# Published/Forthcoming Papers

**Testable Implications of Models of Intertemporal Choice:
Exponential Discounting and Its Generalizations **

*F*

*orthcoming in*

**(Previous title: Testable Implication of Exponential Discounting)**

**Microeconomics***American Economic Journal:***joint with Federico Echenique (Caltech) and Taisuke Imai (LMU Munich). [pdf][online appendix pdf]**

*We present revealed-preference characterizations of the most common models of intertemporal choice: the model of exponentially discounted concave utility, and some of its generalizations. Our characterizations take consumption data as primitives, and provide nonparametric revealed-preference tests. We apply our tests to data from two recent experiments and find that our axiomatization delivers new insights and perspectives on datasets that had been analyzed by traditional parametric methods.*

** The Relation between Behavior under Risk and over Time American Economic Journal: Insight **2 (1): 1-16

**(**This paper subsumes "A Relationship between Risk and Time" and corrects a result in "Strotz Meets Allais: Diminishing Impatience and the Certainty Effect: Comment") joint with Anujit Chakraborty (UC Davis) and Yoram Halevy (University of Toronto). [pdf] [online appendix pdf]

*The paper establishes a tight relation between non-standard behaviors in the domains of risk and time, by considering a decision maker with non- expected utility preferences who believes that only present consumption is certain while any future consumption is uncertain. We provide the first complete characterizations of the two-way relations between the certainty effect and present biased temporal behavior, and between the common ratio effect and temporal reversals related to the common difference effect.*

**Random Intertemporal Choice** 2018 ** Journal of
Economic Theory** 177: 780-815 joint with Jay Lu (UCLA). [pdf]

We provide a theory of random intertemporal choice. Choice is random due to unobserved heterogeneity in discounting from the perspective of a modeler. First, we show that the modeler can identify the distribution of discount rates uniquely from random choice. We then provide axiomatic characterizations of random discounting utility models, including exponential and quasi-hyperbolic discounting as special cases. Finally, we test our axioms using recent experimental data. We find that random exponential discounting is not rejected and the distribution of discount rates is statistically indistinguishable across treatments.

We provide a theory of random intertemporal choice. Choice is random due to unobserved heterogeneity in discounting from the perspective of a modeler. First, we show that the modeler can identify the distribution of discount rates uniquely from random choice. We then provide axiomatic characterizations of random discounting utility models, including exponential and quasi-hyperbolic discounting as special cases. Finally, we test our axioms using recent experimental data. We find that random exponential discounting is not rejected and the distribution of discount rates is statistically indistinguishable across treatments.

**General Luce Model** 2018 ** Economic Theory** joint
with Federico Echenique [pdf]

We extend the Luce model of discrete choice theory to satisfactorily handle zero-probability choices. The Luce model (or the Logit model) is the most widely applied and used model in stochastic choice, but it struggles to explain choices that are not made. The Luce model requires that if an alternative $y$ is never chosen when $x$ is available, then there is no set of alternatives from which $y$ is chosen with positive probability: $y$ cannot be chosen, even from sets of alternatives that exclude $x$. We relax this assumption. In our model, if an alternative $y$ is never chosen when $x$ is available, then we infer that $y$ is dominated by $x$. While dominated by $x$, $y$ may still be chosen with positive probability---even with high probability---when grouped with a comparable set of alternatives.

We extend the Luce model of discrete choice theory to satisfactorily handle zero-probability choices. The Luce model (or the Logit model) is the most widely applied and used model in stochastic choice, but it struggles to explain choices that are not made. The Luce model requires that if an alternative $y$ is never chosen when $x$ is available, then there is no set of alternatives from which $y$ is chosen with positive probability: $y$ cannot be chosen, even from sets of alternatives that exclude $x$. We relax this assumption. In our model, if an alternative $y$ is never chosen when $x$ is available, then we infer that $y$ is dominated by $x$. While dominated by $x$, $y$ may still be chosen with positive probability---even with high probability---when grouped with a comparable set of alternatives.

