POLICY RESEARCH WORKING PAPER 228 0
W illingness to Pay for People in Sofia are willing to
pay 4.2 percent of their
Air Quality Improvements income or more for a
in S Bugaiprogram to improve air
Sn tofia, Bulgaria quality.
Hua Wang
Dale Whittington
The World Bank
Development Research Group
Infrastructure and Environment
January 2000
| PoI.1cY RESFMAR H WVORKDING PAPF 2280
Summary findings
Through a survev, Wang and Whittington study T hey find that people in Sofia are willing to pay up to
willingness to pav for improverments in air quality in about 4 7. percent of their inconme for a program to
Sofia, Bulgaria. improve air quality. The income elasticity of willingness
Using a stochastic pavmrcn card approach -- asking to pay for air quality improvements is aboLut 27 percent.
respondents the likelihood that they would agree to pay For comparison, they also used the referendum
a series of prices - they estimate the distribution ot contingent valuation approach. Results from that
willingniess to pay various prices. approach yielded a higher estimate of willingness to pay.
This paper - a product of inifrastructure and Environment, Development Research Group -is part of a larger effort in
the group to understand the economics of pollution control in developing countries. Copies of thc paper are available fr( e
from the World Bank, 181 8 H Street, NW, Washington, DC 20433. Please contactRoulaYazigi, roomIMC2-533, telephone
202-473-7176, fax 202-522-3230, email address ryazigi( V(Y, P, Eo, Z, s) } (4)
Pr {V(Y-t, P, E, Z, )> V(Y-WTP, P, El, Z, c)}
= Pr {WTP >t}
1- F(t)
where again V is an indirect utility function; Y is income; P is a price vector; Z is a vector
of individual's socioeconomic characteristics; E. is the initial environmental quality,
which would be improved to E, if the air quality management plan is implemented; t is
the price offered to obtain the environmental quality change; and WTP is the individual's
value for the certain change. The likelihood matrix obtained with the stochastic payment
card is a record of an individual's probabilities of accepting different proffered payments.
The cumulative valuation distribution function F(.), the valuation probability
density function, the mean and the variance of the probability function can be estimated
with the likelihood matrix data. The estimation of the valuation distribution is straight
It is possible that introducing uncertainty explicitly in the CV questions could create confusion for the
respondent rather than enabling a respondent to give a more complete valuation response. This concern is
especially pertinent in countries where people do not have a long experience with democratic voting
procedures, such as Bulgaria. However, the results of our case study and the findings of Welsh and Poe
(1998) would appear to indicate that this threat is perhaps not as serious as one might fear.
7
forward. From (4), we have Pi, = I-F,(tj), where Pij is individual i's probability (the
number circled by respondent i on the stochastic payment card) of voting for the
referendum at the jth payment point tj; F,(.) is the person i's CDF. By assuming a
specific functional form for Fi(.), standard statistical software can be used to estimate the
parameters in Fi(.). and the mean 1L, and standard variance vi of individual i's valuation
distribution. For example, if a normal distribution is assumed for F(.), we have,
Pi = I - (X(8u t)
ti = + o-I (1 - Pi)
With a set of ti's and Pi's, a simple regression can be used to estimate jL and a.
For cases where numeric likelihood values cannot be obtained for estimating a
valuation distribution, it might be possible to estimate an upper bound, a lower bound,
and a mean value with some reasonable assumptions about the meaning of the verbal
likelihood data. An estimate of the upper bound of an individual's valuation range is the
lowest price where a respondent gives a "definitely no (0%)" answer. Likewise, the
lower bound of an individual's valuation range can be found at the highest price where a
respondent gives a "definitely yes (100%)" answer. The mean of a valuation distribution
can be obtained from prices where a respondent says "not sure (50%)."
III. Sofia Air Valuation Study
Study Design
In October 1995, we conducted a CV survey in Sofia, Bulgaria, to estimate
households' willingness to pay for air quality improvement. The purpose of the CV
survey included: 1) to estimate people's willingness to pay for air quality improvement in
Sofia, Bulgaria; 2) implement the stochastic payment card value elicitation procedure;
and 2) to compare the stochastic payment card approach with the conventional
referendum CV approach. The CV scenario section of the household questionnaire had
8
five parts: (1) Background: Current Air Quality Conditions in Sofia; (2) A Description of
an Air Pollution Clean-up Plan; (3) Consequences of the Air Pollution Clean-up Plan; (4)
Costs of the Air Pollution Clean-up Plan; and (5) Valuation Question(s). Respondents
were also asked questions about their socioeconomic characteristics, environmental
attitudes and perceptions, and reactions to the air quality improvement program.
