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Improving Willingness to Pay Estimates for Water Quality Improvements through Joint Estimation with Water Quality Perceptions1

John C. Whitehead2 Associate Professor Department of Economics and Finance Cameron School of Business University of North Carolina at Wilmington 601 South College Road Wilmington, NC 28403-5945

April 23, 2003

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The author thanks Tom Hoban and Bill Clifford for use of the data, George Van

Houtven and Subhrendu Pattanayak for comments, and Jeff DeSimone for comments and econometric guidance. Support of this research was provided by the U.S. Environmental Protection Agency through Cooperative Agreement CR824861-01-0.

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e-mail: [email protected]; phone: (910)962-7497; fax: (910)962-7464. 1

Improving Willingness to Pay Estimates for Water Quality Improvements through Joint Estimation with Water Quality Perceptions Abstract

In this paper we argue that contingent valuation studies should include measures of quality perceptions as covariates in the willingness to pay model in order to avoid omitted variable bias. Quality perceptions that vary across respondents are endogenous variables. We address endogeneity bias using an instrumental variable approach in which a measure of quality perceptions is included as a determinant of willingness to pay and is simultaneously determined by various exogenous factors. The willingness to pay and quality perception equations are estimated jointly to allow for correlation of the error terms. We reject exogeneity of perceived quality and quality is a determinant of willingness to pay.

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Introduction

The theoretical construction of willingness to pay for quality improvement shows that willingness to pay is a function of pre-policy and post-policy quality levels, among other variables (Whitehead, 1995). Contingent valuation method (CVM) surveys should carefully describe both quality levels and ask for respondent willingness to pay for the change in quality (Mitchell and Carson, 1989). A crucial assumption is that respondents are valuing the objective quality improvement that the survey asks them to value. This assumption may not hold in many applications, especially those in which one or both quality levels are not explicitly described and heterogeneous respondents have varying levels of prior information about the quality change.

For example, Carson and Mitchell (1993) describe baseline national water quality as "not boatable" and improved water quality as "boatable, fishable, and swimmable." In contrast, the CVM application presented here asks respondents to value a water quality improvement from the current, degraded quality level that is not explicitly described to a quality level that is boatable, fishable, and swimmable. In both cases, but especially when quality is not explicitly described, heterogeneous respondents will have varying subjective perceptions about the quality level. In the current application, some might consider current quality to be too poor for boating, fishing, and swimming. Other respondents might consider current quality to be boatable and fishable but not swimmable. The willingness to pay question will elicit willingness to pay values that vary based on the differences in quality perceptions. The variation in willingness to pay will not be accounted for by the researcher who ignores the differences in quality perceptions,

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adding to the error of the willingness to pay estimates.

Survey respondents bring their own knowledge of quality and other notions to the CVM valuation exercise. Blomquist and Whitehead (1998) and Hoehn and Randall (2002) argue that respondents who are unfamiliar with the change in quality will provide willingness to pay statements that are less valid than familiar respondents. Information provision in the survey instrument can lead to improvements in the validity of willingness to pay as subjective quality converges with objective quality. Information that causes respondents to perceive a larger change in quality will increase willingness to pay. Information that causes respondents to perceive a smaller change in quality will decrease willingness to pay. Empirical results in both studies support the hypothesis.

Ignoring the divergence between perceived quality and objective quality (i.e., quality as described in the survey) in empirical models of willingness to pay leads to the well-known omitted variable problem. For example, Hurley, Otto, and Holtkamp (1999) estimate the willingness to pay for delaying nitrate contamination in drinking water. Stumborg et al. (2001) ask for respondent willingness to pay for a reduction in phosphorus pollution. In both cases the perceived quality change is likely to vary across respondents since the water quality outcomes are not carefully described. Omitted variables will cause bias in the estimates of coefficients on variables that are correlated with perceived quality. Omitted variable bias may help explain some poor results from CVM research such as poor fits and even unexpected signs.

One solution to the omitted variable problem is to include a proxy variable in the model. In the case of willingness to pay for quality improvements the approach is to elicit 4

perceived quality from survey respondents and include these measures as determinants of willingness to pay. Many CVM studies have followed this approach. Kwak, Lee, and Russell (1997) and Yoo and Yang (2002) measure status quo drinking water quality with scale variables measuring "the respondent's attitude toward current tap water quality" and "degree of satisfaction the respondent has with current tap water quality." Both studies find that as satisfaction with current drinking water quality increases willingness to pay decreases. Clearly, subjective perceptions are potentially important determinants of willingness to pay. See Um, Kwak, and Kim (2002) for another example using the averting behavior method.

Most studies that include quality perceptions ignore the fact that varying subjective perceptions are due to the heterogeneity of respondents and the information and attitudes that they bring to the CVM survey. In contrast, Danielson et al. (1995) estimate the determinants of perceived air and water quality and find that they depend on demographics, environmental knowledge, and environmental attitudes. Air and water quality perceptions are then included in a model of willingness to pay. Water quality is a significant determinant of willingness to pay. Air quality is not a factor of willingness to pay.

The approach of Danielson et al. (1995) reveals a problem with including quality perceptions in willingness to pay models. The quality perception is a potentially endogenous variable since it is affected by the same unobserved characteristics that influence willingness to pay. If so, the coefficient on quality perception in the willingness to pay variable will be biased. Econometrically, this is because the error term in the

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willingness to pay model is correlated with the perceived quality variable.

A way to avoid this problem involves estimating a second equation for quality. However, a further problem exists if the quality and willingness to pay models are estimated independently. It is conceivable that quality and willingness to pay will share unobserved factors that determine the variation in each. For example, unobserved tastes may be correlated with both perceived quality and willingness to pay to improve quality. Ignoring this joint correlation causes a loss in econometric efficiency. Jointly estimating quality and willingness to pay models allows for an improvement in econometric efficiency.

