Risk Misperception and Selection in Insurance Markets: An Application to Demand for Cancer Insurance

Transcription

1 UNLV Theses, Dssertatons, Professonal Papers, and Capstones Rsk Mspercepton and Selecton n Insurance Markets: An Applcaton to Demand for Cancer Insurance Davd S. Hales Unversty of Nevada, Las Vegas, halesd2@unlv.nevada.edu Follow ths and addtonal works at: Part of the Economcs Commons, Insurance Commons, and the Psychology Commons Repostory Ctaton Hales, Davd S., "Rsk Mspercepton and Selecton n Insurance Markets: An Applcaton to Demand for Cancer Insurance" (2015). UNLV Theses, Dssertatons, Professonal Papers, and Capstones Ths Thess s brought to you for free and open access by Dgtal Scholarshp@UNLV. It has been accepted for ncluson n UNLV Theses, Dssertatons, Professonal Papers, and Capstones by an authorzed admnstrator of Dgtal Scholarshp@UNLV. For more nformaton, please contact dgtalscholarshp@unlv.edu.

2 RISK MISPERCEPTION AND SELECTION IN INSURANCE MARKETS: AN APPLICATION TO DEMAND FOR CANCER INSURANCE By Davd Scott Hales Scence Baccalaureate n Physcs Massachusetts Insttute of Technology 1994 Bachelor of Scence n Computer Scence Natonal Unversty 1997 Master of Busness Admnstraton Unversty of Hawa, Manoa 2003 A thess submtted n partal fulfllment of the requrements for the Master of Arts Economcs Department of Economcs Lee Busness School The Graduate College Unversty of Nevada, Las Vegas May 2015

3 Copyrght by Davd S. Hales, 2015 All Rghts Reserved

4 We recommend the thess prepared under our supervson by Davd Scott Hales enttled Rsk Mspercepton and Selecton n Insurance Markets: An Applcaton to Demand for Cancer Insurance s approved n partal fulfllment of the requrements for the degree of Master of Arts - Economcs Department of Economcs Mary Rddel, Ph.D., Commttee Char Stephen P. A. Brown, Ph.D., Commttee Member Jeffrey Butler, Ph.D., Commttee Member Hokwon Cho, Ph.D., Graduate College Representatve Kathryn Hausbeck Korgan, Ph.D., Interm Dean of the Graduate College May 2015

5 Abstract Spnnewjn (2013) posts that optmsm about rsk and the effcacy of rsk-reducng effort could cause selecton n nsurance markets. We test for ths usng a survey of 474 subjects demand for hypothetcal cancer nsurance. We elct perceptons of baselne cancer rsk and control effcacy and combne these wth subject-specfc cancer rsks predcted by the Harvard Cancer Rsk Index to develop measures of baselne and control optmsm. We fnd that only 23 percent of our subjects would purchase a far nsurance contract algned to ther true rsk type. Of these subjects, 94 percent also overnvest n preventon, leadng to advantageous selecton.

6 Acknowledgements and Declaraton of Co-Authored Materal Ths thess s based on an artcle of the same ttle, co-authored wth Professor Mary Rddel and submtted n December 2014 to The Economc Journal for publcaton consderaton. Pror to my nvolvement n the research project that supports ths artcle, Dr. Rddel envsoned and developed the theoretcal framework usng the Harvard Cancer Rsk Index (HCRI), created a survey desgn around the HCRI, and wrote the actual Qualtrcs onlne survey that was used n ths study. Dr. Rddel also personally conducted the frst round of data gatherng, solctng Amazon Mechancal Turk responses from 214 female subjects, n October and November of Upon jonng the project n October 2013, I performed a lterature revew and asssted n the data analyss of the ntal 214 subjects. I helped extend the project s scope to nclude males, adaptng the survey to nclude questons relatng to males (n partcular, prostate cancer-related questons), n conformance wth the relatve rsk measures contaned n the HCRI. I conducted my own survey usng Amazon Mechancal Turk n Aprl 2014, on 279 male subjects. In an effort to mprove statstcs for female subjects, I also conducted a survey of an addtonal 56 female subjects, usng Dr. Rddel s orgnal female survey, n September Both Dr. Rddel and I partcpated heavly n the analyss, econometrc modelng, and hypothess testng n support of ths research. We also each wrote sgnfcant portons v

7 of the aforementoned artcle. In complance wth polces of the Graduate College and by consent of the Department of Economcs, I have adapted ths artcle and made addtonal contrbutons, to form the body of the thess. The portons of the thess that rely most heavly on Dr. Rddel s orgnal authorshp are Secton I, Overvew, Secton III, Testng for Selecton n a Hypothetcal Market, and Secton IV, Survey Consderatons. Secton II, Lterature Revew, s prmarly my effort, but wth sgnfcant contrbutons and edtng by Dr. Rddel. Secton V, Indexes for Optmsm and Effort, represents one of my prmary contrbutons to ths effort. In t I descrbe my development of a logarthmc, composte set of ndexes that we appled n the econometrc modelng. Secton VI, Selecton Model and Results, ncorporates sgnfcant contrbutons from both of us. Secton VI.C. (Insurance Selecton Classfcaton Model) was prmarly Dr. Rddel s effort, and Secton VI.D. (Populaton Classfcaton Predctons and Confdence Intervals) was prmarly my effort. In ths latter secton, Dr. Rddel made the crucal recommendaton that I use the Delta Method approach to estmate confdence ntervals, and she provded me helpful references n applyng ths technque. Dr. Rddel and I collaborated and contrbuted jontly to the results porton of Secton VI, as well as to Secton VII, Dscusson, and to Secton VIII, Conclusons. In all portons of the artcle and ths thess, ncludng those parts that are my prmary authorshp, I owe a tremendous debt of grattude to Dr. Rddel for allowng me to jon n v

8 ths research effort, and for her gudance, nspraton, mentorshp, and on more than one occason, her patence n correctng and teachng me economc theory and the art of appled econometrcs, both as an nstructor, as an experenced researcher, and as my thess advsor. Addtonal acknowledgements are due to Dr. Stephen Brown, partcularly for hs suggeston of addng a fnal logc trap queston at the end of the male survey, to detect whether survey respondents were answerng questons n a haphazard manner, but also for hs enormous and consstent gudance, support, and mentorshp snce I frst took hs graduate research semnar, and later as hs teachng assstant, where he taught me how to teach. Dr. Hokwon Cho smlarly provded helpful gudance n helpng me understand bvarate normal dstrbutons, and to apply these n a mathematcally correct manner. As my nstructor n several statstcs courses, he also helped me develop theoretcal bones, on whch best to buld strong econometrcs muscle. Dr. Jeffrey Butler provded helpful behavoral economcs nsghts, both n regards to the current research, and to future possble extensons. Dr. Ian McDonough provded very helpful econometrc advce, as well as some very welcome encouragement. Fnally, the comments provded by partcpants of two conferences I attended wth Dr. Rddel, n whch she presented earler versons of the paper, were very helpful n the wrtng of both the artcle and ths thess: The Harvard Rsk, Percepton, and Response Conference, held at the Harvard School of Publc Health n March 2014, and the v

9 Behavoral Insurance Workshop, held at the Ludwg-Maxmlans Unversty of Munch n December v

10 To my wfe Stephane, for always beng there for me, and for teachng me to celebrate lfe; to my daughters Jame and Jule, for nsprng and encouragng me wth ther sense of wonder of the world; and to my grandson Kaden, for hs youthful, nnocent sprt that never fals to put a smle on my face. v

11 Table of Contents Abstract. Acknowledgements and Declaraton of Co-Authored Materal v Lst of Tables.x Lst of Fgures x I. Overvew. 1 II. Lterature Revew....6 III. Testng for Selecton n a Hypothetcal Market 10 IV. Survey Consderatons..13 IV.A. Rsk Percepton.14 IV.B. Rsk Preference.16 IV.C. Health Hstory and Objectve Cancer Rsk.16 IV.D. Cancer Insurance Demand.17 IV.E. Cogntve Ablty..18 IV.F. Demographcs 18 V. Indexes for Optmsm and Effort. 19 VI. Selecton Model and Results. 28 VI.A. Optmsm and Preventatve Behavor..28 VI.B. Baselne Optmsm and Demand for Insurance.32 VI.C. Insurance Selecton Classfcaton Model 35 VI.D. Populaton Classfcaton Predctons and Confdence Intervals..38 x

12 VII. Dscusson. 48 VIII. Conclusons...51 Appendx I. Notes of Survey Methodology 53 Appendx II. Dervaton of Partal Dervatve of Bvarate Normal Cumulatve Dstrbuton Functon 55 Appendx III. Copy of Qualtrcs Survey.60 References.81 Author s Currculum Vtae..84 x

13 Lst of Tables Table 1 Table 2 Table 3 Table 4 Table 5 OLS Models of Preventon Effort: Dependent Varable s Preventon Effort ndex 29 Effects of a Change n the Independent Varables n Table 1 on Cancer Rsk as a Result of a Change n Preventon Effort 30 Probt Models of Wllngness to Pay for Insurance: Dependent Varable Equals One f the Subject Agreed to the Insurance at the Offered Premum 33 Results of the Bvarate Probt Classfcaton Model 37 Subject Populaton Classfed as Adverse or Advantageous Selectors Based on Bvarate Probt Model, wth Confdence Intervals derved from the Delta Method and Bootstrap Procedure 46 x

14 Lst of Fgures Fgure 1 Fgure 2 Hstograms of Baselne and Control Optmsm for Males and Females 22 Hstograms of Estmated Standard Errors of Indvdual Classfcaton Probabltes 41 x

15 I. Overvew Economsts have long posted that asymmetrc nformaton wth heterogeneous rsk types can lead to adverse selecton n nsurance markets (Rothschld and Stgltz 1976). Indvduals wth prvate nformaton that they are hgh-rsk types tend to buy more coverage than low-rsk types. Hgh-rsk types wll also have hgher clams, leadng to a postve correlaton between nsurance coverage and clams. Such postve correlatons have been found n some markets, but rejected n others. For example, Puelz and Snow (1994) fnd evdence of adverse selecton n the market for automoble nsurance, but Chappor and Salane (2000) do not. By contrast, Fnkelsten and McGarry (2006) reject the hypothess of adverse selecton n ther study of long-term care nsurance. These mxed fndngs concernng adverse and advantageous selecton have led researchers to look for other sources of prvate nformaton and selecton n nsurance markets. De Meza and Webb (2001) develop a model where rsk averson leads to advantageous selecton as more rsk-averse subjects buy more nsurance and smultaneously engage n more preventon behavor leadng to a negatve correlaton between coverage and clams. Fang, Keane, and Slverman (2008) examne the market for Med-gap nsurance (a supplement to Medcare). They found that when cogntve ablty s controlled for, a negatve correlaton between coverage and ex-post clams s found, ndcatve of advantageous selecton. They conclude that the correlaton arses 1

