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Expected Utility Theory and Prospect Theory:
One Wedding and A Decent Funeral
by
Glenn W. Harrison and E. Elisabet Rutström*
June 2006
Abstract. Choice behavior is typically evaluated by assuming that the data is
generated by one latent decision-making process or another. What if there are two
latent decision-making processes generating the observed choices? Some choices
might then be better characterized as being generated by one process, and other
choices by the other process. A finite mixture model can be used to estimate the
parameters of each decision process at the same time as one estimates the probability
that each process applies to the sample. We consider the canonical case of lottery
choices and assume that the data is generated by expected utility theory and prospect
theory decision rules. We jointly estimate the parameters of each theory as well as the
fraction of choices characterized by each. The methodology provides the wedding
invitation, and the data consummates the ceremony with a decent funeral for the
representative agent model that assumes only one type of decision process and
homogenous preferences. The evidence suggests support for each theory, and goes
further to identify under what demographic domains one can expect to see one
theory perform better than the other. We therefore propose a statistical
reconciliation of the debate over two of the dominant theories of choice under risk,
at least for the tasks and samples we consider. The methodology is broadly applicable
to a range of debates over competing theories generated by experimental and nonexperimental data.
*
Department of Economics, College of Business Administration, University of Central Florida,
USA. E-mail contacts: [email protected] and [email protected].
Rutström thanks the U.S. National Science Foundation for research support under grant NSF/IIS
9817518, and Harrison and Rutström are grateful for support under grant NSF/HSD 0527675. We
thank Ryan Brosette, Harut Hovsepyan, David Millsom and Bob Potter for research assistance, and
Steffen Andersen, Vince Crawford, Curt Eaton, John Hey, Peter Kennedy, Jan Kmenta, Peter
Wakker and seminar participants for helpful comments. Supporting data and instructions are stored
at the ExLab Digital Library at http://exlab.bus.ucf.edu.
One of the enduring contributions of behavioral economics is that we now have a rich set of
competing models of behavior in many settings. Debates over the validity of these models have
often been framed as a horse race, with the winning theory being declared on the basis of some
statistical test where the theory is represented as a latent process explaining the data. In other words,
we seem to pick the best theory by “majority rule.” If one theory explains more of the data than
another theory, we declare it the better theory and discard the other one. The problem with this
approach is that it does not recognize the possibility that several behavioral latent processes may
coexist in a population.
Ignoring this possibility can lead to erroneous conclusions about the domain of applicability
of each theory, and is likely an important reason for why the horse races appear to pick different
winners in different domains. Heterogeneity in responses is well recognized as causing statistical
problems in experimental data. However, allowing for heterogeneity in responses through standard
methods, such as fixed or random effects, is not helpful when we want to identify which people
behave according to what theory, and when. For purely statistical reasons, if we have a belief that
there are two or more latent population processes generating the observed sample, one can make
more appropriate inferences if the data are not forced to fit a specification that assumes one latent
population process.
One way to allow explicitly for alternative theories is to simply collect sufficient data at the
individual level, and test the different theories for that individual. One classic example of this
approach is the experimental study of expected utility theory by Hey and Orme [1994]. In one
experimental treatment they collected 200 binary choice responses from each of 80 subjects, and
were able to test alternative estimated models for each individual. Thus, at the beginning of their
discussion of results (p.1300), they state simply, “We assume that all subjects are different. We
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therefore fit each of the 11 preference functionals discussed above to the subject’s stated preferences
for each of the 80 subjects indvidually.” Their approach would not be so remarkable if it were not for
the prevailing popularity of the “representative agent” assumption in previous tests of expected
utility theory.
We consider the more familiar case in which one cannot collect considerable data at the level
of an individual. How is one to account for heterogeneous population processes in such settings? One
solution is to use statistical mixture models, in which the “grand likelihood” of the data is specified
as a probability-weighted average of the likelihood of the data from each of K>1 models, where
each model implies a distinct and latent data-generating process. With two modeling alternatives the
overall likelihood of a given observation is just the probability of model A being true times the
likelihood conditional on model A being true, plus the probability of model B being true times the
likelihood conditional on model B being true.
One obvious application of this approach is to offer a statistical reconciliation of the debate
over alternative theories of choice under risk. A canonical setting for these theories has been the
choice over pairs of monetary lotteries, as reviewed by Camerer [1995]. To keep things sharply
focused, two alternative models are posited here. One is a simple expected utility theory (EUT)
specification, assuming a CRRA utility function defined over the “final monetary prize” that the
subject would receive if the lottery were played out. The other model is a popular specification of
prospect theory (PT) due to Kahneman and Tversky [1979], in which the utility function is defined
over gains and losses separately, and there is a probability weighting function that converts the
underlying probabilities of the lottery into subjective probabilities.1
1
We use the language of EUT, but prospect theorists would instead refer to the utility function as a
“value function,” and to the transformed probabilities as “decision weights.” Our implementation of PT uses
the original version in which there are no editing processes assumed. One could easily extend our approach to
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Our primary methodological contribution is to illustrate how one can move from results that
rely on representative agent assumptions about the decision-making model to a richer characterization
that allows for the potential coexistence of multiple decision-making models. Our focus is on the coexistence of latent EUT and PT data-generating processes, and not just the heterogeneity of behavior
given EUT or PT.
Section 1 discusses our approach in more detail. Section 2 reviews the experimental data,
section 3 the competing models, section 4 presents the results of estimating a mixture model for
both models, and section 5 draws conclusions.
1. Weddings, Funerals and Heterogeneity
One way that heterogeneity can be recognized is by collecting information on observable
characteristics and controlling for them in the statistical analysis. For example, a given theory might
allow some individuals to be more risk averse than others as a matter of personal preference. To
allow for this when we measure risk attitudes we can condition on observable individual
characteristics and evaluate the presence of heterogeneity. Additionally, one can allow for
unobserved individual characteristics when appropriate and the data is in a panel. But this approach
only recognizes heterogeneity within a given theory. This may be important for valid inferences about the
ability of the theory to explain the data, but it does not allow for heterogeneous theories to co-exist in
the same sample.
We seek a statistical reconciliation of the debate over two dominant theories of choice under
risk, EUT and PT. We collect data in a setting in which subjects make risky decisions in a gain
frame, a loss frame, or a mixed frame, explained in detail below. Such settings allow one to test the
allow editing processes or Cumulative PT formulations.
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competing models on the richest domain. All data is collected using standard procedures in
experimental economics in the laboratory: no deception, no field referents, fully salient choices, and
with information on individual characteristics of the subjects. The experimental procedures are
described in section 1.
Our experiments represent a replication and extension of the procedures of Hey and Orme
[1994]. The major extension is to consider lotteries in which some or all outcomes are framed as
losses, as well as the usual case in which all outcomes are frames as gains. The subject received an
initial endowment that resulted in their final outcomes being the same as those in the other frames.
Thus the final income level of the subjects is essentially equalized across all frames.
