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This paper estimates the welfare effects of Brexit, focusing on trade and fiscal transfers. We use a standard quantitative general equilibrium trade model with many countries and sectors and trade in intermediates, as in Costinot and Rodríguez-Clare (2014). We simulate a range of counterfactuals reflecting alternative options for EU-UK relations following Brexit. Welfare losses for the average UK household are 1.3% if the UK remains in the EU's Single Market like Norway (a "soft Brexit"). Losses rise to 2.7% if the UK trades with the EU under World Trade Organization rules (a "hard Brexit"). A reduced form approach that captures the dynamic effects of Brexit on productivity more than triples these losses and implies a decline in average income per capita of between 6.3% and 9.4%, partly via falls in foreign investment. These negative effects are widely shared across the entire income distribution and are unlikely to be offset from new trade deals.

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This paper develops an idea flows theory of trade and growth with heterogeneous firms. New firms learn from incumbent firms, but the diffusion technology ensures entrants learn not only from frontier technologies, but from the entire technology distribution. By shifting the productivity distribution upwards, selection on productivity causes technology diffusion and this complementarity generates endogenous growth without scale effects. On the balanced growth path, the productivity distribution is a traveling wave with an increasing lower bound. Growth of the lower bound causes dynamic selection. Free entry mandates that trade liberalization increases the rates of technology diffusion and dynamic selection to offset the profits from new export opportunities. Consequently, trade integration raises long-run growth. The dynamic selection effect is a new source of gains from trade not found when firms are homogeneous. Calibrating the model implies that dynamic selection approximat ely triples the gains from trade relative to heterogeneous firm economies with static steady states.