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Two core issues in international trade are the allocation of resources across economic activities and the distribution of incomes across factors of production. Recent research has emphasized the allocation of resources across heterogeneous firms, but has largely concentrated on heterogeneity in the product market (productivity and size) rather than the labor market (workforce composition and wages). Developing trade models that incorporate both product and labor market heterogeneity is therefore important for explaining firm data and understanding the consequences of trade liberalization. To the extent that wages vary across firms within sectors, reallocations of resources across firms provide an additional channel for international trade to influence income distribution.

In this paper, we develop a new framework for examining the distributional consequences of trade that incorporates this channel and captures three plausible features of product and labor markets. First, there is heterogeneity in firm productivity, which generates differences in firm profitability. Second, search and matching frictions in the labor market imply that workers outside a firm are imperfect substitutes for those inside the firm, which gives rise to multilateral bargaining between each firm and its workers. Third, workers are heterogeneous in terms of match-specific ability, which can be imperfectly observed by firms. Together these three components of the model generate variation in wages across firms within industries and imply that trade liberalization affects income distribution.