- Email: [email protected]
The value of water supply reliability in California:
Water Policy 3 (2001) 165–174
The value of water supply reliability in California: a contingent valuation study Patricia Kossa,*, M. Sami Khawajab a
Portland State University, Department of Economics, P.O. Box 751, Portland, OR 97207, USA b Quantec Llc, 610 SW Broadway, Suite 505, Portland, OR 97205, USA
Received 14 June 2000; received in revised form 12 February 2001; accepted 18 February 2001
Abstract Water agencies are often faced with the need to estimate the value of water service reliability. Since no explicit market for water supply reliability exists, this study indirectly measures consumers’ valuation of water supply reliability using the contingent valuation method (CVM). Respondents were asked to indicate their willingness to pay in order to avoid the occurrence of water shortages of a given frequency and severity. We employed a ‘‘double bounded’’ dichotomous choice model. The results indicate that customers are willing to pay as much as $16.92/month to avoid a 50% water shortage occurring every 20 years. The goal of such a study is to provide a framework with which water agencies can determine and pursue policies appropriate to the level of reliability desired by customers. The values resulting from the analysis can be assessed in terms of options and the practical bounds of options. # 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction Reliability, along with quality and cost, is an important dimension of urban water policy. Water agencies need to assess the value their customers place on water supply reliability. Tradeoffs need to be made between increased costs and increased reliability. This tradeoff along with the optimal level of water supply reliability are illustrated in Fig. 1. An agency’s reliability goals should be set at that level where the total cost is minimized. Total cost is composed of the
*Corresponding author. Tel.: +1-503-725-3942; fax: +1-503-725-3945. E-mail addresses: [email protected] (P. Koss), [email protected] (M.S. Khawaja). 1366-7017/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 6 - 7 0 1 7 ( 0 1 ) 0 0 0 0 5 - 8
166
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
Fig. 1. Determining the water supply reliability goal.
cost of developing new resources and customer losses that are incurred due to shortages. This paper was intended to provide an assessment of these losses.1 The contingent valuation method (CVM) is one of the standard approaches that is used by market researchers and economists to place a value on goods or services for which no marketbased pricing mechanism exists. For example, CV has been used to evaluate environmental amenities such as clean air or water, or health benefits, such as reduced cancer risks. This method has also been used to estimate the value that customers place on the reliability of service from public utilities.2 Different techniques of asking CV questions, however, provide statistically different estimates of Hicksian surplus (Boyle & Bishop, 1988). Traditionally, the approach used in CV has been to directly ask survey respondents to state their exact maximum willingness to pay (WTP) for the particular non-market good. Such open-ended valuation questions can be unreliable or discourage response, as respondents find it difficult to identify precisely their true point value for access to the non-market good or service. Dichotomous choice approaches have practical advantages over open-ended willingness to pay questions or iterative bidding sequences.3 The 1
This problem has been formalized by Howe and Smith (1994) who identify the optimal level of reliability as that for which the incremental reduction in expected losses from water shortages (i.e., the marginal benefits from increased reliability) should be equated to the marginal costs of achieving that level. A major complication, however, is the estimation of losses over the range of potential shortages. 2 See, for example, Goett, McFadden, and Woo (1988), Doane, Hartman, and Woo (1988), and Howe and Smith (1994). 3 These advantages have been extensively documented elsewhere (Hoehn & Randall, 1987; Boyle & Bishop, 1988; Bowker & Stoll, 1988).
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
167
basic dichotomous choice approach involves asking the consumer only one referendum style question: would (s)he be willing to pay some specific dollar amount for a particular good or service? If the good is valued more highly than the threshold dollar amount, the person answers ‘‘yes’’, otherwise ‘‘no’’. Hanemann, Loomis, and Kanninen (1991) demonstrate that a ‘‘double-bounded’’ dichotomous choice approach, where a follow-up threshold amount is suggested, is asymptotically more efficient than the conventional ‘‘single-bounded’’ approach. In this study, we use a ‘‘double-bounded’’ dichotomous CV survey method to measure the amount that water users in California would be willing to pay for different levels of reliability. Section 2 describes the methodology used to analyze the responses, including the model specification and the statistical approach. Section 3 describes the development of the survey instrument, sampling procedures, survey administration and response rates. Section 4 presents the results of the analysis.
