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       ROBUSTNESS OF VSL VALUES FROM CONTINGENT VALUATION SURVEYS *
                                        By
                                  Anna Alberini
                 Department of Agricultural and Resource Economics
                                 2200 Symons Hall
                              University of Maryland
Address for correspondence:
Anna Alberini
AREC, 2200 Symons Hall
University of Maryland
College Park, MD 20742
USA
Phone 001 301405-1267
Fax 001 301314-9091
e-mail: aalberini@arec.umd.edu
ABSTRACT. This paper examines factors that may influence the estimates of the Value
of a Statistical Life obtained from contingent valuation surveys that elicit the willingness
to pay (WTP) for mortality risk reductions. We examine the importance of distributional
assumptions, the choice of the welfare statistics of interest, the procedure for computing
them, outliers, undesirable response effects, and internal validity of the WTP responses.
We illustrate the importance of these factors using dichotomous-choice and  open-ended
WTP data from four recent contingent valuation surveys.

Key words: contingent valuation,  VSL, WTP,  risk reductions,  robustness, outliers,
endogeneily.

Subject Area Classifications: Health, Valuation, Benefit Cost Analysis
* This research was conducted under Cooperative Agreement 015-29528 with the U.S. Environmental
Protection Agency. I wish to thank Drs. Johannesson, Persson and Gerking for making their data available
to me. I also wish to thank my project officer, Nathalie Simon of the US Environmental Protection Agency,
for her guidance with this project, seminar series participants at the U.S. EPA National Center for
Environmental Economics and session attendees at the annual EAERE meeting in Budapest, Joel Huber,
Trudy Cameron, Melonie Sullivan and Kelly Maguire for their comments on this work.

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       ROBUSTNESS OF VSL VALUES FROM CONTINGENT VALUATION SURVEYS




                                       By



                                  Anna Alberini



1. Introduction.




       The Value of a Statistical Life (VSL) is the rate at which people are prepared to




trade  off income for a reduction in their risk of dying. The VSL is  a key input  for




computing the mortality benefits of environmental and safety policies that save lives. In




recent retrospective analyses of the Clean Air Act and of the Clean Air Act Amendments,



for example, the US Environmental Protection Agency has used a VSL of $6.1 million in




its base analyses ($3.7 million  in  "alternate" analyses), and the resulting monetized




mortality benefits account for over 80% of total benefits of these environmental statutes.




Within the European Commission, DG Environment uses central VSL estimates of about




1.2 million euro, with adjustments for age and for the futurity  of the risk.l



       The VSL figures for cost-benefit  analysis purposes ars typically derived using




three  possible methods: (i)  compensating wage studies, (ii)  consumer behavior studies,




and (iii) contingent  valuation surveys. Compensating  wage studies use data  from labor




markets to infer how much workers have to be compensated to accept riskier jobs—or the




sacrifice  in  income they would  agree to  in exchange for an improvement in their



workplace safety. Viscusi and Aldy (2003) document over 60 compensating wage studies




conducted in  10 countries, noting that in the US most of the labor market studies produce




estimates of the VSL in the range of $4-9 million.




       Consumer behavior  studies observe tradeoffs between  time and  risk, or money




and risk, to place a value on mortality risk reductions.  An early such study (Blomquist,
1 See http://europa .cu.mt/contm/environment^euvecQ/Qlhers/recoinniended interim values.odt'.

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1979) observed whether or not individuals fasten their seatbelts when driving. The VSL




is calculated as the value of the time required for buckling up, divided by the reduction in




the risk of dying in a traffic accident afforded by the use of seatbelts. Atkinson and



Halvorsen (1990) obtain an estimate of the VSL from the higher price of cars with more




sophisticated safety equipment.  The VSL figures from labor market or consumer studies




are often transferred to the environmental policy context. Doing so implicitly assumes




that the preferences of individuals for income and risk do not vary with the context.




       In contingent valuation surveys, respondents are asked to report their willingness



to  pay (WTP) for a specified—and hypothetical—risk reduction.  Contingent valuation




studies have the potential  to circumvent many of the shortcomings for which the other




approaches are sometimes criticized. For example, they lend themselves to valuing risk




reductions in many contexts, and are  thus not limited to workplace risks. Rather than




assuming that people know the exact magnitude of the risks they face, in a well-designed



CV study respondents are educated about them, and the extent of the risk reduction is




spelled out explicitly for them.



       Last but not least, CV allows the researcher to survey directly the beneficiaries of




any proposed  risk-reduction measure. This is regarded as a particularly  advantageous




feature of the method, because when  the risk  reduction measure is an environmental



program, these beneficiaries (e.g.,  the  elderly) are  likely to  be very different than the




population covered in compensating wage studies, and may have different preferences for




income and risk.



       Despite these advantages  and the flexibility of the  approach,  much  debate




surrounds the estimates of VSL from contingent valuation surveys.  This paper focuses on

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two main difficulties associated with the V|SL figures from CV studies. The first is that



many  recent high-quaJity  CV surveys have  elicited  information about  WTP  using




dichotomous-choice questions. Dichotomops-choice question:; have been shown  to be



incentive compatible (Hoehn and Randall, 1987), and are generally thought to be  easier




to answer than open-ended questions. However, the researcher must rely on assumptions




about the distribution of the underlying WTP in order to obtain estimates of mean and




median WTP, and these in turn are typically sensitive to the upper tail  of the distribution




of WTP.




       Second,  it is, in general, difficult to \alue risk reductions. Respondents are not




used to dealing with probabilities, especially when risks are very small, and the cognitive




burden imposed upon them in the survey—or the failure to communicate risks to them in




a meaningful way—may result in undesirable effects, including failure to distinguish




between  risk reductions of different sizes  (Hammitt and  Graham,  1999), confusion



between  absolute  and relative  risk  reductions  (Baron,   1997), protest responses,




completely random answers to the payment questions, etc. (Carson, 2000). One possible




approach  for uncovering  these  problems is to test  for the internal  validity of the




responses, i.e., to check that WTP depends on certain variables in the ways predicted by




economic theory. Alternatively, one may try to fit models that explicitly seek to identify




abnormal responses.




       The purpose  of this paper is to  discuss the importance of distributional and



modeling assumptions, and the effect of econometric  misspecifications  and of the




presence  of abnormal response patterns in the sample on the estimates of the VSL. We




illustrate  our robustness criteria and checks using the data from four recent CV surveys.

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We examine robustness with respect to four possible criteria The first three are specific




to dichotomous-choice WTP responses. First, we examine how the VSL changes with (a)




the distribution WTP is assumed  to follow,  (b) the welfare statistic of interest (e.g.,




median or mean), given the distribution of WTP, and (c) given the distribution and the




welfare statistic, different procedures for calculating the latter.




       Our second set of analyses is similar to the first, except that it focuses on how (a),




(b) and (c) impact the estimated relationship between WTP and specific covariates. Third,




we examine outliers and abnormal  response patterns in dichotomous-choice CV surveys.




Fourth, we look at internal validity  checks.




       The  remainder of this  paper is organized as follows.  Section  II  provides  a




definition of VSL and outlines the  robustness criteria discussed in this paper. Section III




focuses on dichotomous choice CV responses, examining the robustness of VSL to the




assumed distribution  of WTP,  the welfare statistics used,  and the procedure used for




computing  such  welfare  statistics.  Section IV focuses  on  outliers  and  response




mechanisms that do not comply with the economic paradigm, such as  yea-saying, nay-




saying, and completely random responses. Section V examines how internal validity




tests, such as scope tests, are affected by the possible endogeneity of risks and  WTP, and




section VI  focuses on the relationship between WTP and income. Section VII provides




concluding remarks.

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II. Econometric Robustness of VSL Figures


A. Definition of VSL


       The Value of a Statistical Life is the rate at which individuals are prepared to


trade off income  for risk reductions. In an expected utility framework, let U(w) be the


(state-dependent)  utility associated with incpme w if the individual is alive, and V(w) the


utility of income if the individual is dead. If the probability of dying is p, expected utility


is defined as (l-p)U(w)+pV(w). This expression can be further simplified to (l-p)U(w) if


it is assumed that  V(w)=0 (i.e., the utility of income is zero when  one is dead). The VSL


is the rate of substitution between income and risk that keeps expected utility unchanged,



and is in this context equal to — = - — — - .
                            dp   (l'
       The VSL is, therefore, a derivative, but in practice contingent valuation surveys


ask people to report information about their willingness to pay (WTP) for a gjecified —


and  finite — reduction  in their risk  of dying, Ap. The VSL  is estimated  as  WTP/Ap.


Accordingly,  in this paper the robustness of the VSL estimates  and the robustness of


WTP estimates are regarded as interchangeable.





B. Robustness Criteria


       This paper examines robustness with respect to four criteria. Because many recent


high-quality  CV  studies  have  deployed dichotomous-choice  questions  to  elicit


information  about  WTP, the first series of robustness checks refers to  dichotomous-


choice CV data Specifically, we examine by how much WTP changes with  (a) the


distribution WTP is assumed to follow, (b) the welfare statistic of interest (e.g., median or

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mean), given the distribution of WTP,  and (c) given the distribution and the welfare



statistic, different procedures for calculating the latter.




       Our second set of analyses is similar to the first, except that it focuses on how (a),



(b) and (c) impact the estimated relationship between WTP and specific covariates, such




as the age of the respondent.




