Endogenous Technological Thresholds and Jobless Growth: A Schumpeterian Theory of Volatility Trap

Why does rapid technological progress at the global frontier coincide with persistent divergence in follower economies? This paper develops a stochastic growth model that integrates a Schumpeterian technology frontier with a micro-founded human capital threshold to address this puzzle. Our main contribution is to show that the development barrier is not static but an endogenously evolving volatility trap, where the threshold itself becomes a function of frontier-level and volatility. This transforms technological volatility from a cyclical concern into a powerful driver of long-run welfare distributions. The model generates three testable results: (1) It proves the conditions for irreversible collapse (Theorems 2 & 4), providing micro-foundations for the lower "twin peak." (2) It endogenizes the concurrent breakdown of Okun’s Law and the Beveridge Curve (Theorems 6 & 7) as structural symptoms of the trap. (3) It identifies three specific externalities that justify a shift from growth-maximizing to resilience-building policies. The analysis provides a unified framework for understanding jobless recoveries, persistent poverty traps, and the policy imperative of managing catastrophic risk in an era of technological change.