The study design is summarized in Figure 2. A stratified random sample of
households was drawn from neighborhoods throughout the city. The response rate was
about 60%, and reflects some suspicion that people in Sofia feel when a stranger comes to
their home and requests an interview. Five hundred and fourteen in-person interviews
were completed with household heads or their spouses. The sample was first split into
two approximately equal parts. Two hundred and forty three interviews were completed
with respondents who received a survey instrument with a standard referendum CV
question (Version A). Five different referendum prices were used (100, 300, 500, 1000,
2000 levas2 per month); there were thus five split-samples of approximately 48
respondents each. These prices represent from 1% to 18% of the mean household income
of the respondents.
The remaining 271 respondents received a stochastic payment card (Version B).
These respondents were subdivided into two groups: B1 (n = 135) and B2 (n = 136).
Respondents in Group B 1 received a standard stochastic payment card with the full set of
eight prices (25, 50, 100, 300, 500, 1000, 2000, 3000 levas per month); respondents in
group B2 received a truncated stochastic payment card with five prices (100, 300, 500,
1000, 2000 levas per month). Respondents who received versions BI and B2 were given
numeric likelihood values of 0% ("Definitely no"); 25% ("Probably no"); 50% ("Not
sure"); 75% ("Probably yes"), and 100% ("Definitely yes") to indicate the probability
that they would pay the specified prices.
Specifically, respondents were asked the following willingness-to-pay question in
conjunction with the stochastic payment card:
I (the enumerator) want you (the respondent) to suppose that the people of Sofia had an
opportunity to vote for this (air quality improvement) plan. If the majority of people voted for the plan, the
2 In October, 1995, US$1 = 68 levas.
9
plan would go into effect and every household would have to pay. If the majority of people voted against
the plan, no one would have to pay and air pollution would stay as it is now.
Now, I want you to tell me how likely you would be to vote for the air quality improvement plan
in Sofia, if your monthly expenses for transport, electricity, etc. would increase in different amounts. In
other words, I want to know how likely it would be that you would vote for the air quality clean-up plan if
it would cost your household different monthly amounts.
There are no right or wrong answers; we really want to know how you would vote on this
proposal.
If the number indicated in the left column (monthly price in leva) were the increase in your
monthly expenses for the implementation of the air pollution clean-up plan, how likely is it you would vote
for the plan?
Results of Analysis
Overview
Table 1 presents the socioeconomic and demographic information on respondents
who received both Version A and Version B questionnaires. As hoped, there are no
statistically significant differences in these two subsets of sample respondents for any of
the socioeconomic or demographic variables.
Table 2 presents eight possible types of response patterns that respondents could
give to the questions on the stochastic payment card, and the percentage of sample
respondents in each. For the standard version of the payment card, 71% of respondents
gave answers that suggest the individuals' WTP ranges were covered by the payment
card,3 while 11% of respondents had WTP ranges that were partially covered by the card.
Thirteen percent of respondents' WTP ranges were not covered by the card (or these
respondents were unwilling to reveal their WTP ranges). Valuation distributions could
not be estimated for these respondents.
Table 3 summarizes the answers of respondents who received the referendum
valuation question (Version A). Of the 243 referendum interviews, 216 yes/no/not-sure
answers were recorded and could be used for further analyses (27 respondents did not
3 There were six observations -for which respondents gave answers with a higher probability of voting for
the proposal at a higher price. We considered these to be enumerator mistakes and deleted them from the
sample for purposes of analysis.
10
answer the valuation question). As expected, as the price of the air quality improvement
plan increased, the percentage of respondents in each split-sample that rejected the plan
(i.e., that refused to pay) increased.
