We develop a new general equilibrium model of trade with heterogeneous firms, variable demand elasticities and endogenously determined wages. Trade integration favors wage convergence, intensifies competition, and forces the least efficient firms to leave the market, thereby affecting aggregate productivity. Since wage and productivity responses are endogenous, our model is well suited to study the impacts of trade integration on aggregate productivity and factor prices. Using Canada-U.S. interregional trade data, we first estimate a system of theory-based gravity equations under the general equilibrium constraints generated by the model. Doing so allows us to measure 'border effects' and to decompose them into a 'pure' border effect, relative and absolute wage effects, and a selection effect. Using the estimated parameter values, we then quantify the impacts of removing the Canada-U.S. border on wages, productivity, markups, the share of exporters, the mass of varieties produced and consumed, and welfare. We finally provide a similar quantification with respect to regional population changes.