The Institutional Trap Theorem: A Markov Chain Formalization of Topological Barriers to Economic Development

We establish a formal result — the Institutional Trap Theorem — which explains the failure of income convergence between advanced and developing economies as a consequence not only of institutional frictions or missing markets, but of a topological constraint in the global knowledge network. Knowledge diffusion is modeled as an absorbing Markov chain M(Λ) on the Product Space of Hidalgo and Hausmann (2009), where transition probabilities are proportional to φ(p,p′)/S(e) (proximity scaled by topological friction), restricted to edges within the institutional planning horizon Λ. High-complexity products (Economy A: machinery, electronics, pharmaceuticals) are defined as absorbing states. We prove the existence of a critical institutional horizon Λ* such that, for all Λ < Λ*, the expected hitting time from low-complexity products (Economy B: agriculture, textiles, raw materials) to Economy A diverges, i.e., E[T | Λ < Λ*] = ∞. For the Harvard Atlas Product Space (2016, HS 2-digit, φ = 0.40), we estimate Λ* ≈ 5, while for Λ ≥ Λ*, the expected hitting time satisfies E[T] ≈ 25–31 steps. Calibrating Λ* against World Bank Rule of Law data, the threshold corresponds to an index value of approximately −0.5 (38th percentile), below which 77 of 202 countries (38%) in our sample are likely operating. For these economies, market-driven knowledge diffusion within the Product Space cannot yield convergence to Economy A in finite expected time, irrespective of factor prices, trade policy, or macroeconomic stabilization. Corollary (policy implication): convergence requires either (i) increasing the institutional horizon Λ, or (ii) direct public investment to construct the missing intermediate knowledge nodes implied by the network topology. In particular, we identify six gateway products—plastics, paper, glass, rubber, beverages, and ceramics—with expected hitting times E[T] ≤ 13, which form the minimal intervention set required to restore finite-time reachability under constrained Λ.