Authors: Martín Almuzara, Martín García-Vázquez, and Joseph Mullins
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Staff Reports
Ordinal Complementarity
Number 1199
August 2026
August 2026
JEL classification: C1, D1, C4
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.
Author Disclosure Statement(s)
Martín Almuzara
I declare that I have no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
Martín García-Vázquez
I declare that I have no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
Joseph Mullins
I declare that I have no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
I declare that I have no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
Martín García-Vázquez
I declare that I have no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
Joseph Mullins
I declare that I have no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.
Suggested Citation:
Almuzara, Martín, Martín García-Vázquez, and Joseph Mullins. 2026. “Ordinal Complementarity.” Federal Reserve Bank of New York Staff Reports, no. 1199, August. https://doi.org/10.59576/sr.1199
Almuzara, Martín, Martín García-Vázquez, and Joseph Mullins. 2026. “Ordinal Complementarity.” Federal Reserve Bank of New York Staff Reports, no. 1199, August. https://doi.org/10.59576/sr.1199
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