Are high-ability individuals really more tolerant of risk? A test of the relationship between risk aversion and cognitive ability

Accepted Manuscript

Are High-Ability Individuals Really More Tolerant of Risk? A Test of the Relationship Between Risk Aversion and Cognitive Ability Matthew P. Taylor PII: DOI: Reference:

S2214-8043(16)30054-4 10.1016/j.socec.2016.06.001 JBEE 215

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Journal of Behavioral and Experimental Economics

Received date: Revised date: Accepted date:

28 May 2015 18 May 2016 3 June 2016

Please cite this article as: Matthew P. Taylor, Are High-Ability Individuals Really More Tolerant of Risk? A Test of the Relationship Between Risk Aversion and Cognitive Ability, Journal of Behavioral and Experimental Economics (2016), doi: 10.1016/j.socec.2016.06.001

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Highlights • I use an experiment to test whether the inverse relationship between cognitive ability and risk aversion is an artifact of a frequently-used experimental design. • I find that the relationship between cognitive ability and risk aversion is not robust to the use of real monetary incentives and choices with options that require equal effort to be evaluated.

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• The availability of a certain option reduces the likelihood of errors by the lowestability subjects. • High-ability subjects appear to misrepresent their preferences so that they appear more risk tolerant when they make hypothetical choices and the safer option is certain.

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• I find some evidence to suggest that subjects with knowledge of expected value tend to be more risk tolerant.

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Matthew P. Taylor†

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June 15, 2016

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Are High-Ability Individuals Really More Tolerant of Risk? A Test of the Relationship Between Risk Aversion and Cognitive Ability

Abstract

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A body of literature based primarily on experiments suggests that cognitive ability and risk aversion are inversely related. In contrast, studies using observational data often find that lower ability, or lower income, is positively related to risky behaviors. One potential explanation for the conflicting conclusions is that experimental studies tend to measure risk attitudes by presenting subjects with choices between an option with a certain outcome and an option characterized by risk, which requires computation and, hence, cognitive effort. Additionally, these studies have primarily relied on the use of hypothetical choices. I use an experiment to test whether this frequently-used method of measuring risk preferences is biased toward finding results that indicate that individuals with lower cognitive ability are more risk averse than individuals with higher cognitive ability. I find that the inverse relationship between risk aversion and cognitive ability is not robust and that high-ability subjects may misrepresent their preferences when they face hypothetical choices. Also, similar to earlier studies, I find that low-ability subjects are more likely to make errors and show that the availability of a certain option reduces errors for the lowest-ability subjects.

Keywords: decision making, risk, cognitive ability, hypothetical bias

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JEL classification: C91, D80, D83 —————————————

† University

of Montana, Department of Economics, 32 Campus Drive #5472 , Missoula, MT, 59812-5472, (phone: 406-243-4122, email: [email protected]). This research is partially funded by a University of Montana Small Grant. I am grateful for the comments and suggestions that I received from session participants at the 2014 Western Economic Association International Conference and the 2015 Economics Science Association Conference, as well two anonymous referees. I also thank Peregrine Frissell for assisting with the experiment. All errors are my own.

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Introduction

Risk preferences are fundamental to economic decision making because many of the decisions individuals make are characterized by uncertainty. Empirical studies have demonstrated that risk preferences are related to a broad range of economic decisions and outcomes, such as

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wealth, job mobility, and educational attainment (Guiso and Paiella, 2008; Allen et al., 2005; Harrison et al., 2007). Moreover, these choices are often complex, and this complexity may cause low- and high-ability individuals to approach these choices in systematically different ways, which could lead to significant differences in economic outcomes (Cawley et al., 2001). For instance, Heckman et al. (2006) demonstrate that higher cognitive ability is associated

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with higher wages.

Several studies using laboratory experiments have sought to assess whether risk preferences and cognitive ability are related, and, as a whole, these studies find that individuals with higher cognitive ability tend to be more risk tolerant (Frederick, 2005; Campitelli and

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Labollita, 2010; Cokely and Kelley, 2009; Oechssler et al., 2009; Dohmen et al., 2010; Benjamin et al., 2013). Not all experimental studies have come to the same conclusion, however, Branas-

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Garza et al. (2008) do not find a relationship between risk attitudes and math skills, and Taylor (2013) finds that it is only present when the choices are hypothetical.

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Studies that find a relationship between cognitive ability and risk aversion have two things in common that suggest the relationship requires additional scrutiny.1 First, with

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only one exception, they use an elicitation method that asks subjects to choose between a certain option and a risky option.2 For example, a typical choice asks a subject to choose

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between $1,000 for sure or a 75% chance of $4,000 (Frederick, 2005). This format is likely to bias the results toward finding a relationship between cognitive ability and risk aversion because individuals with lower cognitive ability may choose the safe option because it requires 1

Publication bias may be another potential explanation for why the published studies tend to indicate that there is a relationship between cognitive ability and risk aversion. 2 Benjamin et al. (2013) is the exception here. They ask Chilean students to choose between two gambles in one trial of their experiment, but they use small stakes (i.e., no more than $1.60).

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less cognitive effort, not because they are truly more risk averse. For example, a reluctance to exert the cognitive effort to deal with options characterized by risk may explain why individuals with lower levels of educational attainment in a representative sample of Italian households were more likely to refuse to provide an answer or to say that they would pay zero euros to play a gamble with a 50 percent chance of 5,000 euros and a 50 percent chance

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of zero euros (Guiso and Paiella, 2008), suggesting an extraordinary level of risk aversion. Second, these studies use either hypothetical choices or small expected payoffs. Only Dohmen et al. (2010) uses relatively large payoffs (potentially 300 euros), but the expected payoffs were reduced dramatically because only one in seven subjects was actually paid based

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on their decisions. Taylor (2013) suggests the use of hypothetical choices is problematic because the relationship between cognitive ability and risk aversion may depend upon the use of hypothetical choices. In particular, the results show that cognitive ability is unrelated to risk aversion when the choices are real, but it is inversely related to risk aversion when the

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choices are hypothetical because individuals with higher cognitive ability indicate that they are significantly more risk tolerant when they face hypothetical choices.

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This elevated level of risk aversion demonstrated by low-ability subjects in experiments does not appear to be a global attitude toward all risky behaviors. For instance, individuals

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with lower cognitive ability are more likely to participate in risky behaviors such as smoking daily, smoking marijuana, or engaging in unspecified illegal activites (Heckman et al., 2006).

