Abstract:

The structural gravity equation is algebraically equivalent to an iterative proportional fitting procedure (RAS/IPF) for the bi-proportional adjustment of matrices. Under this equivalence, the multilateral resistances (price-aggregators) are exactly the row and column scaling vectors of RAS. The price-invariance theorem of RAS then applies directly: structural gravity is insensitive to changes in price-aggregators.

In practice, this means shock transmission to third countries via substitution effects is not identified in structural gravity, only a size effect is operative in the algebra. This is consistent with Krugman’s 45° rule: countries’ income elasticities and growth rates are correlated in such a way that changes in relative prices are unnecessary to keep the trade balanced. 

Abstract:
The paper argues that two prominent empirical “successes” or consistent results of gravity —the model’s high goodness-of-fit and the near-unit elasticity on the size term— are largely artifacts of regressing a near-identity rather than evidence for its robustness. Empirically, when the identity component is removed, standard trade-cost proxies explain a modest share of variation (about 12% in pooled OLS and 19% with exporter-year and importer-year fixed effects). Finally, the paper shows that the “distance puzzle” arises as a scale artifact linked to the evolution of total world trade, and discusses why log-scale estimators attenuate this effect.

Abstract:
This paper develops a network accounting framework in which national growth rates are mutually interdependent through trade-linked demand flows. Using long-run evidence from the international trade network, it documents a tight empirical regularity: there is a high short-run imports and exports co-movement by country. I show that this co-movement is the exact mathematical transformation of Krugman’s «45-degree rule» (1989), reinterpreted here as an empirical identity. Closing the system for n countries yields a Perron–Frobenius eigenproblem: the long-run vector of relative growth rates is the unique positive eigenvector of a matrix combining import-share weights and export-to-import income-elasticity ratios. The foreign trade multiplier emerges by construction, and international output co-movement follows mechanically from network interdependencies in exports and import patterns.

Abstract:
We develop a method to recover a granular, product-level input-output structure from firm-level customs transactions. Building on an association-rule mining algorithm, we exploit systematic co-occurrences between what firms import and what they export to infer input use in production. Applying the approach to data from several countries, we show that the inferred mappings closely resemble conventional input-output relationships and perform well in external validation exercises. We illustrate the value of these linkages in two applications. First, following China’s WTO entry, export growth is accompanied by a pronounced rise in imports of the inputs our mapping associates with those exports. Second, in the 2018-2019 U.S.-China trade war, tariffed Chinese exports to the United States contract, and the shock propagates upstream: China’s imports of exposed inputs fall, and third-country suppliers that specialize in those inputs experience the declines in their exports to China, especially if China is a key destination market. Overall, simple pattern recognition tools and micro-level trade data can deliver high-resolution input–output linkages that improve exposure measures and empirical assessments of supply-chain propagation.

Link to the working paper