2. The model In the double-bounded dichotomous choice model, respondents are engaged in two rounds of questions. In a WTP experiment, if the response to the initial question ‘‘Are you willing to pay $BID for the program just described?’’ is ‘‘yes’’, the follow-up question uses a higher bid value; alternatively, if the response is no, then the follow-up question uses a lower bid value. As a result, the researcher is able to place each respondent in one of four categories: ‘‘yes/yes’’, ‘‘yes/no’’, ‘‘no/yes’’, and ‘‘no/no’’, all of which correspond to smaller, more informative intervals around each respondent’s WTP amount. The mathematics of the double-bounded model is a straightforward extension of the singlebounded model. The probability of a respondent saying ‘‘yes’’ to the initial bid value offered (BID) is PY i ¼ probðyesÞ ¼ probðWTPi 5BIDÞ
ð1Þ
and the probability of obtaining a ‘‘no’’ response is (1PY i ). An individual’s true WTP is unknown to the researcher and can be treated as a random variable. Hanemann (1989) noted that, where WTP cannot take on negative values, the mean of WTP can be expressed as EðWTPÞ ¼
Z
1
½1 GðbÞdb;
ð2Þ
0
where the cumulative probability density function (CDF) G(b) is Prob{WTP4b}. If the CDF in (2) is assumed to be logistic, then PY i ¼ Gða þ bBIDi Þ ¼
1 ðaþbBIDi þ
1þe
P
di Zi Þ
;
ð3Þ
168
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
where Zi represents a vector of additional explanatory variables. This leads to the standard binary choice log-likelihood function LSB ¼
X i
yi log PY i þ
X
ð1 yi Þlogð1 PY i Þ;
ð4Þ
i
where yi equals 1 if the response is ‘‘yes’’, and 0 otherwise. In the double-bounded logit model, each participant is presented with two sequential bid values and the second bid value is conditional on the first. Following Hanemann et al. (1991), the following response probabilities are obtained for our model: 1 P ¼1 ; PYY i 1 þ eðaþbb BIDU þbr REDUCEþbf FREQþ gi Xi Þ ¼ PNN i PYN ¼ i
1 1 þ eðaþbb BIDL þbr REDUCEþbf FREQþ 1 1 þ eðaþbb BIDU þbr REDUCEþbf FREQþ 1
¼ PNY i
P P
gi Xi Þ
1 1 þ eðaþbb BIDI þbr REDUCEþbf FREQþ
P
gi Xi Þ
;
1
P ; gi Xi Þ 1þe 1þe where REDUCE=the proposed percent reduction in water usage, FREQ=the proposed frequency of water shortages, X=a vector representing respondent’s characteristics (e.g. water consumption, socio-demographic, . . .), BIDI=the initial additional monthly payment, BIDL=the second lower additional monthly payment, BIDU=the second higher additional monthly payment. The double-bounded log-likelihood function is given by X X X X YN YN NY NY IiYY log PYY þ I log P þ I log P þ IiNN log PNN ð5Þ LDB ¼ i i i i i i ; ðaþbb BIDI þbr REDUCEþbf FREQþ
i
P
;
gi Xi Þ
gi Xi Þ
i
ðaþbb BIDU þbr REDUCEþbf FREQþ
i
i 4
IiXX
indicates the response category for each respondent i. where Once the double-bounded logit model has been estimated, the mean WTP may be derived directly from the estimated coefficients as follows: lnð1 þ eaþbr REDUCEþbf FREQþ WTP ¼ bb
P
gi Xi
Þ
:
Our objective is to estimate households’ value of water service reliability. Our approach consists of an analysis of market research data where households are asked to state their preferences among a set of hypothetical water shortage options. The hypothetical options are distinguished by two different attributes of service outage: the ‘‘required percentage reduction in water usage’’, and the ‘‘frequency of the shortage’’. The hypothetical duration of each shortage was fixed at one year. 4
The double-bounded model is premised on the assumption that respondents have the same WTP value in mind when they answer both questions.
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
169
In addition to the size and frequency of water shortages, WTP is likely to be affected by some socio-demographic variables, X. In the double-bounded logit model, each participant is presented with two sequential bid values and the second bid value is conditional on the first. Following Hanemann et al. (1991), WTP is assumed to be dependent on: the proposed percent reduction in water usage, the proposed frequency of water shortages, a vector representing respondent’s characteristics (e.g., water consumption, socio-demographics), the initial additional monthly payment (BIDI), the second lower additional monthly payment (BIDL), and the second higher additional monthly payment (BIDU). Once the double-bounded logit model has been estimated, the mean WTP may be derived directly from the estimated coefficients as follows: P ln 1 þ eaþbr REDUCEþbf FREQþ gi Xi WTP ¼
bb
ð6Þ
The denominator, bb is the coefficient obtained from the double bounded logit model for the bid variable.
3. Data collection: the survey The California urban water agencies (CUWA) contingent valuation survey was a combined mail/telephone survey which asked participants whether they would vote ‘‘yes’’ or ‘‘no’’ in a hypothetical referendum. Participants were told that if a majority voted ‘‘yes’’, their water bills would be increased by a designated amount, and there would be no future water shortages; if a majority voted ‘‘no’’, respondents were told that water bills would remain the same as they otherwise would have been, but water shortages of a specified magnitude and frequency would occur.5 The survey asked each respondent two independent sets of ‘‘double bounded’’ contingent valuation questions. In each of the two sets of questions, respondents were asked to value a water shortage of a given magnitude (ranging from 10% to 50%)6 which occurred with a particular frequency (ranging from once every 3 years to once every 30 years). Magnitudes and frequencies were combined to accomplish two objectives: 1. To cover a wide range of shortage severity; and 2. To present shortage scenarios that would be perceived by respondents as realistic possibilities. Table 1 depicts a 5 5 frequency/shortage grid. Check marks indicate the combinations that were deemed ‘‘reasonable’’ and were included in the surveys. Bid amounts ranged from $1 to $50 per month. Specifically, each respondent was initially asked if they would pay one of $5, $10, $15, or $20 to avoid a given water shortage scenario. If the respondent answered ‘‘yes’’, they were asked if they would be willing to pay a higher amount chosen from among bids of $15, $20, $30, or $50. Alternatively, if the respondent answered ‘‘no’’ 5
In order to avoid responses that were unduly influenced by preferences for or against water resource types, the survey indicated that additional water supplies could come from a variety of unspecified sources. 6 Shortage was indicated from current levels, as such, the results represent the value of relative reliability.
