We characterize those ex-ante restrictions on the random utility model which lead to identification. We first identify a simple class of perturbations which transfer mass from a suitable pair of preferences to the pair formed by swapping certain compatible lower contour sets. We show that two distributions over preferences are behaviorally equivalent if and only if they can be obtained from each other by a finite sequence of such transformations. Using this, we obtain specialized characterizations of which restrictions on the support of a random utility model yield identification, as well as of the extreme points of the set of distributions rationalizing a given data set. Finally, when a model depends smoothly on some set of parameters, we show that under mild topological assumptions, identification is characterized by a straightforward, local test.
We consider the problem of rationalizing choice data by a preference satisfying an arbitrary collection of invariance axioms. Examples of such axioms include quasilinearity, homotheticity, independence-type axioms for mixture spaces, constant relative/absolute risk and ambiguity aversion axioms, stationarity for dated rewards or consumption streams, separability, and many others. We provide necessary and sufficient conditions for invariant rationalizability via a novel approach which relies on tools from the theoretical computer science literature on automated theorem proving. We also establish a generalization of the Dushnik-Miller theorem, which we use to give a complete description of the out-of-sample predictions generated by the data under any such collection of axioms.
We develop a least squares theory for the empirical study of models of preference and individual decision-making. Our approach utilizes common invariance properties of various models to obtain cardinal measurements of preference intensity. Our theory is widely applicable, and provides richer, more granular insights into the drivers of a model’s predictive success or failure than traditional revealed preference methods, while simultaneously remaining computationally simple. We illustrate our methodology on common models of preferences over consumption bundles, dated rewards, lotteries, consumption streams, and Anscombe-Aumann acts.
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.