Our EUT specification is defined over the “final monetary prize” that the subject would
receive if the lottery were played out. That is, the argument of the utility function is the prize plus
the initial endowment, which are always jointly non-negative. Our PT specification defines the utility
function over gains and losses separately, and there is a probability weighting function that converts
the underlying probabilities of the lottery into subjective probabilities. The three critical features of
the PT model are (i) that the arguments of the utility function be gains and losses relative to some
reference point, taken here to be the endowment; (ii) that losses loom larger than gains in the utility
function; and (iii) that there be a nonlinearity in the transformed probabilities that could account for
apparently different risk attitudes for different lottery probabilities. There may be some debate over
whether the endowment serves as a “reference point” to define losses, but that is one thing that is
being tested with these different models.2 We specify the exact forms of the models tested in
2
Some might argue that negative lottery prizes would count as losses only when the subject “earns”
the initial stake. This is a fair point, but testable by simple modification of the design. There is evidence from
related settings that such changes in how subjects receive their initial endowment can significantly change
behaviour: see Cherry, Frykblom and Shogren [2002], Johnson, Rutström and George [2004] and George,
Johnson, and Rutström [2006]. Moreover, one can extend the PT specification to estimate the endogenous
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section 2.
It is apparent that there are many variants of these two models, and many others that deserve
to be considered. Wonderful expositions of the major alternatives can be found in Camerer
[1995] and Hey and Orme [1994], among others. But this is not the place to array every feasible
alternative. Instead, the initial exploration of this approach should consider two major alternatives
and the manner in which they are characterized. Many of the variants involve nuances that would be
hard to empirically evaluate with the data available here, rich as it is for the task at hand.3 But the
methodological point illustrated here is completely general.
The “wedding” arises from the specification and estimation of a grand likelihood function
that allows each model to co-exist and have different weights. The data can then identify what
support each model has. The most intuitive interpretation of these estimated probabilities is that the
sample consists of two types of decisions or decison-makers: those that are relatively well
characterized by EUT, and those that are relatively well characterized by PT. The wedding is
consummated by the maximum likelihood estimates converging on probabilities that apportion nontrivial weight to both models. Thus the data, when allowed, indicates that one should not think
exclusively of EUT or PT as the correct model, but as models that are correct for distinct parts of
the sample or the decisions.
Kirman [1992; p.119] considers the dangers of using representative agent characterizations
reference point that subjects employ: see Harrison, List and Towe [2005] and Andersen, Harrison and
Rutström [2006] for examples.
3
For example, on the EUT side one would prefer to consider specifications that did not assume
constant relative risk aversion after the empirical “wake up call” provided by Holt and Laury [2002]. But the
reliable estimation of the parameters of such specifications likely requires a much wider range of prizes than
considered here: hence the design of Holt and Laury [2002], where prizes were scaled by a factor of 20 for
most of their sample in order to estimate such a flexible specification. For an example on the PT side, there
are a plethora of specifications available for the probability weighting function (e.g., Wu and Gonzalez [1996]
and Prelec [2002]).
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in macroeconomics, and argues that “... it is clear that the ‘representative’ agent deserves a decent
burial, as an approach to economics analysis that is not only primitive, but fundamentally
erroneous.” The “funeral” we offer arises from the ability to identify which individual or task
characteristics are associated with subjects being better characterized as EUT decision-makers rather
than as PT decision-makers, or vice versa. We can “bury” a theory for a specific domain. The
funeral we provide is “decent” because the ability to identify empirically valid domains for each
theory is based on the recognition of the dangers of statistical inference using representative agent
models with homogenous preferences.4 Moreover, within each type, we can identify those
individual characteristics associated with different preferences. For example, we can identify which
EUT decision-makers are more or less risk averse, or which PT decision-makers are more or less
averse to losses.
Mixture models have an astonishing pedigree in statistics: Pearson [1894] examined data on
the ratio of forehead to body length of 1000 crabs to illustrate “the dissection of abnormal
frequency curves into normal curves.” In modern parlance he was allowing the observed data to be
generated by two distinct Gaussian processes, and estimated the two means and two standard
deviations. Modern surveys of the evolution of mixture models are provided by Titterington, Smith
and Makov [1985], Everitt [1996] and McLachlan and Peel [2000]. Mixture models are also virtually
identical to “latent class models” used in many areas of statistics, marketing and econometrics, even
though the applications often make them seem quite different (e.g., Goodman [1974a][1974b] and
Vermunt and Magidson [2003]). In experimental economics, El-Gamal and Grether [1995; §6]
estimate a finite mixture model of Bayesian updating behavior, and contrast it to a related approach
4
Camerer and Ho [1994] remains the most impressive work of this genre, and contains a very clear
statement of the strengths and weaknesses of the approach (p.186).
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in which individual subject behavior is classified completely as one type of the other. Stahl and
Wilson [1995] develop a finite mixture model to explain behavior in a normal form game,
differentiating between five types of boundedly rational players.5
One challenge with mixture models of this kind is the joint estimation of the probabilities
and the parameters of the conditional likelihood functions. If these are conditional models that each
have some chance of explaining the data, then mixture models will be characterized numerically by
relatively flat likelihood functions. On the other hand, if there are indeed K distinct latent processes
generating the overall sample, allowing for this richer structure is inferentially useful. Most of the
applications of mixture modeling in economics have been concerned with their use in better
characterizing unobserved individual heterogeneity in the context of a given theory about behavior,6
although there have been some applications to hypothetical survey data that consider individual
heterogeneity over alternative behavioral theories.7
5
Additional applications of mixture models to experimental data include Stahl [1996][1998], Haruvy,
Stahl and Wilson [2001], Coller et al. [2003], Bardsley and Moffatt [2005], Harrison, Humphrey and
Verschoor [2005] and Andersen et al. [2005][2006].
6
For example, Heckman and Singer [1984], Geweke and Keane [1999] and Araña and León [2005].
The idea here is that the disturbance term of a given specification is treated as a mixture of processes. Such
specifications have been used in many settings that may be familiar to economists under other names. For
example, stochastic frontier models rely on (unweighted) mixture specifications of a symmetric “technical
efficiency” disturbance term and an asymmetric “idiosyncratic” disturbance term; see Kumbhakar and Lovell
[2000] for an extensive review.
7
For example, Werner [1999] uses mixture models to characterize the “spike at zero” and “nonspike” responses common in contingent valuation surveys. Wang and Fischbeck [2004] provide an
application to framing effects within prospect theory, using hypothetical field survey data on health insurance
choices. Their approach is to view the frames as different data generation processes for responses.
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2. Experimental Design
Subjects were presented with 60 lottery pairs, each represented as a “pie” showing the
probability of each prize. The subject could choose the lottery on the left or the right, or explicitly
express indifference (in which case the experimenter would flip a coin on the subject’s behalf). After
all 60 lottery pairs were evaluated, three were selected at random for payment. The lotteries were
presented to the subjects in color on a private computer screen,8 and all choices recorded by the
computer program. This program also recorded the time taken to make each choice. An appendix
presents the instructions given to our subjects, as well as an example of the “screen shots” they saw.
