We develop a multi-country, multi-sector trade model with labor market frictions and equilibrium unemployment. Trade opening leads to a reduction in unemployment if it raises real wages and reallocates labor towards sectors with lower-than-average labor market frictions. We estimate sector-specific labor market frictions and trade elasticities using employment data from 25 OECD countries and worldwide trade data. We then quantify the potential unemployment and real wage effects of implementing the Transatlantic Trade and Investment Partnership (TTIP) or the Trans-Pacific Partnership (TPP), and of eliminating trade imbalances worldwide. The unemployment and real wage effects work in conflicting directions for some countries under some trade regimes, such as the US under TTIP. We introduce a welfare criterion that accounts for both effects and splits such ties. Accordingly, US welfare is predicted to decrease under TTIP and increase under TPP.