170
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
Table 1 Sample design grid Shortage (% reduction from full service)
Frequency (occurrences/years) 1/30
10 20 30 40 50
p p p p
1/20 p p p p
1/10
1/5
1/3
p p p p
p
p
to the initial bid, they were asked if they would be willing to pay a lower amount chosen from among bids of $1, $3, $5, or $10. A total of 3769 surveys were completed between August 1993 and February 1994, and across ten water districts in California.7 Just prior to conducting the survey, an information package was mailed to potential respondents that contained material explaining the purpose of the survey and assisted in helping customers understand the impacts of various shortage magnitudes.8 Each respondent was asked to value two different shortage/reduction scenarios so that there were approximately 538 responses in each checked cell of Table 1. Finally, in estimating the WTP, researchers have either used a linear or a logarithmic functional form. This refers to how the logit model is estimated. In a linear logit model, the explanatory variables enter the equation in their ‘‘raw’’ original form, while in a logarithmic logit model, explanatory variables are first transformed to their natural logs and then enter the equation. The linear logit is commonly used in the literature (Hanemann, 1984). The linear model also often produces estimates of the mean and median that are considerably closer together than the log model. The linear model assumes symmetry in the distribution of people’s WTP, while the log model assumes the distribution to be more asymmetrical (one long tail). Finally, the linear model corrections for the truncation of the data (no negative WTP values allowed), is very straightforward compared to the log model.
7
These include: Alameda county water district (ACWD), Contra Costa water district (CCWD), Los Angeles department of water and power (LADWP), Municipal water district of Orange county (MWDOC), Orange county water district (OCWD), Metropolitan water district of southern California (MWD), San Diego county water authority (SDCWA), City of San Diego, San Francisco water department (SFWD), and Santa Clara valley water district (SCVWD). 8 For example, respondents were informed that a 10–15% water shortage would require some indoor or outdoor conservation, but probably not both. Indoor conservation might include shorter showers, repair of leaks, and using full loads in dishwashers and clothes washers. Outdoor conservation might include some reduction in watering your lawn or patio and washing your car. At the other extreme, a 40–50% water shortage would require extensive indoor and outdoor mandatory conservation actions with penalties imposed for non-compliance. There would likely be a complete ban on such outdoor uses as car washing and lawn watering.
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
171
In the case of this study, we opted for the linear functional form because we believed that it ‘‘fit’’ the data better.9 The log model produced some unacceptable differences between the mean and the median.
4. Results Table 2 displays the results of the reduced model. The vector of respondents’ characteristics consists of the following variables: AREAYRS=Number of years respondent has lived in the area HHSIZE=Number of persons in the household AGE1834=Respondent’s age is in the range of 18–34 yr old AGE3554=Respondent’s age is in the range of 35–54 yr old INCGT50K=1992 household income is greater than $50,000 SNGL FAM=Respondent lives in a single family residence COLGRAD=Respondent is a college graduate The numerical values of the estimated coefficients are difficult to interpret. These estimates, however, are multiplied with the associated values for REDUCE, FREQ, BID, and the various characteristic values for each observation to obtain the WTP as shown in Eq. (2) above. The estimated coefficients for the variables of primary interest (REDUCE, FREQ and BID) have the expected signs and are highly significant. For example, the coefficient for REDUCE is positive (+2.19) indicating that as REDUCE increases (between 10% and 50% shortage) WTP to pay increases. In other words, as the level of possible shortage increases, so does the WTP to avoid it. The variable FREQ indicates the frequency of occurrence of these shortages. The coefficient is negative (0.01) indicating that as the frequency increases once in 10 yr, 20 yr, etc. (keyed into Eq. (2) as 10, 20, etc), the lower the WTP. However, in absolute terms, REDUCE is a more pronounced variable with a coefficient of 2.19 than FREQ with a coefficient of only –0.01. People are more concerned about level of shortage than they are about the frequency. The coefficient of BID is negative as expected. The higher the bid, the lower the WTP. Table 2 also displays the results of the t-test. The rule of thumb with the t-test is that values higher than +2 or lower than –2 are considered statistically significant. In other words, the observed coefficients are unlikely (less than 5%) to have been observed by chance, or we are 95% confident that these coefficients are not equal to zero (i.e., the variable has no impact on the WTP). Of the variables representing the respondent’s characteristics, only AGE1834, INCGT50 K, SNGL FAM and COLGRAD may be considered significant. With the exception of SNGL FAM, each of these variables enter the estimated function with the expected sign.10 9
We attempted to compute some reasonable range of values for the true WTP by taking the high bid plus a random amount between $1 and $10 for the yy responses, the average of the high and the initial bid for the yn responses, the average of the low and initial bid for the ny responses, and the low bid minus a random value between $1 and $10 with negative values set to zero. This resulted in an average of the ‘‘true WTP’’ that was considerably closer to the estimates obtained with the linear model than with the log model. 10 Since people living in a single family dwelling are more likely to bear the responsibility of outdoor yard care, we expected that they would be more likely to be willing to pay to avoid water shortages than people living in multiple family dwellings.