In the gain frame experiments the prizes in each lottery were $0, $5, $10 and $15, and the
probabilities of each prize varied from choice to choice, and lottery to lottery. In the loss frame
experiments subjects were given an initial endowment of $15, and the corresponding prizes from the
gain frame lotteries were transformed to be -$15, -$10, -$5 and $0. Hence the final outcomes,
inclusive of the endowment, were the same in the gain frame and loss frame. In the mixed frame
experiments subjects were given an initial endowment of $8, and the prizes were transformed to be $8, -$3, $3 and $8, generating final outcomes inclusive of the endowment of $0, $5, $11 and $16.9
In addition to the fixed endowment, each subject received a random endowment between $1
and $10. This endowment was generated using a uniform distribution defined over whole dollar
amounts, operationalized by a 10-sided die.
The probabilities used in each lottery ranged roughly evenly over the unit interval. Values of
8
The computer laboratory used for these experiments has 24 subject stations. Each screen is
“sunken” into the desk, and subjects were typically separated by several empty stations due to the staggered
recruitment procedures. No subject could see what the other subjects were doing, let alone mimic what they
were doing since each subject was started individually at different times.
9
These final outcomes differ by $1 from the two highest outcomes for the gain frame and mixed
frame, because we did not want to offer prizes in fractions of dollars.
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0, 0.13, 0.25, 0.37, 0.5, 0.62, 0.75 and 0.87 were used.10
Subjects were recruited at the University of Central Florida, primarily from the College of
Business Administration. Each subject received a $5 fee for showing up to the experiments, and
completed an informed consent form. Subjects were deliberately recruited for “staggered” starting
times, so that the subject would not pace their responses by any other subject. Each subject was
presented with the instructions individually, and taken through the practice sessions at an individual
pace. Since the rolls of die were important to the implementation of the objects of choice, the
experimenters took some time to give each subject “hands-on” experience with the (10-sided, 20sided and 100-sided) die being used. Subjects were free to make their choices as quickly or as slowly
as they wanted.
The presentation of a given lottery on the left or the right was determined at random, so that
the “left” or “right” lotteries did not systematically reflect greater risk or greater prize range than the
other.
Our data consists of responses from 158 subjects making 9311 choices that do not involve
indifference. Only 1.7% of the choices involved explicit choice of indifference, and to simplify we
drop those.11 Of these 158 subjects, 63 participated in gain frame tasks, 37 participated in mixed
frame tasks, and 58 participated in loss frame tasks.
10
To ensure that probabilities summed to one, we also used probabilities of 0.26 instead of 0.25, 0.38
instead of 0.37, 0.49 instead of 0.50 or 0.74 instead of 0.75.
11
For the specification of likelihoods of strictly binary responses, such observations add no
information. However, one could augment the likelihood for the strict binary responses with a likelihood
defined over “fractional responses” and assume that the fraction for these indifferent responses was exactly
½. Such specifications are provided by Papke and Wooldridge [1996], but add needless complexity for present
purposes given the small number of responses involved.
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3. Meet the Bride and Groom
A. Expected Utility Specification
We assume that utility of income is defined by U(s, x) = (s+x)r where s is the fixed
endowment provided at the beginning of the experiment, x is the lottery prize, and r is a parameter
to be estimated. With this specification we assume “perfect asset integration” between the
endowment and lottery prize.12 Probabilities for each outcome k, p(k), are those that are induced by
the experimenter, so expected utility is simply the probability weighted utility of each outcome in
each lottery. Since there were up to 4 implicit outcomes in each lottery i, EUi = 3k [ p(k) × U(k) ]
for k = 1, 2, 3, 4.
A simple stochastic specification was used to specify likelihoods conditional on the model.
The EU for each lottery pair was calculated for a candidate estimate of r, and the difference LEU =
EUR - EUL calculated, where EUL is the left lottery in the display and EUR is the right lottery.13 The
index LEU is then used to define the cumulative probability of the observed choice using the
logistic function: G(LEU) = Λ(LEU) = exp(LEU)/[1+exp(LEU)].
Thus the likelihood, conditional on the EUT model being true, depends on the estimates of
r given the above specification and the observed choices. The conditional log-likelihood is
12
A valuable extension, inspired by Cox and Sadiraj [2005], would be to allow s and x to be
combined in some linear manner, with weights to be estimated.
13
This may be viewed as a deterministic theory of EUT, in the sense that any difference in the EU of
the two lotteries implies that the subject will make the implied choice with certainty. It is possible to extend
this specification to include a “structural” stochastic story. Harless and Camerer [1994], Hey and Orme [1994]
and Loomes and Sugden [1995] provided the first wave of empirical studies including some formal stochastic
specification in the version of EUT tested. There are several species of “errors” in use, reviewed by Hey
[1995][2002], Loomes and Sugden [1995], Ballinger and Wilcox [1997], and Loomes, Moffatt and Sugden
[2002]. Some place the error at the final choice between one lottery or the other after the subject has decided
deterministically which one has the higher expected utility; some place the error earlier, on the comparison of
preferences leading to the choice; and some place the error even earlier, on the determination of the expected
utility of each lottery.
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ln LEUT(r; y,X) = 3i [ (ln Λ(LEU) * yi=1) + (ln (1-Λ(LEU)) * yi=0) ]
where yi =1(0) denotes the choice of the right (left) lottery in task i, and X is a vector of individual
characteristics.
B. Prospect Theory Specification
Tversky and Kahneman [1992] propose a popular specification, which is employed here.
There are two components, the utility function and the probability weighting function.
Tversky and Kahneman [1992] assume a power utility function defined separately over gains
and losses: U(x) = xα if x $ 0, and U(x) = -λ(-x)β for x < 0. So α and β are the risk aversion
parameters, and λ is the coefficient of loss aversion.
There are two variants of prospect theory, depending on the manner in which the probability
weighting function is combined with utilities. The original version proposed by Kahneman and
Tversky [1979] posits some weighting function which is separable in outcomes, and has been
usefully termed Separable Prospect Theory (SPT) by Camerer and Ho [1994; p. 185]. The alternative
version, proposed by Tversky and Kahneman [1992], posits a weighting function defined over the
cumulative probability distributions. In either case, the weighting function proposed by Tversky and
Kahneman [1992] has been widely used: it assumes weights w(p) = pγ/[ pγ + (1-p)γ ]1/γ.
Assuming that SPT is the true model, prospective utility PU is defined in much the same
manner as when EUT is assumed to be the true model. The PT utility function is used instead of the
EUT utility function, and w(p) is used instead of p, but the steps are otherwise identical.14 The same
error process is assumed to apply when the subject forms the preference for one lottery over the
14
We ignore the editing processes that were discussed by Kahneman and Tversky [1979]. They have
not been used in the empirical implementations of SPT by Camerer and Ho [1994] or Hey and Orme [1994],
to take two prominent examples.
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other. Thus the difference in prospective utilities is defined similarly as LPU = PUR - PUL.
Thus the likelihood, conditional on the SPT model being true, depends on the estimates of
α, β, λ and γ given the above specification and the observed choices.15 The conditional log-likelihood
is
ln LPT(α, β, λ, γ; y,X) = 3i l iPT = 3i [ (ln Λ(LPU) * yi=1) + (ln (1-Λ(LPU)) * yi=0) ].
