ESSAYS ON DEMAND FOR WATERBASED
RECREATION IN OKLAHOMA
By
PHUMSITH MAHASUWEERACHAI
Bachelor of Economics
Khon Kaen University
Khon Kaen, Thailand
1998
Master of Economics
National Institute of Development Administration
Bangkok, Thailand
2003
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
DOCTOR OF PHILOSOPHY
May, 2010
ii
ESSAYS ON DEMAND FOR WATERBASED
RECREATION IN OKLAHOMA
Dissertation Approved:
Dr. Tracy A. Boyer
Dissertation Adviser
Dr. Larry D. Sanders
Dr. Jayson L. Lusk
Dr. Brian E. Whitacre
Dr. Lowell M. Caneday
Dr. A. Gordon Emslie
Dean of the Graduate College
iii
ACKNOWLEDGMENTS
Finally, my long journey of finishing dissertation becomes true. Many people have
supported me to complete this dissertation. I would like to express my gratitude to these
individuals for their support and assistance. First, there is my mentor who has taught and
guided me how to stay on track for this long journey: I would especially like to gratefully
and sincerely acknowledge my advisor, Dr. Tracy A. Boyer. She has been a strong and
supportive advisor to me throughout my graduate school career. During my journey, the
road is not always smooth. However, her mentorship has guided me how to deal and pass
the challenge times and provided me a well rounded experience consistent my longterm
career goals.
I would like also to thank all of my committee members. Dr. Jason L. Lusk, who
has provided helpful suggestions for the survey design and econometrics techniques used
in this dissertation. Dr. Brian E. Whitacre, who has always stood beside me whenever I
need his help and support. Finally, I would also like to thank Dr. Larry D. Sanders and
Dr. Lowell M. Caneday for practical advice as well as inspiration.
Additionally, I would like to thank the Department of Agricultural Economics,
Oklahoma State University, for giving me a chance to prove myself with this long and
challenging journey. Both the academic and friendship experiences during the time I have
been here were priceless.
iv
I would also gratefully acknowledge the funding support that I have received
while working on this dissertation. In particular, I thank the Oklahoma Water Resource
Board that had provided funding support for this project. In addition, I also thank the
Graduate College, Oklahoma State University that had provided me the fellowship when
I work on my dissertation.
Additionally, I would like to thank my father and mother back in Thailand for
their love. They are my inspiration and their hearts are always with me any time. Finally,
I am thankful for my beloved wife for supporting me every direction I have turned.
Without her support and love, my long journey would have not become true.
v
TABLE OF CONTENTS
Chapter Page
I. INTRODUCTION................................................................................................. 1
Introduction and Problem Statement ...................................................................... 1
Research objectives ................................................................................................. 2
Valuation Environmental and Natural Resources ................................................... 3
Revealed Preference Approach ........................................................................ 4
Travel Cost Method .................................................................................. 4
Discrete Choice: A Stated Preference Approach ............................................. 5
Discrete Choice Method ........................................................................... 5
Combined Revealed and Stated Preference Data .................................................... 7
Data description ...................................................................................................... 8
Revealed preference data ................................................................................. 9
Stated preference data .................................................................................... 10
II. PREDICTIVE ABILITY: CAN WE RELY ON THE COMBINED
REVEALED AND STATED PREFERENCE MODEL TO PREDICT
THE FUTURE BEHAVIOR? ............................................................................ 15
Introduction ........................................................................................................... 15
Data Description ................................................................................................... 18
Revealed Preference Data .............................................................................. 19
Stated Preference Data ................................................................................... 20
Theory and Econometric Models .......................................................................... 21
Predictive Ability Tests......................................................................................... 24
Estimation Results ................................................................................................ 26
Model Performance: Prediction Tests ................................................................... 29
Discussion and Conclusion ................................................................................... 32
III.VALUING LAKE RECREATIONAL DEMAND: THE CASE OF
TWOSTEP APPROACH WITH TAKING INTO ACCOUNT
POTENTIAL LAKE USERS ............................................................................. 40
Introduction ........................................................................................................... 40
Theory Discussion ................................................................................................ 43
Data Description ................................................................................................... 44
Revealed Preference Data .............................................................................. 45
vi
Chapter Page
Stated Preference Data ................................................................................... 45
Empirical Model ................................................................................................... 47
The Site Choice Selection .............................................................................. 47
The Number of Trips Taken Model ............................................................... 49
Welfare Estimation ........................................................................................ 53
Estimation Results ................................................................................................ 55
Welfare Measures ................................................................................................. 61
Conclusions ........................................................................................................... 64
IV.ESTIMATING DEMAND FOR URBAN FISHERIES
MANAGEMENT: AN ILLUSTRATOPM OF CONJOINT
ANALYSIS AS A TOOL FOR FISHERIES MANAGERS ........................... 74
Introduction ........................................................................................................... 74
Methods................................................................................................................. 76
Study site ....................................................................................................... 76
Survey design ................................................................................................. 77
