Globalization and Social Networks Georg Durnecker University of Mannheim Fernando Vega-Redondo European University Institute September 14, 2012 Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 1 / 20
Motivation Globalization, a distinct (economic) phenomenon of our times What is globalization? From a social network viewpoint: short distances on the social network (a small world ) long-range links supporting far-away interaction Why is it important? local opportunities become soon exhausted hence expansion requires turning global: need for fresh opportunities the social network (key support for exploration & exploitation of new economic opportunities) must also turn global! Some of the questions addressed by the model: How & when such globalization happens? What is the role of geography? Is it a robust/irreversible phemomenon? Is there a role for policy? Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 2 / 20
Related literature Empirical Different specific measures on globalization: trade: Dollar & Kray (2001), Kali & Reyes (2007), Fagiolo et al (2010) direct investment: Borensztein et al (1998) porfolio holdings: Lane and Milesi-Ferreti (2001) Integrated (multidimensional) measures: Dreher et al (2006) Theoretical Dixit (2003): agents located along a ring, play a repeated Prisoner s Dilemma opportunities improve with distance but observability deteriorates external enforcement is needed it only pays if economy is large Tabellini (2008): same spatial setup as Dixit s, with altruism (decaying with distance) social evolution of preferences à la Bisin-Verdier (2001) preferences evolve, possibly reinforcing cooperation Both anchor enforceability or altruism to (fixed) geography/space Here, to endogenous network (formation depends on network+space) Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 3 / 20
Outline 1 The model Basic framework Dynamics: innovation and volatility Game-theoretic microfoundation 2 The analysis Some illustrative simulations Benchmark theory (large-population limit) General theory (finite population) 3 Summary and conclusions Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 4 / 20
Basic framework Finite (large) population N, placed along a ring in fixed position Continuous t 0, state is the social network g(t) = {{i, j} N} each link ij g(t), an ongoing valuable project the link eventually becomes obsolete and vanishes Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 5 / 20
Law of motion: innovation and volatility Innovation (link creation) At each t, every agent i gets an idea at rate η to collaborate with 1 some other j. Such j is selected with probability p ij [d(i,j)]. α The link ij is actually formed if (1) it is not already in place (2) agents i & j are close either geographically: d(i, j) ν(= 1), socially: δ g(t) (i, j) µ, µ N Volatility (link destruction) At each t, every existing link ij g(t) vanishes at rate λ(= 1). parameters η: rate of invention (arrival of new ideas) α: cohesion (parametrizes importance of geography) µ: institutions (efficacy of social network in supporting cooperation) Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 6 / 20
A game-theoretic microfoundation outline A link is conceived as a repeated partnership with two phases: 1 The setup stage: a Prisoner s Dilemma to cover setup costs the project starts only if at least one agent cooperates 2 The operating phase: repeated coordination game high- and low-effort equilibria partnership ends at rate λ. The population game can be played under two norms/equilibria: Bilaterally independent: cooperation in PD supported bilaterally Network-embedded: idem supported by third party punishment, when the social distance from the latter to deviator no higher than µ. The N-embedded norm induces, at equilibrium, postulated law of motion (assume neighbors setup costs are lower and can be bilaterally supported) Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 7 / 20
A first appetizer: simulating a low cohesion scenario α = 0.5 µ = 3 n =1000 Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 8 / 20
A second appetizer: simulating a high cohesion scenario α = 2 µ = 3 n =1000 Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 9 / 20
Benchmark large-population theory (I): steady state condition Given a steady state, let φ be the conditional linking probability of a randomly selected node and let z denote the average degree Steady State Condition (SSC): φ η n = λ z 2 n Assume family steady-state (random) networks can be parametrized by z. Then, given the parameters of the model (η, µ, and λ(= 1)) we can make φ = Φ(z) and write the SSC as Φ(z) η = 1 2 z which induces an equation to be solved in z. Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 10 / 20
Benchmark theory (II): Two cohesion-related scenarios Depending on the value of α, two scenarios: Low Geographical Cohesion (LGC): α 1 High Geographical Cohesion (HGC): α > 1 Key contrast: whether, as n, the space-decaying probability of selecting any finite set of nodes is zero (LGC) or positive (HGC). It all hinges upon whether (n 1)/2 1 lim n d α = lim ζ(α, n) = ζ(α) n d=1 is infinite (LGC, α 1) or finite (HGC, α > 1). Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 11 / 20
