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Multidimensional Sorting: Comparative Statics

Author

Listed:
  • Job Boerma

    (University of Wisconsin-Madison)

  • Andrea Ottolini

    (University of Alabama-Birmingham)

  • Aleh Tsyvinski

    (Yale University)

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.

Suggested Citation

  • Job Boerma & Andrea Ottolini & Aleh Tsyvinski, 2025. "Multidimensional Sorting: Comparative Statics," Cowles Foundation Discussion Papers 2480, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2480
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    File URL: https://cowles.yale.edu/sites/default/files/2025-12/d2480_0.pdf
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