Electronic copy available at: http://ssrn.com/abstract=1883770

On the Development of Risk Preferences: Experimental Evidence

Catherine Eckel, Philip J. Grossman, Cathleen A. Johnson, Angela C. M. de Oliveira*, Christian

Rojas, and Rick Wilson

This Version: 06/01/11

CBEES Working Paper # 2008-5

Using a field experiment eliciting the risk preferences of 490 9th

and 11th

grade students from a

variety of school environments, we examine various factors influencing the development of these

risk preferences. In addition to factors previously considered by economists (gender, ethnicity,

height, and parental education) we also evaluate cognitive (proxied by math literacy) and

emotional (proxied by patience and planning ability) development theories. There is substantially

stronger support for the variables typically considered by economists; consistent with prior work

we find that girls are more risk averse while tall and nonwhites individuals are more risk tolerant.

Next, the impact of school characteristics on the development of risk preferences is examined.

Two effects emerge: a peer effect and a quality effect. For the peer effect, individuals who are in

a school with a higher percentage of students on free or reduced lunches are significantly more

risk averse than those with a lower percentage of students from low-income families. For the

quality effect, individuals in schools that have smaller class sizes and a higher percentage of

educators with advanced degrees have more moderate levels of risk aversion. Further, school

characteristics only influence the 11th

graders in the sample—lending some support to a causal

argument.

JEL Codes: C93, D81,

Keywords: Risk preference, Field experiment, Teen

** We would like to thank Herbert Gintis without whom this project would not have been

possible. Additionally, we thank Eugenia Toma as well as participants in the ESA International

Meetings and the CBEES Conference on Measuring Preferences in a Social Context for their

valuable comments. Funding for this project was provided by the John D. and Catherine T.

MacArthur Foundation. Any errors remain our own.

* Angela C. M. de Oliveira (corresponding): Assistant Professor, University of Massachusetts

Amherst. Ph: 413-545-5716. Fax: 413-545-5853. Email: adeolive@isenberg.umass.edu or

acm.de.oliveira@gmail.com

Electronic copy available at: http://ssrn.com/abstract=1883770

1

I. INTRODUCTION

In economic theory, risk preferences play an important role in understanding behavioral

differences observed between individuals: Examples include health and investment portfolios

(Barsky et al. 1997) and occupational choice (Bonin et al. 2007) among others. Differences

between individuals are assumed to arise from exogenously-determined variation in the

curvature of their utility functions. In recent years, there has been mounting experimental

evidence that individual preferences develop over the course of childhood and adolescence: these

include altruism (Eckel et al. 2010a; Fehr et al. 2011; Häger et al. 2011; Harbaugh and Krause

2000), fairness (Harbaugh et al. 2007), inequality aversion (Almås et al. 2010; Martinsson et al.

2011), risk aversion (Harbaugh et al. 2002; Sutter et al. 2010), competitiveness (Sutter and

Rützler 2010), trust (Harbaugh et al. 2003; Sutter and Kocher 2007), and time and self-control

(Bucciol et al. 2010; Sutter et al. 2010).1 Further, individual preferences can be impacted by

social factors, as in Afridi et al. (2011). We examine factors that influence the development of

risk preferences using a sample of high school students.

While some attempts have been made to understand the underlying factors that may

influence an individual‘s risk preferences, these attempts have been far from complete or even

commonplace. Arguably, the environment in which a person interacts with others may be critical

in shaping preferences. In particular, an individual‘s teenage years may be a pivotal period in the

process of developing many personal tendencies.

1 Further, children‘s preferences often confirm to economic predictions, for example, they have been shown to

conform to GARP as competently as adults by sixth grade (Harbaugh, Krause and Berry 2001), or they deviate in

expected or reasonable manners (Eckel et al. 2010b; Harbaugh, Krause and Vesterlund 2001). Other studies

examining the preferences of children have focused on the role of socio-economic or demographic differences

between children (e.g. for time preference, see Castillo et al. 2008; for competition see Houser and Schunk 2009;

Bartling et al. 2011).

2

We address the development of risk preferences with an ethnically diverse group of 9th

and 11th

grade high school students from Houston, Texas and St. Cloud, Minnesota. We conduct

experiments in a variety of high school environments, from homogeneous schools where the

clear majority of students are of one ethnicity to high schools with substantial diversity.

First, we examine alternative theories of the factors influencing the development of risk

preferences. Second, we investigate the potential for a causal relationship between school

characteristics and elicited individual risk preferences. We find substantially more support for

factors traditionally considered by economists than we do for the proxies for either cognitive or

emotional development. Specifically, and keeping with much of the previous literature, girls are

more risk averse (Eckel and Grossman 2008), while tall (Ball et al. 2010; Dohmen et al. 2009)

and nonwhite individuals are less risk averse.2

The impact of school characteristics on the development of risk preferences is

particularly interesting. We find two effects: a peer effect and a quality effect. For the peer effect,

individuals in schools with a higher percentage of students receiving free or reduced-price

lunches are significantly more risk averse than those with a lower percentage of students

receiving free or reduced-price lunches. For the quality effect, individuals in schools that have

smaller class sizes and a higher percentage of educators with advanced degrees have more

moderate levels of risk aversion. Further, the influence of the school variables only impacts the

elicited risk preference of the 11th

graders in the sample—lending support to a causal argument.

We next highlight the related risk preference development literature, followed by the

experimental design and implementation. We then discuss alternative development theories and

the role of school characteristics in affecting the elicited risk preferences of individuals.

2 Note that the results on ethnicity for teens depend on the type of risk: Whites are more likely to engage in some

risky behaviors, like smoking, while nonwhites are more likely to engage in others, like sexual intercourse or

violence (Blum et al. 2000; Gruber 2001).

