J Stat Phys (2013) 151:523–548 DOI 10.1007/s10955-013-0732-x
The Local Structure of Globalization The Network Dynamics of Foreign Direct Investments in the International Electricity Industry Johan Koskinen · Alessandro Lomi
Received: 8 August 2012 / Accepted: 25 February 2013 / Published online: 8 March 2013 © Springer Science+Business Media New York 2013
Abstract We study the evolution of the network of foreign direct investment (FDI) in the international electricity industry during the period 1994–2003. We assume that the ties in the network of investment relations between countries are created and deleted in continuous time, according to a conditional Gibbs distribution. This assumption allows us to take simultaneously into account the aggregate predictions of the well-established gravity model of international trade as well as local dependencies between network ties connecting the countries in our sample. According to the modified version of the gravity model that we specify, the probability of observing an investment tie between two countries depends on the mass of the economies involved, their physical distance, and the tendency of the network to self-organize into local configurations of network ties. While the limiting distribution of the data generating process is an exponential random graph model, we do not assume the system to be in equilibrium. We find evidence of the effects of the standard gravity model of international trade on evolution of the global FDI network. However, we also provide evidence of significant dyadic and extra-dyadic dependencies between investment ties that are typically ignored in available research. We show that local dependencies between national electricity industries are sufficient for explaining global properties of the network of foreign direct investments. We also show, however, that network dependencies vary significantly over time giving rise to a time-heterogeneous localized process of network evolution. Keywords Dynamic stochastic models for networks · Electricity industry · Foreign direct investments · Globalization · Gravity model · Longitudinal exponential random graph models · Ensemble
J. Koskinen () Social Statistics Discipline Area, University of Manchester, Humanities Bridgeford Street, Manchester M13 9PL, UK e-mail:
[email protected] A. Lomi Faculty of Economics, University of Lugano, Lugano, Switzerland
524
J. Koskinen, A. Lomi
1 Introduction and Motivation The aggregate dynamics of socio-economic systems is often modeled as emerging from the behavior of connected agents capable only of local initiative [62, 80, 81]. This view has stimulated a new generation of analytical approaches to social interaction and economic exchange explicitly inspired by models developed in statistical mechanics [15, 27]. Research on the International Trade Network (ITN), also known as the World Trade Web (WTW), represents a prime example of these recent developments [13, 30, 82, 97]. The cornerstone of empirical economic research on the WTW is the so called gravity model of international trade [5, 11]. First suggested by physicist turned economist Jan Tinbergen [96], the model posits that the volume of trade between two countries (bilateral trade) is proportional to their economic masses—as measured, for example, by their Gross Domestic Product, GDP— and inversely proportional to the distance between them—as measured, for example, by the distance between the main cities [25]. The basic idea is that a mass of resources supplied at the origin (“sender”) country (Vi ) is attracted by demand in the destination (“receiver”) country (Vj ), but the potential flow of resources between the origin and destination countries (Yij ) is reduced by their distance (Dij ). In its simplest form, the gravity equation specified and estimated in empirical models is therefore: Yij = Vi Vj /Dij . The gravity model of trade is one of the most successful empirical models in economics [4, 57]. For this reason, it is frequently adopted as a benchmark for more complex models that try to reproduce the observed network structure of the WTW [26]. The empirical success of the gravity model also stimulated recent attempts to extend its domain of application to binary networks such as, for example, the network of trade agreements [11]. The main objective of this paper is to advance this contemporary line of research by examining the extent to which the dyadic (or “local”) network connections between countries implied by the gravity model of international trade are consistent with the global network structures that are actually observed. More specifically, in this paper we estimate a modified gravity equation that we specify to model change in the binary architecture of the global network of Foreign Direct Investment (FDI) in the international electricity industry. FDI involves the acquisition of direct ownership (represented by voting securities) by a single company located in one country (the parent) of a company located in a different country (the foreign affiliate or target). We show that the modified gravity equation reproduces the insight of the original economic model, while adding important detail about the local structure of dependence relations among countries. Our work extends previous research in three ways. First, we adopt a new