       Next, we turn to the issue of whether it is possible to identify abnormal responses




to dichotomous-choice WTP questions.  To identify  outliers, we  first use  a  "reduced-




form"  approach based on a regression  equation relating the response to  the payment



question  to  observable individual characteristics,  checking if the inclusion of these




observations in the sample affects appreciably the estimates of WTP, and, if so, by how




much.  In  our next step, we seek to model explicitly abnormal response  patterns. By




abnormal  response patterns, we mean answers to the  payment questions  that  do not




comply with the economic paradigm, such as responses motivated by "yea-saying" or



"nay-saying" behaviors, or completely random responses.




       Fourth,  we focus  on internal validity. We  first  work with  a dataset  where




respondents  subjectively assessed their baseline risk and were asked to value a given




reduction  in this  initial  risk.  Economic theory  posits  that  WTP should increase




appreciably with the size of the risk reduction. Moreover, meaningful VSL figures can be



computed only if individuals are valuing the  absolute risk reduction. We examine



whether our ability to empirically check  that the WTP responses are consistent with



economic  theory  and with the  VSL  construct  is  affected  by treating  WTP  as




econometrically endogenous with  risk. The specific application we use to explore these

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issues  elicits WTP using open-ended questions,  producing observations of WTP on a

continuous scale.

       Economic  theory  also  predicts that WTP should  increase with  respondent's

income. We check how the estimated income elasticity of WTP changes as respondents

who would be willing to commit a large fraction of their income to the risk reduction are

excluded  from the sample.  This  has potentially important consequences for benefit

transfer, i.e. the practice of applying the results of the study conducted at one locale to

another population or context.



III. The Data.

       We illustrate out robustness checks using data from four applications,  which we

summarize in table 1.  In the first application (Johannesson et al., 1997), a representative

sample of Swedish adults aged 18-74 were surveyed over the telephone about their WTP

for a reduction in their risk of dying. The survey was conducted in November  1996, and

produced WTP data for a total of 2029  individuals, for a response rate of 83 percent.

The  goal of the study was to study the relationship between the VSL and the age of an

individual.

       Respondents were told that X out of 10000 people of their gender and age would

die during the next year.2 They were also asked to assume that a preventive and painless

treatment  was available that  would reduce by 2 in 10000  the risk  of dying in the next

year, but have  no effects thereafter. Information about WTP was elicited  using single-

bounded  dichotomous-choice questions, with bid values  ranging  from 300  to  10000
2 The baseline risk of death over the next year was 10, 30, 70, and 200 for males in the age groups 18-39,
40-49, 50-59, and 60-69, respectively. For females, the baseline risk values were 5, 20, 40, and 100. All
baseline risks are out of 10000.

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SEK.3 Johanesson et al. estimate the mean WTP to be equal to 6300 SEK (about 954 US

dollars), which corresponds to a VSL of 31.4 million SEK (4.75 million US dollars), and

detect a quadratic relationship between age and WTP that peaks at 40 years of age.

       The  second and third applications  used in this study  employed dichotomous

choice questions  with follow-ups,  and a virtually  identical  survey  instrument for

Hamilton, Ontario (Krupnick et al., 2002)  in Spring 1999 and a national sample of US

respondents (Alberini  et  al.,  2004)  in August  2000.  Both  questionnaires were self-

administered by the respondent using the computer. In  the Hamilton study, respondents

were  asked to go to  a centralized facility to take the survey, whereas in the US studies

they received the questionnaire via Web-TV™.

       By  asking people to  value immediate and  future risk reductions (for  which

payment would have to start immediately), and by recruiting individuals of various ages,

including the elderly,  and  health statuses, these  studies  explore four  main  research

questions.  The first  is  the  relationship between VSL and  age. The  second  is the

relationship between WTP and the health status of the respondent.  This is important for

policy purposes, as some agencies have argued in favor of using Quality  Adjusted Life-

Years (QALY), a construct widely used in medical decisionmaking where values are

adjusted for quality of life, which is presumably lower for chronically ill people.

       The third research question is whether the WTP  for a future risk reduction is less

than the WTP for an immediate risk reduction (as is implied by discounting and by the

fact that the individual may die before he reaches the age when the future risk reduction
3 The payment question read as follows: "It is estimated that X(Y) men (women) out of 10,000 in the same
age as you will die during the next year. Assume that you could participate in a preventive and painless
treatment which would reduce the risk that you will die during the next year, but has no effects beyond that
year. The treatment reduces the risk of your dying during the next year from X(Y) to X-2 (Y-2) out of
10,000. Would you at present choose to buy this treatment if it costs SEK I?"

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would begin), and the fourth is how large is the implicit discount rate (Alberini et al.,




2004).




       Hie  fourth  study  (Persson  et al., ,2001) is a  mail  survey  eliciting  WTP  for




reductions in the risk of dying in a road-traffic related fatality. The survey was conducted




in Sweden in Spring 1998. Questionnaires  were mailed to a representative sample of




Swedes of ages 18-74, for a total of 2884 returned questionnaires (the response rate was




51%).  Two  versions of the questionnaire were created.  The first focused on the risk of




non-fatal injuries, while the other focused on the risk of dying in a road-related accident.




In this paper, attention is restricted on the 935 completed questionnaires about fatal risks.




       In this questionnaire, risks were expressed as X in 100,000, and depicted using a




grid of squares.  People were first shown, as an example, the risks of dying for various




causes (all causes, heart disease, stomach or  esophageal cancer, traffic accident) for a 50-




year-old.  They were then asked to  assess subjectively their risk of dying for any cause,




and in a road-related traffic accident. They were also asked directly to  report their WTP




for a reduction in each of these two risks. Unlike the previous studies, the payment




question  used an  open-ended  format,  resulting  in  observations  about  WTP  on a




continuous scale.




       In this paper, we focus on the WTP for a reduction in the risk of dying in a traffic




accident. This risk reduction is expressed as  a proportion (10%, 30%, or 50%, depending




on the questionnaire version4) of the baseline  risk.  The  risk reduction is  a private




commodity (safety equipment and preventive health care) and is valid for one year. A




reminder of the respondent's budget constraint is provided.
4 Respondents were randomly assigned to one of these possible risk reductions.

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     Table 1. Mortality Risk Studies examined in this paper. All monetary figures in US
    	          dollars, unless otherwise indicated.
       Study
                   Description and VSL
Johannesson et al.
(1997)
Telephone survey of Swedes aged 18-74. Dichotomous-choice
questions  about WTP for 2 in 10,000 reduction in their risk of
dying (from all causes).

VSL = $4.5 million.
Perssonetal. (2001)
Mail survey in Sweden. Elicits WTP for X% reduction in the
risk of dying in a road-traffic accident. Subjective baseline
risks. Open-ended WTP questions.

VSL = $2.84 million (based on WTP for 2 in 100,000 risk
reduction).
Krupnick et al.
(2002)
Survey of persons aged 40-75 years in Hamilton, Ontario.
Self-administered computer questionnaire, centralized facility.
Dichotomous-choice payment questions with dichotomous -
choice follow-up question.

VSL = Can $1.2 to 2.8 million (US $ 0.96 to 2.24 million).
Alberini et al. (2004)
US national survey conducted over Web-TV. Dichotomous-
choice payment questions with dichotomous-choice follow-up
question.

VSL =$700,000 to $1.54 million (based on 5 in 1000 risk
reduction)	
III. Estimation of VSL with Dichotomous Choice Data

       Dichotomous-choice payment questions ask respondents whether they would be

willing to pay a specified amount of money to obtain the risk reduction stated to them in

the questionnaire. The amount of money (usually termed "the bid") is randomly assigned

to the respondent out of a list of preselected values, and is varied across respondents.

Respondents are offered two possible  response categories: "yes"  and  "no."5 Their
5 When the risk reduction is delivered by a public program, the payment question is often phrased in terms
of vote in a referendum on a ballot. The respondent is told that the program would be implemented only if
there are a majority of votes in favor of the program, and that the cost of the program—usually, in the form
of an income tax—for his household is SX. If a majority is not reached, the program is abandoned, and no
                                        10

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responses imply that WTP  is greater ("yes") or less than ("no") the bid, but the exact

WTP amount is not observed.

       Estimates of mean WTP and other welfare statistics (eg., median WTP)  can be

obtained by estimating binary data models that rely on this mapping from the unobserved

WTP amount to the  response to the payment question. For example, if latent WTP is

normal (logistic) with mean  u. and scale a, a probit (logit) model is estimated where the

dependent variable is a dummy indicator that takes on a value of one if the response to

the payment question is a "yes" and zero otherwise, and the right-hand side includes the

intercept and the bid. Cameron and James (1987) show mat mean/median WTP is equal

to -a/fl, where a and B are the probit (logit) intercept and slope, respectively.6

       In the remainder of this section, we  examine the sensitivity of the estimates of

WTP (and hence VSL)  based on dichotomous choice data to the distribution WTP is

assumed to  follow, the welfare statistic one wishes to work with, and the procedure used

by  the researcher  in computing it  To illustrate the consequences of assumptions and

procedures, we use the data in Johannesson et al. (1997),  a telephone survey of Swedes

aged  18-74  about their WTP for a 2-in-10,000  reduction in their risk of dying over the

next year.

       Respondents were informed  about the chance of dying for a person of their age

and gender over the next year, and were queried about their WTP to reduce that risk
additional income taxes are incurred by households. The two possible response categories are "in favor"
and "against" the program.
6 Symmetric distributions like the normal and logistic imply that mean WTP is equal to median WTP. If
WTP is assumed to be a lognormal, the probit equation is amended by replacing the bid in the right-hand
side of the model with its logarithmic transformation. Median WTP is equal to exp(-o/p), and mean WTP
is equal to exp(0.5'(l/p)2 - o/P). With a Weibull distribution, a binary choice model is estimated where
Pr(yes|B)=exp(-{B/a)e)> where 9 and a are the scale and shape parameters, respectively, of the Weibull
variate. Mean WTP isaT( 1/9+1) and median WTP is 
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using dichotomous choice questions. The bid values ranged between 300 and 10,000 SEK

(about $40 to $1400, implying VSL values of $200,000 to $7 million). Johannesson et al.

estimate mean WTP to be 6300 SEK, or about $900.



