testing prospect theory
TRANSCRIPT
Testing prospect theory for gender andexperience1
Vladimír BALÁŽ*1, Viera BAĆOVÁ, Eva DROBNÁ, KatarínaDUDEKOVÁ, Kamil ADAMÍK
AbstractThis research study used the original Tversky andKahneman (1992) methodology to establish values of thekey prospect theory parameters in samples of Slovakconstruction managers and tertiary students. Mediansample values for the gains elicited in both sampleswere fairly similar to those established by theTversky and Kahneman findings (1992). When the sameestimation techniques and data types are used,parameter values seem fairly similar for the standardstudent population, across developed countries atleast. We assume that estimation techniques and data* * Vladimír BALÁŽ, Prognostický ústav Slovenskej akadémievied v Bratislave, Šancová 56, 811 05 Bratislava; e-mail:[email protected]; Viera BAČOVÁ, Ústav experimentálnejpsychológie Slovenskej akadémie vied v Bratislave,Dúbravská cesta 9, 813 64 Bratislava; e-mail:[email protected]; Eva DROBNÁ, Ústav experimentálnejpsychológie Slovenskej akadémie vied v Bratislave,Dúbravská cesta 9, 813 64 Bratislava; e-mail:[email protected]; Katarína DUDEKOVÁ Ústavexperimentálnej psychológie Slovenskej akadémie viedv Bratislave, Dúbravská cesta 9, 813 64 Bratislava; e-mail:[email protected]; Kamil ADAMÍK, Fakultapodnikového manažmentu, Ekonomická univerzita v Bratislave,Dolnozemská cesta 1, 852 35 Bratislava email:[email protected]. 1Článok bol podporený Centrum strategických analýz SAVCESTA.
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types may be more important for determining parametervalues than experimental environments and gender orexperience of the participants.
Keywords: prospect theory, decisions under risk and uncertainty,behavioural economics.
JEL Classification: D01, D03, D81
Introduction: Decisions under risks in the expectedutility and prospect theory
In 1979 Daniel Kahneman and Amos Tversky publishedtheir first version of the prospect theory. The theoryimmediately attracted attention by researchers inbehavioural science. In 2002 Daniel Kahneman wasawarded the Nobel Prize in economics for his work onthe psychology of judgment, decision-making andbehavioural economics (Amos Tversky would have, nodoubt, shared the prize with Kahneman, but died in1996).
The prospect theory can be viewed as an extensionof the expected utility theory, which has dominatedeconomic thought on decision-making on micro-level forover seven decades. John von Neumann and OskarMorgenstern (1944) unified concepts of marginalutility and diminishing marginal utility into theexpected utility theory. The expected utility theorymarries concepts of rationality and risk aversion.According to the von Neumann and Oskar Morgensternpeople frame their economic decisions in terms ofgambles and construct their utility functions on (i)magnitudes of potential outcomes (whether pecuniary ornon-pecuniary), (ii) probabilities of potentialoutcomes, and (iii) risk preferences.
The prospect theory overlaps with the expectedutility theory in many areas but differs in being
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concerned with bounded rationality. There are keysimilarities between these two theories: Both theories consider expected utility to be a
product of utility and probability of the outcome.The prospect theory replaces ‘utility’ with‘prospect’. The term ‘prospect’ accentuatesuncertainty of the outcome.
Both the expected utility theory and the prospecttheory accept neoclassical assumption onequilibriums. They agree that decisions taken byeconomic agents (who maximise their benefits) aimat achieving optimal and/or satisficing solutions.
The expected utility and prospect theories alsoagree about assumptions on non-linear valuating(potential) outcomes.
The expected utility theory refers to basicassumptions by neoclassical economy on rationaleconomic agents, who maximize their benefits. Theprospect theory does not dispute maximizationefforts, which underlie decisions processes.Computation of potential outcomes (prospectsinstead of utilities), however, is defined inrather different way in the prospect theorycompared to the expected utility theory (via addingmore parameters to computation processes), but themodel is still essentially similar.