3

II. PREVIOUS LITERATURE

Using a sample of individuals ages 5-64, Haubaugh et al. (2002) confirm that risk

preferences change with age: In particular, the tendency to underweight low-probability events

diminishes with age. However, the heterogeneity in preferences is relatively stable over time:

The individuals who are more risk averse in the population will continue to be relatively more

risk averse, even if their exact degree of risk aversion changes with age (Levin et al. 2007).3

Further, the preferences of children are impacted by their environment. For example, gender

differences emerge in late childhood, after socialization (Slovic 1966), and the risk preferences

of children can, in part, be explained by the risk tolerance of their parents (Levin and Hart 2003),

though this could be due to either heredity or the environment in which the children are raised.

Several factors influencing risk preferences are well-documented in the economic

literature, including age (Dohmen et al. 2009), gender (e.g., the papers in Croson and Gneezy

2009 and in Eckel and Grossman 2008), height and physical prowess (Ball et al. 2010; Dohmen

et al. 2009), ethnicity (e.g., the contributions in Gruber 2001) and immigration status (e.g.,

Barsky et al. 1997). Further, it has been shown that experiential characteristics are related to risk

preferences, including parental education (Dohmen et al. 2009) and the economic environment of

the community (e.g., Gruber 2001). We extend this research by considering how a different set

of experience characteristics influence risk preference development: high school characteristics.

From a psychological perspective, the underlying process for greater risk-taking by

adolescents than adults (and how the development occurs) is a subject of much debate. Some

scholars argue that there is an internal conflict between ‗cognitive-control‘ and ‗socioemotional‘

mechanisms. The ‗cognitive-control‘ system is thought to be developed around the age of 15,

3 Specifically, Levin et al. (2007) show that a risk choice made three years previously is predictive of current risk

choices for children, even if the choices were not identical.

4

while the ‗socioemotional‘ continues to develop further: As individuals age, they are better able

to override their impulses and make choices based on plans and reason (Steinberg 2007).4

Beyond this perspective, there are four main psychological theories underlying the

development of risk preferences (for a recent summary of each see Boyer 2006). Cognitive

development theories focus on how decision-making skills improve with both age and with the

ability to judge probabilities and make optimal decisions. Emotional development theories focus

on either the role of emotions in changing the relative costs and benefits of a particular choice or

on the ability of individuals to regulate their emotions (in other words, a type of control which

allows them to make an optimal choice, even in a heightened emotional state). Those

investigating biological development theories use neuroscience to examine risk-taking. Finally,

social development theories examine the link between socio-cultural context and risk taking,

with substantial emphasis on peer influences.5 For the present study, we consider an individual

risk-taking choice, which (by construction) does not allow for peer effects. We therefore focus

on the potential for cognitive development theories, which we proxy using math literacy and

emotional development theories, which we proxy with experimental measures of patience and

survey measures of planning ability.6

III. DESIGN

For this study, we employ a sample of 490 9th and 11th graders from several selected

Houston high schools and Tech High School in St. Cloud, Minnesota.7 The high schools were

4 Note that evidence suggests that adolescents and adults are able to similarly evaluate risks (Steinberg 2007 and

references therein). 5 Additionally, Problem Behavior Theory (PBT) integrates ideas from each, but is mainly a social development

theory focusing on the influence of family structure and home environment (e.g., Jessor 1991). Our study collects

data at the teen-level, not at the family-level, so we are unable to evaluate PBT in this setting. 6 We are unable to examine psychobiological theories due to data limitations (neuroeconomic studies of almost 500

students are cost prohibitive). 7 Tech High School is one of two high schools in the Independent School District 742 serving the St. Cloud region.

Experiments were run in HISD in October through November 2003 and in Minnesota in February 2004.

5

chosen to vary ethnic mix and size in order to obtain a heterogeneous subject pool and a broad

range of school cultures. We include data from students in Minnesota to capture the behavior of

a school primarily composed of white students, which we believe to be more similar to the

traditional convenience sample of university students. The 490 subjects (433 from Houston

schools and 57 from Minnesota) participate in a session with three main components. The first is

a set of money-incentivized tasks (experiments) designed to measure attitudes toward risk, time,

altruism, reciprocity, and trust (in that order). This paper is part of a larger investigation, and

here we focus on the risk task only. The second is an extensive socio-demographic which also

includes self-reported behaviors and a number of psychometric scales, including the Temporal

Orientation Scale (e.g., Jones 1994). The third is a math literacy measure consisting of 40

problems, involving the use of mathematics in real-life situations. This test is a subcomponent of

the Educational Testing Service‘s (ETS) Adult Literacy and Life Skills Survey (ALLS).

As mentioned earlier, economic theory suggests a measurement strategy for examining

risk preferences of individuals: looking at the curvature of their utility functions. With this in

mind, any incentivized task that measures the curvature should provide insights regarding these

preferences. Because our sample, by design, includes many low-income individuals, all of whom

are high school students (and not the normal convenience sample of university undergraduates),

we need to use a measure that is simple to understand and that will not be biased by those in the

sample with low math literacy who may be ―computation averse.‖

Therefore, we measure risk attitudes by having subjects choose one gamble, from among

six possible gambles, which they most prefer. The gambles are presented as in Figure 1, with the

instructions available in Appendix A. Table 1 shows the relevant constant relative risk aversion

ranges for each choice. All gambles involve a 50/50 chance of a low or high payoff, and range

6

from a sure thing with zero variance, with the other gambles increasing in both risk (variance)

and expected return. The less variance a subject is willing to accept, the stronger his risk aversion.

Each 50/50 gamble is represented as a circle with the high payoff on the right and the low payoff

on the left. Choices are arrayed from lowest-risk ($18/$18) to highest risk ($-2, $54). The subject

is asked to place an X on the preferred gamble. This is a modified version of the Eckel-Grossman

measure where the gambles are presented graphically rather than in tabular form (Eckel and

Grossman 2008). This particular measure is selected over other methods available (e.g. Holt and

Laury 2002; Becker, DeGroot, and Marschak 1964) because of its simplicity, which we believe

reduces errors and uncouples the choices selected by the participants from their ability to

perform the mathematical expected value calculations.8

[Figure 1 and Table 1]

Our approach in designing these tasks involves tradeoffs between precision and

simplicity. We deliberately structure the tasks to be as simple as possible to make the decisions

as transparent as possible to the subjects while generating sufficient heterogeneity across the

sample. In our previous studies we observe that many subjects find tables of alternatives and

payoffs difficult to understand, so we use graphic representations of the tasks wherever possible.

