Multidimensional Sorting: Comparative Statics

Job Boerma, Andrea Ottolini and Aleh Tsyvinski
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Job Boerma: University of Wisconsin-Madison
Andrea Ottolini: University of Alabama-Birmingham
Aleh Tsyvinski: Yale University

No 2480, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, 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.

Pages: 72 pages
Date: 2025-12-15
New Economics Papers: this item is included in nep-cta, nep-des and nep-mic
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