We construct a simple firm-based automata model for global economic inter-dependence of countries using modern notions of self-organized criticality and recently developed dynamical-renormalization-group methods (e.g., L. Pietronero et al., Phys. Rev. Lett., 72(11):1690 (1994); J. Hasty and K. Wiesenfeld, Phys. Rev. Lett., 81(8):1722, (1998)). We demonstrate how extremely strong statistical correlations can naturally develop between two countries even if the financial interconnections between those countries remain very weak. Potential policy implications of this result are also discussed.