C. The Nuptial
If we let πEUT denote the probability that the EUT model is correct, and πPT = (1-πEUT)
denote the probability that the PT model is correct, the grand likelihood can be written as the
probability weighted average of the conditional likelihoods. Thus the likelihood for the overall
model estimated is defined by
ln L(r, α, β, λ, γ, πEUT; y,X) = 3i ln [ (πEUT × l iEUT ) + (πPT × l iPT ) ].
This log-likelihood can be maximized to find estimates of the parameters.16
We allow each parameter to be a linear function of the observed individual characteristics of
the subject. This is the X vector referred to above. We consider six characteristics: binary variables
to identify Females, subjects that self-reported their ethnicity as Black, those that reported being
Hispanic, those that had a Business major, and those that reported a low cumulative GPA (below
3¼). We also included Age in years. The estimates of each parameter in the above likelihood function
actually entails estimation of the coefficients of a linear function of these characteristics. So the
15
The fact that the SPT specification has three more parameters than the EUT specification is
meaningless. One should not pick models on some arbitrary parameter-counting basis. We refer to SPT or PT
interchangeably.
16
This approach assumes that any one observation can be generated by both models, although it
admits of extremes in which one or other model wholly generates the observation. One could alternatively
define a grand likelihood in which observations or subjects are classified as following one model or the other
on the basis of the latent probabilities πEUT and πPT. El-Gamal and Grether [1995] illustrate this approach in
the context of identifying behavioral strategies in Bayesian updating experiments.
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estimate of r, ^r , would actually be
^r = ^r 0 + (r^FEMALE × FEMALE) + (r^BLACK × BLACK) + (r^HISPANIC × HISPANIC) +
(r^BUSINESS × BUSINESS) + (r^GPAlow × GPAlow) + (r^AGE × AGE)
where ^r 0 is the estimate of the constant. If we collapse this specification by dropping all individual
characteristics, we would simply be estimating the constant terms for each of r, α, β, λ, µ. Obviously
the X vector could include treatment effects as well as individual effects, or interaction effects.17
The estimates allow for the possibility of correlation between responses by the same subject,
so the standard errors on estimates are corrected for the possibility that the 60 responses are
clustered for the same subject. The use of clustering to allow for “panel effects” from unobserved
individual effects is common in the statistical survey literature.18
Flexible as this specification is, it rests on some assumptions, just as many marriages start
with a pre-nuptial agreement. First, we only consider two data generating processes, despite the fact
that there are many alternatives to EUT. Still, two is double the one that is customarily assumed, and
that is the main point of our analysis: to assume more than one data generating process.
Furthermore, there is a natural “family similarity” between many of the alternatives that might make
them hard to identify. This similarity is to be expected, given the common core of “empirical facts”
about violations of EUT that spawned them. But it implies low power for any statistical specification
17
Haruvy, Stahl and Wilson [2001] also explicitly consider within-type diversity in the context of a
between-type mixture model. They find that a measure of the intensity of individual calculator use helps
explain the allocation to types.
18
Clustering commonly arises in national field surveys from the fact that physically proximate
households are often sampled to save time and money, but it can also arise from more homely sampling
procedures. For example, Williams [2000; p.645] notes that it could arise from dental studies that “collect data
on each tooth surface for each of several teeth from a set of patients” or “repeated measurements or recurrent
events observed on the same person.” The procedures for allowing for clustering allow heteroskedasticity
between and within clusters, as well as autocorrelation within clusters. They are closely related to the
“generalized estimating equations” approach to panel estimation in epidemiology (see Liang and Zeger
[1986]), and generalize the “robust standard errors” approach popular in econometrics (see Rogers [1993]).
Wooldridge [2003] reviews some issues in the use of clustering for panel effects, in particular noting that
significant inferential problems may arise with small numbers of panels.
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that seeks to identify their individual contribution to explaining behavior, unless one focusses on
“trip wire” tasks that are designed just to identify these differences by setting up one or other
models for a fall if choices follow certain patterns. Second, we adopt specific parameterizations of
the EUT and PT models, recognizing that there exist many variants. On the other hand, our
parameterizations are not obviously restrictive compared to those found in the literature. Third, we
employ specific parameterizations of the link between latent preferences and observed choices: we
do not allow a “structural stochastic error” story, and we use a logistic cumulative distribution
function. Fourth, we assume that observable characteristics of the individual have a linear effect on
the parameter, and that there are no interactions. Since these characteristics will provide some of the
most entertaining moments of the marriage, as discussed below, this assumption would be worth
examining in future work (with even larger data sets). Finally, we do not consider much variation in
task domain, other than the obvious use of gain, loss or mixed frames. Our priors are that the
relative explanatory power of EUT and PT will vary with demographics and task domain, and
possibly some interaction of the two. To provide sharp results we therefore controlled the variability
of the task domain, and focus on the possible effect of demographics.19 We suspect that significantly
larger samples will be needed to fully examine the effects of demographics and task domain, even in
a simple task such as ours.
19
These priors also imply that we prefer not to use mixture specifications in which subjects are
categorized as completely EUT or PT. It is possible to rewrite the grand likelihood (CC) such that π iEUT = 1
and π iPT = 0 if l iEUT > l iPT, and π iEUT = 0 and π iPT = 1 if l iEUT < l iPT, where the subscript i now refers to the
individual subject. The problem with this specification is that it assumes that there is no effect on the
probability of EUT and PT from task domain. We do not want to impose that assumption, even for a
relatively homogenous task design such as ours. One could use a categorization mixture specification in which
each binary choice was classified as wholly EUT or PT without assuming that task domain has no effect, but
we see no numerical or inferential advantage in doing so compared to our specification.
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4. Results
A. Heterogeneity of Process
Table 1 presents the maximum likelihood estimates of the conditional models and the
mixture model when we assume no individual covariates. The estimates for the conditional models
therefore represent the traditional representative agent assumption, that every subject has the same
preferences and behaves in accord with one theory or the other. The estimates for the mixture model
allow each theory to have positive probability, and therefore makes one major step towards
recognizing heterogeneity of preferences.
The first major result is that the estimates for the probability of the EUT and PT specifications indicate
that each is equally likely. Each estimated probability is significantly different from zero.20 EUT wins by
a (quantum) nose, with an estimated probability of 0.55, but the whole point of this approach is to
avoid such rash declarations of victory. The data suggest that the sample is roughly evenly split
between those subjects that are best characterized by EUT and those subjects that are best
characterized by PT. In fact, one cannot reject the formal hypothesis that the probabilities of each
theory are identical and equal to ½ (p-value = 0.490).
The second major result is that the estimates for the PT specification are very weakly
consistent with the a priori predictions of that theory when the specification is assumed to fit every
subject, but strikingly consistent with the predictions of the theory when it is only assumed to fit some of the subjects.
When the conditional PT model is assumed for all subjects, the loss aversion parameter is greater
than 1, but only equals 1.381. This is significantly different from 1 at the 5% significance level, since
20
The likelihood function actually estimates the log odds in favor of one model or the other. If we
denote the log odds as κ, one can recover the probability for the EUT model as πEUT = 1/(1+exp(κ)). This
non-linear function of κ is calculated using the “delta method,” which also provides estimates of the standard
errors and p-values. Since πEUT = ½ when κ=0, the standard p-value on the estimate of κ provides the estimate
for the null hypothesis H0: πEUT=πEUT listed in Table 1.