As for the above mentioned assumptions the prospecttheory is part of the mainstream economic thought.However, there are a certain number of assumptionswhere the prospect theory departs from the expectedutility theory. The most important differences betweentwo theories refer to (i) different weights assignedto positive and negative outcomes by the decisionmakers; (ii) non-linear weights assigned to small, andmedium and large probabilities; (iii) assumption onreference points (people consider changes in utility
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rather than absolute total of utility), and (iv)concept of rank-dependent utility models. Let’sbriefly examine major differences between the twotheories: The expected utility theory actually uses just one
parameter (curvature of the utility function) tocompute value of the expected utility fromprobability and value of the bet. The prospecttheory includes more parameters for computation ofutilities of the potential outcomes (prospects):loss aversion and non-linear weighting objectiveprobabilities. The prospect theory thus extendscomputation of the maximising processes to cases,which the classical expected utility fails toexplain. The prospect theory therefore provides amore general framework for explaining decision-making processes. The expected utility theory, infact, is a special case of the prospect theory,when (i) there is no difference between valuatinglosses and gains, and (ii) economic agents estimateobjective probabilities smartly and assign decisionweights identical to values of the probabilities.
The expected utility theory assumes equal treatinggains and losses by the decision makers. In otherwords, gain 1000 euros and loss 1000 euros generateutilities with the same magnitudes, but withdifferent signs. The prospect theory assumes thatpsychological costs of losses are in average about2.25 times higher (Kahneman and Tversky 1992) thanutility from the same amount of gains.
The expected utility theory assumes that peopleconsider objective probabilities when making theirdecisions. If the outcome A has probability 0.1 andthe outcome B probability 0.9 then the outcome B isnine times more important for a decision maker thanthe outcome A. That seems a quite clear, but infact, real life behaviour is different. Why so many
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people gamble with their money (in case oflotteries) or health (in case of smoking anddrinking), if the probability plays against them?The prospect theory assumes that decision weightsare assigned to objective probabilities in non-linear way. The people use to overweight lowprobabilities, and underweight moderate and largeones. Overweighting low probabilities explainswidespread interest in lotteries, but alsopopularity of buying insurance against terroristattacks in the air travel. Underweighting mediumand large probabilities is behind low willingnessto stop smoking and/or drive more safely. Like theexpected utility theory, the prospect theoryproposes that sure wins (risk-free gains) areconsidered more valuable than risky ones bydecision makers. Once certainty is removed, non-linear weighting probabilities re-emerges.
The expected utility theory assumes that peopleframe their decisions in terms of gambles and thetotal wealth of an individual is starting point forvaluation of the outcomes. The prospect theoryassumes that gambles are framed only in terms ofgains and losses. This assumption is based on factthat the brain relatively quickly adapts to certainlevel of utility. This level is considered referencepoint and changes are considered carriers of thevalue, rather than total wealth. According to theKahneman and Tversky (1979, p. 277) ‘value shouldbe treated as a function with two arguments: theasset position that serves as reference point andthe magnitude of the change (positive or negative)from that reference point’.
Computation of prospects: formulas and parametervalues
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The expected utility theory replaced expected valueswith the expected utilities. The prospect theoryfurther refined assumptions on reference points andprobability weighting and replaced utilities withprospects:
The expected value is product of probability andvalue: E(V) =p * v; where p = probability and v =value.
The expected utility is product of probabilityand utility: E(U) = p * u(x); where p =probability and u(x) = utility.
The prospect is product of decision weights andvalue of the potential outcome: prospect: P =w(p) * v(x), where w(p) = weighted probability =decision weight, and v(x) = value of the potentialoutcome x. The value of the potential outcome isset as v(x) = xα, for x 1, and v(x) = -(-x)α, forx < 1, where average = 2.25. Transformation ofprobabilities to decision weights is given byformula:
.
Comparison of expected value, expected utility andprospect concepts points to evolution of the economicthought in the microeconomics. The expected valueconcept considers a fully rational individual whoevaluates potential outcomes according to theirobjective values and probabilities. The expectedutility theory is more realistic as it acceptsexistence of the risk attitudes in human beings. Theseare expressed in curvature of the utility function.Individual curvatures of the utility functions areexpressed via additional parameter (e.g. α), whichreflects diverse risk attitudes by decision makers.
