economy of the Eastern Bloc. Geschwister Scholl Institute of Political Science, Ludwig-Maximilians-University Munich, Germany, Phone: +49/ 89 / 2180 9034, E-mail: eva.ziegler@gsi.uni-muenchen.de, paul.thurner@gsi.uni-muenchen.de ú Department of Statistics, Ludwig-Maximilians-University Munich, Germany, Phone: +49/ 89/ 2180 2226, E-mail: michael.lebacher@stat.uni-muenchen.de, goeran.kauermann@stat.uni-muenchen.de

1 1. Introduction The geopolitical strategy of the Cold War (CW) period for the US is best summarized in the Truman Doctrine of 1947 where then President Truman pledged to support any nation that is threatened by or opposed to the Soviet Union. Consequently, the post World War II evolving international arms trade (IAT) was shaped by this split of the world into two blocs. This makes it an interesting case to apply our novel two-stage model in order to study the political economy of IAT. While most previous IAT research neglected the importance to conceive IAT in a networked context, any network analysis so far was only on a binary level. Nonetheless, interdependencies of the binary trade as well as the trade flows are constitutive to explain the observed trade. For a better understanding of IAT we turn to the international trade literature where research demonstrated the need to decompose trade into it s extensive margin (how many senders and receivers) and intensive margin (amount sold). Still, most research on international trade also neglects to model trade interdependencies within a network framework. However, one main important finding as of now from international trade analysis is the requirement to first understand the determinants of the binary trade flows before estimating the amount of flows. Connecting this we present a first stage for the extensive margin where the binary network is estimated and a second stage for the intensive margin where the weighted network is estimated, conditioned on the binary network. The empirical strategy for this two stage model is to model on the first stage the binary decision to trade arms with the inferential network analysis tool Exponential Random Graph Model (ERGM). On the second stage the flow of arms is modelled with a mixed model that has its origins in spatial statistics. This model allows for an analysis of the dependencies among trade flows given the network structure from the first stage. By focusing on the specific period of the Cold War we are able to show that rivalries between two powers not only play out on a bilateral level but can encompass numerous actors. 1 Specifically, the results of the first stage show how the network is driven by network e ects and strategic political considerations while on the second stage economic considerations also play a role. Focusing on this period and applying our approach we add to the existing literature by introducing on the one hand an option to model the binary as well as weighted network. In doing so we are able on the other hand to present new findings in the IAT literature. One has to consider the possibility of di erent e ects working on the first stage compared to the second stage and cannot make inference from one stage to the other. Specific for the Cold War period our model was able to show that in the amount stage the liberal markets of the West follow economic considerations while for the planned economy of the Eastern Bloc intrinsic motives to send more than economically expected are prevalent. The paper is structured as follows. The next section gives an overview on the relevant literature on IAT and connects it to international trade theory.the third section gives insight into the data via selected descriptive statistics. After this the empirical strategy section presents the ERGM and the mixed model and how they are specified for IAT analysis. The results section will discuss the outcome 1 See Kinsella and Tillema (1995) and Harkavy (1994) for information on the nuclear stalemate between the superpowers playing out over proxy fights in e.g. Third World client states.

2 of this in context of outlined political economy of IAT. The final section encloses a summary and conclusion. 2. Connecting Arms Trade Literature with International Trade Theory Literature on Arms Trade Empirical literature on IAT is considerably small and di erent models come to varying results. Early work by Pearson (1989), using linear regression, pointed out that military expenditures have a significant, positive impact on arms imports. Smith and Tasiran (2010) find partial support for a non-linear demand function where arms imports rise with military expenditure but then fall due to development of a domestic arms industry. The result of their random coe cient approach holds cross sectionally but not in time-series. A time-series analysis by Kinsella (2002) describes an action-reaction process due to military-technological uncertainties and with it the perceived need of a state to acquire and maintain military capability. In an older paper Kinsella (1994) investigates with the vector autoregression method the impact of superpower arms transfers on two enduring Third World rivalries during the Cold War. The correlation results show that there is an action-reaction dynamic apparent in superpower transfers although the reactive tendency was more pronounces in the U.S. policy. With the U.S. as the defender of the status quo in the two case studies and the Soviet Union as the revisionist supplier, the arms flow of the challengers of the status quo is partly exogenous to the flow between status quo states. Comola (2012) demonstrates with a fixed-e ects gravity-type tobit how democracies export more arms than autocracies, probably because democracies tend to have more open economies. Using maximum likelihood estimation Blanton (2005) shows for the USA that human rights and democracy played a role for the decision to send arms but for the amount of arms the OLS regression showed only a positive impact for democracy. Those results hold only for the post Cold War period. In contrast, Perkins and Neumayer (2010) find for the period between 1994 to 2004 for the US, UK, France and Germany how they do not limit exports to human rights abusing or autocratic countries. Regarding the e ectiveness of embargoes Brzoska (2008) finds that embargoes work better when multilateral and the more participants it has using bivariate regression. Moore (2010) gives evidence how breaking MCW embargoes is driven by political interests rather then economic interests. However, the results by Erickson (2013) using MCW as well as small arms and light weapons (SALW) present that embargoes e ectively reduce arms transfers. Nevertheless, a recent case study by Schulze et al. (2017) tested with a Heckman selection model the e ectiveness of rules and norms in limiting IAT in Germany. They show that compliance with multilateral arms embargoes is only present after 1990.

