Computing Endogenous Transformations in Processing Networks: A Dynamic Calibration Approach

Abstract

Understanding how global supply chains endogenously transform in response to disruptions requires a parametric model of processing networks with non-neutral substitution elasticities. While cascaded CES production functions provide a rigorous analytical framework, dynamically calibrating their structural parameters from time-series data constitutes a highly non-convex inverse optimization problem. Since enforcing strict microeconomic concavity renders standard monolithic algorithmic approaches computationally intractable, we propose a novel data-driven, structure-exploiting algorithm to bypass this limitation. By leveraging the physical upstreamness topology of the supply chain, our hybrid heuristic effectively breaks the curse of dimensionality inherent in economywide processing networks. Applying this computational framework to United States time-series data, we successfully calibrate the fundamental heterogeneous elasticities. This provides a scalable analytics engine to fully endogenize complex supply chain transformations, thereby offering a practical tool to measure structural productivity and uncover the elastic origins of systemic tail risks in large-scale production networks.