Reply to “A comment on ‘Three reasons to use annual...

Reply to “A comment on ‘Three reasons to use annual payments in contingent valuation’”

Kevin J. Egan†, Jay R. Corrigan and Daryl F. Dwyer*

April 2017

*The authors are associate professor of economics at the University of Toledo, Toledo, OH; professor of economics at Kenyon College, Gambier, OH; and associate professor of environmental sciences at the University of Toledo, Toledo, OH. We acknowledge the United States Department of Agriculture (Grant No. 2006-38894-03732) for funding. The authors thank PJ Glandon and Kathy Krynski for their feedback. †Corresponding author: Kevin J. Egan, 4140-E University Hall, Department of Economics, University of Toledo, Toledo, OH 43606. Phone: (419) 530-4148, Fax: (419) 530-7844, Email: [email protected].

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Reply to “A comment on ‘Three reasons to use annual payments in contingent valuation’”

Abstract

Whitehead (2017) suggests the contingent valuation (CV) data from Egan, Corrigan, and Dwyer (2015) lacks theoretical validity and has a “fat tails” problem, while also questioning our conclusion that CV surveys using annual payments produce willingness to pay (WTP) estimates that better match consumer surplus estimates from a travel cost model. In this reply, we use likelihood ratio tests to show that our CV data is theoretically valid. We use the Turnbull and Kriström distribution-free estimators to show that our CV data generate economically significant WTP estimates with small standard errors. Finally, we apply the sensitivity analyses from our original paper to Whitehead’s results. These sensitivity analyses overwhelmingly support our original conclusion in favor of using annual payments in CV surveys. Keywords: Discounting, Contingent Valuation, Convergent Validity, Willingness to Pay, nonparametric estimation, fat tails problem, Turnbull Estimator, Kriström Estimator I. Introduction

Egan, Corrigan, and Dwyer (2015, henceforth ECD) present three arguments for using annual

payments, as opposed to one-time payments, in contingent valuation (CV) surveys estimating the

value of long-lasting environmental improvements. First, matching payment term with the

duration of environmental improvements spares respondents from performing present value

analysis. Second, ECD’s willingness to pay (WTP) estimates from CV surveys with annual

payments are convergent valid with consumer surplus estimates from a travel cost survey. Third,

budget and credit constraints are less likely to bind with annual payments than with a larger one-

time payment.

Whitehead (2017) argues that ECD’s data lack theoretical validity because respondents’

votes on the CV referendum are not sensitive to the bid value. More specifically, he shows there

is not always a statistically significant decrease in the percentage of respondents voting yes as he

moves from each of the eight bid values to the next in ECD’s Table 2 (reproduced as Table 1

here). This is not surprising given there were eight policy prices for each of three different

survey versions, meaning an average of just 40 respondents were presented with each price-

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version combination. As Whitehead explicitly concedes, there is a negative and statistically

significant relationship between bid value and yes votes for the survey versions with a one-time

payment (p = 0.01) and with perpetual annual payments (p = 0.02). While this is not true for the

survey version with ten annual payments (p = 0.27), in Section 2 we show that there is a negative

and statistically significant relationship when the data from the two annual-payment surveys are

considered together. With this in mind, ECD deemphasized the distinction between ten annual

payments and perpetual annual payments, instead recommending that CV practitioners use

“ongoing annual payments” when valuing long-lasting environmental goods.

Whitehead also argues that our convergent validity conclusions are driven by our choice

of the Turnbull estimator, which he demonstrates by introducing an alternative Kriström

distribution-free estimator. Using the Kriström estimator, Whitehead finds that WTP from the

CV survey with a one-time payment is convergent valid with the consumer surplus estimate from

the travel cost survey. This is contrary to what ECD find. In Section 3 we apply the sensitivity

analyses discussed in ECD to Whitehead’s results. We consider three different opportunity costs

of time, four different discount rates, two different distribution-free estimators, and two different

approaches to incorporating respondent confidence. Of these 48 permutations, three support

Whitehead’s conclusion, one is ambiguous, and the remaining 44 support our original conclusion

in favor of using annual payments in CV surveys, including 83% of comparisons using the

Kriström estimator.

