THE EFFECT OF PERCEIVED SIMILARITY ON SEQUENTIAL RISK-TAKING

ELIZABETH C. WEBB*

SUZANNE B. SHU

* (corresponding author) Elizabeth C. Webb ([email protected]) is Assistant Professor of

Marketing at Columbia Business School, Columbia University, 511 Uris Hall, New York, NY 10027,

(212) 854-7864.

Suzanne B. Shu ([email protected]) is Associate Professor of Marketing at The Anderson

School of Management, University of California, 110 Westwood Plaza, Los Angeles, CA 90095, (310)

825-4818.

Author Note

This work is part of the first author’s dissertation.

Acknowledgement

The authors would like to thank Stephen Spiller, Marissa Sharif, Scott Shriver, Eric Johnson,

Robert Zeithammer, Mariam Hambarchyan, Katelyn Wirtz, Ashley Culver, Melanie Argoff, Carly

Lenniger, The BDM Lab group at UCLA Anderson, and seminar participants at Columbia University and Stanford University for their encouraging comments and support throughout the research process. 1

THE EFFECT OF PERCEIVED SIMILARITY ON SEQUENTIAL RISK-TAKING

Abstract

We examine how perceived similarity between sequential risks affects individuals’ risk-taking behavior.

Specifically, in six studies we find that in sequential choice settings individuals exhibit significant positive state dependence in risk-taking: they are more likely to take a risk when it is similar to a previously taken risk than when it is dissimilar. For example, if an individual has previously taken a health/safety risk, that individual is more likely to take a second health/safety risk than a second risk that is in the financial domain. Since similarity between risks is malleable and can be determined by situational and contextual variables, we show that we can change subsequent risk-taking behavior in a predictable manner by manipulating similarity through framing. Finally, we establish that state dependent risk-taking behavior is driven by increased feelings of self-efficacy and self-signaling through the prior risk-taking experience. We further show that the effect of similarity on preferences is not moderated by the outcome received in the prior risk and holds controlling for individual-level and domain-specific heterogeneity. Taken together, our results demonstrate that the similarity structures that exist between risks have a significant effect on risk-taking preferences in dynamic choice settings.

Keywords: risk, domain-specificity, sequential choice, similarity

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INTRODUCTION

Every day individuals encounter risks of different types and must decide whether or not to engage in those risks. What factors affect these decisions? Economic theory proposes that an individual’s risk attitude is generally stable. As a result, risk-taking should not be affected by how a risky prospect is framed or by how it fits among other past or future risks. An alternative approach is a psychological model in which risk-taking is driven by an affect-based assessment of the level of risk associated with a given choice. In this model, both risk perception and preference vary by domain such that the same individual can be risk-seeking in one domain but risk averse in another, ceteris paribus. In other words, the individual who likes to gamble at casinos (a financial risk) is not necessarily the same person who enjoys skydiving (a recreational risk). But can an individual’s risk preferences be further affected by the relationships between sequential risky prospects? For example, is an individual more or less likely to take a given risk dependent on how similar it is to a risk she has taken before?

Broadly, the research at hand is about how current risk-taking intentions relate to prior risky choices. Research on sequential risk-taking has found that risk-taking increases when a choice is part of a combined set of sequential or simultaneous risks, rather than an isolated decision (Benartzi and Thaler

1999; Gneezy and Potters 1997; Haisley, Mostafa, and Loewenstein 2008; Moher and Koehler 2010;

Read, Loewenstein, and Rabin 1999; Redelmeier and Tversky 1992; Thaler et al. 1997; Webb and Shu

2017; Wedell and Böckenholt 1994). However, most of this research has held similarity between the risks constant by focusing on identical risks. What happens if the risks in a decision sequence are not identical but rather represent varying degrees of similarity?

The research presented here brings together several of these features of risk-taking—similarity, domain-specificity, sequential choice—to explore how individuals’ attitudes towards risk are affected by the similarity structures that exist between risks considered in a sequence. For example, imagine the risk of riding a bicycle without a helmet. An individual who remembers taking a similar risk before (such as riding in a car without a seatbelt) will be more likely to ride a bicycle without a helmet than if that same individual instead remembers taking a dissimilar risk (such as investing in a speculative stock).

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Controlling for existing preferences, sequential dynamics, and individual-level and domain-specific heterogeneity, we manipulate similarity to show positive state dependence in risk-taking intentions. We incorporate the findings related to domain-specific risk-taking by examining risks of several different types (financial, recreational, social, health/safety, and ethical) and show that, while sequential aggregation can increase risk-taking likelihood generally, similarity between risks is an important moderator of the effect.

While similarity determines which risks individuals are more inclined to take, it is also a variable that can be directly manipulated. Since similarity is malleable and can be affected by contextual factors, this ultimately means that the decision to take a given risk can be manipulated by changing similarity between that risk and a prior risk. For example, the risk of riding a motorcycle without a helmet can be framed as a recreational risk or as a health/safety risk by highlighting different facets of the activity (e.g., the possible adrenaline rush versus the freedom of not wearing a helmet). If framed as a recreational risk, then our theory predicts that individuals will feel more open to another recreational risk; however, if framed as a health/safety risk, our theory predicts that individuals will feel more open to another health/safety risk instead. Thus, holding the prior risk in a sequence constant, we can change subsequent risk-taking intentions for a current risk by manipulating its similarity with that prior risk.

While we show positive state dependence in risk-taking and how to manipulate it, we are also interested in the process behind this effect. We propose that similarity between a current risk and a prior risk (1) increases feelings of self-efficacy through experience and familiarity for risks of the same type; and (2) signals to the individual that they prefer risks of a given type more than risks of other types. We show that this shift is occurring through risk attitude since risk perception (subjective beliefs about the level of risk inherent in the activity) does not change with differences in similarity. In other words, individuals do not believe that risks that are more similar to a prior risk are less risky than risks that are dissimilar to that prior risk. Taken together, our empirical results suggest that perceived similarity is an important determinant of risk-taking intentions and that these intentions can be affected by factors that change perceived similarity.

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What value is this deeper understanding of risk to marketers? While psychological models of risk-taking account for risk type and have shown that risk attitude is highly dependent on the type of risk being considered, none have accounted for the potential malleability of risk type in affecting future behavior. If risk type can be manipulated through framing, this suggests that an individual’s likelihood of taking a risk (e.g., trying a new product, switching brands, not purchasing a warranty) can be increased or decreased by changing its perceived similarity to a prior risk.

THEORETICAL BACKGROUND

How does an individual decide to take a risk? First, the choice must be assessed to determine how risky it is. This assessment, risk perception, is a subjective judgment that represents the beliefs or feelings individuals have about the level of risk inherent in the prospect under consideration (Blais and E. Weber

2006; Holtgrave and E. Weber 1993; Mellers, Schwartz, and E. Weber 1997; Slovic, Fischoff, and

Lichtenstein 1978; E. Weber and Hsee 1998; E. Weber, Blais, and Betz 2002). Risk perception has been shown to account for much of the variance in risk preferences across individuals (E. Weber and Hsee

1998; E. U. Weber and Milliman 1997; E. Weber, Blais, and Betz 2002). Risk perception by itself is not enough to determine whether a risk will be taken, however, since two individuals who perceive the same level of risk may still make different choices about that risk. Individual differences in preferences for risk- taking beyond risk perception can come from differences in risk attitude. Within the economics literature, risk attitude is a stable facet of behavior determined by an expected-utility function. In this model, individuals are consistently risk-seeking or risk averse across different types of risk. In accordance with this model, risk-taking behavior is not affected by context, framing, or shifting relationships between risks. Importantly, this means that the likelihood of taking a given risk is the same regardless of whether that risk is being considered in isolation or as part of a sequence, or if that risk is from the same domain or a different domain as another risk.

Much research to date has suggested that models of consistent risk attitude are not descriptive of actual choice (Fox and Tversky 1998; Fox and See 2003; Kahneman and Tversky 1979; March and

Shapira 1987; Payne 2005; Rabin and Thaler 2001; Tversky and Kahneman 1992). Within the psychology

5 literature, risk attitude can be affected by psychological factors wherein individual-level risk-taking is not stable across domains or contexts. Accordingly, risk preferences are malleable and affected by inputs such as affect, loss aversion, and judgmental biases (Johnson and Tversky 1983; Kahneman and Lovallo

1993; Loewenstein et al. 2001; Mandel 2003; Mellers, Schwartz, and E. Weber 1997; Rottenstreich and

Hsee 2001; Rottenstreich and Kivetz 2006; Slovic et al. 2005; 2004). In sum, an economic conception of risk-taking assumes stability across risk types, while a psychological model is very much determined by an individual-level response to the type of risk being considered. In this paper, we assume a psychological model for risk-taking intentions given that such an approach is more descriptive. Furthermore, we separate out the effects of our manipulations on risk perception (beliefs) and risk attitude (intentions) within our studies.

One variable that has been shown to have an important effect on risk-taking is the domain or type of risk being considered (Blais and E. Weber 2006; Holtgrave and E. Weber 1993; E. Weber, Blais, and

Betz 2002). Most individuals display different risk attitudes for different domains, such that, for example, an individual can be risk-seeking for recreational risks but risk averse for financial ones. In two papers that directly address the importance of risk domain, Weber et al. (2002) and Blais and Weber (2006) identify five domains (see Table 1) and they measure domain-specificity via a psychometric scale called the DOSPERT (DOmain-SPEcific Risk-Taking). Their findings suggest that individuals will have a consistent risk attitude within a domain but not necessarily across domains. Ultimately, however, these domain differences are driven by differences in perceived risk. Thus, an individual may be likely to take a recreational risk and unlikely to take a financial risk not because they like recreational risks more than financial risks, but because they see recreational risks as being less risky than financial risks. In their studies, risk perception is highly correlated with preferences, and once perceived risk is controlled for, an individual has a consistent risk attitude across all risk domains.

[INSERT TABLE 1 ABOUT HERE]

The domains used by Weber et al. (2002) were established based on a review of the existing literature and confirmed via factor analysis in the course of developing the psychometric scale. These

6 domain labels are not driven by precise definitions predetermined by the researchers, but rather by a similarity in the structure of responses collected from individuals across several studies, with all activities that loaded on the same factor being considered in the same domain. While this is imprecise in that there is no set of guidelines that can be used to identify a risk as being from one domain versus another, it does highlight the possibility that similarity between risks can act as an input into the decision of whether or not to take a risk. The existence of domain-specificity inherently suggests that individuals may establish connections between risky prospects based on the similarity between them, and that this similarity can be consensus-based or individually determined. Therefore, accounting for perceived similarity can help improve our understanding of risk-taking intentions and extend the findings of domain-specific risk- taking to sequential settings.

