Ordinal Complementarity

Martín García-Vázquez (), Martin Almuzara and Joseph Mullins ()
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Martín García-Vázquez: https://economics.washu.edu/people/martin-garcia-vazquez

No 1199, Staff Reports from Federal Reserve Bank of New York

Abstract: This paper introduces ordinal complementarity: a feature of stochastic production functions that is robust to monotonic transformations of inputs X and output Y. It has two equivalent definitions: supermodularity of the conditional survival function under a first-order stochastic dominance ordering, and supermodularity of E[Q(Y )|X] for all non-decreasing valuations Q. Relative to existing conventions, this definition offers a strengthening with more robust policy implications. Ordinal complementarity is necessary and sufficient for a number of social planner problems to have monotone solutions for all Q, including those with arbitrarily strong redistributive preferences. It is also testable—along with a number of related but weaker production properties—because it can be represented as a set of moment inequalities. An empirical application to the technology of cognitive skill formation for children finds different combinations of these properties at different ages, leading to new insights.

Keywords: complementarity; Skill formation; Supermodularity; stochastic dominance; optimal transport; moment inequalities (search for similar items in EconPapers)
JEL-codes: C1 C4 D1 (search for similar items in EconPapers)
Pages: 62
Date: 2026-08-01
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DOI: 10.59576/sr.1199

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