Papers

People are influenced by their peers when making decisions. In this paper, we study the linear-in-means model which is the standard empirical model of peer effects. As data on the underlying social network is often difficult to come by, we focus on data that only captures an agent's choices. Under exogenous agent participation variation, we study two questions. We first develop a revealed preference style test for the linear-in-means model. We then study the identification properties of the linear-in-means model. With sufficient participation variation, we show how an analyst is able to recover the underlying network structure and social influence parameters from choice data. Our identification result holds when we allow the social network to vary across contexts. To recover predictive power, we consider a refinement which allows us to extrapolate the underlying network structure across groups and provide a test of this version of the model. 

We study a dynamic random utility model that allows for consumption dependence. We axiomatically analyze this model and find insights that allow us to distinguish between behavior that arises due to consumption dependence and behavior that arises due to state dependence. As part of our analysis, we show that it is impossible to distinguish between myopic and dynamically sophisticated agents when there are well defined marginal choices in each period. Building on our axiomatic analysis, we develop a revealed preference test for consumption dependent random utility. Our test can be implemented with real data, and we show that our test offers computational improvements over the natural extension of Kitamura and Stoye (2018) to our environment.

• Partially subsumes "Random Utility, Repeated Choice, and Consumption Dependence"

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 study consumption dependence in the context of random utility and repeated choice. We show that, in the presence of consumption dependence, the random utility model is a misspecified model of repeated rational choice. This misspecification leads to biased estimators and failures of standard random utility axioms. We characterize exactly when and by how much the random utility model is misspecified when utilities are consumption dependent. As one possible solution to this problem, we consider time disaggregated data. We offer a characterization of consumption dependent random utility when we observe time disaggregated data. Using this characterization, we develop a hypothesis test for consumption dependent random utility that offers computational improvements over the natural extension of Kitamura and Stoye (2018) to our setting.

We readdress the problem of nonparametric statistical testing of random utility models proposed in Kitamura and Stoye (2018). Although their test is elegant, it is subject to computational constraints which leaves execution of the test infeasible in many applications. We note that much of the computational burden in Kitamura and Stoye's test is due to their test defining a polyhedral cone through its vertices rather than its faces. We propose an alternative but equivalent hypothesis test for random utility models. This test relies on a series of equality and inequality constraints which defines the faces of the corresponding polyhedral cone. Building on our testing procedure, we develop a novel axiomatization of the random utility model.

• Subsumes "On Graphical Methods in Stochastic Choice" - For further results on cuts of graphs and an axiomatization of the Luce model via the Block-Marschak polynomials, see this earlier version. [pdf] 

We study identification and linear independence in random utility models. We characterize the dimension of the random utility model as the cyclomatic complexity of a specific graphical representation of stochastic choice data. We show that, as the number of alternatives grows, any linearly independent set of preferences is a vanishingly small subset of the set of all preferences. We introduce a new condition on sets of preferences which is sufficient for linear independence. We demonstrate by example that the condition is not necessary, but is strictly weaker than other existing sufficient conditions.

We study random joint choice rules, allowing for interdependence of choice across budgets.  These capture random choice by multiple agents, or a single agent across goods or time periods. Our interest is in separable choice rules, where each agent can be thought of as acting independently of the other. A random joint choice rule satisfies marginality if it induces well defined marginal random choice rules. We offer two characterizations of random joint choice rules satisfying marginality in terms of separable choice rules. While marginality is a necessary condition for separability, we show that it fails to be sufficient. We provide an additional condition on the marginal choice rules which, along with marginality, is sufficient for separability.

The random utility model is known to be unidentified, but there are times when the model admits a unique representation. We offer two characterizations for the existence of a unique random utility representation. Our first characterization puts conditions on a graphical representation of the data set. Non-uniqueness arises when multiple inflows can be assigned to multiple outflows on this graph. Our second characterization provides a direct test for uniqueness given a random utility representation. We also show that the support of a random utility representation is identified if and only if the representation itself is identified.

We propose a framework for identification and estimation of a private values model with unobserved heterogeneity from bid data in English auctions, using variation in the number of bidders across auctions, and extend the framework to settings where the number of bidders is not cleanly observed in each auction. We illustrate our method on data from eBay Motors auctions. We find that unobserved heterogeneity is important, accounting for two thirds of price variation after controlling for observables, and that welfare measures would be dramatically misestimated if unobserved heterogeneity were ignored.