Estimating the opportunity cost of time to calculate the willingness to pay for wetland restoration at Maumee Bay State Park

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1 The University of Toledo The University of Toledo Digital Repository Theses and Dissertations 2011 Estimating the opportunity cost of time to calculate the willingness to pay for wetland restoration at Maumee Bay State Park Allison M. Schnapp The University of Toledo Follow this and additional works at: Recommended Citation Schnapp, Allison M., "Estimating the opportunity cost of time to calculate the willingness to pay for wetland restoration at Maumee Bay State Park" (2011). Theses and Dissertations This Thesis is brought to you for free and open access by The University of Toledo Digital Repository. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of The University of Toledo Digital Repository. For more information, please see the repository's About page.

2 AThesis entitled Estimating the Opportunity Cost of Time to Calculate the Willingness to Pay for Wetland Restoration at Maumee Bay State Park by Allison M. Schnapp Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Arts Degree in Economics Dr.KevinJ.Egan,CommitteeChair Dr. Olugbenga Ajilore, Committee Member Dr. Kristen Keith, Committee Member Dr. Patricia R. Komuniecki, Dean College of Graduate Studies The University of Toledo May 2011

3 Copyright 2011, Allison M. Schnapp This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author.

4 An Abstract of Estimating the Opportunity Cost of Time to Calculate the Willingness to Pay for Wetland Restoration at Maumee Bay State Park by Allison M. Schnapp Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Arts Degree in Economics The University of Toledo May 2011 Two costs are associated with visiting a recreational site: the opportunity cost of time and the travel cost. This research examines the robustness of various estimates of the opportunity cost of time in order to more accurately estimate the willingness to pay for wetland restoration at Maumee Bay State Park. Samples are drawn from the Northwest Ohio Wetland Survey, which was conducted in Because employment classification reveals information about the individual s opportunity cost of time, respondents were split into subgroups based on their employment classification. An individual can be out of the labor market, work a fixed schedule and be underemployed, work a fixed schedule and be overemployed, or an individual can be free to choose their work hours. I also allow for the possibility that an individual working a fixed schedule is content working their current hours. Models using different discount rates, k, were used to estimate the sensitivity of the willingness to pay estimate to various measures of the opportunity cost of time. Using estimates from a bivariate Poisson lognormal model, the willingness to pay estimates varied significantly, from $14.91 per person per year when k = 0 to $56.42 per person per year when k = 1, depending on the opportunity cost of time. Allowing k to vary by employment subgroup leads to a willingness to pay estimate of $26.40, which was similar to the estimate calculated when k was 1/3. iii

5 For my Family. Thank you for teaching me that one person can make a difference, for you have all made a difference in my life.

6 Acknowledgments This project represents the combined effort of many people joined together for one purpose to answer one of the many questions we ask every day. Without these individuals this project would not have been possible. Please know that you have my deepest gratitude: to my committee members Professors Kevin Egan, Olugbenga Ajilore, and Kristen Keith for helping make this project a reality. I could not place a value on thetimeyouhavegiventome; to Professors John Murray and Kristen Keith for comments on early drafts of this document; to my seminar audience for the feedback and advice to help refine this project; to Professor Mike Dowd for creating a program that made the formatting requirements bearable; toprofessorolegsmirnovforhelping with the placement of the figures; to Professor Edward Shapiro for believing in a student he would never know; to Professor Kevin Egan for his dedication to students and contribution to this project. He was never too busy to listen and always there to instruct. v

7 Contents Abstract iii Acknowledgments v Contents vi List of Tables vii List of Figures viii 1 Introduction 1 2 Literature Review 3 3 Theory 7 4 Data 20 5 Results 26 6 Conclusions 31 References 32 vi

8 List of Tables Maumee Bay State Park Survey Summary Statistics Employment Summary Statistics Trips for Those Out of the Labor Market Trips for the Underemployed Trips for the Overemployed Trips for Those Free to Choose Results from the bivariate Poisson lognormal (BVPLN) regression WTP Estimates vii

