Multidimensional Sorting: Comparative Statics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915669694480384 |
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| author | Boerma, Job Ottolini, Andrea Tsyvinski, Aleh |
| author_facet | Boerma, Job Ottolini, Andrea Tsyvinski, Aleh |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_10853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multidimensional Sorting: Comparative Statics Boerma, Job Ottolini, Andrea Tsyvinski, Aleh General Economics Economics Optimization and Control 49Q22 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. |
| title | Multidimensional Sorting: Comparative Statics |
| topic | General Economics Economics Optimization and Control 49Q22 |
| url | https://arxiv.org/abs/2512.10853 |