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Moreover, there is evidence in the financial domain to suggest that lower-income individuals spend a greater proportion of their incomes on state-run lotteries than higher-income

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households (see, for example, Clotfelter and Cook (1989); Oster (2004)), and that lottery participation is negatively related to educational attainment (Clotfelter and Cook, 1989; Perez and Humphreys, 2011).3 3 A particular intriguing strain in the literature has explored a genetic explanation of the relationship between ability and risk aversion. Using a sample of twins, Cesarini et al. (2009) finds that twenty percent of the variation in risk attitudes can be explained by genetic differences. However, like the studies mentioned above, it also measured risk aversion using hypothetical choices and a certain-versus-uncertain choice format. Bra˜ nas-Garza and Rustichini (2011) explore the relationship between pre-natal testosterone exposure (as measured by the ratio of the lengths of the index finger to the ring finger (2d:4d)) and conclude that the

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Two previous studies have considered whether the elicitation instrument used to measure risk preferences can cause low-ability individuals to appear more risk averse than high-ability individuals. Both studies focus on the possibility that more complicated tasks can result in low-ability subjects making “noisier” choices. Dave et al. (2010) find that low-ability subjects tend to make noisier choices relative to high-ability subjects when faced with a more

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complex elicitation task, such as the Holt and Laury multiple-price list (HL MPL), and they conclude that “low-numeracy can produce an effect that looks like risk aversion” (Dave et al., 2010, p.239). Their conclusions imply that a simpler elicitation format should reduce the inconsistency of low-ability subjects and my experimental design allows me to test this

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directly. Andersson et al. (2015) also doubt the robustness of the inverse relationship between risk aversion and cognitive ability, and they introduce a model that shows how errors can make low-ability subjects appear either more or less risk averse depending upon the MPL used to elicit preferences.

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I show how differences in choice complexity and incentives can affect errors and, potentially, the measurement of risk aversion in the context of a HL MPL. I also propose an

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alternate model that explains the relationship between risk aversion and ability as a function of low-ability subjects increased “preference for certainty” and a tendency for high-ability

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subjects to misrepresent their preferences when facing hypothetical choices. I then explore which model explains subjects’ choices better.

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Consistent with Andersson et al. (2015), I find evidence that low-ability subjects are more likely to make errors relative to high-ability subjects, and, similar to Dave et al. (2010),

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I find that the availability of the certain-safe option (the simpler instrument) significantly reduces the likelihood of an error by those subjects at the lowest end of the ability spectrum. However, I do not find that the use of certain-safe options reduces the likelihood of errors, or that hypothetical choices increase this likelihood, to a sufficient degree to explain differences in risk preferences resulting from the difference elicitation methods. Also, similar to Andersson inverse relationship between testosterone and risk aversion is partially mediated by cognitive ability. Again, however, this study used choices with hypothetical payments.

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et al. (2015), I find that the inverse relationship between risk aversion and cognitive ability is not robust and may be an artifact of the elicitation method. However, I do not find evidence that supports my hypothesis that low-ability subjects have a preference for certainty. Rather, the results indicate that high-ability subjects misrepresent their preferences when they face hypothetical choices, at least when the choices

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have a certain-safe option. This finding is consistent with Taylor (2013) that finds evidence to suggest that it is high-ability subjects who behave differently in the hypothetical setting relative to the real setting. Finally, I consider one potential mechanism that may explain this behavior by including a subject’s self-reported familiarity with the concept of expected value

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as a control and find that cognitive ability is not related to risk aversion under any of the treatments when this knowledge is accounted for in the model.

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Experimental Design, Procedures, and Hypotheses

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Structure of the Experiment

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This experiment measured risk aversion using one of two multiple price lists (MPL). Both MPLs present individuals with ten decisions involving a “safe” lottery and a “risky” lottery

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and subjects were asked to indicate which lottery they preferred to play. Half of the subjects were randomly assigned to a treatment in which the safe lottery was characterized by

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uncertainty and the other half were assigned to a treatment in which the safe lottery had a certain outcome. Subjects assigned to the treatments with the uncertain-safe option faced

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the frequently-used multiple-price list introduced by Holt and Laury (2002), and their risk preferences are inferred from the point at which they switch from the safe option to the risky option. Those individuals who switch later in the list, i.e., more safe choices, are indicating that they are more risk averse than subjects who switch earlier. Figure 1 shows the HL MPL that was presented to subjects in this treatment. Option A is the safer of the two options in each choice and had potential payoffs of $30 or $24; Option B is the risky option and it 4

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Figure 1: Holt and Laury multiple price list. Safe option (Option A) has uncertainty.

had potential payoffs of $58 or $1.50. The expected value of the options are structured such

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that an individual with risk neutral preferences would select the safe option for the first four decisions and then switch to the risky option for the remaining six decisions.4

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While half of the sample completed the conventional HL MPL, the other half completed a multiple-price list adapted from the HL MPL so that these subjects made choices between a

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certain option and an uncertain option. Figure 2 shows how the choices with the certain-safe option were presented to subjects assigned to this treatment. Again, the choices in this

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Alternate MPL (AMPL) are structured such that a risk-neutral individual will select the safe option for the first four decisions and then select the risky option for the final six decisions.

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In particular, the coefficients of risk aversion implied by the switch points in the conventional HL MPL were used to generate a certain-safe option that implied the same coefficient of risk aversion.5 4

The payoffs used in this experiments were fifteen times the low, baseline payoffs used in Holt and Laury (2002) 5 Deriving a coefficient of risk aversion requires an assumption about the form of the utility function. I assume that subjects have a utility function with constant relative risk aversion. In particular, I assume 1−r utility is described by U (x) = x1−r , where r is the coefficient of risk aversion and x is income.

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Figure 2: Alternative multiple price list. Safe option (Option A) is certain

In addition to randomly assigning subjects to complete a MPL with either an uncertain-

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safe option or a certain-safe option, subjects were also randomly assigned to either a real or hypothetical treatment. Subjects who completed the risk aversion task in the real setting

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received payment at the end of the experiment for one randomly-selected choice. Those subjects who completed the MPL in the hypothetical setting were asked to indicate what

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option they “would prefer” if the choices had real payoffs and they were instructed to respond “as if” the choices are real. A randomly-selected choice was also used for these subjects to

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show them what they would have won. To summarize, the experimental design involves a a two-by-two factorial design and,

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thus, subjects were randomly assigned to one of four treatments: (1) Real-Uncertain treatment in which subjects were paid based on the outcome of the randomly-selected decision and the safe option was characterized by uncertainty (conventional HL MPL); (2) Real-Certain treatment in which subjects were paid based on the outcome of the randomly-selected decision and the safe option was certain; (3) Hypot-Uncertain treatment in which subjects were

not paid based on the outcome of the randomly-selected decision and the safe option was 6

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characterized by uncertainty; or, (4) Hypot-Certain treatment in which subjects were not paid based on the outcome of there randomly-selected decision and the safe option was certain.

2.2

Measuring Cognitive Ability

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The studies mentioned above use several different methods to measure ability in their samples. Dohmen et al. (2010) use a symbol-digit correspondence task along with a word fluency task, while Benjamin et al. (2013) primarily rely on the standardized test scores from their sample of Chilean students. The remaining studies use the cognitive reflection test (CRT) introduced in Frederick (2005) to measures ability (Cokely and Kelley, 2009; Campitelli

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and Labollita, 2010; Oechssler et al., 2009). The CRT is designed to assess an individual’s System 2 cognitive ability and, thus, it is intended to measure an individual’s ability to solve problems that require “effort, motivation, concentration, and the execution of learned rules” (Frederick, 2005, pp. 26).

