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This paper quantitatively investigates the extent to which variation in the intertemporal marginal rate of substitution can help account for puzzling features of cyclical fluctuations of international trade volumes. Our insight is that, because international trade is time-intensive, variation in the rate at which agents are willing to substitute across time affects how trade volumes respond to changes in output and prices. We use a standard small open economy model with time-intensive international trade, calibrated to match key features of U.S. data and disciplining the variation in the intertemporal marginal rate of substitution using asset price data. We find that variation in the intertemporal marginal rate of substitution helps rationalize puzzling features of import fluctuations and that this mechanism is quantitatively important during both normal and crisis times.