The relationships between risks, such as perceived similarity, are only relevant when an individual is considering multiple risks at once, such as in a temporal sequence, or when prior risks are either recent or highly salient. It is well-established that considering risky choices that are grouped together leads to different preferences than when considering those choices in isolation (Fox, Ratner, and Lieb 2005;

Haisley, Mostafa, and Loewenstein 2008; Read, Loewenstein, and Rabin 1999; Read et al. 2001;

Redelmeier and Tversky 1992). In particular, combining risky choices together leads to an increase in the willingness to take on risk and a reduced use of heuristic strategies (Moher and Koehler 2010; Read,

Loewenstein, and Rabin 1999; Redelmeier and Tversky 1992; Wedell and Böckenholt 1994). The common explanation for these results is that combining risky choices together into one decision shifts the focus from specific characteristics, such as losses, to global characteristics such as aspiration levels (Read,

Loewenstein, and Rabin 1999). However, prior work on sequential risks has held the similarity between risks constant by using identical risks from the same domain. Questions of how risk domain affects sequential risk-taking have remained largely unaddressed. We attempt to fill this gap by looking at how one facet of the relationship between risks—perceived similarity—can affect risk-taking behavior in a dynamic setting where a risk from one domain may be sequentially followed by a risk in either the same or a different domain. Thus, we consider situations where multiple risks are being considered

7 sequentially, but we manipulate the similarity that exists between the first risk in the sequence and subsequent risks.

Judgments of similarity are ubiquitous and often made spontaneously in an attempt to categorize and organize the world (Henderson and Peterson 1992; Kahn and Wansink 2004; Mervis and Rosch 1981;

Morales et al. 2005; Rosch et al. 1976; Simonson, Nowlis, and Lemon 1993; Thaler 1999; 1985;

Ülkümen, Chakravarti, and Morwitz 2010). A key component of similarity judgments is that they are individually determined and affected by the context and saliency of different features (Henderson and

Peterson 1992; Tversky 1977). Furthermore, similarity is driven by an alignment of structural or relational features between a referent and the targets, much as with an analogical reasoning, rather than simply an alignment of perceptual features or attributes (Gentner and Markman 1997; Markman and Gentner 1993;

Medin, Goldstone, and Gentner 1993). Since similarity is determined by the commonality and differences between two objects, these features are determined by the situation and can shift with the context in which they are evaluated. Building on this, we expect that context and salience will also be important for judging similarity among risks, which has heretofore been unexplored outside the context of portfolio theory (T.

Langer and Fox 2005a; b; T. Langer and M. Weber 2001; Markowitz 1952; Steul 2006). Risk-taking behavior can therefore be manipulated through both the saliency of a specific prior risk, which acts as the referent or point of comparison, and the other risk options available, which provide context. For example, imagine an individual has taken a financial risk and is contemplating several subsequent risks across different domains. A subsequent financial risk will be judged as more similar to the prior (referent) risk than a subsequent social risk. However, this judgment of similarity could change if all the subsequent risks under consideration were also from the financial domain—for example, an investment, an expensive purchase, and a gamble—and thus the features defining similarity to the prior risk would shift with the context as determined by the consideration set.

We will show that to the extent that similarity is susceptible to framing or context, so too are risk- taking intentions. In the studies in this paper, we use risk domain as a proxy for similarity, as risks from one domain are generally more similar to each other than to risks from other domains. Thus, we take the

8 domain-specificity of risk-taking and the domain labels used in the previous literature as established, but we also measure similarity as a manipulation check of domain match. While risk domains are useful in predicting similarity, we are also able to show that similarity can be affected by reframing risks, and this then affects subsequent risk-taking likelihood.

So, what is the process behind positive state dependence for risk-taking intentions? The main contribution of this paper is showing that individuals are more likely to take a risk if it is similar to a salient prior risk than if it is dissimilar. Positive state dependence predicts that as a consequence of experiencing a given type of risk, individuals become more likely to take that type of risk in the future

(Heckman 1981; Keane 1997; Roy, Chintagunta, and Haldar 1996; Seetharaman, Ainslie, and

Chintagunta 1999). While state dependence describes the effect we show, it is not an explanation for why the effect occurs. We predict positive state dependence occurs because the prior risk experience affects both feelings of self-efficacy—individuals feel more familiar and competenti with risks that are similar to a risk they have already taken—and preferences via self-signaling—individuals treat the prior risk as a signal that they like or enjoy (or are simply less averse to) such risks relative to other types of risks.

Our process prediction is built on prior research showing that feelings of self-efficacy can have a significant effect on risk-taking behavior (Fox and Tversky 1995; Fox and Levav 2000; Gneezy, List, and

Wu 2006; Huberman 2001; Krueger and Dickson 1994; E. J. Langer 1975). Individuals’ likelihood of engaging in a risk depends not only on the estimated outcomes, but also on their feelings of competence in the risk-taking context (Heath and Tversky 1991), and these feelings of competence are enhanced through familiarity and experience (Schwarzer 1992). Important to our theory, feelings of self-efficacy can be separate from outcome feedback (i.e., an individual can feel competent at a given risky activity even if they have received a negative outcome when engaging in the activity in the past). This is because, in a stochastic setting where outcomes are determined non-contingently to performance, these outcomes will not affect beliefs about personal competence (Bandura 1977). Stated differently, actions that have a probability distribution over potential outcomes do not provide stable reinforcement (positive or negative) for learning and adjustment of self-efficacy expectations. For this reason, self-efficacy expectations can

9 be separate from outcome expectancies. Another reason why feelings of self-efficacy can remain unaffected by outcomes is that self-efficacy can affect how an individual encodes the receipt of outcomes: individuals who consider themselves more competent with a given type of risk can take credit for positive outcomes, but can blame bad outcomes on unexpected circumstances or chance events that could not be predicted (Heath and Tversky 1991; March and Shapira 1987). Thus, we predict that individuals will feel greater self-efficacy for risks that are more similar to a salient prior risk due to increased feelings of familiarity and experience, and that these feelings will not be moderated by outcome type received in the prior risk.

Self-efficacy is just one part of the proposed process behind positive state dependence in risk- taking intentions. We further propose that the prior risk-taking experience acts as a signal to the individual that they are less averse to risks of that type over other types. Research on self-signaling and self- perception has shown that individuals often infer their preferences from their own behavior (Bem 1972).

Thus, individuals infer their attitudes toward a given risk from the prior risk-taking experience (Bodner and Prelec 2002; Sirgy 1982; Yang and Urminsky 2015). This means that the salient prior risk-taking experience influences current intentions by changing the individual’s beliefs about their preferences— they believe they are more likely to take a similar risk because they believe they prefer those risks over other types of risks—even if those past actions do not actually reflect underlying preferences (Bodner and

Prelec 2002).

An alternative process prediction is one driven by a desire for diversification or compensation: individuals may want to diversify or balance their risk-taking behavior and thus would be less likely to take a subsequent risk when it is similar to a prior risk. Work on portfolio theory, balancing, and compensation/licensing all support this prediction (Blanken, van de Ven, and Zeelenberg 2015; Dhar and

Simonson 1999; Fox, Ratner, and Lieb 2005; Khan and Dhar 2006; T. Langer and Fox 2005a; Markowitz

1991; Read and Loewenstein 1995). Under this approach, individuals would be less likely to take a similar risk (or possibly any risk) because they want to compensate for risks already taken or because they want to diversify their risk across the available options. Diversification or balancing would also predict

10 that risk-taking behavior would change with outcome feedback; if an individual received a negative or positive outcome in a prior risk, that outcome would directly affect their willingness to take another similar risk (e.g., the gambler’s fallacy, the hot hand effect, or the house money effect) (Ayton and

Fischer 2004; Croson and Sundali 2005; Demaree et al. 2012; Sundali and Croson 2006; Thaler and

Johnson 1990; Xu and Harvey 2014).ii

It is this difference in sensitivity to outcomes that helps distinguish our proposed process of self- efficacy and self-signaling, where prior outcomes do not moderate risk attitude, from a compensation/licensing process, where individuals’ risk preferences are sensitive to prior outcomes

(Barberis, Huang, and Santos 2001; Croson and Sundali 2005; Faro and Rottenstreich 2007; Hertwig et al.

2004; Sundali and Croson 2006; Thaler and Johnson 1990). For example, in their paper on the house money effect, Thaler and Johnson (1990) find that risk preferences change as a result of prior outcomes

(e.g., individuals become increasingly risk-seeking following a gain and risk averse following a loss). We do not think that our predictions contradict this large body of research, but, rather, that similarity between the risks may be an important moderator of such outcome effects. In the prior research, the sequential risks that were used were highly similar (often identical gambles). We believe that when the risks are identical, outcomes will have a spillover effect on sequential risky choices. However, when the risks are similar but not identical (as in our studies), outcomes will be segregated from the subsequent choices.

Similarity can thus be thought of as a decision rule about whether outcomes are integrated or segregated as proposed in Thaler and Johnson’s quasi-hedonic editing hypothesis (Thaler 1985; Thaler and Johnson

1990). When risks are identical, outcomes will be integrated and, as a result, an outcome received in a prior risk will affect the decision for the next risk. When risks are less than identical, but still similar, outcomes will not be integrated.

The two empirical predictions we have just reviewed, positive state dependence and diversification/compensation, thus result in opposing effects for sequential risk-taking. They also have different predictions for the effect of outcomes. Our proposed process—based on self-efficacy and self- signaling—is not dependent on outcome, as discussed above; however, a process of compensation or

11 balancing could show a significant effect of outcome as individuals are more or less likely to take a risk when it is similar to one for which they received a negative or positive outcome because of compensatory beliefs such as the hot hand or gambler’s fallacy. We will demonstrate that positive state dependence is not moderated by outcome type received in the prior risk and, in so doing, provide further evidence for a process of self-efficacy and self-signaling rather than compensation or balancing.

The paper proceeds as follows. In Study 1, we show our main effect: individuals are more likely to take a risk when it is more similar to a prior risk than to when it is less similar to a prior risk (positive state dependence). In Study 2, we show that we can manipulate risk-taking preferences by manipulating perceived similarity with a prior risk. In Studies 3A and 3B, we demonstrate both components of the mechanism underlying our effect. In Study 4, we introduce explicit outcomes for the prior risk and show that outcome type does not moderate the effect of similarity. Finally, in Study 5, we use an incentive compatible set-up for both the prior and subsequent risks to show that the effect holds over real prior and subsequent risks. Taken together, our results demonstrate that individuals show positive state dependence in risk-taking intentions, and that this dependence is driven by self-efficacy and self-signaling.

