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A unit cost function is employed, in the context of the production theory approach, to estimate the Allen - Uzawa effect of aggregate imports on skilled and unskilled labour in the US. The model corrects for two ubiquitous shortcomings of similar studies: (i) their disregard for the role of nonmanufactured imports, including imports of services, in domestic production, and (ii) their inability to capture, in addition to the conventional domestic-output-substitution effects of the Stolper - Samuelson variety, the impact of imports on the demand for primary factors that is generated via domestic factor-using downstream processes. To circumvent curvature related problems, often associated with similar studies that do not invoke separability, we combine the global imposition of concavity with a symmetric normalized quadratic representation of the unit cost function (that remains flexible after curvature enforcing reparametrizations). The results confirm the notion that imports hurt unskilled labour. However, they also reveal a previously ignored positive impact of aggregate imports on the demand for skilled labour that is qualitatively independent of the measure of skill employed. This result is attributed to skill intensive downstream processes of aggregate imports and reaffirms the importance of 'downstream handling' in stimulating labour demand first identified by Aw and Roberts (Review of Economics and Statistics , 67 , 109 - 17, 1985).