# Pietro Ortoleva

## Associate Professor of Economics

## Department of Economics

Columbia University

## Member of the Cognition and Decision Lab

Columbia University

Research

(Click to expand)

Theoretical Economics, vol. 12 (2017), 377–424

(Previous Title: *Objective Lotteries as Ambiguous Objects: Allais, Ellsberg,and Hedging*)

__Idea__: Model an agent who exhibits both Allais and Ellsberg-like behavior in the setup of Anscombe and Aumann (1963). Generalizes Gilboa and Schmeidler (1989) to allow for Allais-type behavior.

__Abstract__: Two of the most well-known regularities observed in preferences under risk and uncertainty are ambiguity aversion and the Allais paradox. We study the behavior of an agent who can display both tendencies at the same time. We introduce a novel notion of preference for hedging that applies to both objective lotteries and uncertain acts. We show that this axiom, together with other standard ones, is equivalent to a representation in which the agent: 1) evaluates ambiguity using multiple priors, as in the model of Gilboa and Schmeidler (1989); 2) evaluates objective lotteries by distorting probabilities as in the Rank Dependent Utility model, but using the worst from a set of distortions. We show that a preference for hedging is not sufficient to guarantee an Ellsberg-like behavior if the agent violates Expected Utility for objective lotteries; we provide a novel axiom that characterizes this case, linking the distortions for objective and subjective bets.

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Journal of Political Economy, vol. 125, no. 1 (February, 2017), 40–68

(Previous title: *Stochastic Choice and Hedging*)

__Idea__: Experimental paper in which we show that the majority of subjects *choose* to give a stochastic choice. This is in line with the interpretations of stochastic choice as emerging from an explicit preference for randomizing, as opposed to emerging from random utility or mistakes.

__Abstract__: We conduct an experiment in which subjects face the same questions repeated multiple times, with repetitions of two types: 1) following the literature, the repetitions are distant from each other; 2) in a novel treatment, the repetitions are in a row, and subjects are told that the questions will be repeated. We find that a large majority of subjects exhibit stochastic choice in *both* cases. We discuss the implications for models of stochastic choice.

Management Science, vol. 62, no. 8 (August 2016), 2179-2197.

(Previous title: *A Variation on Ellsberg* and *Uncertain Probabilities vs. Uncertain Outcomes: An Experimental Study of Attitudes Towards Ambiguity*)

__Idea__: Modifies Ellsberg experiments to allow for bet directly on the composition of the urn. The behavior observed suggests of restrictions of the set of priors.

__Abstract__: The classical Ellsberg experiment presents individuals with a choice problem in which the probability of winning a prize is unknown (uncertain). In this paper, we study how individuals make choices between gambles in which the uncertainty is in different dimensions: the winning probability, the amount of the prize, the payment date, and many combinations thereof. While the decision-theoretic models accommodate a rich variety of behaviors, we present experimental evidence that points at systematic behavioral patterns: (i) no uncertainty is preferred to uncertainty on any single dimension and to uncertainty on multiple dimensions, and (ii) “correlated” uncertainty on multiple dimensions is preferred to uncertainty on any single dimension.

PDF Download: Paper - Online Appendix - Data

PLOS ONE, 10(10): e0139542. doi:10.1371/journal.pone.0139542 (October 2015)

__Idea__: Study emotional and behavioral responses to anti-smoking pictures on cigaretters packaging.

__Abstract__: In this article we use data from a multi-country Randomized Control Trial study on the effect of anti-tobacco pictorial warnings on an individual’s emotions and behavior. By exploiting the exogenous variations of images as an instrument, we are able to identify the effect of emotional responses. We use a range of outcome variables, from cognitive (risk perception and depth of processing) to behavioural (willingness to buy and willingness to pay). Our findings suggest that the odds of buying a tobacco product can be reduced by 80% if the negative affect elicited by the images increases by one standard deviation. More importantly from a public policy perspective, not all emotions behave alike, as eliciting shame, anger, or distress proves more effective in reducing smoking than fear and disgust.