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The prospect considers two more psychological traits:loss aversion (expressed via the parameter) and non-linear transformation of objective probabilities todecision weights (expressed via the γ parameter).The prospect theory had evolved over time. The
original prospect theory was based on transformationof individual probabilities to decision weights. Thecumulative prospect theory assumes that people most considerextreme outcomes of the choices. Cumulativeprobabilities (which take into account extremeoutcomes) are transformed to decision weights insteadof individual ones. There were many attempts to refineseveral proposition of the prospect theory. The thirdgeneration of the prospect theory (Schmidt et al2008), for example, extends the cumulative prospecttheory by allowing reference points to be uncertain(instead of equal to 0), while decision weights arespecified in a rank-dependent way.
Psychological properties of the weighting functionFurther research in weighting probabilities
(Gonzales and Wu 1999) pointed to some interestingproperties of the weighting function. Weighting maycode two independent, yet intertwined psychologicaltraits: (a) discriminability, and (b) attractiveness.
Discriminability reflects subject’s knowledge aboutthe likely outcomes of the decisions and abilityto discriminate probabilities of the likelyoutcomes. The more an individual knows aboutcertain issue, the more precise discriminationof decision weights. An expert on horse races,for example, may give more realistic estimateson probability by a specific horse winning therace, than an amateur visitor. Thediscriminability is reflected in curvature ofthe weighting function. The more closely thecurve resembles the straight line, the higher
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ability to discriminate probabilities. The step-like function signals low expertise inestimating probabilities and is typical, forexample, for children (the probability is eitherhigh or low, but no precise estimate can beprovided). A migrant can estimate theprobability of getting a job in his field; ameteorologist can estimate chances of goodweather in next three days.
Attractiveness refers to interpersonal (and alsointra-personal) differences in assigningdecision weights to certain probabilities and isexpressed in elevation of the weightingfunction. If one chance domain seems moreattractive than another one, the first domainreceives higher decision weights. The more anindividual wishes certain outcome, the higherweights are assigned and the higher elevation ofthe weighting function. Example: the more I wishto get an employment with a foreign company, themore I would overestimate probabilities ofgetting such job.
Gonzales and Wu (1999) used the two-parameterweighting function to capture effects of thediscriminability and attractiveness. Discriminabilityis expressed by the γ parameter, while theattractiveness by the δ parameter of the weightingfunction:
.
The γ essentially controls the degree of curvature,while the δ essentially controls the elevation of thecurve. The two traits, however, are inter-related. Theless attractive the outcome, the less likely is togenerate interest by the decision maker. A bookmaker
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may successfully estimate probabilities for horseraces, but find himself disinterested and/or unableestimating likely winner of the Eurosong contest. Asnoted by Gonzales and Wu (1999, p. 161) ‘we like whatwe know and we know what we like’.
Eliciting parameters of the prospect theoryProspect theory is central to Kahneman and Tversky
work and, of course, generated a lot of discussionsand controversies. Since 1992, when the cumulativeprospect theory was published, the theory was subjectto many tests and examinations. Most research aimed atadditional measurement of parameters in the value andweighting functions. Table 1 summarises findings byseveral key studies in this field. How the parametersare measured and estimated? Comparison of thecertainty equivalents and actual values of theoutcomes in experiments is the most common method forestablishing parameters of the value and weightingfunctions. Imagine an individual enters a fair game(50:50 chance). The option (A) gives 50% chance to win50 euros and 50% chance to lose 50 euros; the option(B) provides for declining game and accepting somesure reward instead (= certainty equivalent), say 25euros. Amount of the certainty equivalent indicates,whether the individual is fully rational and risk-neutral (if yes, s/he demands certainty equivalent 50euros for declining the game), or risk-seeking (inthis case certainty equivalent is higher than 50euros), or risk-averse (which implies certaintyequivalent lower that 50 euros). The median certaintyequivalent for the abovementioned game is 36 euros(Kahneman and Tversky 1992). Parameters of the valueand weighting functions are estimated from a set ofgames with different probabilities (p = 0.01; 0.05;0.10; ... 0.95; 0.99), and values of potentialoutcomes and respective certainty equivalents.
