Report
Ordinal Complementarity
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.
JEL Classification: C1; D1; C4;
https://doi.org/10.59576/sr.1199
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Bibliographic Information
Provider: Federal Reserve Bank of New York
Part of Series: Staff Reports
Publication Date: 2026-08-01
Number: 1199