9 List of Figures 3-1 Willingness to Pay for a Quality Change Variations in Willingness to Pay Gain in Consumer Surplus (CS) from an Increase in the Discount Factor (k) Interior Solutions: An individual will choose to work if the shadow wage at zero hours is less than the shadow wage at the optimal amount of work hours, h Corner Solutions: An individual with free choice of work hours will choose not to work if the shadow wage at zero hours is greater than the wage Overemployment occurs when the wage rate is greater than the shadow wage at zero hours of work, but less than or equal to the shadow wage at the desired number or work hours Underemployment occurs when the wage rate is greater than the shadow wage at the desired number of work hours, but less than or equal to the shadow wage at the maximum number of hours allowed in the time constraint viii

10 Chapter 1 Introduction A wetland is an area of land that is covered or saturated by water for at least a portion of every year, which for the area of Northwest Ohio, can include marshes, wet meadows, vernal pools, forested wetlands, coastal wetlands, freshwater estuarine wetlands, fens and bogs (Egan, 2008). Calculating the willingness to pay for wetland restoration is important due to the many functions wetlands provide. Not only do wetlands provide aesthetic value, they also serve as a storage place for excess water during flood seasons, a storage place for excess nutrients thereby reducing algal blooms and improving aquatic life, a filtration of runoff and other water contaminants to improve water quality, a breeding place for many species of wildlife, nesting and feeding areas for birds, habitats for animals, and an increase in the overall biodiversity (Egan, 2008). Wetlands also provide recreational activities such as biking, hiking, hunting, fishing, and swimming. Public wetlands are not exchanged in the market, and therefore it is difficult to determine their value. Studying the increase in demand for trips from a hypothetical change in the quality of the wetland allows researchers to place a value on the quality improvement. The Lake Erie coastal wetlands at Maumee Bay State Park had a swimming advisory posted for a total of 148 days from 1999 to 2004 due to bacteria levels that exceeded state standards (Egan, 2008). Swimming in water with high 1

11 bacteria levels has adverse health effects. A proposed solution to the problem is to add restored wetlands to help filter runoff and store excess nutrients. The increase in the consumer surplus from the hypothetical improvement in the water quality will be estimated using different trip prices. The trip prices vary by the opportunity cost of time measure. By placing a dollar value on the improved water quality from the hypothetical addition of restored wetlands, and keeping in mind the value of time, proper policy actions can be implemented. 2

12 Chapter 2 Literature Review Trips are not exchanged in a market and therefore the price of a trip can not be observed from market behavior. Generally there are two costs that must be included in the price of a trip: the opportunity cost of time and the travel cost. To include the opportunity cost of time in the price, a discount factor (k) times the average wage rate times the time spent traveling to the site is added to the travel cost. Different values of k are widely used by different researchers. In addition to different values of k, different travel costs are commonly used. Assumptions made about what should be included in the price and how it is included influence the welfare estimates. Feather and Shaw (1999) used a Random Utility Model (RUM) on survey data collected from the 1994 National Survey of Recreation and the Environment involving 447 individuals participating in river recreation. Through the use of five models using a travel cost of $0.35/mile and different cost of time estimates Feather and Shaw concluded that leisure time has an impact on welfare estimates and that estimates vary with how the cost of the trip is determined. When the value of time was zero and only the travel cost was included in calculating the price of the trip, then the welfare estimates were the lowest with an average of $6.23/trip. With the value of time at 1/3 of the wage rate, the welfare estimates increased to an average of $9.11/trip and at 100% of the wage rate the welfare estimates increased again to an average of 3

13 $16.02/trip. The difference in the estimates partially comes from the inability to assign a value of time to unemployed individuals. Those who are unemployed have a value of time of zero when it is calculated using the wage rate or a fraction of the wage rate. The hedonic wage method assigns a predicted sample mean wage rate to those who do not have a wage. Using this approach, Feather and Shaw found the welfare estimate to be an average of $11.48/trip. Since the hedonic wage method assigns the mean wage to individuals without wages, there is less variation in the wage rate. Feather and Shaw proposed a new method of assigning leisure time cost estimates by using whether individuals are unemployed, underemployed, overemployed or content with their current employment. Feather and Shaw estimated directly the shadow value of leisure time. By focusing on the opportunity cost of leisure time versus the wage rate, both employed and unemployed individuals were assigned a leisure time cost that varied across the sample and was sensitive to labor market positions. With this method they received the second largest welfare estimates of $14.17/trip on average. Lew and Larson (2008) used a telephon -telephone survey of randomly selected households in San Diego County to estimate the value of beach access. A unique opportunity cost of time was estimated for bikers, walkers, and drivers. In addition, drivers were assigned a travel cost of 14.6 cents/mile. Using a repeated nested logit model of participation the compensating variation measure for beach access was $21 $23/day. By studying the hypothetical elimination of fishing resources, Bockstael et al. (1987) found that recreational decisions are sensitive to time considerations. After dividing their sample of southern California sport fishermen by labor market situation and using compensating variation, they found that individuals with fixed work hours would trade time for money at $60/hour and individuals with flexible work hours 4