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European Journal of Political Economy, vol. 40 Part B (December 2015), 333-344

__Abstract__: Recent studies suggest psychological differences between conservatives and liberals, including that conservatives are more overconfident. We use a behavioral political economy model to show that while this is undoubtedly true for election years in the current era, there is no reason to believe that conservative ideologies are intrinsically linked to overconfidence. Indeed, it appears that in 1980 and before, conservatives and liberals were equally overconfident.

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Econometrica, Vol. 83, No. 2 (March, 2015), 693–728

__Idea__: Novel class of preferences that satisfy the Certainty Effect (Allais Paradox) in which the decision maker has a set of utilities and considers the most pessimistic one of them. Characterized via one key axiom, Negative Certainty Independence (plus basic axioms).

__Abstract__: Many violations of the Independence axiom of Expected Utility can be traced to subjects’ attraction to risk-free prospects. The key axiom in this paper, Negative Certainty Independence (Dillenberger, 2010), formalizes this tendency. Our main result is a utility representation of all preferences over monetary lotteries that satisfy Negative Certainty Independence together with basic rationality postulates. Such preferences can be represented as if the agent were unsure of how to evaluate a given lottery *p*; instead, she has in mind a set of possible utility functions over outcomes and displays a cautious behavior: she computes the certainty equivalent of *p* with respect to each possible function in the set and picks the smallest one. The set of utilities is unique in a well-defined sense. We show that our representation can also be derived from a ‘cautious’ completion of an incomplete preference relation.

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American Economic Review, Vol. 105, No. 2 (February 2015), 504-535.

__Idea__: Studies the role of overconfidence in ideology formation and voting, showing how it is linked with ideological extremism and higher turnout. It then tests the predictions in novel survey data, finding a strong support.

__Abstract__: This paper studies, theoretically and empirically, the role of overconfidence in political behavior. Our model of overconfidence in beliefs predicts that overconfidence leads to ideological extremeness, increased voter turnout, and increased strength of partisan identification. Moreover, the model makes many nuanced predictions about the patterns of ideology in society, and over a person’s lifetime. These predictions are tested using unique data that measure the overconfidence, and standard political characteristics, of a nationwide sample of over 3,000 adults. Our numerous predictions find strong support in these data. In particular, we document that overconfidence is a substantively and statistically important predictor of ideological extremeness and voter turnout.

PDF Download: Paper - Online Appendix

American Economic Review, Vol. 105, No. 1 (January 2015), 299–321.

__Idea__: Characterize choice that violate Warp because of an endogenous reference point, like in the case of the attraction effect.

__Abstract__: The goal of this paper is to develop, axiomatically, a revealed
preference theory of reference-dependent behavior. Instead of taking the
reference for an agent as exogenously
given in the description of a choice problem, we suitably relax the Weak
Axiom of Revealed Preference and we the existence of reference alternatives
as well as the structure of choice behavior conditioned on those
alternatives.

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Rivista di Politica Economica, Issue 3 (July-September) 2014, 45–64.

(Previous Title: *Hypothesis Testing and Multiple Priors*)

__Idea__: We extends the model of non-Bayesian updating in Ortoleva (2012), Hypothesis Testing mode, to the case of ambiguity averse agents.

__Abstract__: We study a model of non-Bayesian updating, based on the Hypothesis Testing model of Ortoleva (2012), for ambiguity averse agents. Agents ranks acts following the MaxMin Expected Utility model of Gilboa and Schmeidler (1989) and when they receive new information they update their set of priors as follows: If the information is such that all priors in the original set of priors assign to it a probability above a threshold, then the agent updates every prior in the set using Bayes’ rule. Otherwise: she looks at a prior over sets of priors; she updates it using a rule similar to Bayes’ rule for second order beliefs over sets; finally, she chooses the set of priors to which the updated prior over sets priors assigns the highest likelihood.

