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Mattias Boman, Lindsey Ellingson, Johan Norman and

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Title: Mattias Boman, Lindsey Ellingson, Johan Norman and


1
Pick a Number, but Not Just Any Number
Valuation uncertainty and maximum willingness to
pay
  • Mattias Boman, Lindsey Ellingson, Johan Norman
    and
  • Leif Mattsson

SLU LOGO
2
Motivation
  • Measure of interest from a CV study is maximum
    WTP
  • Assumes respondents can state their maximum WTP
    as a point value
  • But what if they are uncertain and can only state
    that their maximum WTP is within some interval?
  • Is any value within that interval candidates for
    maximum WTP? For example, are the responses
  • I would definitely be willing to pay SEK 100 for
    a new Volvo V70
  • .
  • I would definitely be willing to pay SEK 300 000
    for a new Volvo V70
  • all equally good candidates for applied welfare
    analysis?
  • We think not, and only one value within the
    interval corresponds to maximum WTP without
    uncertainty.

3
Idea
  • We are looking for maximum WTP, i.e. the WTP
    value where the respondent is indifferent between
    having the project and not having it
  • A logical candidate appears to be when the
    respondent has a subjective probability of 0.5
    for acceptance, since then she/he should be
    incapable of even deciding whether she/he leans
    towards acceptance or rejection gt
  • INDIFFERENT

4
Two Questions
  • What value within an interval corresponds to the
    maximum WTP without uncertainty?
  • To what extent do different WTP response formats
    display convergent validity when controlling for
    valuation uncertainty?

5
Maximum individual WTP without uncertainty
Prob (Accept)
X0
WTP
6
Individual distribution of WTP with valuation
uncertainty
7
Methodology
  • Mail Survey (Fall 2008)
  • 1,461 completed surveys (49 r. rate)
  • Question formats with follow up certainty
    questions
  • Open-ended
  • Interval
  • Multiple bounded dichotomous choice
  • Line scale

8
Open-ended (OE)
  • My total allowable cost would be a maximum of
    ________ SEK per visit
  • FOLLOW UP CERTAINTY QUESTIONS
  • How certain were you on your answer in the
    previous question?
  • When I wrote how high my maximum cost would be,
    it is _____ probability that I would really
    accept it.

9
Interval (IOE)
  • My total allowable cost would definitely be
    _______ SEK per visit
  • My total allowable cost would definitely not be
    more than _____ SEK per visit
  • FOLLOW UP CERTAINTY QUESTIONS
  • What do these expressions mean for you?
  • When I wrote how high my cost definitely would
    have become, it is ___ probability that I would
    accept it
  • When I wrote how high my cost definitely not
    would have become, it is ___ probability that I
    would accept it.

10
Multiple bounded dichotomous choice (MBDC)
FOLLOW UP CERTAINTY QUESTIONS What do these
expressions mean for you? When I say definitely
yes to a certain cost, it is ___ probability
that I really would accept it.
11
Line Scale (LS)
NO FOLLOW UP CERTAINTY QUESTIONS The scale of
certainty is implied by the ticks in the line
scale.
12
Analysis of WTP responses
  • Empirical survival curves for OE, IOE, MBDC and
    LS responses using proportions of the sample
    being WTP X or more
  • - Raw proportions of OE/IOE responses
  • - Uncertainty weighted proportions of OE/IOE
    responses
  • - Uncertainty weighted proportions of MBDC/LS
    responses
  • Calculation of arithmetic mean, median and mode
    for the above
  • Calculation of arithmetic mean, median and mode
    for subsample of 100 certain respondents gt
    benchmark

13
Demographics across formats
14
Average probabilities of acceptance
15
Survival curve, unadjusted (OE and IOE)
16
Survival curve, adjusted (OE and IOE)
17
Survival curve, adjusted (MBDC and LS)
18
Central tendency of WTP formats
19
Central tendency of WTP formats
20
Conclusions
  • Different WTP question formats are associated
    with different levels of (un)certainty
  • Empirical WTP distributions are not symmetric
    around the mean
  • Median of uncertain WTP is however stable across
    question formats and coincides with median WTP
    for 100 certain respondents
  • Suggests that the median of uncertain individual
    WTP is a good candidate for maximum WTP
  • Further analyses with different distributional
    assumptions…

21
Thank you!
Questions?
22
Background
  • Contingent valuation method
  • Willingness to pay
  • Alternative question formats
  • Valuation uncertainty

23
CI across WTP questions
24
Logit model of OE data
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