STUDY 1: THE ROLE OF SIMILARITY IN SEQUENTIAL RISK-TAKING

In Study 1, we establish positive state dependence in sequential risk-taking likelihood, such that individuals state they are more likely to take a risk if it is similar to a prior risk than if it is dissimilar. We use the five risk domains identified by Weber et al. (2002) to manipulate similarity under the assumption that risks from the same domain will be seen as more similar to each other than to risks from different domains.iii We then show that participants are more likely to take a second risk when it is from the same domain as a previously taken risk than when it is from a different domain. The positive effect of similarity holds controlling for individual-level differences in perceived risk and differences across risk domains.

Method

Participants (N = 701, MAge = 36.3 years, 49.9% female) were recruited through Amazon’s

Mechanical Turk (“mTurk”).iv Participants were randomly assigned to one of five prior risk domains:

Financial, Recreational, Social, Ethical, Health/Safety. Prior risk domain assignment was used to establish

12 a referent risk to which subsequent risks would be compared. Participants were given a definition and examples of the risk domain they were assigned to (e.g., “health/safety risks are defined as any risks that involve your physical health or put you in a potentially unsafe situation”). They were then asked to write about their most recent experience taking a risk in the assigned prior risk domain. All participants were then shown five risks (one from each domain) and were asked to state their likelihood of taking each of those risks on a scale from 1 (“Not at all Likely”) to 7 (“Extremely Likely”) (Blais and E. Weber 2006).

The order of the subsequent risks was randomized for each participant. Thus, all participants saw the same five subsequent risks, with one of these risks matching the prior risk domain they wrote about and four of these risks not matching the domain of the prior risk; the match between prior and subsequent risk domain provides our manipulation of similarity. We predict that participants will be more likely to take a subsequent risk when it is from the same domain as their prior risk (match) than when it is from a different domain (no-match). If similarity does not matter, then there should be no effect of prior risk domain match on risk-taking likelihood.

Following the likelihood questions, all participants provided risk perception ratings for each risk using a scale from 1 (“Not at all Risky”) to 7 (“Extremely Risky”) (Blais and E. Weber 2006; E. Weber,

Blais, and Betz 2002). We measure risk perception because, according to a psychological model of risk- taking, this measure has been shown to account for much of the variance in risk-taking preferences across individuals and domains (Blais and E. Weber 2006; Holtgrave and E. Weber 1993; March and Shapira

1987; E. Weber and Hsee 1998; E. U. Weber and Milliman 1997; E. Weber, Blais, and Betz 2002).

Measuring risk perception also allows us to determine whether individuals change their risk intentions because perceived risk is lower for similar risks than dissimilar risks (i.e., taking a risk in one domain makes other risks in the same domain seem less risky as a result). If it is not affected, we can control for individual heterogeneity in perceived risk to ensure this is not driving the effect of similarity.

Finally, as a manipulation check, all participants were asked to rate similarity between the prior risk and each of the subsequent risks on a scale from zero (“Completely Different”) to 100 (“No

Difference – Identical”). This is a manipulation check in that we should find that risks from the domain

13 that matches the prior risk are rated as more similar than risks that are from domains that do not match the prior risk. The complete materials for Study 1 can be found in Web Appendix B.

Results

Methodology. First, a note on the statistical analyses for all of our studies. Unless otherwise stated, we control for individual-level effects, prior risk domain fixed effects, and subsequent risk domain fixed effects in all of our analyses with DVs that have multiple measures per participant (e.g., risk perception, similarity, risk-taking likelihood). For example, when we evaluate risk-taking likelihood, we will often run a random effects regression, which includes an individual-specific random effect for each participant.

Whether we use a random effects or fixed effects specification will depend on which model has been determined to be more consistent and efficient via a Hausman specification test (Hausman 1978).v For ease of exposition, we will not report the complete regressions in the text, but all of the regressions from each study are reported in Web Appendix A. Table 2 summarizes the main regression results for our main

DV, risk-taking likelihood, for all studies.

Risk perception. Risk perception is not significantly different depending on whether the subsequent risk matches the prior risk (bMatch = 0.08, SE = 0.06, z = 1.39, p = .165). This means that, on average, participants see a risk as equally risky whether it is similar or dissimilar to a previously taken risk. This rules out an alternative hypothesis that risk preferences are changing because similar risks are perceived as less risky, so we exclude this as a possible process variable and instead control for perceived risk in our analyses to account for individual-level heterogeneity. In all of the analyses in this study and later studies, perceived risk is controlled for unless otherwise noted.

Manipulation check. Perceived similarity is significantly different by domain match, confirming our manipulation of similarity via risk domain (bMatch = 31.96, SE = 1.00, z = 31.94, p < .001; fitted values: Match = 51.93 vs. No-Match = 19.97). Participants see subsequent risks from the same domain as the prior risk as significantly more similar to the prior risk than those from different domains. In this study and all later studies, we will run separate regressions using a domain match indicator and the perceived similarity measure as alternate measures of our main IV, and report results from both approaches.vi

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Risk preferences. Participants are significantly more likely to take a subsequent risk if its domain matches the prior risk than if its domain does not match the prior risk (b = 0.21, SE = 0.07, z =

3.19, p = .001; fitted values: Match = 3.79, No-Match = 3.58) (see Table 2). This suggests that participants show positive state dependence in risk-taking separate from heterogeneity due to subjective risk beliefs, individual-specific effects, and domain-specific effects (prior and subsequent). If similarity is instead included in the regression as an alternate measure of our manipulation, its coefficient is positive and significant, mirroring the effect for match (b = 0.01, SE = 0.001, z = 5.67, p < .001). This suggests that the greater the perceived similarity between a subsequent risk and a prior risk, the more likely an individual is to take the later risk. The first model, using match, is a more conservative test of our hypothesis, while the second model is more general since it holds regardless of whether a participant sees the matching domain risk as the most similar to the prior risk they were assigned to write about.

[INSERT TABLE 2 ABOUT HERE]

Overall, the results of Study 1 suggest that individuals show positive state dependence in risk- taking intentions. Specifically, individuals state they are more likely to take a risk if it is more similar to a risk they have already taken (versus dissimilar to a risk they have already taken). In Study 2 we extend these findings by directly manipulating similarity to show how this affects risk-taking preferences.

STUDY 2: CHANGING SIMILARITY CHANGES RISK-TAKING

In Study 1 we showed that similarity between risks significantly affects risk-taking intentions. If a risk is seen as similar to a salient prior risk, an individual states they are more likely to take that risk than if it is seen as dissimilar. This opens up the interesting possibility that changing perceived similarity between two risks can change risk-taking behavior, even holding the actual prior risk constant. In other words, if a given prior risk is framed as being from one domain, then individuals should be more likely to take a subsequent risk from that domain. But what if that same prior risk is framed as being from a different domain? Our theory suggests that risk-taking preferences will shift along with this change. For example, consider a prior risk such as riding a motorcycle without a helmet. This risk can be framed as either a health/safety risk or a recreational risk. According to our theory, framing this activity as a

15 health/safety risk should increase risk-taking for subsequent health/safety risks; whereas framing it as a recreational risk should increase risk-taking for subsequent recreational risks instead. In Study 2 we directly test the effects of manipulating perceived similarity.

Method

Participants were 150 individuals recruited online through mTurk (MAge = 29.4 years, 31.3% female). Participants were randomly assigned to one of two prior risk conditions: Riding a Motorcycle or

Dangerous Job. Each of these prior risks can be framed as being from one of two domains. Riding a motorcycle without a helmet can be framed as either a health/safety or recreational risk, while working at a dangerous job can be framed as either a health/safety or financial risk. Similarity was thus manipulated through a randomly-assigned risk frame.

To manipulate frame, participants were asked to write about different implications related to the assigned prior risk. For example, participants in the Riding a Motorcycle condition were told, “[p]lease imagine the following: This weekend you rode on a motorcycle without a helmet. Your friend let you borrow his motorcycle but he didn’t have a helmet that you could use. You took the motorcycle out on a highway and some side streets.” In the Health/Safety [Recreational] framing condition, participants were asked to write about the health/safety [recreational] implications of this activity: “Many people would consider there to be several health and/or safety [recreational] implications related to the decision to ride a motorcycle without a helmet. Health/safety implications include potential physical harm, mental trauma, and pleasant or unpleasant health outcomes [Recreational implications include physical overexertion, extreme emotional feelings, and memorable experiences.] We would like you to list the main health and/or safety [recreational] implications that you can think of that are associated with this particular action.” Participants in the Dangerous Job condition were asked to write about either the Financial or

Health/Safety implications of taking a dangerous part-time job (“This weekend you decided to start working a second job part-time to make a little extra money. The job pays pretty well and has good hours, but it is at a packing facility so the employer warned you that there is the possibility of getting injured on the job”).

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After completing the framing-related writing task, participants were asked to rate their likelihood of taking each of two subsequent risks. These risks varied by prior risk condition and were designed so that one risk matched the assigned risk frame (frame-match), while the other did not (frame no-match). Accordingly, participants in the Riding a Motorcycle condition were asked to rate their likelihood of taking both a recreational and a health/safety risk, while participants in the Dangerous Job condition were asked to rate their likelihood of taking both a financial and a health/safety risk.

Participants responded using the same likelihood scale from Study 1. Consistent with the positive matching (similarity) effect we found in Study 1, we predict that participants will be more likely to take the subsequent risk that matches the manipulated framing of the prior risk. In addition to risk-taking likelihood, all participants provided risk perception and similarity ratings using the same scales as in

Study 1. The complete materials for Study 2 can be found in Web Appendix B.

Results and Discussion

Manipulation check. Similarity is not significantly different depending on frame-match status

(bFrame-Match = 3.63, SE = 3.31, z = 1.10, p = .272; fitted values: Frame-Match = 45.67, Frame No-Match =

42.04). This difference is not as large as we expected. This is likely due to two factors: (1) we asked the similarity question at the end of the survey (not directly after the manipulation), and (2) similarity between the two subsequent risks and the prior risk is necessarily close since the prior risk is, by design, more or less similar to two separate risk domains. For both of these reasons, we do not believe that the lack of a significant difference in perceived similarity limits our findings related to the framing manipulation. We also ran a post-test, described more in Appendices A and B, which is suggestive of significant differences in similarity between frames when perceived similarity is collected directly after the manipulation.vii

Risk perception. Risk perception is not significantly affected by the framing manipulation (bFrame-

Match = -0.11, SE = 0.15, t = -0.73, p = .466). As before, we control for it in the following analyses, unless otherwise noted. These regression results are provided in more detail in Web Appendix A.

