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A shor t test for over confidence and pr ospect theor y An. exper imental validation,David Pe n ab Anxo Calvoc Manel Antelod. This ver sion August 2014, Tw o r elevant ar eas in the behavioral economics ar e pr ospect theor y and over confidence Many tests. ar e available to elicit their differ ent manifestations utility cur vatur e pr obability w eighting and loss. aver sion in pr ospect theor y over estimation over placement and over pr ecision as measur es of. over confidence Those tests ar e suitable to deal w ith single manifestations but often unfeasible in. ter ms of time to be per for med t o deter mine a complet e psychological pr ofile of a given r espondent. In this paper w e pr ovide tw o shor t tests based on classic w or ks in the liter atur e to der ive a complete. pr ofile on pr ospect theor y and over confidence Then w e conduct an exper imental r esear ch to. validate the tests r evealing they ar e br oadly efficient to r eplicate the r egular r esults in the liter atur e. Nonetheless some enhancements are suggested as w ell Finally the exper imental analysis of all. measur es of over confidence and pr ospect theor y using the same sample of r espondents allow s us to. pr ovide new insights on the r elationship betw een these t w o ar eas. Keywords Exper imental economics over confidence pr ospect theor y behavior al finance. utility measur ement over estimation over placement over pr ecision. JEL Classification D03 D81 C91, The author s want to thank Paulino Mart nez and Xos Manuel M Filgueir a for their ver y valuable support in. the exper iment design Author s also want to thank Juan Vilar and Jose A Vilar for technical assistance Manel. Antelo acknowledges financial aid fr om the Galician autonomous gover nment Xunta de Galicia thr ough the. pr oject Consolidaci n e estr utur aci n GPC GI 2060 An lise econ mica dos mercados e instituci ns AEMI. a Gr upo BBVA and Depar tament of Financial Economics and Accountancy Univer sity of A Cor una Campus de. Elvi a s n 15071 A Cor u a Email david peon udc es. b Cor responding author, c Depar tament of Financial Economics and Accountancy University of A Cor una Campus de Elvi a s n 15071 A. Cor u a Email anxo calvo udc es, d Department of Economics Univer sity of Santiago de Compostela Campus Nor te 15782 Santiago de.
Compostela Spain E mail manel ant elo usc es,1 I NTRODUCTION. Behavior al biases have been suggested to explain a w ide r ange of mar ket anomalies A. r ecent and gr ow ing field is the analysis of over confidence effects on cr edit cycles e g. R theli 2012 An inter esting step for w ard w ould be to obtain exper imental evidence of. w hether behavior al biases by par ticipants in the banking industr y could feed a r isk seeking. behavior that explains up to some extent the excessive lending by r etail banks To that. pur pose w e or ganized a ser ies of exper imental sessions that w er e divided in tw o par ts The. fir st par t w as a set of questions devised to det er mine the psychological pr ofile based on. pr ospect theor y and over confidence of each par ticipant The second par t w as a str ategy. game designed to r eplicate in an exper imental setting the basics of the decision making. pr ocess of a bank that gr ants cr edit to costumer s under conditions of r isk and uncer tainty. Results of the second par t ar e analyzed elsew her e Pe n et al 2014. The main motivation of this paper is to design for the fir st par t of the exper iment some. simple tests on over confidence and pr ospect theor y We base our w or k on some classic tests. in the liter atur e How ever tr ying to r eplicate them completely w ould be unfeasible in ter ms. of time to be per for med Only to illustr ate the classic w or k by Tver sky and Kahneman. 1992 r epor ts that subjects in their exper iment par ticipated in thr ee separ ate one hour. sessions that w er e sever al days apar t p 305 in or der to complete a set of 64 pr ospects. w hile par ticipants in the tests for over confidence by Moor e and Healy 2008 spent about. 