3 This compendium puts on display how small the number of quantitative literature in IAT is as well as the lack of overall robust findings. In addition to that, we argue that any kind of large-n studies on IAT should be undertaken in a networked context. By conceiving IAT as a network we can account for MCW trade deals that depend on other MCW trade deals. Neglecting these dependencies when modelling IAT leaves reasonable doubts over the legitimacy of previous studies applying traditional regression models. 2 Only few studies have even considered IAT in some basic form of networked context, which can control for dependency. For example Akerman and Seim (2014) who were the first to visualize the MCW trade network 1950-2007. While employing network statistics their empirical strategy relies once again on a regression type model in particular a pooled OLS linear probability model (LPM). Besides the drawbacks of a LPM for this kind of data they do not estimate the amount stage of arms trade. 3 Their findings are that the Warsaw Pact is more strongly centralized around the Soviet Union then the NATO around the UK, the US and France. Also, they find a stable negative relationship between di erences in polity and the likelihood of arms trade during the Cold War but not after it. Further on Childs (2012) added an in-degree centrality statistic to a fixed-e ects panel regression to account how integrated a state is in the global arms market between 1950-2011. Indeed, adding the integration measure has a positive, significant e ect on the import of arms. Even though those papers consider arms trade as a network of relational data they still do not employ a fully network based approach. Published papers, which undertake a truly network analytical approach on IAT are from Kinne (2016) and Thurner et al. (2017). In Kinne (2016) a stochastic actor oriented model (SAOM) is used to asses the impact of formal weapons cooperation agreements (WCAs) on the global arms trade between 1995 2010. He models a coevolutionary process with a network of WCAs between states and a network of arms trade between states. A state s position in one network would then influence the other network s evolution and vice versa. In the SAOM model an actor is maximising his utility and depending on this function a tie is created or terminated by the actor. The results show for the given network how high WCA centrality rises the probability of arms trade. Also, an increase in arms trade increases the probability of WCA ratification. Kinne (2016) presents an extensive application of network analysis with the SAOM. Still, his research s focus is on the coevolution aspect with the WCAs and also covers only a short period of time. In addition, SAOMs work under strong assumptions which in reality might not be fulfilled. 4 Further on Thurner et al. (2017) investigate with a temporal exponential random graph model (tergm) the network structure of international arms trade between 1956 2013. tergms are specifically useful because it is a dynamic model which allow network structures to change over time. Thurner 2 Example for such dependency of triadic relationships: state A is in the decision making process to sell to state B. State A is a recent IAT parter of state C and knows that state C sells to state B, this friendship would have a positive impact on the trade decision. 3 LPM can go over the [0,1] interval. 4 For example the actors only maximise the given function for the next step and not for the long term. Also, the tie generating process is not simultaneous or coordinated either (no negotiations) and therefore one cannot observe collective actions. Besides this doubtful assumption for arms trade the homogeneity assumption for actors in IAT is untenable.

5 and network visualizations. Saramäki et al. (2007) for example study the clustering coe cient in weighted networks for the international trade network (ITN). They find that typically high trade volume countries typically engage in high-volume trade with each other. Fagiolo et al. (2008) expands this research by comparing the results of the binary network approach to the results of the weighted network approach for the topological properties of the ITN. Their findings show how taking into account the magnitude of flows paints a substantially di erent picture compared to the analysis of the binary network. While a binary representation of the ITN gives the impression of a highly connected graph the weighted network tells us that e.g. the majority of existing links are associated to weak trade relationships and countries holding more intense trade relationships are more clustered. Also, the weighted ITN is only weakly disassortative, meaning that there can be well-connected countries that trade with partners that are also well-connected. This research on the topological properties of ITN demonstrates that edge formation should be analysed separately before putting weights on those edges. Further research supports this notion e.g. Squartini et al. (2011a) on binary network analysis and Squartini et al. (2011b) on weighted network analysis. In both cases null models are employed which do not explain the causal underlying mechanisms shaping the network but they signal a strong correlation between e.g. a local network statistic and a higher-order network statistic. In a null model certain country-specific properties (e.g. GDP) are enforced as constraints otherwise the topology is maximally random. Comparing the null model to the observed ITN one can derive which properties are significantly di erent from the null model prediction and which are random. The result of Squartini et al. (2011a) stresses the importance to estimate the determinants of the process governing the creation of a link in a first step. Squartini et al. (2011b) adds to this with the weighted analysis revealing the importance to take in a second step into account indirect interactions besides direct ones in order to improve models of international trade. Also, Squartini et al. (2011b) calls for the need, in order to understand the structure of the international trade system, to reproduce the binary network even if only interested in the weighted. Dueñas and Fagiolo (2013) investigate based on this previous research if the gravity model of trade can explain the topological properties of the ITN. Comparing the observed ITN to the properties of the gravity model estimates of the ITN the binary structure can be very well explained by the gravity model but not the weighted one. To summarize the parts together firstly, previous IAT research is not only limited but neglects to conceive it in a networked context in order to capture interdependencies. Secondly, the few examples of IAT network analysis do only include binary analysis. Thirdly, turning to international trade literature for a theoretical foundation they are facing the similar problem to take into account higher-order patterns of the ITN. Research was able to establish the need to decompose the analysis into an extensive and intensive margin of trade, which is the theoretical basis for our model. Network analysis of the ITN is also limited but the findings so far demonstrate how important it is to know firstly the determinants of the binary network before secondly, turning to the determinants of the weighted network. This further supports our two-stage approach to IAT. The finding that zero trade flows are important to model is also very important for arms trade though we assume di erent determinants not related to market forces. For the second step of estimating the determinants of the amount of

