Matching Workers' Skills and Firms' Technologies Part I: Bundling

We study the workers-to-firms matching when firms' production functions have aggregated skills as multidimensional inputs and workers' multidimensional skills are bundled (markets for stand-alone skills are missing). We provide fundamental welfare theorems when labor markets face such a bundling friction. Sorting is then based on workers' comparative advantage. The bundling friction causes skills' prices to vary across firms, making the (unique) equilibrium wage schedule non-linear in skills. This non-linearity of wages, closely linked to the heterogeneity of workers' skills within firms, depends on the relative prevalence of specialist and generalist workers in the economy. In equilibrium, the wage is log-additive in worker quality and a worker-to-firm sorting effect that may reflect the firm's productivity. We provide descriptive evidence using Swedish matched employer-employee data providing us with direct measures of workers' cognitive and non-cognitive skills. Our companion paper, Choné, Gozlan, and Kramarz, 2024, examines the same questions when markets for stand-alone tasks open and the bundling friction gradually disappears.