Incorrect Belefs Overconfdence Econ 1820: Behavoral Economcs Mark Dean Sprng 2015 In objectve EU we assumed that everyone agreed on what the probabltes of dfferent events were In subjectve expected utlty theory we asked only that the DM behaved consstent wth some belefs There s a thrd possblty: We know what the DM s belefs should be, but they make mstakes E.g. There are many robust examples of people beng bad at statstcal reasonng Base rate neglect Hot hands fallacy Gamblers fallacy In ths lecture we are gong to concentrate on a dfferent form of `ncorrect belefs Overconfdence 1 2 Outlne Examples of overconfdence Overprecson Overplacement Overestmaton Possble causes of overconfdence Economc consequences of overconfdence Excess Entry Three Ter Tarffs Types of Overconfdence Overprecson Overestmaton 3 4 Types of Overconfdence Overprecson Overestmaton Overprecson The belef that you have more precse nformaton about somethng that you actually do How long s the Nle n mles? Provde a number x so that you are 90% sure that the Nle s LONGER than x Provde a number y so that you are 90% sure that the Nle s SHORTER than y Calculate the HIT rate (across populaton or across questons) Probablty that correct answer s between x and y We would expect that the HIT rate should be 80% Generally the HIT rate s below 80% In Soll and Klayman[2003] HIT rate 39% 66% In your data HIT rate 62% (Nle) 71% (Telegraph) 5 6 1
Types of Overconfdence Overprecson Overestmaton Overplacement The belef that you have a hgher rankng that you actually do 37% of one frm s professonal engneers placed themselves among the top 5% of performers at the frm (Zenger, 1992) 93% of a sample of Amercan drvers and 69% of a sample of Swedsh drvers reported that they were more skllful than the medan drver n ther own country (Svenson, 1981) Also apparent n test scores Dean and Ortoleva [2014] asked subject s 17 Raven s Matrx questons Predcton for own score: 12 Predcton for average score: 11 (p=0.001) Your data Predcton for own score: 5.8 Predcton for average score: 6.0 7 8 Types of Overconfdence Overprecson Overestmaton Overestmaton The belef that you are better at somethng than you are Estmated vs Actual Grades [Kennedy et al. 2002] 9 10 Overestmaton The belef that you are better at somethng than you are Estmated vs Actual Grades [Kennedy et al. 2002] Causes of Overconfdence Two classes of model 1. Due to uncertanty about ablty possbly coupled wth mstakes n nformaton processng Your results: Predcted 5.8 Actual 8.0 11 2. Due to delberate bases to protect our ego Do not recall events that make us look bad Msnterpret sgnals tellng us that we are rubbsh Evdence that both effects may be mportant 12 2
Overconfdence due to Informaton Processng Example: Moore and Healy [2008] Imagne that you are takng a quz You thnk your performance depends on S how hard the test was L how good you are Performance X =S+L Before seeng the test, you thnk S s dstrbuted normally wth mean m and varance v s L s dstrbuted normally wth mean 0 and varance v L After takng the test, but before learnng the score, receve sgnal Y =X + E of how well you dd E mean zero error term wth varance v E 13 Overestmaton What are belefs about your own score after recevng sgnal Y? By Bayes rule: weghted average of sgnal and pror E ( X Y (1 ) Y Where ve ve vs If Y s unbased, then n expectaton E ( X Y (1 ) X Predcton Overestmaton for hard tests Underestmaton for easy tests 14 Overplacement What are belefs about someone else s score after beng told you scored X? By Bayes rule, expectaton of the dffculty of the test E ( S X (1 ) X Where vs Because S s the expectaton of others score E ( X j X (1 ) X Belef about other s scores s between the mean and own score Predcton Overplacement for easy tests Underplacement for hard tests 15 Overconfdence due to Informaton Processng: Predctons On average, across all tests, no overpredcton or overestmaton. In a partcular test, depends on the dffculty: Hard test: Overpredcton, Underplacement Easy test: Underpredcton, Overplacement 16 Overconfdence due to Informaton Processng: Predctons There are studes that do fnd both overconfdence and underconfdence e.g. Stankov and Crawford [1997] And over and underplacement Kruger [1999] Is ths related to task dffculty? Moore and Healy Results 17 18 3
