MULTDIMENSORTING: Multidimensional Sorting with Imperfectly Transferable Utility

该项目旨在改变我们对劳动力市场分类的理解，考虑到工人的技能和偏好各不相同，就像工作的技能要求和提供的便利条件各不相同一样，这两个因素对谁最终从事哪项工作至关重要。这两种异质性的存在会影响排序，原因有二：第一，这意味着工人的特征必然是多维的;第二，偏好和舒适度的异质性往往会使效用在匹配的双方之间无法完全转移。这些特征中的每一个本身都是具有挑战性的：在可转移效用（TU）下的多维排序和不完全可转移效用（ITU）下的一维分配的情况下，文献最多只能提供部分答案。在具有不完全可转移效用的多维排序的情况下，这些问题在很大程度上甚至还没有被提出来。我的项目有两个具体目标。首先，我的目标是发展一般理论的结果，根据TU和ITU的多维排序。众所周知，-在一些特殊情况下-多维排序问题不承认解析解TU下，我希望同样的情况下，国际电联;规避这个问题，我计划开发单调的比较静态结果排序。其次，我计划将这些通用工具应用于两个具体问题。第一个问题是，当工人关心他们相对于同事的薪酬时，工人在不同公司之间的分类问题，但这种偏好的强度不同。第二个问题是远程工作的扩散如何影响工作和地点之间的分类：这本来就是国际电联的一个多层面分类问题，因为工人的技能和对远程工作的偏好各不相同，工作的复杂性和在家完成工作的程度也各不相同。

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.