Ordinal Complementarity

<jats:p>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.</jats:p>