We also use substantial stakes for the games. At the end of the experiment we choose one among

all the tasks for payment (recall that the risk task was one of five different tasks). In our

instructions we explain this carefully, and we suggest that subjects treat each decision as if it is

the one they will be paid for. We find that this approach gets the subjects‘ attention better than if

we paid for all tasks in lower amounts and, in theory, it also avoids portfolio effects. If this task

8 Dave et al. (2010) show that the Eckel-Grossman measure is superior to the Holt-Laury measure for adult low-

literacy populations.

7

is the one chosen for payment, then the subject rolls a die to determine the outcome and payoff.

Any losses are deducted from the subject‘s $15 show-up fee.

By enhancing simplicity, we inevitably lose some precision in the measure of risk

aversion. More complex, finer-grid tasks give more precise information for subjects whose skill

level is appropriate to the task. As shown in Dave, et al. (2010), increased complexity produces

higher levels of mistakes among adults with low scores on the ALLS. Mistakes can result in

more ―noise,‖ increasing the variance in the data, making underlying differences more difficult

to detect. More troubling is the possibility that noise can produce bias, which the results in Dave

et al. suggest. For example, if low math ability is associated with a greater tendency to choose

the sure thing in the gamble task (because it does not involve any expected value calculations)

then the use of incentivized tasks will not elicit ―true‖ preferences. Several recent studies show a

marked correlation between mathematical literacy or IQ and risk and time preferences. Dohmen,

et al. (2010) address this relationship in a representative sample of 1000 German adults, and find

that lower cognitive ability is associated with greater risk aversion. Burks et al. (2009) find a

similar result for a sample of workers in a trucking firm. We suspect that the relationship

between cognitive development and risk preferences may be exaggerated by the use of complex,

calculation-based risk attitude measures. More simple tasks assist us to avoid this bias.

IV. IMPLEMENTATION

The study is implemented in eight high schools in the Houston Independent School

District (HISD) and urban high school in Minnesota.

8

School Choice and Characteristics

The Houston schools are chosen for the study based on their size, dominant ethnicity, and

the degree of mixed ethnicity. The schools are described in table 2 below, which illustrates the

variation in important measures across schools.

[Table 2]

Recruitment and Protocol

Subjects are recruited using posters displayed prominently at the schools, and by

announcements in first-period or homeroom classes. The recruitment posters and announcements

state that this is an experiment in decision making, note the time commitment involved, and

promise payment in gift certificates to a variety of stores. The date, time and address of the lab

are noted and it is stressed that their participation is in no way related to their class grade. The

earnings are described as a show-up fee ($15 in gift cards) plus the potential to earn more.

Parental consent is secured before any student participates, and all participation is voluntary.

Forty after-school sessions over 21 days of operation are conducted in the HISD high

schools between October and November of 2003. Note that, while the sessions took place over a

seven-week time span, on most days two sessions were run and experimenters were not present

in any particular school for more than a few days. This was done to limit communication. The

number of participants is 433 students. An additional 57 students participate in two sessions in St.

Cloud, Minnesota in February of 2004.

Subjects are evenly divided between 9th

and 11th

grades. A session consists of only one

grade. The sessions are held in classrooms, lecture rooms and activity rooms at the high school

normally attended by the students. Average session size is 13, with a minimum of 5 and a

maximum of 23. Three experimenters are present for each session, consisting of Johnson or

9

Grossman, plus two Rice University (in Houston) or Saint Cloud State University (in St. Cloud)

student assistants. Average earnings are $35 for a 2-hour session.

Subjects are asked to report to a specific room after school on a specific day. Two

parallel sessions take place each day, one at each of two schools. Subjects first complete a

booklet containing the incentivized tasks as follows: risk, time preference, dictator, ultimatum,

trust.9 The tasks are then followed by the survey booklet, and the numeracy assessment booklet.

When all tasks are completed, subjects are taken one at a time outside the room where one task is

selected at random and the subject is paid for that task. Payment is in gift certificates to a limited

set of stores: the subject chooses how to allocate payment across store-specific gift certificates.

V. RESULTS

Alternative Development Theories

As discussed in the introduction, several theories exist surrounding the development of

risk preferences. These data allow us to examine the relative importance of cognitive and

emotional development as well as individual characteristics previously considered by economists.

The risk measure is discrete and ordered in nature: the gamble choice is scored as one

through six, with each successively higher number representing a preference for taking on

successively more risk. As shown in table 1 (above), gambles one through four indicate

decreasing levels of risk aversion, gamble five corresponds to the risk neutral choice, and gamble

six indicates risk seeking. Results from the ordered probit are shown in table 3, with variable

descriptions available in Appendix B and full marginal effects available in Appendix C.10

Results

are presented for 9th

and 11th

graders separately, and as a pooled model including both grades.

[Table 3]

9 In some sessions the order of the dictator and ultimatum tasks is reversed.

10 Our results are not sensitive to specification as an ordered logit or to OLS (which would impose an underlying

linear structure). Additional details can be found in the notes to table 3.

10

First, we consider cognitive development. Under this theory skills develop with age.

Studies of cognitive development theories largely focus on probability-related decision-making

skills (e.g., Boyer 2006 and citations therein). Applied to our setting, this relates to the ability to

understand risk and evaluate probabilities. We assess math-related decision-making using the 40-

problem ETS Adult Literacy and Life Skills Survey, which has been widely verified: for

example, the score in the test is a strong predictor of income earning ability (Statistics Canada

and OECD 2003).

Contrary to previous results (Burks et al. 2009; Dohmen et al. 2010), we only find a

marginally significant (p≤0.10) relationship for the ninth graders—those who are more math

literate are slightly less risk averse—but, there is no significant relationship on average. The

deviation from the prior literature may be due to the nature of the decision task, since all gambles

involved are 50/50, and the visual design was intended to help break any correlation between

mathematical ability and elicited risk preferences that is due to the complexity of the task.