90 minutes in the labor ator y to complete 18 r ounds of 10 item tr ivia quizzes We need. shor ter tests for our exper iment in a w ay the number of items r equir ed for estimation. pur poses ar e r educed but they do not compr omise efficient r esults Indeed the concer n to. design tests that ar e shor ter and mor e efficient is a classic in the liter atur e e g Abdellaoui. et al 2008 since they w ould enhance the scope for application of behavior al theor ies. Thus the objective of this r esear ch is tw ofold Fir stly the ar ticle is devoted to explain how. w e devised some shor t tests to obtain a basic profile in ter ms of pr ospect theor y and. over confidence of a given individual and the liter atur e that suppor ts our choices Thus on. one hand w e follow Moor e and Healy s 2008 theor y on the thr ee differ ent measur es of. over confidence and design shor ter ver sions of Soll and Klayman s 2004 and Moor e and. Healy s 2008 tests to elicit those measur es at the individual level On the other in r egar ds. to pr ospect theor y w e follow Rieger and Wang s 2008 nor malization of pr ospect theor y. Kahneman and Tver sky 1979 assuming classic par ametr ic functions in the liter atur e. w hile for test design w e mer ge some featur es of Kahneman and Tver sky s 1992 elicitation. method and the appr oach to make an efficient test with a minimum number of questions by. Abdellaoui et al 2008 The second objective of this r esear ch is to validate the tests devised. To such pur pose they w er e implemented to a sample of 126 under and postgr aduate. students in the Univer sity of A Cor una UDC dur ing October 2013 The exper iment w ill be. deter minant to assess the goodness of our tests by compar ing the r esults obtained w ith the. r egular r esults in the liter atur e, Thr ee main contr ibutions of this paper ar e in order Fir st w e design tw o shor t tests that ar e. able to elicit the thr ee measur es of over confidence over estimation over placement and. over pr ecision as w ell as the complete set of par ameter s in pr ospect theor y namely utility. cur vatur e pr obabi lity w eighting and loss aver sion Second w e conduct an exper imental. r esear ch w ith 126 students to validate the tests In the bulk of this paper w e compar e our. r esults w ith those r egular in the liter atur e Thir d the exper imental analysis of all measur es. of over confidence and pr ospect theor y using the same sample is something that to the best. of our know ledge w as not done befor e This allow s us to pr ovide new insights on the. r elationship betw een these tw o r elevant ar eas in the behavior al liter atur e. The str uctur e of the ar ticle is as follow s In Section 2 after br iefly intr oducing theor y and. state of the ar t w e descr ibe how our tests w er e designed fir stly on over confidence and then. on pr ospect theor y Section 3 discusses the r esults and the r eliability of our tests accor ding. to the exper imental evidence Section 4 tests some hypotheses about the r elationship. betw een demogr aphic pr ior s and behavior al var iables Finally Section 5 concludes. 2 OVERCONFIDENCE AND PROSPECT THEORY T HEORY AND EXPERIMENT DESIGN. 2 1 Overconfidence, The pr evalence of over confidence is a classic in the behavior al liter atur e Moor e and Healy. 2008 identify thr ee differ ent measur es of how people may exhibit over confidence in. estimating their ow n per for mance over est imat ion in estimating their ow n per for mance. r elative to other s over placement or better than aver age effect and having an excessive. pr ecision to estimate futur e uncer tainty over pr ecision. For test design w e follow Moor e and Healy 2008 for sever al r easons Fir st the thr ee. measur es of over confidence have been w idely accepted since then e g Glaser et al 2013. Second they w er e able to make a synthesis of the pr evious debate betw een the cognitive. bias interpr etation and the ecological and er r or models Thir d their model pr edicts both. over and under confidence in tw o manifestations estimation and placement Four th they. ask for fr equency judgments acr oss sever al sets of items of diver se difficulty to account for. the evidence that fr equency judgments ar e less pr one to display over confidence and for the. har d easy effect a tendency to over confidence in difficult tasks and under confidence in. easy ones Finally their tests ar e r eally simple allow ing us to implement an efficient test for. over estimation and over placement that r equir es only a few minutes to per for m it. Over pr ecision r equir es an alter native analysis A classic appr oach is to ask for inter val. estimates Soll and Klayman 2004 as opposed to binar y choices Using binar y choices. causes over estimation and over pr ecision to be one and the same Moor e and Healy 2008. so in or der to avoid confusing them w e study over estimation by measur ing per ceptions. acr oss a set of items w hile over pr ecision is analyzed thr ough a ser ies of questions on. inter val estimates,Test design, The tests w ill consist of a set of tr ivial like questions devised to deter mine the degr ee of. over estimation E and over placement P of each r espondent plus a set of additional. questions w her e subjects