A. WTP Responses and WTP Distribution

       We begin  our  examination of the  data  from the Johannesson et al. study by

checking whether (i) the percentage of "yes" responses decline with the bid amount, and

(ii) the bids cover a reasonably wide portion of the range of WTP values.7 As shown in

Figure 1, the  percentage of "yes" responses declines from 51.36% at the  lowest bid

amount, 300 SEK, to 28.83% at the higher bid amount 10,000 SEK, satisfying the first of

these two requirements. Figure 1 also implies that all bids are greater than median WTP,

failing to satisfy requirement (ii), and raising concerns about the stability of the estimates

of WTP. Median WTP is pegged between 300 and 500 SEK.
7 Cooper (1993) emphasizes the importance of using a vector of bids that covers the entire range of possible
WTP  values. Kanninen  (1993) and Alberini  (1995) derive c-optimal  and  d-optimal  designs  for
dichotomous-choicc CV surveys that ruly on only two bid values.
                                        12

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                                        Figure 1.

                        Percent "yes'1 by bid amount
                               Johannesson etal. (1997)
                                                                          n
                300        500       1000       2000
                                       Bid Amount
5000
10000
       We  estimate  mean and  median  WTP  under four  alternative  distributional

assumptions. Mean and median WTP are derived directly from the estimated parameters

of the binary-response models, as explained above. Results are reported in table 2.

       The  most surprising result of table 2 is that the estimates of mean and median

WTP are negative when WTP is assumed to follow the normal or the logistic distribution.

The model based on the  normal distribution predicts that 54% of the respondents have

negative WTP values. Using the Weibull and lognormal distributions, which admit only

non-negative values of WTP and fit the data better,8 circumvents this problem, but results

in a large discrepancy  between median and mean WTP. Mean WTP is very large. The

median WTP amounts predicted by the two  distributions are relatively  close to one

another (239 and 250 SEK for Weibull and lognormal, respectively), but both are less
8 The lognormal and Weibull distribution results in higher Akaike Information Criterion (AIC) values. The
AIC is computed as the log likelihood minus the number of parameters to be estimated, and is frequently
used in applied work to assess the fit of a model.
                                        13

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than what would be inferred by examining the responses to the payment questions, and

less than the smallest bid value offered to the respondents in the study.
        Table 2. Mean and Median WTP for various distributional assumptions
                          (Johannesson et al. study, 1997).

Mean WTP
Median WTP
Log L
Normal
-2096.08
-2096.08
-1349.19
Logistic
-2007.75
-2007.75
-1349.10
Weibull
2,894,292
238.39
-1344.01
Lognormal
Infinity
254.30
-1343.84
       Clearly, these figures are very different from those reported by Johannesson et al.

(1997),  who rely  on  a completely different procedure for estimating mean WTP.

Specifically, they start with fitting a logit model, which implicitly admits negative WTP

values, but compute mean WTP  as the area under the survival curve for positive WTP

values:


(1)


where G(y) is the cdf of WTP. When WTP is a logistic variate with mean n and scale a,

it can be shown that (1) is equal to  (-1 / j3)hi[l -f exp(a)], where a=u/
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B, Changing the Procedure for Estimating f^fean WTP



       In  table 3, we experiment with alternative calculations of mean WTP that are




variants on  four basic procedures. The first procedure follows Cameron and James



(1987). We fit a probit or logit model of the "yes" or "no" responses to the payment




questions,  and compute mean WTP as




(2)          m,=-a/p.




       The second is the procedure followed by Johannesson et al., who fit a logit model




but effectively disregard the portion of the distribution corresponding to negative values.




If WTP follows the logistic distribution, this yields:




(3)          n*-(-l/0)]n[l + exp(a)].




       Our third procedure continues to rely on the fact that mean WTP is the area under




the survival  curve, i.e., [l-F(os + /3y)]s where F( ) is tie cdf of the standardized  WTP




variate.  In earlier applications  of the CV method, researchers estimated mean WTP by



computing the area under the fitted survival curve up to the largest bid amount offered in




the survey (10,000 SEK in the Johannesson et al. study). Our third estimate of mean WTP




is thus:
(4)          m3




       Finally,  Chen and  Randall  (1998) and  Creel  and  Loomis  (1997) describe




semiparametric approaches to modeling the WTP responses. Specifically, they propose to



estimate mj by improving the fit of F(«) through augmenting its argument to include terms
                                       15

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such as the sine and cosine transformations of the bid and of other regressors, in the spirit




of fast Fourier transform approximations.9 The argument of F(.), therefore, becomes:
(5)
                       A  J

                      a=l j=l
                            [i/jfc cos(/kas(x)) - vja sin( jkas(x))],
where x is a vector that includes the bid and other determinants of WTP. For a subset, or




all, of these variables  (the dimension  of this  subset being A), we introduce a scaling




function s(x). This scaling function subtracts the minimum value of x, divides the result




by the maximum value of x (thus forcing the rescaled variables to be between zero and




1), and then multiplies it by (2rc-0.00001). For this rescaling function to be possible, there




must be at least three distinct values for x, which rules out applying this transformation to




dummy variables. The ks  are  vectors  of indices, and the us  are  parameters to be




estimated. Chen and Randall (1998) and Creel and Loomis (1997) suggest that for most




dichotomous choice CV survey applications it is sufficient to consider J=l, in which case




z is simplified to:






(6)
              z = x/3 + 2^ [ua cos(.y(x))- va sin(.





       We apply the semiparametric approach defined by equations (5) and (6) to the




Johannesson  et  al. data, where F(.) is the standard  normal (logistic)  cdf, and z, the




argument of the standard normal (logistic) cdf, includes an intercept, the bid and its sine




and cosine transformations (after rescaling). Formally, we compute mean WTP as





                        [-F(a + fiy
  Chen and Randall also consider polynomial terms in the variables x.
                                        16

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where /= (2n -0.00001)
                            B.
                             max
, Bmin | and BmK are the smallest and largest bid
amounts used in the survey, and B is the upper limit of the integration.

       Following Creel  and Loomis (199t),  we  first set B  equal to he largest bid

amount used in the study (B-B^. This defines our estimate n> of mean WTP. We

subsequently compute n* by letting B in (6) tend to infinity. 1C

       The  results from these alternative calculations are shown in table 3.  Table 3

shows that the largest change in  estimated mean WTP occui's when going from m—

which yields a negative mean WTP—to approaches rn>-nis, which restrict integration to

the positive semiaxis (or a portion of it). Using the standard normal or the standard

logistic cdf gives similar results (table 3, second and third rows). The estimate of mean

WTP is sensitive to the  upper limit of  integration.  As shown in table 3, third and fifth

rows, for the probit model,  when  the upper limit of  integration is  B^, mean WTP is

roughly half the  figure that is  obtained ,by letting  B  tend to  infinity.  A  similar

comparison for the logit model (table 3,  second and fourth rows) confirms these findings.

       The semiparametric approach results in an estimated mean WTP similar to that of

regular  probit  and   logit  models  when  B-B^^,  but that  is  considerably  more

conservative than the regular probit and logit equations when  B tends to infinity.

Assuming that  WTP is normally distributed and that  a conventional probit model is fit,
10 Cooper (2002) points out that it is not clear a priori which of these two estimates—104 or ms—is greater.
This is because, unless additional restrictions are imposed, when we adop: the semiparametric approach
F(z) as defined in (7) can no longer be interpreted as the cdf of the standardized WTP variate. Also see
Crooker and Herriges (2004) for a comparison between the Chen and Randall approach and other models
of dichotomous choice CV responses.
                                         17

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nk is 6434 SEK, whereas ITS based on the semiparametric probit is equal to 4338 SEK (a

33% reduction).

       A  comparison between the probabilities of "yes" responses predicted  by the

semiparametric and conventional probit at  various bid values suggests that the former

outperforms the latter. For example, the former predicts that when the bid is 300 SEK the

probability of "yes" is 0,5172, which is closer to the relative frequency (0.5136) than the

prediction from the conventional probit (0.4794). When the bid amount is 10000 SEK,

the semiparametric probit predicts that the probability of a "yes" is 0.2857 against 0.2669

from the conventional probit. For comparison, the empirical frequency is 0.2883.
                 Table 3. Alternative procedures for computing mean WTP.
                              Johannesson et al. (1997) data
Approach

mi (Cameron and James, 1987)
rife (Johannesson et al., closed-
form expression)
rrt (Numerical integration of the
survival function to infinity)
n% (Numerical integration of the
survival function up to max. bid)
rrfe (Numerical integration of the
survival function up to max. bid)
m* (Creel and Loomis (1998)
semiparametric approach.
Numerical integration up to max.
bid)
ms (Creel and Loomis (1998)
semiparametric approach.
Numerical integration with
*„=«>)
Distribution F( )
Standard logistic
Standard logistic
Standard normal
Standard logistic
Standard normal
Standard normal; probit
model with bid, sin(bid)
and cos(bid)
Standard normal; probit
model with bid, sin(bid)
and cos(bid)
Mean WTP (in SEK)
-2007
6849
6434
3522
3528
3732
4339
                                       18

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C.  The Effect of Regressors

       Would we obtain similar results in situations where regressors are included in the
                                          I

model,  and mean WTP is calculated conditionally  on specific values of the regressors?