6 First Stage Binary Network Estimating determinants of forming an edge Second Stage Valued Network Estimating determinants of values which are put on given edges Result Same covariates in estimation Result Figure 1: Depiction of the two stage process for estimating the IAT. Deriving from insights of international trade research we state the need to investigate the binary and weighted network separately as we cannot simply assume the same results for these two di erent but connected processes. the flows we condition on this binary network while still accounting for interdependencies between the trade flows. The empirical strategy for this model as depicted in Figure 1 will be presented after the description of the data. 3. Data description and preprocessing The data on the international trade of major conventional weapons (MCW) is provided by the Stockholm International Peace Research Institute (SIPRI). This institute collects information on all transfers of MCW from 1950 to 2016 in a comprehensive database. The data on trade flows includes information on the sender country, the receiver country as well as the type of MCW that is traded, this includes for example aircraft, armoured vehicles and ships. See table A1 in the Annex for a comprehensive overview of the types of arms included and A3 for the list of countries included. The volume of the trades is measured in so called TIV-values, shorthand for trend-indicator value. Those values do not represent the sales prices of arms transfers but are based on the production costs and represent the value of military resources that are exported. For detailed explanations on the methodology, see SIPRI (2017b). The SIPRI Arms Transfers Database can be accessed free of charge online at SIPRI (2017a) after agreeing to its terms and conditions. We give an overview of the dynamics of the aggregate volumes of arms trade measured in TIV values. One very prominent feature of the arms trade lies within the fact that only few countries account for the lions share of the international arms exports, leading to export clusters. This is illustrated in Figure 2 on the left, where the aggregated TIV values are plotted against time. Until the year 1960, more than 80% of the international arms exports are originated within the three countries Soviet Union (SUN), United States (US) and United Kingdom (UK). And this pattern is persisent as until 1991 still over 75% of the aggregated exports can be explained by these three countries. It can be seen that the aggragetd value grows almost constantly from 1950 to 1958, followed by a sharp reduction in

7 40000 40000 30000 30000 TIV 20000 TIV 20000 10000 10000 0 0 1950 year countries other SUN UK US 1950 year countries CHN DEU EGY IND IRN IRQ JPN other POL SYR Figure 2: Time Series of aggregated TIV values. Sender perspective on the left, receiver perspective on the right the period from 1959 to 1962. After that, the values climb until they reach their maximum in 1982, followed by a decline that mirrors the end of the cold war. While the structure of the supplier side is quite lucid, the picture on the demand side is much more complicated as the few exporters are faced with many importers. In Figure 2 on the right the nine countries that had the highest import-shares during the whole period, as measured in TIV values, are shown together with the rest of the imports. These countries are China (CHN), Germany (DEU), Egypt (EGY), India (IND), Iran (IRN), Iraq (IRQ), Japan (JPN), Poland (POL) and Syria (SYR). The nine most important importer countries can explain only about one fourth of the whole aggregated arms trade volume. This is in stark contrast to the supply side. Another important thing to recognize is that the most important importers do not match, with the exception of Germany, with the most important exporters. In addition to that, the important importing countries are not necessarily rich, developed countries. Furthermore, we can see that there exists a pronounced reallocation of the import shares over the course of time. While China was the most important importer until 1960, its imports shrink dramatically after the Sino-Soviet split. Germany becomes the most important importer during the period from 1960 to 1978, mirroring its catch-up after the end of the German demilitarisation policies employed by Allied forces. In the years from 1970 to 1980 Iran developed as a major importer of MCW, followed by a strong decline of imports after 1980. The most stable trend can be spotted if one looks at the imports of Japan. While all of this pattern are very interesting considered by itself, they give evidence that the demand side changes much faster and dynamically than the supply side. Additionally, we can see that may developments are influenced by political decisions and events e.g the increase in trade after the Cuban missile crises in 1962. Not only the volume of arms trade increases over time, but also the number of countries that participate in IAT. In the left panel of Figure 3, the number of countries that were considered for the