class of exponential random graph models (ERGMs) [36, 46, 66–68, 88, 101] to represent explicitly the network dependencies between countries linked by a FDI relationship. While some research is available that has considered the role of spatial dependencies in the form of neighbours’ effects [28], to the best of our knowledge this is the first study that attempts to incorporate endogenous degree-based network effects explicitly in the gravity model. Second, we examine how third-country effects shape the global structure of the FDI network. A limited number of contemporary studies have examined the role of third country effects in the formation of dyadic FDI relations between countries [9]. Yet, an underlying assumption of both the theoretical as well as the empirical literature is that FDI decisions are dyadic in nature with no interdependence beyond bilateral trade relations [14]. We are not aware of studies that have linked specific forms of extra-dyadic dependence among countries to the global structure of ITN. Third, the longitudinal ERGM that we specify assumes that tie-variables between each pair of countries evolve in continuous time and an update to the system is governed by the conditional probability of the limiting ERGM distribution. Estimation of the model
The Local Structure of Globalization
525
is performed by means of a Bayesian Markov chain Monte Carlo (MCMC) scheme that iterates between drawing unobserved sample paths connecting the observations and drawing parameters. There is only little experience of using of the statistical model we present [48, 60, 86] and we are not aware of prior empirical studies adopting this model specification and estimation strategy to analyze the dynamics of connected socio-economic systems. The rest of the paper is structured as follows. We begin by introducing and describing the data set. We then emphasize features of the temporal sequence of networks—such as skewed degree distributions and clustering—that represent evident departures from existing model formulations and estimations. We then suggest new model specifications that incorporate both the basic gravity elements as well as extra-dyadic network dependencies. We produce empirical results supportive of our model. We discuss the results with reference to predictive properties and conclude with a discussion that sets a possible agenda for further research. 2 Empirical Setting and Data 2.1 Empirical Setting The dependence relations that are at the core of our modelling efforts are generated by Foreign Direct Investments (FDI) defined as investments: “Involving a long-term relationship and reflecting a lasting interest and control by a resident entity in one economy ([the] foreign direct investor or parent enterprise) in an enterprise resident in an economy other than that of the foreign direct investor . . . ” (UNCTAD 2003: 231 [98]). Current research recognizes FDI as an important financial mechanism for the embedding of local economies into a global network of international relations [94]. We restrict the focus of our analysis of FDI which involve the transfer of control of local companies to foreign owners [8]. Defined in this way FDIs imply an inflow of capital from a country into another and a corresponding outflow of property rights [56]. During the period that we analyze, FDI has progressively become one of the main factors underlying the increased interdependence of national economies [50]. We focus on the electricity industry for two main reasons. The first is more empirical. FDI has been a major force in the globalization of the electricity industry. For example, in 2004 (the last year of observation in our sample) the total value of mergers and acquisitions (the main forms of FDI) in the global electricity industry (including gas) was USD 123.2 bn, 46 % of which were cross borders (USD 57.2 bn), i.e., involved companies in different countries [71]. The second reason relates more directly to our modelling objectives. For a mix of technological, economic, political, and historical factors the international electricity industry has long been considered as an aggregate of national (or “local”) industries with almost no connection across national borders. Before the early 1990s it was almost unconceivable to have national (“local”) electricity companies owned and operated by rival companies located in foreign countries. After two decades of progressive internationalization the electricity industry is recurrently portrayed as a representative example of a truly global industry [7]. Unlike the majority of studies on International Trade Networks (ITN) we are not interested in predicting the aggregate (non-zero) flows of capital between countries [13, 31, 41]. Rather we focus on the change in the binary architecture underlying such flows [26]. Our exclusive focus on network structure is motivated, in part, by recent results suggesting that the structure of international trade networks may be fully characterized in terms of their local topological properties alone [92]. According to Squartini, Fagiolo, and Garlaschelli, for example [93] (2011: 046118-6): “in order to properly understand the structure of the international trade system it is essential to reproduce its binary topology, even if one is interested in a weighted description.”