14 would trade time for money at $17/hour. The higher value placed on time by those who work a fixed work schedule indicates that individuals with fixed schedules are more likely to trade work for leisure. Whitehead et al. (2008) used revealed preference and stated preference data collected from North Carolina beach surveys to calculate the consumer surplus gains from beach access and beach width improvements. The price was calculated using an opportunity cost of time equal to 1/3 of the respondent s average wage rate and a travel cost of $0.37/mile. The results from a random effects Poisson count data model revealed consumer surplus gains of about $25/trip for the improvement in beach access and about $7/trip for the improvement in beach width. Hanley, Bell and Alvarez-Farizo (2003) used a random effects negative binomial panel model to value coastal water quality improvements for swimming waters in Scotland. Using no value for the opportunity cost of time and a travel cost of $0.15/mile, the increase in the consumer surplus from the enhanced water quality was 5.81 pounds per person. Using the exchange rate on April 11, 2009 the consumer surplus estimate in dollars is $8.53/person. By omitting the opportunity cost of time, they acknowledged that the welfare estimate is most likely biased downwards. With data collected from a 1995 telephone survey of eastern North Carolina households, Whitehead, Haab, and Huang (2000) calculated the consumer surplus gain from a quality improvement for the Albemarle Pamlico Sound. The price of recreation demand trips included a travel cost of $0.20/mile and the full inclusion of the respondent s average wage rate. A random effects Poisson model was used to determine that the consumer surplus gain from a quality improvement was $20.85/trip. Poor and Breece (2006) used data collected from a group of charter fishing participants stationed at Solomon s Island, Maryland to calculate welfare gains from a hypothetical water quality improvement at Chesapeake Bay. Through the use of a truncated Poisson count model corrected for endogenous stratification, they found 5

15 the individual consumer surplus from an improvement in the water quality to be $75 per trip when the oppportunity cost of time was 1/4 the average wage rate and the travel cost was $0.34/mile, and $44 per trip when the opportunity cost of time was zero and the travel cost was $0.34/mile. Awondo et al. (2011) used a multivariate Poisson-lognormal model for data collected on-site at Maumee Bay State Park to study the increase in welfare from an increase in water quality. Using vehicle costs of $0.25/mile and an opportunity cost of time equal to 1/3 of the respondent s average wage rate, the average annual willingness to pay for the water quality improvement was $166/person. When the travel cost increased to $0.33/mile the average annual willingness to pay increased to $184.22/person. Palmer (2009) used a count data model to estimate the willingness to pay for wetland restoration at Maumee Bay State Park. The average number of expected trips taken to the site before the quality change was approximately After the proposed improvement to the site, the average number of expected trips increased by 0.62 bringing the total number of trips to approximately 2.5 per year. The increase in consumer surplus from the quality change amounted to $51 (from $154 to $205 after restoration). Shaw and Feather (1999) argued that many recreation demand models are misspecified due to the lack of information about the cost of time. One thing is certain, time is important in the price of a trip. Feather and Shaw argued that asking additional survey questions (pertaining to the individual s value of time) can help lead to a more accurate price and therefore more accurate welfare estimates. 6

16 Chapter 3 Theory There are three types of value an individual can receive from a good: use value, option value, and nonuse value. Use value is the individual s willingness to pay for the direct use of the environmental resource, option value is the individual s willingness to pay for the future ability to use the environmental resource, and nonuse value is the individual s willingness to pay for an environmental resource even though the resource has never and will never be used. The travel cost model is a revealed preference model in which the value of the public good is revealed through an individual s observed behavior. Here the observed behavior is the number of trips taken or the use value of the environmental good. The number of trips taken will vary with an individual s income, quality, and the price of substitute sites. The willingness to pay for the quality improvement to the site can be calculated using the difference in the number of trips taken. The travel cost model can be used to calculate the use value of an environmental resource. At a certain price, which will be called p j (the price of traveling to site j) the individual will take x j number of trips to site j. An individual s total willingness to pay minus the actual price they pay is the consumer surplus they receive from taking the trip. When the quality (q) of the site increases, the number of trips taken will change, which will affect the consumer surplus of the trip. This is also true for 7