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Journal of Economic Theory, Vol. 148, No. 3 (May 2013), 903--934

__Idea__: Model an agent who prefers a smaller menu because of the cost of thinking involved in choosing from the bigger one. Defines a notion of Thinking Aversion, and characterizes this cost.

__Abstract__: We study the behavior of an agent who dislikes large choice sets because of the ‘cost of thinking’ involved in choosing from them. We take as a primitive a preference relation over lotteries of menus and impose novel axioms that allow us to separately identify a ‘genuine’ preference over the content of menus from the cost of choosing from them. Using this, we formally define the notion of *Thinking Aversion*, much in line with the definitions of risk or ambiguity aversion. We characterize such preference as the difference between an affine evaluation of the content of the menu and a function that assigns to each menu a thinking cost. We provide conditions that allow us to interpret the cost of thinking about a menu as the cost that the agent has to sustain to figure out her preferences in order to make her choice.

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American Economic Review, Vol. 102, No. 6 (October 2012), 2410--2436.

__Idea__: A model in which agents are Bayesian after `normal' events, but have non-Bayesian reactions to low probability events, and whose behavior is modeled also after zero-probability ones.

__Abstract__: Bayes' rule has two well-known limitations: 1) it does not regulate the reaction to zero-probability events; 2) a sizable empirical evidence documents systematic violations of it. We introduce a behavioral rule, Dynamic Coherence, and show that it is equivalent to an alternative updating rule, the Hypothesis Testing model. According to it, the agent follows Bayes' rule if she receives information to which she assigned a probability above a threshold. Otherwise, she looks at a prior over priors; updates it using Bayes' rule for second-order priors; and chooses the prior to which the updated prior over priors assigns the highest likelihood. We apply the model to construct, in an example, a refinement of Perfect Bayesian Nash Equilibrium.

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Econometrica, Vol. 80, No. 4 (July, 2012), 1791–1808

__Idea__: Studies incomplete preferences under uncertainty.

__Abstract__: We investigate the classical Anscombe-Aumann model of
decision-making under uncertainty without the completeness axiom. We
distinguish between the dual traits of "indecisiveness in
beliefs" and "indecisiveness in
tastes." The former is captured by the Knightian
Uncertainty model, while the latter by the single-prior expected
multi-utility model. We characterize axiomatically the latter model. Then,
we show that, under Independence and Continuity, these two models can be
jointly characterized by a means of a partial completeness property.

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Games and Economic Behavior, Vol. 69 (2010), 411-424

__Idea__: Characterize status-quo-dependent preferences under uncertainty. The agent keeps her status quo unless there is an option better than it for a set of priors. We also show that this implies that the agent is uncertainty averse.

__Abstract__: Motivated by the extensive evidence about the relevance of status quo bias both in experiments and in real markets, we study this phenomenon from a decision-theoretic prospective, focusing on the case of preferences under uncertainty. We develop an axiomatic framework that takes as a primitive the preferences of the agent for each possible status quo option, and provide a characterization according to which the agent prefers her status quo act if nothing better is feasible for a given set of possible priors. We then show that, in this framework, the very presence of a status quo induces the agent to be more uncertainty averse than she would be without a status quo option. Finally, we apply the model to a financial choice problem and show that the presence of status quo bias as modeled here might induce the presence of a risk premium even with risk neutral agents.

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(Click to expand)

__Idea__: Study axiomatically stochastic choice as the outcome of a deliberate desire to randomize.

__Abstract__: We study stochastic choice as the outcome of *deliberate* randomization. After first deriving a general representation of a stochastic choice function with such property, we proceed to characterize a model in which the agent has preferences over lotteries that belong to the Cautious Expected Utility class (Cerreia-Vioglio et al., 2015a), and the stochastic choice is the optimal mix among available options. This model links stochasticity of choice and the phenomenon of Certainty Bias, with both behaviors stemming from the same source: multiple utilities and caution. We show that this model is behaviorally distinct from models of Random Utility, as it typically violates the property of Regularity, shared by all of them.