Econometric Model ....................................................................................... 80
Results and Discussion ......................................................................................... 84
Conclusions ........................................................................................................... 91
REFERENCES .............................................................................................................. 101
APPENDICES ............................................................................................................... 115
APPENDIX A. INSTITUTIONAL REVIEW BOARD LETTER ..................... 116
APPENDIX B. FIRST COVER LETTER .......................................................... 117
APPENDIX C. POSCARD REMINDER ........................................................... 119
APPENDIX D. SECOND COVER LETTER .................................................... 120
vii
LIST OF TABLES
Table Page
Table 1.1 Descriptive Statistics of Current and Potential Lake Recreationists ...............12
Table 1.2 Attributes and Level in the Lake Recreation Discrete Choice Survey ............13
Table 2.1 Descriptive Statistics of Attribute Level and Variables Used .........................34
Table 2.2 Parameter Estimates for Unweighted and Weighted Models of
Oklahoma Lake Site Choice Models ...............................................................35
Table 2.3 An Example of Trip Prediction for the Unweighted Model for RP
and SP Holdout Samples ..................................................................................36
Table 2.4 An Example of Trip Prediction for the Weighted Model for RP and
SP Holdout Samples ........................................................................................37
Table 2.5 Results of the Predictive Ability Tests over Thirty Sets of
Unweighted Models and RP and SP Holdout Samples ...................................38
Table 2.6 Results of the Predictive Ability Tests over Thirty Sets of
Weighted Models and RP and SP Holdout Samples ........................................39
Table 3.1 Descriptive Statistics of Attribute Levels and Variables Used ........................67
Table 3.2 First Stage Model Results of FCP and FCO Models .......................................68
Table 3.3 Second Stage Model Results of SCP1, SCP2, and SCO Models ....................69
Table 3.4 Mean PerTrip Welfare Estimate for FCP and FCO Models ...........................70
Table 3.5 Mean Annual Welfare Estimates and Changes in Trips due to
an Increase in 1 Foot of Water Visibility for SCP2 and SCO Models .............71
Table 4.1 Descriptive Statistics of Attribute Level and Angler Respondents
using the ClosetoHomeFishing Ponds in the Oklahoma City Metro
Area (20062008) ..............................................................................................94
Table 4.2 Descriptive Statistics of Attribute Level and Angler Respondents
Using the ClosetoHomeFishing Ponds in the Oklahoma City
Metro Area (20062008) ..................................................................................95
Table 4.3 Conditional Logit Regression Results .............................................................96
Table 4.4 Willingness to Pay (WTP; U.S. $2008) by Management Attribute of
Anglers using the ClosetoHomeFishing Program Ponds in the
Oklahoma City Area (20062008) ....................................................................98
viii
LIST OF FIGURES
Figure Page
Figure 1.1 Example of a Discrete Choice Question ........................................................14
Figure 3.1 Trip Demand for Current Recreationists at Current and Improved
Site’s Quality ................................................................................................72
Figure 3.2 Trip Demand for Potential Recreationists at Current and Improved
Site’s Quality .................................................................................................73
Figure 4.1 Example of a Discrete Choice Set for Management Options used to
Assess Angler Willingness to Pay for Management Options at Closeto
HomeFishing Program Ponds in the Oklahoma City Metro Area
20062008 .....................................................................................................100
1
CHAPTER I
INTRODUCTION
Introduction and Problem Statement
The state of Oklahoma has over 300 lakes, more manmade lakes than any other state,
with over one million surface acres of water (Oklahoma Tourism and Recreation
Department, 2007). Many of lakes serve several uses such as hydroelectric power, flood
control, agriculture, and recreation. Since the mid 1950s, demand for lake recreation in
Oklahoma has increased continuously due to the convenience of transportation,
communication, and other new technology such as types of vehicles, and types of new
watercrafts available to public (Caneday, 2000). The outdoor recreation business was
reported as one of the fastest growing businesses in Oklahoma (Caneday et al., 2007).
Even though the demand for lake recreation in Oklahoma is increasing, few recent studies
have analyzed the demand for lake recreation as well as welfare effects from lake use in
term of recreation. Lenard and Badger (1979) studied about lake recreation in Oklahoma
in 1977. However, this study focused on the business impact of lake recreation only.
Caneday and Jordan (2003) studied the behavior of Oklahomans traveling to state parks,
but they did not estimate demand and economic value for water based amenities such as
quality and quantity or estimate total visitation across all wateroriented recreational
2
activities. Therefore, currently, there is no comprehensive explanation for lake
recreational demand in Oklahoma.
Research objectives
This study proposes to determine the relative value of lake recreation in Oklahoma. The
research performed in this study will focus on answering the following questions, “What
factors influence demand for lake recreation?”, “How do we forecast the number of lake
recreational trips”?, “How much does willingness to pay for recreation change according
to lake quality improvements?”, and “How the potential management changes factors of
ClosetoHome Fishing Program (CTHFP) influence anglers preferences?” Answers to
these questions will help many interested groups to clearly understand what factors
influence lake recreational demand and how this impacts visits to them. In addition, these
findings will help policy makers make more informed decisions regarding the Oklahoma
state water plan and current and future management scenarios for lakes in Oklahoma.
Because of the questions mentioned earlier, this dissertation will be separated into
three papers.1
1. The first paper empirically compares the outofsample predictive ability of
joint revealed preference (RP) and stated preference (SP) model to individual
RP and SP models in case of prediction actual and hypothetical trip numbers
taken by lake recreationists.
2. The second paper estimates the twostep model with combined RP and SP
data to estimate the link between site choice selection and the number of trip
1 The first two papers used the same data set, while the third paper used another data set.
3
taken, which would allow us to determine welfare changes from lakes quality
improvement in term of changes in numbers of trips and per choice occasion.
3. The third paper estimates management of urban recreation use using a discrete
choice experiment.
