Hicksian Complementarity and Perturbed Utility Models

This paper studies aggregate complementarity without price or income variation. We show that for a class of utility functions, variation in non-price observables allows one to recover a measure of complementarity similar to Hicksian complementarity. In addition, the entire Slutsky matrix can be recovered up to scale without price variation. We then examine aggregate complementarity in latent utility models used in discrete bundles, stochastic choice, and matching. We show that classical linear instrumental variables can recover Hicksian complementarity for the special case of quadratic utility