PDF Download: Paper (April 2017)

__Idea__: Shows that Willingness to Pay and Willingness to Accept are very poorly correlated, if at all, in 2 large scale studies on representative samples.

__Abstract__: Willingness to pay (WTP) and willingness to accept (WTA) a monetary amount for a lottery should be closely related. In data from an incentivized survey of a representative sample of 3,000 U.S.~adults, we find that WTA and WTP for a lottery are, at best, weakly correlated. Across all respondents, the correlation is slightly negative. For the subgroups that we examine, the correlation is almost always small, typically statistically insignificant, and often negative. The exception is respondents who score highly on a within-study IQ test, where the correlation is around 0.2. A meta-study of similar lab experiments with university students also shows a correlation of around 0.15--0.2. While poorly related to each other, our measures of WTA and WTP are strongly related to different measures of risk aversion, and relatively stable across time. These various patterns allow us to show that this lack of relationship between WTA and WTP is compatible with existing theories, such as Prospect Theory and Stochastic Reference Dependence, only under very specific, and unlikely, correlational structures between parameters. We suggest a simpler formalization.

PDF Download: Paper (May 2017)

(Previous titles: *Is it All Connected? Understanding the Relationship Between Behavioral
Phenomena *, and *Estimating the Relationship between Economic Preferences: A Testing Ground for Unified Theories of Behavior*)

__Idea__: Studies with an experiment the empirical relation between behavioral phenomena like risk, ambiguity, and loss aversion, certainty, present, and status quo bias, endowment effect, updating speed, discounting, etc.

__Abstract__: We study the joint distribution of 11 behavioral phenomena in a group of 190 laboratory subjects and compare it to the predictions of existing models as a step in the development of a parsimonious, general model of economic choice. We find strong correlations between loss aversion and the endowment effect, risk aversion and discounting, compound lottery and ambiguity aversion, and between the Allais paradox and risk aversion. Our results support some, but not all attempts to unify behavioral economic phenomena through extensions to Cumulative Prospect Theory. Overconfidence and gender are also predictive of some behavioral phenomena.

__Idea__: Studies *time lotteries* -- lotteries that pay a fixed amount in a random date. The standard model of Discounted Expected Utility predicts that subjects should always be risk *seeking* over time lotteries. Our expriment strongly rejects this prediction. Shows instead that the model of Epstein Zin (1989) can account for this behavior, offering a new behaivoral motivation for this.

__Abstract__: We study preferences over lotteries that pay a specific prize at uncertain dates. Expected Utility with convex discounting implies that individuals prefer receiving $x in a random date with mean t over receiving $x in t days for sure. Our experiment rejects this prediction. It suggests a link between preferences for payments at certain dates and standard risk aversion. Epstein-Zin (1989) preferences accommodate such behavior, and fit the data better than a model with probability weighting. We thus provide another justification for disentangling attitudes toward risk and time, as in Epstein-Zin, and suggest new theoretical restrictions on its key parameters.

(Previous title: *Aspirations and growth: a model where the income of others acts as a reference point*, and *The Behavior of Others as a Reference Point: Prospect Theory, Inequality, and Growth*)

__Idea__: Study growth when the average consumption of the society acts as a reference point for the consumers. Reference dependence is modeled using prospect theory.

__Abstract__: We study a model in which consumers are reference-dependent, modeled using prospect-theory, and their reference point is the average behavior of the society in that period. We show that in any of the equilibria of the economy after a finite number of periods the wealth distribution will become, and remain, either of perfect equality, or admit a ‘missing class’ (a particular form of polarization). We then study growth rates and show that, if we look at the equilibria with the highest growth, then the society with the highest growth rate is the one that starts with perfect equality. If we look at the equilibria with the lowest growth, however, then the society with a small amount of initial inequality is the one that attains the highest growth rate, while a society with perfect equality is the one with the lowest performance. All of these growth rates are weakly higher than the growth rate of a corresponding economy without reference-dependence.