Valuation Environmental and Natural Resources
Services provided by environmental and natural resources often fall outside of the
market’s pricing system such that they are called nonmarket goods. Markets often
inefficiently allocate environmental and natural resources because their property rights
are not clearly defined. Often actions of private individuals impose external costs upon
others’ use of non market goods in ways for which they are not compensated, something
called a negative externality. In addition, because there is no clear no market system to
value most nonmarket goods, it is difficult to place a value on them and to efficiently
manage them. Because private markets often underprovide public goods or do not
adequately protect them, government agencies often must justify actions to manage
natural resources using costsbenefit analysis. To deal with benefits and costs analysis,
the first step is to measure the benefits of the existence or improvement of a nonmarket
resource, an activity called nonmarket valuation. .
There are a number of methodologies used to value the nonmarket goods. These
methodologies can be classified as revealed preference (RP) approaches and stated
preference (SP) approaches. RP approaches use actual behavioral data to value the nonmarket
goods. Researchers observe individual behavior in response to changes in quantity
and quality of the nonmarket assets, and use this behavior to attempt to value them.
4
Travel cost and hedonic price methods are the common RP methods. Instead of using
behavioral data, SP approaches rely on hypothetical data to value nonmarket goods.
Respondents are directly asked to answer hypothetical questions that model tradeoffs
between changes in their attributes and some monetary measure paid by respondents.
Contingent valuation and discrete choice methods are the example of SP approach. In the
next section, the details of travel cost method and discrete choice method, which are
applied in this study, will be discussed.
Revealed Preference Approach
Travel Cost Method
The travel cost method is the oldest method used to value the environmental and natural
resources (Kjaer, 2005). It has usually been applied for valuing recreational demand such
as hunting, fishing, and forest visitation. The travel cost method is a method that uses
variations in travel costs to a recreational site to estimate the demand for that site.
Specifically, although the experience to visit a recreational site has no market to value its
price, the costs incurred by visitors to visit a site can be used as surrogate values for that
resource. These costs usually include travel costs, entry fees, and time costs. The
rationale behind the travel cost method is that if the price of visit a site (i.e. cost of travel)
increases, the visit rate tends to fall (Hanley and Spash, 1993). By using regression
analysis to estimate the relationship between these two variables, it is possible to
construct the demand curve and hence consumer surplus from visiting particular
recreational site.
5
The travel cost method also assumes that there is the weak complementarity
between the environment goods and consumption expenditure. This can imply that when
consumption expenditure is zero, the marginal utility of environmental goods is also zero.
If fishing trip in Illinois River is too expensive and nobody takes a trip to this river, the
marginal social cost of a decrease in the quality of this river is also zero, for example.
Hence, from this assumption, the travel cost method can only estimate usevalue, but it
cannot estimate nonuse value. This is one of the problems of using travel cost method
for valutation of environmental and natural resources in that cannot estimate the total use
value which includes use and nonuse values. , Nonuse value, refers to the value that
people have (WTP) for specific goods (i.e. rivers, and forest) to keep them available even
though they have never used or plan to use them (Tietenberg and Lewis, 2009). Time
costs are also the vexing problem for the travel cost method. It is difficult to specify what
exactly value of time to individuals for recreational activities. The common approach to
deal with time costs is to value time at fixed percentage of the wage rate. There is,
however, another question of whether just travel time should be included, or whether onsite
time should be included as well (Randall, 1994; Kjaer, 2005). Functional form is also
another concern of the travel cost method. A variety of functional forms has been used
(i.e. linear, loglog, and quadratic) for travel cost model studies. The difference functional
form can produce large changes in consumer’s surplus estimates from a given data set
(Hanley, 1989).
Discrete Choice: A Stated Preference Approach
Discrete Choice Method
6
Choice techniques have been introduced to the marketing field since the early 1970s
(Kjaer, 2005). It is one of several versions of the method known as conjoint analysis in
marketing. Not long after its introduction to marketing field, economists started to apply
this technique to fit with economic theory, known today as random utility theory (Ben
Akiwa, and Lerman, 1985). The development of random utility theory became the
benchmark for the use of choice technique in economics because it provides the linkage
between observed consumer behavior and economic theory (Kjaer, 2005). Because this
technique used in economics form is relied on the random utility theory, the new term
that separates this technique applied in economic field from other fields is “discrete
choice experiment” (DCE) (Ryan and Wordsworth, 2000). This technique was introduced
to the environmental economic literature in the early 1990s (Hanley et al., 2003).
Even though, the DCE technique uses surveys to ask respondents hypothetical
questions such as in the contingent valuation method (CVM), the DCE is able to compare
multiple options with different attributes such that the marginal rate of substitution
between goods is able to be calculated. In a discrete choice experiment, respondents have
choice sets comprised with two or more alternatives, which vary along several
characteristics or attributes of interest, and they are asked to choose one alternative. This
allows the researcher to break down the preferences of respondents by each attribute
instead of just entire products or situations. Another advantage of DCE is that it could
provide more information than CVM by inducing more choices for each respondent. This
would also imply more information about the respondent’s preferences, and hence the
better precision on preferences parameter estimates (Habb and McConnell, 2002).
7
Combined Revealed and Stated Preference Data
As shown in the previous section, travel cost and discrete choice methods represent a
subset of the RP and SP approaches respectively that have been employed to value non
market goods and amenities. In the past, the data from these two approaches are
separately used to estimate the value of non market goods and amenities. However, since
Swait and Louviere (1993) developed the method that allows jointly estimated of
different data sets, much attention has been focused on combining RP and SP data in
order to reduce hypothetical bias which may occur in the latter and improve the accuracy
of valuation estimates.