A similar approach to a slightly different problem is presented by Cameron and Englin (1997). They model the relationship between respondent fishing experience and the willingness to pay for trout abundance. Fishing experience is treated as endogenous in a jointly estimated probit willigness to pay equation and a Poisson experience model. The results indicate that predicted fishing experience is exogenous in relation to the mean of willingness to pay. But, the predicted fishing experience significantly affects the variance of willingness to pay.

Including water quality perceptions in empirical models of willingness to pay is policy-relevant for two reasons. First, the validity of willingness to pay is always of critical concern when CVM estimates are used for policy. Including water quality perceptions in an appropriate way allows us to better assess whether the model coefficients have the expected sign and are significant. As water quality perceptions vary willingness to pay should vary in the expected direction. Willingness to pay should be 6

greater in magnitude the greater the water quality change. In this sense the effect of the perceived water quality variable is a form of scope test (Whitehead, Haab, and Huang, 1998). The second reason for the policy-relevance of including water quality perceptions in willingness to pay models is that willingness to pay estimates are ultimately used for benefit-cost analysis. Sensitivity analysis should always be conducted in benefit-cost analysis. One type of sensitivity analysis is the variation of the scope of the policy. For example, are net benefits of water pollution policy greater for a 10% reduction or for a 25% reduction? Incorporation of changes in water quality perceptions in willingness to pay models allows the development of different willingness to pay estimates for different policy goals. This will increase the applicability of benefit-cost analysis and the appropriateness of benefit-transfer.

In summary, empirical studies of the willingness to pay for quality improvements should include measures of quality perceptions as determinants of willingness to pay. Studies that do not include quality perceptions raise the potential for omitted variable bias in which coefficients on variables that are correlated with quality perceptions may be biased. Studies that include a measure of quality perception specified as an exogenous variable raise the potential for endogeneity bias in which the coefficient on the quality perception variable is biased downward. An efficient econometric approach that avoids omitted variable and endogeneity biases is to include a quality perception variable, but account for its potential endogeneity by estimating the determinants of quality perceptions jointly with those of willingness to pay, allowing the error terms in the two equations to be correlated. 7

The rest of the paper is organized as follows. The theoretical and empirical perceived quality and willingness to pay models are described. The survey used to collect the data and the data used to implement the model are described next. The application is to water quality improvements in the Neuse River, North Carolina. Willingness to pay empirical results using four different quality variables are presented. A summary and conclusions follow.

Model

Suppose consumers have the utility function u(x,q,z), where x is natural resource use, q is a measure of resource quality, and z is a composite of all market goods. The expenditure function, m(p, q, u), is found by solving the consumer problem: min (z + px) s.t. u = u(x,q,z) where p is the use price and pz = 1. The expenditure function measures the minimum amount of money the consumer must spend to achieve the reference utility level and is increasing in p and u and decreasing in q.

Willingness to pay is the maximum amount of money consumers would give up in order to enjoy an improvement in quality. The willingness to pay for the improvement in quality is

WTP = m( p, q, u ) - m( p, q*, u )

where q is a degraded level of quality and q * is an improved level of quality. Expenditures to maintain the utility level decrease with the increase in quality so that WTP > 0.

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Assume the reference level of utility is u* = v(p,q*,y), where y is income and v(.) is the indirect utility function found by solving the problem: max[u(x,q,z)] s.t. y = z + px. Substitution of the indirect utility function into the willingness to pay equation yields the Hicksian variation function

WTP = m[ p, q, v( p, q*, y )] - y = s ( p, q, q*, y )

where s(.) is the equivalent variation measure of welfare. According to reasonable assumptions and economic theory, the variation function is decreasing in own-price, decreasing in degraded quality, q, increasing in improved quality, q*, and increasing (decreasing) in income for q normal (inferior) (Whitehead, 1995).

CVM study design should include each of the four variables in the variation function, among other relevant varables, but few studies do. While the own-price variable is easily constructed as the travel cost, distance is often included as a proxy. In the case study described below, construction of the travel cost variable is problematic because the respondents are in close proximity to natural resource access limiting the variation in the own-price variable. A further problem is that there are a large number of potential access points. Perceptions about the potential to reach the improved quality level are easily elicited from respondents. Yet few studies consider this issue. The current study design also overlooked perceptions about improved quality. We proceed assuming that the ownprice and improved quality variables are constant.

The empirical willingness to pay model that corresponds to the theoretical model and the simplifying assumptions is 9

WTPi = 'X 1i + q i + 1i

where X 1i , i = 1, ... , n, is a vector of independent variables including a constant, income, and other variables that may affect willingness to pay. Omission of the degraded quality variable results in the following model WTPi = 'X 1i + e1i where the error term, e1i = qi + 1i , is not independent of the explanatory variables if perceived quality is correlated with any of the elements of the X 1i vector, violating one of the classical assumptions of regression. This will cause bias in the coefficients on the variables of X 1i that are correlated with perceived quality. In other words, biased coefficients may result if any of the elements of X 1i are also determinants of quality.

Including perceived quality as an independent variable can potentially cause other econometric problems. The degraded level of quality is a subjective measure of quality that varies across individuals, qi . For example, different individuals might consider current quality to be "good" or "poor" depending on the knowledge and experience they bring to the survey. Assuming these quality perceptions are continuous, quality can be explained by the model q i = ' X 2i + 2i where is a coefficient vector, X 2i is a vector of variables that explain the variation in perceived quality, and 2i is a normally distributed error term. 10

With perceived quality as the measure of quality the willingness to pay empirical model becomes WTPi = 'X 1i + q i + 1i = 'X 1i + ( 'X 2i + 2i ) + 1i

In this formulation the error terms may be correlated if the same unobserved factors influence both perceived quality and willingness to pay. This correlation will cause the quality variable and the error term to be correlated, biasing the coefficient on quality, . Positive correlation will bias the coefficient upwards while negative correlation will bias the coefficient downwards. Therefore, an instrumental variable methodology can be used to avoid the endogeneity bias from including perceived quality as a regressor.

