This paper provides a rough test of a broad and prominent class of political economy of trade models and finds them wanting. The class features governments with weighted social welfare functions, including the prominent model of Grossman and Helpman. Whether the government is the single domestic player or there are other players involved (as with the lobbies in the Grossman-Helpman case) the government ultimately acts as a unitary player in international dealings. Recent work has shown that such unitary actors care exclusively about terms of trade in international negotiations. This paper pursues the implication that governments' choice of trade instruments may offer a better test of the unitary government framework than existing empirical work. We use the structure of United States protection to argue that governments consistently choose instruments that sacrifice terms of trade, thus casting doubt on the unitary approach. We offer a discussion of alternative theories of political economy that could accommodate this stylized fact.