17 the individual s income (Y ) and the price of substitute sites (P ). The willingness to pay for the restoration of site j as seen in Figure 3-1 can be calculated by taking the difference between the consumer surplus before the quality change and after the quality change. WTP j = CS(q ) CS(q o ). (3.1) By using the Marshallian use value as if it were the total willingness to pay for a quality change to Maumee Bay State Park, weak complimentarity is assumed, which states that if the private good is not consumed, then the public good is not valued. Relating this to an increase in quality, if zero trips are taken to the park, then there is no extra utility from increases in quality. It is also assumed that the Hicksian use value (from compensated demand functions) is approximately equal to the Marshallian use value (from ordinary demand functions). The basic assumptions of the travel cost model are as follows: time is completely fungible, the price of the trip is utility neutral, no substitutes for the site exist, trips are of equal length, the purpose of trips is for recreation only, and trips to sites cannot be aggregated unless they are identical or nearly so. It is usually reasonable to assume that trips are of equal length so that on-site time can be ignored. The argument can be made that the site is unique, but it is usually not acceptable to assume there are no substitutes for the site and for that reason the price of the next best substitute should be included in the model when possible. There are two types of costs for individual i to travel to site j. First there is the travel cost and second there is the opportunity cost of time. We assume the opportunity cost of time visiting the site is the time the individual could have been working and therefore the price is: 8

18 P ij = C ij + t ij (w ij ). (3.2) Where C ij is the out of pocket cost of individual i to visit site j, t ij is the time that individual i spent traveling to site j, andw ij is the average wage rate of individual i. The average wage rate is the household income divided by 2000 (40 hours/week and 50 weeks/year). The assumption that time is completely fungible is true for few people. Most workers do not control when they work. To control for this extreme assumption a discount factor, (k), is generally included in calculating the price of the trip. The price of the trip becomes: P ij = C ij + t ij (k w ij ). (3.3) C ij represents the direct travel cost and t ij (k w ij ) represents the opportunity cost of time. When k is unknown, a general value is used (generally 1/3). Following Feather and Shaw (1999), the actual opportunity cost of time is calculated by estimating the unique shadow wage (W ) for all respondents equal to their opportunity cost of leisure time. The price of a trip will then become: P ij = C ij + t ij (Wij ). (3.4) The price of a trip affects the number of trips taken. With a different price, the consumer surplus will change, which will impact the willingness to pay for a quality change. As the price increases holding the slope of the demand curve constant, the consumer surplus shrinks, which also decreases the willingness to pay (the difference between the new and old consumer surplus). Variations in willingness to pay estimates are shown in Figure 3-2. Using the method above of assigning a price to trips taken to the wetland requires that both the price and the demand for the good be assigned simultaneously. Given 9

19 the distance the respondent lives from the wetland, allows the usual demand curve to be derived. High price trip takers are those who live further away from the wetland and therefore have to pay more in out of pocket costs (C ij ). As a result of the high price incurred they take less trips to the wetland on average. Low price trip takers pay less in out of pocket costs, and therefore take more trips to the wetland on average. Including the opportunity cost of time reveals that both high price and low price individuals are willing to pay an even larger price to take the given trips, as shown by the increase in price from P 1 to P1 and the increase in price from P 2 to P2. The individual taking X 1 number of trips must travel further to get to the site and therefore must give up more of their time. The individual taking X 2 number of trips travels a shorter distance to get to the site, giving up less of their time, and as a result, the price increase is inproportionate. Figure 3-3 shows that the demand curve becomes more inelastic as the opportunity cost of time is included and as a result the consumer surplus from a quality change increases. The approach for valuing leisure time presented by Feather and Shaw (2000) follows Heckman s model (1974) of estimating the value of time and the potential market wage of nonworking individuals. Both use a standard utility maximization model in which utility from leisure and consumption is maximized subject to both an income and a time constraint. Feather and Shaw s approach adds to Heckman s model the possibility for underemployment or overemployment. In the model, the shadow wage or asking wage function is defined as W = K(h, wh + A, P 1,.,P n ) where K is the shadow wage function, h is the number of hours chosen to work, wh is labor income, A is nonlabor income, and P 1 to P n are the price of market goods. The shadow wage represents the value of an extra unit of free time or what one would need to be paid to give up that hour. Heckman s shadow wage function allows for corner solutions in the labor market allowing an individual to have a shadow wage even if he or she chooses not to work. 10