PDF Download: Paper (March 2014 - *under review*)

__Idea__: Applies the model of "Revealed (P)Reference Theory" to the theory of product differentiation. Obtains that the presence of these biases might lead the economy back to an efficient equilibrium in which the monopolist extracts all the surplus.

__Abstract__: We apply the theoretical model of endogenous reference-dependence of Ok, Ortoleva and Riella (2011) to the theory of vertical product differentiation. We analyze the standard problem of a monopolist who offers a menu of alternatives to consumers of different types, but we allow for agents to exhibit a form of endogenous reference dependence like the attraction effect. We show that the presence of such biases might allow the monopolist to overcome some of the incentive compatibility constraints of the standard problem, leading the economy back towards the efficient equilibrium in which the monopolist extracts all the surplus. We then discuss welfare implications, showing that an increase in the fraction of customers who are subject to the attraction effect might not only increase the monopolist’s profits and total welfare, but consumer’s welfare as well.

PDF Download: Paper (September 2011)

__Idea__: Apply the model in "The price of Flexibility" to a portfolio choice.

__Abstract__: This paper analyzes the investment decision of an agent who has to figure out the correct model to use in order to evaluate all available assets. This is a costly process. She can choose either to endure this cost, or to simplify her choice by looking only at a subset of the available assets. We show that such an agent tends to participate less in the market, to under-diversify her portfolio, or to diversify it naively, by investing equal amounts in a selection of assets. These predictions qualitatively match the empirical observations of the investments of households, both in general investment situations and in the choice of 401(k) plans. Moreover, in a partial equilibrium setting, if agents are not aware that others bear the cost of discovering which model to use, then even a small cost can induce a sizable effect on the equilibrium prices. This is due to a phenomenon similar to a multiplier: agents observe prices that are different than expected, and in turn modify expectations, which affect prices, which in turn affect expectations, and so on.

(Currently no version to Download)

__Idea__: Short note that extends the Hypothesis Testing model to the case of an infinite state space.

__Abstract__: We extend the Hypothesis Testing model of Ortoleva (2010) to the case in which the state space is infinite. We show that almost identical results hold in this case as well.

(Currently no version to download)

Curriculum

- Associate Professor of Economics (untenured), Columbia University, July 2015 -
*present* - Assistant Professor of Economics, Columbia University, July 2013 - June 2015
- Associate Professor of Economics (untenured), California Institute of Technology, May 2012 - June 2013
- Assistant Professor of Economics, California Institute of Technology, July 2009 - May 2012

- Ph.D in Economics, New York University - May 2009

*Advisor*: Efe Ok - Laurea (BA) in Economics, Summa cum Laude, Università degli Studi di Torino - March 2004

- Editorial Board, American Economic Review, January 2017-
*present* - Associate Editor, Journal of Political Economy, July 2016-
*present* - Associate Editor, Mathematical Social Sciences, January 2014 -
*present*

- National Science Foundation, Award SES-1559462, “Incomplete Preferences, Stochastic Choice, And Time And Risk Preferences”, 2016-2019
- National Science Foundation, Award SMA-1329195, “Discovering Deep Links between Behavioral Econographics and Political Attributes: Evidence from a Large, Cross-Country Survey”, 2014-2017
- National Science Foundation, Award SES-1156091, “Understanding the Connections Between Economics Behaviors”, 2012-2014

Last Update, February 2017

Teaching

- G5211: Microeconomic Analysis 1 (Master)

See more on Courseworks - G6211: Microeconomic Analysis 1 (PhD)

See more on Courseworks