Alternatively, as noted in Steinberg (2007), cognitive-control tends to be developed by around

age 15. For our sample, this would mean that the cognitive-control process was still developing

for the 9th

graders (where we see significance) but not for the 11th

graders (where we do not).

Next, we examine emotional development, which considers an individual‘s ability to

regulate their emotional response (e.g., Boyer 2006 and citations therein). Previous research has

shown that, in risky situations, having peers around increases the salience of the potential

rewards relative to the risk (Steinberg 2007). Therefore, emotional development also relates to

the ability of individuals to resist peer influences. We therefore proxy this emotional regulation

with two variables: Patience and Planning Ability. Patience is measured using a series of nine

11

incentivized choices between smaller-sooner and larger-later payoffs (Eckel et al. 2010b).11

The

planning ability measure is a 15-question Temporal Orientation Scale (e.g., Jones 1994) and has

been widely validated (e.g., Mendoza and Pracejus 1997).

Turning to the results, while more patient 11th

graders are moderately less risk averse

(p<0.05), we do not see an overall relationship between the emotional development measures

and risk aversion among our high school students: Patience is not significant for the sample as a

whole and planning ability is only significant at the 10% level. The marginal effects (reported in

Appendix C) further confirm this pattern. For the sample as a whole, patience is not significantly

related to the probability of choosing any particular gamble. Having higher-levels of perceived

planning ability marginally increases the probability of choosing the most risk averse gambles (1

and 2) and decreases the probability of choosing the riskier gambles (4-6, all p≤10).

Finally, we turn to a set of variables that have been previously considered by economists.

Dohmen et al. (2009) find that age and gender (female) are negatively related to risk tolerance

while height and parental education are positively related to risk tolerance. Several of these

effects have been further documented by others (see Croson and Gneezy 2009; as well as Eckel

and Grossman 2008 for gender; Ball, Eckel and Heracleous 2010 for height). Further, ethnicity

has been shown to be related to a variety of risky behaviors (see Blum et al. 2000 and the papers

in Gruber 2001). We address each of these in turn.

First, similar to previous work, we find that girls are more risk averse than boys:

Marginal effects (Appendix C) further confirm that girls are more likely to select the most risk

averse options (gambles 1-2) and are significantly less likely to select either the moderately risk

11

The variable is defined as the total number of patient choices, out of the nine decisions where both the sooner and

later payments were made in the future. Choices are between $20 tomorrow and $20.84, $23.34, $28.33 in one

month; $20 in one month and $20.84, $23.34, $28.33 in two months; and $20 in one month and $25, $40, $70 in

seven months.

12

averse or more risk seeking options (gambles 3-6). The opposite pattern holds for nonwhites,

who are less risk averse than whites (though this difference is really driven by the 9th

graders in

the sample). In order to address the effect of height, we observe that while height and gender

always have explanatory power in the gamble decision, they are highly correlated. We therefore

created a dichotomous variable, ‗Relatively Tall‘ that divides the sample into tall and short

individuals with respect to their gender group. Tall girls (boys) are defined as people whose

height is larger than the median of their gender (median height for girls is 5‘2‖ to 5‘4‖ and for

boys is 5‘6‘‘ to 5‘8‖). Again, similar to previous work, we see that those who are tall relative to

their gender are more risk tolerant: Those who are relatively tall are significantly less likely to

choose the most risk averse gambles (1-2) and significantly more likely to choose gambles

ranging from moderate risk aversion

Contrary to the previous literature, however, we do not see any aggregate difference by

grade or age nor do we see a difference by parental education level. This result is not sensitive to

alternative specifications (available upon request).

School Environment

We now turn to an examination of the role of a students‘ school environment in shaping

their risk preferences. It has been shown that the economic environment of the community is

related to youth risky behavior (e.g., Gruber 2001). It is therefore not a large leap to consider

characteristics of the school environment, where students spend a substantial portion of time.

We consider four key characteristics of the schools: The percentage of students receiving

free or reduced lunches, the student-teacher ratio, the size of the school, and the percentage of

teachers in the school with advances degrees.12

Since these variables are measured at the school-

12

We also test for the impact of the school‘s ethnic heterogeneity and being in the ethnic majority of the school,

neither of which were found to be significant in any specification.

13

level, we cluster on the school to account for this correlation. Results are presented in table 4.

Full marginal effects are reported in Appendix D. Model 1 includes the individual economic

characteristics from table 3, since they are the most strongly related to the elicited risk preference.

[Table 4]

Model 2 considers only the school-level variables, while model 3 considers both sets of

variables simultaneously. The percentage of students in a school on either free or reduced lunch

plans is negative strongly significant, indicating a peer effect. The percentage of students

receiving free lunches provides a proxy for the impact of being surrounded by a larger

population of low-income students. With this in mind, it appears that individuals in schools with

a number of students in a lower income bracket are more risk averse.13

Next we consider the student-teacher ratio, which provides some information about

school-level resources and the level of personal attention that the students are able to receive. We

see that teens in schools with larger average class sizes are more risk averse than teens in schools

with smaller average class sizes. We do not see a significant effect of school size, measured by

the number of students in the school.

Finally, we consider the relationship between the percentage of instructors holding

advanced degrees and the elicited risk preferences, which provides another proxy for school

quality and resources (assuming more educated teachers provide better instruction). There is a

strong positive relationship between a more educated team of teachers and the elicited risk

preferences, indicating more moderate levels of risk aversion among teens in these schools.

The effects for student-teacher ratio and the percentage of teachers with advanced

degrees might at first glance seem counter-intuitive: Why would schools with ‗more‘ or ‗better‘

13

For a subset of the population we also have data on their census block. This result is not sensitive to including

census data as a control for that subset of the sample.

14

resources result in more risk tolerance? Recall that we have only one risk-seeking option, which

very few students choose. Greater risk tolerance in our setting indicates that an individual is

closer to being an expected value maximizer, which is associated with higher expected earnings.

