Working Papers

Axiomatization of Random Utility Model with Unobservable Alternatives joint with Haruki Kono and Alec Sandroni [arxiv]
The random utility model is one of the most fundamental models in discrete choice  analysis in economics. Although Falmagne (1978) obtained an axiomatization of the random utility model, his characterization requires strong observability of choices, i.e., that the frequency of choices must be observed from all subsets of the set of alternatives. Little is known, however, about the axiomatization when a dataset is incomplete, i.e., the frequencies on some choice sets are not observable. In fact, it is known that in some cases, obtaining a tight characterization is NP hard. On the other hand, datasets in reality almost always violate the requirements on observability assumed by Falmagne (1978). We consider an incomplete dataset in which we do not observe frequencies of some alternatives: for all other alternatives, we observe frequencies. For such a dataset, we obtain a finite system of linear inequalities that is necessary and sufficient for the dataset to be rationalized by a random utility model. Moreover, the necessary and sufficient condition is tight in the sense that none of the inequalities is implied by the other inequalities, and dropping any one of the inequalities makes the condition not sufficient.

Approximating Choice Data by Discrete Choice Models joint with  Haoge Chang and Yusuke Narita [arxiv] We obtain a necessary and sufficient condition under which parametric random-coefficient discrete choice models can approximate the choice behavior generated by nonparametric random utility models. The condition turns out to be very simple and tractable.   For the case under which the condition is  not satisfied (and hence, where some stochastic choice data are generated by a random utility model that cannot be approximated), we  provide algorithms to measure the approximation errors. After applying our theoretical results and the algorithm to real data, we found that the approximation errors can be large in practice.

 
Mixed Logit and Pure Characteristics Models joint with Jay Lu [working paper pdf]
Mixed logit or random coefficients logit models are used extensively in empirical work while pure characteristic models feature in much of theoretical work. We provide a theoretical analysis of the relationship between the two classes of models. First, we show an approximation theorem that precisely characterizes the extent and limits of mixed logit approximations of pure characteristic models. Second, we present two conditions that highlight behavioral differences between the two classes of models. The first is a substitutability condition that is satisfied by many pure characteristic models (including the Hotelling model of horizontal differentiation) but is violated by almost all mixed logit models. The second is a continuity condition that is satisfied by all pure characteristic models but is violated by all mixed logit models. Both conditions pertain to choice patterns when product characteristics change or new products are introduced and illustrate the limitations of using mixed logit models for counterfactual analysis.

Repeated Choice: A Theory of Stochastic Intertemporal Preferences  joint with Jay Lu [working paper pdf] [submitted version pdf] [30 min presentation video]
We provide a repeated-choice foundation for stochastic choice. We obtain necessary and sufficient conditions under which an agent's observed stochastic choice can be represented as a limit frequency of optimal choices over time. In our model, the agent repeatedly chooses today's consumption and tomorrow's continuation menu, aware that future preferences will evolve according to a subjective ergodic utility process. Using our model, we demonstrate how not taking into account the intertemporal structure of the problem may lead an analyst to biased estimates of risk preferences. Estimation of preferences can be performed by the analyst without explicitly modeling continuation problems (i.e. stochastic choice is independent of continuation menus) if and only if the utility process takes on the standard additive and separable form. Applications include dynamic discrete choice models when agents have non-trivial intertemporal preferences, such as Epstein-Zin preferences. We provide a numerical example which shows the significance of biases caused by ignoring the agent's Epstein-Zin preferences.

Decision Making under Uncertainty: An Experimental Study in Market Settings Current Version: Dec 06 , 2019 joint with Federico Echenique and Taisuke Imai. [pdf]
We design and implement a novel experimental test of subjective expected utility theory and its generalizations. Our experiments are implemented in the laboratory with a student population and pushed out through a large-scale panel to a general sample of the U.S. population. We find that a majority of subjects' choices are consistent with the maximization of some utility function, but not with subjective expected utility theory. The theory is tested by gauging how subjects respond to price changes. A majority of subjects respond to price changes in the direction predicted by the theory, but not to a degree that makes them fully consistent with subjective expected utility. Surprisingly, maxmin expected utility adds no explanatory power to subjective expected utility. Our findings remain the same regardless of whether we look at laboratory data or the panel survey, even though the two subject populations are very different. The degree of violations of subjective expected utility theory is not affected by age nor cognitive ability,
but it is correlated with financial literacy.

Axiomatizations of the Mixed Logit Model First Draft: July 29, 2017, Current Version: June 17, 2018. [pdf]
A mixed logit function, also known as a random-coefficient logit function, is an integral of logit functions. Necessary and sufficient conditions are provided under which a random choice function can be represented as a mixed logit function. The axioms are based on the social surplus function proposed by McFadden (1978, 1981).

A Relationship between Risk and Time First Draft: February 10, 2011, Current Version: April 23, 2015. [pdf]
This paper investigates a general relationship between risk and time preferences. I consider a decision maker who chooses between consumption of a particular prize in one period and a different prize in another period. The individual believes that today's good is certain, and that, as the promised date for a future good becomes increasingly distant, the probability of his consuming the good decreases. Under these assumptions, this paper shows that the individuals exhibits the common ratio effect, the certainty effect, and the expected utility if and only if he discounts hyperbolically, quasi-hyperbolically and exponentially, respectively.