ar e asked to pr ovide some confidence inter val estimations. devised to deter mine the degr ee of over pr ecision M of each r espondent. Our test for E and P is a simple ver sion of Moor e and Healy 2008 s tr ivia tests indeed. sever al questions w er e taken fr om their tests 1 Par ticipants ar e r equir ed to complete a set. of 4 tr ivia w ith 10 items each one To account for the har d easy effect tw o quizzes w er e. easy and tw o of har d difficulty Since answ er s to questions involving gener al know ledge. tend to pr oduce over confidence w hile r esponses to per ceptual tasks often r esult in. under confidence Stankov et al 2012 w e asked questions of gener al know ledge w ith a. time limit 150 seconds per tr ivia to have a somehow mixed scenar io Pr ior to solving the. tr ivia par ticipants w er e instr ucted and solved a pr actice question to familiar ize w ith the. exper imental setting Then they took the quizzes When time w as over they w er e r equir ed. to estimate their ow n scor es as w ell as the scor e of a r andomly selected pr evious. par ticipant RSPP 2 Finally they r epeated the pr ocess for the other thr ee r ounds. Over estimation is calculated by substr acting a par ticipant s actual scor e in each of the 4. tr ivia fr om his or her r epor ted expected scor e namely. 1 We thank the author s for pr oviding their tests online they wer e r eally helpful to us We would like to be helpful. to other resear cher s as well the questions in our tests are available at www dpeon com documentos. 2 More specifically they were required to estimate the average scor e of other students here today and in similar. experiments with students of this Univer sity, w her e E Xi is individual i s belief about his or her expected per for mance in a par ticular.
tr ivia test and xi measur es his or her actual scor e i n that test We calculate 1 for each of. the 4 tr ivia and then sum all 4 r esults A measur e E 0 means the r espondent exhibits. over estimation w hile E 0 means under estimation Additional infor mation on the har d. easy effect may be available if similar estimations ar e calculated separ ately for the har d and. easy tasks in or der to see if E is negative on easy tasks and positive on har d ones. Over placement is calculated taking into account w hether a par ticipant is r eally better than. other s For each quiz w e use the for mula, w her e E Xj is that per son s belief about the expected per for mance of the RSPP on that quiz. and xj measur e the actual scor es of the RSPP We calculate 2 for each of the 4 tr ivia and. then sum all 4 r esults A measur e P 0 means the r espondent exhibits over placement w hile. P 0 means under placement Again additional information on the har d easy effect may be. available if similar estimations ar e calculated separ ately for the har d and easy tasks in. or der to see if P is positive on easy tasks and negative on har d ones. Over pr ecision is analyzed thr ough a separ ate set of six questions These tests usually. r equir e confidence inter vals estimations but over confidence in inter val estimates may. r esult fr om var iability in setting inter val w idths Soll and Klayman 2004 Hence in or der. to disentangle var iability and tr ue over pr ecision they define the r atio. M MEAD MAD 3, w her e MEAD is the mean of the expected absolute deviations implied by each pair of. fr actiles a subject gives and MAD the obser ved mean absolute deviation Thus M r epr esents. the r atio of obser ved aver age inter val w idth to the w ell calibr ated zer o var iability inter val. w idth Thus M 1 implies per fect calibr ation and M 1 indicates an over confidence bias. that cannot be attr ibuted to r andom er r or w ith the higher over pr ecision the low er M is 3. Soll and Klayman show that differ ent domains ar e systematically associated w ith differ ent. degr ees of over confidence and that asking for three fr actile estimates r ather than tw o. r educes over confidence With these r esults in mind w e devised our test as follow s Fir st w e. 3 Soll and Klayman s methodology also has its flaws Glaser et al 2013 discuss the difficulty to compare the. width of inter vals and different scales and for var ying knowledge levels. ask par ticipants to specify a thr ee point estimate median 10 and 90 fr actiles Second. since w e can only ask a few questions and the r isks of r elying on a single domain w er e. emphasized w e choose to make a pair of questions on thr ee differ ent domains Thus. questions 1 to 4 ar e tr aditional almanac questions on tw o differ ent domains the year a. device w as invented and mor tality r ates Shefr in 2008 Most studies ask judges to