2. Theoretical Validity

Whitehead’s conclusion that our CV data lack theoretical validity is based on data gleaned from

Table 1 (reproducing Table 2 from ECD). In this table, we report the percentage of respondents

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voting yes on the CV referendum at each of eight different bid values across three survey

versions. Whitehead notes that casual inspection shows there are several instances where the

percentage of yes votes increases as the bid value increases. He then conducts pair-wise tests for

consecutive bids. Given that our bids were close together (e.g., $5 and $10 for annual payments)

and on average only 40 respondents were presented with each bid, it is not surprising that there

are several bid pairs where there is not a statically significant decrease in yes votes as the bid

increases. Whitehead then conducts pair-wise tests for non-consecutive bid values and finds

similar results. He concludes that our data fail to pass “the most basic dichotomous choice [CV]

validity test.”

But this conclusion is at odds with Whitehead’s own chi-square tests. Because our bid

values are tightly spaced and because a modest number of respondents are presented with each

bid, a better test of the validity of our CV data is a likelihood ratio test of the entire bid schedule

(Haab and McConnell, 2002). Focusing on the survey with a one-time payment, we reject the

null hypothesis of equal proportions at the 1% level (c2(8) = 38.2). For the survey with perpetual

annual payments, we reject the null hypothesis of equal proportions at the 5% level (c2(8) =

16.8). For the survey with ten annual payments, we cannot reject the null hypothesis of equal

proportions at conventional significance levels (c2(8) = 9.7). But when we combine the results

from the two surveys with annual payments, we can reject the null hypothesis of equal

proportions at the 1% level (c2(8) = 22.7). We feel justified in combining these results because

there is little difference between a ten-year stream of payments and perpetual stream when

respondents discount the future at the 20% annual rate from ECD’s discount rate survey.

Using the Turnbull monotonically smoothed bid values in bold in Table 1, we reject the

hypothesis of equal proportions for all three survey versions; at the 1% level for perpetual annual

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payments (c2(4) = 15.3) and one-time payments (c2(4) = 29.9), and at the 10% level for ten

annual payments (c2(4) = 8.3).

For the reasons discussed above, these likelihood ratio tests are the best indication of the

overall theoretical validity of our CV data, and they clearly show there is a statistically

significant relationship between bid values and yes responses.

3. Kriström distribution-free estimator and sensitivity analysis

Because 42% of respondents voted ‘yes’ at the highest bids included in our survey, Whitehead

states our data suffers from “fat tails”. Parsons and Myers (2016) show this phenomenon is

common. Their review of 86 recent CV studies finds that nearly 50% include at least one

scenario where yes-response rates at the highest bid are above 30%, and more than a quarter

have yes-response rates higher than ours. Since the Turnbull estimator we used in ECD truncates

WTP at the highest bid value, it may be especially sensitive to the survey’s bid design if the fat

tails problem is present. The Kriström distribution-free estimator (Kriström, 1990; Vaughan and

Rodriguez, 2001), by contrast, uses linear extrapolation to estimate a choke price.

Following Whitehead, we focus our attention on the perpetual and one-time payment CV

survey versions. Table 2 presents the smoothed yes-response rates used for calculating the

Kriström CV WTP estimates for these two versions. Table 3 presents TC consumer surplus

estimates along with Turnbull and Kriström CV WTP estimates for these two versions.1 Despite

1Table 3 shows our Kriström one-time payment WTP estimate is $96 which is different from Whiteheads’s $90.37 WTP estimate. On the first author’s website (https://eganomics.wixsite.com/egan is an appendix) showing a detailed explanation of how we calculated the Kriström WTP estimates. Moreover, for replication purposes, we provide our CV data and Gauss code used for all calculations. Finally, to show the ease in using the Turnbull and Kriström estimators, we provide an Excel file that also provides the CV data and shows all the calculations and WTP function graphs.

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Whitehead’s concerns about our CV data, the Kriström estimator generates reasonable WTP

estimates with narrow confidence intervals.