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Because it is common for the modal number of correct responses on the CRT to be zero and the distribution positively skewed, Weller et al. (2013) introduced an eight-item

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test to measure cognitive ability that generates a more symmetric distribution of correct responses and improves the discriminability among individuals at the low end of the ability

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distribution. This test includes two of the three CRT questions. For comparison purposes, I adapt their test by including all three CRT items, so the resulting test has nine-items and an

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individual’s score on this nine-item test is used as the measure of cognitive ability in this

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study. The nine-item test is included in the Appendix.

2.3

Procedures

The experiment was computer-based and the computer terminals were separated by dividers.

A brief introductory statement was read before the experiment began that informed the subjects that they were not competing against the other subjects, that they could leave at anytime, that they would be asked to make some choices, and that there would be a quiz 7

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after the choice tasks that assessed their ability to deal with probabilities and numbers. They were also reminded that they would receive a $10 “show-up” payment for their participation. The full text of this introduction can be found in the Appendix. The experiment was divided into three parts: a risk aversion task, an ambiguity aversion task, and a post-tasks section.6 The post-tasks section included the ability test, a

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Rotter Locus of Control assessment, and a questionnaire that included demographic questions as well as questions about the subject’s preparation in math and economics. Of particular interest, this questionnaire included a question about whether the subject was familiar with the concepts of expected value. The question read as follows:

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Yes

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• Are you familiar with the concept of expected value?

Hypotheses

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Andersson et al. (2015) assume that subjects choose the lottery that maximizes expected

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utility with probability equal to 1 − e, where one type of individual makes errors and chooses

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randomly with probability 0 < e ≤ 1, and the other type always chooses the option with the greater expected utility, so e = 0 (henceforth, ATWH model). They then cleverly demonstrate

that the structure of the MPL can be designed to exploit this error structure such that

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low-ability individuals (i.e., those with e > 0) will make more safe choices than high-ability

MPL.

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individuals on one type of MPL but they will make fewer safe choices on another type of

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Although their results fit nicely with their model’s prediction, the ATWH model does have some drawbacks. First, predictions from the model depend on an a priori assumption about individuals’ true risk preferences. For example, in the context of the MPL used in this experiment, a risk-neutral subject who does not make errors will make four safe choices and a risk-neutral subject who makes errors is expected to make 4 + e safe choices.7 However, an 6

The results of the ambiguity aversion task are not discussed in this paper. For the first four rows, the risk-neutral decision maker chooses the Safe gamble with probability 1−0.5e, and with a probability of 0.5e for the next six rows. Thus, the expected number of safe choices is E[Saf e Choices] = 7

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error-free, risk-averse subject who makes six safe choices would be expected to make 6 − e safe choices if he made errors. Therefore, the predicted direction of the impact that errors have on safe choices depends upon the assumption about subjects’ true risk preferences. Second, the model predicts that subjects who make errors will be biased toward making five safe choices regardless of their true risk preferences. Thus, the model does not

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provide a way to distinguish between a slightly risk averse whose true risk preferences result in five safe choices and an individual who chooses randomly and also ends up making five safe choices.

Despite these drawbacks, the evidence from Dave et al. (2010) and Andersson et al.

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(2015) indicate that errors affect choices in a way that could explain apparent differences in risk aversion among individuals with varying abilities, and the model is useful because it provides several testable hypotheses once we make an assumption about true risk preferences. Predicted Impact of Errors in Certain and Hypothetical Treatments in the ATWH Model

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2.4.1

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Since most studies find that individuals exhibit risk aversion, on average, when faced with the choices typically used in an experiment, this section outlines how errors are expected to

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affect the number of safe choices if subjects are risk averse. If the level of risk aversion is sufficiently strong that subjects make six safe choices, then the ATWH model implies that

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subjects who make errors will make fewer safe choices than subjects who do not, 6 − e < 6.

Simplicity tends to reduce errors. If a subject is less likely to make an error when a

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certain-safe option is available, then the probability of an error is equal to 1 − eγ, where

0 < γ < 1 and captures the reduced likelihood of an error because of the presence of a certain option. This implies that the risk-averse subject who makes errors will make 6 − eγ safe choices when a certain-safe option is available and they will appear more risk averse compared to when they make choices facing uncertain-safe options, 6 − e < 6 − eγ.

4(1 − 0.5e) + 6(0.5e) = 4 + e.

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Conversely, current evidence suggests that hypothetical choices tend to increase noise (Camerer and Hogarth, 1999). If we let θ represents the increased likelihood of making an error when subjects face hypothetical choices, then θ > 1 and a risk-averse subject who errors will make 6 − eθ when she faces hypothetical choices. Thus, if hypothetical choices increase the likelihood of errors and errors impact choices in the way described by ATWH, then we

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should expect low-ability subjects to make fewer safe choices in the hypothetical treatments relative to the corresponding real treatments, 6 − eθ < 6 − e < 6 − eγ. 2.4.2

Alternate Model: Preference for Certainty and Misrepresention

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Although certain-safe options may reduce errors so that risk-averse, low-ability subjects make more safe choices, it is also possible that low-ability subjects have a “preference for certainty” and the availability of certain-safe options leads them to choose more safe choices (Andreoni and Sprenger, 2012). In particular, they may prefer the certain option because it does not

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require computational effort.

Let τ denote a low-ability subject’s preference for certainty that increases the number

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of safe choices a subject makes independent of the likelihood of an error. A risk-averse, low-ability subject will be expected to make more safe choices than a risk-averse, high-ability

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subject when the safe option is certain, 6 + τ > 6, even if low-ability subjects do not make errors. Significantly, this predicted relationship between low- and high-ability subjects’

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measured risk aversion is the opposite of the relationship that we will expect if errors are the source of the difference because 6 − eγ < 6.

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The ATWH model also implies that increased noise due to the use of hypothetical

choices will lead low-ability subjects to appear less risk averse in the hypothetical treatments relative to the real treatments. However, as noted above, prior studies that use hypothetical choices find that low-ability subjects are more risk averse than high-ability subjects, even

when the elicitation method used only one question. Alternatively, Taylor (2013) finds that high-ability subjects may misrepresent their preferences when they face hypothetical choices

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so that they appear more risk neutral. If λ denotes the decrease in high-ability subjects’ safe choices due to their desire to appear risk neutral when the choices are hypothetical, then we would expect high-ability subjects to make fewer safe choices than low-ability subjects when the choices are hypothetical, 6 − λ < 6, because λ = 0 for low-ability subjects.