16 because cogntve ablty s correlated wth both good health and the purchase of health nsurance. A recent paper by Spnnewjn (2013) posts that heterogenety n rsk msperceptons may also affect the relatonshps between coverage and clams, leadng ether to advantageous or adverse selecton. Spnnewjn (2013) recognzes two dmensons of rsk mspercepton. Frst, subjects may be relatvely baselne optmstc, meanng they beleve ther rsk of damages s lower than t actually s. Baselne optmstc subjects are theorzed to demand less nsurance than ther more pessmstc counterparts. Control optmsts overestmate the rsk reductons arsng from engagng n preventatve actvtes and avodng rsky actvtes. As a result, they overnvest n rsk-reducng actvtes relatve to ther true rsk type, leadng to lower expected nsurance clams. Assumng a smple model wth two nsures wth dfferent perceved rsk types and ncentve-compatble equlbrum contracts, Spnnewjn (2013) shows that f one nsuree s more baselne and control optmstc than the other, a postve correlaton between coverage and clams wll occur. A negatve correlaton results f the more control pessmstc type s also relatvely more baselne optmstc. Thus, dependng on the correlaton between the control and baselne optmsm of the two nsurees, ether adverse or advantageous selecton may result. Usng an onlne survey of 478 US adults aged 18 and older, we nvestgate the effects of rsk mspercepton on the wllngness to pay for a hypothetcal cancer nsurance polcy 2

17 and future expected cancer nsurance clams, controllng for rsk preferences, cogntve ablty, and potentally mportant demographc varables. We choose cancer nsurance because much s known about the role demographcs and behavoral choces play n formng cancer rsks. We elct baselne rsk perceptons, perceptons of the effcacy of preventon efforts and rsk factors related to colon, prostate, and bladder cancer for men and colon, bladder and breast cancer for women. We query subjects about ther behavors that may ether reduce or ncrease rsks for one or more of these cancers. We elct estmates of the subject s degree of rsk averson usng the Holt and Laury s (2002) multple prce-lst elctaton method. We measure cogntve ablty usng a short ntellgence assessment. To our knowledge, no other research has emprcally evaluated the role of rsk msperceptons n selecton n nsurance markets. Ths s lkely because there are few nsurable events for whch data are avalable on actual and perceved rsk. Thus, the strength of ths study s that our measures of cancer-rsk mspercepton rest on applyng subjects survey responses to the Harvard Cancer Rsk Index (HCRI) (Coldtz et al. 2000). The HCRI was developed at the Harvard Center for Cancer Preventon, by a workng group of epdemologsts, clncal oncologsts, and other Harvard faculty wth quanttatve expertse focused on cancer and rsk assessment (Ibd.). The HCRI provdes quanttatve relatve rsk (RR) factors for each demographc or health behavoral attrbute that experts beleve bear on the rsk of ncdence of a gven cancer. The HCRI can thus be used to calculate the rsk a subject wll contract cancer, 3

18 condtonal on a set of behavoral and demographc trats. By askng subjects to estmate ther rsk of ncdence of each cancer, and comparng that wth the HCRI estmates, we derve a measure of ther baselne optmsm. Smlarly, by askng subjects how effectve a seres of preventatve measures are n reducng cancer rsk, and how rsky a seres of unhealthy behavors are, and then comparng them wth the correspondng HCRI RR factors, we derve a measure of ther control optmsm. Standard tests for advantageous or adverse selecton rest on the sgn of the correlaton between nsurance coverage and clams: postve correlaton suggests adverse selecton, whereas negatve correlaton mples advantageous selecton. The hypothetcal nature of the survey reported n the current paper necesstates a dfferent approach to testng for selecton. We frst test whether baselne and control optmsm nfluence preventon effort, and thereby affect the rsk of contractng cancer. Next, we test whether baselne optmsm causes people to under-nsure relatve to ther true rsk type. In both models we control for other factors, such as cogntve ablty rsk averson, and demographc varables whch may nfluence wllngness to pay for nsurance and preventon effort. Ths approach allows us to classfy subjects accordng to whether ther wllngness to pay for nsurance and preventon efforts are hgh or low relatve to ther true rsk type and health preferences whle controllng for other factors that may lead to selecton. Gven these classfcatons, we can nfer whether postve or negatve correlaton between coverage and clams wll be present n our sample. 4

19 Our fndngs offer strong support for Spnnewjn s (2013) hypothess that rsk mspercepton can lead to selecton n nsurance markets. We fnd that male subjects who underestmate ther lkelhood of cancer ncdence (baselne optmsts) are wllng to pay less for full nsurance, ceters parbus. The effect s not present for female subjects. We also show control optmsts of both genders engage n more preventon and fewer rsky health behavors, ndcatng that, on average, ther cancer rsks and nsurance clams wll be lower. At the same tme, baselne optmsm leads subjects to engage n less preventatve effort, thereby rasng ther cancer rsk and assocated expected clams. Our classfcaton model ndcates that optmsm causes over 76 percent of our sample to reject an actuarally far nsurance contract. Of the remanng subjects, 23 percent accept the contract and smultaneously engage n excess preventon; the fnal 2 percent accept the contract but under-nvest n preventon. Thus we show that controllng for rsk averson and cogntve ablty, optmsm drves most hgh-rsk types out of the market, leadng to advantageous selecton. 5

20 II. Lterature Revew Rothschld and Stgltz (1976) ntroduced the theory of adverse selecton, hypotheszng that even small amounts of asymmetrc nformaton n compettve markets can lead to sgnfcant dstortons of market-clearng prces and quanttes. They focused ther study on the market for nsurance, where they posted that when nsurees of heterogeneous rsk types have prvate nformaton about ther level of rsk, adverse selecton may result. Indvduals who know they are hgh-rsk types tend to buy more coverage than low-rsk types. Hgh rsk-types wll also have hgher clams, leadng to a postve correlaton between nsurance coverage and clams. Wth the resultng downwardslopng margnal cost curve, the average cost curve s at all tmes above the margnal cost curve, leadng at best to an under-provson of nsurance to those wth the lowest levels of rsk. Dependng on the rsk premums ndvduals place on nsurance, a complete unravelng of an nsurance offerng s possble (see Enav and Fnkelsten (2011) for a more detaled dscusson). The semnal paper by Rothschld and Stgltz (1976) spurred a robust theoretcal and emprcal lterature. Much of the emprcal work nvolved estmatng correlatons between the amount of nsurance coverage and ex-post expendtures on clams predcted by Rothschld and Stgltz (1976). A postve correlaton suggests adverse selecton, whereas a negatve correlatons ponts to advantageous selecton. For example, Chappor and Salane (2000) analyzed data from automoble nsurance 6

21 contracts for young French drvers and found that, when observables are adequately taken nto account, no evdence of asymmetrc nformaton remans. They concluded that ths may be because young drvers do not know ther rsk types, and older drvers do not know more about ther rsk types than do the nsurance companes. However, Cohen (2005) performed a smlar examnaton of automoble nsurance data and found a sgnfcant postve correlaton between coverage and clams for more experenced drvers, suggestng these more experenced drvers may have learned about ther own rsk types to a greater extent than had ther nsurers and less experenced drvers, leadng to nformaton asymmetres that result n adverse selecton. De Meza and Webb (2001) noted several prevous studes that found ether a lack of evdence of adverse selecton, or even a negatve correlaton between coverage and clams. They proposed a model n whch an addtonal factor, rsk averson, plays a key role. They theorzed that less rsk-averse people are less lkely to take precautons, but also less lkely to purchase nsurance. Ths then leads to a negatve correlaton between coverage and rsk, and therefore advantageous selecton, partcularly n the presence of sgnfcant admnstratve costs. In a smlar ven, Fang, Keane, and Slverman (2008) found advantageous selecton n the market for Med-gap nsurance (a supplement to Medcare). They found that, controllng only for gender, age, and state of resdence (the determnants of polcy prces), Med-gap polcyholders spent on average $4,000 per year less on health care 7

22 than smlar-aged Medcare recpents who do not purchase Med-gap nsurance. However, when they ncluded a robust set of controls for health, they found that those wth Med-gap spend about $2,000 more than those wthout Med-gap. They controlled for addtonal ndvdual attrbutes and found that when cogntve ablty s controlled for, a negatve correlaton between coverage and ex-post clams s found, ndcatve of advantageous selecton. They proposed that as cogntve ablty s correlated wth both good health and the purchase of health nsurance, t leads to a negatve correlaton between Med-gap coverage and health rsk. Underscorng the sometmes complex dynamcs underpnnng the demand for nsurance, Fnkelsten and McGarry (2006) dentfed multple forms of prvate nformaton that can potentally affect the correlaton between nsurance coverage and rsk occurrence. They proposed that t s possble for two or more types of prvate nformaton to have offsettng effects, leadng to behavor that lacks a correlaton between rsk type and coverage. In the long-term care nsurance market, they dentfed wealth and healthcare preventve actvtes as beng postvely correlated wth nsurance coverage, and negatvely correlated wth rsk. A range of other studes have produced varyng results, whch the authors attrbute to the partcular characterstcs of the markets under study. For example, Davdoff and Welke (2004) found evdence of advantageous selecton n the reverse mortgage 8

23 nsurance market. He (2008) found adverse selecton n the lfe nsurance market wth sgnfcant correlaton between mortalty rsk and lfe nsurance coverage. More recently, Spnnewjn (2013) advanced the dea that rsk mspercepton may also lead to selecton n nsurance markets. Hs model assumes two types of rsk msperceptons whch, actng together, can lead to ether adverse or advantageous selecton. Polcyholders who are baselne optmstc beleve ther rsks of experencng nsured events are lower than they actually are; such ndvduals demand less coverage and engage n less preventatve effort, ceters parbus. Those who are control optmstc beleve ther efforts to mtgate potental negatve health effects are more effectve than they actually are. Under Spnnewjn s hypothess, control optmstc ndvduals beleve that the margnal return to effort s hgher than t actually s, and therefore overnvest n effort and hence reduce ther expected ex-post clams relatve to an ndvdual wth accurate or pessmstc vews about the return to effort. All other thngs beng equal, an ndvdual who s control optmstc s lkely to have lower clams, due to ther greater amount of preventatve care and avodance of rsky health behavors. Thus, whether adverse selecton s possble rests on the relatve nfluence of baselne and control optmsm on nsurance demand and preventon effort. 9