Examining the marginal effects (Appendix D) we see that individuals in schools with a higher

percentage of teachers with advanced degrees are less likely to choose the most risk averse

options (1-2) and more likely to choose the gambles which reflect moderate levels of risk or that

are expected value maximizing. Further, for both, the marginal effects with the largest

magnitudes are the negative relationship for the perfectly safe option and the positive

relationship for the expected value maximizing choice of gamble 5 (50% change of $2 and 50%

chance of $50). So, in this setting (contrary to other risky behaviors observed among youth, like

smoking or engaging in unprotected sex), greater risk tolerance does not necessarily have

negative consequences.

Do School Characteristics have a Differential Impact on 9th

and 11th

Graders?

In considering the potential impact of school characteristics on the development of risk

preferences we have to consider several possibilities for the correlation observed in table 4, since

correlation does not equate to causation. We therefore look at the 9th

and 11th

graders separately.

If the school characteristics proxy for neighborhood or social class, then school-level variables

should impact the ninth and eleventh graders in approximately the same fashion. However, if the

school level variables matter more for the eleventh graders than for the ninth graders, this would

be consistent with school characteristics impacting the development of risk attitudes. Under the

Texas and Minnesota education systems, high school begins with ninth grade, and so students in

our sample have not been enrolled in a particular school long enough for the school level

15

variables to have an impact. The eleventh grade students, however, have been enrolled in a

particular school for a minimum of two years.

Table 5 estimates model 3 from the previous table separately for 9th

and 11th

graders, with

a full set of marginal effects reported in Appendix E. Quickly note that the magnitude and

strength of demographic factors are stronger for the 9th

graders than the 11th

graders, possibly

indicating that the impact of these variables dissipates over time.

[Table 5]

However, the school variables are strongly correlated with the elicited risk preference of

the 11th

graders in the sample, while largely uncorrelated with the elicited preferences of the 9th

graders. We take this as preliminary evidence that school characteristics can help shape risk

attitudes; however, the direction of the effect depends on the variable under consideration. It

appears that the peer effect (in this case, having a larger number of low income peers) results in

greater levels of financial risk aversion. Variables indicating school quality (having a lower

student teacher ratio and having a more educated teaching team) result in greater risk tolerance,

edging the elicited preferences closer to the expected value maximizing point.

VI. DISCUSSION

In examining factors related to the development of risk preferences among teens, we find

little support for cognitive or emotional development and substantially stronger support for

variables previously considered by economists: ethnicity, gender, and height. In keeping with

much of the prior literature already discussed, this analysis suggests that short, white females

would be the most risk-averse group while tall, nonwhite males would be the most risk tolerant.

We then consider the impact that school environment has on the development of these

elicited risk preferences, and find two main effects: a peer effect and a quality effect. For the

16

peer effect, we observe that individuals who are in a school with a higher percentage of students

on free or reduced lunches are significantly more risk averse than those from schools with a

lower percentage.. For the quality affect, we see that individuals in schools that have smaller

class sizes and a higher percentage of educators with advanced degrees have more moderate

levels of risk aversion. Further, the influence of the school variables only impacts the risk

preference of the 11th

graders in the sample—lending support to a causal argument.

It is important to note that in our setting, less risk aversion may be viewed in a somewhat

positive light, since it leads to higher expected incomes. However, whether these results

generalize to non-financial settings requires further investigation, since many of these risks

(drunk driving, unprotected sex, smoking and so on) are definitely harmful to the student and

potentially to others as well. To the best of our knowledge, the question of optimal risk tolerance,

along with separating ‗positive‘ and ‗negative‘ risks, has not been addressed in the economics

literature on risk preferences and provides an interesting avenue for future study. Further, recent

evidence from Carpenter et al. (2011) suggests that risk preferences are determined, at least in

part, by dopamine receptor genes — providing another interesting avenue to explore in the quest

to better understand the origin and development of preferences.

17

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22

Tables

TABLE 1

Summary of Experimental Design and Gamble Choices

Payoff Percent Choosing Option

Option Low

(50%)

High

(50%) Expected

CRRA

Rangea

9th 11th

1 18 18 18 4.06, ∞ 20.82 20.90

2 14 26 20 1.36, 4.06 22.04 27.46

3 10 34 22 0.83, 1.36 22.86 26.23

4 6 42 24 0.59, 0.83 15.51 9.84

5 2 50 26 0.00, 0.59 15.10 12.30

6 -2 54 26 -∞, 0.0000 3.67 3.28

aCalculated as the range of r in the function U = x

(1-r)/(1-r) for which the subject chooses each

gamble, assuming constant relative risk aversion utility and accounting for the $15 show-up fee.

23

TABLE 2

High School Characteristics, 2003-2004 Academic Yeara

Lee Scarborough Westside Chavez Reagan Madison Lamar Worthing Minnesota

HS1 HS2 HS3 HS4 HS5 HS6 HS7 HS8 HS9

Enrollment 2163 822 2840 2295 1683 2102 3292 1250 1592

Number of Faculty 140 52 154 132 103 120 162 80 76

Student-Faculty Ratio 15.45 15.81 18.44 17.39 16.34 17.52 20.32 15.634 20.94

Median Income, $b 46,563 32,095 52,667 31,762 39,926 36,543 47,703 17,529 41,281

Teacher Characteristics

Average Experience, years 10 14 11 9 14 14 13 14 N/A

Advanced Degrees, % 38 35 33 35 47 42 41 36 53

Attendance Rate, % 98 97 98 98 97 99 97 97 N/A

Female, % 46 45 48 49 46 53 53 50 48

Race/Ethnicity, %

African American 11 20 26 9 7 62 26 95 7

Asian 6 1 9 3 1 1 5 <1 3

Hispanic 78 56 28 83 88 37 31 4 1

Native American 0 <1 <1 0 <1 0 <1 <1 <1

White 5 23 36 4 5 <1 38 1 89

Free/Reduced Lunch, % 94 62 28 85 88 83 28 71 20

Limited English, % 41 15 8 19 15 6 6 1 5

At-Risk 85 74 51 71 74 73 44 74 N/A

Honors Classes 23 29 49 21 19 17 39 21 N/A

Attendance Rate 92.3 92.5 93.5 93.0 93.6 93.5 94.7 91.2 94.8

Dropout Rate 7.1 2.9 2.7 3.3 3.4 1.8 1.4 2.0 0.31

SAT-1

% of Seniors Tested 90 34 84 29 42 46 73 58 N/A

Verbal Average 366 446 498 386 426 395 537 389 N/A

Math Average 388 441 504 406 431 387 537 487 N/A

ACT Composite Average 14.6 18.2 22.0 16.8 16.3 15.7 21.9 16.9 22.7 aDATA: http://www.houstonisd.org/ and http://www.ersys.com/usa/27/2756896/sch_hs.htm (00/01 data). Last accessed 06/23/10. Additional data for MN come