Estimation of Individuals' Valuation Distributions
Valuation functions were calculated for 219 respondents in the group B
subsample (Cases 1, 2, and 3 in Table 2); the mean and the variance of these valuation
functions were estimated using the approach described in Section II. Valuation
distribution functions could not be estimated for the 46 respondents with Case 4-8
response patterns (17 percent of the total number of 271 respondents that received either
the B 1 or B2 version of the questionnaire). The inability of the stochastic payment card
elicitation approach to handle these cases could pose a serious threat to the validity and
usefulness of the method if the excluded respondents are systematically different from
respondents who give Case 1-3 response patterns. However, no systematic difference
between these two groups was found in this study.4
In calculations of mean values and variances of individuals' valuation
distributions, values of 0.005 and 0.995 were used in the regressions instead of 0 and 1
for probability Pi. Assuming the individuals' valuation functions are all normally
distributed,5 the mean values of ,t and (c are 508 and 159 levas respectively (Table 4) 6
The average of the standard variance of the mean WTP estimation is 73 levas, and the
average standard error of the standard variance estimation is 51 levas.
4 However, the average value of the mean WTPs of the sample does change somewhat if responses for
cases 4 and 5 are included with reasonable assumptions on the WTP values. For example, if one assumes a
WTP of 3000 levas for those respondents who gave all "definitely yes" answers and a WTP of 25 levas for
those giving all "definitely no" answers, then the sample mean WTP would be 602 levas rather than 508
levas. We do not feel that there are strong reasons for treating cases 4 and 5 as protest bids. In future
studies, we intend to expand the price range of the payment card.
5 In fact, there is no reason to suppose that each individual in the sample has the same functional form for
his valuation function; we make this assumption for simplicity.
6 The average value of those prices corresponding to the indifferent (50%) responses is about 473 levas
which is very close to the value estimated by modeling the individuals' valuation distributions.
]I
Econometric Analysis of Individuals' Valuation Distributions
Assuming individuals' valuation distributions have the same functional form,7 the
calculated mean WTP and standard variances vary across respondents in systematic ways.
Figure 3 shows how the mean WTP values and the standard variances of the valuation
distributions for Group B 1 respondents vary with household income. As expected,
respondents with higher household incomes have higher mean WTP's and larger
variances.
Table 5 presents the results of three econometric models that attempt to explain
differences across respondents in their mean WTP and the standard variance associated
with their valuation distributions. Both the household income and the education of
respondents had significant effects on respondents' willingness to pay for the air
pollution clean-up plan, with expected, positive signs. The elasticity of mean WTP with
respect to income is about 0.27. Older respondents and women had lower WTP.
However, the models show that people with higher uncertainty about their future income
would be willing to pay more for the air pollution clean-up plan.
There are also several significant variables in the second model in Table 5 that
explain differences in the estimated variances of individuals' valuation functions, i.e., the
variance of an individual's valuation distribution is correlated with individuals'
socioeconomic and demographic status. Men have larger variances of their valuation
distributions than women; respondents with higher uncertainties about their future
income had larger variances in their valuation distribution. Truncation also had a
significant effect, indicating that respondents' answers are sensitive to the payment card
design.
The same variables were generally statistically significant in both the mean value
and variance models. A regression of log(4/t) against other exogenous variables
showed that the variable MALE was positive and statistically significant. Men thus have
a wider variance of WTP than women, even when the mean WTP' s are the same. The
variable UNCERT has the expected positive sign but is not statistically significant.
12
Comparison with the Referendum Approach
After deleting observations with missing values, 194 interviews were available to
estimate probit models explaining the determinants of respondents' answers to the
referendum CV question (Version A). The modeling results are provided in Table 6.
These results are used to estimate mean WTP values for the Group A sample. There were
49 "not sure" ("Don't know" or DK) answers to the referendum questions given by
Group A respondents. Two methods were used for analyzing these data: 1) treating DK
as "no"; 2) the threshold approach developed by Wang (1997a). The two methods gave
consistent results.
The results of these probit models indicated that the price offered to respondents
had a strong negative effect on the likelihood that a respondent would accept the air
quality improvement plan. Income and education have significant, positive effects on the
likelihood of voting for the air quality improvement plan; age has a significant, negative
effect. Contrary to expectations, respondents who have a respiratory disease or who live
in a household in which a family member has a respiratory disease were less likely to
vote for the air quality improvement plan. Female respondents were more likely to give a
'not sure" answer.
Using these estimated probit model results, the mean WTP for the sample was
calculated. When the DK responses were treated as "no's," the mean WTP for the Group
A respondents was 1430.8 Other ways of handling the DK responses resulted in higher
mean WTP estimates. The lowest mean WTP estimated with the referendum CV data is
almost three times the highest mean WTP calculated using the data from the stochastic
payment card (508 levas per month; Table 4)
This difference in the estimated mean WTP between the Group A and Group B
respondents could be a result of several factors because the analyses with the data from
the stochastic valuation approach and the referendum question are based on different
theoretical assumptions and different procedures for handling "problematic" responses.