20 Individuals will choose an optimal amount of work hours h and leisure L that satisfy the time constraint T = L + h. An individual will work if the shadow wage at zero hours is less than the shadow wage at h or w = W h = h >W h =0. Figure 3-4 depicts the case of an individual who chooses to work when they are free to choose their hours of employment. If the shadow wage at zero hours is greater than the wage then the individual will choose not to work (w <W h =0 ). Figure 3-5 shows an individual who chooses not to enter the labor force given free choice of work hours. Heckman assumes that all employed individuals are free to choose their work schedules. However, many jobs have fixed work hours. An individual cannot work more or less even if they wanted to, which leads to underemployment and overemployment. Feather and Shaw (2000) added to the Heckman model by allowing for underemployment and overemployment, but they assumed those who worked a fixed schedule were not free to choose. This paper allows for the possibility that those with a fixed schedule might have chosen the fixed number of hours they work if they were free to choose. Overemployment occurs when the shadow wage of leisure time is greater than the wage, therefore you want to work less than you are currently working, but the wage is more than the shadow wage at zero hours, therefore you are working (W h = 0 <w W h = T L ). Overemployment is shown in Figure 3-6. As shown, the individual can receive more utility from the indifference curve U 2, given the constraint, which would require more leisure and less income. Underemployment occurs when the shadow wage of leisure time is less than the wage rate, therefore you want to work more, but the wage rate is less than the shadow wage at the maximum number of hours allowed in the time constraint, therefore there is a maximum amount of work hours desired (W h = T L <w W h = T ). Underemployment is shown in Figure 3-7. Again the individual can receive more utility given the constraint with 11

21 less leisure and more income, which is shown by the indifference curve U 2. Making accurate measures of the opportunity cost of time is important for revealing accurate willingness to pay estimates. The purpose of calculating the shadow wage or using different values of k is to obtain a value of leisure that reflects the individual s true opportunity cost of time. With the true opportunity cost of time in the price, a more accurate measure for the willingness to pay estimate is achieved, making policy decisions more efficient. 12

22 WTP CS o P jo X j0 X j X (P, q o,y) X (P, q,y) Figure 3-1: When the quality of the site increases, the number of trips taken to the site increases, which is shown by the shift of the demand curve to the right. The willingness to pay for the restoration is the difference in the consumer surplus between the new and old demand curves. 13

23 P j CS o WTP P jo X j0 X (P, q o,y) X j X (P, q,y) Figure 3-2: When the price of the trip increases, holding the slope of the demand curve constant, the consumer surplus shrinks, which is the difference between the benefit from the good (the demand curve) and the price. Since the consumer surplus shrinks, the difference between the new and old consumer surplus also shrinks, which is the willingness to pay. 14

24 P 1 * P 1 CS P 2 * CS o P 2 X(k=0) X(k=1) X 1 X 2 Figure 3-3: Including the opportunity cost of time in the price of the trip, reveals a higher willingness to pay and larger consumer surplus, which is shown from the increase in area CS 0 to area CS.The gain is the result of different travel times. Those who live further away from the site (the person taking X 1 trips), must travel longer giving up more of their time and therefore the price is higher. An increase in k for a high price trip taker will increase the price even more than a low price trip taker (the increase in price from P 1 to P1 is less than the increase in price from P 2 to P2 ). Therefore the demand curve shifts out disproportionately making the demand more inelastic and increasing the consumer surplus. 15

25 Y (Income) U* L* T L (Leisure) Figure 3-4: An individual will choose to work if the shadow wage at zero hours is less than the shadow wage at the optimal amount of work hours, h. The optimal amount of leisure, L,islessthan T which implies that the individual is working (T = h + L) (Feather and Shaw, 2000). 16

26 Y (Income) U* L (Leisure) L* = T Figure 3-5: An individual with free choice of work hours will choose not to work if the shadow wage at zero hours is greater than the wage. The optimal amount of leisure L is equal to T which indicates that h =0(T = h + L) (Feather and Shaw, 2000). 17

