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Multidimensional Sorting: Comparative Statics

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  • Job Boerma
  • Andrea Ottolini
  • Aleh Tsyvinski

Abstract

In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological change in general multidimensional assignment models. Our main result is that any technological change is uniquely decomposed into two distinct components. The first component (gradient) gives a characterization of changes in marginal earnings through a Poisson equation. The second component (divergence-free) gives a characterization of labor reallocation. For U.S. data, we quantify equilibrium responses in sorting and earnings with respect to cognitive skill-biased technological change.

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  • Job Boerma & Andrea Ottolini & Aleh Tsyvinski, 2025. "Multidimensional Sorting: Comparative Statics," Papers 2512.10853, arXiv.org.
    • Handle: RePEc:arx:papers:2512.10853
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    File URL: http://arxiv.org/pdf/2512.10853
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