This question is appropriate, for example, when seeking to answer the question of how

the WTP for a risk reduction varies with age.  Epidemiological evidence (e.g., Pope et al.,

1995)  suggests that the majority  of the lives  saved  by air quality  regulations  and

environmental policies are those of the  elderly, and  some observers have argued that

older people should  be willing to pay less for a risk reduction—and their VSL should be

lower—mirroring their fewer remaining life years.  Economic theory, however, does not

offer unambiguous predictions about the effect of age on WTP (Alberini et al., 2004).''

       Johannesson et al.  run a logit regression that includes age and age squared, plus

gender and education  dummies, income and the respondent's quality-of-life rating,12 and

report  finding a  quadratic relationship  between  age  and WTP  that peaks when the

individual is about 40  years old. To check the sensitivity of these results to the procedure

used in the calculation, we ran logit and probit models with their same regressors (or

subsets of them), and predicted mean WTP at different ages using approaches m, and m*.

In both cases, we let B tend to infinity.

       The results of  these calculations are shown in Figure 2, panels (a)-(d). Panel (a)

plots rrj against  age,  confirming Johannesson et al.'s finding: the relationship between
11 Because a large proportion of the lives saved appear to be those of the elderly, there has been much
recent debate about whether the VSL should be lower for the elderly to reflect their fewer remaining life
years. In the US, the Office of Management and Budget recently repudiated making such adjustment for
age, on the grounds of insufficient evidence that the VSL is lower for elderly persons (Skrzycki, 2003).
  In the Johannesson et al. survey, respondents were asked to rate their quality of life on a scale from 1 to
10, where 1 represents the worst possible quality, and 10 is the best possible quality.


                                          19

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age and WTP is an inverted U that peaks at age 40.13 Similar results are observed when,




as shown in panel  (b), the logit  model is replaced  by a probit, and  mean WTP  is




             r
computed as  I [1 - <&(*,« + fiy)]cfy, where x,  = [1 age  age2 ], a is the vector of probit

             0




coefficients on these variables, and  fl=- I/a.




       In Figure 2, panel (c), we compare the predictions based on the conventional logit




model with Ihose from semiparametric probit models.   Probit Fourier 1 is based on a




probit regression where the right-hand side variables  are the bid, age and age squared,



and trigonometric functions of these variables. In this case, the shape of the relationship




between WTP and age is no longer an inverted-U.  Moreover, this approach produces




estimates of mean WTP that are consistently smaller  than those from the conventional




probit model. The curve labeled Probit Fourier 2 is based on a similar model, except that




the sine and cosine transformations are applied only to  the bid. This time, the relationship



between WTP and age resumes its quadratic shape, but the estimated WTP values remain




consistently lower than those of the regular probit model.




       Figure 2, panel (d) displays the results based on probit models that are similar to




those used for panel (c), except that more regressors—household income, the quality-of-




life rating reported by the respondent, a gender dummy and an educational attainment



dummy—are entered  in the right-hand side of the model.  The curves labeled  Probit



Fourier 1 and Probit Fourier 2 are  different from one another in that the former includes




trigonometric functions of all of the continuous variables, while the latter includes only




the sine and cosine transformations of the bid.
13 Dummy indicators for the "yes" or "no" responses to the payment questions were regressed on an

intercept, the bid amount, age and age squared.
                                        20

-------
       The mean WTP figures plotted in pinel (d) refer to a 50-year-old male (SEX=1)



with high school education (DEDU=1),  the average household income of the sample




(24,490 SEK), and the same quality-of-life rating as the avenige respondent (7.34 on a



scale  from 1 to 10). As  in  panel (c),  Probit Fourier  1 results in a non-monotonic




relationship  between  WTP  and  age,  while Probit  Fourier 2  implies  a  quadratic




relationship. Both predict lower WTP figures 1han the conventional probit model.
                                       21

-------
                                           Figure 2.
Legend: in panel (c), Probit Fourier 1 includes bid, age, age squared, and sine and cosine functions of these
variables; Probit Fourier 2 includes bid, sin(bid), cos(bid), age and age squared.

In panel (d), Probit Fourier 1 includes bid, age, age squared, income, quality of life rating, a gender dummy
and an education dummy, plus sine and cosine terms of ail continuous variables. Probit Fourier 2 includes
bid, sin(bid), cos(bid), age, age squared, income, quality of life rating, a gender dummy and an education
dummy.
WTP in SEI
8000 •

6000 •

4000 •
3000 '

1000

(a) Mean WTP by age: Logit Model, Johannesson et al. Data
<
\
^ 	 ^^
^^"•V.




i
20 30 40 50 60 70
Age
                    (b) Mean WTP by age: Logit and Probit Model,
                              Johannesson etal. Data
   WTP in SEK
      8000
                                                                      log it
       1000
                20
                                                                70
                                              22

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                   (c) Mean WTP by Age: Johanneeeon et al. Data
     8000
WTP in SEK
     7000
               20        30        40       50
                                                                      twobit
                                        60       70
       6000 i
WTP in SEK
       5000
          Mean WTP by Age: Probit Model* with Covarfates, Jotiannesson
                                    et al. Data
         Predictions for a male with high school education, average income and quality
                                    of life rating
               Probit
Fourier 1
                                                                     Probit
                    10      20      30      40       50      60      70       80
                                                23

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       In sum, panels (c) and (d) in Figure 2 suggest that there are no easily discernible




patterns, and that claims about the relationship between age and WTP, and the magnitude




of WTP at various ages, are not robust and may be an artifact of restrictive assumptions.




       We further investigate this  matter by switching to a lognormal distribution for




WTP and  to  median  WTP for specific  ages, which  we  expect to result  in  more




conservative estimates. The results, shown in table 4, suggest that the lognormal model




implies  a quadratic, inverted-U  relationship between age and WTP.  It also suggests,




however, that  the curvature  of the relationship is much sharper than  that predicted by




Johannesson et al. For example, the WTP of a 70-year-old for a reduction in risk of 2 in




10,000 is only 90 SEK, or only about 20% of the WTP predicted for a 40-year-old person




(440 SEK).




       Taken together with the evidence from the semiparametric approach, these results




suggest that detecting the shape of the relationship between WTP and a regressor of




interest  depends crucially on, and is  very sensitive to, three  factors: (i) the distribution




assumed for WTP,  (ii) the  welfare statistic used (mean or median WTP), and (iii) the




procedure used for computing it.
                                        24

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          Table 4. The relationship between age and WTP for a risk reduction:
 lognorrnal WTP and median WTP v. Johannesson et al. logit and truncated mean WTP.
Age
20
30
40
50
60
70
Johannesson et al, 1997.
Mean WTP in
SEK
6100
6900
7200
6900
6000
4600
Implied VSL in
million SEK
30.3
34.6
36.1
34.3
29.8
23.3
Alternative calculation using log
normal WTP.
'Median WTP in
SEK
137.18
307.31
440.77
Implied VSL in
million SEK
0.672
1.505
2.160
404.75 1.983
237.97 1.166
89.57 0.439
IV. Treatment of Outliers

       In this section, we investigate the effect of outliers on the estimates of WTP. We

begin by tackling 1he problem of identifying outliers in dichotomous-choice CV surveys,

and explore the effect of including or excluding these observations from the sample. We

use logit regressions of the WTP responses on individual characteristics  to classify

observations as  outliers. Because outliers  can be caused, among other reasons,  by a

number  of  undesirable response effects, we then  examine whether it is possible to

estimate "structural" models of these response effects.



A. Outliers

       Collett (1991) defines as outliers as "observations that are surprisingly far  away

from the remaining  observations in the  sample," and points out that such values may

occur as a result of measurement errors, execution error (i.e., use of a faulty experimental

procedure),  or be a legitimate, if extreme, manifestation of natural variability.
                                        25

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       Our first order of business is to define outliers when the variable of interest is




binary, as is the case with the responses to dichotomous-choice CV questions.  Copas




(1988) defines an outlier as an observation for which  we predict a low probability of a




one (zero), but we do observe a one (zero).




       We use the Johannesson  et al. (1997) data to  check  (i) how many observations




could be classified as outliers according to several alternative cutoff levels, and (ii) by




how much mean WTP would change if these outliers were  excluded from the sample.




Specifically, we wish to see for how many observations the predicted probability of a




"yes" is less than 0.05, 0.10, etc., but the response to the payment question is a "yes." The




predicted probability is based on Johannesson et al.'s logit regression of the "yes" or "no"




response indicator on respondent age, age squared, income, an education dummy, and a




quality-of-life  rating  subjectively  reported  by  the  respondent in  the  interview:




pi = [1 + exp(-(x,d + )3 • £,)]"', where a  and /3 are the estimated logit coefficients, x is




a vector of regressors, and B is the bid assigned to respondent  i.