17

Risk preferences. For the results of Study 2 to replicate our main finding from Study 1, we should see greater risk-taking likelihood for subsequent risks that match the domain framing of the prior risk. As Table 2 shows, participants are significantly more likely to take a subsequent risk if it is in the domain that matches the framing manipulation than if it is in the domain that does not match the framing manipulation for the prior risk (bFrame-Match = 0.36, SE = 0.17, z = 2.12, p = .034; fitted values: Frame-

Match = 2.96, Frame No-Match = 2.60).

Even though the manipulation’s effect on similarity was not as great as anticipated, we still wanted to test whether similarity affected risk preference. When using perceived similarity in the regression instead of the Frame-Match indicator, perceived similarity has a marginally significant positive effect on risk-taking likelihood (bSimilarity = 0.01, SE = 0.003, z = 1.96, p = .050), suggesting that perceived similarity marginally statistically increases risk-taking more generally. This replicates our findings for perceived similarity from Study 1.

In Study 2 we were able to shift risk preferences through framing by manipulating the same prior risk to seem more or less similar to a particular subsequent risk. The significant positive effect of similarity is especially interesting because it suggests one prior risk-taking situation can be framed in multiple ways to change subsequent intentions. Importantly, manipulating similarity between a previously taken risk and future risks can change risk-taking likelihood without the need to change or reference different past behavior. The results of Study 2 highlight how the malleability of similarity can be used to change—not just predict—risk-taking intentions in sequential settings.

While Study 2 shows that manipulating perceived similarity via framing changes risk preferences in a predictable manner, we still do not have much insight into why perceived similarity increases risk intentions. We have confirmed through Studies 1 and 2 that greater similarity between a prior risk and a subsequent risk increases risk-taking likelihood for the subsequent risk. This supports a hypothesis of positive state dependence, rather than one of diversification or compensation. What aspects of state dependence are changing individuals’ preferences for subsequent risks, however, remains unresolved. We examine two process variables—self-efficacy and self-signaling—separately in Studies 3A and 3B.

18

STUDY 3A: SELF-EFFICACY MODERATES THE EFFECT OF SIMILARITY

In Study 1 we found that individuals are more likely to take a subsequent risk when it is from the same domain as a prior risk than when it is from a different domain (positive state dependence), and that greater similarity between a subsequent risk and a prior risk leads to increased risk intentions for the subsequent risk. In Study 2 we directly manipulated similarity to show that changing similarity via framing also changes risk-taking likelihood. However, Studies 1 and 2 do not provide evidence as to why similarity may have this effect. In Study 3A we explore one component of our proposed mechanism: increased feelings of self-efficacy.viii We postulate that, through the prior risk, an individual gains experience and familiarity with risks of that type which then lead directly to feelings of competenceix and self-efficacy (Bandura 1977; Schwarzer 1992). We propose that these feelings then lead to greater risk- taking for similar risks, since greater competence and self-efficacy generally lead to increased risk-taking

(Heath and Tversky 1991; Kahneman and Lovallo 1993; Krueger and Dickson 1994; E. J. Langer 1975).

If true, then manipulating experience and familiarity should change feelings of self-efficacy within a risk domain, which should, in turn, moderate the effect of similarity.

Method

Participants were 983 individuals recruited through mTurk (MAge = 35.5 years, 57.9% female).

Participants were randomly assigned to one of the five prior risk domains used in Study 1. To manipulate experience and familiarity with a given risk type, we randomly assigned participants to one of two experience conditions. In the High Experience condition, participants were asked to list eight times they took a risk in their assigned domain; in the Low Experience condition, we had participants list only one time they took a risk in their assigned domain. Participants who think of more times they engaged in a specific type of risk should feel that they have more experience and familiarity with that risk type relative to other types. These increased feelings of experience and familiarity (self-efficacy) should then moderate the effect of similarity for subsequent risk-taking. Accordingly, we expect to see participants in the High

Experience condition state they are more likely to take a matching risk (i.e., a risk from the same domain as the risk type in the manipulation) than participants in the Low Experience condition. If self-efficacy is

19 not driving the effect of similarity, then there should be no difference in risk-taking between the High and Low Experience conditions for matching risks.

After the experience manipulation, we asked participants three manipulation check questions specific to the assigned domain. These questions asked participants to rate how much experience they had for [assigned domain] risks (experience); how familiar they found [assigned domain] risks (familiarity); and how much they agreed with the statement, “I am the type of person who likes taking [assigned domain] risks” (self-perception). If our manipulation of experience and familiarity is successful, then we expect to find ratings on the measures of familiarity and experience to be significantly higher in the High

Experience condition relative to the Low Experience condition. For self-perception, we would expect greater agreement in the High Experience condition as well, since more experience with a risk type should also act as a stronger signal to the self of preference for similar such risks.

Following the manipulation check questions, we asked participants across all conditions to rate their likelihood of taking five subsequent risks—one from each of the five risk domains. We used the same likelihood scale as in Studies 1 and 2. All participants saw the same five target risks with order randomized and counterbalanced, with one risk matching the domain of the risk(s) that they were assigned to list in the experience manipulation. This matching domain risk serves as our manipulation of similarity.

After the likelihood questions, all participants were asked to rate the level of perceived risk and similarity with the prior risk(s) for each subsequent risk they saw.

Finally, we asked participants to rate familiarity and experience for each of the five subsequent risks to test whether these proposed process measures were higher for subsequent matching domain risks versus subsequent non-matching risks. The scales used for these questions were the same as those used in the manipulation checks. The complete materials used in Study 3A are available in Web Appendix B.

Results and Discussion

Manipulation checks. As expected, participants in the High Experience conditions took significantly longer to complete the writing task and wrote about significantly more experiences than participants in the Low Experience conditions (recall time: MHigh = 205.78 seconds vs. MLow = 51.57

20

" seconds, t(789.66) = -17.95, p < .001; recall count: MHigh = 7.70 vs. MLow = 1, ! (7) = 966.98, p <

.001).x The number of prior risks recalled in the High Experience condition did not vary by risk domain assignment (!"(28) = 27.75, p = .478).

We took two measures to check our manipulation of self-efficacy for the assigned risk domain: experience and familiarity. We also measured self-perception to show that this variable is similarly affected by the manipulation. The experience and familiarity measures were highly significantly correlated (r = 0.60, p < .001), so we combined them into a single self-efficacy index. This self-efficacy index was significantly higher in the High Experience condition than the Low Experience condition (bHigh

= 0.39, SE = 0.09, t = 4.43, p < .001; fitted values: High = 4.74, Low = 4.35), implying that our manipulation of self-efficacy was successful. We also found that the self-perception measure was higher in the High Experience condition (bHigh = 0.24, SE = 0.10, t = 2.30, p = .022; fitted values: High = 3.62,

Low = 3.38). Aligned with our hypotheses, more instances of prior risk-taking send a greater signal to the individual that they are the type of person to take risks similar to the prior risk domain.

We measured perceived similarity to ensure that participants saw subsequent risks that were from the same domain as the prior risk(s) as more similar than subsequent risks from a different domain.

Confirming our manipulation, participants saw subsequent risks from the matching domain as significantly more similar to the prior risk type than subsequent risks whose domains did not match (bMatch

= 45.08, SE = 1.05, z = 43.02, p < .001; fitted values: Match = 72.49, No-Match = 27.42). Similarity between matching and non-matching risks is not significantly different by experience condition (bMatch x

High = 2.51, SE = 2.10, z = 1.19, p = .234). Thus, our experience manipulation significantly affects feelings of self-efficacy and self-perception but does not affect perceived similarity structures between the risks.

Risk perception. Risk perception is not significantly affected by either the similarity manipulation

(bMatch = 0.06, SE = 0.05, t = 1.08, p = .279) or the experience manipulation (bHigh = -0.02, SE = 0.05, z =

-0.43, p = .671). There is, however, a significant interaction effect between match and Experience condition (bMatch x High = 0.08, SE = 0.03, z = 2.92, p = .003). A simple effects analysis shows that participants in the High Experience condition see matching domain subsequent risks as significantly more

21 risky than non-matching domain subsequent risks (bMatch = 0.22, SE = 0.08, z = 2.89, p = .004; fitted values: Match = 3.87, No-Match = 3.64). In the Low Experience condition, participants do not see matching subsequent risks as more or less risky than non-matching subsequent risks (bMatch = -0.08, SE =

0.07, z = -1.17, p = .243). Again, this suggests that any significant positive interaction between similarity and experience is not the result of reducing the perceived risk associated with similar subsequent risks relative to dissimilar subsequent risks. As before, we control for risk perception unless otherwise noted.

Risk preferences. We find a significant positive interaction between matching domain and the

High Experience condition (bMatch x High Experience = 0.10, SE = 0.03, z = 3.70, p < .001) (both variables contrast-coded). We visualize this interaction in Figure 1, and the results are reported in Table 2. A simple effects analysis shows this effect is being driven primarily by the High Experience condition: in the High

Experience condition, domain match significantly increases risk-taking likelihood (fitted values: HighMatch

= 4.39 vs. HighNo-Match = 3.90, Delta-Method SE = 0.08, z = 6.19, p < .001). However, in the Low

Experience condition, the effect of domain match is attenuated (LowMatch = 4.07 vs. LowNo-Match = 3.98,

Delta-Method SE = 0.07, z = 1.29, p = .196). These results suggest that self-efficacy moderates the effect of similarity such that greater feelings of self-efficacy increase the effect of similarity (lead to greater risk- taking intentions for risks when they are similar to a prior risk), while lower feelings of self-efficacy attenuate it.

Process. A process of self-efficacy is further confirmed if we look at the measures of familiarity and experience for the subsequent risks. These two measurements are highly correlated (r = 0.70, p <

.001), so we combined them into a self-efficacy index. A random effects regression shows there is a significant interaction effect on this measure (bMatch x High = 0.08, SE = 0.02, z = 3.16, p = .002). Thus, self- efficacy is higher for more similar subsequent risks when individuals have more experience with a given risk type. There is also a significant simple effect of match (bMatch = 0.12, SE = 0.03, z = 4.80, p < .001), suggesting that similarity is a necessary part of the story: increasing feelings of experience/familiarity for one risk type leads to increased feelings of self-efficacy only for other risks that are of the same type, and not for risks that are of a different type.

