Inferring Complementarity from Correlations rather than Structural Estimation

According to the Hicksian criterion, two products are complements if their (compensated) cross-price elasticity is negative. While attractive in theory, the implementation of the Hicksian criterion can be hard: computing elasticities requires the estimation of structural models allowing for both complementarity and substitutability. Here, we instead investigate the correlation criterion, whose implementation only requires the comparison of observed market shares. We show that, in a large class of non-parametric models, the correlation criterion satisfies all the axioms by Manzini et al. (2018) and how, in mixed logit models, it can be used to learn about the Hicksian criterion.