       For ease of comparison, we use Ihe same procedure for estimating mean WTP as




in Johannesson  et al.'s  work (see section III).  The  resulting mean  WTP figures are




reported in column (C) of table 5. We also fit a binary  data model of the responses based




on an alternate distribution—the Weibull—and report estimates of mean and median




WTP based on the latter in columns (D) and (E) of table 5, respectively.
                                        26

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Table 5.  Outliers in the Johannesson et al. data (based on logit regression, n=1660):
                             All WTP figures in SEK
(A)
Definition of
outlier
No outliers
identified
Prob(yes)< 0.05
and yes observed
Prob(yes)<0.10
and yes observed
Prob(yes) <0,20
and yes observed
Prob(yes) <0.25
and yes observed
Prob(yes) <0.30
and yes observed
(B)
How
many?
None
None
None
5
26
59
(C)
Johannesson et
al. procedure
Mean WTP*
6732
673(2
6732
6141
4846
3767
(D)
Weibull:
Mean WTP*
2.894 million
2.894 million
2. 894 million
1.1 50 million
193,481
36,114
(E)
Weibull:
Median
WTP*
238
238
238
302
338
369
       *.
        : Welfare statistics after excluding outliers.
       Table 5  shows that outliers according to the Copas' definition were found only

when the cutoff for identifying an outlier was set to 0.15 or higher. When the cutoff is set

to 0.25,  for example, a total  of 26 observations would be considered outliers, and

dropping them  from the usable sample would reduce Johannesson et al.'s  mean WTP

from 6732 to 4846 SEK—a 30% reduction. A cutoff of 0.30 results in the exclusion from

the usable sample of 33 more  individuals, and in a further reduction of mean WTP to

3767 SEK—a 45% reduction.

       As shown in column (D) of table 5, using a Weibull distribution generally results

in implausibly large mean WTP values. The mean WTP, however, does get smaller when

outliers are excluded from the sample. By  contrast, median WTP (shown in column (E)),

which is 338 SEK for the full sample, increases slightly  when outliers are omitted  from
                                       27

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the sample, which suggests that the skewness of the distribution of WTP has become a




little less pronounced.








B.  Undesirable Response Effects: Yea-saying, Nay-saying, and Random Responses




       Contingent valuation studies about mortality  risk reduction rely crucially on the




respondent's comprehension of the risk and risk reductions being valued. Many recent




survey questionnaires  deploy visual aids and practice questions about risks, but, despite




these efforts,  it is  possible that some respondents still  remain confused  about the



commodity being valued, and  that their answers to the  payment  questions may  be




affected by undesirable response effects.




       Carson (2000) describes  three types of undesirable response effects that may




occur in dichotomous-choice CV surveys. The first is yea-saying, whereby a respondent




answers "yes" to the bid  question with probability 1, regardless of the bid amount. This



may be done  in an effort to please the interviewer, or in the hope of terminating the




interview sooner.




       The opposite phenomenon  is nay-saying,  which occurs  when the respondent




answers "no" to the payment question with  probability  1, regardless of the bid amount.




Respondents engaging in  nay-saying may dislike new public programs and new taxes, or



might be afraid of committing to something they do not fully understand.



       It is also possible that some people give completely random responses, answering




"yes" to the payment question with probability 0.5 (and hence, "no" with probability 0.5),




regardless of the bid amount. Completely random responses may be due to  confusion
                                       28

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about the scenario, failure to understand th$ commodity being valued, no interest in the



survey, poorly written survey questions or survey materials, or simply a data entry error.




       In practice, not all respondents in a contingent valuation survey will be subject to



these undesirable effects.  To  accommodate for this possibility, we consider  discrete




mixtures. For simplicity, attention is restricted to discrete mixtures with two components,




where a fraction of the sample (a-100%) is affected by one of these undesirable response




effects, while the  remainder answers the payment questions in the usual fashion (i.e., by




saying "yes" if latent WTP is greater than the bid, aid "no" otherwise). The researcher's




problem is that—unless respondent or interviewer debriefs are used—it is not possible to




tell from which component of these two  populations  the  respondent is  drawn. This



requires estimating a (discrete) mixture of distributions.




       Figures 3  and  4 show how mixtures alter the estimated survival curve of WTP.




Figure 3 depicts  the  true and observed survival curve when one  of the two  mixing




components is yea-saying.  (By true survival curve, we mean the survival curve that refers



to the non-degenerate component of the mixture.) Yea-saying raises the observed survival



curve at every bid value, which implies that mean WTP will be overestimated. The extent




of this positive bias depends on severity of the yea-saying (i.e., on the value of a).




       The converse will be true with a nay-saying component. Figure 4 shows that if the




sample is contaminated with a small number of people who answer the payment question



in a completely random fashion, the observed  survival  curve is tilted, crossing the true




survival function from below at the median, and remaining above it for higher bid values.




This implies that both the mean and variance of WTP will be overestimated, but that the
                                        29

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median WTP should not be affected by the presence of completely random responses, as

long as the mixture contains only these two components.
C. Likelihood Functions for Two-component Mixtures

       Absent any other undesirable response effects, the log likelihood function with

dichotomous choice responses is:
(8)
              log/, = J>, log Pt(yi = 1 1 5.) + (1 -x)log Pi-a = 0 1 Bt)
where .y is an indicator that takes on a value of 1 if the response is a "yes" and zero if it is

a "no," B denotes the bid, and F(Bi;B)  is the  cdf of WTP evaluated at the bid value, 0

being the vector of parameters indexing F.

       In this paper, we consider a two-component mixture where (l-a)-lOO percent of

the population answers the payment questions according to the usual assumption ("yes" if

WTP  is greater than  the  bid,  "no"  otherwise).  The  distribution  of WTP for this

component of the  mixture is non-degenerate.  If the remaining  ct-100 percent of the

population consists of yea-sayers, who answer  "yes"  to the payment question  with

probability I,14 the probability of observing a "yes" in equation  (8),  Pr^, = 1 1 B,), is

equal to:

(9)
14 In practice, one would expect the data from a contingent valuation survey to come from mixtures with
more than two components. The simple cases considered in this paper should, therefore, be interpreted as
the situations where the researcher stands his or her best chance to identify the components.
                                         30

-------
"No" responses must come from the non-degenerate component of the mixture:




(10)          Pr(>v = 0| Bf) = (!-«)• F(B.;d).




       If the sample is described by a discrete mixture with nay-sayers, the probability of




a "yes" is:




(11)          Pt(y,;=1| B,) = (!-«)• [1-




and the probability of observing a "no" is:




(12)




       Finally, if the sample is a mixture comprising persons who answer in a completely




random fashion, the probabilities of a "yes" and "no" response are




(13)




(14)




respectively.
Pr(>>, = 0] Bt) = (1 -a) - F(B, ;fl) + a - 0.5,
                         31

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          Figure 3. Effect of yea-saying.
 % willing to pay •
     l-F(-)
                                                 Observed
                             True curve
                                             Bid amount
          Figure 4. Effect of Completely Random Responses.
% willing to pay
    l-F(-)
                                               Observed
                           Median
                           WTP
Bid amount
                                                  32

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 C. Application

       We  apply  these  two-component mixtures  to  the data from  the CV  survey

conducted in Hamilton, Ontario, by Krupnipk et al. (2002). Participants in this study took

a self-administered computer questionnaire at a centralized facility. After a probability

tutorial, the study participants were shown the risk of dying for all causes for a person of

their age and gender.

       They were asked  to value a total  of three risk reductions by answering payment

questions in a dichotomous-choice format with follow-up.15 Each of these risk reductions

would be taking place  over 10 years, and would be  delivered by a hypothetical product.

The  risk reduction was  context-free, in that it was not associated with air  pollution

reductions or another public program.

       In this paper we focus on WTP for the 5 in 1000 risk reduction. We assume that

WTP is a Weibull variate, and begin with fitting the models  described by equations (9)-

(14)  to  the responses to  the  initial payment questions. In  a subsequent round  of

estimation, we amend equations (9)-(14) to accommodate for the responses to follow-up

questions (double-bounded models).  Table 6 reports mean  and median WTP for the

component of the mixture that behaves  following the  usual  economic paradigm (after

filtering out the degenerate components).16

       As shown in table 6, panel (i), in our mixture based on single-bounded models we

find  no evidence of yea-saying: in column (ii), the estimated a is identically equal to

zero.  By contrast, column (iii) suggests that as much as 26%  of the sample may be
15 The three risk reductions were 5 in 1000 and 1 in 1000 occurring over the next 10 years, and 5 in 1000
beginning at age 70,
16 We use the constrained maximum likelihood routine in GAUSS to force a to lie between 0 and 1.
                                        33

-------
comprised of nay-sayers.17 Column (ii) displays an even more implausible result: in the

mixture with completely random responses,  we estimate that over 50% of the sample

answers the payment questions in a completely random fashion.

       Because we do not know whether a specific hdividual  does or does not answer

the payment question at random, this implies that each observation has a probability

equal to  0.51 of being a completely random response. This finding is in sharp contrast

with the answers to debriefing questions and the gpod internal consistency and validity

shown by study participants, raising doubts about the ability of single-bounded models of

WTP to capture the correct proportion of subjects  engaging in degenerate response

mechanisms.

       In theory, double-bounded estimation should produce more reliable results, thanks

to the narrower intervals around the respondent's unobserved WTP  amounts afforded by

the follow-up payment question. Table 6, panel (ii) reports estimation results based on

double-bounded models.  While any evidence of nay-saying seems to have vanished

(column  (iii)),  almost two-thirds of the respondents are predicted  to be answering the

payment questions in a completely random fashion (column (ii)). Clearly, this result is

not plausible.

       To seek for an explanation for this finding, we turn to evidence from Monte Carlo

simulations. Alberini and Carson (2001) report that  mixture models like  (9)-(14) give

reliable results  only when (a) F(«) is correctly specified, (b) the mixture type is correctly

specified, and (c) a is not too small. In most other cases, the estimated coefficient a

appears to pick up any divergence between the assumed F(«) and the true distribution, or
17 We view this as a somewhat alarming result, but this percentage is comparable to the probability of yea-
saying (20%) estimated by Kanninen (1995) using double-bounded data from a contingent valuation survey
about wildlife and wetland habitat protection in California's San Joaquin Valley.
                                        34

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any other misspecification in the type of mixture. We conclude that it nay be difficult to

estimate mixtures using existing CV data about mortality risk reductions, and that a study

capable of identifying the components of a mixture would probably have to be designed

specifically for that purpose.

