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Increasingly, international trade policy analysis explores the economic effects of changes in ad‐valorem tariffs or equivalent nontariff measures on vertically integrated markets for which high quality data are unavailable. Standard Constant Elasticity of Substitution (CES) Armington models fail to account for either vertical linkages or parameter uncertainty. Here, we introduce a vertically integrated, nested two‐sector Armington model that incorporates uncertainty in the estimates of Armington elasticities through Monte Carlo simulation. As an illustrative case, we model the effects of changes in country of origin labeling (COOL) rules on the market shares of cattle in the U.S. beef market. By accounting for parameter uncertainty in this way, we are able to estimate the distribution of potential effects of repealing mandatory COOL. Ultimately, we predict that, in all but the most extreme cases, Mexico and Canada would not gain as much market share from the repeal of mandatory COOL as they claim in their World Trade Organization (WTO) filings against the regulation.