This paper investigates the problem of model selection and testing in decision theory. We consider a consumption space equipped with an endogenous notion of ‘abstract numeraire,’ and characterize those preferences for which the quantity of numeraire needed to compensate an agent between a pair of alternatives provides a consistent, cardinal measure of the magnitude of preference. This framework includes all quasilinear or homothetic preferences on classical consumption spaces, stationary preferences over dated rewards, von Neumann-Morgenstern preferences on lottery spaces, and a wide range of preferences over monetary acts, including those represented by subjective expected utility, Choquet expected utility, maxmin expected utility, variational, and dual-self functionals. For data consisting of observed or experimentally elicited compensation differences, we show a simple least-squares methodology provides a systematic means of estimating the ‘best-fit’ preferences for an inconsistent data set from a given model, and allows for meaningful comparisons of goodness of fit across models. In the presence of cross-sectional data, our approach allows for nonparametric statistical testing of rationalizability at the population level.
We analyze mergers and entry in a differentiated products oligopoly model of price competition. Any merger that does not yield efficiencies is unprofitable if it induces entry sufficient to preserve pre-merger consumer surplus. Thus, mergers occur in equilibrium only if barriers limit entry. Mergers that increase consumer surplus can occur in equilibrium for specific magnitudes of efficiencies and post-merger entry, and these combinations are identified from pre-merger market shares. The entry costs that would rationalize post-merger entry similarly can be bounded using pre-merger market shares. An application to the T-Mobile/Sprint merger illustrates the theoretical framework.
Cycles in revealed preference data are often interpreted as fundamental units of choice-theoretic inconsistency. We fully characterize the manner in which the structure of a choice environment can lead to non-trivial dependence relations between cyclic choice patterns in data. We show that for any finite data set, while there may not be a unique maximal independent collection of choice cycles that explain the entirety of the inconsistency, the size of any such collection of cycles is well-defined. We utilize this to provide a means of controlling for the influence of experimental structure in the construction of inconsistency indices for choice data.
We investigate the manner in which the power of the weak axiom of revealed preference is affected by the completeness of the choice environment. We fully characterize those domains on which the weak axiom coincides with strong rationalizability for arbitrary choice correspondences. We also provide a related result that characterizes those domains on which the strong rationalizability of a choice correspondence is equivalent to (i) the satisfaction of the weak axiom, and (ii) the strong rationalizability of its restrictions to suitable collections of small sets. Our proof technique involves a generalization of many of the differential concepts of classical demand theory to the abstract choice model. We conclude with an application to the problem of aggregating incomplete preferences.