Suppose the willingness to pay variable is continuous and censored at zero: WTP * if WTP = if 0 WTP* > 0 WTP* 0

where WTP* is the unobserved true willingness to pay. In this case the Tobit model is appropriate. In order to avoid endogeneity bias, the empirical willingness to pay model is a simultaneous equations instrumental variables model. The willingness to pay model is a Tobit regression and the quality model is an ordinary least squares regression: ^ WTPi = ' X 1i + q i + 1i qi = 'X 2i + 2i

= corr[ 1i , 2i ]

^ where q i is the predicted variable from the quality model. The estimation method is full 11

information maximum likelihood allowing for correlation in the normally distributed ^ error terms, . The test for the exogeneity of q i is a t-test for = 0 . The model is described in Smith and Blundell (1986) and estimated with the LIMDEP econometric software (Greene, 1998).

The variables in the X 2i vector but not in the X 1i vector are the identifying variables. These variables should have high explanatory power in the instrumenting equation and low correlation with willingness to pay and its error term. We test this last condition with a Bassman-type identification test. We regress the error terms from the jointly estimated willingness to pay model on all of the explanatory variables ^ 1i = ' X 2i + i ^ where 1i are the residuals from the Tobit regression, is a vector of coefficients and i is a normally distributed error term. The test statistic is the product of the sample size and the R2 value, which is distributed chi-squared with degrees of freedom equal to the number of variables in the X 2i vector, j, minus the number of variables in the X 1i vector, k, minus 1

2 = n × R 2 (d . f . = j - k - 1)

If the test statistic is less than the critical value then we conclude the model is properly identified.

Since the willingness to pay model is a Tobit the expected willingness to pay

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value is a nonlinear function E (WTP ) = (Z )( 'X 1 + q + ) Z=

' X 1 + q (Z ) = ( Z )

where the mean values of the independent variables, X 1 and q , are used, () is the

standard normal density function, () is the standard normal distribution function, and

is the standard error of 1i . The standard errors for the expected willingness to pay are

constructed using the Delta Method (Greene, 1997). The marginal effect of an independent variable, say q, on expected willingness to pay is E (WTP ) = (Z ) q where Z is evaluated at the mean of all variables including quality. Since 0 < (Z ) < 1 , the marginal effect will always be smaller in absolute value than the coefficient estimate.

Data

The data was collected in 1998 through a stratified random sample telephone survey of landowners from the 12 counties of the upper, middle, and lower Neuse River basin (Hoban and Clifford, 1999). Forty percent are from the upper, 33% are from the middle, and 27% are from the lower Neuse River basin. The sample includes 41% farm and 59% non-farm landowners. All summary statistics and empirical results are weighted to reflect the geographic and farm/non-farm stratification of the sample. The response 13

rate (completions divided by completions plus refusals) is 75%. After deleting cases with missing data the sample size is 663 for a 48.7% useable response rate.

The description of variables is presented in Table 1. Survey respondents are presented with the contingent valuation scenario: "We already pay for government environmental programs through taxes, water bills, and other means. However, government will need more money if water quality in the Neuse River is to be protected. This money would pay for government programs to control pollution, monitor water quality, protect fish habitat, and educate people about ways to reduce pollution. The goal would be to make sure water quality in the Neuse River is safe enough for fishing, swimming, and drinking treated water from the River."

The valuation question presents respondents with a hypothetical situation: "Would you and your household be willing to pay $A1 each year for these programs, if you knew the money would be used to make sure water quality in the Neuse River is safe?" The starting dollar amount (A1) took on nine values with a random start ranging from $10 to $200 (10, 25, 50, 75, 100, 125, 150, 175, 200). The starting points were pretested to determine if the range covered the expected range of willingness to pay.

Respondents are asked follow up questions with the next highest or lowest dollar amount. When respondents change their answer in response to a change in the price (e.g., yes/no, no/yes) the responses are used to construct upper and lower bounds for individual willingness to pay and the continuous willingness to pay variable is measured at midpoint between the bounds. For respondents who are not willing to pay $10, willingness to pay is equal to the response to the follow-up question: "What is the most that you and your 14

household would be willing to pay each year for these programs?" For respondents who are willing to pay $200 the willingness to pay variable is top-coded at $200. The maximum willingness to pay variable is MAXWTP.

There are four water quality perception variables. The first is the general question (WQRATE1): "When you think of water quality please consider its suitability for various uses (such as swimming, fishing, or drinking). Would you say it is excellent, good, fair, or poor?" The second water quality question is specific to the respondent's community (WQRATE2): "How would you rate water quality in your own community? Would you say it is excellent, good, fair, or poor?" The third water quality variable is specific to the Neuse River (WQRATE3): "How would you rate the water quality in the Neuse River? Would you say it is excellent, good, fair, or poor?" The fourth quality variable is specific to drinking water (WQDRINK): "How would you rate the quality or purity of your home drinking water as it comes from the faucet? Would you say it is excellent, good, fair, or poor?" For each of the water quality variables the scale variable is increasing in quality. "Excellent" water quality is coded at 4, "good" is coded at 3, "fair" is 2 and "poor" is 1.

Income (INCOME) is measured at the midpoint of income categories following the question: "Which of the following categories best represents your family's 1997 total income before taxes?" The categories are less than $5000, between $5000 and $10,000, between $10,001 and $20,000, between $20,001 and $30,000, between $30,001 and $40,000, between $40,001 and $50,000, between $50,001 and $60,000, between $60,001 and $80,000, between $80,001 and $100,000, between $100,001 and $200,000, and more than $200,000. Those respondents who state that income is more than $200,000 are top-

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coded at $200,000.

Several dummy variables measure the respondent's proximity to water and waterrelated problems. RURAL is equal to one if the respondent's home is in a "rural area" and equal to zero if the home is in a city, suburb, or small town. SEPTIC is equal to one if the respondent answers either "septic" or "both septic and sewer" to the question: "Does your home have central sewer service or a septic tank?" PRIVWELL is equal to one if the respondent answered either "private well" or "both city and well" to the question: "Does your home get its water from a public water system or your own private well?" PROPERTY is equal to one if the respondent answered "yes" to the question: "Is your property located next to any rivers, streams, or other bodies of water?" For each question, the variable is equal to zero if it is not equal to one.