Using the Kriström estimator, Whitehead finds CV WTP with a one-time payment is

convergent valid with our TC consumer surplus estimates. In this section, we apply the same

sensitivity analyses to the Kriström estimates that ECD discussed regarding the Turnbull

estimates: (1) considering three different values for the percentage of the wage rate used as the

opportunity cost of time, (2) using four different discount rates, and (3) incorporating the results

of a question asking respondents how confident they were in their CV response. Thus, we have

3´4´2 = 24 different comparisons of the Kriström CV WTP estimates and the TC consumer

surplus estimates presented in ECD. Table 4 summarizes the results of these 24 comparisons,

along with the results of 24 similar comparisons of the Turnbull CV WTP estimates and TC

consumer surplus estimates. CV WTP estimates using annual payments outperform estimates

using one-time payments in 92% of comparisons, including 83% of comparisons using the

Kriström estimator. The following subsections detail those comparisons.

3.1 Considering different opportunity costs of time

ECD considered three different specifications of the travel cost model, using an opportunity cost

of time equal to 33% of the average wage rate (baseline), 50%, and 75%. Table 5 presents these

TC estimates as annual consumer surplus and in present value (using the 20% annual discount

rate from ECD’s discount rate survey). Increasing the fraction of the wage rate from 33% to 75%

more than doubles the annual consumer surplus from $19 to $42. While the 95% confidence

intervals overlap for the 33% and 50% wage rates, annual consumer surplus using 33% of the

wage rate is statistically significantly smaller than the 75% estimate.

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Whitehead shows that when the opportunity cost of time is 33% of the wage rate, the $96

one-time Kriström CV estimate is convergent valid, meaning its 95% confidence interval of

($80, $112) overlaps with the 95% confidence interval of the TC estimate in present value. This

is not true for the annual Kriström estimate, contradicting the conclusions in ECD. But this result

is sensitive to the choice of opportunity cost of time. When the opportunity cost of time is 50%

of the wage rate, the results are ambiguous in that both annual and one-time Kriström CV

estimates have 95% confidence intervals that overlap with that of the TC estimate. And when the

opportunity cost of time is 75% of the wage rate, only the annual Kriström CV estimate is

convergent valid.

3.2 Considering different discount rates

In ECD, we consider four different annual discount rates for calculating the present value of

annual WTP estimates: 5%, 10%, 15%, and 20%. Using the Turnbull estimator, we find that for

all four discount rates annual CV WTP estimates outperform one-time estimates in terms of how

closely they match TC consumer surplus estimates. Using the Kriström estimator and a 21%

annual discount rate, Whitehead finds the opposite. Namely, that the one-time CV WTP estimate

is a closer approximation of the TC consumer surplus estimate.

Table 6 presents the same comparison using the four annual discount rates from ECD and

the three opportunity costs of time from section 3.1. Three of these twelve comparisons favor

one-time CV WTP estimates over annual CV WTP estimates either because the one-time

estimates are convergent valid with the TC consumer surplus estimates in present value (33%

wage/20% discount rate and 33% wage/15% discount rate) or because the one-time estimates

provide a closer approximation of TC consumer surplus estimates (33% wage/10% discount

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rate). In another case (50% wage/20% discount rate), the results are ambiguous in that 95%

confidence intervals for both CV WTP estimates overlap with the TC consumer surplus

confidence interval. The remaining eight comparisons favor annual CV WTP estimates over one-

time CV WTP estimates, consistent with the Turnbull results from ECD.

3.3 Incorporating respondent uncertainty

In ECD we discussed how we might incorporate respondent uncertainty by adjusting CV

responses based on answers to a follow-up question providing a 5-point certainty scale.

Incorporating uncertainty would reduce WTP estimates for any of the three payment frequencies

(Li and Mattsson, 1995; Champ, 1997). We stated that incorporating uncertainty would not

change our conclusion given that all Turnbull WTP estimates were already lower than TC

consumer surplus estimates. The “Recoded %Yes” columns in Table 2 present the lower yes

responses at each bid level from recoding any “yes” response as “no” if the certainty level was 3

or less on a 5-point scale. Over all, yes responses decrease from 51% to 38% for the perpetual

annual payments and from 38% to 23% for the one-time payment. Table 2 also shows that yes

responses fall at each bid level, thus lessoning the fat tails issue, though yes responses still do not

decrease monotonically as bid values rise.