7 The results with the normal distribution assumption were used in the econometric analyses.
13
To isolate the effect of the two elicitation procedures on the estimated mean WTP, we
conducted additional analyses in which we treated the data obtained from the stochastic
payment card at a specific price as if it were the individual's answer to a single
referendum question. A new data set was thus constructed for Group B respondents by
randomly assigning a price to each respondent. In this way, we were able to use the
answers from all of Group B respondents (except the six with inconsistent responses).
This new data set for the Group B respondents was then analyzed in exactly the same way
as the data set for the Group A respondents.
Six different ways were used to encode the likelihood answers from the stochastic
payment card as yes/no/not-sure answers in order to generate a referendum CV sample
for the WTP estimation for respondents in Group B:
(1) "definitely yes" answers in the stochastic payment card treated as "yes" in the
referendum model; "probably yes", "not sure" and "probably no" treated as "don't
know's"; "definitely no" treated as "no";
(2) "definitely yes" and "probably yes" answers in the stochastic payment card
treated as "yes" in the referendum model; "not sure" treated as "don't know's"; "probably
no" and "definitely no" treated as "no";
(3) answers in the stochastic payment card simply treated as an ordered ranking;
(4) "definitely yes" answers in the stochastic payment card treated as "yes" in the
referendum model; all others treated as "no";
(5) "definitely yes" and "probably yes" answers in the stochastic payment card
treated as "yes" in the referendum model; all others treated as "no";
(6) "definitely yes" and "probably yes", "not sure" answers in the stochastic
payment card treated as "yes" in the referendum model; all others treated as "no."
Because the results for the Group B respondents depend upon the price a particular
respondent is assigned, we conducted a Monte Carlo analysis with different trial price
8 The estimated model was used to calculate the WTP for each respondent in the sample; 1430 levas is the
mean of these values.
14
assignments, and calculated the sample mean WTP for each trial. For each of these six
ways of converting likelihood answers to a referendum format, 1000 trial price
assignments to Group B respondents were made. The sample mean WTP result presented
for Group B respondents for each way of converting likelihood answers from the
stochastic payment card to a referendum format is the mean of the 1000 trial price
assignments.
Table 7 shows that the highest mean WTP obtained from the stochastic payment
card data is 523 levas, when "definitely yes," "probably yes," and "not sure" are all
treated as "yes" responses in a referendum model. This estimated mean WTP number is
still much lower than the lowest estimate obtained using the referendum value elicitation
approach (1430 levas).9 This Monte Carlo analysis confirms that the difference in the
mean WTP estimates obtained from the stochastic payment card data and the referendum
data is largely due to the elicitation procedure itself, and not to the assumptions
underlying the calculation procedures.
V. Discussion
The stochastic payment card approach presented in this paper is a preliminary,
exploratory attempt to collect data that can be used to estimate individuals' valuation
distributions. It requires respondents to give subjective probabilities about whether a
hypothetical action would be taken. The approach assumes that the probability that a
respondent is going to take an action is the probability that respondent's utility value
increases. This in turn is based on a rational choice assumption that individuals take
actions when and only when their utility values increase. The procedure proposed for
estimating an individual's valuation distribution is simple and does not require the use of
sophisticated econometric models. However, the analyst must assume a functional form
for individuals' valuation distribution functions. The evidence from our Sofia case study
9 The ordered probit modeling approach for the stochastic payment card data gives a sample mean WTP
estimate of about 516 levas (Wang, 1997b).
15
suggests that the mean value and the variance of the valuation distributions are not very
sensitive to specific functional form assumed.
The stochastic payment card approach seems to have worked reasonably well in
the case study. At the lowest price all respondents would ideally choose "definitely yes,"
and at the highest price, all responses would be "definitely no" (assuming the survey
designers succeed in selecting low and high prices that bound all respondents' valuation
distribution functions). Eighty two percent of respondents who received the full
stochastic payment card (B1) gave "definitely yes" answers to the lowest price offered
(25 levas) and 88% gave "definitely no" answers to the highest payment point (3000
levas). The results of the Sofia case study do indicate, however, that respondents'
likelihood answers to questions on the stochastic payment card can be affected by the
way payment cards are designed.'° At a price of 100 levas (the lower end of the truncated
payment card), respondents were more likely to give positive answers if they received the
truncated payment card," i suggesting that they interpreted that lowest price as an
indication that it was acceptable. One approach for dealing with this possible bias may be
to extend the range of prices presented on the stochastic payment card, possibly including
zero as the minimum price. Before we.conducted the case study, we were concerned that
respondents' unfamiliarity with democratic voting processes in Bulgaria would affect
people's ability to answer CV questions in general, and the stochastic payment card
questions in particular. However, based on our experience in Sofia during the fieldwork,
we do not believe that this is a serious threat to the validity of our results.
