Endogenous Topological Development: A Network Externality Theorem for the Dynamic Product Space

This paper extends previous companion work showing that transitions from low- to high-complexity production in the Product Space can be modeled as an absorbing Markov chain with a critical institutional threshold Λ* ≈ 5. While earlier models treated the Product Space topology as exogenous, this study introduces an endogenous dynamic Markov framework in which each new country entering a product increases proximity φ(p,q) with neighboring products. This process: Converts structural bridges (S(e)=11) into triangulated paths (S(e)=3) Reduces expected transition times E[T] for countries in the local network We formally establish the Network Externality Theorem: ∂E[φ{t+1}(p,q)]/∂N_t(p) > 0_ for products q adjacent to p Holds under the Capable Entrant assumption (new entrants are more likely to co-export related goods) This result follows from the definition of proximity as a conditional co-export probability: each additional country exporting product p raises the likelihood that countries exporting q will also export p, increasing φ(p,q). Empirical validation is conducted using 2,813 product-year observations (Harvard Atlas HS-92, 232 countries, 1995–2024): Correlation between diffusion and proximity growth: r = 0.241 (p < 0.001) Stronger effect for gateway products: r = 0.301 Largest marginal externality occurs in early stages (N_t ≤ 10) Externalities decline as products mature (N_t > 50) A case study of China’s entry into electronics (HS85, circa 2000) shows: 28% increase in φ(Electronics, Machinery) by 2004 Enabled structural transformation in Vietnam, Indonesia, and Thailand Policy implication (central result): Market failure: private agents do not internalize topological externalities Gateway products are systematically underprovided relative to their social value This provides a micro-founded, topologically explicit rationale for coordinated industrial policy: Target high-externality gateway products Prioritize early-stage diffusion (low N_t) Follow a sequenced intervention strategy based on network position