We can infer which explanation is more likely by comparing which type of subject

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makes relatively fewer safe choices in the hypothetical treatment compared to the real treatment. If low-ability subjects make fewer safe choices when hypothetical choices are used and high-ability subjects do not, then we have evidence that errors are source of the difference. Conversely, if high-ability subjects make fewer safe choices and low-ability subjects

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do not, then we have evidence to suggest that misrepresentation and not errors is the reason for the apparent difference in risk preferences.

Reformulating the model in the above way leads to three hypotheses about the relationship between ability and risk aversion in the various treatments.

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Hypothesis 1: There will not be a relationship between cognitive ability and risk aversion in the REAL-UNCERTAIN treatment. In this task both options are characterized

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by uncertainty, so an individual must exert effort to evaluate both options and low-ability subjects’ preference for certainty does not affect these choices. Moreover, each decision has

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the potential of determining the subject’s payoff so ex ante there is a real monetary incentive for the subject to put forth the effort to evaluate each option and act in accordance with her

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true preferences.

In contrast, if low-ability subjects make errors in the manner described by the ATWH

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model, then we will observe low-ability subjects make fewer safe choices than high-ability subjects in this treatment, 6 − e < 6.

Hypothesis 2: There will be a relationship between cognitive ability and risk aversion

in the HYPOT-CERTAIN treatment. If low-ability subjects have a preference for certainty and high-ability subjects misrepresent their preferences when they face hypothetical choices, then a low-ability subject will make 6 + τ safe choices and a high-ability subject will make

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6 − λ safe choices, and 6 + τ > 6 − λ. This task most closely resembles the hypothetical

choices often presented to individuals to measure risk aversion and a high-ability subject will appear to be less risk averse than a low-ability subject, on average. However, if errors are the source of apparent differences in risk aversion, then we will observe low-ability subjects make fewer safe choices than high-ability subjects in this

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treatment, 6 − eγθ < 6.

Hypothesis 3: There will be a relationship between cognitive ability and risk aversion

in the HYPOT-UNCERTAIN treatment: The results in Taylor (2013) suggest that, even when both options are characterized by uncertainty, individuals with higher cognitive ability will

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indicate that they are more tolerant of risk when the choices are hypothetical compared to when the choices are real because they are less likely to make an error and they misrepresent their preferences. Thus, low-ability subjects will make more safe choices than high-ability subjects, 6 > 6 − λ.

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Conversely, if errors by low-ability subjects are driving the differences, then low-ability

Results

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subjects will make fewer safe choices than high-ability subjects, 6 − eθ < 6.

The experiment was conducted at the University of Montana between November 2013 and

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March of 2014. Subjects were recruited via email from a variety of courses, to include: philosophy, history, mathematics, chemistry, forestry, principles of microeconomics, and

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principles of macroeconomics. Therefore, the 184 subjects who participated in the experiment have a diverse array of majors. The mean scores on the nine-item ability test and the subset of CRT questions are

shown in the first two rows of Table 1. A one-way analysis of variance (ANOVA) suggests the means of ability (p = 0.9793) and CRT (p = 0.8054) do not differ across the four treatments. In fact, on average, subjects are not significantly different across treatments along any of the

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dimensions shown in Table 1.

Table 1: Selected Summary Statistics Comparison of Means or Proportions Across Treatments

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Ageβ More Than One Year of College Income Less Than $10,000 How Much to Feel Rich (in thousands)γ Liquidity Constrained Have Seen Test Distracted Observations

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Task Risk Attitude, Self-Report (averse=0, loving=2)α General Risk Attitude, Self-Report (unwilling=1, willing=10)

T2 Real Certain 5.62 1.00 0.51 0.18 0.60 0.58 0.29 0.84 5.49 21.0 0.38 0.71 50 0.47 0.02 0.07 45

T3 Hypothetical Uncertain 5.72 1.04 0.57 0.22 0.65 0.72 0.28 0.69 5.89 23.2 0.50 0.70 60 0.57 0.02 0.11 46

T4 Hypothetical Certain 5.79 1.19 0.50 0.33 0.62 0.76 0.38 0.95 5.75 21.6 0.57 0.74 70 0.45 0.00 0.05 42

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Ability CRT score Female Expected Utility Expected Value Prob & Stats Course Business or Econ Major

T1 Real Uncertain 5.69 1.15 0.46 0.27 0.62 0.65 0.23 0.80 5.68 21.5 0.44 0.79 65 0.40 0.00 0.10 48

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Notes: α Does not include five subjects who indicated that they were “unsure” and two that did not provide a response. β Two subjects did not provide a response. γ Median reported. One subject did not provide a response.

Figure 3 shows the distribution of ability scores for each treatment. The overall mean

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ability score is shown in each figure with a vertical line. Although it is not obvious from visual inspection, there is a slight left skew of the scores (skew=-0.573, p=0.0022 ). However,

Consistency

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3.1

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there is support at both ends of the distribution in all four treatments.

Given the role that errors play in the ATWH model, it is important to explore whether consistency differs by treatment and whether ability is related to consistency. An error, or reversal, in these tasks is defined as any time that a subject chooses the safe option after having already switched over to the risky option, and Figure 4 shows the proportion of subjects at each ability level who made at least one reversal. Low-ability subjects are clearly 13

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Figure 3: Distribution of Ability Scores by Treatment

Note: Ability scores range from 0 to 9. Vertical line in each figure denotes the mean ability score. The median ability score is 6 and the s.d. is 1.77.

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more likely to make errors than high-ability subjects. Indeed, nine of the sixteen inconsistent subjects answered three or fewer questions correctly on the ability test. Considered another

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way, fifty percent of the eighteen subjects who scored three or less on the nine-item ability test made at least one reversal in the risk aversion task, whereas only 4.3 percent of the

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subjects who scored four or greater were inconsistent.8 Table 2 shows the proportion of subjects who were inconsistent in each treatment.

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On average, subjects were not significant less likely to make an error when the safe option was certain rather than uncertain. Approximately twelve percent of subjects (11/94) were

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inconsistent in the two treatments with uncertain-safe options (Treatments 1 and 3) and approximately six percent of subjects (5/87) were inconsistent in the two treatments that had certain-safe options (Treatments 2 and 4). However, a test of the null that an equal proportion of subjects were inconsistent in the certain treatments and the uncertain treatments fails to 8

Similarly, approximately 12.7 percent of the subjects with a CRT score of zero or one were inconsistent, whereas only 1.6 percent of subjects with scores of two or three were inconsistent.

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Figure 4: Proportion of Subjects Who Made Reversals by Ability

Note: The maximum score on the ability test is nine.

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reject the null (p-value=0.159).

Subjects were not significantly more likely to make errors in the hypothetical treatments

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than the real treatments, either. Eleven percent of subjects made inconsistent choices in the hypothetical treatments (Treatments 3 and 4) and only 6.5 percent of subjects made

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inconsistent choices in the real treatments (Treatments 1 and 2), but a test of the null that these two proportions are equal also fails to reject (p-value=0.247).

