This paper presents a model with monopolistic competition, productively heterogeneous firms, and business cycle aggregate shocks. With firm-specific productive heterogeneity, weaker firms quit when faced with a negative aggregate shock. Consequently, trade does not always increase firm-level aggregate productivity as negative shocks on the home market can be compensated for by positive shocks elsewhere. Weaker firms, which would otherwise quit in autarky, can continue to operate by exporting. Despite this, trade can still improve welfare for the risk-averse consumer by reducing aggregate price fluctuations
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