172
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
Table 2 Double-bounded logit estimation results Explanatory variable
Coefficient
t-Statistic
CONSTANT REDUCE FREQ BID AREAYRS HHSIZE AGE1834 AGE3554 INCGT50K SNGL_FAM COLGRAD
3.24 2.19 0.01 0.12 0.002 0.03 0.18 0.02 0.14 0.10 0.11
16.48 10.82 3.65 62.62 1.43 1.45 2.303 0.32 2.65 1.90 2.25
Statistical goodness of fit tests were applied to test the explanatory power of the model. Traditionally, discrete choice models use McFadden’s R2 and pseudo R2 as measures of ‘‘goodness of fit’’. Both of these measures compare the amount of information gained by constructing the model to the amount of information available without the model (the null case). In a single bounded logit model, the null case is simply that for which respondents are randomly allocated to the two (yes/no) groups. Hence in a single-bounded logit model, R2 measures the model’s predictive power improvement from this random null case. In a double-bounded scenario, the structure is more complex. No easy approach is available for allocating respondents to the four (yy, yn, ny, and nn) groups with the model (i.e., randomly) because the second response is a function of the first, so we cannot allocate observations based on a ‘‘joint’’ response. Kanninen and Khawaja (1995) offer the ‘‘sequential classification procedure’’ as a possible alternative to the standard goodness-of-fit approaches. This measure explicitly takes into account the sequential and conditional nature of the double-bounded model. This procedure sequentially counts the proportion of ‘‘fully, correctly classified cases’’ (FCCC): the correctly classified cases with respect to the first question alone are identified; using this subset, the correctly classified cases for the second question are then counted. Thus, for an observation to be described as ‘‘fully and correctly classified’’, the model must predict its group membership correctly for both bids. Using this method, our model classifies 32% of the observations correctly. Kanninen and Khawaja suggest the ‘‘maximum chance’’ criterion11 as the appropriate rejection criterion. The ‘‘maximum chance’’ is the percentage of correctly classified cases that would result if all observations are placed in the group with the largest proportion of cases. For our survey, most of the 3647 participants (27%) belong to the no/yes response category. Thus, our model outperforms the percentage of correctly classified cases that would have resulted if we had simply classified all respondents as the most frequent case. Table 3 presents the mean WTP for each magnitude and frequency of shortage. WTP figures represent increments to monthly water bills. Blank cells in the table reflect scenarios which were 11
Hair, Anderson, and Tatham (1984, pp. 89–90).
173
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174 Table 3 Mean monthly WTP (additional $/month) Shortage (% reduction from full service) 10 20 30 40 50
Frequency (occurrences/years) 1/30
1/20
$11.71 $13.13 $14.61 $16.15
$12.39 $13.84 $15.35 $16.92
1/10
1/5
1/3
$11.67 $13.08 $14.56 $16.10
$12.00
$12.14
Table 4 Carson and Mitchell (1987) WTP results Shortage scenario
Annual WTP (1987$)
Monthly WTP (1987 $)
Monthly WTP (1993 $)
30–35% once every 5 years 10–15% once every 5 years 30–35% once every 5 years and 10–15% once every 5 years 10–15% twice every 5 years
$114 $83 $258
$9.50 $6.92 $21.50
$12.02 $8.75 $27.20
$152
$12.67
$16.03
not part of the survey. WTP varies from a low of $11.67/month to avoid a 10% shortage once every 10 years, to a high of $16.92/month to avoid a 50% shortage every 20 years. As expected, respondents are willing to pay more for larger shortages and for shortages that occur with higher frequency. However, the response to frequency variations is considerably smaller than the impact of the magnitude of the water shortage (as indicated by the magnitude of the associated coefficients shown in Table 2 above). Thus, it appears that residential customers believe that infrequent large shortages impose higher losses than more frequent small shortages. This type of conclusion may be important to agencies as they plan resource additions and make system operations decisions. To avoid even apparently minor shortage scenarios (e.g., 10% once every 10 years), respondents are willing to pay substantial amounts. This type of ‘‘threshold’’ response is not uncommon in surveys of this type and indicate that respondents regard even a mild shortage scenario as an inconvenience that they want to avoid. Consistent with the approach typically used in the literature to calculate confidence intervals for CV results, we have estimated a range around the WTP associated with the mean shortage frequency and magnitude. Using this approach, the 95% confidence interval is 0.43. In other words, there is a 95% probability that the WTP to avoid this average shortage lies within a
$0.43 range of the estimated WTP. While there are few previous comparable studies, these results do appear to be consistent with a 1987 contingent valuation survey conducted in southern California and the Bay area by Carson and Mitchell.12 While the results are not directly comparable because of differing survey and 12
QED Research Inc., ‘‘Economic value of reliable water supplies for residential water users in the state water project service area’’. 9 June 1987.
174
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
analytical approaches and different shortage scenario definitions, their similarity is striking. The Carson–Mitchell results are presented in Table 4. References Bowker, J. M., & Stoll, J. M. (1988). Dichotomous choice in resource valuation. American Journal of Agricultural Economics, 70, 372–382. Boyle, K. J., & Bishop, R. C. (1988). Welfare measurements using contingent valuation: A comparison of techniques. American Journal of Agricultural Economics, 70, 20–28. Carson, R.T., & R. Mitchell (1987). Economic value of reliable water supplies for residential water users in state water project service area. Report to Metropolitan Water District, Los Angeles. Doane, M. J., Hartman, R. S., & Woo, C.-K. (1988). Households’ perceived value of service reliability: An analysis of contingent valuation data. The Energy Journal, 9, 135–149. Goett, A. A., McFadden, D. L., & Woo, C.-K. (1988). Estimating household value of electrical service reliability with market research data. The Energy Journal, 9, 105–120. Hair, J. F., Anderson, R. E., & Tatham, R. L. (1984). Multivariate data analysis. New York: MacMillan. Hanemann, M. (1984). Welfare evaluations in contingent valuation experiments with discrete responses. American Journal of Agricultural Economics, 66, 332–341. Hanemann, M. (1989). Welfare evaluations in contingent valuation experiments with discrete responses: Reply. American Journal of Agricultural Economics, 71, 1057–1061. Hanemann, M., Loomis, J., & Kanninen, B. (1991). Statistical efficiency of double-bounded dichotomous choice contingent valuation. American Journal of Agricultural Economics, 73, 1255–1263. Hoehn, J. P., & Randall, A. (1987). A satisfactory benefit cost indicator from contingent valuation. Journal of Environmental Economics and Management, 14, 226–247. Howe, C. W., & Smith, M. G. (1994). The value of water supply reliability in urban water systems. Journal of Environmental Economics and Management, 26, 19–30. Kanninen, B. J., & Khawaja, M. S. (1995). Measuring goodness of fit for the double-bounded logit model. American Journal of Agricultural Economics, 77, 885–890.
