Stable marriage with and without transferable utility: nonparametric testable implications

We show that transferable utility has no nonparametrically testable implications for marriage stability in settings with a single consumption observation per household and heterogeneous individual preferences across households. This completes the results of Cherchye, Demuynck, De Rock, and Vermeulen (2017), who characterized Pareto efficient household consumption under the assumption of marriage stability without transferable utility. First, we show that the nonparametric testable conditions established by these authors are not only necessary but also sufficient for rationalizability by a stable marriage matching. Next, we demonstrate that exactly the same testable implications hold with and without transferable utility between household members. We build on this last result to provide a primal and dual linear programming characterization of a stable matching allocation for the observational setting at hand. This provides an explicit specification of the marital surplus function rationalizing the observed matching behavior.