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Although there are not significant average differences in subject consistency across treatments, the predictions of ATWH’s model are derived from the assumption that low-

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ability subjects make more errors than high-ability subjects and Figure 4 suggests that the lowest-ability subjects do. Indeed, the availability of a certain-safe option reduces the error rate of the lowest-ability subjects. Only two of the eight subjects who scored three or less on the ability test were inconsistent in the certain-safe options, while seven out of ten were inconsistent in the treatments with uncertain-safe options (p-value=0.058). In contrast, certain-safe options did not impact the consistency of subjects with higher ability scores—3.8

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percent made errors when the safe option was certain and 4.8 percent made errors when it was uncertain (p-value=0.762). Table 2: Proportion of Inconsistent Subjects by Treatment

Treatment 2 Real Certain Safe 45 1 0.022

Treatment 3 Hypothetical Uncertain Safe 46 6 0.150

Treatment 4 Hypothetical Certain Safe 42 4 0.095

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Observations Inconsistent Subjects∗ Proportion Inconsistent

Treatment 1 Real Uncertain Safe 48 5 0.104

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Notes: ∗ Consistent subjects committed zero reversals. Three subjects were dropped from the analysis because they selected the safe option for Decision Number 10.

Low-ability subjects are not more likely to make errors in the hypothetical treatments relative to the real treatments, however. Approximately half of the lowest-ability subjects were inconsistent in both types of treatments and a test that these proportions are equal fails

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to reject the null (p-value=0.629).

Although it appears that the availability of a certain option reduces the likelihood of

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an error for this small fraction of lowest-ability subjects, this result depends on a somewhat arbitrary cut-off about what constitutes “low-ability.” To test whether the use of certain-safe

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options or hypothetical choices affects the consistency of subjects’ choices without the use of an arbitrary cut-off, a logit model in which the dependent variable is an indicator variable

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equal to one if a subject made at least one inconsistent choice, and zero otherwise, was estimated. As can be seen in Column 1 of Table 3, the coefficient estimates from this model,

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which includes controls for whether the subject made choices in the Certain treatments or the Hypothetical treatments and their interaction, are consistent with the non-parametric results above that suggest that are not significant differences in consistency across treatments in this sample. A specification that includes Ability and its interactions with each treatment was also estimated and the coefficient estimate on Ability in Column 2 of Table 3 shows that

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high-ability subjects were less likely to be inconsistent in all four treatments and that there are not significant differences across treatments.

Table 3: Ability and Inconsistency

Certain

-1.632 (1.119) 0.255 (0.646) 1.278 (1.313) —

. . . ×Certain Ability . . . ×Certain

—

. . . ×Hypothetical

—

—

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. . . ×Certain×Hypothetical

-2.152∗∗∗ (0.474) Controls No Observations 181 Log-likelihood -51.855 Robust standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Controls include the following indicator variables: Female, Prob. & Stats Course, Liquidity Constrained, and Business/Economics Major. None of which are statistically significant.

3.2

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Constant

-1.046 (2.411) 0.119 (2.147) 0.377 (3.458) -0.781∗∗ (0.345) -0.124 (0.456) -0.007 (0.475) 0.176 (0.754) 0.679 (2.044) Yes 181 -37.586

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Hypothetical

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Logit regression in which the dependent variable is an indicator variable equal to one if a subject made at least one reversal. (1) (2)

Risk Aversion and Cognitive Ability

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On average, subjects who faced hypothetical choices with certain-safe options indicated that they were significantly less risk averse than the rest of the subjects in the experiment. Table 4 provides the means of the Last Safe Choice (i.e., the switch point) and the Total Safe Choices,

which is the number of safe choices a subject made. Mean Last Safe Choice is 4.81 in the Hypot-Certain treatment, but 5.64 in the other three treatments. A Wilcoxon rank-sum test rejects the null hypotheses that Last Safe Choice is distributed equally in the Hypot-Certain 17

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treatment and the other treatments, either pooled (p < 0.01) or individually (p < 0.03 when compared to Real-Uncertain and Hypot-Uncertain treatments, p < 0.08 when compared to Real-Certain).9 The results are similar when comparing Total Safe Choices across treatments. Table 4: Choice Results

Treatment 3 Treatment 4 Hypothetical Hypothetical Uncertain Safe Certain Safe 5.80 4.81 5.48 4.64 46 42

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Treatment 2 Real Certain Safe 5.47 5.42 45

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Treatment 1 Real Uncertain Safe Last Safe Choice 5.65 Total Safe Choices 5.41 Observations 48

It is possible that this apparent difference in risk preferences in the Hypot-Certain treatment is due to a shift by both low- and high-ability subjects. However, it is also possible that this apparent difference in risk preferences is generated by the errors of low-ability

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subjects (e) or misrepresentation of preferences by high-ability subjects (λ). Low-ability subjects are more likely to make errors, but the estimates in Table 3 indicate that the

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relationship between ability and the likelihood of making an error does not significantly differ by treatment. Still, as a starting point, it is necessary to establish whether errors affect the

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total number of safe choices that a subject makes in the direction predicted by the ATWH model.

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Table 5 shows that the lowest-ability subjects do make fewer Total Safe Choices, on average, than the rest of the sample—5.11 versus 5.27. The difference is not significant,

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though, and this result only shows that errors could affect a risk-averse subject’s Total Safe

Choices in the direction that ATWH predict.

In fact, Total Safe Choices is not significantly related to ability when it is modeled using a Poisson regression. The coefficient estimate on Ability≤3 in Column 1 of Table 6 is 9

A simple OLS regression, as well as a poisson specification, which model Last Safe Choice as a function of treatment, verify that subjects in Hypot-Certain made significantly fewer safe choices.

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Table 5: Choice Results by Low- and High-Ability

Low-Ability (Ability Score≤3) High-Ability (Ability Score≥4) Wilcoxon rank-sum test p-value

Observations 18 163

Total Safe Choices Last Safe Choice 5.11 6.33 5.27 5.34 0.600 0.046

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not significant. Moreover, the interactions with this indicator variable for low-ability and the treatment controls are not significant, either. The specification shown in Column 2 replaces the indicator variable for low-ability with the individual’s ability score and produces comparable results. Therefore, taken together, although errors can affect low-ability subjects’ Total Safe Choices in the direction predicted by ATWH’s model, the effect is not significant

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and error rates do not significantly change in response to the use of either hypothetical choices or certain-safe options to an extent that explains any differences in Total Safe Choices. Although the ATWH model makes predictions about the total number of safe choices, it is doubtful that Total Safe Choices is the appropriate measure to use to compare risk

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preferences given that it is insensitive to the number of reversals a subject makes, as well as the gap between them. In contrast, a subject’s Last Safe Choice (i.e., the switch point) is

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sensitive to a subject’s errors, and low-ability subjects appear significantly more risk averse than high-ability subjects when compared using this measure of risk aversion—6.33 versus

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5.34. We know that a portion of this difference is attributable to errors made by some low-ability subjects and a simple comparison of means overestimates the difference, but we

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can control for the effect of errors in a parametric model of Last Safe Choice and estimate the relationship between risk aversion and ability. Using Total Safe Choices as the measure

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of risk aversion, in contrast, does not allows us to explore risk preferences while accounting for the impact of errors.