The value of water supply reliability in California: a contingent valuation study Patricia Kossa,*, M. Sami Khawajab a
Portland State University, Department of Economics, P.O. Box 751, Portland, OR 97207, USA b Quantec Llc, 610 SW Broadway, Suite 505, Portland, OR 97205, USA
Received 14 June 2000; received in revised form 12 February 2001; accepted 18 February 2001
Abstract Water agencies are often faced with the need to estimate the value of water service reliability. Since no explicit market for water supply reliability exists, this study indirectly measures consumers’ valuation of water supply reliability using the contingent valuation method (CVM). Respondents were asked to indicate their willingness to pay in order to avoid the occurrence of water shortages of a given frequency and severity. We employed a ‘‘double bounded’’ dichotomous choice model. The results indicate that customers are willing to pay as much as $16.92/month to avoid a 50% water shortage occurring every 20 years. The goal of such a study is to provide a framework with which water agencies can determine and pursue policies appropriate to the level of reliability desired by customers. The values resulting from the analysis can be assessed in terms of options and the practical bounds of options. # 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction Reliability, along with quality and cost, is an important dimension of urban water policy. Water agencies need to assess the value their customers place on water supply reliability. Tradeoffs need to be made between increased costs and increased reliability. This tradeoff along with the optimal level of water supply reliability are illustrated in Fig. 1. An agency’s reliability goals should be set at that level where the total cost is minimized. Total cost is composed of the
*Corresponding author. Tel.: +1-503-725-3942; fax: +1-503-725-3945. E-mail addresses: [email protected] (P. Koss), [email protected] (M.S. Khawaja). 1366-7017/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 6 - 7 0 1 7 ( 0 1 ) 0 0 0 0 5 - 8
166
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
Fig. 1. Determining the water supply reliability goal.
cost of developing new resources and customer losses that are incurred due to shortages. This paper was intended to provide an assessment of these losses.1 The contingent valuation method (CVM) is one of the standard approaches that is used by market researchers and economists to place a value on goods or services for which no marketbased pricing mechanism exists. For example, CV has been used to evaluate environmental amenities such as clean air or water, or health benefits, such as reduced cancer risks. This method has also been used to estimate the value that customers place on the reliability of service from public utilities.2 Different techniques of asking CV questions, however, provide statistically different estimates of Hicksian surplus (Boyle & Bishop, 1988). Traditionally, the approach used in CV has been to directly ask survey respondents to state their exact maximum willingness to pay (WTP) for the particular non-market good. Such open-ended valuation questions can be unreliable or discourage response, as respondents find it difficult to identify precisely their true point value for access to the non-market good or service. Dichotomous choice approaches have practical advantages over open-ended willingness to pay questions or iterative bidding sequences.3 The 1
This problem has been formalized by Howe and Smith (1994) who identify the optimal level of reliability as that for which the incremental reduction in expected losses from water shortages (i.e., the marginal benefits from increased reliability) should be equated to the marginal costs of achieving that level. A major complication, however, is the estimation of losses over the range of potential shortages. 2 See, for example, Goett, McFadden, and Woo (1988), Doane, Hartman, and Woo (1988), and Howe and Smith (1994). 3 These advantages have been extensively documented elsewhere (Hoehn & Randall, 1987; Boyle & Bishop, 1988; Bowker & Stoll, 1988).
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
167
basic dichotomous choice approach involves asking the consumer only one referendum style question: would (s)he be willing to pay some specific dollar amount for a particular good or service? If the good is valued more highly than the threshold dollar amount, the person answers ‘‘yes’’, otherwise ‘‘no’’. Hanemann, Loomis, and Kanninen (1991) demonstrate that a ‘‘double-bounded’’ dichotomous choice approach, where a follow-up threshold amount is suggested, is asymptotically more efficient than the conventional ‘‘single-bounded’’ approach. In this study, we use a ‘‘double-bounded’’ dichotomous CV survey method to measure the amount that water users in California would be willing to pay for different levels of reliability. Section 2 describes the methodology used to analyze the responses, including the model specification and the statistical approach. Section 3 describes the development of the survey instrument, sampling procedures, survey administration and response rates. Section 4 presents the results of the analysis.