Next, we use the Kriström estimator to estimate WTP based on adjusted yes responses

from the perpetual and one-time survey versions. The WTP estimate decreases from $30 to $23

for the perpetual annual payments and decreases from $96 to $60 for the one-time payments.2

Table 7 compares these CV WTP estimates with the TC consumer surplus estimates using the

2 The new $23 Kriström WTP estimate has a standard error of $1.76 and 95% C.I. of ($20, $26). The new $60 Kriström WTP estimate has a standard error of $6.54 and 95% C.I. of ($47, $73).

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four annual discount rates and the three opportunity costs of time from sections 3.1 and 3.2.3

Consistent with the results from ECD, all twelve comparisons favor annual CV WTP estimates

over one-time CV WTP estimates.

4. Kriström distribution-free estimator and fat tails

In this section, we use our Kriström estimates to address Whitehead’s concern that our CV data

suffers from “fat tails”. The fat tails problem is when there is a long “fat” tail on the right side of

the WTP distribution with a large proportion of the respondents voting “yes” at the highest

included bid (and possibly to ever higher bids as well if they were included). Since the Turnbull

estimator truncates WTP at the highest included bid, the Turnbull estimator will be sensitive to

the researcher’s choice of the highest bid value, especially if the common fat tails problem is

present.

Obviously, the researcher must choose the bid values when designing a CV survey. And

when estimating mean WTP by integrating under the WTP function, it is inevitable that the

highest bids will be the largest contribution. For example, using the Turnbull estimator and

ECD’s CV data with perpetual annual payments, 80% of the mean WTP is from the yes

responses at the highest bid. This is in line with Parsons and Myers’s (2016) review of recent CV

studies, where they find that the highest bids account for between 69% and 91% of mean WTP.

3 One issue with incorporating uncertainty with the Kriström estimator is that WTP function points are decreased nonuniformly depending on the recoding at each bid. Thus, the slope of the last two downward sloping WTP function points can change substantially and the resulting extrapolated choke bid can also change substantially. As Parsons and Myers (2016) and Haab and McConnell (1997) point out, mean WTP estimates can be sensitive to the assumed choke bid. To minimize the influence of the choke bid, we keep the choke bid the same as before recoding. Future research should explore alternative linear extrapolation methods to calculate the choke bid, such as using the average slope from the entire WTP function instead of just the last two downward-sloping points. Using the average slope from the entire function should lead to a more stable choke bid.

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Using the Kriström estimator and ECD’s CV data with perpetual annual payments, 75% of the

mean WTP is from yes responses at the highest bid interval (see Figure 1), with the estimated

choke bid potentially having a large influence on mean WTP.

But the researcher makes choices that are just as consequential when analyzing travel

cost data. Most importantly, the researcher must estimate the opportunity cost of time. This

choice is highly subjective. Awondo, Egan, and Dwyer (2011), for instance, find examples of

travel cost studies estimating the opportunity cost of time at as little as 0% of the average wage

and as much as 100% of the average wage. With ECD’s data, the various CV specifications

change the mean WTP estimates by a maximum of 104%, while changing the TC specification

from 33% wage rate to 75% changes the mean TC consumer surplus estimate by 121%.

Thus, we predict that fat tails will continue to be an issue for CV practitioners the same

way TC practitioners will continue to struggle with the “appropriate value of travel time”

problem, in that both problems will be “stubbornly resistant to satisfying solutions” (McConnell,

2011, page 14).

Further research is warranted regarding the fat tails problem. Our opinion is that

researchers should seriously consider the criticisms Kanninen (1995) discusses about including

bid values in the tails of the WTP distribution. Moreover, since the bid values are presented as a

cost to the respondent, unrealistically high bid costs may undermine a CV survey’s

consequentiality (Russo and Egan, 2016; Rheinberger and Schlapfer, 2015; Schlapfer, 2008;

Carson and Groves, 2007). We recommend that researchers include several reasonable bid

values, as we did in ECD, then use the Turnbull estimator to estimate mean WTP truncated at the

highest bid, and the Kriström estimator to estimate mean WTP truncated at a reasonable linearly

extrapolated choke bid. If a high proportion of respondents still vote yes at the highest reasonable

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bid costs, we have done our jobs in terms of benefit-cost analysis as the environmental public

good is easily proven to be efficient with large positive net benefits.