                                         Table 6.
                                 Discrete1 Mixture Models:
     Results for Krupnick et al. (2002) (Canada study) Bootstrap standard errors in
                                    parentheses.


      1. using only the responses to the initial payment questions (single-bounded)^

a (probability of
yea-sayers, nay-
sayers, etc.)
Mean WTP ($)
Median WTP($)
(i)
No mixture

1176.94
(306.55)
445.99
(44.02)
(ii)
Mixture with
completely
random
responses
0.5108
(0.13)
594.55
(n/a)
551.04
(146.05)
(iii)
Mixture
with nay-
sayers
0.2644
(0.05)
969.57
(n/a)
859.61
(134.10)
(iv)
Mixture with
yea-sayers

1176.94
(n/a)
445.99
(44.02)
 II. using the responses to the initial and follow-up payment questions (double-bounded).

a (probability of
a yea-say er, nay-
say er, etc.)
Mean WTP ($)
Median WTP ($)
(0
No mixture

826.41
(70.85)
323.83
(20.96)
Mixture with
completely
random
responses
0.6577
(0.0448)
831.24
(70.92)
323.75
(21.10)
(iii)
Mixture
with nay-
sayers

826.41
(70.85)
323.83
(20.96)
(iv)
Mixture with
yea-sayers

826.41
(70.85)
323.83
(20.96)
                                        35

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V. Internal Validity: Scope Tests and Endogenous Risks.

A. Subjective Risks and Risk Reductions

        In this section, we consider the situation where respondents are  asked to assess

their subjective baseline risks (Gerking et al., 1988; Johannesson et al., 1991 ;18 Perssonet

al., 2001). If the risk reduction is expressed as a specified proportion of the baseline risk

(e.g., 20%), then the risk reduction varies  across respondents, allowing one to test for

sensitivity of WTP with respect to the size of the risk reduction—the so-called "scope"

effect 19

        In  this  section, we  ask  three related  questions.  First,  should  WTP  and risk

reduction be treated as endogenous in such studies? Second, does this affect conclusions

about the "scope" effect? Third, does treating risk  reduction as endogenous with WTP

affect  our  conclusions about whether  subjects  respond to  absolute  or relative risk

reductions when they announce their WTP amounts (Baron, 1997; McDaniel, 1992)?

        To answer these questions, we use the data  from the Persson et al. (2001) study

about transportation safety.  Persson  et al.  conducted a mail  survey of 18-74-year-old

Swedes in  1998. Respondents were asked  to  estimate their own risk of dying from any

cause (EIGRISK), and to value a specified  reduction  in this risk. The reduction was
ls Johannesson et al. (1991) ask hypertensive patients in a health care facility to assess both baseline risks
and risk reductions associated with hypertension medication. In this case, it seems reasonable to expect that
WTP and risk reductions should be endogenous.
19 Hammitt and Graham (1999) review over 25 contingent valuation studies where the size of the risk
reduction was exogenously varied to the respondents. They find that the scope effect is more often satisfied
when the size of the risk reduction is varied within a respondent (an internal test) than when it is varied
across respondents (an external test), and that there are several studies where WTP does not vary
systematically with the size of the risk reduction. They also report that in internal tests WTP is rarely found
to be strictly proportional to the size of the risk reduction. In studies that conducted external scope tests
WTP generally exhibits little responsiveness to the size of the risk reduction, and generally fails to be
strictly proportional to the risk reduction.
                                           36

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expressed as a percentage of the baseline rjsk, this percentage being selected at random




among a predetermined set of values (10%, 30% or 50%).




       Respondents were next asked to assess their own risk of dying in a road-traffic




accident  (DEGRISK), and  to  value a  risk reduction  of 10%,  30%, 50%  or 99%




(RISKMD). Both risk reductions are private goods and are valid for one year only. In this




paper, attention is restricted to the risks of dying in road accidents.






B. Hypotheses




       We assume that:




(15)          WTP = exp(x,0,) • ABSR1SK?1 • exp(e,)




where x is a Ixk vector of individual characteristics thought to influence risks, ABSRISK




is the absolute risk change (ABSRISK=DEGRlSKxRISKMD), and e is an error term. On




taking logs,




(16)          log WTP = x, ft + j32 log ABSRISK, + et,




which can be re-written as:




(17)          log WTP = x,/j, + J32 log DEGRISK. + /J3 log RISKMD, + e.,




where  RISKMD is the percentage risk reduction, which is randomly assigned to the




respondent in  the survey, and is  therefore considered  an exogenous variable. If log




DEGRISK and log WTP share  common, unobservable respondent-specific factors, they




are econometrically  endogenous,  which makes  the OLS  estimate of  /32 biased and




inconsistent.  This problem  can be  addressed  using instrumental-variable estimation




techniques, such as two-stages least squares (2SLS).
                                      37

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       In equation (17), the coefficients of log DEGRISK and log RISKMD are allowed




to be  potentially different from  each other in order to test hypotheses  about  the




determinants of WTP and about scope effects. Specifically, if /32 = /33 , then respondents




correctly valued  the absolute risk  reduction,  which allows us to estimate the VSL. If




/32 = /J3 = 1 ,  then WTP  is strictly proportional to the size of the risk reduction, as




economic theory suggests should be the case with small risks (Hammitt and Graham,




1999).




       Should we find that /32 * /33 , and that both /32  and /33 are different from zero,




we would conclude that at least some weight has been given to the baseline risk (Baron,




1997; McDaniels, 1992). By contrast, if & # & , )32 =0 and ft, * 0 , then WTP depends




exclusively on the proportion, but not on the absolute risk reduction, and it is not possible




to compute a meaningful VSL.  One would expect  the outcome of these tests of




hypotheses to  depend on whether  baseline risks, DEGRISK, are treated as endogenous




with WTP.
C. Endogeneity of Risks and WTP




       If log DEGRISK is endogenous with log WTP, we need an additional equation




explaining log DEGRISK:




(18)          logDEGRISK = zj, + w.y2 -l-r],




where z is a vector of instruments that overlap  with some of the regressors x in equation




(15), w is a vector of instruments excluded from the right-hand side of the WTP equation
                                       38

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to ensure identification, y, and  y2 are vectors of coefficients, and 7], is an error term, e

and T| are potentially correlated within a respondent.

       We estimate the system  of equations (17)-(18) by 2SLS using the broader of the

two samples used by Persson et at.  (2001).20 The results of OLS estimation of (18) are

reported in table 7 because they are  of independent interest and because they are the first

stage  of the 2SLS procedure. Table 7 shows that subjective risks are related to age and

age squared, and  to  miles driven per year. Other  individual characteristics, such as

gender, do not appreciably influence subjective risks.

       As shown  in table 7, we included jn this regression various dummies, such as

whether the respondent travels by bicycle, moped or motorcycle, and whether he wears a

helmet when doing so, for two reasons. First, these variables are thought to influence the

subjective chance  of dying in a road traffic accident Second, because they are excluded

from the WTP equation, these variables provide identification restrictions for the 2SLS.

However, table 7  shows that they are not significant predictors of subjective risks. We

reach the same conclusion for  the  two education dummies (high  school diploma and

college degree), which were included in this equation for the same reasons.

       Table 8 reports the results of OLS  and 2SLS regressions  of WTP on various

regressors, including subjective risks. In addition to the risk  variables,  the regressors

include the  logarithmic transformations  of income and age, the square of log age,21 log

miles driven, a dummy indicating whether the respondent has ever been injured in an
20 Specifically, following Persson et al., we form the sample by taking all observations with positive WTP,
and replacing zero WTP values with a small positive number (i.e., WTP=2 SEK). Observations with
missing baseline risk and/or missing WTP, baseline risk smaller than 1 in 100,000, WTP less than 1 and or
WTP greater than 5% of annual income are excluded.
21 Including the logarithmic transformation of age and its square, rather than age and age squared, which
were included in the first-stage regression, should help in identifying the coefficients of the WTP equation.
                                         39

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accident,  and education  and family  composition dummies. As shown  in table  8,



regardless of the specification, the estimation techniqus used, and the restrictions placed




on the  parameters, WTP is well predicted  by income, miles traveled,  and the risk



reduction. The effect of age is weak at best, and education and  family status  are not




important.




       In columns (A) and (B) of table 8, the restriction that /32 =  /33  is imposed, which




means that WTP is  regressed on the size of the absolute risk reduction.  Column (A)




reports  the results of OLS  estimation that treats subjective risks, and hence the risk




reduction, as  exogenous, whereas column (B) reports the results of 2SLS estimation that




treats subjective  risk as endogenous with  WTP  and imposes  the abovementioned




restriction.



       Column (A) shows that WTP does increase systematically with the size of the risk




reduction, but in a less-than-proportional fashion:  /32 is less than 1. The responsiveness




of WTP to the size of the risk reduction is weak: doubling the  size of the risk reduction




would increase WTP by only 18%. With 2SLS (column (B)), one concludes that WTP E




more responsive to the size of the risk reduction, since the 2SLS /52 is more than twice as




large as its counterpart in column (A), implying that doubling the risk reduction increases




WTP by 41%. The null hypothesis that absolute risk is exogenous is rejected soundly.



