Economists James E. Anderson, Mario Larch and Yoto V. Yotov have introduced a new way to work backward from desired economic outcomes to the trade-cost changes that could deliver them—an approach they describe as “inverting” the structural gravity model of trade.
Gravity models are a workhorse of international economics, typically used to predict how trade flows respond to barriers such as tariffs, transport costs, or policy frictions. The authors flip that standard workflow. Instead of asking what welfare effects follow from a given change in trade costs, they ask what trade-cost changes would be required to hit specified welfare targets.
A central result is that when a welfare target is feasible, using one policy instrument for each target produces a single, well-defined answer. In other words, the method does not yield a range of possible trade-cost adjustments: it pins down a unique change in the relevant instrument, provided the target can be achieved within the model’s constraints.
The paper also offers a practical approximation for how large those instrument changes need to be. Holding producer prices fixed and working to a first-order (small-change) approximation, the required percentage change in a given instrument is the welfare target divided by that instrument’s own share in expenditure. This relationship has an intuitive implication: instruments that account for only a small fraction of spending must shift more dramatically to generate a given welfare improvement.
That logic shows up in a striking contrast the authors emphasize. The “domestic” change—affecting home-market conditions—tends to be roughly similar in size to the welfare target itself. By comparison, the change needed on the import side is typically multiple times larger, reflecting the smaller expenditure share associated with imports for many economies. Put differently, improving welfare by manipulating import-related costs often requires bigger proportional adjustments than achieving the same goal through domestic channels, at least under the paper’s assumptions.
Beyond targeting welfare changes, the inversion technique can be applied directly to observed data. By reversing from actual trade flows, the method recovers trade-cost changes separately for each direction of trade between two countries. That feature matters because trade frictions are not necessarily symmetric: the cost of shipping from A to B can move differently than the cost from B to A due to policy, logistics, or other bilateral factors. The authors’ approach yields a distinct implied trade-cost change for each direction within a country pair, rather than forcing a single bilateral number.
The researchers demonstrate the value of the framework through applications to NAFTA and to world trade more broadly, using these settings to illustrate how the inversion method can clarify the trade-cost movements consistent with observed outcomes or policy goals.
The authors acknowledge feedback from multiple scholars and seminar audiences, including participants at the Philadelphia Trade Group Workshop in 2025 and seminars in Louvain-la-Neuve, Mons, and at Universitas Mercatorum in 2026. They also note that “Claude Code” assisted in writing and compressing an earlier 104-page draft. The study is disseminated through the National Bureau of Economic Research (NBER), with the standard disclaimer that the conclusions are those of the authors and not necessarily those of the NBER.
Why it matters
Governments routinely set goals—such as raising national welfare or cushioning shocks—without a clear map from targets to the scale of policy changes required. By turning the gravity model around, this work offers a more direct way to infer how much trade costs would need to move, and in which direction, to hit those goals. The approach also highlights an asymmetry policymakers often overlook: because imports are a smaller slice of spending in many economies, achieving welfare gains through import-cost changes may demand much larger proportional shifts than expected.