Abstract

Some recent publications have implemented a nonlinear iterative Fitness-Complexity (FC) algorithm, which is claimed to represent the `Fitness' of national economies in the network of global trade as well as the `Complexity' of the products that are traded.  In this paper, we provide arguments from both the fields of complex networks and of economics for why the underlying assumptions that define the FC metrics are unjustified, and the conclusions that can be drawn from its use are unfounded.   By evaluating the historical and current literature in international trade, we explain why this methodology's assumption that growth can be predicted simply by exports is unreasonable.  We further provide theoretical and numerical evidence for the intrinsic instability in the nonlinear definition of the FC algorithm, where huge variations in Fitness or Complexity are produced by small changes in the trade network.  We show that the algorithm will often assign zero `Fitness' to countries with many exports, and that these cases are unavoidable without arbitrarily cutting off the iterations.  Finally, we perform an in-depth evaluation of the algorithm's Fitness and Complexity rankings in two real world networks:  the global trade network of countries exporting various products, and the patent network of countries filing triadic patents of various technological classes.  In both networks, we find evidence of the wild instabilities predicted theoretically, and show that products or patents classified according to the method as highly `Complex' tend often to be those that countries rarely bother to produce, rather than those that are intrinsically difficult to produce.  Taken as a whole, our results cast fundamental doubt upon any conclusion that can come from the implementation of the FC algorithm and metrics.