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History-Dependent Risk Attitude



History-Dependent Risk Attitude∗ David Dillenberger† University of Pennsylvania Kareen Rozen‡ Yale University November 2010 Abstract We propose a model of history-dependent risk attitude (HDRA), allowing the attitude of a decision-maker (DM) towards risk at each stage of a T -stage lottery to evolve as a function of his history of disappointments and elations in prior stages. We establish an equivalence be- tween the existence of an HDRA representation and two documented cognitive biases. First, the DM overreacts to news: after suffering a disappointment, the DM lowers his threshold for elation and becomes more risk averse; similarly, after an elating outcome, the DM raises his threshold for elation and becomes less risk averse. This makes disappointment more likely after elation and vice-versa, leading to statistically cycling risk attitudes. Second, the DM dis- plays a primacy effect: early outcomes have the strongest effect on risk attitude. “Gray areas” in the elation-disappointment assignment are connected to optimism and pessimism in deter- mining endogenous reference points. Keywords: history-dependent risk attitude, disappointment cycles, overreaction to news, pri- macy effect, endogenous reference dependence, betweenness, optimism, pessimism JEL Codes: D03, D81, D91 ∗First version June 2010. This paper previously circulated under the title “Disappointment Cycles.” We are grateful to Simone Cerreia-Vioglio for helpful conversations. We also benefitted from comments and suggestions by Larry Samuelson and seminar participants at Boston University, Northwestern University, University of British Columbia, University of Pennsylvania and Yale University. †Department of Economics, 160 McNeil Building, 3718 Locust Walk, Philadelphia, Pennsylvania 19104-6297. E-mail: [email protected] ‡Department of Economics and the Cowles Foundation for Research in Economics, 30 Hillhouse Avenue, New Haven, Connecticut 06511. E-mail: [email protected] I than

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