In the economic valuation literature, analysts have generally used the option price
approach to deal with the issue of uncertainty in future outcomes. This option price
approach assumes a single point value in an individual's mind even when there exist
obvious uncertainties. An option price can be estimated with data collected by a
traditional contingent valuation survey with dichotomous choice valuation questions.
The stochastic valuation approach, on the other hand, does not assume that a respondent
IO An exponential increase of prices on the payment card could also have an effect on the valuation
distribution estimation. One consequence could be an overestimate of the correlation of variance and the
mean value of a valuation distribution.
This is consistent with Rowe et al. (1996)'s findings (they did not find range and centering biases).
16
has a single point value for his maximum willingness to pay, even for a market good.
The Sofia air valuation study suggests that the single point value assumption may be
incorrect, because estimated variances of individuals' valuation distributions are
correlated with uncertainty levels. The single value assumption would suggest that the
variances estimated are white noise.
The valuation information obtained with the referendum elicitation procedure is
necessarily incomplete, a fact well recognized by CV practitioners. A yes/no answer only
gives information about one point on a valuation distribution function (with 0 or 1
representing a probability that should often be a number between 0 and 1). Because a
yes/no answer is quite easy for respondents to offer (a positive side of the approach), such
a yes/no answer might be offered without respondents seriously considering the question.
The stochastic payment card approach attempts to obtain a more complete description of
each individual's preferences. It focuses on measuring each individual's valuation
intensity information; this information is relatively complete compared to that obtained
from a single dichotomous choice question. The sample size required for a study using a
stochastic payment card approach should thus be smaller than for a conventional
referendum CV study.
The stochastic payment card approach, however, requires respondents to give
numeric likelihood values; some respondents may have difficulty doing this. Significant
confusion may be induced in some respondents if a study is not well designed. Providing
corresponding verbal or visual aids may help respondents report likelihood values, but
this may not solve the problem, especially for illiterate respondents. More research is
needed to assess the nature of subjective probabilities that respondents give in CV
interviews. However, as discussed in Section II of this paper, even when the numerical
likelihood information obtained is not sufficient to construct a model to estimate an
individual's underlying valuation distribution, reasonable assumptions can be made based
on the verbal likelihood data to estimate an upper bound, a lower bound and a mean
value.
The traditional procedures used to implement the referendum CV approach are
problematic if one does not assume that an individual's valuation is a single point
17
estimate. The error terms in the value estimation models proposed by Hanemann (1984)
and Cameron (1989) are assumed to be homogeneous over the population; according to
the stochastic theory of economic valuation they should be heterogeneous. The empirical
study presented in this paper shows that the traditional dichotomous choice CV gave an
estimate of people's WTP that was 2-3 times higher than the stochastic approach, despite
the fact that the two approaches found the same determinants of WTP. More research is
warranted to better understand the reasons for this difference.
Acknowledgements:
We would like to thank Dr. Dafina Gercheva for her guidance and advice on
survey design and implementation issues in Sofia, and Dr. David Guilkey for his many
helpful suggestions on the econometric analyses.
18
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Contingent Valuation Method, Resources for the Future, Washington, D.C.
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Wang, Hua. 1997b. Contingent Valuation of Environmental Resources: A Stochastic
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20
Figure 1. An Example of the Stochastic Payment Card Design
(Please circle one number for each payment)
How would you vote if the
passage of this envir. plan
meant your utility bill would Definitely Probably Not Probably Definitely
increase by $x per month Yes Yes Sure No No
for one year?