22

[INSERT FIGURE 1 ABOUT HERE]

To test for mediation, we ran a bootstrapped (50,000 iterations) moderated mediation model

(Model 8) with risk-taking likelihood as the DV, the match indicator as the IV (dummy-coded), the measured self-efficacy index as the mediator, the High Experience condition as the moderator (dummy- coded), and with risk perception, participant fixed effects, subsequent risk domain, and prior risk domain as covariates (Hayes 2013). This analysis shows complementary mediation for the High Experience condition: the indirect effect of the self-efficacy index is positive and significant (a x b = 0.15, SE = 0.04, z = 3.74, p < .001, bias-corrected CI: [0.07, 0.23]) and the direct effect is positive and significant (c’ =

0.38, SE = 0.08, t = 4.71, p < .001). However, for the Low Experience condition there is no-effect non- mediation (a x b = 0.05, SE = 0.04, z = 1.43, p = .154, bias-corrected CI: [-0.02, 0.12]; c’ = 0.05, SE =

0.07, t = 0.65, p = .515). This analysis implies that more risk-taking in one domain increases feelings of self-efficacy for risks that are from the same domain (similar risks), which then increases risk-taking likelihood for those risks.

The results from Study 3A provide a partial answer for why similarity increases risk-taking.

Specifically, more experience with a given risk type increases feelings of self-efficacy, which in turn, increase risk preferences for subsequent risks similar to that risk type. We demonstrate this by manipulating self-efficacy directly and showing that it moderates the effect of similarity. We also use measured self-efficacy for the subsequent risks to show that feelings of self-efficacy partially mediate the effect of similarity in the High Experience condition, but not in the Low Experience condition. While we show that our manipulation of experience affects self-perception, such that more experience with a risk signals a preference for a given type of risk over other risk types, we do not directly manipulate this variable. In Study 3B, we examine the effect of manipulating self-perception directly.

STUDY 3B: SELF-SIGNALING MODERATES THE EFFECT OF SIMILARITY

Study 3A shows that more experience with a given risk type increases feelings of self-efficacy, which in turns increases risk intentions for subsequent similar risks. While this is part of the process behind positive state dependence, we also propose another mechanism: self-signaling. Specifically, taking

23 a prior risk acts as a signal to the individual that they are more willing to take risks of that type relative to other types. In order to further explore this process, we directly manipulate the signal sent in the prior risk-taking experience and show that self-signaling also moderates the effect of similarity.

Method

Participants were 922 individuals recruited online through mTurk (MAge = 35.8 years, 56.8% female). Participants were randomly assigned to one of the five prior risk domain conditions and then further randomly assigned to one of two Self-Signaling conditions (Positive, Negative) in a 5 x 2 between-subjects design. In the Self-Signal: Positive condition, participants were asked to write about a time they had the opportunity to take a risk in the assigned prior risk domain and they decided to take it; in the Self-Signal: Negative condition, participants were asked to write about a time they had the opportunity to take a risk in the assigned prior risk domain and they decided not to take it. For example, a participant in the Health/Safety, Self-Signal: Negative condition was given a definition and examples of health/safety risks and then saw the following: “Now, think back to a time when you did not take a health/safety risk. In other words, think about a time you had the opportunity to take a health/safety risk but you chose not to. Try to think of the most recent experience possible. Please describe, in about a paragraph, what the health/safety risk was and why you chose not to take this health/safety risk.”

The Self-Signal: Positive condition was identical to the manipulations used in Study 1. The Self-

Signal: Negative condition was designed to send a signal of risk aversion to participants by making salient to them a time they chose not to take a risk in a given domain. We predict that participants in the Self-

Signal: Positive conditions will show positive state dependence (i.e., more likely to take matching than non-matching risks), whereas participants in the Self-Perception: Negative conditions will not show state dependence (i.e., they will not be more or less likely to take matching than non-matching risks).xi

Following the manipulations, participants were asked two manipulation check questions for the prior risk. One question, self-perception, was the same as in Study 3A (“I am the type of person who likes taking [assigned prior risk domain] risks”); the second question asked participants to rate how much they agreed with the statement, “I enjoy taking [assigned prior risk domain] risks” (enjoyment). We added this

24 second question to show that the act of engaging in the prior risk-taking experience increases liking for risks of the same type (but not other types). All participants were then asked to rate their likelihood of taking five subsequent risks across domains (as in previous studies). Finally, participants were asked to rate risk perception and similarity as in the previous studies. The complete materials for Study 3B can be found in Web Appendix B.

Results and Discussion

Manipulation checks. First, we evaluated whether our manipulation of self-signaling was successful. Enjoyment and self-perception were highly significantly correlated (r = 0.90, p < .001), so we combined the two measures into a single self-signaling index. Participants in the Self-Signal: Positive condition scored significantly higher on this index than participants in the Self-Signal: Negative condition

(bPositive = 0.32, SE = 0.10, t = 3.27, p = .001; fitted values: Positive = 3.31 vs. Negative = 2.99). Thus, participants who wrote about a time they took a risk perceived their actions to be more of a signal of

(positive) preference than participants who wrote about a time they did not take a risk in a given domain.

Similarity is significantly higher for subsequent risks whose domain matched the prior risk than for subsequent risks whose domain did not match (bMatch = 29.54, SE = 0.97, z = 30.45, p < .001; fitted values: Match = 52.39 vs. No-Match = 22.85), confirming our manipulation of similarity via domain match between the prior and subsequent risks. There is no significant effect of Self-Signaling condition on similarity (p = .619).

Risk perception. Risk perception is marginally significantly higher for matching domain risks than non-matching domain risks (bMatch = 0.09, SE = 0.05, z = 1.72, p = .086), suggesting that participants see same domain risks as marginally significantly riskier than risks that are from a different domain. Risk perception is also marginally significantly higher in the Self-Signal: Positive (vs. Negative) condition when controlling for match (bPositive = 0.10, SE = 0.06, z = 1.68, p = .094). There is not a significant interaction effect between match and self-signal condition on risk perception (p = .439). These weak effects suggest that the process behind the effect of similarity is not due to a reduction in perceived risk

25 for risks that are more similar to the prior risk. We control for risk perception in the analyses that follow, unless otherwise noted.

Risk preferences. We find a significant positive interaction between match and the Self-Signal:

Positive condition (both contrast-coded), suggesting that the effect of similarity is moderated by the risk preference signal sent to the individual from the prior risk-taking experience (bMatch x Positive = 0.06, SE =

0.02, z = 2.25, p = .025). This interaction is visualized in Figure 2. A simple effects analysis shows that in the Self-Signal: Positive condition, participants are significantly more likely to take a subsequent risk whose domain matches the prior risk than a subsequent risk whose domain does not match (bMatch = 0.21,

Delta-Method SE = 0.07, z = 2.94, p = .003; fitted values: Match = 3.97 vs. No-Match = 3.76). However, participants in the Self-Signal: Negative condition are equally likely to take matching and non-matching risks (bMatch = -0.02, Delta-Method SE = 0.07, z = -0.22, p = .826). As hypothesized, individuals are more likely to take risks that are more similar to a salient prior risk because the prior risk acts as a signal to the individual that they are more open to risks of that type. When individuals do not see the prior risk as a signal of preference, even though the risk domain is quite salient, they are not more likely to take matching domain risks.xii

[INSERT FIGURE 2 ABOUT HERE]

Together, Studies 3A and 3B have directly investigated the reasons for positive state dependence in risk-taking intentions. Specifically, Study 3A showed that feelings of self-efficacy moderate the effect of similarity such that when individuals have more experience with a given risk type (higher self-efficacy) they state they are more likely to take a subsequent similar risk than a less similar one. This is only part of the story, however, as the prior risk-taking experience also acts as a signal to an individual that she is less averse to risks that are similar to a previously taken risk compared to risks that are dissimilar to that risk.

In Study 3B, we show that changing the valence of the signal from the prior risk-taking experience also moderates the effect. Specifically, individuals are more likely to take subsequent similar risks only when the previous choice acts as a signal of positive risk preference. The effect of similarity does not hold when the previous risk-taking choice does not act as such a signal. The lack of a negative effect in this condition

26 may be due to general risk aversion, status quo effects, or an omission bias, in which a failure to act is judged as less informative or severe than an action taken (Ritov and Baron 1992).

One potential shortcoming of our findings so far is that they have not specifically addressed the role of outcomes. It’s possible that outcomes moderate the effect of similarity as well, such that the effect only holds when an individual receives a positive (or negative) outcome in the prior risk. We predict that since the process behind the effect is self-efficacy and self-signaling, both of which come from the act of taking the risk and not outcome expectancies, these feelings and signals exist regardless of outcome type received. Thus, outcome type should not moderate the effect. To explore this, we manipulate outcome feedback directly in Study 4.

STUDY 4: THE ROLE OF OUTCOME FEEDBACK

In the previous studies we asked participants to either write about or imagine prior risk-taking experiences. Since these experiences are from the past, outcomes were often entailed. However, we remained largely unconcerned with the outcome type received in our treatment of the effect of similarity, and we did not explicitly ask participants to think about outcomes. The reason for this is two-fold: (1) theoretically, the increased self-efficacy and the positive self-signal underlying positive state dependence should not be moderated by outcome type, and (2) there are many situations in which an individual encounters a new risk after a prior risk-taking experience but before an outcome has been received (e.g., buying a lottery ticket). If outcome type moderates the effect of similarity, this could suggest compensation/balancing rather than state dependence. For instance, individuals might be less likely to take a risk similar to one for which they received a positive outcome because of compensatory beliefs such as the gambler’s fallacy. Since there are many risk-taking instances where outcomes are immediately received or resolved, we broaden our risk situations in Study 4 to explicitly manipulate outcomes.

Method

Participants were 961 individuals (MAge = 35.8 years, 52.8% female) who were recruited online via mTurk. Participants were randomly assigned to one of the five prior risk domains and further randomly assigned to one of two outcome types (Positive, Negative) in a 5 x 2 between-subjects design. Participants

27 were first given a general definition of the assigned risk domain and then asked to write about a time they took a risk of that type. Participants in the Positive outcome conditions were asked to describe a time they took the assigned risk type and something good happened, while participants in the Negative outcome conditions were asked to describe a time they took the assigned risk type and something bad happened.

Following the writing task, all participants were asked to rate their likelihood of taking each of five subsequent risks—one from each domain—using the same likelihood scale as in the previous studies.

Following the likelihood questions, we asked all participants to rate each subsequent risk on the following dimensions: perceived risk, familiarity, experience, self-perception, and similarity. These measures were the same as those used in Study 3A. These measures were included to ensure our manipulation of similarity via risk domain was successful and to replicate our earlier process findings regarding self- efficacy and self-signaling. The complete materials used in Study 4 are included in Web Appendix B.

Results & Discussion

Manipulation check. To ensure that our manipulation of similarity was successful, we looked at whether perceived similarity ratings were higher for subsequent risks that matched the assigned prior risk domain than for subsequent risks that did not match. Results confirm that perceived similarity was rated as significantly higher for matching risks than for non-matching risks (bMatch = 25.51, SE = 0.87, z =

29.47, p < .001; fitted values: Match = 44.62, No-Match = 19.11). Similarity for matching and non- matching risks is not affected by outcome condition (bOutcome = -0.45, SE = 1.11, z = -0.41, p = .684).