5. Conclusions

We find little support for Whitehead’s claim that the CV data from ECD lack theoretical validity.

When considering all eight bid values, there is a statistically significant negative correlation

between yes responses and bid values for the one-time and perpetual annual payment

frequencies. The same is true for annual payments in general after combining data from surveys

with perpetual and ten annual payments. Pooling bid values back, as with the Turnbull estimator,

all three survey versions show a statistically significant negative correlation between bid values

and yes responses. ECD’s central result is that annual CV payments outperform one-time

payments for long-lasting environmental improvements. Whitehead counters this by using the

Kriström estimator to show that the CV WTP estimate for the one-time payment survey is

convergent valid with our TC consumer surplus estimate. We show this result is driven by his

choice of discount rate, the opportunity cost of time, and treatment of respondent uncertainty. Of

the 48 permutations presented in this reply, only three directly support Whitehead’s conclusion.

One is ambiguous in that both CV payment formats are convergent valid. The remaining 44

permutations support ECD’s conclusion that annual CV payments outperform one-time

payments.

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References

Awondo, S.N., K.J. Egan, and D.F. Dwyer. 2011. “Increasing Beach Recreation Benefits by Using Wetlands to Reduce Contamination,” Marine Resource Economics, vol. 26:1-15.

Carson, R.T., and T. Groves. 2007. “Incentive and informational properties of preference questions,” Environmental and Resource Economics, vol. 37: 181-210.Egan, K.J., J.R. Corrigan, and D.F. Dwyer. 2015. “Three Reasons to Use Annual Payments in Contingent Valuation Surveys: Convergent Validity, Discount Rates, and Mental Accounting”, Journal of Environmental Economics and Management, vol. 72, 2015, pp. 123-136.

Champ, Patricia A. 1997. “Using Donation Mechanisms to Value Nonuse Benefits from Public Goods,” Journal of Environmental Economics and Management, vol. 33: 151-162.

Egan, K.J., J.R. Corrigan, and D.F. Dwyer. 2015. “Three Reasons to Use Annual Payments in Contingent Valuation Surveys: Convergent Validity, Discount Rates, and Mental Accounting”, Journal of Environmental Economics and Management, vol. 72, 2015, pp. 123-136.

Haab, T.C., and K.E. McConnell. 1997. “Referendum Models and Negative Willingness to Pay: Alternative Solutions”, Journal of Environmental Economics and Management 32, 251-270.

Haab, T.C., and K.E. McConnell. 2002. “Valuing Environmental and Natural Resources, The Econometrics of Non-Market Valuation,” Edward Elgar Publishing, Inc., Massachusetts, USA.

Kanninen, B.J. 1995. “Bias in Discrete Response Contingent Valuation,” Journal of Environmental Economics and Management, vol. 28: 114-125.

Krinsky, I., Robb, A. L., 1986. “An approximation of the statistical properties of elasticities,” Review of Economics and Statistics 68(4):715-719.

Kriström, Bengt, 1990. “A Non-Parametric Approach to the Estimation of Welfare Measures in Discrete Response Valuation Studies,” Land Economics, vol. 66(2): 135-139.

Li, Chuan-Zhong, Leif Mattsson. 1995. “Discrete Choice under Preference Uncertainty: An Improved Structural Model for Contingent Valuation,” Journal of Environmental Economics and Management, vol. 28: 256-269.

McConnell, K.E. 2011. “Joint estimation of stated and revealed welfare measures: the conceptual basis,” in Preference Data for Environmental Valuation, Combining Revealed and Stated Approaches, John Whitehead, Tim Haab and Ju-Chin Huang (editors), Routledge, Taylor & Francis Group, 2011.

Parsons, G.R., and K.H. Myers, 2016. “Fat Tails and Truncated Bids in Contingent Valuation: An Application to An Endangered Shorebird Species,” Ecological Economics, vol. 129: 210-219.

Rheinberger, C.M., and F. Schlapfer, 2015. “It’s the Cost Credibility, Stupid! A Comment on “Consequentiality: A Theoretical and Experimental Exploration of a Single Binary Choice,” working paper, Toulouse School of Economics.