Functional form problems and variable inclusion, which can create a
multicolinearity problem, are serious concerns in using the travel cost and hedonic price
analysis methods (Azevedo et. al., 2003). Moreover, RP approaches have been based on
real behavioral data. If the quality and quantity change of amenities of nonmarket goods
go beyond the experience of a set of respondents or the variation in the data set, models
that are based on RP data may not correctly value the new environmental quality and
quantity of nonmarket goods. SP approaches avoid these concerns because respondents
may be asked hypothetical questions that are outside the current set of experiences. In
addition, in a discrete choice experiment, the use of factorial statistical designs results in
orthogonal attribute data, which can avoid the multicollinearity problem (Earnhart, 2001).
However, the SP approach has been criticized because it does not rely on actual behavior.
When people answer the hypothetical questions, they may not understand or lack
experience about the things asked in the questions. Furthermore, they may ignore or
downplay their budget constraint when answering the questions (Swait and Louviere,
8
1993; Louviere et al., 2000). These may cause hypothetical bias in the valuation
estimates.
Due to the drawbacks of each approach, economists have begun to combine RP
and SP data. The benefits from combining them are as follows. The SP information could
provide information of consumer preferences which cannot be observed in the market.
Moreover, multicolinearity problems could be reduced by SP data so the attribute effects
that were previously unidentified due to multicolinearity problems can now be identified
(Adamowicz et. al, 1994). And, the estimators from the jointly estimated model still rely
on true parameters because they are also based on real behavior from RP information.
Data description2
Data for papers one and two were collected by mailed survey on Oklahoma Lake Use
(2007) for travel cost and discrete choice experiments. IRB approval was obtained with
approval number AG0734 (the IRB approval letter is in Appendix). Data on travel
distances and lake characteristics were compiled from GIS maps from Oklahoma Water
Resource Board (OWRB), which was created by Caneday and Jordan (2003), lakes
website, and phone interviews with lake managers.
The survey was mailed to 2,000 individuals, who were randomly chosen, in every
county of Oklahoma State during fall 2007. A random sample was obtained from Survey
Sampling Inc, Fairfield CT stratified across 6 regions of Oklahoma. The survey was first
distributed during the last week of September 2007 by mail. Standard Dillman procedures
2 This part provides detail only about the data set used in the first and the second papers. The detail of data
set used in the third paper is provided directly in the third paper.
9
were used to get the highest possible response rate (Dillman, 2000). The letter, postcard
reminder, and follow up letters are provided in Appendix. The survey and cover letter,
which explained the importance and objective of this survey, were mailed to 2,000
recipients. Two weeks after the survey was mailed; the postcard reminder was mailed to
people who had not responded. Then, two weeks later, the follow up survey with cover
letter was mailed individual who had not reply to the survey. Following this method,
from 2,000 surveys, 401 were returned. Thirtynine of them were unusable and allowing
for 150 undeliverable surveys due to no forwarding addresses, the net response rate was
19.57 percent. The descriptive statistics of these respondents are shown in Table 1.1.3
There are two groups of respondents used in this study. The first group is the respondents
who have experienced visiting a lake(s) before. This group is later referred as current lake
recreationists. The second group of respondents has never visited a lake before, but they
answered the discrete choice questions about potential visits. This group of respondents
later is referred to as potential lake recreationists. Since the purpose of this paper was to
combine RP and SP data, the survey was designed to obtain both types of data.
Revealed preference data
Respondents were asked to report their visitation patterns for singleday trips to 144
public lakes in Oklahoma in 2007. They were also asked to report their activities in lakes
as well as features of lakes that are important to them. In order to obtain the effect of
water quality on lake recreation demand, the water quality data were gathered from the
Beneficial Use Monitoring Program (BUMP) database of OWRB. Other amenity data
3 49 respondents who did not answer the discrete choice questions were not used in this study. Therefore,
the total number of respondent used is 313.
10
was collected for each lake including the types and numbers of restrooms, docks,
campsites and boat ramps, etc. These amenity data were collected from the lake websites
and/ or by phone interview. TransCAD software was used to calculate the distance from
each ZIP code to 144 lakes via roads. Then, the distances were expressed as round trip
travel cost, which was combined with outofpocket expenditure and opportunity cost of
time.4
Stated preference data
The survey also solicited SP data. Each respondent faced two discrete choice sets which
presented possible alternative lake recreational opportunities at differing lake amenity
levels and distances. These choice sets were orthogonally designed to estimate the
willingness to pay for quality and amenity improvements at a lake similar to the lake
respondents most often visited (which they indicated in the RP portion of the same
survey). The SP questions elicited lake visitor preferences for lake characteristics,
including availability of lake amenities and distance. Six measurable attributes associated
with lake recreation experiences of either 2 or 6 levels were determined (Table 1.2). This
created 4 3 2 6 2,304 possible combinations. Each combination was then
randomly paired with another combination (Lusk and Norwood, 2005). The third option
was stated as the respondents most frequently visited lake as given in the revealed
preference data.
4
The outofpocket expenditure was estimated by multiplying distance with $0.48/ mile, which was
reported by AAA 2006, and the opportunity cost of time was calculated as one third of an hourly
individual’s wage rate time by travel time, which was assumed speed of 50 mile/hour (Haener et. al., 2001,
and Boxall et. al. 2003).