dr aw. infor mation only fr om their know ledge and memor y Soll and Klayman intr oduce a. var iation domains for w hich par ticipants could dr aw on dir ect per sonal exper ience We do. the same in questions 5 and 6 to ask inspir ed by Soll and Klayman about time r equir ed to. w alk fr om one place to another in the city at a moder ate 5 km h r ate. The pr ocedur e w e implement to estimate M is as follow s We use a beta function to estimate. the implicit subjective pr obability density function SPDF of each r espondent Then w e. estimate MEAD and MAD Fir st for each question w e calculate the expected sur pr ise implied. by the SPDF to obtain the expected absolute deviation EAD fr om the median Then the. mean of the EADs for all questions in a domain is calculated MEAD Second for each. question w e calculate the obser ved absolute deviation betw een the median and the tr ue. answ er and then the mean absolute deviation MAD of all questions in a same domain Then. w e calculate a r atio M for each domain Consequently w e have 3 differ ent estimations of the. r atio M could then simply be calculated as either the aver age M avg or the median M med. of the 3 differ ent estimations,2 2 Prospect theory. Pr ospect theor y PT is the best know n descr iptive decision theor y Kahneman and Tver sky. 1979 pr ovide extensive evidence that w hen making decisions in a context of r isk or. uncer tainty most individuals i show pr efer ences that depend on gains and losses w ith. r espect to a r efer ence point and ii for m beliefs that do not cor r espond to the statistical. pr obabilities Thus assume tw o mutually exclusive states of the w or ld s1 and s2 state s1. occur r ing w ith pr obability p 0 p 1 and consider a simple binar y lotter y w ith payoff c1 in. s1 and c2 in s2 c1 c2 PT changes both the w ay utility is measur ed pr oviding a value function. v that is defined over changes in w ealth and the w ay subjects per ceive the pr obabilities. of the differ ent outcomes by applying a pr obability w eighting function w p to the. objective pr obabilities p as follow s, The value function has thr ee essential char acter istics r efer ence dependence diminishing. sensitivity and loss aver sion The pr obability w eighting function makes low pr obabilities. close to both 0 and 1 to be over w eighted The combination of both functions implies a. four fold pat t er n of r isk attitudes confir med by exper imental evidence r isk aver sion for. gains and r isk seeking for losses of moder ate to high pr obability r isk seeking for gains and. r isk aver sion for losses of low pr obability, The value and w eighting functions suggested by Kahneman and Tver sky 1979 ar e able to.
explain that four fold pattern How ever pr ospect theor y as initially defined may lead to a. violation of in betw eenness To avoid this Tver sky and Kahneman 1992 intr oduced. cumulative pr ospect theor y CPT w hich applies the pr obability w eighting to the cumulative. distr ibution function in a w ay Eq 4 becomes, for binar y lotter ies Yet Rieger and Wang 2008 obser ve that not all pr oper ties of CPT. cor r espond w ell w ith exper imental data and that ther e ar e some descr iptive r easons. favor ing the or iginal for mulation of PT Hens and Rieger 2010 The solution they offer. allow s to gener alize pr ospect theor y to non discr ete outcomes and to make it continuous. Their appr oach is computationally easier than CPT it simply star ts w ith the or iginal. for mulation of pr ospect theor y in 4 and fixes the violation of in betw eeness by simply. nor malizing the decision w eights w p so that they add up to 1 and can be inter pr eted again. as a pr obability distribution Hens and Bachmann 2008 The appr oach goes back to. Kar makar 1978 w her e for tw o outcome pr ospects the PT values ar e nor malized by the. sum of the w eighted pr obabilities Thus the nor malized w eights w p ar e calculated as. w her e w p means nor malized w eights accor ding to this so called nor malized pr ospect. theor y NPT NPT has some advantages Fir stly it cur es the violations of state dominance. in lotter ies w ith tw o outcomes and avoids violations of in betw eenness completely Hens. and Bachmann 2008 In addition it is show n that the nor malized PT utility conver ges to a. continuous distr ibution Rieger and Wang 2008 call the r esulting model smooth pr ospect. theor y SPT Finally it is an easier appr oach to compute that in par ticular simplifies the. computation of the loss aver sion par ameter in our questionnair es Consequently r ather. than the cumulative pr ospect theor y mor e fr equently used in the liter atur e NPT is the. appr oach w e w ill follow