Risk perception. Risk perception is significantly higher for matching domain risks compared to non-matching domain risks (bMatch = 0.10, SE = 0.05, z = 2.00, p = .045; fitted values: Match = 4.69, No-

Match = 4.59). This suggests that participants see subsequent risks whose domain matched the prior risk as significantly more risky than subsequent risks whose domain did not match. Risk perception is not significantly affected by the Outcome manipulation (bOutcome = -0.06, SE = 0.06, z = -1.13, p = .260), nor is there is no significant interaction between match and outcome type on risk perception (p = .634). We control for risk perception in the following analyses unless otherwise noted.

28

Risk preferences. Next, we turn to our main DV of interest: risk intentions as measured by risk- taking likelihood. We find there is no significant interaction between match and the Outcome: Positive condition (both contrast-coded) (bMatch x Positive = 0.01, SE = 0.03, z = 0.37, p = .711). Thus, outcome type does not moderate the effect of similarity. Removing the non-significant interaction from the regression, and instead including a dummy-coded indicator for the Positive Outcome condition and match, finds no significant main effect of outcome type (bPositive = 0.07, SE = 0.06, z = 1.23, p = .219) (see Web Appendix

A). We find a marginally significant main effect for match when controlling for outcome (bMatch = 0.11,

SE = 0.06, z = 1.92, p = .055). If we use the similarity measure instead of the match indicator, this effect is positive and significant (bSimilar = 0.01, SE = 0.001, z = 7.35, p < .001). This suggests that receipt of a positive or negative outcome in a prior risk-taking experience does not have a significant effect on risk- taking likelihood more generally. While this may be surprising in light of prior literature, which has found increased risk-taking after a gain and decreased risk-taking after a loss (Thaler and Johnson 1990), a crucial difference is that the risks in our study are not identical to the risks for which the outcome was received, as in prior studies.

Process. Since we measured feelings of familiarity and experience (self-efficacy) and self- perception for each subsequent risk, we can test for mediation of the matching effect jointly by self- efficacy and self-perception. Feelings of experience and familiarity were highly correlated (r = 0.57, p <

.001) and combined into a single self-efficacy index. Both self-efficacy and self-perception are significantly different by match (self-efficacy: bMatch = 0.25, SE = 0.05, z = 5.26, p < .001; fitted values:

Match = 3.70, No-Match = 3.46; self-perception: bMatch = 0.23, SE = 0.05, z = 4.64, p < .001; fitted values: Match = 2.98, No-Match = 2.75).

To test for mediation, we ran Hayes’ (2013) bootstrapped (50,000 iterations) multiple mediation model (Model 6) with risk-taking likelihood as the dependent variable, the dummy-coded match indicator as the independent variable, self-efficacy index and self-perception as the mediators, risk perception and the dummy-coded indicator for the Positive Outcome condition as covariates, and fixed effects for participant, prior risk domain, and subsequent risk domain. This analysis finds indirect-only mediation by

29 both self-efficacy (a x b = 0.03, SE = 0.01, z = 2.68, p = .007, 95% bias-corrected CI: [0.01, 0.05]) and self-perception (a x b = 0.10, SE = 0.02, z = 4.24, p < .001, 95% bias-corrected CI: [0.06, 0.15]). The direct effect of matching domain on risk-taking likelihood is no longer significant (c’ = -0.05, SE = 0.05, t

= -0.88, p = .378). This replicates our finding that risk intentions are higher for subsequent similar risks because the prior risk-taking experience both increases feelings of self-efficacy for similar risks and signals to the individual that they prefer risks that are more similar to the prior risk.

Overall, Study 4 found that the effect of similarity is not moderated by the outcome type received in the prior risk (positive vs. negative). This bolsters a process of self-efficacy and self-signaling, as neither of these are contingent on the outcome received. While Study 4 shows a replication of the main effect of similarity and helps us further understand the mechanism behind the effect, like most of our studies thus far it is not incentive compatible. Further, all of our studies rely on a remembered or hypothetical prior risk. It is possible that the effect of similarity only holds when the experience of the prior risk is removed in time from the subsequent risk. It’s also possible that the null effect of outcome found in Study 4 is the result of the way we manipulate the prior risk domain; since participants are remembering experiences, the emotions caused by outcomes may be dulled by time and memory. While we believe the null effect for outcome is the result of the process through which the effect of similarity works, we have not empirically confirmed this with real (versus remembered) outcomes.

In order to rule out the possibility that our effect is the result of hypothetical choice or remembered prior risks, we designed Study 5 to be fully incentive compatible. In this study, we have participants experience a first (prior) risk in real time, receive an actual positive or negative outcome, and then use an incentive-compatible procedure to elicit preferences for subsequent risks.

STUDY 5: THE EFFECT OF SIMILARITY IN AN INCENTIVE COMPATIBLE SETTING

The use of recall tasks or hypothetical scenarios for the prior risks in our studies thus far limits our ability to generalize our findings in that it relies on remembered outcomes and emotions, which may not have the same effect as outcomes and emotions experienced in the moment. While we show that the effect holds when the prior risk is remembered, we cannot say definitively that the same effect will hold when

30 the prior risk is experienced contiguously to the subsequent risk. Does the prior risk experience need to be removed in time in order for the effect of similarity to hold? We directly address this question in Study

5.

Method

Participants were 379 individuals recruited through mTurk (MAge = 37.4 years, 52.5% female).

Participants were told they were going to have to engage in an actual risk as part of the study. They were further told that we could not tell them what this specific risk was beforehand, but that the risk was deemed “minimal” by an Independent Review Board. All participants who agreed to participate were given a $1 bonus and told that it may have to be used in the risks they encountered. Participants who did not agree to participate were paid the baseline compensation but were not given the bonus.

Participants were randomly assigned to one of two prior risk domain conditions (Social,

Financial). Participants had to take an actual risk in the domain to which they were assigned. Participants in both conditions had the opportunity to drop out of the survey after seeing the actual risk, forfeiting their bonus payment but still being paid the baseline compensation. In the Social condition, participants were told they would have to reveal a personal secret and that there was a 50% probability this secret would be posted online (anonymously) based on the draw of a random number between 1 and 100. To ensure participants understood the prior risk and the outcome possibilities, they had to correctly respond to three multiple choice questions about the task (e.g., “If your secret is posted online, who can see your secret?”).

Participants were only allowed to proceed once all the responses to these questions were correct.

Following the comprehension questions, all participants shared their secret. Following this, participants were shown their randomly drawn number. Participants were then told their outcome (positive: their secret was not posted; negative: their secret was posted online) based on the number they received.xiii

Participants in the Financial condition were told they had to play “the financial game.” In this game, they had to pay $0.50 (out of their $1 bonus) to play a gamble that had a 50% chance of winning $1

(the $0.50 entrance fee plus an additional $0.50) and a 50% chance of losing the $0.50 they paid to play.

They were told their outcome would be determined by a randomly drawn number between 1 and 100. As

31 in the Social condition, participants were asked three comprehension questions about the financial game that they had to answer correctly before proceeding. Following the comprehension questions, participants saw their randomly drawn number. They were then informed of their outcome (positive: won an additional $1 for a total bonus of $1.50; negative: lost $0.50 for a total remaining bonus of $0.50).

Participants in both conditions were then asked to rate their likelihood of taking two subsequent risks: one financial and one social. The financial risk was playing a gamble that had a 2/3 chance of winning $0.50 and a 1/3 chance of losing $0.50. The social risk was posting about their personal beliefs on their social media (e.g., Facebook, twitter, Instagram). Participants responded to the two subsequent risks on a six-point likelihood scale ranging from 1 (“Extremely Unlikely”) to 6 (“Extremely Likely”), without an indifference midpoint. In an incentive compatible elicitation procedure for the subsequent risks, participants were told that they may have to take one of the subsequent risks depending on their responses, so they should respond as if they would be actually confronted with the described risks. In particular, they were told that, based on a random draw at the end of the survey, if they said they were likely to take the risk, they would indeed be shown the actual risk.

After the likelihood questions, all participants responded to six questions about each of the subsequent risks: perceived risk, familiarity, experience, self-perception, enjoyment, and similarity, using the same scales as in Study 3B. After these questions, participants were shown the number drawn in the incentive compatible lottery procedure. They were reminded of their actual response for the risk the number corresponded to. If a participant said they were unlikely to take the risk, they were taken to the end of the survey. If a participant said they were likely to take the risk, they were shown the actual risk and asked whether they wanted to take it. Participants who said “Yes” actually engaged in the risk. For the social risk, participants had to take a screenshot of an actual post on their social media. For the financial risk, participants took the gamble and actually won or lost an additional $0.50. Gains were paid as part of the bonus payment (which ranged from $0 to $2); losses were subtracted from any remaining bonus payment. The complete materials for Study 5 can be found in Web Appendix B.

32

Results & Discussion

Since there are participants who dropped out of the survey (6.9% of those recruited), the results do suffer from selection bias: only participants who were willing to take the prior risks stayed in the survey, so our results do not necessarily generalize to individuals who are extremely risk averse (either in general or to social/financial risks specifically). In the analyses that follow, we will make statements about the treatment effect (prior risk domain) that imply causation, but this caveat related to selection bias and endogeneity (though relatively small) must be acknowledged. For more details on selection bias and sensitivity analyses related to selection bias, please see Web Appendix A.

Manipulation check. Similarity is rated as significantly higher between the prior risk and the subsequent risk if their domains were the same (bMatch = 42.04, SE = 1.73, t = 24.23, p < .001; fitted values: Match = 60.80, No-Match = 18.78), suggesting our manipulation of similarity via risk domain was successful. Similarity was not significantly affected by the outcome received in the prior risk (p = .84).

Risk perception. Risk perception is not significantly different depending on match status (whether the subsequent risk domain matched that of the prior risk) (bMatch = 0.001, SE = 0.10, z = 0.01, p = .989).

Risk perception is also not significantly affected by whether the participant received a positive or negative outcome in the prior risk (bPrior Win = -0.07, SE = 0.11, z = -0.60, p = .551). There is also no significant interaction effect between match and outcome on risk perception (p = .972). We control for risk perception in the following analyses unless otherwise noted.

Risk preferences. We find a replication of our main effect: participants show significant positive state dependence such that they are significantly more likely to take a subsequent risk when its domain matches the domain of the prior risk than when its domain does not match (bMatch = 0.54, SE = 0.09, z =

5.74, p < .001; fitted values: Match = 4.35, No-Match = 3.81; see Table 2). This effect holds for both domains (social and financial) and is visualized in Figure 3. If we use the similarity measure instead of the match indicator, these results are replicated. Overall, the results suggest that the effect of similarity between sequential risks is not dependent on remembered risks and holds even when the risks are

33 temporally contiguous and outcomes are experienced directly before a judgment is made about the subsequent risks.