24 III. Testng for Selecton n a Hypothetcal Market To our knowledge, a database that ncludes subject-level coverage and clams data as well as measures of subjectve control and baselne optmsm related to cancer rsk and nsurance does not exst. As such, we take a novel approach to nvestgatng selecton n nsurance markets. Rather than analyzng hstorcal nsurance coverage and clams data, we classfy subjects nto four classes accordng to dfference n wllngness to pay and exerton efforts relatve to the correspondng values gven ther true rsk type. We then determne who wll purchase an nsurance contract wth fxed coverage at a gven premum and how much effort they wll exert. Ths allows us determne how optmsm nfluences the composton of nsured partes and the effort they exert. If the market s domnated by low-rsk types who exert hgh levels of effort, we nfer advantageous selecton. Assume a group of rsk-averse subjects who are dentcal n all respects save for ther levels of baselne and control optmsm. The subjects wllngness to pay for nsurance f coverage R gven ther true rsk type s prce P* P where f P s the actuarally far prce and s equal to the rsk premum the subject s wllng to pay. If a subject s baselne pessmstc, then they perceve ther rsk to be hgher than ther true rsk type, h and they wll be wllng to pay P P* for coverage R. Baselne optmsts wll be wllng l to pay P P*. Thus f an nsurer offers coverage R at P*, baselne optmsts wll reject 10

25 the coverage thereby undernsurng relatve to ther true rsk type, whereas baselne pessmsts wll purchase t, consderng t to be a bargan. Of course, whether ths leads to adverse or advantageous selecton depends on how baselne and control optmsm nfluence behavor. Assume that f the subjects understood the actual effcacy of preventon effort, they would nvest E* n effort. If the combned effects of baselne and control optmsm lead the subject to overnvest n h effort relatve to ther true rsk type and preferences, then the nvest E E*, l undernvestment attrbutable to baselne and control optmsm s then E E*. Defne class h C where 1 f E E E* and 0 otherwse and j 1 f P P h P* j and 0 otherwse. Thus, class C 11 expends more preventon effort and has a surplus wllngness to pay, whle C 10 expends excess effort but undernsures relatve to ther true rsk type. To understand how ths classfcaton reveals selecton, consder the case where only two classes exst n the market, C 10 (excess effort, defcent wllngness to pay) and C 01 (defcent effort, excess wllngness to pay). As classed, these subjects are equal n all respect save for ther level of control and baselne optmsm and correspondng effort and wllngness to pay. If far nsurance based on the true rsk type s offered, C 10 class wll contnue to overnvest n effort but wll not nsure snce ther wllngness to pay s less than the premum offered. They wll only enter the market f the prce s dropped below P *. The market wll be domnated by the C 01 type snce 11

26 ther wllngness to pay exceeds the far prce plus the rsk premum. Ths wll cause adverse selecton snce the type that nsures also undernvests n preventon effort. The outcome wll dffer dependng on the mx of types. Another smple case arses when the market s comprsed of solely the C 11 and C 00 types. The former type wll buy far nsurance and overnvest n effort whereas the latter type wll reject the nsurance even as they undernvest n preventon effort. Thus the hgh-rsk, low-effort type s drven out of the market by ther optmsm and the market wll be composed of the lowrsk type, leadng to advantageous selecton. 12

27 IV. Survey Consderatons We conducted an onlne survey of 474 men and women aged 18 and over on Amazon Mechancal Turk (AMT) 1. The AMT web servce s essentally a labor market desgned to match employers who need short tasks completed whch requre human ntellgence to workers wllng to complete the task. The tasks, whch typcally requre between 5 and 45 mnutes to complete, range from surveys and wrtng bref product descrptons to transcrbng audo recordngs. Employers sgn up for the servce and post task descrptons together wth a per-task compensaton amount. Employees select tasks usng the web as the employer/employee nterface. AMT has become ncreasngly popular over the past fve years wth socal scence and busness researchers because of the ease of use of the platform and the streamlned and rapd process for recrutng study volunteers. Buhrmester, Kwang, and Goslng (2011) found that AMT s an nexpensve source for hgh-qualty data. They showed that partcpants are slghtly more dverse than a typcal nternet sample and much more dverse than a sample based on unversty students. They also found that the data qualty was at least as hgh as a standard nternet or telephone survey desgn. 1 Note that we collected survey data from a total of 559 respondents (280 women, and 279 men); of these, we excluded a total of 85 survey responses for several reasons: 1) the survey respondent ndcated she or he currently or prevously had cancer, renderng the HCRI relatve rsk factors, and therefore our survey desgn, unapplcable; 2) the Amazon Mechancal Turk-provded lattude and longtude suggested the respondent was located outsde the Unted States; 3) the respondent s Amazon Mechancal Turk Identfcaton Number or Internet Protocol address suggested a duplcate response. 13

28 For our study, the task was descrbed to potental partcpants as a survey related to ther belefs about the cancer rsks that would take about 20 mnutes. Subjects were gven between $2.25 and $4.50 to complete the survey. The survey used a splt-sample desgn. One half of the partcpants began the survey wth nformaton about the causes, rsk factors, and preventon strateges for one of the three cancers of nterest (colon, bladder and breast for women and bladder, colon, and prostate for men). Followng the nformaton secton, these subjects began the questonnare. The other half of the subjects commenced wth the questonnare wthout any pror nformaton gven about cancer rsks. We created an ndcator varable, nfo, whch we use n our modelng efforts to control for the effects of the nformaton booklet. The questonnare has sx components, descrbed below: IV.A. Rsk Percepton Rsk percepton and mspercepton have two dmensons n the survey. We frst quered subjects about ther belefs about the effcacy of cancer-preventon actvtes and perceptons of the rskness, n terms of ncreased cancer rsk, of dfferent rsky health behavors. The responses were combned wth the expert-assessed effcacy of dfferent actvtes and used to form measures of control optmsm. The second dmenson relates to the subject s vew of ther own rsk of contractng each one of the cancers. Comparng the subjectve assessment of rsk to the actual rsk predcted by the HCRI allows us to calculate a measure of baselne optmsm. Below, we brefly descrbe the 14

29 rsk-percepton elctaton questons. The formulas for the actual calculatons for the two types of optmsm are descrbed n secton V. Subjects were frst asked to grade the decrease (ncrease) n relatve rsk n contractng a gven cancer, contngent on undertakng specfc preventatve (rsky) actvtes. 2 The actvtes consdered vared wth the cancer. 3 For example, rsk factors for bladder cancer ncluded smokng and exposure to chemcals, whereas rsks for colon cancer ncluded excessve red meat consumpton and a low-calcum det among others. Preventon actvtes for colon cancer ncluded regular exercse, takng multvtamns and takng a daly asprn, among others. Followng the questons about relatve rsks, subjects were asked to state ther personal rsk of gettng each one of the cancers n ther lfetme, compared to the typcal subject of ther same age and gender. The possble outcomes ranged from zero rsk of gettng the cancer (Zero. There s no chance of me gettng ths cancer), to very hgh rsk (very much above average, fve tmes or more above average). 2 The relatve rsks for each preventatve actvty were presented as both ranges and qualtatve descrptors as follows: not effectve/does not reduce cancer rsk, somewhat effectve/reduces rsk 10% to 20% below the average person of the same age and gender, moderately effectve/reduces rsk 30% to 60% below the average, very effectve/reduces rsk 60% to 80% below the average, and extremely effectve/reduces rsk by more than 80% below the average. 3 The relatve rsks for each characterstc or behavor were presented as both ranges of relatve rsk and a qualtatve descrptor as follows no rsk ncrease, small rsk ncrease, rsk s hgher but less than double the average rsk, moderate rsk ncrease to 2 to 4 tmes the average rsk, large rsk ncrease to 4 to 8 tmes the average rsk, and very large rsk ncrease to more than 8 tmes the average rsk. 15

30 IV.B. Rsk Preference Ths secton elcted a range for the rsk averson coeffcent for the Constant Relatve Rsk Averson utlty functon defned over mortalty rsks usng the sequental multple prce lst aucton. Detals of ths aspect of the experment can be found n Rddel and Kolstoe (2013). Brefly, the subjects read the followng text descrbng the gambles they wll face: Hypothetcal Health Rsk: Assume you have been dagnosed wth a dsease that wll certanly be fatal n a year wthout treatment. There are two treatments, but nether s effectve 100% of the tme. Assume the costs of the treatment are the same, and nether treatment has sde effects. The subjects were then gven a sequence of pared lotteres, and asked to select the one they preferred. For example, the frst gamble presented was: Treatment A means a 30% chance of 8 more years of lfe and a 70% chance of 2 more years. Treatment B gves a 90% chance of 1 more year (the treatment fals) and a 10% chance of 13.5 more years. In subsequent gamble pars, the outcome n treatment B was vared so that E[ A] E[ B] gradually decreases, and eventually becomes negatve. The analyst notes where the subject swtches from preferrng lottery A to preferrng lottery B, wth later swtch ponts ndcatng hgher levels of rsk averson. IV.C. Health Hstory and Objectve Cancer Rsk Subjects were asked a detaled hstory of ther actvtes, behavors, and famly hstory for thngs that may nfluence ther rsks of contractng the three cancers of nterest. Questons covered ther famly hstory of the cancers n queston and health related 16

31 behavors such as exercse, vtamn use, smokng, chemcal exposure, and alcohol use. The responses to these questons were used to provde an objectve estmate of ther rsk of gettng each of the cancers, usng the HCRI from Coldtz et al. (2000). 4 IV.D. Cancer Insurance Demand The subjects next faced a sngle-bounded contngent valuaton exercse to determne ther demand for cancer nsurance. The nsurance for males n the sample was descrbed as follows: Assume that there s an nsurance polcy avalable that wll cover any and all costs related to the covered cancers. The cancers covered by the nsurance are bladder cancer, prostate cancer, and colon cancer. 5 Consderng your current budget, would you be wllng to pay the followng monthly premum for ths nsurance assumng t covered all related costs ncludng dagnostc testng, offce vsts for specalsts, hosptal stays, treatment costs ncludng chemotherapy and radaton, as well as FDA approved expermental treatments. There are no copays or deductbles and you would be able to choose your own doctors and hosptals. Please assume that your current nsurance wll not cover these cancers and that you wll have to pay all of the costs yourself f you get any of these cancers. Subjects were randomly assgned a bd amount rangng from $5 to $135 per month and asked f they would be wllng to pay that amount for the nsurance as descrbed. 4 Note that the resultng (relatve) rsk estmates are normed aganst the U.S. populaton of persons of the same age and gender. Although we know of no method of estmatng cancer rsk that can clam to be wthout error or possble bas, we assume that rsk estmates derved usng the HCRI methodology are suffcently accurate to use n estmatng subjects levels of baselne and control optmsm. 5 Women were asked about nsurance that covers bladder, colon and breast cancer. 17

