Does trade affect the equilibrium rate of unemployment? To answer this question, we propose a small open economy model that incorporates realistic features of labour markets. The model predicts that a sustained improvement in the terms of trade lowers unemployment. We test this prediction for the case of Australia, an economy that is subject to large terms of trade movements. We use a novel technique to estimate the structural model based on a combination of traditional econometric procedures and the calibration of time-varying parameters. Both reduced form and the structural estimates reveal strong evidence that higher export prices, capital accumulation in tradeable goods industries and lower unemployment benefits reduce the equilibrium unemployment rate.