Since approximately half of the participants in each condition received a positive outcome, and half received a negative outcome, we can test whether we replicate our outcome findings from Study 4.

To do this we ran the same regression described above, but with an interaction between match and positive outcome received (both contrast-coded). The interaction term is not significant (p = .508) (see

Table 2). This implies that the effect of similarity for subsequent risks is not moderated by the outcome received in the prior risk and participants are equally likely to take a similar subsequent risk whether they received a negative or a positive outcome in the prior risk. If we remove the interaction term from the regression and instead include a dummy-coded indicator for positive outcome received as a covariate, we also see that there is no main effect of outcome type (p = .382) (details in Web Appendix A). This replicates our findings from Study 4.

[INSERT FIGURE 3 ABOUT HERE]

Process. For both of the subsequent risks we measured familiarity and experience (self-efficacy) and self-perception and enjoyment (self-signaling). Familiarity and experience are highly significantly correlated (r = 0.43, p < .001), so we combined them into a single self-efficacy index. This index is not significantly higher for matching risks as it was in our previous studies (p = .913). This result was surprising but may be due to the simplistic nature of the subsequent financial risk (the gamble) or how common the subsequent social risk was (posting on social media). Self-perception and enjoyment were also highly significantly correlated (r = 0.88, p < .001), so we combined the two measures into a single self-signaling index. This index was significantly higher for matching risks than non-matching risks

(bMatch = 0.32, SE = 0.10, z = 3.27, p = .001; fitted values: Match = 3.88, No-Match = 3.56). This suggests that taking the prior risk acted as a signal of preference for subsequent risks similar to the prior risk, but not for subsequent risks that were less similar.

To test for mediation, we ran Hayes’ (2013) bootstrapped (50,000 iterations) multiple mediation model (Model 6) with risk-taking likelihood as the dependent variable, the dummy-coded match indicator

34 as the independent variable, the self-efficacy and self-signaling indices as the mediators, risk perception and the dummy-coded positive outcome received indicator as covariates, and with fixed effects for participant, prior risk domain, and subsequent risk domain. This analysis finds partial, complementary mediation by self-signaling (a x b = 0.13, SE = 0.05, z = 2.81, p = .005, 95% bias-corrected CI: [0.04,

0.23]), but not by self-efficacy (a x b = 0.001, SE = 0.01, z = 0.09, p = .935, 95% bias-corrected CI: [-

0.02, 0.02]). The direct effect of matching domain on risk-taking likelihood remains significant (c’ = 0.41,

SE = 0.09, t = 4.66, p < .001). This confirms that risk-taking is higher for subsequent risks similar to a prior risk in part because the prior risk-taking experience signals to the individual that they prefer these risks. While we did not confirm our other mechanism, self-efficacy, this could be related to the nature of the risks we chose for the subsequent risks, which were necessarily limited by the incentive compatible set-up.

Overall, Study 5 extends our previous findings for the effect of similarity to a fully incentive- compatible design. Study 5 confirms that there is positive state dependence in risk-taking even when the prior risk is experienced directly before the subsequent risk. After taking a prior risk, participants state they have a higher intention to take risks that are similar to that prior risk (versus dissimilar). Our process findings suggest that this is because the prior risk-taking experience acts as a signal to the individual that they are less averse to risks similar to the prior risk versus risks dissimilar to the prior risk. This state dependence is especially interesting given that participants were not recalling a past experience they chose to participate in as in the earlier studies. We were not able to confirm the role of self-efficacy in this study, but we believe this is a limitation of the risks we had to use to achieve incentive compatibility in an online setting, rather than a failure of our theory. We also continued to find a null effect of the prior risk’s outcome on the effect of similarity. Participants who received a negative outcome were equally as likely to take subsequent similar risks as participants who received a positive outcome. We can now rule out the possibility that the lack of moderation by outcome type in Study 4 was because the memory of an outcome was not as powerful as experiencing the outcome directly before the subsequent risk decision.

35

GENERAL DISCUSSION

In six studies we have explored positive state dependence in sequential risk-taking. We find that risk-taking is significantly affected by similarity between sequential risks. Specifically, individuals are significantly more likely to continue taking risks of the same type versus risks of different types. For example, an individual is more likely to take a financial risk if they just took a financial risk than if they just took a social risk. We also show that this positive state dependence is not the result of individual-level or domain-specific heterogeneity.

We were further able to identify that this state dependence is the result of both self-signaling and self-efficacy. In regard to the former, the prior risk-taking experience signals to the individual that they like risks similar to the prior risk more than risks that are dissimilar. As a result, individuals are more likely to choose subsequent risks that are similar to the prior risk. This means that the prior risk-taking experience changes preferences, which we further confirm by showing that subjective beliefs about the level of risk inherent in the subsequent risks are not causing the state dependence. In regard to the second process—self-efficacy—we find that the prior risk-taking experience increases feelings of personal competence or self-efficacy (via experience and familiarity with the risk), which in turn increases risk- taking for risks similar to the prior risk. This happens because the prior risk-taking experience makes individuals feel that they have more experience with one type of risk (versus other types), and as a result they are more willing to take those risks types. These feelings of self-efficacy are not directly tied to outcomes since they are contingent on feelings of experience and familiarity, which can be produced regardless of outcome type. Prior research has also found that greater feelings of competence with risks can lead individuals to misattribute the cause of outcomes (e.g., that good outcomes are due to talent or skill and bad outcomes are due to chance/bad luck), which also implies that individuals can feel greater self-efficacy regardless of outcome type (Heath and Tversky 1991; March and Shapira 1987).

Implications

The exploration of the effect of perceived similarity on risk-taking behavior has important implications for consumer behavior. By better understanding how consumers approach and perceive risks,

36 we can more accurately predict important behaviors such as trying new or innovative products, mitigating product risk, and purchase timing. This work contributes to the field of consumer risk-taking by showing how individuals’ behavior is affected by perceived similarity between sequential risks.

Specifically, we have shown how similarity affects the proclivity to engage in future risks, which can help marketers determine promotion strategies, new product adoption, and product switching. For example, if companies are targeting consumers with a promotion for an activity that entails risk (e.g., trying a new product or buying a product that is tied to risk-taking), our research suggests that they should target these same consumers with additional promotions or purchase opportunities that are similar to the original promotion.

Perhaps the most interesting implication of the research at hand is that risk exposure is not fungible—people are not equally willing to take on different types of risk, even controlling for individual heterogeneity. Prior risks and the relationship between those risks and future risks are important inputs into an individual’s decision calculus. However, similarity is but one contextual factor that affects sequential risk-taking. A further exploration of the fluid or situational factors that affect sequential risk- taking could help us better understand the complexity of risk-taking behavior.

Limitations and Future Directions

In Studies 4 and 5 we found, as predicted, that outcomes did not moderate the effect of similarity.

Individuals were not more or less likely to take a risk similar to one they already took dependent on the outcome they received in the prior risk. As stated before, we believe that similarity between sequential risks may be an important moderator of the effect of prior outcomes, such that when the risks are identical, outcomes will have a spillover effect on sequential risky choices. However, when the risks are similar but not identical (as in our set-up), outcomes will be segregated from the subsequent choices.

Our data from Study 5 are also suggestive of this. If we conduct a floodlight analysis of risk-taking likelihood with an interaction between outcome received and similarity (instead of the match indicator), we find that prior outcomes have a significant effect when similarity is at its highest values. Specifically, the Johnson-Neyman point for similarity is 74.43. When similarity is greater than 74.43 (only 17.2% of

37 observations are), then a prior positive outcome has a significant negative effect on risk-taking, such that participants are less likely to take a (highly) similar risk when they have received a positive outcome in a prior risk (e.g., they become increasingly loss averse). For example, when similarity is rated at 100

(its greatest level), a prior positive outcome reduces risk-taking by -0.45 units on a six-point scale (SE =

0.22, t = -2.03, p = 0.043). Investigating whether similarity moderates the effect of prior outcomes on probabilistic inferences, such as the gambler’s fallacy, is an interesting avenue for future research.

Another caveat related to the outcomes we use is that they are necessarily limited in their degree of severity. Since we rely mostly on recalled outcomes and experiences, the outcomes that participants remember are unlikely to be extremely severe. Given that highly extreme outcomes are less likely for more common risks, the likelihood that a participant in our study experienced an extreme outcome is necessarily low. If the outcome is perceived to be very severe or traumatic (e.g., an individual incurs severe emotional trauma from a bicycle accident and refuses to ever ride a bicycle again), individuals could be conditioned to avoid the risks. We do not believe that the effect of similarity would override these extremely strong emotional or conditioned responses to risk. In fact, in such instances, the effect of similarity may be negative such that individuals would be less likely to take risks that are more similar to a traumatic risk they engaged in before. While we believe that the outcomes and experiences used in this paper are representative of the vast majority of risks experienced by individuals, we are not able to rule out the possibility that more extreme experiences would not be subject to the same finding.

It is also worth noting that the prior risks we rely on are either remembered or experienced directly before participants are asked to make choices over subsequent risks. This means that the saliency or recency of a prior risk is a necessary component of our effect. Furthermore, the prior risk has to be considered in context with the current risk (the choices have to be bracketed together) (Read,

Loewenstein, and Rabin 1999). Since our paradigm forces the integration of past risks with current risks, we would not expect our effect to hold if individuals are not thinking of a prior risk-taking experience when considering current risks. This also means that our effect is only externally valid to the extent that individuals will consider a temporally contiguous risk to be related to future sequential risks. This may

38 hold as risks occur closer in time, but individuals might not spontaneously contextualize risks as part of the same choice history if not forced to do so by a situational cue or constraint. Consideration of how these effects apply to risk situations with clear beginning and ending points (such as a well-defined portfolio of risks), rather than simply sequential risks, is another area for future work.

In all of our studies, we used domain match between prior and subsequent risks as a proxy for similarity. While we measured similarity in all of our studies and verified our manipulation, it should be noted that the effect is always stronger when using measured similarity instead of the match indicator.

Thus, measured similarity is a better metric for the similarity structures that exist between risks, since similarity is ultimately an individually determined measure. While domain match is a good way to manipulate similarity at an aggregate level, knowing what perceived similarity is at the individual-level will be more informative and helpful in predicting our effect. Our effect, at the individual-level, is very much dependent on being able to identify what risks will be viewed as most similar to each other a priori.

