From Innovation to Diversification: A Simple Competitive Model

Current models of economic growth consider the relationship between the inputs of countries' goods production and their effects on overall productivity, but without taking into consideration the diversity of those inputs. Understanding how countries develop new productive capabilities and expand their export baskets is fundamental to explaining patterns of economic development and prosperity.

Hidalgo and Hausmann first proposed a new metric for comparing the competitiveness of countries through a fitness model based on the complexity of exported products. This approach was subsequently optimized by Tacchella and colleagues, who analyzed the binary export matrix derived from Revealed Comparative Advantage (RCA). This matrix defines the adjacency structure of a bipartite network connecting countries to products, through which it is possible to derive a product network based on the co-occurrence of goods in the export baskets of different countries.

The product space represents products as nodes in a network, with connections indicating that the capabilities needed to produce one product are similar to those needed for another. Countries navigate this space by developing new products adjacent to their existing capabilities. The productivity processes appearing in a country can thus be understood through the directed network structure of the product space.

Previous approaches to modeling this evolution required the introduction of abstract concepts like "capabilities"—latent productive factors that countries must acquire to produce specific goods. While conceptually valuable, this abstraction made it difficult to connect the model directly to observable economic data and limited its predictive power.

We present an algorithm for product innovation that can replicate the evolution of the binary export matrix without introducing the abstract concept of capabilities. In our algorithm, the evolution of the export matrix is driven by the dynamical evolution of the product network itself, in which different countries occupy different nodes representing the products they currently export.

In this framework, innovation appears through two concurrent and competing mechanisms. The first is the introduction of brand new products with respect to the entire product space—representing true innovation that expands the boundaries of what is produced globally. The second mechanism is the copying or adoption of products from neighboring positions in the product space—representing incremental diversification based on similar capabilities.

The countries' product development dynamics are formalized through a power law relationship plus an offset term. The power law component is responsible for the product copying dynamic, capturing how countries tend to develop products similar to what they already produce or what similar countries produce. The offset represents the pure innovation process—the development of entirely new products that don't follow from existing capabilities.

Our model successfully reproduces the main characteristics of the historical patterns observed in export matrices, including the pace at which countries diversify, the tendency for innovation to cluster in certain regions of product space, and the path-dependent nature of economic development. By grounding the model directly in observable network evolution rather than unobservable capabilities, we provide a more transparent and testable framework for understanding economic diversification and innovation.