Computing Endogenous Transformations in Processing Networks: A Dynamic Calibration Approach

Satoshi Nakano and Kazuhiko Nishimura

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Abstract: Understanding how supply chains endogenously transform requires a parametric model of processing networks with non-neutral substitution elasticities. While the Cascaded CES production function provides a rigorous framework, dynamically calibrating its structural parameters from time-series data constitutes a highly non-convex inverse optimization problem. Since enforcing strict microeconomic concavity renders standard monolithic approaches computationally intractable, we propose a novel structure-exploiting algorithm to bypass this limitation. By leveraging the physical upstreamness topology of the network, our hybrid heuristic effectively breaks the curse of dimensionality inherent in economywide processing networks. Applying this framework to U.S. time-series data, we provide a scalable computational engine to fully endogenize complex supply-chain transformations, ultimately uncovering the elastic origins of asymmetric macroeconomic tail risks.

Date: 2026-09, Revised 2026-09
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