       Columns (C) and (D) use OLS and 2SLS, respectively, but relax the restriction




that  J32 = /33. F  tests of the null that these coefficients are equal reject the null at the




conventional levels with OLS estimation, but fail to reject it with 2SLS. Inspection of the




coefficient estimates  and their t statistics, however, suggest that in both cases people were



responding to the proportions, rather than the absolute risk reductions. This suggests that






                                        40

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                                        I
with CV surreys about mortality risk reductions that present the risk reduction as a


specified proportion of the baseline risk one should check whether subjects were truly


responding to the absolute risk reduction, or simply  to the percentage risk reduction,


without considering the baseline. In testing |these results, however, it is important to pay


attention to the possible endogeneity of baseline risk with WTP, as conclusions may be
                                                              <

sensitive to whether baseline risk is treated as endogenous with WTP.
                  Table 7. First-stage regression - Person et ai. data.
                     Dependent variable: log DEGRISK. N=S18.

Intercept
Age
Age squared
Male
Log km traveled in a car
Travels by moped or
motorcycle (dummy)
Travels by bicycle (dummy)
Wears helmet when bicycling
(dummy)
Uses seatbelt when in back
seat of car (dummy)
High school diploma (dummy)
College degree (dummy)
Coefficient
1.1095
-0.0647**
0.00068**
-0.0613
0.2816**
Q.0077
0.0735
0.1875
-0.1374
0.0489
-0.0578
T statistic
1.85
-3.44
3.16
-0.69
3.83
0.06
0.42
1.36
-1.28
0.39
-0.46
** =
     significant at the 1% level.
                                        41

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                  Table 8. Second-stage results - Persson et at. data
                 Dependent variable: log WTP. T stats in parentheses.

Intercept
Log income per
household member
Log km traveled in car
LogDEGRISK
LogRlSKMP
Injured in accident
(Dummy)
Log age
Log age squared
High school diploma
College degree
Household members
jigesO-3
Household members
ages 4- 10
Household members
ages 11-17
Household members
ages 18+
A
OLS
n=676
-1.0221
(-0.45)
0.4213**
(2.47)
0.4949**
(3.19)
0.1850**
(2.32)
0.1850**
(2.32)
0.3779
(1.58)
-0.4943A
(-1.68)
-0.0085
(-0.17)
-0.1275
(-0.47)
0.1298
(0.47)
0.1754
(0.75)
0.2401
(1-59)
-0.0445
(-0.26)
0.0543
(0.43)
B
2SLS
N=579
-2.4185
(-0.97)
0.4777**
(2.50)
0.4368**
(2.60)
0.4092**
(2.38)
0.4092**
(2.38)
0.4372A
(1.71)
-0.3308
(-1.03)
-0.0105
(-0.18)
0.0829
(0.28)
0.3539
0.16)
0.1008
(0.42)
0.3410*
(2.14)
0.0366
(0.20)
0.1545
(1.14)
C
OLS
n=676
0.0810
(0.04)
0.3747*
(2.19)
0.5502**
(3.52)
0.0671
(0.73)
0.5467*
(3-35)
0.3659
(1.53)
-0.5770*
(-1.96)
-0.0211
(-0.42)
-0.0635
(-0.23)
0.1627
(0.59)
0.1441
(0.62)
0.2396
(1.60)
-0.1594
(-0.09)
0.0372
(0.30)
D
2SLS
N=579
-0.5672
(-0.18)
0.4373*
(2.19)
0.6573**
(2.47)
-0.6332
(-0.65)
0.4420**
(2.47)
0.4262
(1.63)
-0.6910
(-1.48)
0.0350
(0.45)
0.1567
(0.50)
0.3249
(1.03)
0.0552
(0.22)
0.3088A
(1.87)
0.0269
(0.14)
0.1494
(1.07)

Test: p2=P3


F=6.44
Pval=0.011
4
F=1.18
Pval=0.277
6
Observations with missing baseline risk and missing WTP, observations with baseline
risk smaller than 1 in 100,000, observations with WTP less than 1 and with WTP greater
than 5% of annual income are excluded. Observations with WTP equal to zero are
replaced by WTP=2.
                                       42

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VI. Internal Validity: The Relationship Between WTP and Income

       Income  is  an important  independent variable in regressions relating WTP to

individual  characteristics  of the  respondent.  There are  at least two  reasons why

researchers regress WTP on household (or personal) income. First, this is  a common

practice  for testing the internal validity of the WTP responses,  as  theory suggests that

WTP for mortality risk reductions should be positively associated with income. Second,

there is much interest in the income elasticity of WTP for the purpose of predicting WTP

at specified levels of income within the sample, or for benefit transfer purposes.22 23

       In many contingent valuation surveys about environmental quality or other public

goods, researchers expect WTP to  be a small fraction of the  respondent's income. This

expectation has led them, in some cases, to exclude from the  sample respondents  whose

implied WTP is greater than, say, 5% of the respondent's  income.

       With reductions in one's own risk of dying, there is no  particular reason to believe

that WTP should be a small proportion of income. However, Persson et al. do omit from

the usable sample respondents whose WTP exceeds 5% of household income, and Lanoie

et al. (1995) find that their estimate of VSL for workers in the Montreal area, which is

Can $22-27 million,  drops to Can $15  million after excluding from the sample three
22 It is recognized, however, that knowing the income elasticity of WTP in a cross-sectional sample sense
does not answer the important policy question of whether VSL should change over time, as income grows
and the tradeoffs people are prepared to make between income and risk reductions change. Costa and Kahn
(2002)  circum'ent this problem by estimating compensating wage studies for different years in the US.
Using Census micro-data and fatality risk figures from the Bureau of Labor Statistics for 1940, 1950, 1960,
and 1980, Costa and Kahn conclude that the quantity  of safety has increased over time, and that the
compensating differential has increased. The  implied elasticity of VSL witi respect to per capita GNP is
1.5 to  1.7. A meta-analysis of compensating  wage studies by Viscusi and Aldy (2003) pegs the income
elasticity of VSL to be 0.5-0.6, and certainly  less than one. DeBlaeij et al. (2000) conduct a meta-analysis
of the WTP to reduce transport risks, finding a considerable higher income elasticity of 1.33. Liu et al.
(1997) compare estimates of the VSL from compensating wage studies in T&iwan based on 1982-1986 data
with predictions based on VSL-income relationship from developing countries.
23 Alberini (2004) discusses difficulties associated with measuring income ir surveys.
                                          43

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workers  whose WTP  is  one-third  of  their pre-tax  income.24 It seems,  therefore,

appropriate to check for respondents  whose  announced WTP  is  a relatively large

proportion of income, and to examine how much the estimates of mean WTP and of the

income elasticity of WTP change when these respondents are excluded from the sample.

Respondents with very high announced WTP relative to income may, for example, have

failed  to  give  proper  consideration  to their  budget  constraint,  have  intentionally

misrepresented their income, or have simply miscalculated it.

       We  use the data from  two mortality risk  surveys conducted  in  the US  and

Sweden, respectively—Alberini et  al.  (2004), and Persson et al. (2001)—to investigate

these issues. We begin  with  the  data from the Alberini et  al. study.  Results from

estimating mean WTP  after  excluding  respondents with WTP greater  than  a given

percentage of income are shown in Table 9.25 We vary this percentage from 25 (the least

stringent criterion)  to 2.5 (the most stringent criterion), showing how doing so excludes

from 68 to 133 respondents (almost one-third of the sample). As shown in table 9, mean

and median WTP do decline as we exclude  more observations from the sample, but the

change is within 10-12% of the original figures.

       By contrast, what does change dramatically is the income elasticity of WTP, a key

quantity  when  one  wishes to (i) extrapolate study results to the general population, (ii)

focus on the economically disadvantaged,  and (iii) attempt benefit transfers  to other

countries or locales where income  levels are different. As shown in table 9, the income
24 Lanoie et al. (1995) value risk reductions in the car safety and workplace safety contexts. They survey
employees of firms in the Montreal area, asking both willingness-to-pay and willingness-to-accept (WTA)
questions. The Can $22-27 million VSL  figure refers to WTP for job safety (which is judged as more
reliable than WTA).
25 These estimates are based on a Weibull interval-data model that combines the responses to the initial
WTP questions and to the follow-up questions in a double-bounded fashion.
                                         44

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elasticity of WTP is 0.16 when the full sample is used, 0.29 when persons whose implied

WTP amount is greater than 10% of household income are  excluded, 0.52 when we

exclude persons whose WTP is greater than 5% of household  income, and, finally, 0.92

when the most stringent criterion is used. Predictions for WTP as income changes would,

therefore,  vary dramatically, depending  on' which of these "cleaned" samples, and tie

corresponding income elasticity of WTP,  one opts for.
                      Table 9. Outliers with respect to income.
  Alberini et al. US Survey. WTP for 5 in 1000 risk reduction, wave 1, cleaned sample*

Least
stringent

Most
stringent
Exclude if. . .
(all sample)
WTP > 25% of
household
income
WTP > 10% of
household
income
WTP > 5% of
household
income
WTP > 2.5% of
household
income
N
551
483
477
458
418
Mean WTP
($)
752.84
(88.37)
755.56
(90.84)
747.53
(90.02)
719.25
(89.21)
678.39
(91.64)
Median WTP
($)
346.21
(28.45)
362.38
(31.97)
355.14
(29.24)
339.33
(30.02)
302.26
(28.67)
Income
elasticity of
WTP
0.16
0.16
0.29
0.52
0.92
* Excludes those respondents who failed the probability quiz and the probability choice.
       Further  investigation reveals that the  65 respondents  who violated the most

stringent exclusion criteria were slightly older than the remainder of the sample, but not

significantly so (average ages were 57 and 54, t statistic of the null of no difference -

1.38), significantly  less educated than the remainder  of the sample (11.75 years of
                                       45

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schooling vs. 13.3, t statistic = -6.27), and reported much lower annual household income

than the rest of the sample (sample  averages: $17,942 v. 56,151, t statistic -22.18).26 27

Moreover, they were twice as likely to indicate, in the debriefing section of the survey,

that they had misunderstood the timing of the payment (27% of this group versus 13% of

the remainder of the sample, t statistic = -4.66).

