The Comparative Statics of Sorting

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.