To study the effects of tariffs on gross domestic product (GDP), one needs import demand elasticities at the tariff line level that are consistent with GDP maximization. These do not exist. The authors modify Kohli's (1991) GDP function approach to estimate demand elasticities for 4,625 imported goods in 117 countries. Following Anderson and Neary (1992, 1994) and Feenstra (1995), they use these estimates to construct theoretically sound trade restrictiveness indices, and GDP losses associated with existing tariff structures. Countries are revealed to be 30 percent more restrictive than their simple or import-weighted average tariffs would suggest. Thus, distortion is nontrivial. GDP losses are largest in China, Germany, India, Mexico, and the United States.