526
J. Koskinen, A. Lomi
Table 1 Density: (i,j )∈V (2) xij (tm )/(n(n − 1)); and Hamming distance: (i,j )∈V (2) |xij (tm ) − xij (tm−1 )|; for Foreign direct investment ties between 97 countries over 10 years, tm , m = 0, . . . , 9. Starting year t0 = 1994 m
1
2
3
4
5
6
7
8
9
10
Density
0.002
0.004
0.006
0.005
0.007
0.01
0.004
0.009
0.008
0.006
Distance
–
40
66
62
87
110
103
104
104
97
Two main questions guide our empirical analysis: how did the current structure of the FDI network come about? What are the micro-mechanisms driving its change over time? The answers we provide emphasize the endogenous network mechanisms underlying change in each individual tie as a function of the presence or absence of other ties in its neighborhood [69]. 2.2 Data Description Here we provide some basic descriptive characterization of data to motivate the statistical model. The change in density of the FDI networks over time provides a first characterization of the process (Table 1). Network density increases with time until 1999, after which the density decreases. There is thus a considerable number of ties being created and ties being deleted across time. This is mirrored by an increase in the Hamming distances between consecutive years until 1999, after which it decreases. There is thus considerable change over time as well as between consecutive time-points. The networks after 1994 are all characterized by having one large component and many isolates (on average 58 isolates and six countries that remain isolates for all ten years). The in- and out-degree distributions across the years are given in Fig. 1. The distribution of the number of investment ties received is relatively homogeneous and does not change noticeably over the years. The maximum number of investment ties received from other countries is 7 (the USA in 1999). The number of FDI ties sent varies a great deal more and the distribution of out-degrees is much more skewed than the in-degree (one country, the USA, sent ties to 23 other countries in 1999). The network aggregated over the years with nodes positioned geographically is reported in Fig. 2. The USA and Europe are the two main geographical hubs. Ties are generally geographically clustered (especially within Europe but also in the Americas and for example in Austral-Asia) but there are also some longer-range (inter-continental) ties. The geographical hubs and clustering are in accordance with the gravity model (“mass” and “distance”) but some triangles, indicating extra-dyadic clustering are also evident. To examine evidence of dependence beyond the dyads we compare the triad-census (or triadic motifs [65]) for the observed networks against the corresponding triad-census predicted by a uniform distribution. In particular, we generate reference networks from the U |MAN distribution [44], which is a conditionally uniform distribution over all graphs that have a prescribed dyad census. The dyad census counts the number of mutual (M), asymmetric (A), and null (N ) dyads. The triad census for 1994–2003 normalized for each year by the mean and standard deviation according to the corresponding U |MAN distribution is given in Fig. 3 (the triads are labeled according to [44]). This gives a structural profile of the network over time. Across the board it is apparent that there is considerable residual structure beyond the dyadic level. As an example, there are many more null triads (“003”) in data cross-sectionally than we would expect had the dyads been distributed at random.
The Local Structure of Globalization
527
Fig. 1 The in- and out-degree distributions for the FDI networks with log-log plot (insert)
Fig. 2 The symmetrized network (dotted lines are reciprocated ties) of FDI ties aggregated across time with nodes positioned in the geographical centers of the countries
This suggests that dyads tend to cluster together. An example of how they cluster together is the out-star (“021D”) where one country invests in two countries that are themselves neither directly tied, nor linked to the origin country by reciprocated ties. This may suggest outdegree centralization. We also note that reciprocated dyads do not tend to exist in isolation (“102”) but tend to involve one node that invests in a third party (“111U”). Of particular interest is the large number of transitive triads (“030T”). The fact that these are over represented in combination with cycles (“030C”) being few might suggest that the process of foreign direct investment is locally hierarchal.