8 150 0.018 100 0.016 Number 50 Density 0.014 0 0.012 1950 year countries Involved in the Trade Not involved in Trade 1950 year Figure 3: Number of Countries in the Arms Trade Network (left), Density of the network (right) analysis is plotted together with the number of countries that actively participate in the arms trade network is plotted. 5 One can see that the number of countries included in the analysis is steadily increasing. The number of countries that are engaged in arms trade parallel this trend until 1980 when it declines in analogy to the volume of the traded arms. However, the number of countries involved has roughly doubled from 1950 to 1991. In the right panel of Figure 3, thedensity of the network is plotted against time. The measure Density is defined as the number of edges that exist in the network in relation to the number of theoretically possible edges. Therefore, this measure gives an impression of the intensity of arms trade given the number of actors in the network. As shown in Figure 3 the Density first increases for a couple of years and decreases sharply in 1960 when many former colonies entered the network that are not yet integrated in the arms trade network. However, in the following years the density climbs up again as the arms market becomes more globalized, followed by two sharp declines in 1985 and 1991 reflecting the impact of the decline and end of the Soviet Union on the arms trade network. In Figure 4 we see a scatterplot that displays on a logarithmic scale the degree (left Outdegree, right Indegree) versus the TIV values. It becomes clear that there seems to be a connection between the outdegree and the aggregated exports of a country in a given year. This gives strong evidence for the hypothesis that sending countries with a lot of receivers tend to export more arms as measured in TIV values. The same is true for receivers which have many senders who receive a higher amount of arms the more incoming ties they have. 5 We considered all countries in a given year that existed and where reliable values for the covariates of the further analysis are available. The List of countries can be found in Annex A3. Active participation is defined as having imported or exported arms in a given year.

9 1e 01 1e+01 1e+03 1 2 5 10 20 50 Outdegree vs. TIV value, logarithmic scale Export TIV value Outdegree 1e 01 1e+00 1e+01 1e+02 1e+03 1 2 5 10 Indegree vs. TIV value, logarithmic scale Import TIV value Indegree Figure 4: Aggregated Degree Distributions A visual overview of the binary network is given in Figure 5 for the years 1952 and 1991. Note that there are two dominant features. One is the clustering of trade activity. This becomes very clear at the top of Figure 5. There the trade is organized around Great Britain, the United States and the Soviet Union. It is harder to see this structure in the net in 1991 but it is still there, with the Soviet Union (SUN), United States (US), United Kingdom (UK), France (FRA), Switzerland (CHE), Canada (CAN) and Germany (DEU) as central actors. So the trade activity is organized in clusters around the sending countries. The second feature we see is that the networks can be separated into blocs. There is the Western Bloc (blue) and the Eastern Bloc (red). This leads to a separation of the network into three subgraphs. The first subgraph contains the Eastern Bloc, which consists in essence of the trade flows from the Soviet Union to its satellites. The second subgraph that contains the United States, Canada and West Europe which is also the center of the third subgraph, representing the non-aligned states. In addition, the Western Bloc seems to be more open with respect to flows out of its own bloc, while the Eastern Bloc is rather hermetic. Also, note that the non-aligned states are more interwoven in the Western Bloc network part then the Eastern.

10 Arms trade network in 1952 ZWE FIN JOR IRQ LBN LKA BEL SAU THA NLD NOR PAK IDN SYR PER GBR IND HND ZAF PRT NZL ISR IRN ITA HTI POL BGR FRA TWN ALB AUS DNK SWE USA CHE YUG GRC HUN PRK CZE CAN LUX PHL PRY ROM SUN DOM JPN CHN URY CHL KOR EGY COL TUR CUB ARG YEM MNG MYM VEN GDR Arms trade network in 1991 ARG PRY LSO AUT TGO GIN BRN MAR NER QAT BEL PNG RWA URY COL DJI BFA GRC BOL CHL MEXPHL TUR CYP BHR PRT ZAF GTM ESP FRA TUN SWE DNK SLV CHE IRL NOR ISR ITA VEN BWA USANLD ARE BHS CAN IDN ECUAUS KOR JPN DEU SAU PER KEN PAK FIN TWN BRA SGP GNBNGA NZL GBR KWT ROMIND THA MYS EGY HUN BGD POL CHN IRN TON MHL SLB BGR AFG SUN YUG MYM DZA PRK LKA ZWE SDN JOR GHA MRT ETH CZE CUB YEM HRV SYR Figure 5: International Arms Trade Network 1952, 1991. Trade flows within the Eastern Bloc in red, within the Western Bloc in blue. Edge size and vertex size proportional to the TIV value traded.

