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 as a bundle of tasks optimally assigned to a type of worker. The model allows us to study how occupations evolve—e.g., changes in their boundaries, wages, and employment—in response to changes in the economic environment, making it useful for analyzing the implications of automation, skill-biased technical change, offshoring, and skill upgrading by workers, among others. I characterize how the wages and marginal product of workers, the substitutability between worker types, and the labor share depend on the assignment. In particular, I show that these properties depend on the productivity of workers in tasks along the boundaries of their occupations. As an application, I study the rise in automation observed in recent decades. Automation is modeled as a choice of the optimal size and location of a mass of identical robots in the task space. The firm trades off the cost of the robots, which varies across the space, against the benefit of reducing the mismatch between tasks’ skill requirements and workers’ skills. The model rationalizes observed trends in automation and delivers implications for changes in wage inequality, unemployment, and the labor share.