528
J. Koskinen, A. Lomi
Fig. 3 Observed triad census standardized by the predicted census under the conditional uniform U|MAN distribution (i.e., a uniform distribution over graphs with a prescribed number of mutual, asymmetric and null dyads [44]). The horizontal dashed line is the origin for reference and counts are given as violin-plots sequentially for years 1994 through 2003. Vertical axis is given as standard deviation units and MCMC p-values (multiplied by 100) are provided below and atop violins (alternatingly). Violin-plots display data as both a box plot and a kernel density estimate [42]
Thus, according to the patterns in Fig. 3 there is residual structure over and above the dyadic level. A question central to the analysis of FDI concerns the possible sources of this residual structure. The corresponding dependencies may be due to: (i) over-propensities prescribed by the gravity model; (ii) endogenous processes such as preferential attachment or triadic closure; and, (iii) dependence on initial conditions, i.e. any structure is due to the first observation. It has been argued that triadic features may be captured by spatial embedding [18], a key feature of the gravity model, and it is well known that extra-dyadic dependencies may stem from unobserved nodal and dyadic variates [43] (substantively, these variates represent for example homophily or propinquity [64]). As Daraganova et al. [24] demonstrate, spatial embedding and endogenous dependencies are complimentary in explaining triadic and other extra-dyadic features. The initial condition is not modelled, hence subsequent observations may exhibit extra-dyadic structure even if the process that generated them is to all intents and purposes ‘random’ whenever the first observation has features that depart from ‘random’. In order to address these questions we employ a statistical procedure that allows us to analyze all of these aspects simultaneously. We discuss the modeling framework next (Sect. 3). To summarize: the descriptive analysis shows that there is change over time in the FDI network, that the ties are spatially embedded and that there is evidence of extra-dyadic dependencies liking the countries.
The Local Structure of Globalization
529
3 Longitudinal Exponential Random Graph Models 3.1 Notational Preliminaries We consider di-graphs G(V , E) on a fixed set of nodes V = {1, 2, . . . , n}, with a stochastic arc-set E ⊂ V (2) (V (2) = {(i, j ) ∈ V × V : i = j }). For the purposes of modelling, a graph G(V , E) is represented by its n × n binary adjacency matrix X = (Xij : (i, j ) ∈ V 2 ), where the tie-indicator Xij is equal to one or zero according to whether (i, j ) ∈ E or not, (2) respectively. The space of all adjacency matrices X = {0, 1}V has dimensions 2n(n−1) . 3.2 Exponential Random Graph Models We define and ERGM process as the process on X for which the limiting distribution is an ERGM. ERGMs [36, 46, 88, 101] for cross-sectional networks are a well-researched family of models that evolved out of statistical mechanics and are becoming increasingly popular in the social sciences [66–68]. The ERGM is an ensemble model on X , where the probability mass function is of an exponential family distribution form, Prθ (X = x) = exp g(x; θ ) − ψ(θ ) , where g(·; θ ) is the potential function and ψ(θ ) = log x∈X eg(x;θ) is the (log) partition function, ensuring that the distribution sums to unity on X . The potential function may be a fairly general real-valued function of the network (and fixed graph attributes) that reflect substantively interesting properties of the network. However, principled considerations suggests that g(·; θ ) should be a linear combination of a collection of graph statistics that reflect dependencies between tie-variables. While the Bernoulli-graph [29, 91], with g(x; θ ) = xij , has been used extensively in social network analysis as a null-model, the first model to fully draw on properties of the exponential family and go beyond independent tie-variables was proposed by [46] and [34]. This model was developed from the point of view of standard statistical techniques for modelling binary data and it was not until the seminal paper by Frank and Strauss [36] that the methods for statistical mechanics developed by [12] and [95] were brought to bear on network data. Frank and Strauss [36] proposed that tie-variables may be interdependent but that two tie-variables Xij and Xk (for undirected graphs) are conditionally independent given {Xuv : {u, v} ∈ V2 /{i, j, k, }} if {i, j } ∩ {k, } = ∅. Imposing some homogeneity restriction, xthis i+ (x) = dependence assumption implies an ERGM with sufficient statistics k-stars s k i k (k = 1, 2, . . . , n − 1), and triangles t (x) = i