Russo, A.N., and K.J. Egan, 2016. “With the Contingent Valuation Method, using Exogenous Property Tax Rates and a Home-value-linked Payment Vehicle to Estimate the Efficiency of Community Recreation Centers,” working paper.

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Schlapfer, F. 2008. “Contingent valuation: A new perspective,” Ecological Economics, vol. 64: 729-740.

Whitehead, J.C. 2017. “A Comment on “Three Reasons to Use Annual Payments in Contingent Valuation,” Journal of Environmental Economics and Management, forthcoming.

Vaughan, W.J., and D.J. Rodriguez, 2001. “Obtaining Welfare Bounds in Discrete-Response Valuation Studies: Comment,” Land Economics, vol. 77(3): 457-465.

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Table 1. Original bid values and Turnbull monotonically smoothed bid values (in bold).

Perpetual Annual Payments Ten Annual Payments One-time Payment

N= Bid valu

e

%Yes

Turnbull %Yes

N=

Bid valu

e

%Yes

Turnbull %Yes

N=

Bid valu

e

%Yes

Turnbull %Yes

47 $5 0.70 0.70 38 $5 0.63 0.63 43 $20 0.47 0.47 43 $10 0.58 0.58 38 $10 0.63 Pooled 38 $40 0.39 Pooled 37 $15 0.49 0.50 30 $15 0.47 0.53 52 $60 0.54 Pooled 36 $20 0.50 Pooled 43 $20 0.51 Pooled 44 $80 0.43 0.43 37 $25 0.49 Pooled 47 $25 0.55 Pooled 40 $100 0.33 0.32 43 $30 0.53 Pooled 26 $30 0.61 Pooled 43 $120 0.16 0.28 40 $40 0.30 0.36 41 $40 0.46 0.46 42 $160 0.29 Pooled 38 $50 0.42 Pooled 48 $50 0.40 0.40 33 $200 0.42 Pooled

Avg.

0.51 0.53 0.38

14

Table 2. Bid values, original yes-response rates, monotonically smoothed yes-response rates, yes-response rates adjusted for respondent confidence, and monotonically smoothed yes-response rates adjusted for respondent confidence.

Perpetual Annual Payments One-time Payment

N Bid value

Original %Yes

Kristrom %Yes

Recoded %Yes

Kristrom %Yes

N Bid value

Original %Yes

Kristrom %Yes

Recoded %Yes

Kristrom %Yes

47 $5 0.70 0.70 0.57 0.57 43 $20 0.47 0.47 0.30 0.30 43 $10 0.58 0.58 0.47 0.47 38 $40 0.39 0.47 0.18 0.29 37 $15 0.49 0.50 0.32 0.35 52 $60 0.54 0.47 0.37 0.29 36 $20 0.50 0.50 0.33 0.35 44 $80 0.43 0.43 0.23 0.23 37 $25 0.49 0.50 0.35 0.35 40 $100 0.33 0.32 0.23 0.23 43 $30 0.53 0.50 0.40 0.35 43 $120 0.16 0.28 0.09 0.15 40 $40 0.30 0.36 0.28 0.28 42 $160 0.29 0.28 0.07 0.15 38 $50 0.42 0.36 0.26 0.26 33 $200 0.42 0.28 0.33 0.15

Avg. 0.51 0.38 0.38 0.23

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Table 3. Contingent valuation willingness to pay and travel cost consumer surplus estimates.

Contingent valuation- Perpetual annual payments

Contingent valuation- One-time payment

Travel cost- Annual consumer surplus

Turnbull estimator

Kriström estimator

Turnbull estimator

Kriström estimator

$18a

($15, $21)b $30c

($26, $34)d $47e

($38, $57)f $96g

($80, $112)h $19

($14, $24)i

a Assuming a choke bid equal to the highest bid of $40. b From an estimated standard error of $1.46. c From linear extrapolation of the last two smoothed bid points, assuming a choke bid of $74.88. d From an estimated standard error of $1.87. e Assuming a choke bid equal to the highest bid of $120. f From an estimated standard error of $4.87. g From linear extrapolation of the last two smoothed bid points, assuming a choke bid of $323.36. h from an estimated standard error of $7.99. i Estimated using the Krinsky and Robb (1986) technique.