Benchmark theory (III): large-population assumptions Maintained hypothesis: Steady states can be represented as random networks for large populations. Then, building upon the theory of random networks, the following assumptions can be made on the function Φ(z) by taking limit n on counterpart properties applying for finite populations: A1 Let α 1. Then, ẑ > 0 s.t. for all z ẑ, Φ(z) = 0. A2 Let α > 1. Then, Φ(0) = [ζ(α)] 1 > 0. Also, we make some regularity assumptions (differentiability, monotonicity) on the function Φ(z) Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 12 / 20
Benchmark theory (IV): results We posit the dynamical system: ż = η Φ(z; α) z 2 Proposition 1 Let α 1. Then, the state z = 0 is asymptotically stable. Proposition 2 Let α >1. Then, if η > 0, the state z = 0 is not asymptotically stable. Furthermore, there is a unique state z > 0 which satisfies: ɛ > 0 s.t. z(0) (0, ɛ), ϖ[z(0), t] z. Therefore, whether or not the social network can be built from scratch depends on whether or not there is sufficient geographic cohesion. Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 13 / 20
Benchmark theory (V): results, cont. Proposition 3 Given any α > 1, denote by z (η) the unique limit state z established above. For any z, there exists some η such that if η η, then z (η) z. Proposition 4 ᾱ such that if 1 < α < ᾱ, the function z ( ) is upper-discontinuous at some η = η 0 > 0. Therefore, if geographic cohesion is above the required threshold (α > 1) the steady-state connectivity can be made arbitrarily large as η grows. Furthermore, if such cohesion is not too large, such dependence on η displays an upward discontinuity at some η 0. Recall this behavior was observed in our earlier illustrative simulations. Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 14 / 20
General theory (I) To understand better the role of local congestion and institutions, we need to consider a general (finite-population) framework. But, for finite populations, an analytical approach is intractable so we pursue a numerical computation of equilibria that involves a numerical determination of the function Φ(z) This allows a precise computation of the equilibria and, correspondingly, a full-fledged comparative analysis. Here, we focus on two issues: The role of institutions and innovation rate on optimal cohesion α The effect of institutions on long-run connectivity Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 15 / 20
General theory (II): numerical determination of equilibrium Having computed Φ(z) for every α, η, µ, find z s.t. Φ(z ) = z /(2η) Graphically: Finite population (n = 1000) induces significant local saturation -- mainly for high α Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 16 / 20
General theory (III): optimal degree of cohesion Trade-off between better environmental conditions (higher µ and η) and the optimal degree of cohesion α (n = 1000) η =5 η =10 η =20 Op#mal value α Ins#tu#ons µ Innova#on rate η Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 17 / 20
General theory (IV): the role of institutions The effect of institutions on long-run network connectivity displays a step-like form: α =0.3 α =0.5 α =0.7 α =1 Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 18 / 20
Summary Our stylized model stresses the following features of globalization: 1 It is a property of social networks: short network paths spanning long geographic distances and connecting a large disperse population 2 It must underlie dense economic activity/collaboration by overcoming local saturation & expanding the set of opportunities 3 Robust phenomenon that, under low cohesion, arises abruptly (by triggering self-feeding effects on network formation) 4 Importance of social ( geographic ) cohesion: some is crucial, but beyond a point it is detrimental 5 Equilibrium multiplicity & hysteresis opens up a role for policy: temporary measures (e.g. rise in η) may produce persistent effects Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 19 / 20
Some reflections on methodology and interdisciplinarity Question: Can economics [that must extricate itself from its current conceptual crisis] benefit from methods/insights of other disciplines? Answer: Yes, in particular can profit from (statistical) methods developed to study large systems of interacting entities... and this is an example! But a number of very important caveats, often ignored by non-economists! Here, I emphasize just two, underlying historical success of the discipline: 1 Economic systems consist of rational (purposeful) individuals: (a) incentives are essential component of economic insight (b) payoffs are unavoidable basis for welfare analysis & policy evaluation 2 Economic agents are forward looking: (a) expectations are essential component of economic insight (b) coherent formation of expectations (possibly through learning) must underlie useful welfare/policy analysis: Lucas critique Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social Networks September 14, 2012 20 / 20