Despite great leaps in science, technology, and human civilization since World War II, many countries in the world have been stuck in “middle income” traps or remained hopelessly poor. To understand this reality,we introduce a new metric, the revealed comparative wealth (RCW), and develop a theory of global hierarchical order (GHO), which is characterized by a Zipf–Mandelbrot law (ZML) for the yearly ranked RCW for all the countries in the world. Major factors contributing to the existence of GHO have been identified. Various types of behavior, including equilibria characterized by largely constant RCW, strongly coupled advanced economies modulated by business cycles, strongly competing developing and underdeveloped economies opposite-phase locked to advanced economies, and steadily growing or decaying economies synergistically interact to create ZML. The mathematical structure of ZML imposes fundamental limits to world economic development and sheds light on why “middle income” traps have persisted.