11 4. Empirical Strategy Motivation The dominant model class in inferential network analysis is still the Exponential Random Graph Model (ERGM), as introduced by Holland and Leinhardt (1981), see also Frank and Strauss (1986) and Lusher et al. (2012). Indeed it is possible to extend the ERGM framework to valued networks. The most recent proposals for modelling valued networks are by Krivitsky (2012) and Desmarais and Cranmer (2012). Those models allow for discrete valued counts (Krivitsky, 2012) and transformation of the weights on the edges into the interval [0, 1] (Desmarais and Cranmer, 2012), putting the dependence structure essentially in the quantiles. Both approaches seem not to be suitable for the given application, because the TIV values are continuous which excludes the work of Krivitsky (2012) and because the valued ERGM framework of Desmarais and Cranmer (2012) is not feasible at that time, because of computational constraints. In addition to that we are confronted with the following problem: If we take a network based perspective on the MCW trade, we would have a very heavy censoring at zero, which cannot be accounted for at the moment with the valued ERGM. 6 We therefore try another estimation strategy based on breaking down the problem in two steps. Stage One: Modelling the binary Network The binary arms trade network is modelled by the means of ERGMs. For the well disposed reader please refer to the Annex for a more formal derivation. At this point a more basic but intuitive version will be presented. Formalized in (1) the concept refers to the probability of a given network over all networks one could have observed. P (Ỹt X t = x t )= exp{ T t s(ỹt,x t )}, (1) Ÿ( t ) Ỹ t is the network realization given the exogenous covariates X t = x t. The vector of valued statistics from the network is s( ) and t is a parameter vector of covariates. The term Ÿ( t )representsthe normalization constant, ensuring that the probability distribution sums up to one. While previously Ÿ( t ) was infeasible to calculate for non-trivial networks, work by Geyer and Thompson (1992) and Hummel et al. (2012) now allows us to stable estimate ERGMs for medium sized networks that were not estimable before. This also holds for the given application, where the year wise ERGM estimation procedure did not converge with other methods. We are aware that there are possibilities to estimate dynamic ERGMs, as for example the temporal Exponential Random Graph Model (the tergm, see Hanneke et al., 2010) or the Separable temporal 6 In a network representation with N t actors in time point t, we would have N t (N t 1) potential trade flows. As the network is rather sparse we would have an excessive amount of zero valued flows.

12 i j Figure 6: Illustration of dyadic network statistics. Outdegree on the left and Indegree on the right. i j i j Figure 7: Illustration of triadic network statistics. Dyadwise Shared Partners (DSP) on the left and Edgewise Shared Partners (ESP) on the right. Exponential Random Graph Model (the StERGM, see Krivitsky and Handcock, 2014) but we are explicitly interested in allowing for parameters that can change with each discrete time step. Note that for example the tergm was already employed for this dataset by Thurner et al. (2017). Specifying the binary Model Edges: A frequently used network statistic included in virtually all ERGM models. The statistic sums up the number of existing edges in the network. The related coe cient can be thought as analogous to the intercept in a linear regression (see Hunter et al. (2008)). However it has a meaningful interpretation as it indicates how dense the analysed network is. Geometrically weighted degree (GWD): The statistics geometrically weighted outdegree (GWO) and geometrically weighted indegree (GWI ) are parametric statistics that were proposed in order to include the indegree- and outdegree-distribution and help to avoid the endemic problem of degeneracy. These terms build on the indegree and the outdegree statistics (see Figure 6), counting how many ties are outgoing from i or ingoing to j, respectively. The weighted statistics are essentially defined such that they downweight the counts for indegree or outdegree as the degree increases. We can interpret a positive coe cient on GWO (GWI ) as sign that the network has a tendency to contain high outdegrees (indegrees). 7 7 Interpretation of GWD is not intuitive e.g. often positive estimates of GWD are interpreted as measures of popularity but indicate dispersion of edges. A good overview of the e ects of the parameters gives the application by Michael Levy, see https://michaellevy.shinyapps.io/gwdegree/