32 IV.E. Cogntve Ablty. Subjects were asked to answer a seres of 7 questons used n the Wonderlc cogntve ablty test. The subject scored a one on each queston f they gave the correct answer and a zero otherwse. The varable Cogntve Ablty was calculated as the sum of the ndvdual scores. IV.F. Demographcs. Subjects were asked ther gender, age, ncome, ethncty, educaton level, and martal status. Varable Age s measured n years, varable Income s measured n thousands of dollars of annual ncome, whle Boolean ndcator varables are assgned based on whether one has completed at least a bachelor s degree (College,) whether one s Marred, s Male, s Afrcan Amercan (Black), or Asan Amercan (Asan). 18

33 V. Indexes for Optmsm and Effort Gven subjects perceptons of ther rsk of contractng cancer and ther belefs about the effcacy of preventon efforts, we need to form measures of baselne and control optmsm. Whle there s no generally agreed on formula for combnng perceved and actual rsks, we beleve that any measure allows us to easly understand the degree of optmsm n terms of a relatve rsk.e. subject beleves ther rsk s half that of ther true rsk type. Consstent wth ths thnkng, we developed the measures descrbed below. V.A. Measure of Baselne Optmsm A subject s baselne optmstc f they underestmate ther true rsk of cancer relatve to those n the US populaton of ther own age (and, n the case of breast and prostate cancers, of ther same age and gender). Thus, we measure Baselne Optmsm by comparng each subject s stated populaton-relatve rsk estmate of ncdence for each of the three cancers, wth the subject s actual populaton-relatve rsk factor ( ARR ). We calculate the ARR by applyng each subject s responses to demographc, famly hstory, and lfestyle questons n our survey to the rsk estmates tabulated for those behavors n the HCRI. Gven each subject s survey answers, we then estmate the ARR of subject 's rsk of ncdence of cancer j as follows: ARR j 1 PD ko ( j) k1 RR jk (1) 19

34 where k0 j s the number of relatve rsk factors for cancer j dentfed n the HCRI, s a vector of subject s demographc characterstcs, famly hstory, and lfestyle RR s the HCRI relatve rsk measure for subject for factor k of cancer j, choces, jk and PD s a populaton denomnator derved from the Natonal Cancer Insttute s Survellance, Epdemology, and End Results (SEER) Program. 6 As cted n Coldtz et al. 2000, the resultng populaton-relatve rsk factor gves expert opnon-derved estmates of gven subject s rsk of ncdence of cancer j, relatve to the US populaton of persons the same age (and for breast and prostate cancers, gender). Thus, a ARR,j value of 1.0 mples subject has an average rsk of cancer j ncdence equal to the average of persons n the U.S. of the same age and gender; a value of 2.0 suggests cancer rsk that s twce the average, and a value of 0.5 suggests cancer rsk that s half the U.S. average. The survey asked subjects to estmate ther rsk of contractng each of three cancers (colon, bladder, and breast for women; colon, bladder, and prostate for men), agan relatve to persons ther same age and gender. Consstent wth the methodology suggested n Coldtz et al. (2000), we structured survey questons to range from Very much below average rsk, correspondng to a relatve rsk value of 0.2, to Very much above average rsk, correspondng to a relatve rsk value of We label subject s 6 Note that as we dd not have access to the SEER populaton denomnator for prostate cancer, we used an estmate of , based on the average (non-normalzed) relatve rsk factors of our sample of 218 men. 7 In addton to the seven levels of relatve rsk suggested n Coldtz et al. 2000, we also allowed survey respondents to select No rsk, whch we code as a relatve rsk factor equal to

35 stated estmates of relatve rsk of cancer j as SRR j, and then usng values for ARR j and SRR j, we can create a measure of subjects baselne optmsm as follows: Baselne Optmsm ARR j log. (2) SRR j j 2 Here, a value for Baselne Optmsm of 0.0 mples that a subject s own estmates of cancer ncdence rsk (for cancer j) are dentcal to the expert-derved HCRI estmates, based on her responses to survey questons regardng demographc, famly, and lfestyle characterstcs. A Baselne Optmsm value of 1.0 ndcates that the subject s estmates of cancer ncdence rsk are half of the expert-derved value (makng her rsk perceptons relatvely optmstc), and a Baselne Optmsm value of -1.0 ndcates the subject s rsk estmates are twce that of the expert value (makng her rsk percepton relatvely pessmstc). Each ncrease (decrease) of one pont n our measure thus has the effect of doublng the amount by whch expert rsk assessments exceed (are exceeded by) subjects own-rsk estmates. Next, we calculate on overall all estmate of each subject s tendency to exhbt baselne optmsm by takng the average of the separate measures for each of the three cancers consdered n our study: 3 3 ARR 1 1 j Baselne Optmsm 3Baselne Optmsmj 3log2. (3) j1 j1 SRR j 21

36 Densty Densty Densty Fgure 1 gves the dstrbuton of Baselne Optmsm for males and females. Roughly ¾ of each gender n our sample are baselne optmstc. The dstrbuton for females s somewhat hgher varance (std. dev.=1.55) than that of males (std. dev.=1.24). Baselne Optmsm: Males Control Optmsm: Males Baselne_Optmsm Control_Optmsm Baselne Optmsm: Females Control Optmsm: Females Baselne_Optmsm Control_Optmsm Fgure 1. Hstograms of Baselne and Control Optmsm for Males and Females 22

37 V.B. Measures of Control Optmsm We label a subject as Preventon Control Optmstc f she beleves that engagng n benefcal actvtes s more effectve n reducng cancer rsks than t actually s. Smlarly, we label a subject as Rsk Control Optmstc f he beleves that engagng n a partcular rsky actvty s more lkely to lead to cancer than t actually s; we therefore nfer that he overestmates hs ablty to reduce cancer rsks by avodng or curtalng the rsky actvty n queston. The survey contaned a set of questons for each cancer about perceptons of the relatve rskness of dfferent actvtes that ncrease or decrease cancer rsk. For a gven cancer j and benefcal actvty k, subjects were asked to estmate rsk-reducng factors between no rsk reducton effect (RR=1.0) and a rsk reducton of ten-fold (RR=0.1). Comparng these estmates wth actual expert estmates for each cancer and preventatve measure assocated wth each cancer, subject s level of preventon control optmsm s then estmated as: APRR Preventon_Control_Optmsm 3 kprev ( j) 1 jk 3 log2 kprev ( j) j1 k1 SPRR jk j1 (4) where kprev j s the number of preventatve measures dentfed n the HCRI for cancer j, APRR jk s the HCRI-assessed actual post-preventatve behavor k relatve rsk of cancer j, and SPRR jk s the subject s estmates of relatve rsk of ncdence of cancer j, 23

38 assumng behavor k (wth possble responses coded wth RR values rangng from 0.1 to 1.0). By takng the base-2 logarthm of ths rato, and averagng over the total number of preventatve measures dentfed for each of the three cancers n queston, we arrve at a measure of optmsm exhbted by subject for a typcal preventatve measure. A Preventon_Control_Optmsm value of 0.0 suggests the subject s estmates of preventon effectveness are, on average, equal to the actual expert estmates. A measure of 1.0 mples that on average, the subject beleves preventatve measures are twce as effectve as they actually are; a measure of -1.0 mples that on average, the subject beleves preventatve measures are half as effectve as they actually are. Smlarly, but wth one crucal dfference, we estmate each subject s level of rsk control optmsm as follows: SRRR Rsk_Control_Optmsm 3 krsk ( j) 1 jk 3 log2 krsk ( j) j1 k1 ARRRjk j1 (5) where krsk j s the number of rsky actvtes dentfed n the HCRI for cancer j, ARRR jk s the HCRI-assessed actual post-preventatve behavor k relatve rsk of cancer j, and SRRR jk s the subject s estmates of relatve rsk of ncdence of cancer j, assumng behavor k (wth responses coded wth RR values rangng from 1.0 to 5.0). Note that to produce a consstent meanng the rato between stated and actual rsk factors s 24

39 nverted relatve to preventatve actvtes. That s, f a subject s stated rsk estmate for a gven cancer and rsky behavor s double the actual expert relatve rsk value, she s a Rsk Control Optmst for that partcular actvty and cancer combnaton. Fnally, we average the values of the two varables for each subject, to arrve at a characterstc level of control optmsm for each subject: 8 1 Control Optmsm 2 Preventon_Control_Optmsm Rsk _ Control _ Optmsm (6) An overall Control Optmsm measure of 0.0 ndcates that the subject accurately assesses the effcacy of preventon efforts. When Control Optmsm = 1, the subject beleves engagng n preventatve measures (avodng rsky actvtes) s twce as effectve n reducng cancer rsk than s actually the case; a measure of -1 mples that, on average, the subject beleves exertng such effort s half as effectve n reducng cancer rsk as t actually s. The dstrbuton of Control Optmsm for males and females s gven on the rght-hand sde of Fgure 1. Roughly 93% of males and 90% of females are optmstc about preventon actvtes. Both the male and female Control Optmsm dstrbutons have sgnfcant rght skew, wth the male dstrbuton beng markedly platykurtc, and the female dstrbuton somewhat less so. 8 Note that we elected to weght values for preventon and rsk control optmsm equally n ths estmate, rather than weghtng by the number of preventatve or rsk-related attrbutes for each cancer. We dd ths to avod overweghtng the nfluence of rsk-related attrbutes, of whch more were dentfed n the HCRI (29 for women, 24 for men) than were preventatve-related attrbutes (18 for women and 13 for men). 25