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Table 6: Poisson Models of Total Safe Choices

Certain Hypothetical . . . ×Certain Ability≤3 . . . ×Certain . . . ×Hypothetical

Ability . . . ×Certain . . . ×Hypothetical

—

—

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. . . ×Certain×Hypothetical

—

1.684∗∗∗ (0.039) Observations 181 Log-Likelihood -360.772 χ2 11.028 Robust standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

—

—

—

-0.017 (0.018) 0.009 (0.033) 0.034 (0.030) -0.044 (0.044) 1.785∗∗∗ (0.101) 181 -360.540 11.520

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Constant

-0.049 (0.177) -0.183 (0.164) 0.087 (0.248) —

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. . . ×Certain×Hypothetical

0.012 (0.066) 0.021 (0.064) -0.175∗ (0.097) 0.065 (0.103) -0.152 (0.149) -0.096 (0.135) 0.122 (0.209) —

(2)

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Dependent variable is Total Safe Choices. (1)

Table 7 shows the results of four Poisson regressions that model Last Safe Choice.

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All four specifications include indicator variables for the treatments and the interactions of each treatment with ability. The Real-Uncertain treatment is the baseline treatment

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in this specification. Because this study is focused on whether the relationship between ability and risk aversion is present in each treatment, rather than on whether the relationship differs across treatments, the coefficient estimates on ability and its interactions with all four treatments are shown as the total effect of ability on Last Safe Choice conditional on treatment. For example, the coefficient on Ability×Real-Uncertain is an estimate of the slope of the relationship between safe choices and ability in the Real-Uncertain treatment and the 20

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coefficient on Ability×Real-Certain is an estimate of the slope of the relationship between safe choices and ability in the Real-Certain treatment, not the difference in slopes as is commonly shown. Showing the coefficients in this way eases interpretation and provides a direct test of whether the relationship between ability and risk aversion is significantly different from zero in each treatment, without the necessity of combining coefficients and using Wald tests.10

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The coefficients on Ability and its interaction with each treatment in Column 1 show that high-ability subjects appear significantly less risk averse than low-ability subjects in two out of the four treatments when the switch point is modeled without a control for the number of reversals (i.e., errors). However, once we control for a subject’s errors, the estimates in

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Column 2 show that ability and risk aversion are not significantly correlated in three of the four treatments. Thus, the results in Column 2 support both Hypothesis 1—there is not an inverse relationship between risk aversion and cognitive ability when there are real payoffs and both options are characterized by uncertainty—and Hypothesis 2—there is a relationship

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when the choices are hypothetical and the safe option is certain.11

The negative coefficient estimate on Ability×Hypot-Certain in Column 2 of Table 7 is

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not the result of low-ability subjects making more safe choices in this treatment because they have a preference for certainty. Instead, high-ability subjects make significantly fewer safe

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choices when they face a certain-safe option in the hypothetical context. Figure 5 shows the predicted switch points by ability for each treatment, and it demonstrates that the negative

10

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coefficient is capturing high-ability subjects’ tendency to misrepresent their preferences in

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Although it common to use a structural model to estimate risk aversion and noise parameters with data from these experiments, it is important to note that noise differs from consistency, but the structural model tends to conflate the two. To illustrate this point, when the sample is restricted to only those 165 subjects who made wholly consistent choices, a simple structural model estimates a noise parameter equal to 1.61, but a specification that restricts the sample to the consistent subjects who made fewer than five safe choices and more than seven results in a noise parameter equal to 4.97. In other words, even though all sixty-six subjects in the latter sample made choices that were completely consistent (i.e., they made no errors), the estimate of the noise parameter suggests that these subjects’ choices are significantly noisier. A structural approach estimates the coefficient of risk aversion using maximum likelihood methods and assumption about the form of the utility function and the stochastic error structure. It is common to assume constant relative risk aversion 1−r r utility function, u(w) = w1−r and to model the latent index using a Fechner specification, ∇ = EUs −EU , µ where EU is the expected utility of the respective lottery and µ captures the noise in subjects’ choices. 11 Comparable analysis using the three-item CRT indicates that CRT scores are unrelated to risk aversion.

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the Hypot-Certain treatment, rather than low-ability subjects’ preference for certainty.

Table 7: Poisson Models of Last Safe Choice Dependent variable is Last Safe Choice.

(2)

(3)

(4)

-0.167 (0.189) -0.016 (0.191) -0.078 (0.167) -0.037∗ (0.020) -0.014 (0.028) -0.030 (0.027) -0.052∗∗ (0.020) — —

-0.023 (0.169) -0.004 (0.156) -0.042 (0.122) -0.011 (0.017) -0.007 (0.027) -0.005 (0.024) -0.029∗ (0.016) 0.181∗∗∗ (0.024) —

—

—

Expected Value × Hypot-Uncertain

—

—

Expected Value × Hypot-Certain

—

—

1.942∗∗∗ (0.112) No 181 -367.282 21.916

1.751∗∗∗ (0.096) No 181 -363.334 111.851

-0.068 (0.175) -0.162 (0.175) -0.029 (0.130) -0.006 (0.017) 0.000 (0.026) -0.000 (0.024) -0.016 (0.014) 0.192∗∗∗ (0.028) -0.162∗∗ (0.069) -0.112 (0.099) 0.086 (0.087) -0.268∗∗∗ (0.080) 1.820∗∗∗ (0.104) No 181 -360.210 104.887

-0.077 (0.176) -0.150 (0.170) -0.051 (0.129) -0.004 (0.017) 0.003 (0.026) -0.001 (0.023) -0.011 (0.015) 0.188∗∗∗ (0.028) -0.163∗∗ (0.070) -0.108 (0.097) 0.086 (0.088) -0.259∗∗∗ (0.080) 1.809∗∗∗ (0.126) Yes 181 -359.943 111.417

Hypot-Uncertain treatment Hypot-Certain treatment Ability × Real-Uncertain Ability × Real-Certain Ability × Hypot-Uncertain Ability × Hypot-Certain # Reversals Expected Value × Real-Uncertain

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Constant

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Expected Value × Real-Certain

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Real-Certain treatment

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(1)

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Controls Observations Log-Likelihood χ2 ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Robust standard errors in parentheses. Negative binomial specifications fail to reject the ordinary Poisson model. Controls include the following indicator variables: Female, Prob. & Stats Course, Liquidity Constrained, and Business/Economics Major. None of which are statistically significant.