from personal correspondence with Brenda Sprenger 8/30/10. N/A indicates that the data is not available. bBased on Zip code of school: http://factfinder.census.gov, 2000 Census. Last accessed 06/23/10;

(Zip codes: 77057, 77092, 77077, 77017, 77008, 77045, 77098, 77051, 56301)

24

TABLE 3

Alternative Development Theoriesa

Variables 9th

11th

Pooled

Cognitive

Math Literacy 0.160† -0.121 0.008

(0.09) (0.09) (0.06)

Emotional

Patience -0.013 0.072* 0.031

(0.03) (0.03) (0.02)

Planning Ability -0.009 -0.006 -0.008†

(0.01) (0.01) (0.005)

Economic

Female -0.509***

-0.561***

-0.486***

(0.15) (0.16) (0.11)

Nonwhite 0.660**

0.003 0.306*

(0.21) (0.22) (0.15)

Relatively Tall 0.433**

0.284† 0.360

***

(0.15) (0.15) (0.10)

Grade 11 … … -0.067

(0.10)

Mother‘s Education 0.008 0.016 0.016

(0.04) (0.04) (0.03)

N 230 240 470

LnL -374.56 -377.90 -760.17

χ2 (p) 29.71 (0.00) 26.38 (0.00) 45.86 (0.00)

Pseudo R2 0.04 0.04 0.03

† p ≤ 0.10

* p ≤ 0.05

** p ≤ 0.01

*** p ≤ 0.001

aModeled as an ordered probit. The dependent variable is the gamble choice: 1=$18/$18,

2=$14/$26, 3=$10/$34, 4=$6/$42, 5=$2/$50, 6= -$2/$54. Standard errors are in parentheses.

Coefficients are reported above as a summary measure. Marginal effects are reported in

Appendix C for the full model: Since we have an ordered probit, marginal effects are for each of

the six possible outcomes.

Key results are not sensitive to the following: Using Father‘s education instead of Mother‘s

education, including both, or excluding both; modeling as an ordered logit, assuming a linear

underlying structure and modeling as OLS, OLS with robust standard errors, OLS with

clustering at either the school or session level. The exception is that we lose significance on

Relatively Tall for 11th

graders when we cluster at the session level. Under some of these

alternative specifications, Math Literacy (Patience) is significant at the 5% level for 9th

grade

(the pooled model), but the significance level is not robust.

25

TABLE 4

The role of Individual, Experience, and School in Explaining Risk Preferencesa

(1) (2) (3)

Variable Individual Only School Only Full Model

Female -0.511***

… -0.513***

(0.08) (0.08)

Nonwhite 0.280***

… 0.384***

(0.07) (0.11)

Relatively Tall 0.316***

… 0.297***

(0.08) (0.08)

Grade 11 -0.092 … -0.111

(0.07) (0.09)

Mother‘s Education 0.018 … 0.009

(0.03) (0.03)

% Free Lunch … -0.674***

-0.541**

(0.160) (0.19)

Student/Teacher … -0.152**

-0.108*

(0.06) (0.05)

Number Students/1000 … 0.090 0.04

(0.09) (0.07)

% Advanced Degrees … 2.792**

2.624***

(0.99) (0.72)

log-likelihood -792.10 -812.03 -788.78

χ2 (p) 90.02 (0.00) 38.51 (0.00) 444.67 (0.00)

Pseudo R2 0.026 0.004 0.0307

† p ≤ 0.10

* p ≤ 0.05

** p ≤ 0.01

*** p ≤ 0.001

aModeled as an ordered probit with clustering at the school level, based on 488 subjects for

which we have full responses. The dependent variable is the gamble choice: 1=$18/$18,

2=$14/$26, 3=$10/$34, 4=$6/$42, 5=$2/$50, 6= -$2/$54. Coefficients shown. Standard errors

are in parentheses. Marginal effects are reported in Appendix D.

Key results are not sensitive to removing the clustering or to clustering at the session level,

though significance levels may change slightly. Likewise, model is not sensitive to specification

as an ordered logit (with or without clusters) or as an OLS (traditional, robust standard errors,

school or session clusters).

Additionally, for a subset of the population, we have address data which allows us to use census

tract variables as a proxy for family income. Key results are not sensitive to their inclusion.

26

TABLE 5

Development of Risk Preferences, 9th

versus 11th

Gradea

Variable 9th

11th

Female -0.634***

-0.503**

(0.16) (0.16)

Nonwhite 0.736***

0.062

(0.11) (0.16)

Relatively Tall 0.353* 0.234

†

(0.14) (0.14)

Mother‘s Education 0.021 -0.010

(0.02) (0.06)

% Free Lunch -0.138 -0.910***

(0.21) (0.28)

Student/Teacher -0.020 -0.185**

(0.07) (0.06)

Number Students/1000 -0.152 0.185

(0.13) (0.12)

% Advanced Degrees 2.035† 3.483

***

(1.19) (1.03)

n 242 244

log-likelihood -393.37 -385.93

χ2 (p) 233.60 (0.00) 954.02 (0.00)

Pseudo R2 0.04 0.03

† p ≤ 0.10

* p ≤ 0.05

** p ≤ 0.01

*** p ≤ 0.001

aBased on Table 2, Model 3. Modeled as an ordered probit, clustering at the high school level.

