The Comparative Statics of Sorting

46 Pages Posted: 4 Jun 2019 Last revised: 17 Jun 2021

See all articles by Axel Anderson

Axel Anderson

Georgetown University - Department of Economics

Lones Smith

University of Wisconsin at Madison - Department of Economics

Date Written: May 12, 2019

Abstract

We create a general and tractable theory of increasing sorting in pairwise matching models with transferable utility. Our partial order, positive quadrant dependence, subsumes Becker (1973) as the extreme cases with most and least sorting. It implies sorting by correlation of matched partners, or distance between partners. Our theory turns on synergy --- a local notion of Becker's supermodularity:--- the cross partial difference or derivative of match production. This reflects basic economic forces: diminishing returns, technological convexity, insurance, and match learning dynamics.

We prove that sorting increases if match synergy globally increases, and is also cross-sectionally monotone or single-crossing. Our theorems shed light on major economics sorting papers, affording immediate proofs and new insights. They open the door to fast predictions for new pairwise sorting models in economics.

Keywords: Matching, Sorting, Monotone Comparative Statics

JEL Classification: C02, D13, D51, J01

Suggested Citation

Anderson, Axel and Smith, Lones, The Comparative Statics of Sorting (May 12, 2019). Available at SSRN: https://ssrn.com/abstract=3388017 or http://dx.doi.org/10.2139/ssrn.3388017

Axel Anderson (Contact Author)

Georgetown University - Department of Economics ( email )

Washington, DC 20057
United States

Lones Smith

University of Wisconsin at Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706-1393
United States
608-263-3871 (Phone)
608-262-2033 (Fax)

HOME PAGE: http://www.lonessmith.com

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