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Selected studies (Table 1) in the prospect theoryindicate that:a) most estimates of the value function parameter α
(curvature of the utility function) lie in interval0.52 – 1.00 i.e. that most people are risk averse;
b) most estimates of the weighting function parameterγ lie in interval 0.60 – 0.71 for gains and 0.51 –0.76 for losses. It means that the decision weightstend to significantly differ from the subjectiveprobabilities for most people.
Most research on the prospect theory took place indeveloped countries. Students with in high-qualityuniversities are typical sample members inexperiments. Majority of research studies uselaboratory experiments with student populations toelicit the risk aversion –, loss aversion and theweighting function parameters. Experiments take placein controlled environments and most participants areundergraduate and postgraduate students of psychology,economics and finance, who may have good chances tounderstand the logics behind the experiment. Numbersof participants varied from 10 (Gonzales and Wu 1999)to 420 (Wu and Gonzales 1996). The choice ofcontrolled environment (laboratory) and studentspopulations is often criticised as distant from realworld. Homogeneity of the sample is important foravoiding potential bias resulting from diverse socio-economic and socio-demographic backgrounds of thesubject, however in reality individual decisions aresignificantly impacted by a set of socio-economic andsocio-demographic factors (age, education, income,employment status, etc.).
Overuse of the student population also raisesquestions about transferability of the prospect theoryfindings to real world. Would parameter estimates besimilar across diverse cultural environments and
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particular population groups? Are these parameters forexample sensitive to gender and effects of perceivedcompetence and/or life experience?
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Table 1: Selected studies estimating parameters of theprospect theory
SourceValue
function(α)
Weightingfunction
(γ)
Lossaversion
()
Sample characterand size
Tversky and Kahneman (1992)
0.88 0.61 2.25 25 students
Tversky and Fox (1995) 0.88 (0.69) x 141 students
Wu and Gonzales (1996)
0.52 0.71(0.68) x 420 students
Wu and Gonzales (1999)
0.49 0.68 x 10 students ofpsychology
Abdellaoui (2000) 0.89 0.60
(0.60) x 64 students
Bleichrodt and Pinto (2000)
0.77 0.67(0.55) x 51 students of
economics
Kilka and Weber (2001)
0.76-1.00
(0.30-0.51) x 55 students of
financeAbdellaoui et al. (2003)
0.91 (0.76) x 52 students
Stott (2006) 0.19 0.96 x 96 students
Abdellaoui et al (2008) 0.86 0.60 2.61
48 students ofmathematics and
psychologyAbdellaoui et al (2011) 0.79 0.73 2.47 48 students of
managementAuthors (2013) 1.02 0.58 2.50 19 construction
managers
Authors (2013) 1.00 0.62 2.10
96 students ofeconomic andpsychology
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Notes: Value of the parameter of the weighting function forlosses in parenthesis.
We tried to address the abovementioned researchquestions via two experiments aimed at elicitingprospect theory parameters in Slovakia. The SlovakRepublic is a less developed EU and OECD membercountry (median net monthly wage was 514 euros in2012). Prospect theory assumption has never beenexamined in Slovakia so far. We designed experimentsfor two population groups and different researchenvironments: (i) experiment with sample of 19construction managers was performed in the field,while (ii) experiment with sample of 96 Universitystudents was done in controlled laboratoryenvironment. We structured samples in such way as tolook at potential differences in parameter values interms of gender and previous experience with riskyevent (labour and/or student migration). Researchquestions were addressed by two hypotheses:
H1: The prospect theory tests risk attitudes under‘pure risk’ gambles. Distributions of the ‘generalrisk’ trait seem fairly stable across population(Weber et al 2002, Zuckerman and Kuhlman 2000), fordeveloped countries at least. The prospect theoryparameters elicited with the same methodology shouldbe similar across various countries, so the parametervalues in Slovakia would not differ from the resultsso far.H2: Risk taking attitudes examined via the prospecttheory are not impacted by gender and previousexperience and/or perceived competence. There wouldnot be substantial difference in the prospect theoryparameters for males/females and migrants/non-migrants.
