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Trade policymaking is the result of a process of mapping local preferences onto a national trade policy. At the local level, legislators need to balance the demands from winners and losers from trade liberalization in their local districts, including owners of specific factors in importing competing and exporting industries, as well as labor, which is assumed to be mobile across sectors within regions. The level of protection granted to local interests, in turn, is constrained by international bargains where the level of the domestic tariffs is balanced against market access in partner countries. We extend the model developed in Gawande et al 2021 to account for the relative influence of exporters and characterize the legislative bargaining process under which trade policy is enacted. The model uncovers the tradeoffs faced by policymakers when choosing to grant protection to import competing interests in their districts. We are able to structurally estimate the relative weights of local interests that are reflected in the level of protection enacted at the national level. We use data from the 435 Congressional districts in the U.S. in the early 2000s, when the structure of the U.S. economy was dramatically affected by international trade shocks resulting from trade liberalization at the global level. We compare the estimated welfare weights implied by the vector of tariff and non-tariff measures enacted at the national level. Consistent with our previous findings, the estimates suggest that specific factor owners in import competing sectors are more influential than predicted in earlier work. Yet we also find that specific factors in exporting industries play a sizable role, constraining the level of protection resulting from the legislative bargain at the national government in the shadow of potential retaliation from governments abroad. We use these structurally estimated weights to construct a measure of the mismatch between national tariffs and local demands for protection: these estimates reveal that while the influence of import competing interests is reflected in trade policymaking, the demand for protection at the local level is larger than the one received. This ``unmet'' demand for protection, we argue, is a force behind the political backlash against globalization.