Results of DF-GLS unit-root test and unit-root tests with both exogenous structural breaks and endogenous ones indicate the non-stationarity of Taiwan's unemployment rates. This paper therefore uses a small-open economy model to analyze the hysteresis of Taiwan's unemployment rates. Assuming uneven technology progress between the small-open economy and the rest of the world, its terms of trade would embed a stochastic trend and its natural rate of unemployment, affected by the terms of trade, thus has a unit root. The model is estimated by using the Kalman filter and tested with the maximum likelihood ratio test. Our empirical results support the hypothesis that the unit root in unemployment rates is driven by terms of trade. Furthermore, we find that considering structural breaks only insignificantly improves the explanation of our model.