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Research design
Methods of parameter estimates and research toolIn the prospect theory estimates of parameters vary
with the type of data used, estimation techniques, andnumber and experience of subjects. Original researchon the weighting function estimated the one-parameter(γ) form of the function and used the cash equivalentdata to fit the function w(p) = pγ/[pγ + (1-pγ)]1/γ (Tverskyand Kahneman 1992). Other researchers also consideredone-parameter function, but differed in terms ofestimation techniques (nonlinear regression of cashequivalents versus fitting stochastic choicefunctionals) and data uses (choice versus cashequivalent) (Abdellaoui, 2000; Tversky & Fox, 1995; Wu& Gonzalez, 1996). Gonzales and Wu (1999) used themedian data and the individual subject data toestimate two-parameter weighting function: w(p) =δpγ/[δpγ + (1-pγ)]γ. All studies found broadly similarparameter estimates (Table 1), but also considerablediversity at the level of individual subjects.Diversity at the individual data translates todifferences in parameter estimates computed frommedian and individual data. The same finding appliesto the value function parameter (α), While moststudies found median estimates of the α parameter ofthe power function in interval 0.77-1.00, individual-level data use to account for standard deviations over45% means and 55% medians (Abdellaoui et al 2007).
We designed an online-based software whichreplicated Tversky and Kahneman (1992 procedures foreliciting prospect theory parameters. The parameters αand γ were elicited from the median cash equivalentsfor the gains only (we did not consider gambles withnegative outcomes). An overwhelming majority ofstudies used median fitted parameters and student
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populations to establish parameter estimates (see Foxand Poldrack 2008 for an excellent review of theprospect theory parameters). Medians of the cashequivalents were entered into a non-linear regressionassuming a power value function (v(x) = xα), and either(i) single-parameter weighting function w(p) = pγ/[pγ + (1-pγ)]1/γ or (ii) two-parameter weighting function: w(p) =δpγ/[δpγ + (1-pγ)]γ.
The Levenberg-Marquardt algorithm (based on thedamped least-squares method) was applied forestimating the prospect theory parameter values. Thealgorithm provides a numerical solution to the problemof minimising a non-linear function over a space ofparameters of the function and is frequently used inthe least squares curve fitting (Levenberg 1944). Theparameter values were estimated from the median samplevalues, individual-level medians and individual means(Table 2).
Sample size and structureData were collected in two samples. The researchers
firstly provided participants with introductorytraining. Participants were connected to the online-based software tool and performed their tasks on thenotebooks. All data were automatically recorded to thecentral database.
The sample 1 consisted of 19 construction managers(university graduates) aged 27-32. The sample wasdominated by young and relatively well paid men withabove-average income (there were just four females inthe sample). Seven out of total construction managershad migration history and previously worked in the UK,USA, Austria and the Netherlands. The sample 1participants were not paid for their participation.Experimental procedures were performed in the field.
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The sample 2 consisted of 96 undergraduate andpostgraduate students (76 women a 20 men aged 20-26)of the economics (the University of Economics), andpsychology and pedagogics (Comenius University inBratislava). Nineteen participants had a migrationhistory, they mostly participated in the ERASMUSexchange and/or had at least 6 months workingexperience in the UK, Austria, Germany, USA and othercountries. Students were paid 10 euros for theirparticipation. Reimbursement for participantscorresponded with about median net daily income ofSlovak students. Experimental procedures used the sameonline-based software tools as in sample 1, but tookplace in the computer rooms of the abovementionedUniversities.
