Reply to A comment on Three reasons to use annual payments in contingent valuation. April 2017

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1 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 ) 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 Phone: (419) , Fax: (419) , kevin.egan@utoledo.edu.

2 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 onetime 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- 1

3 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 2

4 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 (c 2 (8) = 38.2). For the survey with perpetual annual payments, we reject the null hypothesis of equal proportions at the 5% level (c 2 (8) = 16.8). For the survey with ten annual payments, we cannot reject the null hypothesis of equal proportions at conventional significance levels (c 2 (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 (c 2 (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 3

5 payments (c 2 (4) = 15.3) and one-time payments (c 2 (4) = 29.9), and at the 10% level for ten annual payments (c 2 (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 1 Table 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 ( 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. 4

6 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 = 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. 5

7 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 6

8 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 onetime 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). 7

9 four annual discount rates and the three opportunity costs of time from sections 3.1 and 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. 8

10 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 9

11 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. 10

12 References Awondo, S.N., K.J. Egan, and D.F. Dwyer Increasing Beach Recreation Benefits by Using Wetlands to Reduce Contamination, Marine Resource Economics, vol. 26:1-15. Carson, R.T., and T. Groves Incentive and informational properties of preference questions, Environmental and Resource Economics, vol. 37: Egan, K.J., J.R. Corrigan, and D.F. Dwyer 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 Champ, Patricia A Using Donation Mechanisms to Value Nonuse Benefits from Public Goods, Journal of Environmental Economics and Management, vol. 33: Egan, K.J., J.R. Corrigan, and D.F. Dwyer 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 Haab, T.C., and K.E. McConnell Referendum Models and Negative Willingness to Pay: Alternative Solutions, Journal of Environmental Economics and Management 32, Haab, T.C., and K.E. McConnell Valuing Environmental and Natural Resources, The Econometrics of Non-Market Valuation, Edward Elgar Publishing, Inc., Massachusetts, USA. Kanninen, B.J Bias in Discrete Response Contingent Valuation, Journal of Environmental Economics and Management, vol. 28: Krinsky, I., Robb, A. L., An approximation of the statistical properties of elasticities, Review of Economics and Statistics 68(4): Kriström, Bengt, A Non-Parametric Approach to the Estimation of Welfare Measures in Discrete Response Valuation Studies, Land Economics, vol. 66(2): Li, Chuan-Zhong, Leif Mattsson Discrete Choice under Preference Uncertainty: An Improved Structural Model for Contingent Valuation, Journal of Environmental Economics and Management, vol. 28: McConnell, K.E 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, Parsons, G.R., and K.H. Myers, Fat Tails and Truncated Bids in Contingent Valuation: An Application to An Endangered Shorebird Species, Ecological Economics, vol. 129: Rheinberger, C.M., and F. Schlapfer, 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, 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. 11

13 Schlapfer, F Contingent valuation: A new perspective, Ecological Economics, vol. 64: Whitehead, J.C 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, Obtaining Welfare Bounds in Discrete-Response Valuation Studies: Comment, Land Economics, vol. 77(3):

14 Table 1. Original bid values and Turnbull monotonically smoothed bid values (in bold). Perpetual Annual Payments Ten Annual Payments One-time Payment Bid Bid Bid %Ye Turnbul N %Ye Turnbul N %Ye valu valu valu s l %Yes = s l %Yes = s e e e N= Turnbul l %Yes 47 $ $ $ $ $ Pooled 38 $ Pooled 37 $ $ $ Pooled 36 $ Pooled 43 $ Pooled 44 $ $ Pooled 47 $ Pooled 40 $ $ Pooled 26 $ Pooled 43 $ $ $ $ Pooled 38 $ Pooled 48 $ $ Pooled Avg

15 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 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ Avg

16 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 $18 a ($15, $21) b $30 c ($26, $34) d $47 e ($38, $57) f $96 g ($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 $ 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 $ h from an estimated standard error of $7.99. i Estimated using the Krinsky and Robb (1986) technique. 15

17 Table 4. Sensitivity analyses showing which contingent valuation payment frequency produces WTP estimates more consistent with travel cost consumer surplus estimates. Opportunit y cost as percent of average wage rate Annual discount rate 5% 10% 15% 20% Turnbull estimator 33% Annual a Annual Annual Annual 50% Annual Annual Annual Annual 75% Annual Annual Annual Annual Turnbull estimator adjusted for confidence 33% Annual Annual Annual Annual 50% Annual Annual Annual Annual 75% Annual Annual Annual Annual Kriström estimator 33% Annual One-time One-time One-time 50% Annual Annual Annual Ambiguous 75% Annual Annual Annual Annual Kriström estimator adjusted for confidence 33% Annual Annual Annual Annual 50% Annual Annual Annual Annual 75% 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 onetime 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. 16

18 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 surplus b 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. 17

19 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. Annual discount rate 5% 10% 15% 20% Contingent valuation WTP estimate Present value of travel cost consumer surplus estimate One-time payment Present value of perpetual annual payments Opportunity cost = 33% of wage rate Opportunity cost = 50% of wage rate Opportunity cost = 75% of wage rate $91 ($76, $106) $602 ($528, $675) $380 ($280, $480) $480 ($340, $600) $840 ($560, $1080) $87 ($73, $101) $301 ($264, $338) $190 ($140, $240) $240 ($170, $300) $420 ($280, $540) $83 ($70, $97) $201 ($176, $225) $127 ($93, $160) $160 ($113, $200) $280 ($187, 360) $80 ($67, $93) $150 ($132, $169) $95 ($70, $120) $120 ($85, $150) $210 ($140, $270) 18

20 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. Annual discount rate 5% 10% 15% 20% Contingent valuation WTP estimate Present value of travel cost consumer surplus estimate One-time payment Present value of perpetual annual payments Opportunity cost = 33% of wage rate Opportunity cost = 50% of wage rate Opportunity cost = 75% of wage rate $57 ($45, $69) $460 ($391, $528) $380 ($280, $480) $480 ($340, $600) $840 ($560, $1080) $54 ($43, $66) $230 ($195, $264) $190 ($140, $240) $240 ($170, $300) $420 ($280, $540) $52 ($41, $63) $153 ($130, $176) $127 ($93, $160) $160 ($113, $200) $280 ($187, 360) $50 ($39, $61) $115 ($98, $132) $95 ($70, $120) $120 ($85, $150) $210 ($140, $270) 19

21 Figure 1. Kriström monotonically smoothed WTP function for perpetual annual payments showing the components of the $30 mean WTP estimate. 20