       Results  for the Persson  et  al. data are displayed in tables  10  and 11. One

respondent in  Persson  et al.'s sample reports a WTP  amount that is  83% of annual

household income. Fortunately, tiie  rest of the sample is more reasonable: Ninety-nine

percent of the sample holds a WTP amount for reducing the risk of a fatal auto  accident

that is equal  to or less than 12.5% of household income. In their analysis, Persson et al.

discard from the  usable sample observations such that WTP accounts for more than 5%

of annual household income.  This loses 29 observations.

       Table  10  displays  mean WTP  for the  full sample,  and when  persons with

relatively high WTP/income ratios are excluded from the usable sample. This table shows

that while median WTP remains  the same for the various exclusion criteria, mean WTP

jumps from  1875 to  2778 SEK  when we reinstate into the  sample those respondents

whose WTP was  more than 5% of household income. This is a 50% increase in WTP.
26 The median annual household income is $17,500 and $55,000, respectively.
27 It is possible that these respondents miscalculated or intentionally underreported their income.  We
regressed log income on age, age squared, education and the gender dummy for the full sample, and used
the results of this regression to compute predicted income. For the 65 respondents with high WTP/income
ratio, income predicted on the  grounds  of education, gender and age was always larger than reported
income.
                                         46

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                           Table 10. Person et al. study.
    Effect of excluding observations with large annual WTP/household income ratios.
                             All values in 1998 SEK.
Exclusion criterion
None
Respondents with zero income but
positive WTP
WTP greater than 50% of household
income (least stringent)
WTP greater than 25% of household
income
WTP greater than 20% of household
income
WTP greater than 12.5% of
household income
WTP greater than 10% of household
income
WTP greater than 5% of household
income (most stringent)
Number of
observations in
the sample
637
;637
636
633
632
631
629
618
Sample
average
wrp
2778
2778
2635
2163
2151
2143
2134
1875
Sample
Median WTP
1000
1000
1000
1000
1000
1000
1000
1000
       Table 11  displays the income elasticity of WTP when observations where WTP

accounts for a relatively large share of household income are omitted from the sample.

As  explained in section V, we estimate  a system of simultaneous equations for log

baseline  risk and log WTP. The right-hand side of the WTP  equation  includes the

logarithmic transformation of the absolute risk reduction, log miles traveled in a car in a

year, a dummy accounting for previous injuries sustained in a car accident, log age, log

age squared, two education dummies, and  dummies for the size of the household in

various  age  groups. Table 11 shows that income elasticity of WTP doubles when we

move from the sample created with the least restrictive criterion to the most stringent

criterion. It remains, however, relatively low (0.28).
                                       47

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       We conclude that while there is no unambiguous criterion for considering one's




WTP "large" relative to this person's income,  researchers should experiment with




checking how the estimates of WTP and other coefficients of interest are affected by



including/excluding  from the usable sample those respondents whose announced WTP is




high relative to income. In the two examples presented in this section, doing so had a




completely different impact on the estimates of mean WTP and on the income elasticity




of WTP. These checks also pointed out that observations with a large WTP relative to




income may be due to the respondent's failure to understand or retain details of the risk



reduction scenario, as shown by the example based on the Albermi et al. data. They may




also result from an  inaccurate calculation or a deliberate misreporting of income on the




part of the respondent.
                                       48

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                            Table 11. Persson et al. study.
 Effect of excluding observations with large WTP/household inc ome ratio on the income
 elasticity of WTP. 2SLS estimation, dependent variable: log WTP for risk of dying in a
                                road traffic accident.
Exclusion criterion with respect to income •
None
Respondents with zero personal income but
positive WTP
WTP greater than 5% of household income
WTP greater than 10% of household,
income
WTP greater than 12.5% of household
income
WTP greater than 20% of household
income
WTP greater than 25% of household^
income
WTP greater than 50% of household
income
Number of
observations
514
514
501
509
510
511
512
514
Income
elasticity
ofWTP
0.1475
0.1475
0.2850
0.2264
0.1937
0.1668
0.1418
0.1475
Standard
error
0.1136
0.1136
0.1109
0.1139
0.1129
0.1126
0.1119
0.1136
Observations with missing baseline risk and missing WTP, observations with baseline risk smaller
than 1 in 100,000, observations with WTP less than 1. Other regressors in the WTP equation: log
degrisk, log riskmd, log miles traveled in a car, previously injured in a traffic accident (dummy),
log age, log age squared, two education dummies, dummies for household members.
Coefficients of log degrisk and tog riskmd are restricted to be equal.
VII. Discussion and Conclusions

       This paper examines the issue of the robustness of the estimates of the VSL from

CV studies that elicit WTP for a reduction in the risk of dying. We illustrate the effects of

maintained assumptions and techniques using the data from four recent CV surveys.

       When dichotomous choice questions are used, we emphasize the importance  of

spreading bids nicely over a broad portion of the range of WTP (Cooper, 1993). We also

show that the estimate of mean WTP from dichotomous-choice CV data can be extremely

sensitive to the distributional assumption made by the researcher about the  latent WTP
                                        49

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variable, and to the procedure used for calculating the welfare statistics.  Median WTP




tends to be less affected by these factors.  We also find that claims about the shape of the




relationship between WTP and certain covariates of interest (e.g., age) may no longer be




valid when alternative distributional assumptions are made, alternative welfare statistics




are used, or alternative (e.g., semiparametric) procedures are employed.




       Outliers can, in general, be  defined as  observations  that are  distant from the




remainder of the sample. How exactly  "distant" is defined is, of course, a matter of




interpretation. In this paper,  we examine outliers in dichotomous choice CV samples in




the sense of Copas (1988).




       We also attempt to estimate discrete  mixtures to identify yea-sayers, nay-sayers,




and persons who answer the payment questions in a completely random fashion—another




possible cause for outliers—but obtain implausible results that we attribute to the fact that




the distribution assumed for WTP and/or the mixture we choose to work with fits the data




poorly.




       Next, we examine the internal validity of the WTP responses. Specifically,  we




look at the scope effect and at the  association between WTP and income. Carson  (2000)




emphasizes that a CV study about  mortality risk reductions must satisfy the "scope" test




for the quality of the survey and its data to be considered acceptable. Testing for scope




requires that the risk reduction be varied to the respondents by virtue of the experimental




design.  WTP will pass a  "weak" scope test if it increases  systematically with the size of




the risk reduction. It will pass a "strong" scope test if it is proportional to the size of the




risk reduction.
                                        50

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       Testing for scope is straightforward when people are asked to value objective risk

reductions which are  varied to them in the study.28 Testing for scope can be more

complex when people are subjectively  assessing their own baseline risks and/or risk

reductions. This  is  because both of these variables  may be affected by unobserved

individual  factors, which results in their econometric endogeneity. The Persson et al.

survey is an example of one such study.

       Using the Persson et al.  data, we find that the sensitivity of WTP to the size of the

risk  reduction is  indeed  more pronounced when risk reductions  meant as a specified

proportion of a subjectively assessed baseline are treated as econometrically endogenous

with WTP. We also  show that with CV surveys conceived in this fashion it is important

to test for whether  people were  truly valuing absolute risk  reductions, or the mere

proportion, without applying the latter to their baseline risks. In the Persson et al. study,

people indeed appear to  be responding to the percentage risk  reduction, but  not to the

baseline risk, which makes it problematic to compute the VSL.

       Turning to the  other internal validity issue, we tackled the question whether one

should omit observations with  large WTP relative to income.  We illustrate our checks

using two applications where the omissions of these variables from the sample has the

opposite effect on mean WTP and on the income elasticity of WTP, a key quantity when

one  wishes to (i) extrapolate study  results to the general  population, (ii) focus on the

economically  disadvantaged, and (iii) attempt benefit transfers to other countries or

locales where income levels are different.
28 Ideally, the scope tests should be external, i.e., performed using independent samples where respondents
are faced with risk reductions of different size.
                                        51

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       For the Alberini et al.  application, further checks suggest that individuals with




high announced WTP relative to income may have misunderstood some key aspects  of




the survey's risk reduction provision. This and the earlier checks imply that researchers




should explore and report variants of their models driven by different assumptions, and




attempt to recognize outliers and respondents who may have misunderstood some aspects




of the valuation scenario.
                                       52

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                                     References
Alberini, Anna (1995), "Optimal Designs  for Discrete  Choice Contingent Valuation
       Surveys:  Single-bound,  Double-bound  and  Bivariale Models,"  Journal of
       Environmental Economics and Management, 28, 187-306.

Alberini, Anna, and Richard T. Carson (2001), "Yea-Sayers, Nay-sayers, Or Just Plain
       Confused? Mixtures of Populations b Contingent Valuation Survey Responses,"
       presented at annual meeting of die European Association of Environmental and
       Resource Economists, Southampton,1 England, June 2001.

Alberini, Anna, Maureen Cropper, Alan Knapnick, and Nathalie Simon (2004), "Does the
       Value of a Statistical Life Vary  with Age and Health Status? Evidence  from the
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