ResultsSample 1 generated values α = 1.02, γ = 0.58 and
= 2.50. Median value of the γ and parameters werequite close to that by Tversky and Kahneman (1992),while the α value was somewhat higher. Males seemedmore risk seeking than females (respective values ofthe α parameter were 1.021 and 1.018), and also weredoing better in discriminating probabilities(respective values of the γ parameter were 0.578 and0.529). Migrants accounted for somewhat lower levelsof the risk-aversion. Median sample value of the powerfunction (α parameter) was 1.018 for migrants and1.015 for non-migrants. The migrants, however,accounted for slightly lower levels of the lossaversion. The median value of the parameter was 2.23for migrants and 2.50 for the non-migrants. Thehighest differences between the two groups were inmedian values of the γ parameter: 0.660 for migrantsand 0.529 for non-migrants. Migrants seemed to dobetter in setting decision weights closer to objectiveprobabilities when transforming probabilities to
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decision weights. This observation was taken from realworld, and is not directly comparable with samples ofstudents examined in controlled environments. Thesample size also was too small to claim representativeresults. It however, is interesting that median valuesof the key parameters in the total sample ofconstruction managers (α = 1.00, = 2.50, and γ =0.58) were not far from values established by theTversky and Kahneman (α = 0.88, = 2.25, and γ =0.61. High standard deviations for the individualmeans of α, γ, parameters indicated very diverseattitudes to risk-taking, loss-aversion andprobability weighting in sample 1 as well. However,all studies on the prospect theory parameters foundconsiderable variation at individual level (see Foxand Poldrack 2008 for discussion).
Most findings from sample 1 were replicated insample 2. The sample 2 generated values α = 1.00, γ =0.62, and = 2.10. These values also were quite closeto those estimated by the Tversky and Kahneman (1992).Median sample values for particular population groupindicated that males were rather more risk seekingthan females (respective values of the α parameterwere 1.007 and 1.002) and also accounted for betterdiscriminating probabilities (respective values of theγ parameter were 0.626 and 0.480). Migrants accountedfor somewhat higher levels of the loss-aversion. Themedian value of the parameter was 2.30 for migrantsand 2.10 for the non-migrants. High heterogeneity inindividual vales of α, γ, parameters (attested byhigh standard deviations) was confirmed for sample 2.
High heterogeneity in individual values of γparameter was reflected in very diverse shapes of theweighting function (Figures 1-4). Figure 1 comparesshapes of weighting functions for gains establishedvia median cash equivalents by Tversky and Kahneman
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(1992) (γ = 0.61) and authors (γ = 0.62). Thefunctions have typical shapes of inverse S.
Figure 2 exemplifies step-like shape of theweighting function with low values of γ parameter(participant no 5 in sample 1, γ = 0.262). The step-like function indicates less sensitivity to changes inprobability than the linear function, except near 0and 1. Low values of γ associate with the poor abilityto discriminate probabilities and ‘corresponds to thecase in which an individual detects ‘‘certainly will’’and ‘‘certainly will not,’’ but all other probabilitylevels are treated equally’ (Gonzales and Wu 1999:137). For values of the γ parameter higher than 1 theshape of the weighting function resembles S. Values ofthe γ parameter higher than 1 are rather scarce. Wefound five such participants in sample 2 (96 students)and none in sample 1 (19 construction managers).
Figure 3 displays shape of the weighting functionfor participant no 37 in sample 2 (γ = 1.579). Finallyweighting functions with γ parameters close to 1indicate good ability to estimate probabilities andtheir shapes blend with straight lines assumed inlinear weighting (Figure 4, participant no 2 in sample2, γ = 0.898). Linear or near-linear shapes of theweighting functions indicate high sensitivity torelatively small changes in odds and are sometimesfound for certain professionals gambling in theirdomain of expertise (Thaler and Ziemba 1988).
Next we used sample medians and applied the two-parameter weighting function: w(p) = δpγ/[δpγ + (1-pγ)]γ toelicit values of the δ parameter in samples 1 and 2.The δ parameter of weighting function refers toelevation of the weighting function due assigninghigher decision weights to certain probabilities whichseem attractive to decision maker.
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In sample 1 the total sample median value of δparameter was 1.0. Values for the respectivesubpopulations were 0.797 for males, 0.870 forfemales, 0.943 for migrants, and 0.870 for non-migrants.