Information about water quality is measured by three dummy variables: "Have you ever heard of the term watershed?" (WATERSHD), "Have you ever heard of the term nonpoint source pollution?" (NONPOINT) and "Have you ever heard of the term Pfiesteria?" (PFIESTER). Each dummy variable is equal to one if the respondent had heard of the term and zero otherwise.

Finally, several demographic variables are included in the analysis. NONWHITE is equal to one if the respondent is "black," "American Indian," "Asian," "Mixed Race" and equal to zero if "white." FEMALE is equal to one if the respondent is female and zero if male. AGE is the age of the respondent. FARM is equal to one if the respondent is part of the farm sample and zero otherwise.

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The summary statistics are presented in Table 2. Average willingness to pay is $76. The average dollar amount initially presented to respondents, A1, is $103. The average income is $71,290. Missing income data are imputed with the conditional mean from a wage equation used to estimate the determinants of income. The income model is estimated with 758 cases and specified with the standard variables including education, potential experience, race and gender. Also, dummy variables are included for the farm sample and respondents who lived in a city. The dependent variable is the log of income. Missing income data are replaced with the midpoint of the income interval closest to the exponential of the predicted log income value.

Drinking water quality is rated the highest of the water quality variables, 3.03 on the 4 point scale. Water quality in the community is next highest at 2.70. General water quality is 2.46. Water quality in the Neuse River is rated the lowest at 1.66. Fifty-two percent of the sample lives in a rural area. Sixty-four percent of the sample is on a septic tank, 41% gets their water from a private well, and 37% lives near water. Only 16% of the sample had heard of nonpoint source pollution. Seventy-seven percent of the sample had heard of both Pfiesteria and watershed. Fourteen percent are nonwhite. Forty-three percent are female. The average age is 51 years. Thirty-five percent is part of the farm sample.

The frequency distribution for the willingness to pay variable is presented in Table 3. The largest group of respondents is willing to pay zero (29%). The next largest groups of respondents are willing to pay $62.50 (15%), $112.50 (12%), and $200 (11%). In the other categories, 17% are willing to pay between zero and $37.50, about 11% are

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willing to pay between $137.50 and $187.50, and 5% percent are willing to pay $87.5.

The frequency distributions for the water quality variables are presented in Table 4. Forty-two percent consider general water quality to be fair, 41% consider it good, and 13% consider it poor. Only 4% consider general water quality excellent. Water quality in the community is rated good by 52%, fair by 26%, poor by 12% and excellent by 10%. Water quality in the Neuse River is rated poor by 54%, fair by 34%, good by 11%, and excellent by only 0.3%. Fifty-one percent rate drinking water quality good, 26% rate it excellent, 19% rate it fair, and only 4% rate it poor. These data illustrate the large amount of variation in quality perceptions among heterogeneous respondents.

Results

We estimate independent and jointly quality/willingness to pay models for each of the quality variables. Since water quality is the instrumenting equation we use all exogenous variables as instrumental variables in the X 2i vector to get the most precise predicted quality value. Water quality is specified to depend on the tax amount, income, knowledge, water-related, and demographic variables in Table 1. We have no a priori expectations of the signs of the coefficients in the water quality model.

Demographic variables are excluded in X 1i and serve as the identifying variables. We choose demographics as the identifying variables because they tend to be strongly related to perceived water quality and unrelated to willingness to pay. The willingness to pay equation is specified to depend on the tax amount, income, knowledge, water-related variables, and perceived quality. The coefficient on the tax amount will be statistically 18

significant if the data is subject to starting point bias. The coefficient on INCOME will be positive (negative) if water quality is a normal (inferior) good. The coefficient on the water quality variable is expected to be negative; higher perceived water quality leads to lower willingness to pay for water quality improvements. We have no a priori expectations of the signs of the other coefficients in the willingness to pay model.

We assume that each respondent perceives that ex-post water quality (i.e., water quality after the programs are implemented) will be drinkable, swimmable, fishable, and boatable. Since the entire sample lives within the Neuse River basin, there is little variation in the travel costs to the river and, therefore, little variation in the own-price. Therefore the ex-post water quality and own-price variables are assumed to be constant and captured by the constant.

WQRATE1: General Water Quality

In the independently estimated model the determinants of perceived general water quality (WQRATE1) are estimated by ordinary least squares (Table 5). Perceived water quality is higher with higher income and if the respondent gets their drinking water from a private well. Perceived water quality is lower if the respondents' property is located near water or if they had heard of the term watershed. No other coefficient on the independent variables is statistically significant. The model has a R2 value of 0.062 which indicates little explanatory power.

In the independently estimated willingness to pay model, the coefficient on the tax variable is positive and statistically different from zero indicating starting point bias.

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The coefficient on the income variable is positive and statistically significant indicating that water quality is a normal good. Willingness to pay is lower for rural respondents and higher for those with property near water. General perceived water quality is not a factor affecting willingness to pay.

Next the water quality and willingness to pay models are jointly estimated. In the water quality model most of the coefficients retain their statistical significance. The coefficient on PROPERTY is no longer statistically significant. Those who are older perceive higher water quality when the model is jointly estimated. In the willingness to pay equation the coefficients on RURAL and PROPERTY are no longer statistically significant. Most importantly, the coefficient on the predicted value of WQRATE1 is negative and statistically significant, as expected. This indicates that as perceived general water quality increases the willingness to pay for improved water quality decreases, as expected.

The correlation of the error terms in the willingness to pay and quality equations,

, is statistically different from zero indicating that the perceived water quality variable

is endogenous in the willingness to pay equation. The result from the Bassman-type test indicates that the joint model is appropriately identified ( 2 = 7.48[4 d . f .] ).

WQRATE2: Community Water Quality

The results from the community water quality and willingness to pay model are in slight contrast to the general water quality results (Table 6). In addition to the positive effect of INCOME and PRIVWELL and the negative effect of PROPERTY on perceived

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water quality, those who are on septic tanks perceive lower community water quality. Those who are older perceive higher water quality. The determinants of willingness to pay include A1, INCOME, RURAL, and PROPERTY as before. In addition, those who get their water from a private well are willing to pay less. Community water quality is not a determinant of willingness to pay when quality and willingness to pay are estimated independently.