her e, For elicitation pur poses w e ar e going to use a par ametr ic specification They ar e gener ally. less susceptible to r esponse er r or and mor e efficient than non par ametr ic methods. Abdellaoui et al 2008 in the sense that the latter r equir e mor e questions to be. implemented This is impor tant for a test that r equir es to be simple w ith a shor t number of. questions and that seeks to minimize the possible effects of r esponse er r or s and. misunder standing by the r espondents We choose tw o classic specifications Fir st the. piecew ise pow er function by Tver sky and Kahneman 1992. w her e x accounts for gains if x 0 or losses if x 0 measur es sensitivity to gains. does the same to losses and measur es loss aver sion is the most w idely used par ametr ic. family for the value function because of its simplicity and its good fit to exper imental data. Wakker 2008 Second the classic Pr elec I w eighting function Pr elec 1998 given by. w p exp log p 8, w her e 0 to estimate the pr obability w eighting function w ith decision w eights w p being. subsequently nor malized to w p follow ing NPT, To sum up w e have five par ameter s and to estimate How ever w e must. deal w ith the pr oblem w ith loss aver sion neither a gener ally accepted definition of loss. aver sion nor an agr eed on w ay to measur e it is available In r egar ds to the fir st issue loss. aver sion as implicitly defined by Tver sky and Kahneman 1992 depends on the unit of. payment Wakker 2010 only w hen loss aver sion can be a dimensionless. quantity Alter native inter pr etations of loss aver sion w er e pr ovided see Booij et al 2010. for a discussion but none of them ar e a str aight index of loss aver sion instead they. for mulate it as a pr oper ty of the utility function over a w hole r ange. A second dispute is how to measur e loss aver sion r equir ing to deter mine simulatenously. the utility for gains and losses Some author s pr ovide alter native solutions see for instance. Abdellaoui et al 2008 Booij et al 2010 but the debate is still open We opt for a solution. inspir ed by Booij et al 2010 by picking up all t he quest ions ar ound t he zer o out come. p 130 and by the empir ical finding that utility is close to linear for moder ate amounts of. money Rabin 2000 Thus w e ask for a few pr ospects w ith small amounts of money and. assume 1 to estimate as either a mean or median acr oss pr ospects 4. 4 We are aware this only ser ves as an imperfect solution to a mor e complex pr oblem as an index that is. constructed by taking the mean or median of the r elevant values of x is not an arbitrar y choice Booij et al. 2010 In addition Por and Budescu 2013 discuss some violations of the gain loss separ ability which may limit. the gener alization of results fr om studies of single domain pr ospects to mixed pr ospects. Test design, For par ameter estimation var ious elicitation methods have been pr oposed in the liter atur e.
Our method mer ges some char acter istics of Tver sky and Kahneman s 1992 appr oach to. elicit cer tainty equivalents of pr ospects with just tw o outcomes and Abdellaoui et al s. 2008 pr oposal to make an efficient test with a minimum number of questions Thus the. elicitation method consists of thr ee stages w ith fifteen questions in total six questions. involving only positive pr ospects i e a chance to w in some positive quantity or zer o to. jointly calibr ate and and six questions for negative pr ospects to calibr ate and. using a nonlinear r egr ession pr ocedur e separ ately for each subject Finally thr ee questions. r egar ding the acceptability of mixed pr ospects in order to estimate. Sever al aspects w er e consider ed in all thr ee stages Fir st utility measur ements ar e typically. of inter est only for significant amounts of money Abdellaoui et al 2008 w hile utility is. close to linear for moder ate amounts Rabin 2000 Hence pr ospects devised to calibr ate. and used significant albeit hypothetical amounts of money of 500 1 000 and. 2 000 eur os in multiples of 500 eur os to facilitate the task Abdellaoui et al 2008 Second. only the thr ee questions devised to estimate used small amounts of money for r easons. alr eady descr ibed Since lar ger amounts might affect the per ception of the smaller ones in. the elicitation these thr ee questions w er e asked in fir st or der Finally pr ior to solving any. tr ial r espondents answ er ed a pr actice question Instr uctions emphasized ther e w er e no. r ight or w r ong answ er s Booij et al 2010 but that completing the questionnair e w ith. diligence w as a pr er equisite to par ticipate in the str ategy game Pe n et al 2014 they w er