-15-
the p-value is 0.088 and a one-sided test is appropriate here given the priors from PT that λ>1. But
the size of the effect is much smaller than the 2.25 estimated by Tversky and Kahneman [1992] and
almost universally employed.21 However, when the same PT specification is estimated in the mixture
model, where it is only assumed to account for the behavior of some of the subjects, the estimated
value for λ jumps to 5.781 and is even more clearly greater than 1 (although the estimated standard
error also increases, from 0.223 to 1.612). Similarly, the γ parameter is estimated to be 0.942 with the
conditional PT model, and is not statistically different from 1 (p-value = 0.266), which is the special
EUT case of the probability weighting function where w(p)=p for all p. But when the mixture model
is estimated, the value of γ drops to 0.681 and is significantly smaller than 1, against consistent with
many of the priors from PT.22 Finally, the risk aversion coefficients α and β are not significantly
different from each other under the conditional model, but are different from each other under the
mixture model. This difference is not critical to PT, and is often assumed away in applied work with
PT, but it is worth noting since it points to another sense in which gains and losses are viewed
differently by subjects, which is a primary tenet of PT.
B. Heterogeneity of Process and Parameters
Table 2 presents estimates from the mixture model with all individual characteristics
included. In general we see many individual coefficients that are statistically significant, and an
overall F-test that all coefficients are jointly zero can be easily rejected with a p-value of 0.0003.
Apart from indicating marginal statistical significance, the detailed coefficient estimates of Table 2
21
For example, Benartzi and Thaler [1995; p.79] assume this value in their evaluation of the “equity
premium puzzle,” and note (p.83) that it is the assumed value of the loss aversion parameter that drives their
main result.
22
This prior is not universally held: see Humphrey and Verschoor [2004] for a review of the literature
and some contrary evidence that γ>1 in some settings.
-16-
are not particularly informative. It is more instructive to examine the distribution of coefficients
across the sample, generated by predicting each parameter for each subject by evaluating the linear
function with the characteristics of that subject.23 Such predictions are accompanied by estimated
standard errors, just as the coefficient estimates in Table 1 are, so we also take the uncertainty of the
predicted parameter value into account.
Figure 1 displays the main result, a distribution of predicted probabilities for the competing
models. The two panels are, by construction, mirror images of each other since we only have two
competing models, but there is pedagogic value in displaying both. The support for the EUT
specification is extremely high for some people, but once that support wanes the support for PT
picks up. It is not the case that there are two sharp modes in this distribution, which is what one
might have expected with priors that there are two types of subjects. Instead, subjects are better
characterized as either “clearly EUT” or “probably PT.” It is as if EUT is fine for city folk, but PT
rules the hinterland.24 No doubt this is due to many subjects picking lotteries according to their
estimate of the expected value of the lotteries, which would make them EUT-consistent subjects
that are risk neutral (r=1). The average probability for the EUT model is 0.51, as is the median,
despite the apparent skewness in the distributions in Figure 1.
Figure 2 indicates the uncertainty of these predicted probabilities. Consistent with the use of
discrimination functions such as the logistic, uncertainty is smallest at the end-points and greatest at
the mid-point. Since EUT has more of it’s support from subjects that are at one extreme probability,
23
For example, a black 21-year-old female that was not hispanic, did not have a business major, and
had an average GPA, would have an estimate of r equal to ^r 0 + ^r FEMALE + ^r BLACK + ^r AGE × 21. She would
have the same estimate of r as anyone else that had exactly the same set of characteristics.
24
Andersen et al. [2006] report the reverse qualitative pattern when considering dynamic lottery choices
in which subjects could accumulate income. We again caution that the relative explanatory power of EUT and
PT likely interacts with task domain.
-17-
this implies that one can be more confident about declaring a subject as better characterized by EUT
than one can about the alternative model.
Figures 3 through 7 display stratifications of the probability of the EUT model being correct
in terms of individual characteristics. The results are striking. Figure 3 shows that men have a much
stronger probability of behaving in accord with the EUT model than women. Figure 4 shows that
“whites” have a dramatically higher probability of being EUT decision makers than “blacks” or
“hispanics.” Consider the implications of these two Figures for the dramatic differences that List
[2002][2003][2004] finds between subjects in field experiments on the floor of sportscard shows and
conventional lab experiments with college students. The vast majority of participants on those shows
are white males. No doubt there is much more going on in these field experiments than simply
demographic mix, as stressed by Harrison and List [2004], but one might be able to go a long way to
explaining the differences just on these two demographics alone.25
Figure 5 shows that business majors exhibit behavior that is much more consistent with
EUT, helping us track homo economicus down among, thankfully, the Econ. Figure 6 expands on this
characteristic by showing that EUT is more common for those subjects with a lower GPA as
compared to those with a higher GPA; the closing credits of Animal House remind us, of course, that
those with lower GPA might become the political and economic leaders of the future. Figure 7
shows some modest effects of age on support for EUT. Our sample obviously has a limited range in
terms of age, with these ages also confounded with “standing” within the undergraduate program.
25
Haigh and List [2005] report contrary evidence, using tasks involving risky lotteries and comparing
field traders from the Chicago Board of Trade and students. However, the behavior they observe can be easily
explained under EUT using a specification of the utility function that allows non-constant relative risk
aversion, such as the expo-power specification favored by Holt and Laury [2002] in their experiments. Thus
one should not count this as contrary evidence to the claim in the text unless one constrains EUT to the
special case of CRRA.
-18-
But there does appear to be a marked reduction in support for EUT as subjects age or get more
university education.
Finally, Figures 8 and 9 display the distributions of the parameters of each model. The raw
predictions for all 158 subjects include some wild estimates, but for completely sensible reasons. If
some subject has a probability of behavior in accord with PT of less than 0.0001, then one should
not expect the estimates of α, β, λ or γ to be precise for that subject. In fact, most of the extreme
estimates are associated with parameters that have very low support for that subject, or that have
equally high standard errors. Thus, we restrict the displays in Figures 8 and 9 to those subjects
whose probability of behaving in accord with EUT or PT, respectively, is at least ¼.
Figure 7 displays results for the EUT subjects that are slightly lower than those reported in
Table 1. The average EUT subject has a CRRA coefficient r equal to 0.70, with the same median,
whereas the estimate from Table 1 was 0.85 when all EUT subjects were assumed to have the same
risk attitude. In Figure 7 we observe two modes close to the risk-neutral case, r=1, reflecting the
ability of the mixture model that includes individual characteristics to allow for heterogeneity of risk
attitudes within the subset of the sample that behave according to EUT. Some subjects exhibit
considerable risk aversion (r<1), and some even exhibit mild risk-loving behavior (r>1). From Table
2 we see that the characteristics that drive this heterogeneity include sex, ethnicity, and age.