When these models are estimated jointly, each of the determinants of perceived water quality are identical to the independently estimated model. In the willingness to pay equation, the coefficients on RURAL, PRIVWELL, and PROPERTY are no longer statistically significant. But, community water quality is negatively related to willingness to pay when the predicted water quality variable is used.

The correlation of the error terms in the willingness to pay and quality equations is statistically different from zero indicating that the perceived water quality variable is endogenous in the willingness to pay equation. The result from the Bassman-type test indicates that the joint model is not appropriately identified at the p = .10 level ( 2 = 8.41[4 d . f .] ). Considering the individual coefficients, PFIESTER is related to the unexplained variance of willingness to pay.

WQRATE3: Neuse River Water Quality

We expected perceived Neuse River water quality to be the most closely related to willingness to pay for Neuse River water quality relative to other quality variables. Surprisingly, the results for Neuse River water quality are poor (Table 7). This is

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probably related to the skewed distribution of the WQRATE3 in which 88% rate water quality as either poor or fair. In the independent model, Neuse River water quality is negatively related to being on a septic tank and knowledge of Pfiesteria and positively related to getting water from a private well. Willingness to pay is related to the tax amount, income, rural residence and property near water as in previous models. Also, as in previous independently estimated models, willingness to pay is not related to perceived water quality.

In the jointly estimated model, perceived water quality is related to being on a septic tank and knowledge of Pfiesteria. Willingness to pay is not related to any of the explanatory variables. In addition to these troubling results, the correlation in error terms is very high and the Bassman-type test does not reject overidentification. Clearly the skewed distribution of the Neuse River water quality variable limits application of the model.

WQDRINK: Drinking Water Quality

Another surprising development is that perceived drinking water quality is the best performing among the four quality variables in terms of its ability to be modeled and its relationship to willingness to pay. The R2 value in the independently estimated model is more than twice as large as the other R2 values (Table 8). In contrast to the paucity of statistically significant coefficients in the other quality models, seven of the thirteen variables have significant coefficients when explaining the variation in drinking water quality. Perceived drinking water quality is higher for rural respondents, and if the respondent gets their drinking water from a private well. Quality increases with age and 22

for farm residence. Perceived water quality is lower if the respondent is on a septic tank and if the respondents' property is located near water. Those who are nonwhite perceive lower water quality.

In the independently estimated willingness to pay model, the coefficient on the tax variable is positive and statistically different from zero indicating starting point bias. The coefficient on the income variable is positive and statistically significant indicating that water quality is a normal good. Willingness to pay is lower for rural respondents and higher for those with property near water. General perceived water quality is not a factor affecting willingness to pay.

In the jointly estimated water quality equation most of the coefficients retain their statistical significance. The coefficients on SEPTIC and NONWHITE are no longer statistically significant. Those with higher incomes and who have heard about Pfiesteria perceive higher water quality. Female respondents perceive lower water quality when the model is jointly estimated. In the willingness to pay equation the coefficients on RURAL and PROPERTY are no longer statistically significant. Those who get their drinking water from a private well are willing to pay more. Those who have heard of the terms Pfiesteria and watershed are willing to pay more. Most importantly, the coefficient on the predicted value of WQRATE1 is negative and statistically significant. This indicates that as perceived drinking water quality increases the willingness to pay for improved water quality decreases, as expected.

The correlation of the error terms in the willingness to pay and quality equations is statistically different from zero indicating that the perceived water quality variable is 23

endogenous in the willingness to pay equation. The result from the Bassman-type identification test indicates that the joint model is appropriately identified ( 2 = 7.13[4 d . f .] ).

Quality and Willingness to Pay

The marginal effect of water quality perceptions on willingness to pay is presented in Table 9. The marginal effects are computed at the means of the independent variables. Estimates from the independent and joint models are presented for each of the water quality variables. The marginal effect estimates from the independent models are very low and not statistically different from zero. Those from the WQRATE2 and WQRATE3 models have the wrong sign.

The marginal effects from the joint models vary widely with a range of $203. The lowest estimate is with the WQDRINK model. The marginal effect from this model suggests that a one unit increase in drinking water quality perceptions (e.g., "fair" to "good") reduces mean willingness to pay by $53. The marginal effect from the WQRATE1 model suggests that a one unit increase in general water quality perceptions reduces mean willingness to pay by $88. The marginal effect from WQRATE2 model suggests that a one unit increase in community water quality perceptions reduces mean willingness to pay by $119. The largest marginal effect is from Model 3 which did not perform adequately. The difference in the marginal effects between the independent and joint models is a measure of the extent of the potential bias from ignoring the endogeneity of water quality perceptions.

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Expected willingness to pay estimates are constructed for each of the jointly estimated quality models and presented in Table 10. Willingness to pay is assessed at each of the four perceived water quality levels. In the WQRATE1 model, willingness to pay decreases from $288 to $0 as baseline water quality perceptions increase from "poor" to "excellent." In the WQRATE2 and WQRATE3 models, willingness to pay decreases from $421 and $351 to $0 as baseline water quality perceptions increase from "poor" to "excellent." Willingness to pay falls from $254 to $19 as drinking water quality perceptions increase from "poor" to "excellent."

The willingness to pay estimates from the independently estimated models are not shown in this table. However, considering the marginal effects in Table 9, willingness to pay does not significantly differ with differences in water quality perceptions. In Table 10 we see that the range of expected willingness to pay estimates is large and differences are economically significant with the more appropriate jointly estimated instrumental variable quality/willingness to pay model. Using the inappropriate independently estimated willingness to pay model for benefit-cost analysis would lead to a reduction in the magnitude of the effect of the baseline quality on willingness to pay.

