A task-based theory of occupations with multidimensional heterogeneity

I develop an assignment model of occupations with multidimensional heterogeneity in production tasks and worker skills. Tasks are distributed continuously in the skill space, whereas workers have a discrete distribution with a finite number of types. Occupations arise endogenously as bundles of tasks optimally assigned to a type of worker. The model allows us to study how occupations respond to changes in the economic environment, making it useful for analyzing the implications of automation, skill-biased technical change, offshoring, and worker training. Using the model, I characterize how wages, the marginal product of workers, the substitutability between worker types, and the labor share depend on the assignment of tasks to workers. I introduce automation as the choice of the optimal size and location of a mass of identical robots in the task space. Automation displaces workers by replacing them in the performance of tasks, generating a cascading effect on other workers as the boundaries of occupations are redrawn.