These results do not support Hypothesis 3—the coefficient estimate on Ability × Hypot-

Uncertain is effectively zero in this specification. Thus, in the context of this experiment, it appears that it is the interaction of hypothetical choices and certain-safe options that induces this behavior in high-ability subjects. 22

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Figure 5: Predicted Switch Points By Ability and Treatment

Note: Predicted Switch Point From Model in Column 2 of Table 7

Risk Aversion and Knowledge of Expected Value

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3.2.1

It is possible that the relationship between cognitive ability and risk aversion is the result of

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knowledge of probabilities and concepts such as expected value and risk neutrality. In fact, the hypothesis that individuals misrepresent their preferences implicitly assumes that it is.

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Approximately sixty-two percent of the sample indicated that they were familiar with the concept of expected value, and, interestingly, the correlation between Expected Value and

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Ability is small (Spearman’s ρ=0.0564, p=0.451). Yet, on average, subjects familiar with the concept of expected value have a lower Last Safe Choice than those subjects who indicated

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that they were unfamiliar with the concept—5.23 versus 5.79, respectively, and a Wilcoxon rank-sum test indicates they are statistically different (pooled, p = 0.048). The specification shown in Column 3 of Table 7 tests whether familiarity with the

concept of expected value is related to subjects’ switch points. If subjects who are familiar with expected value attempt to make choices based on which option has a greater expected value, then all the coefficient estimates on the four terms that are interacted with Expected 23

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Value should be negative and significant. If this behavior is only exhibited when the choices are hypothetical, then the coefficient estimates for Expected Value×Hypot-Uncertain and Expected Value×Hypot-Certain should be significant. However, the results do not present a consistent picture on this question. Instead, the coefficients are negative and statistically different from zero for Expected Value×Real-Uncertain and Expected Value×Hypot-Certain,

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but are insignificant for the other two treatments. Thus, we are unable to make any clear conclusions about how the experimental design may affect the relationship between knowledge of expected value and risk aversion. However, importantly, the inclusion of a subject’s knowledge of expected value in the model diminishes the significance of the interaction term,

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Ability×Hypot-Certain, such that there is no longer a statistically significant relationship between risk aversion and ability in any of the treatments.

As a robustness check of these findings, the specification shown in Column 4 of Table 7 controls for whether a subject completed a probability and statistics course, whether he is

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liquidity constrained, whether he indicated that he is a business or economics major, and gender. The coefficient estimates and their corresponding standard errors are substantially

Discussion & Conclusion

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4

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unchanged from the results shown in Column 3.12

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Several studies find that risk aversion is inversely correlated with cognitive ability. These studies have primarily elicited risk preferences using an instrument that asks individuals

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to choose between a “safe” option that has a certain payoff and an “unsafe” option that has an uncertain payoff. Choices presented in this way may be biased toward finding that individuals with lower cognitive ability are more risk averse because the options in each 12

The coefficient of risk aversion, r, is estimated to be 0.35 using a structural approach with Fechner-error specification, indicating a mild level of risk aversion, and the structural noise parameter, µ, to be 1.84. A EUs1/µ model with a Luce latent index, ∇ = 1/µ 1/µ , was also estimated and produced similar results except EUs +EUr that the coefficient on ability in Hypot-Certain treatment remains significant even when knowledge of expected value is included in the model.

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choice are not computationally equivalent. Moreover, these studies tend to use hypothetical scenarios without real payoffs or they reduce the expected payoff by selecting only a random proportion of individuals to actually receive real payments based on their decisions. Therefore, the benefit to lower-ability individuals to put forth the effort to evaluate the option with uncertainty may not outweigh the computational cost. Conversely, the effort necessary for a

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high-ability individual to evaluate the uncertain option may be negligible to the point that real monetary payoffs are not even required to induce her to evaluate the uncertain option. Potentially, a high-ability individual may even enjoy the task.

This experiment presented here tests whether the relationship between risk aversion

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and cognitive ability holds when the complexity of the options presented to subjects is held constant so that the computational effort required to evaluate each option does not differ. Further, it also tests whether the relationship holds for both real and hypothetical choices. Similar to Andersson et al. (2015), the results of this experiment indicate that the relationship

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between risk aversion and cognitive ability is not robust. Ability was not significantly correlated with risk preferences in either of the treatments in which real payoffs were used

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or any either of the treatments in which both options were characterized by uncertainty. Only when the payoffs are hypothetical and the safe option is certain is the relationship

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significant because it appears that high-ability subjects misrepresent their preferences so that they appear more risk tolerant.

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Similar to Andersson et al. (2015) and Dave et al. (2010), I find that low-ability subjects are more likely to make inconsistent choices. I also find that the availability of

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a certain-safe option significantly reduces the likelihood of an error for the lowest-ability subjects. However, I do not find that either complexity or incentives impact errors sufficiently to explain differences in risk preferences. Still, together these studies indicate that efforts to evaluate the relationship between risk aversion and ability must account for how the elicitation method may differentially impact error rates of low- and high-ability subjects, and how errors are expected to affect the measure of risk aversion.

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Finally, given the tendency for high-ability subjects to misrepresent their preferences when they face hypothetical choices, I explored whether a subject’s familiarity with the concept of expected value can explain this apparent misrepresentation of preferences and find that including self-reported knowledge of expected value in the model diminishes the relationship between ability and risk aversion for hypothetical choices with certain-safe options.

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Individuals familiar with expected value indicated that they were less risk averse, on average, but the relationship is only statistically significant for two of the four treatments. Still, these results raise an intriguing question and suggest that experiments exploring the relationship between ability and risk aversion should also control for a subject’s knowledge of expected

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value.

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Andersson, Ola, Jean-Robert Tyran, Erik Wengstro¨ om, and Hakan J. Holm, “Risk Aversion Relates to Cognitive Ability: Preferences or Noise,” Journal of the European Economic Association, 2015, Forthcoming.

Andreoni, James and Charles Sprenger, “Risk Preferences Are Not Time Preferences,”

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American Economic Review, December 2012, 102 (7), 3357–3376.

Benjamin, Daniel J., Sebastian A. Brown, and Jesse M. Shapiro, “Who is “Behavioral”? Cognitive Ability and Anomalous Preferences,” Journal of European Economics

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Association, December 2013, 11 (6), 1231–1255.

Bra˜ nas-Garza, Pablo and Aldo Rustichini, “Organizing Effects of Testosterone and

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Economic Behavior: Not Just Risk Taking,” PloS ONE, 2011, 6 (12), e29842. , Pablo, Pablo Guillen, and Rafael L´ opez del Paso, “Math skills and risk attitudes,”

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Economics Letters, 2008, 99, 332–336.

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Camerer, Colin F. and Robin M. Hogarth, “The Effects of Financial Incentives in Experiments: A Review and Capital-Labor-Production Framework,” Journal of Risk and

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Uncertainty, 1999, 19 (1), 7–42.