Moore and Healy Results Other Examples of Ratonal Overconfdence: It may be ratonal for more than 50% of people to say that they are better than average! 19 20 Other Examples of Ratonal Overconfdence: Benot and Dubra [2011] 3 possble drver skll levels (equally lkely): Hgh (prob of accdent 1/20) Medum (prob of accdent 9/16) Low (prob of accdent 47/80) Drver does not know skll level, only whether or not they crashed Overall 40% of drvers crash What s the belef of those that do not crash P(hgh no crash)= 19/36 P(med no crash)=35/144 P(low no crash)=11/48 So for 60% of the drvers Most lkely outcome s they are better than average More than 50% chance they are better than average 21 Is All Overconfdence Ratonal? Burks et al [2013] study whether the Benot and Dubra explanaton works n a large sample They show that the Bayesan model mples that for any stated quantle k, the modal share must be from quantle k.e. lookng at people who say they are n the mddle 20%, most must be n the mddle 20% 22 Is All Overconfdence Ratonal? Also, overconfdence related to personalty factors Below medan n socal domnance: 33% thnk they are n the top 20% Above medan: 55% thnk they are n the top 20% In both cases, 20% are n the top 20% 23 Is All Overconfdence Ratonal? Mobus et al [2013] study how people respond to sgnals about how they have done n a test All subjects take the test Elct belefs about the probablty they are n the top half of performers Elct p such that they are ndfferent between a p probablty of wnnng $10 and wnnng $10 f they are n the top half of performers Provde 4 sgnals about whether they are n the top half of performers that are 75% accurate.e. f you are n the top half of performers, get a sgnal that says that you are n the top half 75% of the tme and that you are n the bottom half 25% of the tme Elct belefs after each sgnal 24 4
Is All Overconfdence Ratonal? Effects of Overconfdence Key fndng: subjects respond dfferently to postve and negatve news Entry nto a market Prcng of contracts Those that receve 2 postve and 2 negatve sgnals ncrease ther belefs by 4.8% on average 25 26 Effects of Overconfdence Entry nto a market Prcng of contracts 27 Excess Entry Many new busnesses fal Between 1963 and 1982 62% of new manufacturng busnesses closed wthn 5 years and 80% wthn 10 years Has lead people to ask f there s excess entry Too many new frms jonng the market Overconfdence could lead to excess entry Overestmaton Overplacement Camerer and Lovallo [1999] examne ths n an expermental settng 28 Experment Everyone receves $10 Players can choose to stay out of the market (and earn 0) If they enter the market, ther earnngs wll depend on the number of other entrants, ther rank and market capacty Experment Rank determned ether by chance or by skll Each subject played 12 round of each condton Rank not determned untl after the entry game Two subject pools Standard recrutment Subjects told ablty at trva could mprove earnngs 29 30 5
Results Effects of Overconfdence Much more entry n the `skll treatment that n the random treatment Expected proft $1.31 hgher n the random treatment (p<0.0001) Evdence of reference group neglect Dfference n ndustry profts $27.10 n the selected group (experments 5 8) $9.18 n non selected group (experments 1 4) Entry nto a market Prcng of contracts 31 32 Sellng to Overconfdent s [Grubb 2009] Imagne you are a Verzon Fxed cost per consumer of $50 Varable cost 5c per mnute values mnutes at 45c per mnute up to a sataton pont, 0c after Perod 1: sgn contract Perod 2: use mnutes Sataton pont unknown at tme of contract sgnng 1/3 100 mns 1/3 400 mns 1/3 700 mns Optmal Contract for a Ratonal Assume that you are a monopoly 2 part tarff Margnal cost prcng (5c per mnute) Extract all the surplus usng up front fee Expected value of 5c per mnute s $160 1/3 40c x 100+ 1/3 40c x 400+ 1/3 40c x 700 Charge $160 up front fee 33 34 Optmal Contract for an Overconfdent In real lfe we often see 3 part tarffs Fxed fee up front Low costs up to a certan pont Hgh costs after that pont Can 3 part tarffs be explaned by overconfdent consumers? Optmal Contract for an Overconfdent Consder a consumer who beleves wth probablty 1 that ther future demand wth be 400 An example of overprecson Optmal contract Charge 0c for the frst 400 mnutes 45c thereafter Extract all surplus wth an up front fee 3 part tarrf! 35 36 6
Optmal Contract for an Overconfdent Why s ths optmal? Consder mnutes 100 400 Reducng the prce from 5c to 0 costs the frm $15 f consumer has sataton levels 400 or 700 $10 n expectaton Value to the consumer s $15 because they assume that they wll always use these mnutes Can ncrease up front charge by $15 at the cost of $10 Consder mnutes 400 700 Increasng prce from 5c to 45c s $120 f consumer has sataton level 700 $40 n expectaton Cost to the consumer s 0 because they assume they wll never use these mnutes Can charge $180 up front Summary Psychologsts/Economsts have dentfed (at least) 3 dfferent types of overconfdence Overprecson Overplacement Overespectaton Further research has shown these effect to be more nuanced Evdence of under confdence Some effects can be the result of ratonal sgnal processng under uncertanty Evdence of overconfdence bas remans E.g. asymmetrc responses to good and bad nformaton These bases have potentally mportant economc consequences Excess Entry Prcng strateges of frms 37 38 7