In our model of risk-taking preferences, we constrained the effect of similarity to be homogenous across individuals and domains, such that every individual and domain sees the same increase in risk- taking preferences (though the starting point, or intercept, is different depending on the individual and the domain being considered). While our intent in this paper was to show the effect of similarity in sequential risk-taking more broadly (across individuals and risk types), it is a more restrictive model. It may be an interesting endeavor for future research to incorporate additional heterogeneity in the model (i.e., by allowing each prior and subsequent risk domain combination to have its own effect). Relatedly, we also used a subset of risks for the subsequent risks in our studies. While we attempted to vary the risks we used across studies, we by no means were able to capture the entire universe of subsequent risk possibilities.

For this reason, it is possible that certain subsequent risks will not show a positive effect of similarity .

We cannot rule out this possibility within the results of our paper.

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43 portfolio with a well-defined beginning and end. The risk tasks in our studies are typically sequential risks independently considered rather than risks that are part of a well-defined portfolio. iii A pilot study testing the degree of overlap between judgments of similarity and previously established risk domains confirms that individuals see varying degrees of similarity between risks and that similarity largely coincides with previously established risk domains (see Web Appendix A for details). Risks from the same domain are seen as significantly more similar to each other than to risks from different domains

(using a continuous scale from 0 (“Completely Different”) to 100 (“Identical – No Difference”): MSame =

40.52 vs. MDifferent = 18.60, t(142.98) = 8.70, p < .001). These results imply that we can use risk domain as a way to manipulate similarity, since subsequent risks will be seen as more similar to a prior risk if they are from the same domain. We also confirm this by measuring perceived similarity in all our studies. iv Details about each study such as the number of participants recruited and any exclusions are reported in

Web Appendix A by study. v A Hausman specification test (also called the Durbin-Wu-Hausman test), compares the consistency of an estimator to an alternative estimator that is known to be consistent but not necessarily more efficient. In our studies, this results in a comparison between a random effects specification (more efficient, but not necessarily consistent) and a fixed effects specification (consistent but not necessarily efficient). We only use random effects when this has been shown to be more consistent than a fixed effects regression, otherwise we default to a fixed effects specification. vi Note that since perceived similarity is a single-item manipulation check of our main IV, it is not appropriate to use as a mediator in our models (Zhao, Lynch, and Chen 2010; Tate 2015). Instead we treat it as an alternate measure of our manipulation (risk domain) and report results using both approaches. vii We also ran a post-test (N = 393 mTurk participants, MAge = 35.2 years, 48.9% female) where participants completed the same writing manipulation as described in Study 2, but only responded to the perceived similarity question (no risk likelihood or perception questions). Perceived similarity was significantly higher for subsequent risks whose domain matched the prior risk framing manipulation than

44

for subsequent risks whose domain did not match the manipulation (MFrame -Match = 43.17 vs. MFrame No-

Match = 37.10, t(783.84) = 2.71, p = .007). We believe this post-test lends further support to the success of our framing manipulation and suggests that if we had asked about perceived similarity directly after the manipulation, we would have seen a more significant difference in this measure between frame-match and frame no-match subsequent risks. Additional details can be found in Web Appendices A and B. viii Before conducting Study 3A or 3B, we ran an exploratory process study to confirm our proposed process measures and to rule out other possible mechanisms (e.g., changing outcome expectancies). The details of this exploratory study are provided in Web Appendices A and B. ix Competence with regards to a risky activity can include increased illusions of control and skill, but can also include a sense of greater coping ability. The latter means that through experience and familiarity with a risk type, individuals feel that they have better coping skills and are thus more prepared to handle a risky situation than they would have been without such experience (Bandura 1977). x Previous research on ease of recall (Schwarz and Vaughn 2002) suggests that participants in the High

Experience conditions might feel less experience and familiarity than participants in the Low Experience conditions if they have difficulty recalling eight instances of having taken a certain type of risk and then infer this difficulty is because they do not take many risks in the assigned domain. However, 92.2% of participants in the High Experience conditions successfully recalled eight prior risks in the assigned domain, suggesting that most participants did not have difficulty coming up with eight prior risk examples. xi We do not a priori predict a negative effect of similarity (significantly lower risk-taking likelihood for subsequent risks whose domain match the prior risk) in the Self-Signal: Negative conditions. This is because we believe individuals are generally risk averse and either there is a floor effect on risk preferences or the negative self-signal is the status quo. Prior research also supports this supposition:

Weber et al. (2002) specifically looked at individual-level perceived-risk attitudes (risk attitudes once risk perception was controlled for) and found that perceived-risk seeking was very rare, even though they

45 targeted respondents who appeared risk-seeking based only on a likelihood measure. Very few of their respondents were willing to engage in activities that they considered to be risky, with the vast majority of respondents (85.3%) being perceived-risk averse for all or most of the five domains, 12.1% of respondents being perceived-risk neutral, and no respondents being perceived-risk seeking for all domains. Prior research on self-perception also suggests that “making an initial attitude more salient should diminish the degree to which self-attributions can be altered by observation of overt behavior”

(Bem 1972). xii These results also rule out an alternative explanation for the matching effect: priming of the risk domain. In the self-signaling manipulation, priming of the risk domain is held constant between the two conditions, only the action taken in regard to the domain changes. xiii For the Social prior risk, we did not actually post any secrets online. The IRB asked us to use deception rather than actually post any secrets in order to keep the risk minimal. All participants were told about this deception in a debriefing form at the end of the survey. Participants had to view the debriefing form before they could be compensated for the survey.

46

TABLES

Table 1 Established Risk Domain Descriptions and Examples

Domain General Description Examples

Activities that involve some probability of Casino gambling, betting on a sporting Financial monetary gain or loss event, investing in a speculative stock

Activities in which there is a probability Riding a bicycle without a helmet, eating of physical harm or adverse health effects, Health/Safety foods past their expiration dates, engaging but also entail a probability of greater in unprotected sex enjoyment

Activities that are primarily taken for fun or amusement but which include a Bungee-jumping, sky-diving, white-water Recreational potential negative outcome (e.g., physical rafting injury or death)

Cheating on an exam, taking credit for Activities that involve unethical or Ethical work that is not your own, stealing a small immoral actions item from a store

Moving to a new city alone, disagreeing Activities that affect an individual’s social Social with an authority figure, admitting your standing opinions differ from those of your friends

Note: Examples come from Weber et al. (2002) and Blais and Weber (2006).

47 Table 2 Regression Results for Risk Intentions, All Studies

DV: Risk (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Likelihood Study 1 Study 1 Study 2 Study 2 Study 3A Study 3B Study 4 Study 5 Study 5 Study 5 0.21** 0.36* 0.15*** 0.05+ 0.05+ 0.54*** 0.27*** Match (0.07) (0.17) (0.03) (0.02) (0.03) (0.09) (0.05) 0.01*** 0.01+ 0.01*** Similarity (0.001) (0.003) (0.002) 0.06+ Experience (0.03) Match x 0.10*** Experience (0.03) Similarity x Experience 0.11*** Self-Signal (0.03) Match x 0.06* Self-Signal (0.02) 0.04 -0.05 Outcome (0.03) (0.05) Match x 0.01 -0.03 Outcome (0.03) (0.05) Perceived -0.58*** -0.59*** -0.72*** -0.78*** -0.44*** -0.51*** -0.53*** -0.36*** -0.37*** -0.37*** Risk (0.02) (0.02) (0.07) (0.07) (0.01) (0.01) (0.02) (0.04) (0.04) (0.04) 5.82*** 5.79*** 6.25*** 6.48*** 4.14*** 4.14*** 5.03*** 5.36*** 5.31*** 5.63*** Constant (0.12) (0.12) (0.44) (0.43) (0.11) (0.11) (0.11) (0.14) (0.15) (0.13) 3,505 300 4,915 4,610 4,805 758 N (701 groups) (150 groups) (983 groups) (922 groups) (961 groups) (379 groups) R2 0.35 0.35 0.32 0.31 0.49 0.52 0.38 0.22 0.21 0.22 + p < .10, * p < .05, ** p < .01, *** p < .001

Notes: (1) Match is an indicator variable, 1 = domain of subsequent risk matches prior risk, 0 = domain of subsequent risk does not match prior risk. (2) Similarity is a 0-100 continuous scale measure, higher values indicate greater similarity. (3) Where interactions are included, variables are contrast-coded. (4) Standard errors are reported in parentheses below coefficients. (5) All regressions include individual-level random effects and risk domain fixed effects. See Web Appendix A for more details. 48

FIGURES

Figure 1 Risk-Taking Likelihood by Subsequent Risk Domain, Study 3A 5.0 High Experience Low Experience 4.39 4.5 4.07 3.90 3.98 4.0

3.5

3.0 Taking Likelihood Taking - 2.5 Risk

2.0

1.5

1.0 Match No-Match Matching Status

Notes: (1) Values shown are fitted values from the regression described in the main text and Web Appendix A. (2) Match indicates that the domain of the subsequent risk matched the domain of the prior risk(s). No-Match indicates the domain of the subsequent risk did not match the domain of the prior risk. High Experience and Low Experience indicate the randomly assigned Experience condition. (3) Standard error bars are for Delta-method standard errors from a marginal effects analysis of the regression.

49 Figure 2 Risk-Taking Likelihood by Match and Self-Signaling Condition, Study 3B

4.5 Match No-Match 3.97 4.0 3.76 3.64 3.66

3.5

3.0

2.5 Taking Likelihood Taking -

Risk 2.0

1.5

1.0 Positive Negative Self-Signaling Condition

Notes: (1) Values are fitted values from the regression described in the main text and Web Appendix A. (2) Match indicates that the domain of the subsequent risk matched the domain of the prior risk, No- Match indicates that the domain of the subsequent risk did not match the domain of the prior risk. (3) Error bars are Delta-method standard errors from a marginal effects analysis of the regression. 50 Figure 3 Risk-Taking Likelihood for Each Subsequent Risk, Study 5

5.5 Prior Risk Domain Social Prior Risk Domain Financial 5.0 4.85

4.5 4.16

4.0 3.84 3.45 3.5 Taking Likelihood Taking

- 3.0

Risk 2.5

2.0

1.5

1.0 Social Financial Subsequent Risk Domain

Notes: (1) Values shown are raw likelihood values (not fitted values from the regression). (2) Subsequent risks are considered matching when the domain of the subsequent risk matches the domain of the prior risk. In the chart above, the matching likelihood for the Social subsequent risk is shown in orange (Prior Risk Domain Social). The matching likelihood for the Financial subsequent risk is shown in blue (Prior Risk Domain Financial). (3) Standard errors are from a t-test comparing risk-taking likelihood for each subsequent risk domain by prior risk domain (Social vs. Financial).