The stochastic spatially extended generalized Lokta-Volterra approach was introduced a few years ago and was applied using analytical (field theory and statistical mechanics methods), numerically (computer experiments) and empirical (gathering and processing real data) techniques to a wide range of natural, biological, economic and social systems. In this talk I will describe its recent application to the study of interactions between economic sectors, countries and blocks. The theory predicts robustly in a very wide range of conditions systematic regularities in the growth rates evolution of various subsystems. The after-shocks J-curve phenomenon (economic decay and rebound induced by the emergence of singular growth centers) is revisited and more empirical support is given to the theory. In particular we show that the data support to the connection between the economic minimum and the crossover of the new emergent leading sector with the old decaying one. We describe the Growth Alignment Effect (GAE), its theoretical basis and demonstrate it empirically for numerous cases in the international and intranational economies. The GAE is the concept that in steady state the growth rates of the GDP per capita of the various system components align. We differentiate the GAE predictions from the usual convergence or divergence conceptual framework that dominated in economic studies until now.