Untangling the Lattice: A Multi-Stage Value-Added Gravity Model for Global Value Chains

This essay addresses the growing complexity of global value chains by developing a fully structural, multi-stage value-added gravity model. In today’s hyper-fragmented production networks, goods routinely cross borders multiple times before reaching final consumers. Standard gravity models, which measure trade in gross terms, double-count intermediate crossings and bias elasticity estimates upward. My model overcomes these limitations by explicitly mapping value-added flows through each stage of production and trade. Methodologically, I derive the gravity equation from a Hicksian, cost-minimizing dual formulation, which isolates pure substitution effects from income changes. I embed stage-by-stage value-added contributions into a nested CES cost kernel, ensuring that each leg of the supply chain—direct, upstream, and downstream—can be identified and estimated separately. Empirically, I implement a Poisson Pseudo-Maximum Likelihood estimator on a 2017–2023 ADB MRIO dataset covering 14 RCEP economies, controlling for multilateral resistance and zero-trade flows. Baseline estimates confirm that de-duplicating intermediate crossings and applying Hicksian compensation both attenuate distance and tariff elasticities compared to gross models. The multi-stage specification further uncovers substantial heterogeneity: border and trade-cost frictions differ markedly across production legs, and my approach sheds light on anomalies—such as negative border effects—observed in highly integrated sectors.