The dependent variable is the gamble choice: 1=$18/$18, 2=$14/$26, 3=$10/$34, 4=$6/$42,

5=$2/$50, 6= -$2/$54. Coefficients shown. Standard errors are in parentheses. Marginal effects

are reported in Appendix E.

Key results are not sensitive to excluding this clustering, or to clustering at the session level,

though exact significance levels may vary. Model is not sensitive to specification as an ordered

logit (with or without clusters), as a traditional OLS, OLS with clustered standard errors, or OLS

with robust standard errors.

27

Figures

FIGURE 1

Decision Form

-$ 2 $ 54 $ 18 $ 18

$ 2 $ 50 $ 14 $ 26

$ 6 $ 42 $ 10 $ 34

28

APPENDIX A

Instructions (text only)

Task 1

For this task you will select from among six different gambles the one gamble you will play. The six

different gambles are illustrated below.

Each gamble has two possible outcomes, LOW or HIGH.

For every gamble, each outcome is equally likely, or has a 50% chance of happening.

At the end of the study, if this task is randomly selected, you will roll a ten-sided die to determine

which outcome will occur.

If you roll a 1, 2, 3, 4 or 5, you will receive the LOW outcome.

If you roll a 6, 7, 8, 9 or 0, you will receive the HIGH outcome.

You must select one and only one of these gambles. To select a gamble, put a mark (a large X) on

circle for the pair of outcomes that you select. Mark only one.

Your earnings for this task will be determined by:

which of the six gambles you select; and

whether you roll HIGH or roll LOW.

For example, say you select the $6, $42 gamble and you roll HIGH (a 6, 7, 8, 9 or 0) with the 10-sided die,

you will be paid $42. If you roll LOW (a 1, 2, 3, 4 or 5), you will be paid $6.

Question:

Pretend you want to select the gamble for $10, $34. Mark your choice with an X on that pair of outcomes.

1. What must you roll if you are to earn $10?

_________________________________

2. What must you roll if you are to win $34.

_________________________________

Note that if you choose the -$2, $54 gamble and you roll LOW, $2 will be taken from your $15

participation fee.

Task 1

You must select one and only one of these gambles. To select a gamble, put a mark (X) on the pair of

outcomes that you prefer. Mark only one.

Once you have finished with your decision, close your booklet.

If this task is selected as the one determining your actual earnings, we will have you roll a die to

determine the outcome.

29

APPENDIX B

Variable Descriptions (in order of appearance)

Variable Mean Std. Dev. Min Max N Description

Math Literacy -0.468 0.912 -2.94 1.90 488 Math Literacy measure from ALLS,

Stats Canada

Patience 4.450 2.475 0 9 489 Experimental patience measure.

Total number of patient choices from nine decisions

between smaller, sooner and larger, later payoffs.

Planning Ability 68.316 10.561 19 95 474 Jones (1994) Intertemporal Orientation Scale

Female 0.611 0.488 0 1 489 Dummy Variable =1 if female, 0 otherwise

Nonwhite 0.832 0.374 0 1 489 Dummy Variable =1 if nonwhite, 0 otherwise

Relatively Tall 0.378 0.485 0 1 489 Dummy Variable =1 if tall relative to their gender,

0 otherwise

Grade 11 0.499 0.501 0 1 489 Dummy Variable =1 if in 11th

grade, 0 otherwise

Mother‘s Education 2.898 2.050 0 6 488 Highest level of mother‘s education

0=No mother at home/DK; 1=some grade school or HS

2=high school; 3=vocational/trade; 4=some college;

5=college; 6=advanced degree after college

% Free Lunch 0.593 0.283 0.20 0.94 489 Percentage of students in the high school on

free or reduced lunch

Student/Teacher 18.026 1.733 15.45 20.95 489 Student-teacher ratio for the high school

Number Students/1000 2.207 0.673 0.822 3.292 489 Number of students in the high school, divided by 1000

% Advanced Degrees 0.396 0.063 0.33 0.53 489 Percentage of teachers with advanced degrees

working in the high school

30

APPENDIX C

Marginal Effects for the Pooled Model in Table 3a

Variables 1=$18/$18 2=$14/$26 3=$10/$34 4=$6/$42 5=$2/$50 6= -$2/$54

Cognitive

Math Literacy -0.002 -0.001 0.00 0.001 0.001 0.000

(0.02) (0.01) (0.00) (0.01) (0.01) (0.00)

Emotional

Patience -0.009 -0.004 0.002 0.003 0.005 0.002

(0.01) (0.00) (0.00) (0.00) (0.00) (0.00)

Planning Ability 0.002† 0.001

† -0.000

† -0.001

† -0.001

† -0.001

†

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

Economic

Female 0.126***

0.063***

-0.020**

-0.046***

-0.087***

-0.036***

(0.03) (0.02) (0.01) (0.01) (0.02) (0.01)

Nonwhite -0.091† -0.031

* 0.024 0.032

* 0.049

* 0.016

*

(0.05) (0.01) (0.02) (0.02) (0.02) (0.02)

Relatively Tall -0.094***

-0.046**

0.016**

0.035***

0.064***

0.026**

(0.03) (0.02) (0.01) (0.01) (0.02) (0.01)

Grade 11 0.019 0.008 -0.004 -0.007 -0.012 -0.004

(0.03) (0.01) (0.01) (0.01) (0.02) (0.01)

Mother‘s Education -0.004 -0.002 0.000 0.002 0.003 0.001

(0.01) (0.00) (0.00) (0.00) (0.00) (0.00)

Predicted Prob. of Outcome 0.192 0.259 0.264 0.130 0.127 0.028 † p ≤ 0.10

* p ≤ 0.05

** p ≤ 0.01

*** p ≤ 0.001

aModeled as an ordered probit, with a marginal effect for each of the six possible outcomes. Standard errors in parentheses.

