We introduce the novel notion of an abstract numeraire commodity, consisting of a family of self-transformations of an abstract consumption space. We provide necessary and sufficient conditions for such a family to be able to provide a complete and consistent system of measurements of preference intensity for a given collection of preferences. Using measurements of this form, we develop a least squares regression theory for quantifying the predictive accuracy of a wide range of models of preference and individual decision making. Our approach allows for straightforward estimation of a model’s underlying primitives and provides granular insights into the drivers of a model’s predictive success or failure, often at an axiom-by-axiom level. In the presence of stochastic data, we provide a general class of non-parametric statistical tests of rationalizability for a variety of models.
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.