๐ค AI Summary
็ ็ฉถ้่ฟๆๅบไธ็งๆฐ็็ฎๆณ่งฃๅณไบไพๅบ้พๅ
็ๆง่ฝฌๅ็ๅจๆๆ กๅ้ฎ้ข๏ผ่ฏฅ็ฎๆณๅฉ็จ็ฝ็ป็็ฉ็ๅฑ็บง็ปๆ่ฟ่กไผๅใ
๐ Abstract
Understanding how supply chains endogenously transform requires a parametric model of processing networks with non-neutral substitution elasticities. While the Cascaded CES (CCES) production function provides a rigorous framework for these multi-layered linkages, dynamically calibrating its structural parameters from time-series data constitutes a highly non-convex inverse optimization problem. Enforcing the strict microeconomic concavity constraint causes standard monolithic approach to fail due to extreme ill-conditioning and the curse of dimensionality. To overcome this computational bottleneck, we propose a novel structure-exploiting algorithm. By leveraging the physical upstreamness topology of the network, our hybrid heuristic alternates between a vertical cascade-sequential descent and a horizontal block coordinate descent. Our framework successfully calibrates the fundamental elasticities of a 10-sector marcoeconomic model of the United States, providing a tractable computational engine to fully endogenize and predict complex supply-chain transformations.