Figure 8 displays results for the PT parameters that are generally consistent with the
estimates in Table 1. The parameters α and β are generally less than 1, consistent with mild risk
aversion in the usual sense. The average estimate for α is 0.59, with a median of 0.50. The loss
aversion coefficient λ is generally much greater than 1, consistent with the subjects that behave in
accord with PT having significant loss aversion. The average estimate for λ is 5.9, with a median of
6.8. Of course, this applies only to the fraction of the sample deemed to have certain level of
-19-
support for PT; the value of λ for EUT subjects is of course 1, so the weighted average for the
whole sample would be much smaller (as Table 1 indicates, it is 1.381 when estimated over all
subjects). The probability weighting coefficient γ is generally less than 1, which is the value at which
it collapses back to the standard EUT assumption that w(p)=p for all p. The average estimate is
0.89, and the median is 0.77.
5. Conclusion
Characterizing behavior in lottery choice tasks as generated by potentially heterogenous
processes generates several important insights.
First, it provides a framework for systematically resolving debates over competing models.26
This method does not rest on exploiting structural aspects of one type of task or another, such as
have been a staple in tests of EUT. Such extreme domains are still interesting of course, just as the
experiments employed here deliberately generated loss frames and mixed frames. But the test of the
competing models should not be restricted to such trip-wire tests, which might not characterize
behavior in a broader domain.
Second, it provides a more balanced metric for deciding which theory does better in a given
task, rather than extreme declarations of winners and losers. If some theory has little support, this
approach will still show that.
Third, the approach can provide some insight into when one theory does better than another,
through the effects of individual characteristics and treatments on estimated probabilities of support.
This insight might be fruitfully applied to other settings in which apparently conflicting findings
26
The approach readily generalizes to other contexts, such as competing models of intertemporal
discounting behavior. See Andersen et al. [2005] and Coller et al. [2003] for applications.
-20-
have been reported. We fully expect that the relative explanatory power of EUT and PT will vary
with task domain as well as demographics. So the constructive challenge is to characterize those
domains so that we know better when to use one model or the other.
Fourth, the approach readily generalizes to include more than two models, although
likelihoods are bound to become flatter as one mixes more and more models that have any support
from the data. The obvious antidote for those problems is to generate larger samples, to pool data
across comparable experiments, and to marshall more exhaustive numerical methods.
-21-
Table 1: Estimates of Parameters of Models With No Individual Covariates
Estimates from Conditional Models
Parameter
or Test
Estimate Standard Error
Estimates from Mixture Model
p-value
Lower 95%
Confidence
Interval
Upper 95%
Confidence
Interval
Estimate
Standard Error
p-value
Lower 95%
Confidence
Interval
Upper 95%
Confidence
Interval
r
0.837
0.025
0.000
0.788
0.886
0.846
0.044
0.000
0.759
0.933
α
β
λ
γ
0.730
0.733
1.381
0.942
0.033
0.062
0.223
0.052
0.000
0.000
0.000
0.000
0.665
0.611
0.943
0.841
0.796
0.854
1.820
1.044
0.614
0.312
5.781
0.681
0.057
0.132
1.612
0.047
0.000
0.019
0.000
0.000
0.501
0.052
2.598
0.587
0.727
0.572
8.965
0.774
0.550
0.450
0.072
0.072
0.000
0.000
0.407
0.308
0.692
0.592
πEUT
πPT
H0: πEUT=πPT
H0: α=β
H0: λ=1
H0: γ=1
0.490
0.973
0.088
0.266
0.046
0.003
0.000
-22-
Table 2: Estimates of Parameters of Mixture Model With Individual Covariates
0.509
0.006
0.827
0.002
0.001
0.266
0.560
Lower 95%
Confidence
Interval
-0.931
-0.473
-0.408
-0.965
0.028
-0.305
-0.113
Upper 95%
Confidence
Interval
0.464
-0.079
0.327
-0.222
0.100
0.085
0.208
0.370
0.647
0.550
0.054
0.957
0.839
0.798
0.485
0.260
0.735
0.324
0.754
0.582
0.817
0.685
0.038
0.014
0.354
0.160
0.860
0.029
0.000
0.976
0.100
0.147
0.104
0.447
0.739
0.002
0.215
0.661
0.105
0.223
0.429
-0.482
-0.519
-0.743
0.000
-0.457
-0.366
-2.348
-0.811
-0.224
-0.818
-0.014
-0.673
-0.232
-13.726
-24.411
-8.969
-9.253
-0.593
-7.287
-3.918
0.059
0.320
-0.254
-0.190
-0.037
-0.069
-0.475
-2.473
0.610
-1.374
-5.204
-0.260
-0.478
-0.721
0.181
0.323
0.397
0.045
0.483
0.449
1.809
1.704
0.824
1.157
0.042
0.928
0.411
17.366
16.068
-0.264
-1.062
1.647
1.213
3.275
1.067
0.661
0.262
2.142
0.006
0.727
0.211
3.479
2.696
6.062
8.181
0.025
2.034
1.688
Parameter
Variable
Estimate
Standard Error
p-value
r
Constant
Female
Black
Hispanic
Age
Business
GPAlow
Constant
Female
Black
Hispanic
Age
Business
GPAlow
Constant
Female
Black
Hispanic
Age
Business
GPAlow
Constant
Female
Black
Hispanic
Age
Business
GPAlow
Constant
Female
Black
Hispanic
Age
Business
GPAlow
Constant
Female
Black
Hispanic
Age
Business
GPAlow
-0.234
-0.276
-0.041
-0.594
0.064
-0.110
0.047
0.119
-0.151
-0.098
-0.173
0.022
0.013
0.042
-0.269
0.446
0.300
0.170
0.014
0.127
0.090
1.820
-4.171
-4.616
-5.157
0.527
-3.037
-0.322
0.563
0.490
0.004
0.976
-0.016
0.329
-0.132
0.503
1.653
2.344
1.489
-0.118
0.778
0.483
0.353
0.100
0.186
0.188
0.018
0.099
0.081
†
0.168
0.213
0.288
0.012
0.238
0.206
1.052
0.637
0.265
0.500
0.014
0.405
0.163
7.871
10.247
2.204
2.073
0.567
2.152
1.821
0.255
0.086
0.130
0.590
0.011
0.201
0.174
1.507
0.528
1.882
3.388
0.072
0.636
0.610
α
β
λ
γ
κ‡
Notes: † The standard error for the constant is not reliably estimated.
‡ κ is the log odds of the probabilities of each model, and πEUT = 1/(1+exp(κ)) .
