This paper shows that standard international business cycle models can be reconciled with the empirical evidence on the lack of consumption risk sharing. First, we show analytically that with incomplete asset markets productivity disturbances can have large uninsurable effects on wealth, depending on the value of the trade elasticity and shock persistence. Second, we investigate these findings quantitatively in a model calibrated to the U.S. economy. With the low trade elasticity estimated via a method of moments procedure, the consumption risk of productivity shocks is magnified by high terms of trade and real exchange rate (RER) volatility. Strong wealth effects in response to shocks raise the demand for domestic goods above supply, crowding out external demand and appreciating the terms of trade and the RER. Building upon the literature on incomplete markets, we then show that similar results are obtained when productivity shocks are nearly permanent, provided the trade elasticity is set equal to the high values consistent with micro-estimates. Under both approaches the model accounts for the low and negative correlation between the RER and relative (domestic to foreign) consumption in the data—the "Backus-Smith puzzle".
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