31

APPENDIX D

Marginal Effects for Table 4, Model 3a

Variables 1=$18/$18 2=$14/$26 3=$10/$34 4=$6/$42 5=$2/$50 6= -$2/$54

Female 0.134***

0.065***

-0.021***

-0.049***

-0.093***

-0.037***

(0.02) (0.01) (0.01) (0.01) (0.02) (0.01)

Nonwhite -0.117***

-0.035***

0.032* 0.040

*** 0.061

*** 0.019

***

(0.03) (0.01) (0.01) (0.01) (0.02) (0.00)

Relatively Tall -0.079***

-0.037**

0.014**

0.029***

0.053**

0.020***

(0.02) (0.01) (0.00) (0.01) (0.02) (0.01)

Grade 11 0.031 0.013 -0.006 -0.011 -0.020 -0.007

(0.02) (0.01) (0.00) (0.01) (0.02) (0.01)

Mother‘s Education -0.002 -0.001 0.000 0.001 0.002 0.001

(0.01) (0.00) (0.00) (0.00) (0.01) (0.00)

% Free Lunch 0.150**

0.065* -0.030

** -0.055

* -0.096

** -0.034

**

(0.05) (0.03) (0.01) (0.02) (0.03) (0.01)

Student/Teacher 0.030* 0.013* -0.006

** -0.011

* -0.019

* -0.007

*

(0.01) (0.01) (0.00) (0.01) (0.01) (0.00)

Number Students/1000 -0.012 -0.005 0.002 0.004 0.007 0.003

(0.02) (0.01) (0.00) (0.01) (0.01) (0.00)

% Advanced Degrees -0.725***

-0.314***

0.145***

0.266***

0.464***

0.165**

(0.21) (0.08) (0.03) (0.08) (0.14) (0.06)

Predicted Prob. of Outcome 0.196 0.257 0.260 0.131 0.129 0.027 † p ≤ 0.10

* p ≤ 0.05

** p ≤ 0.01

*** p ≤ 0.001

aModeled as an ordered probit, with a marginal effect for each of the six possible outcomes. Standard errors in parentheses. Marginal

effects on option 6 are estimated based on few observations, so caution in warranted in their interpretation.

32

APPENDIX E

Marginal Effects for Table 5: 9th

Gradea

Variables 1=$18/$18 2=$14/$26 3=$10/$34 4=$6/$42 5=$2/$50 6= -$2/$54

Female 0.167***

0.076**

-0.013 -0.066**

-0.119***

-0.045**

(0.04) (0.03) (0.01) (0.02) (0.03) (0.02)

Nonwhite -0.237***

-0.050***

0.055**

0.087***

0.113***

0.031*

(0.04) (0.01) (0.02) (0.01) (0.02) (0.01)

Relatively Tall -0.092**

-0.044† 0.006 0.038

† 0.068

* 0.025

**

(0.03) (0.02) (0.00) (0.02) (0.03) (0.01)

Mother‘s Education -0.006 -0.002 0.001 0.002 0.004 0.001

(0.01) (0.00) (0.00) (0.00) (0.00) (0.00)

% Free Lunch 0.038 0.016 -0.004 -0.016 -0.026 -0.009

(0.06) (0.02) (0.01) (0.02) (0.04) (0.01)

Student/Teacher 0.006 0.002 -0.001 -0.002 -0.004 -0.001

(0.02) (0.01) (0.00) (0.01) (0.01) (0.00)

Number Students/1000 0.042 0.018 -0.005 -0.017 -0.028 -0.010

(0.03) (0.02) (0.00) (0.01) (0.02) (0.01)

% Advanced Degrees -0.557† -0.241 0.061 0.229 0.380

† 0.128

(0.32) (0.15) (0.04) (0.14) (0.23) (0.09)

Predicted Prob. of Outcome 0.193 0.235 0.242 0.164 0.139 0.027 † p ≤ 0.10

* p ≤ 0.05

** p ≤ 0.01

*** p ≤ 0.001

aModeled as an ordered probit, with a marginal effect for each of the six possible outcomes. Standard errors in parentheses. Marginal

effects on option 6 are estimated based on few observations, so caution in warranted in their interpretation.

33

APPENDIX E, CONTINUED

Marginal Effects for Table 5: 11th

Gradea

Variables 1=$18/$18 2=$14/$26 3=$10/$34 4=$6/$42 5=$2/$50 6= -$2/$54

Female 0.129**

0.068***

-0.031**

-0.042***

-0.088**

-0.035*

(0.04) (0.02) (0.01) (0.01) (0.03) (0.02)

Nonwhite -0.018 -0.007 0.006 0.005 0.010 0.004

(0.05) (0.02) (0.01) (0.01) (0.03) (0.01)

Relatively Tall -0.064† -0.029 0.018

† 0.020 0.040

† 0.015

(0.04) (0.02) (0.01) (0.01) (0.02) (0.01)

Mother‘s Education 0.003 0.001 -0.001 -0.001 -0.002 -0.001

(0.02) (0.01) (0.01) (0.01) (0.01) (0.00)

% Free Lunch 0.252***

0.110**

-0.078***

-0.080**

-0.152**

-0.054**

(0.07) (0.04) (0.00) (0.03) (0.05) (0.02)

Student/Teacher 0.051**

0.022* -0.016

*** -0.016

** -0.031

** -0.011

**

(0.02) (0.01) (0.00) (0.01) (0.01) (0.00)

Number Students/1000 -0.051 -0.022† 0.016 0.016 0.031 0.011

(0.03) (0.01) (0.01) (0.01) (0.02) (0.01)

% Advanced Degrees -0.969**

-0.423***

0.295**

0.307***

0.583***

0.206*

(0.31) (0.12) (0.10) (0.09) (0.17) (0.09)

Predicted Prob. Of Outcome+ 0.197 0.284 0.274 0.101 0.118 0.025

† p ≤ 0.10

* p ≤ 0.05

** p ≤ 0.01

*** p ≤ 0.001

+ Predicted probabilities do not sum to 1 due to rounding.

aModeled as an ordered probit, with a marginal effect for each of the six possible outcomes. Standard errors in parentheses. Marginal

effects on option 6 are estimated based on few observations, so caution in warranted in their interpretation.