40 V.C. Measure of Preventatve Effort and Assocated Change n Cancer Rsk To estmate the level of effort each subject exerts n relaton to cancer-avodng or cancer-nducng actvtes, we employ a composte ndex based on the relatve rsks from the HCRI for three actvtes assocated wth reducng at least one of the three cancers (exercsng at least three hours a week, takng a daly vtamn D supplement, and takng a daly baby asprn) and three rsky behavors (hgh red meat consumpton, hgh alcohol consumpton, and cgarette consumpton): 9 Preventatve Effort log RR 6 m 2 m m1 (7) where m s a boolean operator, ndcatng whether subject engages n preventatve/rsky behavor m, and RR m s the relatve rsk assocated wth actvty m. We construct the ndex such that engagng n rsk-reducng actvtes wll contrbute a postve value to our ndex of preventatve effort, whle engagng n rsk-ncreasng actvtes wll contrbute negatve values to the ndex. Note that to more accurately dentfy a potental causatve effect between rsk percepton and rsk-related behavor, we restrct the actvtes n our ndex to those that can be drectly controlled by subjects n the near- to md-term. Thus, we exclude relatve rsk measures for, say, a subject s body mass ndex, as one s body weght may 9 Note that for cgarette consumpton, the HCRI dentfes four dfferent levels of rsk: 1) nonsmoker; 2) smokng less than 1 pack per day; 3) smokng between 1-2 packs per day; 4) smokng more than 2 packs per day. 26

41 not be a drect measure of near- to md-term choces, but rather may be a result of lfelong eatng and exercsng habts, as well as genetcs. A Preventatve Effort ndex value of 0.0 mples that a subject engages n none of these sx behavors wth bearng on cancer rsk, or alternatvely that he engages n a combnaton of rsky and preventatve behavors n such a way that hs rsk s the same as f he engaged n none of them. An ndex value of 1.0 mples that when confronted wth the decson of engagng or not engagng n each of these sx behavors, the subject s choces are such that (n aggregate) hs rsk of ncdence of one or more of the dentfed three cancers s half what t would be f he engaged n none of these actvtes. An ndex value of -1.0 mples hs rsk s twce what t would otherwse be. Importantly, the preventon ndex can be used to translate dfferences n preventon effort nto expected dfferences n cancer rsk, usng the formula: Preventatve _ Effort % Cancer Rsk 100[2 1]. (8) 27

42 VI. Selecton Model and Results As noted above, rather than nferrng selecton from correlatons between actual coverage and clams, we nvestgate how baselne and control optmsm nfluence the composton and behavor of consumers n our hypothetcal cancer-nsurance market. To do so, we must frst gauge how optmsm nfluences wllngness to pay for coverage and preventon effort. In the models results below, we determne f optmsm nfluences cancer-preventon actvty, hence cancer rsk and expected clams. In the subsequent sub-secton, we estmate models of wllngness to pay for nsurance as a functon of optmsm and a set of control varables. For both sets of models, we nclude a model wth all subjects as well as models of the ndvdual genders to account for the fact that males and females were asked about a dfferent set of cancers. VI.A. Optmsm and Preventatve Behavor To test whether optmsm affects behavor, we examne the relatonshp between engagng n ether rsky health behavors or preventon actvtes as a functon of baselne and control optmsm. Preventon and rsk-takng behavor s captured n the ndex for preventon, Preventon Effort, descrbed above. It s possble that preventon effort and optmsm are endogenous. We test for endogenety usng the Durbn-Wu- Hausman test (Wooldrdge 2003 pg. 506). There s no evdence of endogenty, so we estmate the model usng least-squares regresson wth standard errors corrected for heteroskedastcty. The regressons also control for other attrbutes of each subject that 28

43 are lkely to correlate wth preventon effort such as cogntve ablty, rsk preferences, age, ncome, educaton, martal status and ethncty. The results are reported n Table 1: Table 1. OLS Models of Preventon Effort: Dependent Varable s Preventon Effort ndex The frst column ncludes all subjects, whle the second and thrds columns estmate models for subsamples of men and women, respectvely. Because Preventon Effort s constructed accordng to a log 2 scale, drect nterpretaton of the coeffcents s dffcult. To ad the reader n understandng the model results, we have calculated the change n 29

44 cancer-mortalty rsk for changes from a specfed baselne relatve rsk for each of the statstcally sgnfcant ndependent varables. The results are reported n Table 2: 10 Table 2. Effects of a Change n the Independent Varables n Table 1 on Cancer Rsk as a Result of a Change n Preventon Effort Accordng to the models, ethncty, martal status, ncome, rsk averson, and cogntve ablty are not sgnfcant predctors of preventon n any of the three models. Age s not sgnfcant n the female model, but has a convex relatonshp wth preventon effort n the all-subjects and male models. The mnmum effort level occurs at 45 years age n both models, suggestng that as subject s age, ther preventon effort declnes untl 10 To calculate the percent change n cancer rsk attrbutable to the relevant ndependent varable, we frst calculate the change n the preventon for a change n varable X j as Effort Preventatve _ Effort( X j) X j. The change n cancer rsk s then X Preventatve _ Effort ( X j ) Cancer Rsk X. j % 100[2 1] j 30

45 about the populaton medan age (about 46 years old n the U.S.), then ncreases thereafter. Thus, f the average 45-year old male were to change hs behavor so as to engage n preventatve effort at the same level as the average 31-year old (the 25th percentle of the populaton age dstrbuton), hs age-adjusted rsk of cancer would drop by 8%. Smlarly, s he were to boost hs preventatve efforts to match those of the average 58-year old, hs age-adjusted cancer rsk would fall by 8.2%. The model results ndcate that baselne optmsm leads to hgher cancer rsks for the majorty of the subjects n the sample. Subjects wth baselne optmsm measures n the hghest quartle of dstrbuton engage n behavors that, as a result of ths optmsm, ncrease ther cancer rsk by at least 13.7%. The fgure s slghtly lower for males (11.5%) and hgher for females (15.6%). For the medan subject, cancer rsks are ncreased by 4.9% n the all-subjects model. The lowest quartle of subjects, who are baselne pessmstc, actually experence a modest declne n ther cancer rsk. We hypotheszed that control optmsts, belevng that preventatve actvtes are more effectve than they actually are, would engage n more effort and thereby lower ther cancer rsks. The model results bear ths out. In the all subjects model, the most optmstc 25% of the sample experence a 13.3% or greater declne n ther cancer rsk as a result of relatvely hgh level of preventon effort. As wth baselne optmsm, the effect s slghtly stronger for females. The effect of control optmsm on cancer rsk s 31

46 stll qute large at the medan and n the lowest quartle, wth cancer rsks fallng by 8.9% and by as much as 4.2%, respectvely, n the all-subjects model. VI.B. Baselne Optmsm and Demand for Insurance The second component of selecton concerns the wllngness to pay for full nsurance. We estmate three probt regressons (all subjects, male and female) wth the dependent varable Yes 1 f the subject agrees to pay the stated premum for nsurance and zero otherwse. The regressors nclude Premum (the nsurance premum offered to the subject), Cogntve Ablty, Rsk Averson, and a set of demographc controls. To nvestgate the effect of baselne optmsm on the demand for nsurance, the models nclude Baselne Optmsm and the Baselne Optmsm*Info nteracton varable. The nteracton varable allows us to test whether the nformaton on cancer rsks and causes provded mmedately pror completng the survey mtgates the dstortonary nfluence that optmsm about one s cancer rsk may have on the nsurance-purchase decson. Agan, we conducted a Durbn-Wu-Hausman test (Wooldrdge 2003 pg. 506) and faled to reject the null hypothess of exogenety of Baselne Optmsm n the probt model. The model results appear n Table 3. In the all-subjects model, the coeffcent of the premum amount s negatve and statstcally sgnfcant, ndcatng that as the plan premum ncreases, people demand less cancer nsurance, all else equal. Older subjects and hgher-ncome subjects have a hgher wllngness to pay for the nsurance than ther 32

47 younger, lower-ncome counterparts. Subjects who report that they are of Afrcan or Asan descent have a hgher wllngness to pay than those who self-report as Caucasan or Hspanc. Cogntve ablty and rsk averson are not sgnfcant n the model. The average wllngness to pay for nsurance s $51.03 per month. Table 3. Probt Models of Wllngness to Pay for Insurance: Dependent Varable Equals One f the Subject Agreed to the Insurance at the Offered Premum The model results for males appear n column 2. The average wllngness to pay for males s lower than the full sample at $36.34 per month. The coeffcent of the baselne optmsm varable s negatve and statstcally sgnfcant (p-value=0.06), whereas the coeffcent of the Baselne Optmsm*Informaton nteracton varable s postve and statstcally sgnfcant (p-value=0.04). We nfer that the hgher the subject s baselne optmsm, the less lkely the subjects s to agree to purchase the nsurance at the stated 33

48 premum amount. As a consequence, the wllngness to pay for nsurance s lower for male subjects who are overly optmstc about ther cancer rsks. The effect s sgnfcantly attenuated for subjects who receved the nformaton on rsk and preventon strateges pror to fllng out the questonnare, as evdenced by the postve and sgnfcant coeffcent of the nteracton of the optmsm and nformaton varables. Lke the model ncludng all of the subjects, black men are wllng to pay sgnfcantly more for the nsurance than Caucasans. Wllngness to pay s ncreasng n ncome, wth an addtonal $1000 of ncome ncreasng wllngness to pay by about $0.65 per month. Accordng to the model, wllngness to pay for men s ndependent of age, martal status, and whether or not they have a college degree. Rsk averson and cogntve ablty are also not statstcally sgnfcant. Column 3 gves the results of the nsurance model for females. As expected, the coeffcent of the premum amount s negatve and sgnfcant, ndcatng that the hgher the premum offered to the subject, the more lkely they are to refuse the nsurance. The average wllngness to pay for nsurance mpled by the model s $63.67 per month. As wth the model for males, cogntve ablty and rsk averson are not statstcally sgnfcant. In contrast wth the males n the sample, baselne optmsm does not appear to nfluence female wllngness to pay for nsurance. Rather, demographc varables seem to be most mportant. Whle age dd not play a role among males, the coeffcent of age n the female sample s postve and sgnfcant. Accordngly, women are wllng 34

49 to pay roughly $1 per month more for nsurance as they age one year. As n the male sample, wllngness to pay for nsurance s ncreasng n ncome, wth an addtonal $1000 n ncome ncreasng wllngness to pay by about $0.35 per month. Asan women are wllng to pay more for nsurance than those of other ethnctes. VI.C. Insurance Selecton Classfcaton Model We now turn to an effort to classfy the male subjects n our sample accordng to ther excess wllngness to pay for nsurance and excess preventon effort. 11 We defne the two varables that represent excess preventon and excess wllngness that results from optmsm, holdng all other model varables constant: Excess Preventon Effort Control Optmsm Baselne Optmsm ExcessWTP CO, PE BO, PE Baselne Optmsm BO, WTP where CO, PE and BO, PE are the estmated coeffcents of Control Optmsm and Baselne Optmsm, respectvely, n the preventon effort models, and BO, DEM s the estmated coeffcent of Baselne Optmsm n the nsurance demand model. Note that these varables measure effort and wllngness to pay for nsurance relatve to what the subject would engage n f he knew hs true rsk type. Thus postve (negatve) values represent excess (defcent) effort and wllngness to pay relatve to the true rsk type. We allow our measures of excess wllngness to pay and effort to vary wth X, a column vector of ndvdual s characterstcs; β and β, column vectors of prev wtp 11 Because we dd not fnd evdence that female demand for nsurance s correlated wth baselne optmsm, we conducted ths partcular exercse for male subjects only. 35