13 Geometrically weighted triads: Two other important statistics are geometrically weighted edgewise shared partners (GWESP) and the geometrically weighted dyadwise shared partners (GWDSP). Both concepts are built upon the idea of counting the k directed two-paths between two countries i and j (see Figure 7). Again both statistics are weighted down. While GWDSP represents a parametric summary measure of the tendency of two countries being connected via directed two-paths, regardless whether they are tied or not, GWESP only counts the directed two-paths of two countries connected by an edge. If GWDSP and GWESP are both used in a model one can think of GWDSP being a baseline e ect that gives information whether directed two-paths are probable, while GWESP isolates the e ect of having a tie, given that a certain number of directed two-paths is present. Note that with a positive coe cient of GWESP or GWDSP the log-odds of forming a new directed edge increase monotonic but sub-linear with the number of partners they have in common (see Goodreau et al. (2008) and Goodreau et al. (2009)). This implies diminishing returns. 8 Besides the endogenous network statistics we also include exogenous covariates. All of those, except the measures for Path-Dependency are lagged by two years because of the substantial time lag between ordering and delivering of arms. 9 Economic Quantities: Standard covariates for trade data are the logarithmic GDP of the sender as well as the receiver, formalized as Sender GDO and Receiver GDP. The GDP data are taken from Gleditsch (2013) which covers socialist and communist countries prior to 1992. We decided to use GDP and not GDP per capita because arms trade represents a share of the GDP and we want to model the propensity of trade. Because we assume that the military expenditure of the potential receiver has a role to play, we include Receiver Military Expenditure as an explanatory variables. The data is available from Correlates of War Project (2017) in the national material capabilities data set with Singer et al. (1972) as the basic reference on the data. As it is not unlikely that a high value of goods trade leads also to a high level of arms trade we additionally include the logarithmic volume of goods trade, lagged goods trade, available from Gleditsch (2013). Because there might be some path-dependency in the data, we also include the lagged logarithmic arms trade (lagged arms trade) as explanatory variable. If there was no lagged trade of arms or normal goods we set the variable to zero. Political Quantities: As the political landscape at the time period of the Cold War is characterized by two political blocs we include dummy variables for trade between countries within the Western Bloc or in the Eastern Bloc. A detailed list of the countries included in each bloc is given in A4. A common result in network analysis is that similar actors are subject to stronger gravity than 8 Parts of the explanations stem from the very helpful comments of Steven M. Goodreau at the Statnet Help Site as well as from useful comments he gave via Email. Please also note that we have used a downweighting parameter of 1.5 in all parametric statistics. 9 We add this from a theoretical standpoint. Indeed, if we do not introduce the lag the results remain almost the same.

14 dissimilar ones. We therefore include a measure for the similarity of political regimes. A standard measure is the so called polity score, ranging from the spectrum 10 (hereditary monarchy) to +10 (consolidated democracy). This data can be downloaded as annual cross-national time-series, see Center for systemic Peace (2017) for the data and Marshall and Jaggers (2002) as a basic reference. In our model we operationalise Absolute Di erence Polity Score the distance between political regimes by using the absolute di erences between the scores. Stage Two: Modelling the trading amount given the network structure After the network structure is estimated, we model in a second step the amount of trading. Here, we assume that the network structure in Ỹt leads to correlations among the trade flows. A possible approach is employing the tools developed in spatial statistics and spatial econometrics (see Kauermann et al., 2012 for a comprehensive overview). This has already been done in several applications and such class of models is called network autocorrelation model in the social network methodology (see for example Leenders, 2002 and Hays et al., 2010). The problem comes with the fact, that network analysis without physical analogue lacks the classical geometry that is exploited in spatial statistics. A possible solution is to construct an, so to speak, artificial spatial structure from the network. We will construct a simultaneous error model structure (see Cressie, 2015) to account for the network dependencies. Note that this is a very di erent approach in comparison to modelling the connection between vertices like in the section above as the analysis is concerned with modelling processes defined on the network graph where the graph itself is taken as given. As we are modelling the dependencies among trade flows we will use the term tradecorrelation for the phenomena under study. The models from spatial statistics often build on mixed models because they allow the variables of interest to be dependent. This dependency is incorporated in the model via random e ects, imposing structure in the Variance-Covariance of the error term (see for example Fahrmeir et al., 2013). The general model is a linear mixed model and given by log(y t,ij )=X T t,ij t + u t,ij + t,ij (2) where log(y t,ij )representsthen t logarithmic valued trade flows from i to j at time point t and X t,ij represents the covariates, the coe cient t represents the vector of coe cients on the fixed e ects. The unknown vector t,ij N(0, 2 t ) is the i.i.d. unstructured error term and for the unknown vector u t containing all random e ects u t,ij it holds that u t N(0, and t,ij is zero. t). The expected mean value of u t,ij The vector u t,ij can be further decomposed (please refer for a more formal derivation again to the Annex) and to subsume by imposing structure into t the model becomes a correlated random e ect model (see Cressie, 2015 or Wall, 2004). Following this we specify that a trade flow from i to j depends on all other exports of i and the potential reciprocal trade flow from j to i. With this structure we