e. about to per for m in the same session w her e they w ould compete for a pr ize. The fir st thr ee questions r egar ding the acceptability of a set of mixed pr ospects w er e then. pr ovided to participants in sequential or der Specifically r espondents w er e asked a classic. question Hens and Bachmann 2008 p 120 someone offer s you a bet on t he t oss of a coin. If you lose you lose X eur What is t he minimal gain t hat would make t his gamble accept able. w her e X took the values 1 10 and 100 eur os in thr ee consecutive iter ations Posed this w ay. all questions to calibr ate loss aver sion set pr obabilities of success and failur e equal to 50. p 0 5 Since w 0 5 0 5 under NPT the answ er pr ovided makes the utility of a gain V. equivalent to the disutility of a loss V Hence for the pow er value function w e have. w her e G means gains L losses and loss aver sion equals the r atio G L w hen in. par ticular if as w e assumed 1 for small amounts of money. In the second stage a set of six questions involving only positive pr ospects w as pr oposed. again in sequential or der Figur e 1 show s one of the iter ations par ticipants had to answ er. Respondents had also time to pr actice a sample question. Inser t Figur e 1 her e, In ever y iter ation par ticipants had to choose betw een a positive pr ospect left and a ser ies. of positive sur e outcomes r ight Infor mation w as pr ovided in numer ical and gr aphical. for m Ever y time a subject answ er ed w hether she prefer r ed the pr ospect or the sur e gain a. new outcome w as pr ovided The pr ocess w as r epeated until the computer infor med the. question w as completed and she could continue w ith another pr ospect The pr obabilities of. success in all six pr ospects w er e differ ent having two questions w ith pr obability of success. 50 and one w ith 99 95 5 and 1 r espectively w hich w as emphasized to avoid. w r ong answ er s 5 Follow ing Abdellaoui et al 2008 to contr ol for r esponse er r or s w e. r epeated the last sur e outcome of the fir st ser ies at the end of each tr ial Then the cer tainty. equivalent of a pr ospect w as estimated by the midpoint betw een the low est accepted value. and the highest r ejected value in the second set of choices Tver sky and Kahneman 1992. emphasize this pr ocedur e allow s for the cash equivalent to be der ived fr om obser ved. choices r ather than assessed by the subject, Finally the thir d stage included a set of six questions involving only negative pr ospects We. pr oceeded similar ly Par ticipants had time to pr actice a sample question We emphasized. ever y now and then that pr ospects and sur e outcomes w er e now in ter ms of losses We also. emphasized that pr obabilities w er e in ter ms of pr obabilities of losing Cer tainty equivalents. w er e estimated similar ly for values in absolute ter ms. 3 EXPERIMENTAL RESULTS GOODNESS OF TEST RESULTS, We or ganized a ser ies of five exper imental sessions dur ing October 2013 in the Faculty of. Business and Economics Univer sit y of A Cor una UDC A sample of students of differ ent. levels and degr ees w as selected To make the call w hich w as open to the tar get gr oups w e. 5 The ser ies of sure outcomes per pr ospect wer e removed fr om two sets following Tver sky and Kahneman. 1992 in spir it the fir st set logarithmically spaced between the extreme outcomes of the pr ospect and the. second one linear ly spaced between the lowest amount accepted and the highest amount rejected in the fir st. set All sur e outcomes wer e r ounded to a multiple of 5 to facilitate the task. got in dir ect contact w ith students to explain w hat the exper iment w ould consist of that. they w ould be invited to a coffee dur ing the per for mance of the tests and that one of the. tests they w ould complete consists of a game Pe n et al 2014 w her e one of par ticipant. per session w ould w in a pr ize of 60 eur os 6 In total 126 volunteer s all of them under and. postgr aduate students par ticipated in the exper iment All sessions took place in a computer. r oom par ticipants in the same session complet ed all tests at the same time each. r espondent in a separ ate computer, Befor e completing the tests subjects signed a consent for m and completed a questionnair e. on demogr aphic infor mation about their a gender b age academic backgr ound about. c level and d degr ee and e pr ofessional exper i ence Then they completed the tests In. w hat estimations for the behavior al var iables is concer ned Table 1 summar izes the basic. univar iate statistics,Inser t Table 1 her e, This section aims to assess the r eliability of the par ameter s that w er e estimated For such.