**The Perception-Adjusted Luce model** 2018 ** Mathematical
Social Sciences** 93(1): 67–76 joint with Federico Echenique and Gerelt
Tserenjigmid (Virginia Tech). [pdf]

We develop an axiomatic model that builds on Luce's (1959) model to incorporate a role for perception. We identify agents perception priorities from their violations of Luce's axiom of independence from irrelevant alternatives. Using such perception priorities, we adjust choice probabilities to account for the effects of perception. Our axiomatization requires that the agents' adjusted random choice conforms to Luce's model. Our model can explain the attraction, compromise, and similarity effects, which are well-documented behavioral phenomena in individual choice.

We develop an axiomatic model that builds on Luce's (1959) model to incorporate a role for perception. We identify agents perception priorities from their violations of Luce's axiom of independence from irrelevant alternatives. Using such perception priorities, we adjust choice probabilities to account for the effects of perception. Our axiomatization requires that the agents' adjusted random choice conforms to Luce's model. Our model can explain the attraction, compromise, and similarity effects, which are well-documented behavioral phenomena in individual choice.

**On path independent stochastic choice** (Previous
Title: Average Choice) 2017 ** Theoretical Economics** 13(1): 61–85 joint with David Ahn (UC
Berkeley) and Federico Echenique. [pdf]

*We investigate stochastic choice when only the average and not the entire distribution of choices is observable, focusing attention to the popular Luce model. Choice is path independent if it is recursive, in the sense that choosing from a menu can be broken up into choosing from smaller submenus. While an important property, path independence is known to be incompatible with continuous choice. The main result of our paper is that a natural modification of path independence, that we call {\em partial path independence}, is not only compatible with continuity but ends up characterizing the ubiquitous Luce (or Logit) rule.*

**Response Time and Utility** 2017 ** Journal of Economic
Behavior and Organization** 139(15): 49–59 joint with Federico
Echenique. [pdf]

Response time is the time an agent needs to make a decision. One fundamental finding in psychology and neuroscience is that, in a binary choice, the response time is shorter as the difference between the utilities of the two options becomes larger. We consider situations in which utilities are not observed, but rather inferred from revealed preferences: meaning they are inferred from subjects' choices. Given data on subjects' choices, and the time to make those choices, we give conditions on the data that characterize the property that response time is decreasing in utility differences.

Response time is the time an agent needs to make a decision. One fundamental finding in psychology and neuroscience is that, in a binary choice, the response time is shorter as the difference between the utilities of the two options becomes larger. We consider situations in which utilities are not observed, but rather inferred from revealed preferences: meaning they are inferred from subjects' choices. Given data on subjects' choices, and the time to make those choices, we give conditions on the data that characterize the property that response time is decreasing in utility differences.

**Testing theories of financial decision making **(Previous
title: Testable Implications of Translation Invariance and Homotheticity)

2016 ** Proceedings of the National Academy of Sciences **113(15): 4003–370
joint with Federico Echenique and Chris Chambers (UC San Diego). [pdf]
[submitted
version] [online
appendix (Proof of Theorem 4)]

*We provide revealed preference axioms that characterize models of translation invariant preferences. In particular, we characterize the models of variational, maxmin, CARA and CRRA utilities. In each case we present a revealed preference axiom that is satised by a dataset if and only if the dataset is consistent from the corresponding utility representation. Our results complement traditional exercises in decision theory that take preferences as primitive.*

**Impure Altruism and Impure Selfishness **2015 ** Journal
of Economic Theory** 158: 336–370. [pdf]

Altruism refers to a willingness to benefit others, even at one's own expense. In contrast, selfishness refers to prioritizing one's own interests with no consideration for others. However, even if an agent is selfish, he might nevertheless act as if he were altruistic out of selfish concerns triggered when his action is observed; that is, he might seek to feel pride in acting altruistically and to avoid the shame of acting selfishly. We call such behavior impurely altruistic . Alternatively, even if an agent is altruistic, he might nevertheless give in to the temptation to act selfishly. We call such behavior impurely selfish . This paper axiomatizes a model that distinguishes altruism from impure altruism and selfishness from impure selfishness. In the model, unique real numbers separately capture altruism and the other forces of pride, shame, and the temptation to act selfishly. We show that the model can describe recent experiments on dictator games with an exit option. In addition, we describe an empirical puzzle that government spending only partially crowds out consumers' donations, contrary to the prediction based on standard consumer theory.