-23-
Figure 1: Probability of Competing Models
EUT Model
15
PT Model
15
10
Percent
Percent
10
5
0
5
0
.1
.2
.3
.4 .5 .6
Probability
.7
.8
.9
1
0
0
.1
.2
.3
.4 .5 .6
Probability
.7
.8
.9
1
Figure 2: Uncertainty In Predicted Probability of Models
Predicted probabilities and standard errors from estimates in Table 2
Quadratic regression line added
1
.8
Predicted
Standard
Error of
Probability
.6
.4
.2
0
0
.2
.4
.6
Predicted Probability of EUT Model
-24-
.8
1
Figure 3: Sex, EUT and Prospect Theory
Males
40
30
Percent
Percent
30
20
10
0
Females
40
20
10
0
.1
.2 .3 .4 .5 .6 .7 .8
Probability of EUT Model
.9
1
0
0
.1
.2
.3 .4 .5 .6 .7 .8
Probability of EUT Model
.9
1
Figure 4: Race, EUT and Prospect Theory
Black (N=16)
80
40
20
0
80
60
Percent
Percent
60
Hispanic (N=19)
40
20
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Probability of EUT Model
0
Others (N=123)
60
Percent
80
40
20
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Probability of EUT Model
-25-
0
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Probability of EUT Model
Figure 5: Business Majors, EUT and Prospect Theory
Non-Business Majors
25
20
20
15
15
Percent
Percent
Business Majors
25
10
10
5
5
0
0
.1
.2 .3 .4 .5 .6 .7 .8
Probability of EUT Model
.9
0
1
0
.1
.2
.3 .4 .5 .6 .7 .8
Probability of EUT Model
.9
1
.9
1
Figure 6: GPA, EUT and Prospect Theory
Low GPA
30
Higher GPA
30
20
Percent
Percent
20
10
0
10
0
.1
.2 .3 .4 .5 .6 .7 .8
Probability of EUT Model
.9
1
-26-
0
0
.1
.2
.3 .4 .5 .6 .7 .8
Probability of EUT Model
Figure 7: Age, EUT and Prospect Theory
17 or 18
50
19
50
30
30
30
Percent
40
Percent
40
Percent
40
20
20
20
10
10
10
0
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Probability of EUT Model
20 and Over
50
0
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Probability of EUT Model
0
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
Probability of EUT Model
Figure 8: CRRA Parameter of the EUT Model
15
Percent
10
5
0
0
.25
.5
.75
-27-
1
1.25
Figure 9: Parameters of the PT Model
ë
Percent
Percent
á
0
.25
.5
.75
1
1.25
0
1
2
3
4
5
6
7
8
9
10 11
ã
Percent
Percent
â
0
.25
.5
.75
1
1.25
-28-
0
.5
1
1.5
2
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-32-
Appendix A: Experimental Instructions (NOT FOR PUBLICATION)
This is an experiment about choosing between lotteries with varying prizes and chances of
winning. You will be presented with a series of lotteries where you will make choices between pairs
of them. There are 60 pairs in the series. For each pair of lotteries, you should indicate which of the
two lotteries you prefer to play. You will actually get the chance to play three of the lotteries you
choose, and will be paid according to the outcome of those lotteries, so you should think carefully
about which lotteries you prefer.
Here is an example of what the computer display of such a pair of lotteries will look like.
The display on your screen will be bigger and easier to read.
-33-
The outcome of the lotteries will be determined by the draw of a random number between 1
and 100. Each number between (and including) 1 and 100 is equally likely to occur. In fact, you will
be able to draw the number yourself using a special die that has all the numbers 1 through 100 on it.
In the above example the left lottery pays five dollars ($5) if the number on the ball drawn is
between 1 and 40, and pays fifteen dollars ($15) if the number is between 41 and 100. The yellow
color in the pie chart corresponds to 40% of the area and illustrates the chances that the ball drawn
will be between 1 and 40 and your prize will be $5. The black area in the pie chart corresponds to
60% of the area and illustrates the chances that the ball drawn will be between 41 and 100 and your
prize will be $15.
We have selected colors for the pie charts such that a darker color indicates a higher prize.
White will be used when the prize is zero dollars ($0).
Now look at the pie in the chart on the right. It pays five dollars ($5) if the number drawn is
between 1 and 50, ten dollars ($10) if the number is between 51 and 90, and fifteen dollars ($15) if
the number is between 91 and 100. As with the lottery on the left, the pie slices represent the
fraction of the possible numbers which yield each payoff. For example, the size of the $15 pie slice
is 10% of the total pie.
Each pair of lotteries is shown on a separate screen on the computer. On each screen, you
should indicate which of the lotteries you prefer to play by clicking on one of the three boxes
beneath the lotteries. You should click the LEFT box if you prefer the lottery on the left, the
RIGHT box if you prefer the lottery on the right, and the DON’T CARE box if you do not prefer
one or the other.
You should approach each pair of lotteries as if it is one of the three that you will play out. If
you chose DON’T CARE in the lottery pair that we play out, you will pick one using a standard six
-34-
sided die, where the numbers 1-3 correspond to the left lottery and the numbers 4-6 to the right
lottery.
After you have worked through all of the pairs of lotteries, raise your hand and an
experimenter will come over. You will then roll a 20 sided die three times to determine which pairs
of lotteries that will be played out. One lottery pair from the first 20 pairs will be selected, one from
the next 20 pairs, and finally one from the last 20 pairs. If you picked DON’T CARE for one of
those pairs, you will use the six sided die to decide which one you will play. Finally, you will roll the
100 sided die to determine the outcome of the lottery you chose.
For instance, suppose you picked the lottery on the left in the above example. If the random
number was 37, you would win $5; if it was 93, you would get $15. If you picked the lottery on the
right and drew the number 37, you would get $5; if it was 93, you would get $15.
Therefore, your payoff is determined by three things:
•
by which three lottery pairs that are chosen to be played out in the series of 60 such pairs
using the 20 sided die;
•
by which lottery you selected, the left or the right, for each of these three pairs; and
•
by the outcome of that lottery when you roll the 100 sided die.
This is not a test of whether you can pick the best lottery in each pair, because none of the
lotteries are necessarily better than the others. Which lotteries you prefer is a matter of personal
taste. The people next to you will have difference lotteries, and may have different tastes, so their
responses should not matter to you. Please work silently, and make your choices by thinking
carefully about each lottery.
All payoffs are in cash, and are in addition to the $5 show-up fee that you receive just for
being here. In addition to these earnings you will also receive a randomly determined amount of
-35-
money before we start. This can be any amount between $1 and $10 and will be determined by
rolling the 10 sided die.
When you have finished reading these instructions, please raise your hand. We will then
come to you, answer any questions you may have, let you roll the 10 sided die for the additional
money, and start you on a short series of practice choices. The practice series will not be for
payment, and consists of only 6 lottery pairs. After you complete the practice we will start you on
the actual series for which you will be paid.
As soon as you have finished the actual series, and after you have rolled the necessary dice,
you will be paid in cash and are free to leave.
Practice Session
In this practice session you will be asked to make 6 choices, just like the ones that you will be
asked to make after the practice. You may take as long as you like to make your choice on each
lottery.
You will not be paid your earnings from the practice session, so feel free to use this practice
to become familiar with the task. When you have finished the practice you should raise your hand so
that we can start you on the tasks for which you will be paid.
-36-
B. Individual Characteristics Questionnaire27
Stage 2: Some Questions About You
In this survey most of the questions asked are descriptive. We will not be grading your
answers and your responses are completely confidential. Please think carefully about each question
and give your best answers.
1.
What is your AGE? ____________ years
2.
What is your sex? (Circle one number.)
01
3.
Male
02
Female
Which of the following categories best describes you? (Circle one number.)
01
02
03
04
05
White
African-American
African
Asian-American
Asian
06
07
08
09
Hispanic-American
Hispanic
Mixed Race
Other
4. What is your major? (Circle one number.)
01
02
03
04
05
06
07
08
09
10
11
12
13
14
5.
What is your class standing? (Circle one number.)
01
02
03
6.