27 Y (Income) U2 U* L* T L (Leisure) Figure 3-6: Overemployment occurs when the wage rate is greater than the shadow wage at zero hours of work, but less than or equal to the shadow wage at the desired number or work hours. Given the choice, the individual would have chosen to work less and consume more leisure as shown by the indifference curve U 2 (Feather and Shaw, 2000). 18

28 Y (Income) U2 U* L (Leisure) L* T Figure 3-7: Underemployment occurs when the wage rate is greater than the shadow wage at the desired number of work hours, but less than or equal to the shadow wage at the maximum number of hours allowed in the time constraint. Given the choice, the individual would have chosen to work more and consume less leisure as shown by the indifference curve U 2 (Feather and Shaw, 2000). 19

29 Chapter 4 Data Researchers at the University of Toledo collected the data used for this research project in the summer of ,000 surveys titled The Northwest Ohio Wetlands Survey were randomly mailed to select Northwest Ohio residents. The survey included information about the benefits of wetlands and asked respondents how many trips they took to visit the wetlands of Northwest Ohio in 2007, how long the trips lasted on average, would they answer yes or no to a hypothetical referendum to improve the quality of the water at Maumee Bay State Park, and their demographic information. The numbers of trips collected to Maumee Bay State Park are split into two categories. By asking the respondent how many trips they expect to take to Maumee Bay State Park in 2008, the anticipated number of trips without the quality change is collected. To get the anticipated number of trips with the quality change, the respondents were asked how many additional trips they would take to Maumee Bay State Park in 2008 if the wetlands were restored. The data for calculating the opportunity cost of time was collected in a similar manner discussed in Feather and Shaw (2000). Respondents were first asked for their current employment status. Employed individuals were then asked if the number of hours worked per week were scheduled or if they were free to choose when and how 20

30 long they work. Those with fixed schedules were asked if they would work fewer hours for less income, more hours for more income if they had the opportunity, or the same amount of hours. If respondents answered yes to working more or less they were asked by how many hours per week. Respondents who wanted to work more are considered underemployed, respondents who wanted to work less are considered overemployed, and respondents who would not change their work schedule are considered free to choose their work hours. Summary statistics for the full sample of 895 individuals is included in Table 4.1. The variable etrip is the expected trips to Maumee Bay State Park without the quality improvement and the variable y 2 is the expected trips plus the additional trips with the quality improvement. If additional trips were reported as zero, then y 2 equals the expected trips. As can be seen from the table, the mean of y 2 is greater than the mean of etrip (2.07 > 1.57) which indicates that there is an increase in consumer surplus from the increase in quality. Respondents were dropped if they did not answer expected trips or if no value was created for y 2. The variables gender and school are dummy variables where gender is coded 1 for male and 0 for female and school is coded 1 for some college or greater and 0 for high school graduate or less. Since the mean of these variables is greater than 0.5, the majority of the sample consists of males and individuals with some college experience. The variable hh is the household size, which is created by adding the number of children and adults. On average the household size is Income and age are categorical variables. Respondents were assigned the midpoint of the category they selected. The maximum income assigned was $200,000 and the minimum was $7,500. Missing values were assigned the mean of the responses that were entered. Summary statistics for employment variables are included in Table 4.2. An individual is out of the labor market if they are unemployed, retired, or if they are a student. Underemployed individuals are those who work a fixed schedule and stated 21

31 Table 4.1: 2008 Maumee Bay State Park Survey Summary Statistics Variable Min. Max. Mean Std. Dev. etrip y age gender school hh income they would like to work more hours for more pay and overemployed individuals are those who work a fixed schedule and stated they would like to work less hours for less pay. Individuals who are free to choose stated that they are free to choose their schedule or they stated they work a fixed schedule, but they are happy working the hours they work. As seen from the table, 37% of the sample is out of the labor market, 12% of the sample is underemployed, 8% of the sample is overemployed, and 43% of the sample is free to choose their work hours. Table 4.2: Employment Summary Statistics Variable n Min. Max. Mean Std. Dev. out of the labor market underemployed overemployed free to choose workmore workless optimalhours Of the individuals who are underemployed on average they would like to work hours more per week which is shown by the workmore variable. The workless variable indicates that the overemployed individuals would like to work hours less per week on average. The optimalhours variable is equal to zero for those out 22