2. The model In the double-bounded dichotomous choice model, respondents are engaged in two rounds of questions. In a WTP experiment, if the response to the initial question ‘‘Are you willing to pay $BID for the program just described?’’ is ‘‘yes’’, the follow-up question uses a higher bid value; alternatively, if the response is no, then the follow-up question uses a lower bid value. As a result, the researcher is able to place each respondent in one of four categories: ‘‘yes/yes’’, ‘‘yes/no’’, ‘‘no/yes’’, and ‘‘no/no’’, all of which correspond to smaller, more informative intervals around each respondent’s WTP amount. The mathematics of the double-bounded model is a straightforward extension of the singlebounded model. The probability of a respondent saying ‘‘yes’’ to the initial bid value offered (BID) is PY i ¼ probðyesÞ ¼ probðWTPi 5BIDÞ
ð1Þ
and the probability of obtaining a ‘‘no’’ response is (1PY i ). An individual’s true WTP is unknown to the researcher and can be treated as a random variable. Hanemann (1989) noted that, where WTP cannot take on negative values, the mean of WTP can be expressed as EðWTPÞ ¼
Z
1
½1 GðbÞdb;
ð2Þ
0
where the cumulative probability density function (CDF) G(b) is Prob{WTP4b}. If the CDF in (2) is assumed to be logistic, then PY i ¼ Gða þ bBIDi Þ ¼
1 ðaþbBIDi þ
1þe
P
di Zi Þ
;
ð3Þ
168
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
where Zi represents a vector of additional explanatory variables. This leads to the standard binary choice log-likelihood function LSB ¼
X i
yi log PY i þ
X
ð1 yi Þlogð1 PY i Þ;
ð4Þ
i
where yi equals 1 if the response is ‘‘yes’’, and 0 otherwise. In the double-bounded logit model, each participant is presented with two sequential bid values and the second bid value is conditional on the first. Following Hanemann et al. (1991), the following response probabilities are obtained for our model: 1 P ¼1 ; PYY i 1 þ eðaþbb BIDU þbr REDUCEþbf FREQþ gi Xi Þ ¼ PNN i PYN ¼ i
1 1 þ eðaþbb BIDL þbr REDUCEþbf FREQþ 1 1 þ eðaþbb BIDU þbr REDUCEþbf FREQþ 1
¼ PNY i
P P
gi Xi Þ
1 1 þ eðaþbb BIDI þbr REDUCEþbf FREQþ
P
gi Xi Þ
;
1
P ; gi Xi Þ 1þe 1þe where REDUCE=the proposed percent reduction in water usage, FREQ=the proposed frequency of water shortages, X=a vector representing respondent’s characteristics (e.g. water consumption, socio-demographic, . . .), BIDI=the initial additional monthly payment, BIDL=the second lower additional monthly payment, BIDU=the second higher additional monthly payment. The double-bounded log-likelihood function is given by X X X X YN YN NY NY IiYY log PYY þ I log P þ I log P þ IiNN log PNN ð5Þ LDB ¼ i i i i i i ; ðaþbb BIDI þbr REDUCEþbf FREQþ
i
P
;
gi Xi Þ
gi Xi Þ
i
ðaþbb BIDU þbr REDUCEþbf FREQþ
i
i 4
IiXX
indicates the response category for each respondent i. where Once the double-bounded logit model has been estimated, the mean WTP may be derived directly from the estimated coefficients as follows: lnð1 þ eaþbr REDUCEþbf FREQþ WTP ¼ bb
P
gi Xi
Þ
:
Our objective is to estimate households’ value of water service reliability. Our approach consists of an analysis of market research data where households are asked to state their preferences among a set of hypothetical water shortage options. The hypothetical options are distinguished by two different attributes of service outage: the ‘‘required percentage reduction in water usage’’, and the ‘‘frequency of the shortage’’. The hypothetical duration of each shortage was fixed at one year. 4
The double-bounded model is premised on the assumption that respondents have the same WTP value in mind when they answer both questions.
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
169
In addition to the size and frequency of water shortages, WTP is likely to be affected by some socio-demographic variables, X. In the double-bounded logit model, each participant is presented with two sequential bid values and the second bid value is conditional on the first. Following Hanemann et al. (1991), WTP is assumed to be dependent on: the proposed percent reduction in water usage, the proposed frequency of water shortages, a vector representing respondent’s characteristics (e.g., water consumption, socio-demographics), the initial additional monthly payment (BIDI), the second lower additional monthly payment (BIDL), and the second higher additional monthly payment (BIDU). Once the double-bounded logit model has been estimated, the mean WTP may be derived directly from the estimated coefficients as follows: P ln 1 þ eaþbr REDUCEþbf FREQþ gi Xi WTP ¼
bb
ð6Þ
The denominator, bb is the coefficient obtained from the double bounded logit model for the bid variable.
3. Data collection: the survey The California urban water agencies (CUWA) contingent valuation survey was a combined mail/telephone survey which asked participants whether they would vote ‘‘yes’’ or ‘‘no’’ in a hypothetical referendum. Participants were told that if a majority voted ‘‘yes’’, their water bills would be increased by a designated amount, and there would be no future water shortages; if a majority voted ‘‘no’’, respondents were told that water bills would remain the same as they otherwise would have been, but water shortages of a specified magnitude and frequency would occur.5 The survey asked each respondent two independent sets of ‘‘double bounded’’ contingent valuation questions. In each of the two sets of questions, respondents were asked to value a water shortage of a given magnitude (ranging from 10% to 50%)6 which occurred with a particular frequency (ranging from once every 3 years to once every 30 years). Magnitudes and frequencies were combined to accomplish two objectives: 1. To cover a wide range of shortage severity; and 2. To present shortage scenarios that would be perceived by respondents as realistic possibilities. Table 1 depicts a 5 5 frequency/shortage grid. Check marks indicate the combinations that were deemed ‘‘reasonable’’ and were included in the surveys. Bid amounts ranged from $1 to $50 per month. Specifically, each respondent was initially asked if they would pay one of $5, $10, $15, or $20 to avoid a given water shortage scenario. If the respondent answered ‘‘yes’’, they were asked if they would be willing to pay a higher amount chosen from among bids of $15, $20, $30, or $50. Alternatively, if the respondent answered ‘‘no’’ 5
In order to avoid responses that were unduly influenced by preferences for or against water resource types, the survey indicated that additional water supplies could come from a variety of unspecified sources. 6 Shortage was indicated from current levels, as such, the results represent the value of relative reliability.