Accounting
Economics
Finance
Business Administration, other than Accounting, Economics, or Finance
Education
Engineering
Health Professions
Public Affairs or Social Services
Biological Sciences
Math, Computer Sciences, or Physical Sciences
Social Sciences or History
Humanities
Psychology
Other Fields
Freshman
Sophomore
Junior
04
05
06
Senior
Masters
Doctoral
What is the highest level of education you expect to complete? (Circle one number)
01
Bachelor’s degree
27
In the original experiments question #35 was inadvertently a repeat of question #31. We show
here the correct question #35, but the responses for these experiments for question #35 are invalid. This has
no effect on any of the results in the text, since these questions were not employed in the statistical analysis
reported here.
-37-
02
03
04
7.
What was the highest level of education that your father (or male guardian) completed?
(Circle one number)
01
02
03
04
05
8.
Single and never married?
Married?
Separated, divorced or widowed?
On a 4-point scale, what is your current GPA if you are doing a Bachelor’s degree, or what
was it when you did a Bachelor’s degree? This GPA should refer to all of your coursework,
not just the current year. Please pick one:
01
02
03
04
05
06
07
08
13.
Yes
No
Are you currently...
01
02
03
12.
U.S. Citizen
Resident Alien
Non-Resident Alien
Other Status
Are you a foreign student on a Student Visa?
01
02
11.
Less than high school
GED or High School Equivalency
High School
Vocational or trade school
College or university
What is your citizenship status in the United States?
01
02
03
04
10.
Less than high school
GED or High School Equivalency
High school
Vocational or trade school
College or university
What was the highest level of education that your mother (or female guardian) completed?
(Circle one number)
01
02
03
04
05
9.
Master’s degree
Doctoral degree
First professional degree
Between 3.75 and 4.0 GPA (mostly A’s)
Between 3.25 and 3.74 GPA (about half A’s and half B’s)
Between 2.75 and 3.24 GPA (mostly B’s)
Between 2.25 and 2.74 GPA (about half B’s and half C’s)
Between 1.75 and 2.24 GPA (mostly C’s)
Between 1.25 and 1.74 GPA (about half C’s and half D’s)
Less than 1.25 (mostly D’s or below)
Have not taken courses for which grades are given.
How many people live in your household? Include yourself, your spouse and any
dependents. Do not include your parents or roommates unless you claim them as
dependents.
___________________
-38-
14.
Please circle the category below that describes the total amount of INCOME earned in 2002
by the people in your household (as “household” is defined in question 13).
[Consider all forms of income, including salaries, tips, interest and dividend payments,
scholarship support, student loans, parental support, social security, alimony, and child
support, and others.]
01
02
03
04
05
06
07
08
15.
Please circle the category below that describes the total amount of INCOME earned in 2002
by your parents. [Consider all forms of income, including salaries, tips, interest and dividend
payments, social security, alimony, and child support, and others.]
01
02
03
04
05
06
07
08
09
16.
Part-time
Full-time
Neither
Before taxes, what do you get paid? (fill in only one)
01
02
03
04
18.
$15,000 or under
$15,001 - $25,000
$25,001 - $35,000
$35,001 - $50,000
$50,001 - $65,000
$65,001 - $80,000
$80,001 - $100,000
over $100,000
Don’t Know
Do you work part-time, full-time, or neither? (Circle one number.)
01
02
03
17.
$15,000 or under
$15,001 - $25,000
$25,001 - $35,000
$35,001 - $50,000
$50,001 - $65,000
$65,001 - $80,000
$80,001 - $100,000
over $100,000
_____ per hour before taxes
_____ per week before taxes
_____ per month before taxes
_____ per year before taxes
Do you currently smoke cigarettes? (Circle one number.)
00
01
No
Yes
If yes, approximately how much do you smoke in one day? _______ packs
For the remaining questions, please select the one response that best matches your reaction
to the statement.
19.
“I believe that fate will mostly control what happens to me in the years ahead.”
Strongly
Disagree
Disagree
Slightly
Disagree
Slightly
Agree
-39-
Agree
Strongly
Agree
20.
“I am usually able to protect my personal interests.”
Strongly
Disagree
21.
Slightly
Disagree
Slightly
Agree
Agree
Strongly
Agree
Agree
Strongly
Agree
“When I get what I want, it's usually because I'm lucky.”
Strongly
Disagree
22.
Disagree
Disagree
Slightly
Disagree
Slightly
Agree
“In order to have my plans work, I make sure that they fit in with the desires of people who
have power over me.”
Strongly
Disagree
23.
Disagree
Slightly
Disagree
Slightly
Agree
Agree
Strongly
Agree
Disagree
Slightly
Disagree
Slightly
Agree
Agree
Strongly
Agree
Disagree
Slightly
Disagree
Slightly
Agree
Agree
Strongly
Agree
Disagree
Slightly
Disagree
Slightly
Agree
Agree
Strongly
Agree
“When I make plans, I am almost certain to make them work.”
Strongly
Disagree
28.
Strongly
Agree
“I feel like other people will mostly determine what happens to me in the future.”
Strongly
Disagree
27.
Agree
“Chance occurrences determined most of the important events in my past.”
Strongly
Disagree
26.
Slightly
Agree
“Whether or not I get into a car accident depends mostly on the other drivers.”
Strongly
Disagree
25.
Slightly
Disagree
“I have mostly determined what has happened to me in my life so far.”
Strongly
Disagree
24.
Disagree
Disagree
Slightly
Disagree
Slightly
Agree
Agree
Strongly
Agree
“Getting what I want requires pleasing those people above me.”
Strongly
Disagree
Disagree
Slightly
Disagree
Slightly
Agree
-40-
Agree
Strongly
Agree
29.
“Whether or not I get into a car accident depends mostly on how good a driver I am.”
Strongly
Disagree
30.
Disagree
Disagree
Disagree
Slightly
Disagree
Agree
Agree
Strongly
Agree
Disagree
Slightly S
Disagree
lightly
Agree
Agree
Strongly
Agree
Disagree
Slightly
Disagree
Slightly
Agree
Agree
Strongly
Agree
Disagree
Slightly
Disagree
Slightly
Agree
Agree
Strongly
Agree
“I think that I will mostly control what happens to me in future years.”
Strongly
Disagree
35.
Slightly
“Whether or not I get into a car accident is mostly a matter of luck.”
Strongly
Disagree
34.
Strongly
Agree
“Most of my personal history was controlled by other people who had power over me.”
Strongly
Disagree
33.
Agree
“When I get what I want, it's usually because I worked hard for it.”
Strongly
Disagree
32.
Slightly
Agree
“Often there is no chance of protecting my personal interests from bad luck.”
Strongly
31.
Slightly
Disagree
Disagree
Slightly
Disagree
Slightly
Agree
Agree
Strongly
Agree
“People like myself have very little chance of protecting our personal interests when they
conflict with those of strong pressure groups.”
Strongly
Disagree
36.
Disagree
Slightly
Disagree
Slightly
Agree
Agree
Strongly
Agree
“It's not always wise for me to plan too far ahead because many things turn out to be a
matter of good or bad fortune.”
Strongly
Disagree
Disagree
Slightly
Disagree
Slightly
Agree
-41-
Agree
Strongly
Agree