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1 the Role of Salience and Attention In THE ROLE OF SALIENCE AND ATTENTION IN CHOICE UNDER RISK: AN EXPERIMENTAL INVESTIGATION MILICA MORMANN AND CARY FRYDMAN* May 2016 We conduct two experiments that test a recently proposed theory of context-dependent choice under risk called salience theory. The theory predicts that a decision maker’s attention is drawn to precisely defined salient payoffs, and these payoffs are overweighted in the choice process. In our first experiment, subjects make a series of highly incentivized choices between a risky lottery and a certain option while their eye-movements are recorded. In the second experiment, subjects choose between a risky lottery and a certain option, but we exogenously manipulate the visual salience of the risky lottery. We find three main results. First, the data on lottery choices is broadly consistent with salience theory as risk-taking increases when the upside of the risky lottery becomes more salient. Second, using eye-tracking data, we find that subjects do not pay more attention to the state that is theoretically salient, which is inconsistent with the theory; instead, subjects pay more attention to the risky lottery compared to the certain option when the risky lottery’s upside is salient. Third, risk taking is reduced when a lottery’s downside becomes visually salient. More generally, our results provide evidence that attention is an important and causal factor in determining choice under risk. JEL Codes: C91, D81, D87 *Authors contributed equally to this work. Mormann is at the Department of Finance, University of Miami School of Business, [email protected]; Frydman is at the Department of Finance and Business Economics, USC Marshall School of Business, [email protected]. We are thankful for comments and suggestions from Kenneth Ahern, Nicholas Barberis, Pedro Bordalo, Ben Bushong, Tom Chang, Nicola Gennaioli, Alison Harris, Lawrence Jin, Chad Kendall, Ian Krajbich, Yaron Levi, Andrei Shleifer, Neil Thakral and from seminar participants at Harvard University, Maastricht University, University of Miami, University of Southern California, Society for Neuroeconomics Conference, and Southern California Finance Conference. We thank Mike Lupp and Brad Swain for research assistance. 1 I. INTRODUCTION A key tenet of expected utility theory is that preferences are stable over time and are independent of the context in which choices are presented. These preferences guarantee that choices are consistent across environments and are not affected by context-specific features such as visual cues or the choice set itself. However, starting with Allais (1953), a large body of evidence documents robust violations of context-independent choice1. For example, when confronted with a choice between two lotteries with similar expected values, experimental subjects often exhibit a preference reversal: they choose the less risky lottery but are willing to pay more for the riskier lottery (Lichtenstein and Slovic 1971). The systematic nature of these context-independent choice violations suggests that preferences are malleable and influenced by the environment. Theorists have thus begun to formalize a new class of models where the choice set can distort the relative weights that a decision-maker attaches to attributes of an alternative. Bordalo, Gennaioli and Shleifer (2012) (henceforth BGS) propose the first economic model in this spirit, salience theory, to explain context-dependent risk preferences. BGS assume that attention is directed towards salient lottery payoffs, and the decision maker then overweights these payoffs when computing the lottery’s utility. Bordalo, Gennaioli and Shleifer (2013a, 2013b, 2015) use this same core intuition – that attribute weighting is a function of the choice set – to explain context-dependencies in consumer choice, asset pricing, and industrial organization. Other recent models share this intuition but assume that the range of utilities across an attribute distort the associated attribute weight (Koszegi and Szeidl 2013; Cunningham 2013; Bushong, Rabin, and Schwartzstein 2016)2. While the salience model of BGS can deliver many classic violations of context- independent choice, its core assumptions represent a departure from the standard economic model 1 See Camerer (1995) for a review. 2 Earlier work by Loomes and Sugden (1982) is also driven by attribute-based comparisons, although the interpretation in that work is based on anticipatory regret and rejoicing. 