Price
0 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
2 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
4 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
6 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
8 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
10 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
12 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
100 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Figure 2. Sofia Air Valuation Study Design
(Total Sample Size N=5 14)
Version B Version A
(Stochastic Payment Card) (Referendum)
N=271 N=243
I
F j P100 N=47
Version BI Version B2 P300 N=54
Standard Card Truncated Card P500 N=47
N=135 N=136 P1000 N=42
P2000 N=53
21
Figure 3. Income vs Mean Value and Standard
Variance of an Individual's WTP Distribution
1200
100
w aS i
TP 4 k vmean-std
Va 6C0 mean
e 40( i A, meanstd wvar
2C0.
~~2
00 DO CC DO ° DO00 °°00 °° 00
C - 0 C, -C C- 0 Go
1ncome Group
Table 1: Description of Major Socioeconomic and Demographic Variables
Variable Description of Variables Mean Value Mean Value
Name (Std Dev) of (Std Dev) of
Sample A Sample B
Price Hypothetical monthly cost in levas
INC Household monthly income in levas. 11,925 12,925
(8,424) (10,908)
SCHOOL Number of years a respondent attended a 13 12
school. (2.3) (2.6)
MALE 1=the respondent is male; 0=otherwise. 0.37 0.47
AGE Age of a respondent. 46 47
(14) (15)
MARRY l=the respondent was married; 0.77 0.83
0=otherwise.
RESP l=there were respiratory diseases found in 0.43 0.34
a household; 0=otherwise.
UTNCERT 1 =the respondent did not know how the 0.18 0.18
household income would change over the
next five years; 0=otherwise.
No. of Obs. 243 245
22
Table 2. Eight Possible Types of Response Patterns to Valuation Questions in the
Stochastic Payment Card
Cases Type of Response Pattern Standard Version Truncated Version
(BC ) (B2)
1 Set of responses includes both 96 71
"definitely yes" and "definitely (71%) (52%)
no" answers
2 Set of responses includes 6 23
"definitely yes" but not (4%) (17%)
"definitely no" answers
3 Set of responses includes 9 14
"definitely no" but not (7%) (10%)
"definitely yes" answers
4 "Definitely yes" response at the 7 4
highest prices (5%) (3%)
5 "Definitely no" response at the 11 20
lowest prices (8%) (15%)
6 All responses "probably-yes" 0 2
(1%)
7 All responses "not-sure" 0 2
(1%)
8 All responses "probably-no" 0 0
9 Inconsistent answers 6 0
(4%)
Total 135 136
23
Table 3: Percent of Respondents Giving Different Answers
to Referendum CV Questions by Price
Referendum Prices ( Levas/Month)
WFP 100 300 500 1000 2000
Answers
No 4 14 24 29 42
NotSure 2 6 11 24 6
Yes 94 80 65 46 52
Table 4: Sample Means of Individuals' Estimated Mean WTP and Standard Variance of
WTP
Distribution Normal
Parameters Distribution
Mean WTPs
Mean 508
Std. Dev. 458
Std Var of WTP
Mean 159
Std. Dev. 135
Average R2 0.86
24
Table 5: Econometric Analyses of Individuals' Valuation Distributions
Dependent Dependent Dependent
Variable: Variable: Variable:
log(0) 10g(6) 0g(6y/WL)
Constant 3.4 2.7 -1.3
(3.5)*** (2.4)** (-19.9)***
log(INC) 0.27 0.21
(2.64)*** (1.84)*
SCHOOL 0.07 0.06
(3.16)*** (2.31)**
MALE 0.36 0.53 0.16
(3.08)*** (3.96)*** (1.93)*
AGE -0.02 -0.02
(-4.02)*** (-3.81)***
RESP 0.24 0.14
(1.76)* (1.59)
UNCERT 0.30 0.44 0.14
(2.02)** (2.55)** (1.24)
Shorter 0.44 0.39
Card (3.96)*** (2.99)***
Adj-R2 0.27 0.23 0.02
N 198 198 198
***-Statistically significant at the 1% level
**-Statistically significant at the 5% level
*-Statistically significant at the 10% level
25
Table 6: Model Results for Referendum Data (Group A Respondents)
Data Treating "not sure" as Threshold Approach
Treatment "no"
