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，考虑到工人在技能和偏好上的差异，就像工作在技能要求和提供的便利上的差异一样，这两者对谁最终从事什么工作都至关重要。这两种异质性的存在影响排序有两个原因：首先，这意味着员工的特征必然是多维的；其次，偏好和舒适的异质性往往使效用在匹配的各方之间不能完全转移。这些特征中的每一个本身都具有挑战性：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还没有被提出。我的项目有两个具体目标。首先，我的目标是发展关于TU和ITU下多维排序的一般理论结果。众所周知，除了少数特殊情况外，多维排序问题在TU下不允许采用分析解决方案，我预计国际电联下的情况也是如此；为了避免这个问题，我计划开发关于排序的单调比较静力学结果。其次，我计划将这些通用工具应用于两个具体问题。第一个问题是员工在不同公司之间的分拣问题，当员工关心自己相对于同事的工资多少，但这种偏好的强度不同时。第二个问题是远程工作的普及如何影响跨工作岗位和地点的分类：对于国际电联来说，这本质上是一个多维分类问题，因为工作人员的技能和对远程工作的偏好不同，工作的复杂性和可以在家完成的程度也不同。

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.