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There are two widely accepted explanations of why politically motivated governments make trade agreements. There is an informal explanation, which I shall call the ′practitioners′ story′, even though it is most economists′ informal view as well. And there is a formal explanation in the economics literature, which I shall call the ′standard model′, referring to the basic structure shared by the Bagwell-Staiger and Grossman-Helpman models. Unfortunately, the practitioners′ story and the standard model contradict each other at every crucial point. For example, in the practitioners′ story, trade agreements are about reducing politically motivated protectionism; and getting an agreement depends on political support from exporters. But in the standard model, trade agreements never reduce such protectionism; and politics plays no role in securing an agreement. This paper expounds the contradictions between the practitioners′ story and the standard model, which have gone largely unremarked. It refutes suggestions by defenders of the standard model that the contradictions are illusory. It identifies the different assumptions made by the two explanations that generate the contradictions. It gives reasons for skepticism about the standard model. And it discusses why all of this matters.