Complexity Measures and Macroeconomic Stability of Centralized and Decentralized Exchange: Evidence from Cross-Cultural Anthropological Data

Centralized exchange has a worst-case size-complexity many orders of magnitude lower than decentralized monetary exchange. As long as its computational limits are not exceeded, therefore, a centralized exchange may approach Pareto-efficiency more rapidly than a decentralized exchange. Wealth holdings sufficient to guarantee Pareto-efficient exchange may also be more easily achieved by a centralized exchange. In a centralized exchange, the sufficiency condition is that the central agent should begin each period with wealth equal to all other agents’ excess demands. In a decentralized monetary system, by contrast, each agent should begin each period with wealth equal to its own excess demand. If centralized wealth sufficiency is more reliably maintained, then it may have – in addition to its size-complexity advantage – greater macroeconomic stability than decentralized monetary exchange. Supporting this conjecture, historical evidence and tests on cross-cultural anthropological data suggest that the first economies with a complex division of labor were centralized “storehouse economies,†rather than the decentralized monetary systems. Econometric estimates are used to demonstrate a further implication of size-complexity theory: that the historic limits of centralized systems, and the eventual prevalence of decentralized monetary exchange, were associated with increased division of labor, rather than increased population