In sample 2 the total sample median value of δparameter 0.753. As for the subpopulation medianvalues, these were 0.876 for males, 0.701 forfemales, 0.762 for migrants, and 0.749 for non-migrants.
Most values of the δ parameter fall into interval0.6-1.00. Values of the δ parameter found in ourresearch corresponded with those established byAbdellaoui (2000) (0.65), Abdellaoui et al (2005)(0.77), Tversky and Fox (1995) (0.77) and Stout (2006)(1.00).
Higher values of δ are reflected in higherelevation of the weighting function and associatedwith less risk aversion for gains and more riskaversion for losses. Sample median values of α and parameters seem to confirm this pattern formales/females and migrants/non migrants in sample 2 inparticular. Males and migrants found gambling moreattractive.
Values of δ lower than 1 indicate that the decisionweights of complementary events sum to less than one(w(p) + w(1p)˂1) for a typical decision maker (Fox andPoldrack 2008: 156). This property is known assubcertainty (Kahneman and Tversky, 1979 ) and issatisfied whenever δ ˂ 1.
Experiments with samples 1 and 2 indicated that theprospect theory parameters elicited with the samemethodology in the Slovak samples as a whole did notdiffer from the results found in the other countries(Hypothesis 1).
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Table 2: Estimates of the prospect theory parametervalues in the Slovak samples
19 construction managersin Slovakia 96 students in Bratislava
Datatype
Medianvalue
Individual-level
median
Individual-level mean
Medianvalue
Individual-level
median
Individual-level mean
All subjectsValue function(α)
1.021(0.008)
1.035 1.042(0.059)
1.003(0.005)
1.016 1.027(0.046)
Weighting function(γ)
0.578(0.040)
0.571 0.541(0.202)
0.623(0.033)
0.499 0.578(0.423)
Loss aversion()
2.500 2.300 2.584(1.063) 2.100 2.300 2.404
(1.021)
MalesValue function(α)
1.021(0.008)
1.035 1.049(0.050)
1.007(0.004)
1.013 1.032(0.045)
Weighting function(γ)
0.578(0.040)
0.571 0.532(0.197)
0.656(0.033)
0.626 0.642(0.414)
Loss aversion()
2.500 2.500 2.713(1.010) 2.167 2.033 2.297
(1.217)
FemalesValue function(α)
1.018(0.011)
1.036 1.014(0.090)
1.002(0.005)
1.016 1.026(0.047)
Weighting function(γ)
0.529(0.041)
0.546 0.579(0.247)
0.596(0.034)
0.480 0.561(0.426)
Loss aversion
1.767 1.800 2.100(1.275)
2.100 2.300 2.433(0.970)
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()MigrantsValue function(α)
1.015(0.009)
1.015 1.045(0.066)
1.002(0.004)
1.016 1.033(0.051)
Weighting function(γ)
0.660(0.064)
0.621 0.594(0.203)
0.681(0.039)
0.597 0.605(0.422)
Loss aversion()
2.233 2.300 2.586(1.275) 2.300 2.700 2.514
(1.253)
Non-migrantsValue function(α)
1.018(0.011)
1.045 1.040(0.579)
1.001(0.005)
1.016 1.026(0.045)
Weighting function(γ)
0.529(0.041)
0.478 0.511(0.204)
0.601(0.038)
0.485 0.571(0.426)
Loss aversion()
2.500 2.400 2.583(0.982) 2.100 2.300 2.377
(0.936)
Notes: Standard deviations in parenthesis. All valuescomputed from the single-parameter weighting function.
Testing prospect theory parameters for gender andmigration experience
Parameter estimates computed both from the mediansample data and individual-level data found that malesaccounted for the higher values of the γ parameterthan females and migrants than non-migrants. As forthe α and parameters, no clear pattern wasestablished.
Sample 1 (construction managers) was too small fortaking reasonable tests on differences in parameters
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stemming from gander and/or previous migrationexperience. In Sample 2 (Slovak students) theabovementioned differences were examined via the Mann-Whitney U-test:
As for the gender, the test values establishedfor the parameters α (Z = -0.140, sig. 0.889), γ(Z = -1.015, sig. 0.310), and (Z = -0.629,sig. 0.529) indicated no significant differencesbetween males and females.