Campitelli, G. and M. Labollita, “Correlations of Cognitive Reflection with Judgments and Choices,” Judgment and Decision Making, 2010, 5 (3), 182–191.

Cawley, John, James J. Heckman, and Edward J. Vytlacil, “Three Observations on Wages and Measured Cognitive Ability,” Labour Economics, 2001, 8, 419–442.

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Cesarini, David, Christopher T. Dawes, Magnus Johannesson, Paul Lichtenstein, and Bj¨ orn Wallace, “Genetic Variation in Preferences for Giving and Risk Taking,” The Quarterly Journal of Economics, May 2009, 124 (2), 809–842.

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Clotfelter, Charles T. and Philip J. Cook, Selling Hope: State Lotteries in America,

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Dave, Chetan, Catherine C. Eckel, Cathleen A. Johnson, and Christian Rojas, “Eliciting Risk Preferences: When is Simple Better?,” Journal of Risk and Uncertainty, 2010, 41, 219–243.

Dohmen, T., A. Falk, D. Huffman, and U. Sunde, “Are Risk Aversion and Impatience

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Related to Cognitive Ability?,” American Economic Review, 2010, 100 (3), 1238–1260.

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Frederick, Shane, “Cognitive Reflection and Decision Making,” Journal of Economic Perspectives, Autumn 2005, 19 (4), 25–42.

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Guiso, Luigi and Monica Paiella, “Risk Aversion, Wealth, and Background Risk,” Journal

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of European Economics Association, 2008, 6 (6), 1109–1150. Harrison, Glenn W., Morten I. Lau, and E. Elisabet Rutstr¨ om, “Estimating Risk

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109 (2), 341–368.

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Holt, Charles A. and Susan K. Laury, “Risk Aversion and Incentive Effects,” American Economic Review, 2002, 92 (5), 1644–55. Oechssler, J, A Roider, and PW Schmitz, “Cognitive abilities and behavioral biases,” Journal of Economic Behavior & Organization, 2009, pp. 147–152.

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from Micro Data,” Public Finance Review, 2011, 39 (4), 551–570.

Taylor, Matthew P., “Bias and Brains: Risk Aversion and Cognitive Ability Across Real and Hypothetical Settings,” Journal of Risk and Uncertainty, 2013, 46, 299–320. Weller, Joshua A., Nathan Dieckmann, Martin Tusler, C.K. Mertz, William J.

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Burns, and Ellen Peters, “Development and Testing of an Abbreviated Numeracy Scale: A Rasch Analysis Approach,” Journal of Behavioral Decision Making, April 2013, 26 (2),

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198–2013.

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5

Appendix

5.1

Variable Descriptions

• Female: an indicator variable equal to one if the subject is female familiar with the concept of expected value

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• Expected Utility: an indicator variable equal to one if the subject indicated that she is • Expected Value: an indicator variable equal to one if a subject is familiar with the concept of expected value

• Prob & Stats Course: an indicator variable equal to one if a subject indicated that she has completed a course in which two or more weeks were spent on probability or

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statistics

• Business or Econ Major: an indicator variable to one for business or economics majors

• Task Risk Attitude, Self-Report: subjects’ self reports of their risk attitudes on this task • General Risk Attitude, Self-Report: subjects’ self reports of their risk attitudes in general • Age: age

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• More Than One Year of College: an indicator variable equal to one if a subject indicated that she had completed more than one year of college

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• Income Less Than $10,000 : an indicator variable equal to one if the subjected reported less than $10,000 in annual income

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• How Much to Feel Rich: annual income subjects reported would make them “feel rich” • Liquidity Constrained: an indicator variable equal to one if the subject indicated that

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she did not have at least $1,000 in one of their accounts to pay for an unforeseen emergency

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• Have Seen Test: an indicator variable equal to one if the subject indicated that she had previously seen the ability test

• Distracted: an indicator variable equal to one if the subject that she was “distracted at all” during the experiment

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5.2

Text of Introduction

Thank you for participating in this experiment. Your participation will allow us to explore questions economists have about individual decision making. In this experiment, you will be asked to make some choices. There are no right or

experiment, you are not competing against anyone.

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wrong choices. Additionally, although there are other people simultaneously completing the

After you have completed the choice tasks, we ask that you complete the post-task questionnaire. This questionnaire includes some questions to measure your ability to deal with probabilities and numbers, as well as some additional questions about you.

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After you have completed the experiment and the questionnaire, you will reach a page that displays your total payoff for participation in the experiment today. This page asks you to stop and raise your hand so that we can verify your payoff, please quietly raise your hand when you reach this page and we will verify your payoff and prepare your payment.

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You will be paid in cash today before you leave. Your payment will include a $10 show-up payment. If you decide to leave early, you may do so. If you do leave early, you will

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be allowed to keep the $10 show-up payment, but you will forfeit any experimental earnings. We understand that you may have questions, but it is important that we maintain

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the integrity of the experiment by minimizing talking and other disruptions. If you have any questions before or during the experiment, please write it down on the card next to your

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computer, raise your hand, and wait until one of us comes over to your computer terminal. If it is a question that can be answered without compromising the integrity of the experiment,

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then we will do so.

Finally, we ask that you do not discuss this experiment with anyone who may also

participate in this experiment. Thank you.

5.3

Cognitive Ability Test

Please answer the following questions to the best of your ability. 31

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1. Imagine that we roll a fair, six-sided die 1,000 times. (That would mean that we roll one die from a pair of dice.) Out of 1,000 rolls, how many times do you think the die would come up as an even number? 2. In the BIG BUCKS LOTTERY, the chances of winning a $10.00 prize are 1%. What is your best guess about how many people would win a $10.00 prize if 1,000 people each buy a single ticket from BIG BUCKS?

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3. In the ACME PUBLISHING SWEEPSTAKES, the chance of winning a car is 1 in 1,000. What percent of tickets of ACME PUBLISHING SWEEPSTAKES win a car? 4. If the chance of getting a disease is 10%, how many people would be expected to get the disease out of 1000 people: 5. If the chance of getting a disease is 20 out of 100, this would be the same as having a % chance of getting the disease.

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6. Suppose you have a close friend who has a lump in her breast and must have a mammogram. Of 100 women like her, 10 of them actually have a malignant tumor and 90 of them do not. Of the 10 women who actually have a tumor, the mammogram indicates correctly that 9 of them have a tumor and indicates incorrectly that 1 of them does not have a tumor. Of the 90 women who do not have a tumor, the mammogram indicates correctly that 81 of them do not have a tumor and indicates incorrectly that 9 of them do have a tumor. The table below summarizes all of this information. Imagine that your friend tests positive (as if she had a tumor), what is the likelihood that she actually has a tumor?

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Figure A.1.: Table provided for subjects

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7. A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost? [CRT question] 8. In a lake, there is a patch of lilypads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? [CRT question]

9. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? [CRT question]

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