pur pose w e conduct an analysis to compar e our r esults w ith the r egular r esults in both the. theor etical and empir ical liter atur e We conduct this analysis separ ately for each section. 3 1 Reliability of tests on Overconfidence,Tr ivial t est s indicat or s E and P. Par ticipants completed the four tr ivia in about 15 minutes instr uctions included Ther e. w er e no r elevant incidents r espondents declar ed a per fect under standing of instr uctions. all r esponses w er e coher ent and ther e w er e no missing values of any kind The r esults. suppor t tests w er e designed satisfactor ily for the follow ing r easons. Fir st subjects on aver age exhibited over estimation clear ly and under placement Thus the. aver age r espondent over estimated her per for mance by 2 9 r ight answ er s in 40 questions. a bias per sistent in both easy and har d tests Besides the aver age r espondent consider ed. her self below aver age by 2 7 cor r ect answ er s w ith the bias being mostly attr ibutable to an. under placement in har d tasks These findings ar e consistent with the liter atur e suppor ting. a gener al bias tow ar ds over estimation of our abilities Lichtenstein et al 1982 De Bondt. 6 A classic pr oblem of field exper iments is in r egar ds of their exter nal validity Incentives often impr ove exter nal. validity see Pe n et al 2014 Thus we incor porated the incentive of a 60 eur o prize in the str ategy game while. participants were informed that their r ight to claim the pr ize was conditioned to their diligent behavior in the. behavioral tests They wer e also informed that the check questions in the PT test wer e to be used to identify. those participants that wer e inconsistent in their responses No winner s wer e eventually penalized. and Thaler 1995 Daniel et al 2001 except on easy tasks or in situations w her e success is. likely or individuals ar e par ticular ly skilled Moore and Healy 2008 and a gener al bias. tow ar ds underplacing our per for mance r elative to other s on difficult tasks Moor e and. Small 2007 Table 2 summar izes aver age r esponses out of 10 questions per tr ivia. Inser t Table 2 her e, Second ther e is a str ong cor r elation betw een E and P That is though the biases along the. sample ar e tow ar ds over estimation and under placement par ticipants with the highest. over estimation tend to consider themselves above aver age or at least featur e a low er. under placement and vice ver sa This suppor ts the inter pr etation of over estimation and. over placement as inter changeable manifestations of self enhancement Kw an et al 2004. Finally the tr ivia tests w er e devised to contr ol for the har d easy effect but r esults suggest. w e failed to pr opose pr oper easy tests As w e may see in Table 2 above har d tr ivia tests T2. and T3 had aver age median cor r ect answ er s of 2 29 2 0 and 2 75 3 0 w her e 2 0. cor r ect anw er s may be attr ibuted on aver age only to good luck 7 How ever easier tests T1. and T4 w er e expected to yield cor r ect answ er s of 7 0 to 8 0 on aver age 8 but r espondents on. aver age median only hit the r ight answ er 5 4 5 0 and 5 58 6 0 out of 10 questions This. w ould r epr esent a couple of tests of a medium r ather than easy difficulty for r espondents. In any case r esults ar e good for har d tests and coher ent w ith liter atur e for easy medium. tests since over placement r educes fr om 2 4 in har d tests to about zer o in easy ones w hile. over estimation does not incr ease a gener al bias tow ar ds over estimation is appr eciated. Figur e 2 helps to appr eciate this effect mor e clear ly. Inser t Figur e 2 her e, Most obser vations for the har d tests gr aph on the RHS in Figur e 2 meet the mentioned. tendency tow ar ds over estimation and under placement For tests w ith a medium difficulty. gr aph on the LHS the gener al dr ift upw ar ds is noticeable w hat implies that low er levels. of under placement for easy tests ar e gener al along the sample w hile over estimation is. similar on aver age but w ith less obser vations tow ards higher levels Mor eover the above. mentioned cor r elation betw een over estimation and over pr ecision exists in both instances. 7 Each test consisted of ten questions with five possible answer s each Hence par ticipants had a pr obability of. 20 to hit the r ight answer by chance 2 0 r ight answer s out of 10. 8 Those were the results obtained in a pre test with similar questions perfor med by several volunteer s We. attr ibute the eventual differences between the experiment and the pre test to differ ences in age and exper ience. between both samples Other wise r eader s may also attr ibute it to r esearcher s over confidence. Test on confidence int er vals indicat or M, Par ticipants completed the six questions on confidence inter vals to infer their individual. degr ee of over pr ecision estimator M in about 6 to 8 minutes instr uctions included. Though r esults show a vast tendency tow ar ds over pr ecision that is suppor ted by most. empir ical findings in the liter atur e e g Jemaiel et al 2013 w e ar e concer ned about the. r eliability of the estimations obtained at the individual level. These ar e the main r esults obtained Fir st judges w er e significantly over confident The. aggr egate r esults show a str ong tendency to over pr ecision the 80 confidence inter vals. contained the cor r ect answ er only 38 3 of the time higher than the 14 over confidence. obser ved by Soll and Klayman 2004 for thr ee point estimates but about the same level. than for a r ange estimate Over confidence var ied acr oss domains as expected the low est. degr ee of over pr ecision cor r esponds to the domain w her e par ticipants could dr aw on. per sonal exper ience time to w alk How ever they w er e still over confident 80 inter vals. hit the r ight answ er 62 0 of the time, When the M r atios ar e estimated to account for t he effects of var iability over pr ecision.