170
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
Table 1 Sample design grid Shortage (% reduction from full service)
Frequency (occurrences/years) 1/30
10 20 30 40 50
p p p p
1/20 p p p p
1/10
1/5
1/3
p p p p
p
p
to the initial bid, they were asked if they would be willing to pay a lower amount chosen from among bids of $1, $3, $5, or $10. A total of 3769 surveys were completed between August 1993 and February 1994, and across ten water districts in California.7 Just prior to conducting the survey, an information package was mailed to potential respondents that contained material explaining the purpose of the survey and assisted in helping customers understand the impacts of various shortage magnitudes.8 Each respondent was asked to value two different shortage/reduction scenarios so that there were approximately 538 responses in each checked cell of Table 1. Finally, in estimating the WTP, researchers have either used a linear or a logarithmic functional form. This refers to how the logit model is estimated. In a linear logit model, the explanatory variables enter the equation in their ‘‘raw’’ original form, while in a logarithmic logit model, explanatory variables are first transformed to their natural logs and then enter the equation. The linear logit is commonly used in the literature (Hanemann, 1984). The linear model also often produces estimates of the mean and median that are considerably closer together than the log model. The linear model assumes symmetry in the distribution of people’s WTP, while the log model assumes the distribution to be more asymmetrical (one long tail). Finally, the linear model corrections for the truncation of the data (no negative WTP values allowed), is very straightforward compared to the log model.
7
These include: Alameda county water district (ACWD), Contra Costa water district (CCWD), Los Angeles department of water and power (LADWP), Municipal water district of Orange county (MWDOC), Orange county water district (OCWD), Metropolitan water district of southern California (MWD), San Diego county water authority (SDCWA), City of San Diego, San Francisco water department (SFWD), and Santa Clara valley water district (SCVWD). 8 For example, respondents were informed that a 10–15% water shortage would require some indoor or outdoor conservation, but probably not both. Indoor conservation might include shorter showers, repair of leaks, and using full loads in dishwashers and clothes washers. Outdoor conservation might include some reduction in watering your lawn or patio and washing your car. At the other extreme, a 40–50% water shortage would require extensive indoor and outdoor mandatory conservation actions with penalties imposed for non-compliance. There would likely be a complete ban on such outdoor uses as car washing and lawn watering.
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
171
In the case of this study, we opted for the linear functional form because we believed that it ‘‘fit’’ the data better.9 The log model produced some unacceptable differences between the mean and the median.
4. Results Table 2 displays the results of the reduced model. The vector of respondents’ characteristics consists of the following variables: AREAYRS=Number of years respondent has lived in the area HHSIZE=Number of persons in the household AGE1834=Respondent’s age is in the range of 18–34 yr old AGE3554=Respondent’s age is in the range of 35–54 yr old INCGT50K=1992 household income is greater than $50,000 SNGL FAM=Respondent lives in a single family residence COLGRAD=Respondent is a college graduate The numerical values of the estimated coefficients are difficult to interpret. These estimates, however, are multiplied with the associated values for REDUCE, FREQ, BID, and the various characteristic values for each observation to obtain the WTP as shown in Eq. (2) above. The estimated coefficients for the variables of primary interest (REDUCE, FREQ and BID) have the expected signs and are highly significant. For example, the coefficient for REDUCE is positive (+2.19) indicating that as REDUCE increases (between 10% and 50% shortage) WTP to pay increases. In other words, as the level of possible shortage increases, so does the WTP to avoid it. The variable FREQ indicates the frequency of occurrence of these shortages. The coefficient is negative (0.01) indicating that as the frequency increases once in 10 yr, 20 yr, etc. (keyed into Eq. (2) as 10, 20, etc), the lower the WTP. However, in absolute terms, REDUCE is a more pronounced variable with a coefficient of 2.19 than FREQ with a coefficient of only –0.01. People are more concerned about level of shortage than they are about the frequency. The coefficient of BID is negative as expected. The higher the bid, the lower the WTP. Table 2 also displays the results of the t-test. The rule of thumb with the t-test is that values higher than +2 or lower than –2 are considered statistically significant. In other words, the observed coefficients are unlikely (less than 5%) to have been observed by chance, or we are 95% confident that these coefficients are not equal to zero (i.e., the variable has no impact on the WTP). Of the variables representing the respondent’s characteristics, only AGE1834, INCGT50 K, SNGL FAM and COLGRAD may be considered significant. With the exception of SNGL FAM, each of these variables enter the estimated function with the expected sign.10 9
We attempted to compute some reasonable range of values for the true WTP by taking the high bid plus a random amount between $1 and $10 for the yy responses, the average of the high and the initial bid for the yn responses, the average of the low and initial bid for the ny responses, and the low bid minus a random value between $1 and $10 with negative values set to zero. This resulted in an average of the ‘‘true WTP’’ that was considerably closer to the estimates obtained with the linear model than with the log model. 10 Since people living in a single family dwelling are more likely to bear the responsibility of outdoor yard care, we expected that they would be more likely to be willing to pay to avoid water shortages than people living in multiple family dwellings.
172
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
Table 2 Double-bounded logit estimation results Explanatory variable
Coefficient
t-Statistic
CONSTANT REDUCE FREQ BID AREAYRS HHSIZE AGE1834 AGE3554 INCGT50K SNGL_FAM COLGRAD
3.24 2.19 0.01 0.12 0.002 0.03 0.18 0.02 0.14 0.10 0.11
16.48 10.82 3.65 62.62 1.43 1.45 2.303 0.32 2.65 1.90 2.25
Statistical goodness of fit tests were applied to test the explanatory power of the model. Traditionally, discrete choice models use McFadden’s R2 and pseudo R2 as measures of ‘‘goodness of fit’’. Both of these measures compare the amount of information gained by constructing the model to the amount of information available without the model (the null case). In a single bounded logit model, the null case is simply that for which respondents are randomly allocated to the two (yes/no) groups. Hence in a single-bounded logit model, R2 measures the model’s predictive power improvement from this random null case. In a double-bounded scenario, the structure is more complex. No easy approach is available for allocating respondents to the four (yy, yn, ny, and nn) groups with the model (i.e., randomly) because the second response is a function of the first, so we cannot allocate observations based on a ‘‘joint’’ response. Kanninen and Khawaja (1995) offer the ‘‘sequential classification procedure’’ as a possible alternative to the standard goodness-of-fit approaches. This measure explicitly takes into account the sequential and conditional nature of the double-bounded model. This procedure sequentially counts the proportion of ‘‘fully, correctly classified cases’’ (FCCC): the correctly classified cases with respect to the first question alone are identified; using this subset, the correctly classified cases for the second question are then counted. Thus, for an observation to be described as ‘‘fully and correctly classified’’, the model must predict its group membership correctly for both bids. Using this method, our model classifies 32% of the observations correctly. Kanninen and Khawaja suggest the ‘‘maximum chance’’ criterion11 as the appropriate rejection criterion. The ‘‘maximum chance’’ is the percentage of correctly classified cases that would result if all observations are placed in the group with the largest proportion of cases. For our survey, most of the 3647 participants (27%) belong to the no/yes response category. Thus, our model outperforms the percentage of correctly classified cases that would have resulted if we had simply classified all respondents as the most frequent case. Table 3 presents the mean WTP for each magnitude and frequency of shortage. WTP figures represent increments to monthly water bills. Blank cells in the table reflect scenarios which were 11
Hair, Anderson, and Tatham (1984, pp. 89–90).
