Study Challenges Standard “Trade Elasticity” Metric, Suggesting Economists May Misjudge Welfare Gains from Global Trade

Economists often quantify the benefits countries receive from international trade by relying on a single number: a “trade elasticity” that summarizes how readily buyers switch between foreign suppliers when relative prices change. That constant elasticity is typically estimated from substitution patterns across foreign countries, then fed into standard formulas that convert observed import shares into implied welfare gains from trade.

In a new study, Jonathan Vogel argues that this common shortcut can miss an important margin. When preferences are general and homothetic—broadly, when spending patterns scale proportionally with income—the welfare impact of moving from today’s trading equilibrium toward autarky depends not just on the initial share of spending devoted to domestic goods, but on how substitution between home and foreign goods evolves as prices shift along the way. Vogel’s key object is a home–foreign elasticity function: an elasticity that is allowed to vary with the economy’s domestic expenditure share as relative prices move along a hypothetical path to autarky.

A central complication is that this elasticity function can, in principle, depend on the specific sequence of price changes used to “walk” the economy toward autarky. Vogel shows that this path-dependence disappears under a widely used structural restriction—weak separability—under which the choice between home and foreign goods can be analyzed independently from substitution patterns within the set of foreign suppliers. Under weak separability, the home–foreign elasticity function becomes a stable object that can be used to calculate gains from trade based on the initial domestic spending share and the elasticity function evaluated along the relevant range.

The paper also tackles a practical question: can such elasticity functions be identified from data without imposing strong parametric assumptions? Vogel provides conditions under which the function is nonparametrically identifiable, then proceeds to estimate sector-level home–foreign elasticity functions using price changes induced by tariff adjustments associated with trade agreements. The approach leverages the fact that tariff changes create measurable shifts in relative prices between domestic and imported goods, allowing the responsiveness of domestic expenditure shares to be traced out across different levels of home bias.

Using input–output datasets from the World Input-Output Database (WIOD) and the OECD Inter-Country Input-Output (ICIO) tables, Vogel finds a systematic pattern: estimated home–foreign elasticities tend to be higher in situations where the domestic expenditure share is already high. In other words, when sectors or countries are more home-oriented in their spending, the marginal responsiveness of that home share to price changes is often stronger.

Those estimated functions matter quantitatively in a standard multi-sector trade model that includes intermediate inputs—an important feature for capturing how trade affects production costs through supply chains. When Vogel computes gains from trade using the varying elasticity functions, the median welfare gain across WIOD countries is 19.37 log points. By contrast, if each country–sector elasticity is incorrectly treated as constant and fixed at its initial value, the median gain rises to 24.43 log points—suggesting that the conventional constant-elasticity practice may overstate benefits in this setting.

Vogel credits Arnaud Costinot, Gene Grossman, Eduardo Morales, and Andres Santos for comments, and notes that the views are his own and not necessarily those of the National Bureau of Economic Research (NBER), which circulates working papers and other research outlets.

Why it matters

Policy debates about tariffs and trade agreements often lean on quantitative models whose results hinge on assumed trade elasticities. If the responsiveness of spending to prices changes with the degree of home bias, then using a single, constant elasticity can systematically mismeasure welfare gains from openness. Future work—and policy modeling—will need to pay closer attention to how substitution between domestic and foreign goods evolves as economies move along large price changes, not just small deviations around today’s equilibrium.