Increasing wage inequality between similar workers plays an important role for overall inequality trends in industrialized societies. To analyze this pattern, we incorporate directed labor market search into a dynamic model of international trade with heterogeneous firms and homogeneous workers. Wage inequality across and within firms results from their different hiring needs along their life cycles and the convexity of their adjustment costs. The interaction between wage posting and firm growth explains some recent empirical regularities on firm and labor market dynamics. Fitting the model to capture key features obtained from German linked employer-employee data, we investigate how falling trade costs and institutional reforms interact in shaping labor market outcomes. Focusing on the period 1996-2007, we find that neither trade nor key features of the Hartz labor market reforms account for the sharp increase in residual inequality observed in the data. By contrast, inequality is highly responsive to the increase in product market competition triggered by domestic regulatory reform.