Conclusions

The theoretical definition of willingness to pay for quality improvement includes both pre-policy and post-policy quality as determinants of willingness to pay. The measurement of quality change is not straightforward since respondents are heterogeneous and may have differing perceptions of pre-policy and post-policy quality. Empirical studies should include measures of quality perceptions as covariates in the 25

willingness to pay model in order to avoid omitted variable bias. Coefficients on other variables in the willingness to pay model that are correlated with quality perceptions may be biased when the quality variables are omitted.

Quality perceptions that vary across respondents are endogenous variables. Endogenous quality perceptions include a random error term. The coefficient on the quality perception variable in the willingness to pay equation is potentially biased if the error terms from the quality and willingness to pay equations are correlated. We propose an instrumental variable approach to address endogeneity bias. We estimate the determinants of quality perceptions and willingness to pay jointly allowing the error terms to be correlated and including the predicted quality variable in the willingness to pay equation.

Our results indicate that endogeneity bias is a problem. We reject tests for exogeneity of perceived quality. In these models the coefficients on quality variables are biased downward in independently estimated models that do not account for endogeneity. In the instrumental variable willingness to pay models, degraded water quality has negative effects on willingness to pay as expected. In other words, respondents who perceive that water quality is "poor" are willing to pay more for a quality improvement than those who think water quality is "fair" or better. The marginal effects of these variables are of realistic magnitude.

One interesting result is that of the four water quality perception variables that are candidates for inclusion in the willingness to pay models, the one that was considered the poorest choice a priori performs best. Perceived drinking water quality is best explained 26

by the instrumental variables, it is a statistically significant determinant of willingness to pay, and the joint model outperforms the others. One reason for this result may be that drinking water quality is more salient to respondents. Their primary intersection with Neuse River water quality is through the tap. Negative perceptions of Neuse River surface water quality may taint their perceptions about treated drinking water. A similar result is found by Um, Kwak, and Kim (2002).

Researchers who pursue this methodology should consider several issues that are not addressed in this paper. The simultaneous equations Tobit model that is programmed in LIMDEP software requires a censored dependent variable for willingness to pay and a continuous dependent variable for quality. Ordinary least squares estimation of quality requires an assumption of linearity of the categorical quality variable. Estimation of the determinants of quality when quality is a categorical variable should proceed with a qualitative dependent variable model such as the ordered probit. The extent to which the assumption of linearity and the use of ordinary least squares to estimate the predicted quality variable biases these results is not known.

Another limitation is the use of the continuous willingness to pay data. One troubling result with the continuous data is starting point bias. Another problem, not specifically addressed in this paper, is the incentive incompatibility of the follow-up valuation questions that are used to construct continuous willingness to pay (Whitehead, 2001). Dichotomous choice data is preferred for willingness to pay.

Considering both issues, joint estimation with a probit for willingness to pay and ordered probit for categorical quality variables would be most appropriate with these 27

data, given the current state of the art in survey research and the CVM. A two-step probit/ordered probit model is feasible. In this model the predicted value from the first step ordered probit quality equation would be included in the probit willingness to pay equation. The feasibility of joint probit/ordered probit model with current canned routines in statistical software packages is questionable -- a potential limitation of the proposed approach.

Policy makers who use benefit-cost analysis require benefit estimates that correspond to the true, or objective, change in resource allocation (e.g., quality) that will result from the policy or program. One problem that most all CVM research faces is that objective quality change is described to respondents, yet willingness to pay statements are made based on subjective quality. As such, willingness to pay estimates from CVM research are of little use to policy makers unless an adjustment can be made so that subjective willingness to pay is consistent with objective willingness to pay.

This paper demonstrates that when estimated appropriately the marginal effects of perceived quality can be used to adjust willingness to pay estimates so that they are more consistent with objective quality. For example, if most respondents believe that current water quality is "fair" but experts believe that water quality is "good", the willingness to pay estimate associated with "good" quality could be used for policy analysis. This, of course, ignores another policy analysis problem. It is possible that benefits can be achieved by changing perceptions through an information campaign even if objective quality is not changed. In this case, benefits are real only if the information moves perceptions more closely to reality.

28

In conclusion, CVM researchers should consider the implications of omitted variable bias and endogeneity bias whenever quality changes are to be valued by respondents and there is the potential for a divergence between perceived and objective quality. This is especially true when those willingness to pay statements are used in benefit-cost analysis and considered by policy makers.

29

References

Blomquist, Glenn C. and John C. Whitehead, "Resource Quality Information and Validity of Willingness to Pay in Contingent Valuation," Resource and Energy Economics, 20, 179-196, 1998.

Cameron, Trudy Ann, and Jeffrey Englin, "Respondent Experience and Contingent Valuation of Environmental Goods," Journal of Environmental Economics and Management, 33, 3, 296-313, 1997.

Carson, Richard T., and Robert Cameron Mitchell, "The Value of Clean Water: The Public's Willingness to Pay for Boatable, Fishable, and Swimmable Quality Water," Water Resources Research, 29, 7, 2445-2454, 1993.

Danielson, Leon, Thomas J. Hoban, George Van Houtven, and John C. Whitehead, "Measuring the Benefits of Local Public Goods: Environmental Quality in Gaston County, North Carolina" Applied Economics, 27, 1253-1260, 1995.

Greene, W.H., LIMDEP Version 7.0: User's Manual, Econometric Software, Bellport, N.Y., 1998.

Hoban, Thomas J. and William B. Clifford, "Landowners' Knowledge, Attitudes, and Behavior in The Neuse River Watershed," Final Report to the United States Environmental Protection Agency and the North Carolina Department of Environment and Natural Resources, 1999.

Hoehn, John P. and Alan Randall, "The Effect of Resource Quality Information on 30

Resource Injury Perceptions and Contingent Values," Resource and Energy Economics, 24, 13-33, 2002.

Hurley, Terrance M., Daniel Otto, and Janie Holtkamp, "Valuation of Water Quality in Livestock Regions: An Application to Rural Watersheds in Iowa," Journal of Agricultural and Applied Economics, 177-184, April 1999.

