MULTDIMENSORTING: Multidimensional Sorting with Imperfectly Transferable Utility

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This project aims to change our understanding of labour market sorting by taking into account that workers differ both in their skills and in their preferences, just as jobs differ both in their skill requirements and the amenities they provide and that both of these are critical for who ends up in which job. The presence of both types of heterogeneity affects sorting for two reasons: First, it means that workers' characteristics are necessarily multidimensional; second, heterogeneity in preferences and amenities often makes utility imperfectly transferable between the matched parties. Each of these features is challenging in itself: In the case of both multidimensional sorting under transferable utility (TU) and one-dimensional assignment under imperfectly transferable utility (ITU), the literature provides partial answers at best. In the case of multidimensional sorting with imperfectly transferable utility, the questions have largely not even been asked yet. My project has two specific goals. First, I aim to develop general theoretical results regarding multidimensional sorting under TU and ITU. It is well known that---outside a few special cases---multidimensional sorting problems do not admit analytical solutions under TU, and I expect the same to be the case under ITU; to circumvent this problem, I plan to develop monotone comparative statics results with respect to sorting. Second, I plan to apply these general tools to two specific problems. The first is the question of workers' sorting across firms when workers care about how much they are paid relative to their co-workers, but differ in the strength of this preference. The second is the problem of how the proliferation of remote work affects sorting across both jobs and locations: This is inherently a multidimensional sorting problem with ITU, because workers differ in skill and their preference for remote work, and jobs differ in their complexity and the extent to which they can be performed from home.