15 assume that the tradecorrelation of the flow log(y i,j ) is mostly related to the exporting country i, that regards the other exports as well as the import (j, i) in its decision on the volume of the arms trade to country j. This structure will lead to sender-based clusters of trade activity. To make this more intuitive we present an example. Example In the top left of Figure 8 we see the original logarithmic values of the trade flows, encoded in colours, ranging from yellow (low values of log(y t,ij )) to red (high values of log(y t,ij )). The network structure is generated from the neighbourhood structure specified above. On the right we see the fit of a simple linear model, using the logarithmic GDP of the sender and the receiver, as well as the absolute di erence of the polity score as explanatory variables, together with labels of the trade flows. We see that the imposed dependency structure leads indeed to a clustering of trade activity. We see a big cluster for trade activity of the United States, a cluster for the United Kingdom and one for the Soviet Union. Additionally we have a smaller cluster for Canada. By assumption we have, that the western cluster is connected via the reciprocal flows, i.e. the USA-cluster is connected to the GBR cluster via the flows USA GBR and GBR USA. The same is true for their connection to the cluster of Canada. In the bottom left we see the residuals of the simple linear model. And now the advantages of the chosen specification become visible. The trade activity of the Soviet Union is for example underestimated, as the residuals are almost all positive, while the trade activity of Canada is overestimated with negative residuals. The model that was used in the bottom right uses the model specified above in order to use this additional information in the residuals. If we compare the colours on the two diagonal plots, we see that the fit is pretty good. Also a comparison of the standard errors of the linear model (2.22) and the mixed model (1.27) shows that the chosen specification might be useful. In addition to that, we have fl = 0.73, being a sign of high within-cluster correlation. Specifying the valued Model In order to be consistent with the estimation of the ERGMs we will estimate model (2) first year wise and in addition to that we will estimate the model jointly for all years, together with time fixed e ects. For the exogenous covariates we are using exactly the same as for the binary model. In addition to that we split the constant for the model into di erent arms categories. The reason for that is, that in a given arms export, it is of vital importance what share of arms category is traded. If for example the share of ships is very high, the flow is often unusually high. Constant: We divide the constant into the share of aircraft and air-defence, the share of battleships, the share of artillery, the share of armoured vehicles and the share of other military equipment.

16 Real Trade Flows, sd= 2.59 Linear Model, se= 2.22 GBR-NZL GBR-FRA GBR-THAGBR-JOR GBR-SYRGBR-AUS GBR-BEL GBR-LKA GBR-ITA GBR-NLD GBR-YUG GBR-SAU GBR-LBN NLD-BEL GBR-PAK SWE-CHE GBR-IRQ GBR-DNKGBR-ZAF GBR-FINGBR-CHE CZE-EGY GBR-IND GBR-ISR GBR-NOR GBR-ZWE GBR-SWE SWE-DOM GBR-USA GBR-CAN NLD-IDN CZE-CHE SWE-ISR USA-GBR USA-SWE USA-LUX USA-YUG USA-ITAUSA-ZAF USA-ISR USA-HND USA-IND USA-CHL USA-GRC USA-JPN USA-NOR USA-NLD USA-DOMUSA-DNK USA-CUB USA-PRY USA-FRA USA-PER USA-AUS USA-PHL USA-KOR USA-HTI USA-BELUSA-CAN USA-NYE USA-PRT USA-SAU USA-COL USA-IRN USA-CHE USA-URY USA-TUR USA-TWN USA-THA USA-PAK USA-IDN USA-ARG USA-VEN SUN-PRK SUN-ALB SUN-HUN CAN-GBR SUN-BGRSUN-POL SUN-ROM SUN-CHNSUN-MNG SUN-CZE CAN-TUR SUN-GDR CAN-USACAN-MMR CAN-COL CAN-CHL CAN-URY Residuals Spatial HGLM model, se= 1.27 rho= 0.73 Figure 8: Tradecorrelation in 1952. Colours range from yellow (low values of log(y t,ij )) to red (high values of log(y t,ij )). Time fixed e ects: For the joint estimation from 1952 to 1991 we are using dummy variables for each year. Random e ects: For the joint estimation from 1952 to 1991 we are using random e ects for the tradecorrelation. Note that we assume that the network structure in t 1 is not allowed to act on the tradecorrelation in t.

17 5. Results ERGM The results for the ERGM are provided as time series in Figures 9 and Figure 10. Starting on the top left panel of Figure 9 we analyse the network statistics first. For Edges the consistently negative and significant coe cient increases over time when the network becomes denser. In general the network is rather sparse and only a few countries that could possibly form trade relationships do so. While international trade is much more developed, the IAT network is thinner than one could randomly expect. The coe cient on the geometrically weighted outdegree (GWO) shows some fluctuations but it is consistently significant and negative, mirroring the fact that countries with a high outdegree are unlikely in the given network. This is in line with the theory that only a minor share of countries has the ability and political power to produce and export arms. Most countries are restricted to simply having no exports. The negative parameter stands for a higher probability of an edge on a high degree node than a lower-degree node. Also, due to the fact that a negative GWO stands for a more centralized network we can see the network becoming even more centralized from 1972 to 1977 when it increases back to the previous level. In comparison to the GWO the geometrically weighted indegree (GWI ) does not deliver a clear result. There is a downward trend for the coe cient but it is not significant for a long time probably because the networks are too small. The GWI coe cient is significant and negative from the 1980ies onwards. Such a negative tendency is in line with the idea that most countries are restricted to be delivered by only one or two suppliers. The tendency that there are fewer indegrees then randomly expected could be traced back to the fact that there are indeed only a few possible suppliers as Figure 2 shows but could also be due to numerical problems with the estimation algorithm. Informative for the structure of the IAT are the GWDSP and GWESP. Using GWDSP as a baseline e ect it becomes clear how there is no general tendency in the networks that two-paths relations form. The coe cient is negative and significant most of the time. So on a network level, we have predominantly a structure of stars, a few countries with high outdegree and dependent countries with one indegree. The coe cient of the GWESP is mostly positive and significant from 1970 on. Putting this result in contrast to the GWDSP result we see that although there is no tendency to have indirect trade relationships, there is indeed a higher probability to form a trade once an intermediate path is already there. We might interpret this from two angles. On the one hand, it is plausible that indirect network relationships could hint to states having some kind of defence agreement not controlled for in the fixed e ects. On the other hand, the economic costs and risks might be lower if one sells to countries where already another receiver country is delivering to. Considering it is the Cold War period the friend-of-a-friend logic seems to apply here. Also, the few indirect relationships could hint to the fact that the IAT market is almost only served by three main producers and only from 1970 onwards the TIV share of other producers increases.