Full Model Reduced Full Model Reduced
Form Form
PRICE -0.8e-3 -0.8e-3 0.8e-3 0.8e-3
(-4.8)*** (-4.8)*** (5.0)*** (5.3)***
Constant 2.6 1.6 2.8 1.9
(3.1)*** (3.2)*** (3.5)*** (39)***
INC 0.3e-4 0.2e-4 0.3e-4 0.2e-4
(1.9)** (1.6)* (2.0)** (1.7)*
SCHOOL -0.1 -0.05
(-1.4) (-1.1)
MALE 0.2 0.1
(1.1) (0.5)
AGE -0.02 -0.02 -0.02 -0.02
(-2.0)** (-1.9)* (-2.4)** (-2.3)**
MARRY -0.3 -0.3
(-1.0) (-1.1)
RESP -0.4 -0.4 -0.4 -0.4
UNCERT 0.02 0.02
(0.08) (0.06)
threshold:
Constant 0.2 0.2
(4.1)*** (4.2)**
Male -0.1 -0.1
(-1.6) (-1.7)*
Mean WTP 1429 1618
Std Error of 212 200
Mean WTP
Std Dev of 525 533
WTP
Sample Size 194 194
***-Statistically significant at the 1% level
**-Statistically significant at the 5% level
*-Statistically significant at the 10% level
26
Table 7: Estimation of WTP with Data from the Stochastic Payment Card, Using
Traditional Referendum Modeling Methods and Monte Carlo Simulation
Models I II III IV V VI
Likelihood DY as DY/PY 5 DY as DY/PY DY/PYI
Answer yes; PY, as yes; Ordered yes; as yes; NS as
Treatment NS & NS as Answers others as others as yes;
PN as DK; no no others as
DK; DN DN/PN no
as no as no
Modeling Ordered Ordered Ordered Probit Probit Probit
Method Probit Probit Probit
Mean 354 392 360 14 267 523
WTP
Std. Dev. 63 61 64 138 74 62
of WTP
N 265 265 265 265 265 265
DY Definitely yes; PY = Probably yes; NS = Not sure; DK = Don't Know;
PN = Probably no; DN = Definitely no
27
Conltact
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WPS2265 The Political Economy of Distress Paola Bongini JI -;ry 2000 R. Vo
In East Asian Financial Institutions Stijn Claessens 33722
Giovanni Ferri
WPS2266 The Impact of Adult Deaths on Martha Ainsworth Ja&iuary 2000 S. Fallon
Children's Health in Northwestern Innocent Semali 38009
Tanzania
WPS2267 Do High Interest Rates Defend Aart Kraay January 2000 R, Bonfield
Currencies during Speculative Attacks? 31248
WPS2268 The Structure of Social Disparities Deon Filmer January 2000 S. Fallon
In Education: Gender and Wealth 38009
WPS2269 Context Is Everything: Measuring Nauro F. Campos January 2000 J. Victor
Institutional Change in Transition 36549
Economies
WPS2270 The Optimal Income Tax When Waly Wane January 2000 H. Sladovich
Poverty Is a Public "Bad" 37698
WPS2271 Corporate Risk around the World Stijn Claessens January 2000 R. Vo
Simeon Djankov 33722
Tatiana Nanova
WPS2272 Ownership versus Environment: Ann P. Bartel January 2000 S. Fallon
Disentangling the Sources of Public Ann E. Harrison 38009
Sector Inefficiency
WPS2273 The Value of Preventing Malaria Maureen L. Cropper January 2000 T. Tourougui
In Tembien, Ethiopia Mitiku Haile 87431
Julian A. Lampietti
Christine Poulos
Dale Whittington
WPS2274 How Access to Urban Potable Water Anqing Shi January 2000 P. Sintim-Aboag)
and Sewerage Connections Affects 37644
Child Mortality
WPS2275 Who Gained from Vietnam's Boom Paul Glewwe January 2000 P. Sader
In the 1990s? An Analysis of Poverty Michele Gragnolati 33902
An Analysis of Poverty and Hassan Zaman
Inequality Trends
WPS2276 Evaluating the Case for Export Arvind Panagariya January 2000 L. Tabada
Subsidies 36896
Policy Research Working Paper Series
Contact
Title Author Date for paper
WPS2277 Determinants of Bulgarian Brady Nina Budina January 2000 N. Budina
Bond Prices: An Empirical Tzvetan Mantchev 82045
Assessment
WPS2278 Liquidity Constraints and Investment Nina Budina January 2000 N. Budina
in Transition Economies: The Case Harry Garretsen 82045
of Bulgaria
WPS2279 Broad Roads in a Thin Country: Andres G6mez-Lobo January 2000 G. Chenet-Smith
Infrastructure Concessions in Chile Sergio Hinojosa 36370
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