173
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174 Table 3 Mean monthly WTP (additional $/month) Shortage (% reduction from full service) 10 20 30 40 50
Frequency (occurrences/years) 1/30
1/20
$11.71 $13.13 $14.61 $16.15
$12.39 $13.84 $15.35 $16.92
1/10
1/5
1/3
$11.67 $13.08 $14.56 $16.10
$12.00
$12.14
Table 4 Carson and Mitchell (1987) WTP results Shortage scenario
Annual WTP (1987$)
Monthly WTP (1987 $)
Monthly WTP (1993 $)
30–35% once every 5 years 10–15% once every 5 years 30–35% once every 5 years and 10–15% once every 5 years 10–15% twice every 5 years
$114 $83 $258
$9.50 $6.92 $21.50
$12.02 $8.75 $27.20
$152
$12.67
$16.03
not part of the survey. WTP varies from a low of $11.67/month to avoid a 10% shortage once every 10 years, to a high of $16.92/month to avoid a 50% shortage every 20 years. As expected, respondents are willing to pay more for larger shortages and for shortages that occur with higher frequency. However, the response to frequency variations is considerably smaller than the impact of the magnitude of the water shortage (as indicated by the magnitude of the associated coefficients shown in Table 2 above). Thus, it appears that residential customers believe that infrequent large shortages impose higher losses than more frequent small shortages. This type of conclusion may be important to agencies as they plan resource additions and make system operations decisions. To avoid even apparently minor shortage scenarios (e.g., 10% once every 10 years), respondents are willing to pay substantial amounts. This type of ‘‘threshold’’ response is not uncommon in surveys of this type and indicate that respondents regard even a mild shortage scenario as an inconvenience that they want to avoid. Consistent with the approach typically used in the literature to calculate confidence intervals for CV results, we have estimated a range around the WTP associated with the mean shortage frequency and magnitude. Using this approach, the 95% confidence interval is 0.43. In other words, there is a 95% probability that the WTP to avoid this average shortage lies within a
$0.43 range of the estimated WTP. While there are few previous comparable studies, these results do appear to be consistent with a 1987 contingent valuation survey conducted in southern California and the Bay area by Carson and Mitchell.12 While the results are not directly comparable because of differing survey and 12
QED Research Inc., ‘‘Economic value of reliable water supplies for residential water users in the state water project service area’’. 9 June 1987.
174
P. Koss, M.S. Khawaja / Water Policy 3 (2001) 165–174
analytical approaches and different shortage scenario definitions, their similarity is striking. The Carson–Mitchell results are presented in Table 4. References Bowker, J. M., & Stoll, J. M. (1988). Dichotomous choice in resource valuation. American Journal of Agricultural Economics, 70, 372–382. Boyle, K. J., & Bishop, R. C. (1988). Welfare measurements using contingent valuation: A comparison of techniques. American Journal of Agricultural Economics, 70, 20–28. Carson, R.T., & R. Mitchell (1987). Economic value of reliable water supplies for residential water users in state water project service area. Report to Metropolitan Water District, Los Angeles. Doane, M. J., Hartman, R. S., & Woo, C.-K. (1988). Households’ perceived value of service reliability: An analysis of contingent valuation data. The Energy Journal, 9, 135–149. Goett, A. A., McFadden, D. L., & Woo, C.-K. (1988). Estimating household value of electrical service reliability with market research data. The Energy Journal, 9, 105–120. Hair, J. F., Anderson, R. E., & Tatham, R. L. (1984). Multivariate data analysis. New York: MacMillan. Hanemann, M. (1984). Welfare evaluations in contingent valuation experiments with discrete responses. American Journal of Agricultural Economics, 66, 332–341. Hanemann, M. (1989). Welfare evaluations in contingent valuation experiments with discrete responses: Reply. American Journal of Agricultural Economics, 71, 1057–1061. Hanemann, M., Loomis, J., & Kanninen, B. (1991). Statistical efficiency of double-bounded dichotomous choice contingent valuation. American Journal of Agricultural Economics, 73, 1255–1263. Hoehn, J. P., & Randall, A. (1987). A satisfactory benefit cost indicator from contingent valuation. Journal of Environmental Economics and Management, 14, 226–247. Howe, C. W., & Smith, M. G. (1994). The value of water supply reliability in urban water systems. Journal of Environmental Economics and Management, 26, 19–30. Kanninen, B. J., & Khawaja, M. S. (1995). Measuring goodness of fit for the double-bounded logit model. American Journal of Agricultural Economics, 77, 885–890.