becomes even mor e pr evalent almost 75 of r espondents exhibit over pr ecision M 1 in. the domain with the low est level 97 6 in the highest and 97 6 median if a single r atio. per judge is obtained Finally w e use Soll and Klayman s alter native r efinement to estimate. M to see9 over pr ecision is mainly attr ibutable to nar r ow size inter vals Table 3 summar izes. all these r esults,Inser t Table 3 her e, As w e may see w hen M is estimated assuming the median is in the middle of the distr ibution. r ather than using the par ticipant s r esponse denoted M 2 over pr ecision slightly incr eases. This means most r espondents w ith an asymmetr ic SPDF tended to pr ovide median. estimates that r educed the er r or s This r esult is coher ent w ith Soll and Klayman s empir ical. finding that thr ee point estimates r educe over confidence. Though r esults on aggr egate ar e consistent with empir ical liter atur e w e ar e concer ned. about the r eliabi lity of data at the individual level for sever al r easons Fir st ther e is evidence. that some par ticipants did not under stand the instructions Incidents include a r espondent. 9 The or iginal refinement takes the estimates of MEAD and MAD based on the beta function that better fits the. three point estimations by the r espondent Alter natively Soll and Klayman 2004 suggest to measur e MAD. assuming the median is in the middle of the distribution They denote M 3 the fir st r atio and M 2 the second one. w ith missing r esponses minimum and maximum boundar ies sw apped answ er s pr ovided. in a differ ent or der than r equir ed and median estimations identical to a boundar y 10 In. futur e r esear ch w e suggest to ask par ticipants to fill some boxes in the or der low er bound. median upper bound Accor ding to Soll and Klayman 2004 if or der of estimates has. effects they ar e complex ones p 311 w hich suppor ts our suggestion that a specific or der. w ill not bias the r esults but helps r espondents to better under stand the task. The second r eason w hy w e ar e concer ned about r eliability of data is because individual. estimations of M ar e highly var iable depending on the r efinement method and w hether. indicator s ar e estimated as the median or the aver age of the r atios acr oss domains In. par ticular w e compar ed thr ee alter native r efinement methods the tw o alr eady descr ibed. and a thir d one w her e both MEAD and MAD computations assume a nor mal distr ibution. and for each of them w e computed the individual indicator M as either the mean or median. of the r atios acr oss domains We get the r esults summar ized in Table 4. Inser t Table 4 her e, Fir st the last r efinement method that assumes nor mality yields the most extr eme r esults. We w ill see this effect is not a pr oblem of this method but an evidence of a w eakness of the. test Second indicator s computed as aver age r atios ar e higher Thir d if w e compar e how. many individuals have an estimator that var ies substantially 11 w hether w e use medians or. aver ages about half of the individuals have a sensible indicator This effect is par ticular ly. per nicious w hen the M r atios yield conflicting qualitative r esults that is a same individual. w ith over pr ecision M 1 or under pr ecision M 1 depending on the method used This. happens to 4 of par ticipants in the standar d r efinement and up to 9 6 in the w or st case. Finally if w e do this compar ison acr oss r efinement methods12 instead of median vs. aver age w e obtain similar r esults, Why this happened Basically because in our sear ch for a simplicity efficiency equilibr ium. w e heeled heavi ly over simplicity six questions r evealed not enough If a judge happens to. pr ovide an answ er to a question that is ver y close to the tr ue answ er AD w ill be near to. zer o When only having tw o questions per domain this makes MAD 0 and M which. 10 For tunately we could contact par ticipants after the experiment to confirm their answer s Thus err or s like. swapped boundaries or r esponses in a par ticular or der could be amended Other s like missing values or median. estimations equal to a boundar y were not modified as it would represent an alteration of the exper iment results. 11 We consider a substantial variation of 25 between median and average estimations for median estimations. of M about 0 40 this makes 0 10 in absolute terms This variation is equivalent to the median var iations obser ved. along the sample for the three r efinement methods 0 09 0 10 accor ding to Table 4. 12 This comparison acr oss methods analyzes the minimum and maximum estimations for each individual using.


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