Kwak, Seung-Jun, Junsoo Lee and Clifford S. Russell, "Dealing with Censored Data from Contingent Valuation Surveys: Symmetrically-Trimmed Least Squares Estimation," Southern Economic Journal, 63, 743-750, 1997.

Mitchell, Robert Cameron, and Carson, Richard T., Using Surveys to Value Public Goods: The Contingent Valuation Method, Resources for the Future, Washington, D.C., 1989.

Smith, R., and R. Blundell, "An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply," Econometrica, 54, 679-685, 1986.

Stumborg, Basil E., Kenneth A. Baerenklau, and Richard C. Bishop, "Nonpoint Source Pollution and Present Values: A Contingent Valuation Study of Lake Mendota," Review of Agricultural Economics, 23, 120-132, 2001.

Um, Mi-Jung, Seung-Jun Kwak, and Tai-Yoo Kim, "Estimating Willingness to Pay for Improved Drinking Water Quality Using Averting Behavior Method with Perception Measure," Environmental and Resource Economics, 21, 287-302, 2002.

31

Whitehead, John C., "Willingness to Pay for Quality Changes: Comparative Statics and Theoretical Interpretations of Empirical Results," Land Economics, 71, 207-215, 1995.

Whitehead, John C., "Incentive Incompatibility and Anchoring with Iterative Valuation Questions, Land Economics, 78, 2, 285-297, 2002.

Whitehead, John C., Timothy C. Haab, and Ju-Chin Huang, "Part-Whole Bias in Contingent Valuation: Will Scope Effects Be Detected with Inexpensive Survey Methods?" Southern Economic Journal, 65, 160-168, 1998.

Yoo, Seung-Hoon and Hee-Jong Yang, "Application of Sample Selection Model to Double-Bounded Dichotomous Choice Contingent Valuation Studies," Environmental and Resource Economics, 20, 147-163, 2001.

32

Table 1. Variables

Variable MAXWTP WQRATE1 WQRATE2 WQRATE3 WQDRINK A1 INCOME RURAL SEPTIC PRIVWELL PROPERTY NONPOINT PFIESTER NONWHITE FEMALE AGE FARM

Description Maximum willingness to pay Perception of general water quality Perception of community water quality Perception of Neuse River water quality Perception of drinking water quality Randomly assigned tax amount Family income (in thousands) 1 if rural resident 1 if has septic tank 1 if gets water from private well 1 if property is near water 1 if heard of nonpoint source pollution 1 if heard of Pfiesteria 1 if nonwhite 1 if female age 1 if family owns farm

WATERSHD 1 if heard of watershed

33

Table 2. Data Summary

Variable MAXWTP WQRATE1 WQRATE2 WQRATE3 WQDRINK A1 INCOME RURAL SEPTIC PRIVWELL PROPERTY NONPOINT PFIESTER WATERSHD NONWHITE FEMALE AGE FARM Cases

Mean 75.95 2.46 2.70 1.66 3.03 103.13 71.29 0.52 0.64 0.41 0.37 0.16 0.77 0.77 0.14 0.43 51.09 0.35 663

Std.Dev. Minimum Maximum 70.57 0.73 0.80 0.73 0.82 62.44 61.50 0.50 0.48 0.49 0.48 0.37 0.42 0.42 0.35 0.49 14.75 0.48 0 1 1 1 1 10 2.5 0 0 0 0 0 0 0 0 0 20 0 200 4 4 4 4 200 200 1 1 1 1 1 1 1 1 1 89 1

34

Table 3. Willingness to Pay Frequency Distribution

MAXWTP Frequency 0 5 17.5 37.5 62.5 87.5 112.5 137.5 162.5 187.5 200 191 2 48 63 102 31 82 13 38 17 76

Percent 28.81 0.3 7.24 9.5 15.38 4.68 12.37 1.96 5.73 2.56 11.46

35

Table 4. Water Quality Perception Frequency Distribution

WQRATE1 Frequency Poor Fair Good Excellent 88 278 273 24 Percent 13.27 41.93 41.18 3.62

WQRATE2 Frequency 77 173 344 69 Percent 11.61 26.09 51.89 10.41

WQRATE3 Frequency 361 224 76 2 Percent 54.45 33.79 11.46 0.3

WQDRINK Frequency 28 124 336 175 Percent 4.22 18.7 50.68 26.4

36

Table 5. Willingness to Pay and Quality Models: WQRATE1 Independent WQRATE1 Coeff. ONE A1 INCOME RURAL SEPTIC PRIVWELL PROPERTY NONPOINT PFIESTER WATERSHD NONWHITE FEMALE AGE FARM WQRATE1 V R U

2

Joint MAXWTP WQRATE1 Coeff. 2.298 0.000 0.001 -0.058 -0.084 0.284 -0.090 -0.012 -0.122 -0.175 0.018 -0.059 0.005 0.088 t-ratio 15.659 0.769 3.037 -0.697 -0.942 4.127 -1.506 -0.151 -1.590 -2.364 0.295 -1.351 2.615 1.617 -157.301 83.627 -2324.448 0.800 2.643 -2.636 22.720 MAXWTP Coeff. 403.223 0.351 0.305 -24.114 4.055 32.140 5.333 2.715 -17.168 -2.952 t-ratio 2.649 3.861 2.609 -1.417 0.202 1.344 0.390 0.168 -1.028 -0.191 t-ratio 1.079 5.539 1.882 -2.996 1.424 -1.377 3.072 -0.480 1.197 0.589

t-ratio 14.943 0.939 2.261 -0.652 -0.240 4.513 -2.434 0.493 -1.602 -1.626 -0.088 0.703 0.405 0.095

Coeff. 18.608 0.309 0.110 -29.094 15.366 -11.966 22.519 -4.702 10.530 5.205

2.416 0.000 0.001 -0.054 -0.021 0.311 -0.143 0.040 -0.116 -0.121 -0.008 0.046 0.001 0.008