11
Each respondent was asked to answer two experimental choice questions. Each of
them contains two options of hypothetical lake choice (Figure 1.1). Because some
attributes of the SP question, number of boat ramps, water clarity, and distance, were
asked by increasing in numbers, the information from lakes that were most visited by
each respondent were used as the base information to adjust the levels of those attributes
to be the same as RP data. For example, if Tenkiller Lake was the lake most visited by a
respondent, the number of boat ramps in SP question was added to the actual number of
boat ramps in Tenkiller Lake. Moreover, the SP questions also asked the number of trips
respondents would take given the lake they choose from conjoint choice question. This
would allow us to determine the number of trips they would take under the hypothetical
situation.
12
Table 1.1. Descriptive Statistics of Current and Potential Lake Recreationists
(Percentage by Category)
Variable Current Lake User Potential Lake User
Yearly income
< 20000 8.20% 14.50%
2000039999 26.40% 36.64%
4000059999 21.40% 36.64%
6000099999 29.70% 15.27%
> 100000 14.30% 14.50%
Age
< 26 2.75% 0.76%
2634 10.99% 3.05%
3549 30.22% 19.85%
5059 25.27% 33.59%
> 60 30.77% 42.75%
Education level
< High school 3.29% 2.17%
High school 18.14% 25.83%
Some college/ Vocational school 33.52% 35.01%
College graduate 29.67% 26.51%
Advanced degree 15.38% 10.48%
Gender
Male 68.70% 50.40%
Female 31.30% 49.60%
Number of respondents 182 131
13
Table 1.2. Attributes and Levels in the Lake Recreation Discrete Choice Survey
Attribute Factor Levels
Increase in public boat ramp None
1 Boat ramp
2 Boat ramp
3 Boat ramp
Campsites None
Available
Available with electric service
Public restroom None
Portapotties/ Pit toilets
Restroom with flush toilets
Restroom with flush toilets and showers
Lodge None
Available
Water clarity No improvement
1 foot increase of water visibility dept
from surface
2 foot increase of water visibility dept
from surface
3 foot increase of water visibility dept
from surface
Increase in distance from home 0 miles increase
(oneway) 10 miles increase
20 miles increase
30 miles increase
40 miles increase
50 miles increase
14
Figure 1.1. An Example of a Discrete Choice Question
Compared to the lake you most visit, would you choose a lake such as A or B? Or would
you choose to stay with the one you currently visit, C? Please choose one.
Attribute Option A Option B Option C
Increase in public boat
ramps
2 Boat ramp 1 Boat ramp
NO CHANGE:
I would rather keep
the management of
this lake the way it is
today
Campsites
Available with electric
service
Available with electric
service
Public restrooms
Restroom with flush
toilets and showers
Restroom with flush
toilets and showers
Lodges None Available
Water clarity
1 foot increase of
water visibility dept
from surface
No improvement
Increase in distance
from home (oneway)
20 miles increase 40 miles increase
I would choose (Please
check only one) □ A □ B □ C (I would not
want either A or B)
Given your choice above, how many trips per year would you take?
Number of single day trips □ same number or ___#less or ___# more
15
CHAPTER II
PREDICTIVE ABILITY: CAN WE RELY ON THE COMBINED
REVEALED AND STATED PREFERENCE MODEL TO
PREDICT THE FUTURE BEHAVIOR?
Introduction
The state of Oklahoma has over 300 lakes, more manmade lakes than any other state,
with over one million surface acres of water (Oklahoma Tourism and Recreation
Department, 2007). Many of these lakes are used for several reasons such as
hydroelectric power, flood control, agriculture, and recreation. Some of these water uses
can have either negative effect or positive effect on other uses. Water stored in a reservoir
at a high level, for instance, could provide benefits for hydroelectric power and
recreation; however, it could also reduce the supply of water available for agricultural
activities.
Recent conflict over water use between agricultural and recreational uses during
periods of prolonged drought in Oklahoma has driven home the need for valuation of
nonmarket benefits of the state’s extensive manmade reservoir network for the ongoing
16
state water planning process. Valuing nonmarket goods using revealed preference (RP)
and stated preference (SP) approaches involves tradeoffs in the reliability of the valuation
estimate. The RP approach, which is based on actual behavioral data, is often assumed to
provide a lower bound for willingness to pay (Louviere, Hensher et al., 2000). However,
if the quality and quantity levels of proposed changes in amenities of non market goods
go beyond the experience set of respondents, models based on RP data may not be able to
predict how respondents prefer new management or quality upgrades (Morikawa, 1994;
Hensher et al., 1999; Earnhart, 2001).
The stated preference approach avoids those concerns because researchers can ask
hypothetical questions that contain quality and quantity of amenities outside the current
set of respondents’ experiences. In addition, in choicebased conjoint analysis, thanks to
factorial statistical designs, the attribute level results in orthogonal attribute data, thus
avoiding multicollinearity problems (Earnhart, 2001). However, the SP approach has
been criticized because it does not rely on actual behavior. When people answer the
hypothetical questions, they may not understand or lack experience about the things
being valued or they may ignore their budget constraint when responding to the survey.
These issues may cause bias in the estimators as well as over or under estimates of
welfare. Due to the drawbacks of each approach, combining the RP and SP data could
provide information on consumer preferences which cannot be observed in the market.