2 and remain untested. In this paper, we conduct two experiments that allow us to perform novel tests of the key psychological mechanism that drives decision-making under risk according to salience theory. In the first experiment, subjects make highly incentivized decisions between a risky lottery and a certain option while we collect eye-tracking data. This combination of data on lottery choices and eye-tracking enables us to test both the model’s assumption about the psychological mechanism and the model’s predictions about risk taking. To understand how the eye-tracking data is used to test the model’s assumption, we briefly describe the intuition of the BGS model here. A lottery payoff is defined as salient if “it is very different in percentage terms from the payoffs of the other available lotteries (in the same state of the world)” (pg. 1244). A decision-maker’s (DM) attention is then drawn to the salient payoff, and the DM subsequently overweights the state in which the salient payoff is delivered. When a lottery’s upside is salient, the DM overweights the lottery’s upside and exhibits risk- seeking behavior; when its downside is salient, the DM exhibits risk-averse behavior. The key restriction of the BGS model is that it precisely defines which state of the world is salient as a function of the choice set. Therefore, we are able to test (i) whether a subject’s attention is drawn to the state that is predicted to be salient, and (ii) whether risk taking is greater when the lottery’s upside is salient. Overall, the choice data reveal that risk preferences are systematically unstable across choice sets, and this instability is largely consistent with salience theory. We find that the basic prediction of the BGS model is upheld: risk taking is greater when the lottery’s upside is salient compared to when the downside is salient. We then compare salience theory with the leading behavioral model of choice under risk, cumulative prospect theory (CPT) (Tversky and Kahneman 1992). After structurally estimating each model, we find that both can fit the data reasonably well, with salience theory providing a slightly better fit than CPT. Our structural estimation reveals that much of the variation in risk taking is explained by the context-dependent 3 weighting function of salience theory, while CPT relies heavily on a large degree of concavity in the value function. At the eye-tracking level, the results are less supportive of the precise psychological mechanism that is assumed to generate context-dependent risk preferences in salience theory. The model’s key assumption implies that subjects should pay more attention to the state that is theoretically salient. We do not find support for this prediction at the eye-tracking level. However, because of the richness of the eye-tracking data, we conduct additional exploratory analyses to better understand what factors do govern the attention allocation process. We find that when the gain state is theoretically salient, subjects allocate more attention overall to the risky lottery compared to the certain option. Moreover, the amount of attention that subjects pay to the risky lottery relative to the certain option is a strong predictor of the ultimate choice. This result is consistent with a recent model from the neuroeconomics literature that predicts that the computation of decision values is modulated by attention (Krajbich, Armel, and Rangel 2010). In our second experiment, we examine another dimension of salience and its impact on risky choice. The salience function in BGS that maps payoffs into a salience measure is motivated by the literature on visual perception3. In the same manner that BGS propose that extreme economic payoffs are salient, the literature on visual perception identifies those attributes of visual stimuli that are salient and attract a DM’s attention (Itti and Koch 2001; Wolfe and Horowitz 2004; Knudsen 2007). For example, the color, brightness, or shape of an object can make it “pop-out” against the environment. To make the distinction between these two sources of salience clear, we refer to the salience driven by economic payoffs in BGS as “economic salience” and the salience driven by simple visual features of objects in the environment as “visual salience.” A lottery payoff that is extreme compared to the magnitude of other payoffs is economically salient; however, this same payoff may not be visually salient if it is displayed in 3 Woodford (2012) also argues for motivating the assumptions of behavioral economic models from the literature on visual perception. 4 faint gray font on a dark gray background compared to another payoff displayed in bold black font on the same gray background. While the motivation for economic salience in BGS is firmly rooted in the well-known properties of visual salience, BGS do not explicitly incorporate visual salience into their model. However, recent research in neuroeconomics shows that visual salience interacts with economic value in riskless choice (Towal, Mormann, and Koch 2013). We therefore hypothesize that incorporating visual salience into any model of risky choice can provide extra explanatory power. As a first step in formally testing this hypothesis, we generalize the BGS model to explicitly incorporate visual salience, which we call the full salience model. In this second experiment, we exogenously manipulate the visual salience of lotteries to test the full salience model. In the control condition, as in Experiment 1, subjects make decisions between a risky lottery and a certain option, where all information is displayed in the same font. In the “visually salient” condition, we increase the visual salience of the state of the world that is economically salient by displaying it in bold font.
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