32 of the labor market. The optimalhours variable is equal to the number of hours the respondent reported working plus the hours they would like to work more if they are underemployed. It is equal to the number of hours the respondent reported working minus the hours they would like to work less if they are overemployed. Lastly, the optimalhours variable is equal to the number of hours they reported working if they are free to choose their work hours. On average, individuals in the sample would like to work hours after adjusting for underemployment and overemployment. Tables 4.3, 4.4, 4.5, and 4.6 show summary statistics by employment status. As expected, the average number of trips taken by the overemployed is less than the number of trips taken by the underemployed both before and after the quality change (1.08 < 2.06 and 1.63 < 3.11) and the average household income is greater for the overemployed than the underemployed (83, > 66,891.33), which suggests that the overemployed may be more willing to trade income for leisure (additional trips). Those who are free to choose their work schedules have an average household income in between the averages for the underemployed and the overemployed (66, < 81, < 83,519.54) as well as the average number of trips (1.08 < 1.77 < 2.06 and 1.63 < 2.2 < 3.11). Since those who are able to choose their work hours have the value of leisure they desire, we can assume those who are free to choose have the optimal number of trips and household income. Table 4.3: Trips for Those Out of the Labor Market Variable n Min. Max. Mean Std. Dev. etrip y age gender school income hh

33 Individuals out of the labor market have the lowest average household income and take less trips than the underemployed, but more trips than the overemployed. Since the average age of this subgroup is 67.5, this suggests that a large portion of the sample of those out of the labor market is retired and therefore may take fewer trips as a result. Table 4.4: Trips for the Underemployed Variable n Min. Max. Mean Std. Dev. etrip y age gender school income hh With the number of anticipated trips without the quality change, anticipated trips with the quality change, and the price of the trip including the measure of the opportunity cost of time, the welfare estimate can be obtained by taking the difference between the new and the old consumer surplus. Table 4.5: Trips for the Overemployed Variable n Min. Max. Mean Std. Dev. etrip y age gender school income hh

34 Table 4.6: Trips for Those Free to Choose Variable n Min. Max. Mean Std. Dev. etrip y age gender school income hh

35 Chapter 5 Results When calculating the price of the trip, a travel cost of $0.25/mile and different values of k were used to test the sensitivity of the welfare estimate to the opportunity cost of time. In five separate models, every individual was assigned: k = 0 (the travel cost only), k =1/4, k =1/3, k =1/2, and k = 1 (the travel cost plus the average wage rate). Then, in a sixth model, individuals were assigned a value of k based on their employment classification to model different values of leisure time. In the sixth model, k = 1/5 for those out of the labor market, k =1/4 forthe underemployed, k = 1/2 for the overemployed, and k = 1/3 for those with free schedules. Individuals out of the labor market are assigned the smallest k value because they have the most leisure time. The overemployed are assigned a larger k value than the underemployed because the overemployed value leisure time more (they want to work less). Individuals with free schedules are in the middle because they are where they want to be (their value of leisure time is not greater than or less than the overemployed and the underemployed). Table 5.1 (p. 28) displays the results to the bivariate Poisson lognormal (BVPLN) regression where the coefficients to the price without the quality change (β P 1 ), the price with the quality change (β P 2 ), income without the quality change (β i1 ), income with the quality change (β i2 ), age (β a ), age squared (β asq ), school (β s ), household size 26

36 (β hh ), gender (βg), and the variance (σ) all of which help determine the likelihood of taking trips to Maumee Bay State Park. The six models are presented below with the estimates for the coefficients where * denotes significance at the 1% level, ** denotes significance at the 5% level, and the standard errors are given in the parentheses. 27