18 Overall the network statistics deliver a very interesting insight into the structure of arms trade. Relationships are uncovered which have not been estimated on a year wise basis before. The results show the importance to consider the endogenous process within IAT. Turning to the results of the covariates we can state the following. While the sender GDP has a consistently positive and significant impact on the probability of forming a tie there is no such result for the Receiver GDP. The natural interpretation is on the one hand how indeed only wealthy countries have the possibility to have a high-performing arms industry and they supply other countries, that are often less economically developed, mainly because of strategical reasons. Note that this result stands diametral to the standard results from Gravity model. On the other hand it seems as if the sender country does not consider a state with a high Receiver GDP more likely as a possible receiver then a country with less Receiver GDP. Those results give an impression that the economic prowess and the likeliness of fulfilling a contract are not driving the decision of the sender to sell arms or not. This is to a certain extent further supported with the result of the Receiver Military Expenditure coe cient. If a high receiver military budget is more attractive for a seller the coe cient would be positive. However, any significant results are negative besides one. This negative coe cient is surprising, but can be rationalized by the idea a countries with high Receiver Military Expenditure are more likely to produce arms for themselves. Finally, the political quantities reveal how the decision to sell arms during the CW is strongly driven by strategic political considerations. There is a tendency for both blocs to have higher intra-bloc trade than out-of-bloc-trade but this is only a tendency for the Western Bloc and a very solid and high e ect for the Eastern Bloc coe cient. This is in line with our theory where we expected an impact of the bloc divide on the decision to sell arms. Taken together with the path dependency below, especially the Eastern Bloc spurs a lock in e ect. While the Western Bloc is less discriminatory to non-aligned partners or aligned partners not automatically can expect eligibility one can assume for Eastern Bloc countries almost a guaranteed access to Soviet arms, and only for those. A path dependency in form of the lagged arms trade and lagged goods trade can be clearly derived from the positive and significant coe cients. A (high) trade in arms as well as in goods in the period before increases the probability of having another trade rapidly. Considering time e ects the rise and drop for lagged arms trade around the 1960ies can be traced back to the high number of former colonies joining the dataset but who have not yet taken part in arms trade. The decrease of the lagged goods trade coe cient over time reflects the increase of the global trade and it s decline impact on IAT decisions. Regime dissimilarity has no impact on the trade decision. Given the results above it is not too remarkable that the absolute Di erence in Polity Score has not a big role to play. It is reasonable to assume that given the bloc structure both parties, the Soviet Union as well as the United States preferred to send arms to nations within the bloc or against the hostile bloc, rather than looking at political distances. This is a remarkable result as previous papers (e.g. Akerman and Seim (2014), Comola (2012)) were concentrating on the question of polity score having a negative e ect or none. Introducing the bloc divide variable seems a better predictor for a state s decision to sell arms. To summarize these ERGM results we firstly can state that there is a need to conceive IAT as a

19 network. In doing so we can take into account endogenous network processes which, as the results have shown, are a very important factor in explaining the formation of the IAT network structure. They can already reveal political considerations such as a friend of a friend structure. Secondly, states with a high Receiver GDP and/or Receiver Military Expenditure do not have an impact on the probability that they are more likely to receive arms. These two factors, which could serve as economic incentives for a sender do not impact the binary decision to sell. This leads to the third point we can derive from the results. The political quantities can clearly show how the CW split has substantial explanatory power for the formation of the IAT network. The ideological alignment of the receiver is even more important within the Eastern Bloc while the liberal markets of the Western Bloc react to supply and demand forces outside this realm. In addition, a path dependency e ect in form of Lagged Arms Trade and Lagged Goods Trade is to be associated with the network structure. Overall, strategic political considerations due to network dependencies as well as political factors such as the East vs. West ideology are the main drivers of the binary decision to sell arms. 10 10 As the goodness of fit measures are very extensive in the given application, please contact the authors for those results. The diagnostics show that the model fits well.