Altruism refers to a willingness to benefit others, even at one's own expense. In contrast, selfishness refers to prioritizing one's own interests with no consideration for others. However, even if an agent is selfish, he might nevertheless act as if he were altruistic out of selfish concerns triggered when his action is observed; that is, he might seek to feel pride in acting altruistically and to avoid the shame of acting selfishly. We call such behavior impurely altruistic . Alternatively, even if an agent is altruistic, he might nevertheless give in to the temptation to act selfishly. We call such behavior impurely selfish . This paper axiomatizes a model that distinguishes altruism from impure altruism and selfishness from impure selfishness. In the model, unique real numbers separately capture altruism and the other forces of pride, shame, and the temptation to act selfishly. We show that the model can describe recent experiments on dictator games with an exit option. In addition, we describe an empirical puzzle that government spending only partially crowds out consumers' donations, contrary to the prediction based on standard consumer theory.

**Savage in the Market** 2015 * Econometrica *83:
1457–1495. joint with Federico Echenique. [pdf]
[online
appendix]

We develop a behavioral axiomatic characterization of Subjective Expected Utility (SEU) under risk aversion. Given is an individual agent's behavior in the market: assume a finite collection of asset purchases with corresponding prices. We show that such behavior satisfies a "revealed preference axiom'' if and only if there exists a SEU model (a subjective probability over states and a concave utility function over money) that accounts for the given asset purchases.

We develop a behavioral axiomatic characterization of Subjective Expected Utility (SEU) under risk aversion. Given is an individual agent's behavior in the market: assume a finite collection of asset purchases with corresponding prices. We show that such behavior satisfies a "revealed preference axiom'' if and only if there exists a SEU model (a subjective probability over states and a concave utility function over money) that accounts for the given asset purchases.

**Preferences for Flexibility and Randomization under
Uncertainty** 2015. ** American Economic Review ** 105: 1246–1271.
[pdf]
[online
appendix]

An uncertainty-averse agent prefers betting on an event whose probability is known, to betting on an event whose probability is unknown. Such an agent may randomize his choices to eliminate the effects of uncertainty. For what sort of preferences does a randomization eliminate the effects of uncertainty? To answer this question, we investigate an agent's preferences over sets of acts. We axiomatize a utility function, through which we can identify the agent's subjective belief that a randomization eliminates the effects of uncertainty.

An uncertainty-averse agent prefers betting on an event whose probability is known, to betting on an event whose probability is unknown. Such an agent may randomize his choices to eliminate the effects of uncertainty. For what sort of preferences does a randomization eliminate the effects of uncertainty? To answer this question, we investigate an agent's preferences over sets of acts. We axiomatize a utility function, through which we can identify the agent's subjective belief that a randomization eliminates the effects of uncertainty.

**Social Preferences under Risk: Equality of Opportunity
vs. Equality of Outcome **2013. ** American Economic Review **103: 3084–3101.
[pdf]

This paper introduces a model of inequality aversion that captures a preference for equality of ex-ante expected payoff relative to a preference for equality of ex-post payoff by a single parameter. On deterministic allocations, the model reduces to the model of Fehr and Schmidt (1999). The model provides a unified explanation for recent experiments on probabilistic dictator games and dictator games under veil of ignorance. Moreover, the model can describe experiments on a preference for efficiency, which seem inconsistent with inequality aversion. We also apply the model to the optimal tournament. Finally, we provide a behavioral foundation of the model.

This paper introduces a model of inequality aversion that captures a preference for equality of ex-ante expected payoff relative to a preference for equality of ex-post payoff by a single parameter. On deterministic allocations, the model reduces to the model of Fehr and Schmidt (1999). The model provides a unified explanation for recent experiments on probabilistic dictator games and dictator games under veil of ignorance. Moreover, the model can describe experiments on a preference for efficiency, which seem inconsistent with inequality aversion. We also apply the model to the optimal tournament. Finally, we provide a behavioral foundation of the model.

**Strotz Meets Allais: Diminishing Impatience and the
Certainty Effect: Comment** 2011** American Economic Review** 101: 2271–2275.
[pdf]

*Halevy (2008) states the equivalence between diminishing impatience (i.e., quasi-hyperbolic discounting) and the common ratio effect. The present paper shows that one way of the equivalence is false and shows the correct and general relationships: diminishing impatience is equivalent to the certainty effect and that strong diminishing impatience (i.e., hyperbolic discounting) is equivalent to the common ratio effect.*