Learning from a Piece of Pie

We investigate the empirical content of the Nash solution to two-player bargaining games. The bargaining environment is described by a set of variables that may affect agents' preferences over the agreement sharing, the status quo outcome, or both. The outcomes (i.e. whether an agreement is reached, and if so the individual shares) and the environment (including the size of the pie) are known, but neither are the agents' utilities nor their threat points. We consider both a deterministic version of the model in which the econometrician observes the shares as deterministic functions of the variables under consideration and a stochastic one in which because of latent disturbances only the joint distribution of incomes and outcomes is recorded. We show that in the most general framework any outcome can be rationalized as a Nash solution. However, even mild exclusion restrictions generate strong implications that can be used to test the Nash bargaining assumption. Stronger conditions further allow to recover the underlying structure of the bargaining, and in particular, the cardinal representation of individual preferences in the absence of uncertainty. An implication of this finding is that empirical works entailing Nash bargaining could (and should) use much more general and robust versions than they usually do.