We incorporate a union bargaining framework into a standard specific factor trade model, in which an increase in the relative price or capital stock in the export sector raises the demand wage that firms can afford to pay relative to workers’ fall-back income, and consequently lowers equilibrium unemployment. The magnitude of the effects depends on the fall-back income, the weight unions attach to employment and the elasticity of labor demand. The empirical section of the paper focuses on estimating these parameters using data on Singapore. The results show that labor unions in Singapore care more about employment than wages. Together with a small fall-back income and elastic labor demand, we show that given the same percentage change in relative export prices and capital accumulation in the export sector, the effect on unemployment is larger for the former. However, the empirical importance of capital accumulation in the export sector dominates increases in relative export prices in reducing unemployment since the manufacturing sector experienced a tremendous increase in capital inputs throughout the sample period, whereas the relative price of exports experienced a far smaller increase and only in the early part of the sample period. We conclude that through a very open trading regime, the tremendous increase in capital stock of the exporting sector has been the main reason behind Singapore’s declining unemployment rate.