50 parameters; and correspondng measurement and/or observaton errors u prev, and u, wtp, as follows : Excess Preventon Effort X β u (9 a) wtp wtp, prev prev, Excess WTP X β u (9 b) For example, the jont probablty that the subject falls n Class C 11 s then: p P( Excess Preventon Effort 0; ExcessWTP 0) (10) 11, X βprev prev, 0; X βwtp wtp, 0 X βprev prev, ; X βwtp wtp, P u u P u u If we make the smplfyng assumpton that the measurement/observaton errors are ndependently and dentcally dstrbuted, wth a bvarate normal dstrbuton and 2 correlaton, wth 0 and prev 0,.e. 2 wtp uprev, u wtp, 0 1, N,, (11) prev wtp 0 1 then a consstent estmator for the classfcaton probablty s: 11, 2 prev wtp prev wtp pˆ X βˆ ; X β ˆ ˆ, ˆ, ˆ, (12) where parameters ˆ, ˆ, and ˆ, and parameter vectors β ˆ prev and β ˆ wtp are estmated p d usng bvarate probt. We then apply the resultng parameter estmates and ndvdual characterstc vector X to (12) to estmate the respectve probabltes of subject fallng nto each of the four classes, p11,, p10,, p01,, and p00, For clarty s sake, and wthout loss of generalty, we wll restrct our dscusson throughout ths secton to estmates for the C 11 classfcaton. Calculatons for the three classes (C 10, C 01, and C 00 ) nvolves a straghtforward swtchng of the ndces and the correspondng sgns of the probt regressands. Alternatvely, we could change the drecton of one or more of the nequaltes n (10), and then adjust the cdf calculaton n (12) accordngly. For example, 36

51 One must be cautous when nterpretng these classfcatons. They represent subjects excess wllngness to pay and excess effort relatve to ther true rsk type, after extractng other sources of heterogenety n these varables. As such, they gve us nformaton about how optmsm alone may nduce selecton, controllng for other factors such as cogntve ablty and rsk averson that could also potentally lead to selecton n an nsurance market. Thus, they are not tests for selecton n total, but only represent the possble contrbuton of optmsm to selecton. Nevertheless, when aggregated over a szable populaton they gve helpful nsghts nto the type of nsurance purchasng and preventatve-related behavor n whch members of the populaton are lkely to engage. The results of the bvarate probt model are reported n Table 4. Dependent Varable Preventon Effort Indcator WTP Indcator Coef. Std. Err. Coef. Std. Err. Rsk Averse Cogntve Ablty Black Asan Age Age^ Income ($000) College Marred * n 218 rho Wald chsquared(18) (p-value = 0.553) Table 4. Results of the Bvarate Probt Classfcaton Model X βˆ X βˆ PX ˆ, ˆ ˆ βprev uprev P X βprev uprev, ; X βwtp uwtp, X ˆ ˆ ˆ ; ˆ ˆ, ˆ, ˆ βprev prev X βprev X β wtp prev wtp. pˆ P u ; u 10, prev prev, wtp wtp,

52 VI.D. Populaton Classfcaton Predctons and Confdence Intervals One useful applcaton of ths model s to estmate the proporton of our sample that falls nto each of the four classfcatons. Gven consstent estmates for ndvdual classfcaton probabltes, derved by applyng (12) above, a lnear combnaton of these estmates yelds a consstent estmator for populaton classfcaton ratos: n n 11, n ˆ ˆ ˆ ˆ ˆ ˆ n prev wtp prev wtp X β X β Pˆ E p ;,,, (13) where P 11, s the estmated proporton of the populaton that fall n the C 11 classfcaton 13. Constructon of confdence ntervals on the classfcaton estmator s not nearly as straghtforward, due to the fact that the estmator employs a non-lnear transformaton, the bvarate normal cumulatve dstrbuton functon 2. Therefore, we cannot 2 2 employ a smple lnear combnaton of estmated varances ˆ prev and ˆwtp to n turn estmate the varance and thus the standard error ˆ P11 of classfcaton probablty ˆP 11. To solve ths problem, we employed two methods: the delta method, and bootstrappng. 13 As before, for smplcty s sake we wll restrct our dscusson to the C 11 classfcaton. However, calculaton of classfcaton predctons for the other three classes nvolves a straghtforward swtchng of the ndces and the correspondng sgns of the probt regressands. 38

53 VI.D.1. Usng the Delta Method to Construct Classfcaton Confdence Intervals As outlned n Greene (2012, pp ), Feveson (1999), and Oehlert (1992), the delta method can be used to estmate the standard errors of a vector of transformed parameters. Here, we follow and adapt the dervaton from Greene for a bvarate probt objectve functon. We frst defne f β ˆ β ˆ X ˆ ˆ ˆ pˆ 11, 2 X β ˆ X β ˆ ˆ ˆ ˆ ;,,, ;,, (14) prev wtp prev wtp prev wtp prev wtp as a functon of the least squares estmators of the two latent bprobt ndexes. We take vector X, contanng observatons on each of the p 9 regressors for subject, as well as sample populaton parameters ˆ, ˆ, and ˆ, as gven and determned. prev wtp Then, droppng the exogenous terms for clarty s sake, and assumng that f ˆ ; ˆ βprev β wtp s both contnuous and contnuously dfferentable at true parameter values β, wtp we then defne β prev and T f ˆ ; ˆ (β prev β wtp ) ˆ T β prev C(βˆ ; ˆ prev β wtp ) (15) f ˆ ; ˆ (β prev β wtp ) ˆ T βwtp as a 1 2p row vector of frst dervatves, wth respect to each of the 2 p parameters. For the sake of clarty, the dervaton of the partal dervatves specfed n (15), for a bvarate normal cumulatve dstrbuton functon, s shown n detal n Appendx II. 39

54 By applyng the Slutsky theorem (Greene 2012, pg. 1073) to (15), we then have: plm f (βˆ ; β ˆ ) f (β ; β ) (16 a) prev wtp prev wtp T and f (β prev; β wtp ) T β prev plm C(βˆ ; ˆ prev β wtp ) Γ. (16 b) f (β prev; β wtp ) T βwtp To apply the delta method, we then expand functon f usng a frst-order Taylor seres approxmaton, and have: βˆ prev β prev ˆ ; ˆ f(β prev β wtp ) f(β prev; β wtp ) Γ (17) ˆ βwtp βwtp Then, applyng Greene s dervaton (Greene 2012, pg. 69) to the bvarate normal cumulatve dstrbuton functon, the estmator of the asymptotc covarance matrx s then: T T X X ˆ X X ˆ ˆ ˆ prev prev wtp ˆ Est. Asy. Var f (βˆ ; β ˆ ) C C. (18) 2 T p11, prev wtp 1 1 T 2 T X X X X ˆ ˆ ˆ ˆ prev wtp wtp 40

55 Densty Densty Densty Densty Estmates for ˆ p11, and ˆ ˆ are then readly derved from the observed data. 2 p11, p11, Fgure 2 contans hstograms depctng the dstrbuton of estmated standard errors, ˆ, for each of the four ndvdual classfcaton probablty estmators. p XX, p10stderr p11stderr (a) Dstrbuton of ˆ (b) Dstrbuton of ˆ p10, p11, p00stderr p01stderr (c) Dstrbuton of ˆ (d) Dstrbuton of ˆ p00, p01, Fgure 2. Hstograms of the Estmated Standard Errors of Indvdual Classfcaton Probabltes 2 If we assume the ndependence of each subject s estmate ˆ, we can show that the classfcaton estmator meets the condtons for the Lapunov Central Lmt Theorem p11, 41

56 and the Lndeberg-Feller Central Lmt Theorem, and therefore conclude that the dstrbuton of 1985, pg. 92). n 1 n 1 ˆ 2 p11, s asymptotcally normal (Rao 1973, pg. 127, also Amemya Then, we have: n n n 2 ˆ 1 ˆ 1 ˆ ˆ ˆ ˆ P Var P Var n p11, n( n1) Var p11, Cov p11,, p11, j 1 1 j n n ˆ ˆ ˆ n( n1) p 0 11, n( n1) p11, n1 p ˆ ˆ P11 n1 p11 ˆ 2 p11 ˆ P. (19) 11 n 1 Applyng the normalty assumpton, the two end ponts for a 1 percent confdence nterval, for the populaton classfcaton estmate P, 11 can then be constructed as: P Pˆ t ˆ (20) 11, LB 11 n1, /2 P11 P Pˆ t ˆ 11, UB 11 n1, /2 P11 The resultng confdence nterval estmates for 0.05 are shown n Table 5, alongsde estmates derved from the bootstrappng method. 42

57 VI.D.2. Usng Bootstrappng to Estmate Classfcaton Confdence Intervals To motvate our use of bootstrappng, we frst defne Z 11 to be the total number of members of sample populaton n who properly fall wthn classfcaton C Snce the ndvdual classfcaton probabltes are assumed to be ndependent, we can express Z11as the sum of n Bernoull varables: Z 11 n b, where P( b 1) p11,, P( b 0) 1 p11,. (21) 1 Note that f the values for p11, p0 n, that s, f ndvdual classfcaton probabltes are all equal, and determnstc (.e., measured wthout error), then the probablty mass functon for Z 11 would follow a bnomal dstrbuton, wth mean np 0 and varance np 1 p (Ross 2010, pg. 54). From there t would be straghtforward to calculate the probablty mass functon of populaton classfcaton rato P Z and, 11 n 11 because bnomal dstrbutons are asymptotcally normal as n, to apply the 1 p 0 Central Lmt Theorem and estmate confdence ntervals for the dstrbuton of P 11 (Wackerly 2008, pg. 379). Snce nether of these premses s true, we must fnd another way of estmatng the probablty mass functon of Z, and therefore to derve confdence ntervals for 11 P 11. In addton to the Delta Method descrbed n secton VI.D.1., we can also employ the bootstrap method. 14 As before, we follow the dscusson for classfcaton C 11 only, for smplcty s sake. 43

