This paper develops and estimates a model of the labor market with strategic interactions in wage setting and two-sided heterogeneity to explain wage inequality. The authors provide a tractable characterization of the equilibrium, demonstrating its existence and uniqueness. They derive comparative statics and use counterfactuals to assess the contributions of worker skill, preference for amenities, and strategic interactions to wage inequality. Using instrumental variables, they identify labor demand and supply parameters from matched employer-employee data from Denmark. The estimated structural model is used to perform counterfactual analyses to evaluate the main sources of wage inequality in Denmark. The paper contributes to the literature on imperfect competition in labor markets, identification of production functions, and matching models. It relaxes assumptions made in previous models, allowing for worker-level unobserved heterogeneity and imperfect information. The authors find that wages are marked down by about 17% below the marginal revenue product of labor, with significant heterogeneity in labor supply elasticities across establishments and workers. They also estimate the distribution of establishment and worker-type specific labor productivities and find that more educated workers have higher productivity. The paper's counterfactual experiments highlight that all primary channels in the model drive wage inequality, with some mechanisms increasing inequality and others decreasing it.This paper develops and estimates a model of the labor market with strategic interactions in wage setting and two-sided heterogeneity to explain wage inequality. The authors provide a tractable characterization of the equilibrium, demonstrating its existence and uniqueness. They derive comparative statics and use counterfactuals to assess the contributions of worker skill, preference for amenities, and strategic interactions to wage inequality. Using instrumental variables, they identify labor demand and supply parameters from matched employer-employee data from Denmark. The estimated structural model is used to perform counterfactual analyses to evaluate the main sources of wage inequality in Denmark. The paper contributes to the literature on imperfect competition in labor markets, identification of production functions, and matching models. It relaxes assumptions made in previous models, allowing for worker-level unobserved heterogeneity and imperfect information. The authors find that wages are marked down by about 17% below the marginal revenue product of labor, with significant heterogeneity in labor supply elasticities across establishments and workers. They also estimate the distribution of establishment and worker-type specific labor productivities and find that more educated workers have higher productivity. The paper's counterfactual experiments highlight that all primary channels in the model drive wage inequality, with some mechanisms increasing inequality and others decreasing it.