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Table 4. Sensitivity analyses showing which contingent valuation payment frequency produces WTP estimates more consistent with travel cost consumer surplus estimates.

Opportunity cost as

percent of average

wage rate

Annual discount rate

5% 10% 15% 20%

Turn

bull

estim

ator

33% Annuala Annual Annual Annual

50% Annual Annual Annual Annual


Turn

bull

estim

ator

ad

just

ed fo

r co

nfid

ence




Kris

tröm

est

imat

or

33% Annual One-time One-time One-time

50% Annual Annual Annual Ambiguous


Kris

tröm

est

imat

or

adju

sted

for

conf

iden

ce 33% Annual Annual Annual Annual



a A comparison is classified as supporting annual payments if only the annual CV WTP estimate is convergent valid with TC consumer surplus, or if neither CV estimate is convergent valid but the annual CV estimate is closer to TC consumer surplus in absolute terms. A comparison is classified as supporting a one-time payment if only the one-time CV WTP estimate is convergent valid with TC consumer surplus, or if neither CV estimate is convergent valid but the one-time CV estimate is closer to TC consumer surplus in absolute terms. A comparison is classified as ambiguous if both CV estimates are convergent valid with TC consumer surplus.

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Table 5. Travel cost annual and present value consumer surplus estimates using alternative assumptions for the opportunity cost of time. Opportunity cost of time Annual

consumer surplus

95% C.I.a Present value of consumer

surplusb

95% C.I.a

33% of wage rate (baseline)

$19 ($14, $24) $95 ($70, $120)

50% of wage rate $24 ($17, $30) $120 ($85, $150) 75% of wage rate $42 ($28, $54) $210 ($140, $270)

a Estimated using the Krinsky and Robb (1986) technique. b Assuming a 20% annual discount rate.

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Table 6. A comparison of Kriström contingent valuation WTP estimates with travel cost consumer surplus estimates, varying the annual discount rate and the opportunity cost of time.


5% 10% 15% 20%

Con

tinge

nt v

alua

tion

WTP

est

imat

e One-time payment

$91 ($76, $106)

$87 ($73, $101)

$83 ($70, $97)

$80 ($67, $93)

Present value of perpetual

annual payments

$602 ($528, $675)

$301

($264, $338) $201

($176, $225) $150

($132, $169)

Pres

ent v

alue

of t

rave

l cos

t co

nsum

er su

rplu

s est

imat

e Opportunity cost = 33% of

wage rate

$380 ($280, $480)

$190 ($140, $240)

$127 ($93, $160)

$95 ($70, $120)

Opportunity cost = 50% of

wage rate

$480 ($340, $600)

$240 ($170, $300)

$160 ($113, $200)

$120 ($85, $150)


wage rate

$840 ($560, $1080)

$420 ($280, $540)

$280 ($187, 360)

$210 ($140, $270)

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Table 7. A comparison of Kriström contingent valuation WTP estimates adjusted for respondent confidence with travel cost consumer surplus estimates, varying the annual discount rate and the opportunity cost of time.


5% 10% 15% 20%

Con

tinge

nt

valu

atio

n W

TP

estim

ate

One-time payment

$57 ($45, $69)

$54 ($43, $66)

$52 ($41, $63)

$50 ($39, $61)

Present value of perpetual

annual payments

$460 ($391, $528)

$230

($195, $264) $153

($130, $176) $115

($98, $132)

Pres

ent v

alue

of t

rave

l co

st c

onsu

mer

surp

lus

estim

ate


wage rate

$380 ($280, $480)

$190 ($140, $240)

$127 ($93, $160)

$95 ($70, $120)


wage rate

$480 ($340, $600)

$240 ($170, $300)

$160 ($113, $200)

$120 ($85, $150)


wage rate

$840 ($560, $1080)

$420 ($280, $540)

$280 ($187, 360)

$210 ($140, $270)

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Figure 1. Kriström monotonically smoothed WTP function for perpetual annual payments showing the components of the $30 mean WTP estimate.

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