58 Note that two stages of randomzaton are requred to properly employ bootstrappng n ths context: a frst stage to randomly assgn values to measurement/observaton errors u and u,, and thereby to calculate ndvdual classfcaton probabltes p ; 11, and, prev, wtp a second stage of randomzaton to test whether each ndvdual Bernoull varable results n a classfcaton or non-classfcaton, as specfed n (21). The number of ndvduals thus classfed then represents one bootstrapped measurement of Z, and 11 by repeatng ths procedure a number of tmes, we can estmate the dstrbuton functon of Z, and thereby of 1 11 P Z enablng us to estmate confdence ntervals, 11 n 11 for the proporton of our sample properly classfed n C 11. In our frst step, we randomly assgn values to measurement/observaton errors u prev, and uwtp, for each ndvdual, usng our assumpton from (11) that these stochastc error terms are ndependently and dentcally dstrbuted, wth a bvarate normal dstrbuton and wth correlaton : uprev, u wtp, 0 1, N,. prev wtp 0 1 Once we have selected approprate values for these error terms, we then use them to calculate the resultng (perturbed) classfcaton probablty for each ndvdual: pˆ ˆ X u ; ˆ X u ˆ, ˆ, ˆ. (22) * * * 11, 2 prev prev, wtp wtp, prev wtp 44

59 In our second stage of randomzaton, we generate a separate unform random varable v Unform (0,1) for each ndvdual, then sum the number of ndvduals whose ndvdual classfcaton probablty p * ˆ11, dong so, we satsfy the Bernoull condton specfed n (21). exceeds ther correspondng value for v. By Now, as a functon defned on stochastc varables, Z 11 s tself stochastc, wth ts own (unspecfed) dstrbuton, whch may not necessarly be normal. To construct an nterval wth confdence level 1, we then emprcally calculate endponts k Z11, LB arg max Count Z11, q m, and k q0 2 m Z11, UB arg mn Count Z11, q m. (23) k qk 2 Fnally, we construct end ponts for each respectve populaton classfcaton confdence nterval as: P Z 1 11, LB m 11, LB 1 11, UB m Z11, UB (24) P The classfcatons arsng from the model, wth m 80, are gven n Table 5. 45

60 Classfcaton C11: Increased Effort, Increased Ins Demand (Advantageous) C10: Increased Effort, Decreased Ins Demand (Adverse) C01: Decreased Effort, Increased Ins Demand (Adverse) C00: Decreased Effort, Decreased Ins Demand (Advantageous) Estmated Proporton n Class Standard Error on Estmate (Delta Method) % Confdence Interval (Delta Method) * % Confdence Interval (Bootstrappng) Table 5. Subject Populaton Classfed as Adverse or Advantageous Selectors Based on Bvarate Probt Model, wth Confdence Intervals derved from the Delta Method and Bootstrap Procedure 15 VI.E. Classfcaton Results Some 77 percent of our male subjects are thus estmated to fall nto ether class C 00 or C 10, ndcatng that these subjects wll reject a polcy wth premum equal to the far prce plus a rsk premum. By contrast, a smaller porton (~22 percent) of our male subjects are estmated to fall nto the C 11 class, mplyng ther pessmsm about ther cancer rsk would lead them to purchase the nsurance contract at the far prce plus a premum, whle smultaneously engagng n more preventon effort than they would f 15 * - Note that for the C01 classfcaton, pˆ s of the same order of magntude as ˆ p 0.008, 01 and the estmated lower bound for ˆp s actually negatve, whch has no economc meanng. We are 01 therefore hestant to conclude that the normalty approxmaton s suffcently accurate for ths partcular classfcaton, and take the constructed confdence nterval as suggestve only. 46

61 they knew ther true rsk type. Indeed, they wll see ths polcy as a bargan. Only a small number of subjects (~2 percent) are predcted to fall n the C 01 class, mplyng purchase of the nsurance contract whle smultaneously under-nvestng n preventatve measures, leadng to adverse selecton 16. Thus, controllng for rsk averson and cogntve ablty, our sample s consstent wth a market that s composed prmarly of relatvely low-rsk types who engage n more preventon than the subjects who refuse the far nsurance. Subjects who are optmstc about ther cancer rsk, who comprse most of our sample, reject far nsurance. Thus, pessmsm about cancer rsk and optmsm about the effcacy of preventon effort lead to advantageous selecton. 16 Only 2 percent of our male subjects are estmated to be classfed n the C01 quadrant; ths s an unsurprsng result, consderng the strong tendency for all subjects, both male and female, to be both control optmstc and baselne optmstc. In order to be classfed n the C01 quadrant, one would have to exhbt both baselne pessmsm (leadng to hgher wllngness to pay) and have a control pessmsm measure of a relatvely large magntude, enough to overcome the effects of baselne pessmsm on preventatve effort (n net, leadng to decreased exerton). Our results suggest we cannot be confdent any of our subjects exhbted such a combnaton of rsk msperceptons. 47

62 VII. Dscusson The models show that heterogenety n rsk perceptons can ndeed play a key role n selecton n nsurance markets. For one, we show that 77 percent of our sample are baselne optmstc whle 90 percent are control optmstc, ndcatng that people s perceptons of rsk and preventon effcacy are not well algned wth expert s assessments. We show that baselne optmsm lowers male subjects wllngness to pay below what t would be f they knew ther true rsk type. We also show that baselne optmsm dscourages preventon effort, rasng overall cancer rsk. Nevertheless, control optmsm leads subjects to engage n more effort, thereby lowerng ther aggregate rsk of the cancers n queston. Our classfcaton model ndcates that the nteracton of baselne and control optmsm on subject s wllngness to pay for nsurance and preventon efforts results n advantageous selecton where hgh-rsk types reject coverage and only low-rsk types wth hgh levels of preventon effort are nsured. Of course, dfferent samples could gve dfferent outcomes. If, for example, our sample was domnated by subjects who were suffcently pessmstc about preventon effcacy that they under-nvested n preventon, they we would have nferred adverse selecton rather than the advantageous selecton we found here. 48

63 One of the perhaps more ntrgung fndngs s the dfference between the nsurance models for males and females. Whle baselne and control optmsm nfluence preventatve behavor for both genders, the average woman s wllngness to pay for nsurance s not a functon of baselne optmsm. Of course, women and men were quered about a dfferent set of cancers. It could well be that ths s the source of ths dsparty, rather than any nherent dfferences between how men and women act on ther rsk perceptons. Others have shown that hghly-publczed rsks, especally assocated wth a dreaded dsease such as breast cancer, may lead to exaggerated perceptons of dsease rsk (Slovc 1987). Ths could be leveragng the results for women. Another ntrgung fndng of the nsurance model s that the effects of baselne optmsm on the demand for nsurance were largely nullfed for subjects who receved the cancer-rsk nformaton pror to takng the survey. To further nvestgate the effect of nformaton, we regressed the optmsm varables on nformaton and demographc controls. We found that nformaton dd not nfluence baselne optmsm sgnfcantly, but nformaton acted to ncrease the level of control optmsm. These are nterestng results that we plan to explore further n future papers. Past research has found evdence that rsk averson and cogntve ablty nfluence demand n some nsurance markets [Guso and Paella (2005), Barsky et al. (1995), Cohen and Segelman (2010), Enav and Fnkelsten (2011)]. We estmated a smple 49

64 nsurance model that ncluded the premum and the rsk averson varable as the only covarates, and found that coeffcent of the rsk averson varable was postve and statstcally sgnfcant. Smlarly, the coeffcent of cogntve ablty s postve and statstcally sgnfcant n an nsurance model that excludes all varables except the measure of cogntve ablty and the nsurance premum. Ths may be a symptom of multcollnearty among the varables that s elevatng the standard errors of the coeffcents of rsk averson and cogntve ablty when the full range of covarates s ncluded. Thus, we are hestant to conclude decsvely that cogntve ablty and rsk averson do not play a role n cancer nsurance demand. It could well be that measurement error and/or multcollnearty are leadng to an overestmate of ther standard errors n the nsurance models. Nonetheless, rsk averson and cogntve ablty are not sgnfcant predctors of preventon effort even n smple models, and therefore the case for any selecton arsng from these varables n ths sample s very weak. 50

65 VIII. Conclusons In ths paper, we report the results of a survey of 474 men and women that analyzes wllngness to pay for cancer-care nsurance, factors that affect the demand for nsurance, and varables that nfluence cancer-preventon actvtes. In partcular, we seek to test whether rsk mspercepton leads to selecton, controllng for other possble sources of selecton such as cogntve ablty and rsk averson. We offer evdence that supports Spnnewjn s (2013) hypothess that selecton may occur as a result of subjectve msperceptons about baselne cancer rsks and the effcacy of health-rsk reducton actvtes. Our statstcal results ndcate that the more optmstc a male subject s concernng hs baselne cancer rsk, the lower hs wllngness to pay for cancer nsurance. We do not fnd evdence of ths effect wth females, however. We also fnd that subjects (both male and female) who over-estmate the return to preventatve behavors are more lkely to nvest n preventatve effort, thereby lowerng ther cancer rsk and expected assocated health-care costs. The pattern of nsurance, choce, preventon behavor, and rsk mspercepton can lead to adverse or advantageous selecton, dependng on the relatve nfluence of control and baselne optmsm on behavor. The models control for other varables, such as rsk averson and cogntve ablty that have been shown to lead to selecton n nsurance markets. We fnd weak evdence that 51

66 these varables nfluence wllngness to pay for nsurance, but no evdence that they are correlated wth preventatve effort. Stll, these relatonshps may be present but clouded by multcollnearty and/or measurement error problems. We recommend that future studes elct alternatve measures of cogntve ablty and rsk averson to further examne ther nfluence on demand for nsurance and preventon actvtes. Ths s the frst emprcal study we know of that nvestgates rsk mspercepton as a source of selecton. We beleve the results reported here are useful to researchers nterested n rsk communcaton, rsk percepton as well as selecton n nsurance markets. That sad, there are lmtatons to the analyss. For one, the data s based on a hypothetcal market so that people never actually purchased or refused the nsurance. People may well make dfferent choces n a hypothetcal market, n the context of a survey, than they make when purchasng actual nsurance polces. 52