Moreover, the attribute effects that were previously unidentified due to multicollinearity
can now be identified (Adamowicz etal., 1994).
As welfare measures estimated by combining RP with SP methods have gained
attention, consistency tests between both data have shown them to yield different results
17
(e.g. Adamowicz et al., 1997; Whitehead et al., 2000; Earnhart, 2001; and Azevedo et al.,
2003). In addition, some studies have focused on the insample tests of predictability to
measure the benefit gained from combining the RP and SP data (e.g. Adamowicz et al.,
1997; Verhoef and Franses, 2003). However, few studies especially in environmental
economics, adopt an outofsample prediction as a test of gains from combining the RP
and SP data. Insample tests of predictability result in two main concerns in the economic
literature. The first concern is that it would not be reliable on unmodelled structural
change. Another concern is data mining, i.e., researchers may search for several
alternative predictive models to find the model that fits well (Lo and MacKinlay, 1990;
Foster et al., 1997). These two problems of insample prediction would lead to
exaggerated predictive ability (West, 1996; Goyal and Welch, 2003). An outofsample
prediction method, on the other hand, could avoid the spurious predictive ability because
its estimated samples are different from the predicted samples, so structural changes that
would not be captured by insample prediction would be captured by outofsample
prediction (Foster et al., 1997). Hence, outofsample prediction would likely to provide a
more accurate test of gains from combining the RP and SP data than by using insample
prediction.
In addition, recent research that tested the predictive ability of joint models in the
environmental economics literature used only RP data as a holdout sample for prediction
of trip numbers (BenAkiva and Morikawa, 1990; Haener et al., 2001). However, to my
knowledge, there is no study that also uses SP data as a holdout sample to predict trip
numbers for testing the accuracy gained from combining RP and SP data. As mentioned
by previous research SP data has provided useful information for prediction beyond the
18
current market features (Louviere et al., 2000; Grijalva et al., 2002; Whitehead, 2005).
Using SP data along with RP data as holdout samples to predict number of trips taken
may provide insight into the predictive performance of the models in terms of actual
behavior and future behavior.
In this paper the data used derives from a statewide survey of Oklahomans about
lake recreation at 144 public lakes conducted in Fall 2007. The survey elicited
information on all public lake trips statewide and also included an orthogonally designed
set of discrete choice experiments to estimate willingness to pay for quality and amenity
improvements at a lake similar to the lake respondents most often visited.
This paper augments the existing knowledge base of methodology for combining
RP and SP data by (1) combining the RP data with SP data to estimate lake recreation
demand, (2) comparing the outofsample predictive ability of the joint model with the
travel cost model and discrete choice model for RP and SP holdout samples.
Furthermore, this study will also examine the determinants of lake visitation in
Oklahoma. These results will be of interest to individuals involved in nonmarket
valuation seeking information regarding which models could give superior explanation
and prediction. In addition, a solid understanding of the factors that affect lake visitation
is of interest to policy makers seeking to improve lakes amenities management to match
with lake visitor’s preference.
Data Description
Data used in this study were collected by a mail survey entitled, “Oklahoma Lake Use”
(2007) for travel cost and discrete choice experiments. Data on travel distances and lake
19
characteristics were compiled from GIS maps from Oklahoma Water Resource Board
(OWRB), which was created by Caneday and Jordan (2003), individual lake websites,
and phone interviews with lake managers.
The survey was mailed to 2,000 individuals, who were randomly chosen, in every
county of Oklahoma State during fall 2007. A random sample was obtained from Survey
Sampling Inc, Fairfield CT stratified across 6 regions of Oklahoma. The survey was first
distributed during the last week of September 2007 by mail. Standard Dillman procedures
were used to get the highest possible response rate (Dillman, 2000). The survey with
cover letter, which explained the importance and objective of this survey, was mailed to
2,000 recipients. Two weeks after the survey was mailed; the postcard reminder was
mailed to people who had not responded. Then, two weeks later, the follow up survey
with cover letter was mailed individuals who had not replied to the survey. As a result,
401 surveys out of 2000 were returned. Two hundred and eighteen of them were unusable
and allowing for 150 undeliverable surveys due to no forwarding addresses, the net
response rate was 10 percent.5 Descriptive statistics of attribute levels and variables used
are given in Table 2.1. Since both revealed and stated preferences data are used, the
survey was designed to obtain both types of data.
Revealed Preference Data
Respondents were asked to report their visitation patterns for singleday trips to 144
public lakes in Oklahoma in 2007. They were also asked to report their activities in lakes
as well as features of lakes that are important to them. In order to obtain the effect of
5 Among 218 unusable surveys, 179 of them are actually completed survey, but these respondents have
never visited a lake before. Since this study focuses on analyzing current lake users, we dropped these
respondents from our sample.
20
water quality on lake recreation demand, water clarity was used as the proxy for water
quality because lake recreationists often identify clear water ashigh quality water as an
indicator of lack of contaminants or pathogens and ecosystem health (David et al., 1991;
Azevedo et al. 2001; Caneday et al., 2001). Furthermore, detailed information on
alternative chemical analysis or indices of water quality was not available statewide.
