Trade elasticities are critical for price or structural change analysis. The Armington demand model is used to estimate trade elasticities, the country-of-origin bias, and the impact of the U.S. BSE outbreak on preferences. OLS estimation generates theoretically wrong signs, including a positive impact of U.S. BSE on other countries’ demand for imported beef. Results of a Bayesian hierarchical model show that import demand of countries that tend to import more beef from the U.S., such as Japan, Canada, Korea, and Russia, are affected more by the U.S. BSE outbreak than countries, such as the EU that tend not to import from the U.S.