67 Appendx I: Notes on Survey Methodology As descrbed n the Acknowledgements, we receved a total of 549 completed survey responses. An addtonal 42 respondents began, but dd not complete, the surveys. Of the completed surveys we receved, we rejected 71 (leavng 478), for the followng reasons: - Duplcate Internet Protocol Address or Amazon Mechancal Turk ID: 28 - Had Cancer: 23 - Lattude/Longtude Outsde Unted States: 11 - Completed Survey n Under 5 Mnutes: 9 - Total: 71 As descrbed n the Overvew, we conducted the survey usng Qualtrcs, and solcted respondents through Amazon Mechancal Turk (AMT). Surveys were conducted on separate dates, between October 2013 and September Separate surveys were ssued for colon, bladder, breast, and prostate cancers, and for each of these, a further dfference was that half of the surveys contaned nformaton booklets at the begnnng of the survey, and others dd not. Respondents were unaware that the surveys were dfferent; the only dfference they were able to perceve was whether a survey was meant for women or men. Each survey was open for several days, and was cut off automatcally by AMT when we reached the target number of desred respondents. We rejected surveys that were completed n under 5 mnutes, reasonng that such surveys were lkely not carefully read or answered by respondents. We also rejected surveys that orgnated from the same IP address, or usng the same AMT ID, as a prevous survey, reasonng that these were lkely the same respondent, or possbly a household member. In ether case, selecton bas could be present f we allowed more than one response per IP address or AMT ID. We rejected surveys from those who have had or currently have cancer, because the HCRI relatve rsk factors do not apply to such ndvduals, and hence any measures we could develop for these ndvduals usng the HCRI would be nvald. Fnally, we rejected survey responses that orgnate from outsde the Unted States, as the HCRI relatve rsk factors are specfc to the U.S. populaton. A possble source of measurement error that could bas results s that due to respondents who began, but dd not complete the survey. As noted above, 42 of the 53

68 591 persons who ntated the survey dd not complete t. The vast majorty of these qut the survey wthn the frst mnute, as measured and recorded by Qualtrcs. As cted n Gravelle and Lachapelle (2015), procedures for handlng mssng data, and for mputng nonresponse n surveys, s addressed n Allson (2001), Lttle and Rubn (2002), and Rubn (1987). However, the majorty of our ncomplete surveys contaned no responses at all; by desgn wthn Qualtrcs, we were able to force responses to all questons we posed to respondents. We were left wth 549 fully complete surveys, and 42 surveys that contaned lttle or no data at all. Therefore, technques for mputng nonresponse were not applcable to the majorty of the 42 ncomplete surveys. We nevertheless should consder the possblty that these aborted surveys may have led to measurement error n one or more of our estmatons. We reason that whle some of these termnated surveys may have been due to nternet connecton or other techncal dffcultes, whch would lkely have been uncorrelated wth the regressors and therefore unlkely to bas results, the majorty of these termnated surveys were lkely due to respondent fatgue, or lazness. If lazness s then correlated wth one of our regressors, such as age, gender, ncome, or educaton level, then ths would tend to bas our results. However, as the majorty of termnated surveys occurred before demographc questons were asked, many n the booklet phase before any questons at all had been asked, we have no way of estmatng possble correlatons for these subjects. Wth a 7 percent survey abort rate, we do however conclude that any bas n our results s lkely to have been small. 54

69 Appendx II: Dervaton of Partal Dervatve of Bvarate Normal Cumulatve Dstrbuton Functon In (15) we reference the partal dervatves of the bvarate normal cumulatve f ˆ ˆ (β prev; β wtp ) f ˆ ˆ (β prev; β wtp ) dstrbuton functons, and, whch we wll develop here. ˆ T β ˆ T β From (14) we have: prev β ˆ β ˆ 2 X β ˆ X β ˆ ˆ ˆ ˆ f ; ;,,. prev wtp prev wtp prev wtp From Johnson and Wchern (2007, pg. 151), we have the bvarate normal probablty densty functon: prev, prev, wtp, wtp, 2 prev, prev, prev wtp prev prev wtp wtp prev, wtp, ˆ ˆ prev wtp wtp 2, exp ( II.1) X βˆ X βˆ wth,, X βˆ X βˆ E, and E. prev prev prev wtp In the followng dervaton, we substtute nto (II.1) our parameter estmates ˆ prev, ˆ wtp, ˆ, ˆ ˆ 1 prev n X β prev, and ˆ ˆ wtp n X β wtp. 1 n 1 n 1 The bvarate normal probablty densty functon s ntegrable, leadng to the followng specfcaton for the bvarate normal cumulatve dstrbuton functon: ˆ dxdy prev, wtp, x 2 xy y 2 prev,, wtp, exp 2 2 2ˆ ˆ ˆ 2 1 ˆ prev, wtp, 1 prev, wtp, ˆ ˆ ; ˆ x xy y f βprev βwtp exp dxdy ( II.2) 2 2 2ˆ ˆ 1 ˆ 2 1 ˆ prev wtp 55

70 As stated prevously, we wll take β ˆ prev and β ˆ wtp to be vectors of estmated coeffcents of the latent bvarate probt ndexes. Wthout loss of generalty, and for clarty s sake, we arbtrarly chose a coeffcent n vector β ˆ prev, say ˆ j, wth values for j between 1 and p, and then calculate the partal dervatve of f wth respect to ˆ j. Note that ˆ j s stochastc, and as the bvarate normal dstrbuton s both contnuous and contnuously dervable across ts doman, we have: β ˆ ; βˆ f β ˆ ; βˆ, f ˆ ˆ prev wtp prev wtp prev j prev, j ( II.3) The rght-hand sde of the product n (II.3) s readly derved as X βˆ ˆ X ˆ ˆ ˆ ˆ j j prev prev, prev prev j prev, ( II.4) where X j s the observaton for exogenous varable j made on subject. We can then apply the Fundamental Theorem of Calculus (Golberg and Cho 2010, pg. 11) to the left-hand sde of the product n (II.3): f β ˆ ; βˆ 2,,, prev wtp prev wtp prev, prev, prev, wtp, x 2 ˆ xy y exp dxdy 2 2 2ˆ ˆ 1 ˆ ˆ prev, 2 1 prev wtp wtp, 1 1 x 2 ˆ x exp 2 2ˆ ˆ 1 ˆ 2 1 ˆ prev wtp 2 2 prev, prev, 2 dx ( II.5) Then, ratonalzng the exponent n (II.5) we have: x 2 ˆ x 2 2ˆ ˆ 2 ˆ 2 2,, 1, 1 prev prev x x prev prev, ˆ 2 1 ˆ 56

71 2 1 ˆ x ˆ 2 prev, x 2 ˆ x ˆ prev, y prev, 2, 1 prev 2 2 prev, ˆ 1 ˆ ˆ 2, 1 ˆ prev x prev, ˆ 2 Substtutng back nto (II.5), we have: f ˆ ˆ wtp, β β 2 2 ; 1 1 x ˆ e exp dx ( II.6) 2 2 prev, 2 1 ˆ ˆ 2 1 ˆ prev wtp prev wtp prev, /2 prev, Now, changng varables of ntegraton and substtutng nto (II.6), let x ˆ prev, 2 u du dx 1 du 2 2 dx 1 ˆ 1 ˆ 2 ˆ ˆ wtp, f βprev; β wtp 1 2, /2 1 x ˆ prev prev, e exp dx 2 2 prev, 2 1 ˆ ˆ ˆ 2 1 ˆ prev wtp 2 ˆ ˆ ˆ prev wtp 2 A u 2 prev, / e e 1 ˆ A 1 1 2, /2 u 1 prev 2 prev e e ˆ wtp 2ˆ du prev 2 ˆ wtp f β ˆ ; βˆ 1, 1A prev wtp prev prev, ˆ wtp ˆ du A 1, 1, ( II.7) 1 where A ˆ wtp, prev, 2 1 ˆ. Combnng results from (II.4) and (II.7) nto (II.3), we have: 57

72 β ˆ ; βˆ β ˆ ; βˆ 1, 1 f prev wtp f prev wtp, prev A prev X j ˆ ˆ ˆ ˆ j prev, j wtp prev f ˆ ˆ βprev; βwtp X ˆ j wtp, prev, 1 prev, 1 ˆ ˆ 2 j prev wtp 1 ˆ ( II.8) where agan for clarty we have substtuted: X βˆ ˆ X βˆ ˆ, prev prev wtp wtp prev, wtp, ˆ ˆ prev wtp. Snce ˆ j was chosen arbtrarly from β ˆ prev, we can smlarly derve the other partal dervatves n ˆ ˆ f ˆ ; ˆ (β prev β wtp ) : ˆ T β prev wtp, prev, X 1 1 prev, 1 2 X wtp, prev, f (β prev; β wtp ) prev, 1 2 ˆ T 1 ˆ β ˆ ˆ prev prev wtp X ˆ 1 ˆ ˆ ˆ wtp, prev, p 1 prev, ˆ T f ˆ ˆ ˆ (β prev; β wtp ) 1 wtp, prev, 1 prev, 1 X ˆ T ˆ ˆ 2 β prev prev wtp 1 ˆ ( II.9) Now, by symmetry we can repeat steps descrbed above n (II.3) through (II.9) for any arbtrary ˆk nβ ˆ wtp, yeldng: 58

73 f βˆ ; βˆ X ˆ,, wtp prev wtp k prev wtp 1, 1 ˆ ˆ ˆ 2 k prev wtp 1 ˆ ( II.10) and f ˆ ˆ ˆ (βprev; β wtp ) 1 prev, wtp, 1 wtp, 1 X ˆ T ˆ ˆ 2 βwtp prev wtp 1 ˆ ( II.11) Fnally, substtutng (II.9) and (II.11) nto (15), we arrve at T f ˆ ˆ ˆ (β prev; β wtp ) wtp, prev, 1, 1 ˆ T prev X 2 1 ˆ prev β ˆ ˆ 1 prev; C(β β wtp ) ˆ ˆ prev wtp f ˆ ; ˆ (β prev β wtp ) ˆ prev, wtp, ˆ T 1 wtp, 1 X 2 βwtp 1 ˆ T, ( II.12) for whch values can readly be calculated gven observaton vector X, and estmates prevously derved for ˆ, ˆ, and ˆ; the resultng vector prev 2 substtuted nto (18) to yeld a consstent estmate for ˆ. prev p11, C can then be 59

74 Appendx III: Copy of Qualtrcs Survey In the followng twenty pages we show a copy of the survey used for men, for colon cancer. Smlar surveys were used for women for colon cancer, and for both women and men for the other three cancers, as approprate. Note that approxmately half of survey respondents were presented wth nformaton on one of the three cancers, and the other half were not. 60

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