As for the previous migration experience, thetest values established for the parameters α (Z= -0.372, sig. 0.710), γ (Z = -0.352, sig.0.730), and (Z = -0.369, sig. 0.712) indicatedno significant differences between migrants andnon-migrants.
We accept Hypothesis 2 that there is no substantialdifference in the prospect theory parameters for malesand females, and migrants/non-migrants.
Conclusions
This research study used the original Tversky andKahneman (1992) methodology to establish values of thekey prospect theory parameters in samples of Slovakconstruction managers and tertiary students. Mediansample values for the gains (based on cashequivalents) elicited in both samples were fairlysimilar to those established by the Tversky andKahneman findings (1992), but also those by Abdellaouiet al (2008). Parameter values are sensitive tomethods of estimation technique and data use. When thesame estimation techniques and data types are used,parameter values seem fairly similar for the standardstudent population, across developed countries atleast (Hypothesis 1). Interestingly, similar values of
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α, γ, and δ parameters were found in our samples 1and 2, which differed in terms of (i) age, occupation,gender and income structure, and (ii) experimentalenvironments (field work versus laboratories). Weassume that estimation techniques and data types maybe more important for determining parameter valuesthan experimental environments andgender/occupation/income structure of sample. Thisassumption, however, must be verified on largersamples.
There is an extensive literature on genderdifferences in the broader field of research on risk.A meta-analysis of 150 studies (Byrnes, Miller, andSchaffer 1999), for example, found that men were morerisk tolerant in 14 out of 16 observed types of riskbehaviour. Individual willingness to take risks may berelated to optimism and overconfidence (Lovallo andKahneman 2003). Individuals may account for positivebeliefs about their personal knowledge andcapabilities when dealing with risks. Most research onindividual risk-taking focuses on financial decisions,reflecting the prominence of the topic and theavailability of data from financial markets andinstitutions. Almost all research studies on financialrisk-taking indicate higher risk aversion in women(e.g., Bernasek and Shwiff 2001; Schubert et al.1999). Studies of financial risk-taking, however, aremade in a competence-informed context, where priorknowledge is brought to play. Studies of financialrisk-taking cannot explain gender differences in a‘pure chance’ risk context, such as gambling. Studiesexamining gender attitudes to risks in laboratoryenvironments (Daruvala 2007, Ronay and Kim 2006) foundno significant differences in risk-taking by males andfemales. The procedure used to derive parameters ofthe prospect theory is free of the competence effectsand simulates ‘pure risk’ environment. Parameter
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values should not be impacted by perceived competenceand/or previous experience and account for similarlevels across selected socio-demographic groups. Wetested this hypothesis for gender and previousmigration experience. In our research study (sample 2)we found the median sample values and median ofindividual values of the α parameter higher for malesthan females. The difference, however, wasinsignificant.
The γ parameter essentially measures ability toestimate probabilities of events. This parameter couldbe affected by previous experience with various eventswith uncertain outcomes (such as weather forecasting,horse race betting or investing on financial markets).There is some evidence that shape of the probabilityweighting function is source dependent (Kilka andWeber 2001) and determined by a subject’s ability todiscriminate probabilities (Fox et al 1996, Thaler andZiemba 1988). Migrants had opportunities to live/studyin foreign countries. Any migration is a riskyundertaking with uncertain outcomes. It could beassumed that migrants may have better training andability for estimating probabilities, but this abilitymay be related to migration risks only. In ourresearch males and migrants seemed to account forhigher values of the γ parameter, but this differencealso was found insignificant on 0.05 level.
Our research also has several importantlimitations. The Sample 1 was too small to examinedifferences related to particular socio-demographicgroup. The Sample 2 accounted an adequate size, butwas dominated by females (76 out of total 96) and non-migrants (77 of total 96). Further research mayconsider samples of higher size and better structurein terms of gender and migration experience.
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Figures 1-4: Examples of shapes of the weighting function
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