Water clarity information was gathered from the Beneficial Use Monitoring Program
(BUMP) database of OWRB (Beneficial Use Monitoring Program Report, 2007).6 Other
amenity data were collected for each lake including the types and numbers of restrooms,
docks, campsites and boat ramps, etc. These amenity data were collected from the lake
websites and/ or by phone interview. TransCAD software was used to calculate the
distance from each ZIP code to 144 lakes via roads by assuming that respondents selected
to travel by shortest path (TransCAD, 2008). Then, the distances were expressed as
round trip travel cost, which was combined with outofpocket expenditure and
opportunity cost of time.7
Stated Preference Data
The survey solicited SP data. Each respondent faced two discrete choice sets which
presented possible alternative lake recreational opportunities at differing lake amenity
levels and distance. These choice sets were orthogonally designed with quality and
amenity improvements at a lake similar to the lake respondents most often visited (which
they indicated in the RP portion of the same survey). The SP questions elicited visitors’
6
The water quality data used is secchi disk depth that measures the distance under the surface of the water
at which the disk is no longer visible.
7
The outofpocket expenditure was estimated by multiplying distance with $0.48/ mile, which was
reported by AAA (2006), and the opportunity cost of time was calculated as one third of an hourly
individual’s wage rate time by travel time, which was assumed speed of 50 mile/hour (Haener et al., 2001;
Boxall et al., 2003).
21
preferences for lake characteristics, including availability of lake amenities and distance.
Six measurable attributes associated with lake recreation experiences of either 2 or 6
levels were determined (Table 1.2). This created 4 3 2 6 2,304 possible
combinations. Each combination was then randomly paired with another combination
(Lusk and Norwood, 2005). The third option was stated as the respondent’s most
frequently visited lake as given in the revealed preference data.
Each respondent was asked to answer two experimental choice questions. Each of
them contains two options of hypothetical lakes (Figure 1.1). Because some attributes of
the SP questions such as the number of boat ramps, water clarity, and distance, were
asked as a quality improvement, i.e. an increase in amenities, the information from lakes
that were most visited by each respondent was used as base information to adjust the
levels of those attributes to be the same as RP data. For example, if Tenkiller Lake was
the lake most visited by a respondent, the number of boat ramps in SP question was
added by the actual number of boat ramps in Tenkiller Lake. Moreover, the SP questions
also asked the number of trips respondents would take given the lake they choose from
discrete choice question. This allows us to determine the number of trips they would take
under a hypothetical situation.
Theory and Econometric Models
The conditional logit model is applied to analyze the choice between alternative lakes
sites. The conditional logit model is based on a Random Utility Model (RUM) that
assumes that lake visitors will choose the option (in this case, a lake) that provides them
with the highest utility. However, in reality, the real utility of the respondent could not be
22
specified. Only the indirect utility function of the respondent denoted as can be
observed, and the unobservable part or stochastic component of the utility that is
unknown denoted as . Therefore, the utility can be represented as following
2.1
where is the real utility function. The indirect utility function would be revealed by
either examining the respondent’s actual behavior or the responses to the discrete choice
questions in which the attributes are arguments. Hence, can be expressed as a function
of attributes accompanying each alternative
2.2 ,
where X is the vector of attributes, is a coefficient vector, is alternative specific
constant (ASC), and is an alternative in choice sets . The probability that site will be
visited by a respondent is equal to the probability that the utility gained from selecting
site is greater than that from other sites. Let us assume the distribution of the stochastic
component is independently and identically distributed (IID) according to the Gumbel
random variable, so the probability of choosing choice among those available (1,
2,…, ) can be expressed in closed form as
2.3 Pr
!"#$
% &
Σ%() !"#$
% % % &
where $ is a scale parameter. The scale parameter in case of single set of data could not
be identified, so it is set equal to 1 (Boxall, Englin, and Adamowicz, 2003). From (2.3),
the likelihood functions of individual RP and SP models have the following forms
23
(2.4) RP: *+,   . /
+,012 /
+,
/
+,4+,, +,
,5()6
78
978
/:;
(2.5) SP: *<,   . /
<,
,5()6
=8
9=8
/:;
012 /
<,# /
<,4<,, <,&
where yin 1 if a respondent selects choice , yin = 0 otherwise, 1 represents the index of
respondents from the RP and SP data, 2 /
+,
/
+,4+,, +, and 2 /
<,# /
<,4<,, <,& are
the probabilities of a respondent choosing choice in the RP and SP samples,
respectively.
When jointly estimating models from two or more data sources, the ratio of scale
parameter should be identified. According to Louviere, Hensher, and Swait (2000), the
ratio of scale factor is inversely related to the ratio of variance between two data sets.
This relationship can be shown as follows:
2.6
>+,
?
><,
?
@? 6$+,
⁄ ?
@? 6$<,
⁄ ?
B
$<,
$+,
C
?
,
where >? is variance of each data set. Following Louviere et al. (2000), the likelihood
function of the pooled data is the sum of the conditional log likelihoods of RP and SP
data that is showed as following
2.7 *)+,<,   . /
+,012 /
+,# E
FG4FG, FG&
GHIJK
LM
NLM
E:;
  . /
<,
GHIJKOM
NOM
E:;
012 /
<,# E
PG4PG, PG, $<,&
24
where $<, is the ratio of the scale parameter of SP data to the scale parameter of RP
data.8 Generally, . /
+, and . /
<, are 0 and 1. However, in the RP data for this analysis, each
respondent can visit more than one site in choice set provided in the questionnaire. This
may create an overweighting problem for each RP observation since the SP question is
considered as one choice set and each respondent provides one response in each choice
set. To solve this problem, equation (2.7) is also estimated by weighting the RP log
likelihood function. Instead of coding . /
+, as 0 and 1, it is weighted by trip proportions,
and these proportions also add up to one over each RP choice set (Adamowicz et al.,
1997; Haener et al., 2001). For example, if some respondents visited three different lakes,
those three lakes will be weighted by one third and the rest of lakes are weighted by zero.