37 Table 5.1: Results from the bivariate Poisson lognormal (BVPLN) regression. Six models are presented here, with standard errors in parentheses presented below the coefficients estimates. Note that * denotes significance at the 1% level and ** denotes significance at the 5% level. Parameters k=0 k=1/4 k=1/3 k=1/2 k=1 k varies α * 1.43* 1.27* 0.79** * (0.41) (0.37) (0.40) (0.39) (0.37) (0.38) α * 1.68* 1.53* 1.07* 0.88** 1.50* (0.41) (0.37) (0.40) (0.39) (0.36) (0.38) β P * -3.98* -3.60* -2.77* -1.69* -3.56* (0.34) (0.20) (0.17) (0.15) (0.09) (0.17) β P * -3.29* -3.00* -2.30* -1.41* -2.98* (0.30) (0.18) (0.15) (0.13) (0.08) (0.15) β i * 0.93* 1.11* 1.39* 0.95* (0.15) (0.13) (0.12) (0.14) (0.14) (0.13) β i * 0.71* 0.87* 1.12* 0.73* (0.14) (0.12) (0.12) (0.13) (0.14) (0.12) β a ** -2.67** (1.43) (1.39) (1.38) (1.35) (1.33) (1.36) β asq (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) β s 30.86* 20.27** 29.46* 35.87** 34.19* 25.20** (11.74) (9.86) (10.19) (14.80) (11.86) (10.49) β hh (4.29) (3.77) (3.97) (3.91) (3.74) (3.86) β g * 28.33* (11.18) (10.71) (12.06) (10.76) (9.86) (11.83) σ 1.36* 1.37* 1.34* 1.34* 1.37* 1.36* (0.04) (0.04) (0.04) (0.04) (0.04) (0.04) log likelihood The first model (k = 0) has six statistically significant parameters (α 1, α 2, β P 1, β P 2, β s,andσ), the second (k =1/4) and third model (k =1/3) both have nine 28

38 statistically significant parameters (α 1, α 2, β P 1, β P 2, β i1, β i2, β a, β s,andσ), the fourth model (k =1/2) has nine statistically significant parameters (α 1, α 2, β P 1, β P 2, β i1, β i2, β s, β g,andσ), the fifth model (k = 1) has eight statistically significant parameters (α 2, β P 1, β P 2, β i1, β i2, β s, β g,andσ), and the final model (kvaries) has eight statistically significant parameters (α 1, α 2, β P 1, β P 2, β i1, β i2, β s,andσ). Estimates for the price without the quality change, the price with the quality change, and age are negative indicating that the number of trips taken decreases as the price of the trip increases and as age increases. Income without the quality change, income with the quality change, school, and gender have positive estimates indicating that the number of trips taken increases as income increases (normal good), that individuals with higher level of schooling are more likely to take trips, and it is more likely for males to take trips. With a BVPLN model the consumer surplus for access to the site is calculated by the number of trips (x) taken to the site by individual i divided by the negative of the coefficient on the price: CS i = X i / β p. (5.1) To calculate the willingess to pay, the consumer surplus before the quality change is subtracted from the consumer surplus with the quality change: ˆ WTP i =(X 3 (q )/ ˆβ P 3 ) (X 2 (q 0 )/ ˆβ P 2 ). (5.2) Table 5.2 shows the willingess to pay estimates from the six models using different opportunity costs of time. When the value of k was zero, the willingness to pay was the lowest at $14.91 per person per year. The highest willingness to pay estimate occuredwhenthevalueofk was one ($56.42 per person per year). As the value of k increases the welfare estimate increases, just as expected from theory. The welfare 29

39 estimate for kvaries is similar to the welfare estimate for k =1/3 (26.40 per person per year versus per person per year). Table 5.2: WTP Estimates Value of time WTP/person 95% Confidence Intervals k= k=1/ k=1/ k=1/ k= k varies

40 Chapter 6 Conclusions The assumptions made regarding the value of the opportunity cost of time influence the price and therefore the consumer surplus and willingness to pay estimates. As reflected in Table 5.2 the willingess to pay estimate is sensitive to the discount factor, k, included in the price of the trip. As the value of k increases, the willingness to pay for wetland restoration increases. Using a different value of k for subgroups in the sample depending on employment classification, the kvaries scenario, resulted in a willingness to pay estimate similar to the willingness to pay estimate calculated when k was 1/3. The most likely explaination for this occurence is that k =1/3 was assigned to the base (those who are free to choose their work schedules), which makes up roughly 43% of the sample. As a result, the different values of k average out. Future research should include a variety of k values to account for the sensitivity of the willingness to pay estimate to the value of the opportunity cost of time. Values of k between 1/4 and 1/2 are most reasonable. It is not likely that k =1sincetime is not completely fungible and individuals will not keep their full wage rate (taxes). Assuming the drive is not enjoyable, there is a value placed on avoiding travel time which also means it is also not likely that k =0. 31

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