-2.404 86.383 0.062 -794.050 -2986.968

-0.489 28.879

LogL

37

Table 6. Willingness to Pay and Quality Models: WQRATE2 Independent WQRATE2 Coeff. ONE A1 INCOME RURAL SEPTIC PRIVWELL PROPERTY NONPOINT PFIESTER WATERSHD NONWHITE FEMALE AGE FARM WQRATE2 V R U

2

Joint MAXWTP WQRATE2 Coeff. 2.401 0.000 0.002 0.073 -0.202 0.359 -0.189 -0.016 0.002 -0.067 0.003 -0.050 0.004 0.066 t-ratio 16.580 0.614 2.980 0.867 -2.270 4.824 -3.008 -0.179 0.027 -0.842 0.058 -1.349 2.200 1.461 -216.133 84.095 -2367.724 0.897 2.269 -2.197 22.685 MAXWTP Coeff. 566.349 0.361 0.407 -3.557 -25.556 66.925 -18.236 -0.028 7.796 5.800 t-ratio 2.233 2.883 2.238 -0.140 -0.806 1.560 -0.758 -0.001 0.367 0.299 t-ratio 0.119 5.505 1.727 -3.034 1.506 -1.633 3.222 -0.484 1.243 0.649

t-ratio 13.473 0.668 3.195 0.944 -2.260 5.122 -2.859 -0.259 -0.242 -0.893 -0.410 0.229 2.138 0.630

Coeff. 2.025 0.307 0.102 -29.508 16.321 -14.303 23.687 -4.744 10.908 5.718

2.356 0.000 0.002 0.085 -0.215 0.382 -0.182 -0.023 -0.019 -0.072 -0.039 0.016 0.005 0.057

4.040 86.381 0.083 -853.773 -3001.015

0.884 28.883

LogL

38

Table 7. Willingness to Pay and Quality Models: WQRATE3 Independent WQRATE3 Coeff. ONE A1 INCOME RURAL SEPTIC PRIVWELL PROPERTY NONPOINT PFIESTER WATERSHD NONWHITE FEMALE AGE FARM WQRATE3 V R U

2

Joint MAXWTP WQRATE3 Coeff. 2.055 0.000 -0.001 0.049 -0.269 0.099 -0.035 0.112 -0.322 -0.102 0.009 -0.022 0.002 0.030 t-ratio 16.602 -0.603 -1.222 0.653 -3.098 1.405 -0.574 1.345 -4.749 -1.348 0.365 -0.936 1.275 0.945 -446.427 83.713 -2313.404 0.967 2.643 -1.252 22.833 MAXWTP Coeff. 966.533 0.172 -0.241 5.819 -107.577 36.591 7.469 54.302 -130.971 -25.931 t-ratio 1.256 0.714 -0.725 0.136 -1.038 0.704 0.234 0.893 -1.063 -0.605 t-ratio 0.376 5.526 1.862 -3.004 1.481 -1.517 3.163 -0.497 1.337 0.669

t-ratio 12.178 -0.074 -0.491 0.632 -2.206 1.628 -1.125 0.925 -5.587 -1.525 0.483 1.278 1.336 0.077

Coeff. 6.099 0.308 0.109 -29.170 16.051 -13.025 23.094 -4.868 12.090 5.908

1.946 0.000 0.000 0.052 -0.192 0.111 -0.066 0.074 -0.400 -0.112 0.042 0.083 0.003 0.006

2.961 86.378 0.091 -796.676 -3001.231

0.593 28.880

LogL

39

Table 8. Willingness to Pay and Quality Models: WQDRINK Independent WQDRINK Coeff. ONE A1 INCOME RURAL SEPTIC PRIVWELL PROPERTY NONPOINT PFIESTER WATERSHD NONWHITE FEMALE AGE FARM WQDRINK V R U

2

Joint MAXWTP WQDRINK Coeff. 2.303 0.000 0.001 0.179 -0.135 0.424 -0.100 0.053 0.122 0.012 -0.089 -0.084 0.008 0.258 t-ratio 15.488 -0.563 1.635 2.123 -1.500 5.809 -1.639 0.569 1.727 0.173 -1.229 -1.623 3.852 3.477 -96.147 84.834 -2328.782 0.610 3.670 -3.888 22.258 MAXWTP Coeff. 257.185 0.275 0.169 2.398 5.213 32.641 12.898 9.044 20.985 19.394 t-ratio 3.951 3.911 2.329 0.147 0.337 2.024 1.351 0.746 1.854 1.664 t-ratio 2.409 5.457 1.971 -2.590 1.323 -0.872 2.974 -0.327 1.351 0.822

t-ratio 14.425 -0.582 1.597 1.962 -1.645 5.970 -1.784 0.552 1.486 0.135 -1.773 -0.616 2.986 3.825

Coeff. 40.546 0.303 0.115 -25.340 14.225 -7.660 21.645 -3.194 11.823 7.235

2.374 0.000 0.001 0.166 -0.147 0.419 -0.107 0.045 0.110 0.010 -0.159 -0.041 0.006 0.323

-10.895 85.989 0.221 -784.560 -2998.651

-2.352 28.886

LogL

40

Table 9. Marginal Effect of Water Quality Perception on Willingness to Pay WQRATE1 WTP/q Independent Joint -1.31 -88.39 S.E. -0.49 2.64 WQRATE2 WTP/q 2.21 -118.83 S.E. 0.88 -2.20 WQRATE3 WTP/q 1.62 -256.27 S.E. 0.59 -1.25 WQDRINK WTP/q -5.96 -52.80 S.E. -2.35 -3.89

41

Table 10. Expected Willingness to Pay WQRATE1 Water Quality Poor Fair Good Excellent E(WTP) 287.83 132.65 21.67 0.41 S.E. 3.23 5.14 1.73 0.32 WQRATE2 E(WTP) 421.15 205.22 28.28 0.09 S.E. 2.56 3.12 1.88 0.20 WQRATE3 E(WTP) 350.60 5.25 0.00 0.00 S.E. 1.52 0.33 0.03 0.01 WQDRINK E(WTP) 253.57 158.45 72.92 19.22 S.E. 5.12 6.52 19.78 2.23

42

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