In the SP choices, because each SP question is considered as one choice set, . /
<, is still
coded either 0 or 1 over each choice set. By weighting the data in this manner, the RP and
SP observations are given equal weight.
To estimate model parameters, all coefficients of RP and SP are constrained to be
equal and a full information maximum likelihood method will be employed to
simultaneously optimize equation (2.7) with respect to all parameters.
Predictive Ability Tests
To improve the accuracy of predictability tests, the method of Haener et al. (2001) is
applied. Thirty different estimation and holdout samples were randomly drawn from the
data sets. However, in a departure from Haener et al. (2001), instead of randomly
selecting estimation and holdout samples from the RP data only, the SP data also
8
In order to find the relative scale factors, we normalize the inclusive value of parameter associated with
RP data to unity.
25
randomly selected as holdout samples. This way there are two sets of holdout samples,
which are the RP holdout sample, and the SP holdout sample. Each of them is predicted
by RP model, SP model, and a combined RP and SP model.
Various predictive ability tests have been developed to measure the predictive
accuracy of choice models. Some of them are based on an aggregate level test, while
others operate at the individual level. In this study, both the aggregate level test and
individual level test are applied.
The aggregate level test used for measuring the accuracy of outofsample
prediction is the root mean square error (RMSE), which provides an idea of closeness of
the prediction. The formula of RMSE is shown as following:
2.8 RMSE R
1
S

T/ UTV
/ ?
9
/:;
where S is the number of holdout sample, and T/ and TV
/ are the total numbers of
observed trips and predicted trips of individual 1, respectively.
Besides using an aggregate level test, an individual level test is also employed,
which directly compares the individual’s observed and predicted trips. Two individual
level tests are used in this study. The first test is overall correlation coefficient between
actual and predicted trips, W . The second test is the mean of individual correlation
coefficient, developed by Haener, Boxall, and Adamoxicz (2001), which relies on the
individualspecific correlation coefficients between observed and predicted trips. This
test can be presented as follows
2.9 WY
1
S

cov(Z/,,, Z/,[
\var(Z/,, \var(Z/,[
N
E:;
26
where Z/,, and Z/,[ are the vector of predicted and observed trips for individual 1,
respectively.
To estimate the predictive ability test statistics, each set of holdout sample is used
to calculate the vectors of probabilities of choosing lake for each respondent. After that,
individual vectors of probabilities are multiplied by their total trip number to calculate the
vector of predicted trip distribution for each respondent. The individual predicted trip
distributions are used to calculate the overall correlation coefficient and individualspecific
correlation coefficients, equation (2.9). In addition, to calculate the RMSE, the
individual predicted trip distributions are summed across all individuals, and compared to
the aggregate observed trip numbers.
After conducting these statistical tests for each holdout sample, the predictive
ability of each model is ranked in each holdout sample by using 1 for the best prediction
model, 2 for the second best prediction, and 3 for the poorest prediction. Then, these
ranking are averaged for each model to clarify which models provide the best prediction
for RP and SP holdout samples.
Estimation Results
Two sets of models are estimated. Each set contains three different models, which are the
combined RP and SP model (CM model), the RP model (RP model), and the SP model
(SP model). The first set is an unweighted model, for which the RP log likelihood
function is not weighted by trip proportions. The second set is a weighted model, for
which RP and SP choice sets are given equal weight. Thirty different estimations are
estimated from thirty different estimation samples. To simplify the presentation and get
the information about the parameter estimates, the results estimated from entire
27
observation are represented in Table 2.2. Starting with unweighted model, most of
coefficients in these three models are consistent with theory and previous research on
lake recreation. For example, travel costs in those three models are negative, which
implies that given other variables a lake located closer to an individual home has higher
chance to be visited than a lake farther away. In addition, lakes with higher attribute
quantities and quality such as numbers of boat ramp, availability of flush toilets with
shower, and higher water clarity are preferred. For the unique variables of the RP data,
the area attributes reveal that lakes located in Northeast, and Southeast regions are more
preferred to lakes located in Northwest region, while lake recreationists may consider the
quality of lakes located in Southwest region are the same as those located in Northwest
region because its coefficient is not statistically significant. Major lakes, for which the
surface area is more than 5,000 acres, are also preferred by lake recreationists. Generally,
most parameters in the RP and SP models show the similar pattern of preferences across
the attributes, except for the availability of campsite and availability of campsite with
electricity. However, the effect of each attribute is quite different between these two
models. This may imply the differences in the variances of RP and SP data. The RP and
SP data are combined to estimate the CM model. The signs of most coefficients are
consistent with RP and SP models, but the size of some coefficients, travel cost, boat
ramp, and flush toilet, are clearly similar to those from the RP model. The relative scale
parameter that takes into account the differences in variances of RP and SP data is also
statistically significant. In addition, the value of the relative scale parameter is
statistically less than one. This means that the variance of SP data is higher than that from
RP data. However, when the equality between the vectors of RP and SP data after taking
28
into account the scale differences is tested, the test find that the coefficient vectors
between those two data are significantly different (]? 89.38, ^_ 9 .
Turning now to weighted model, this set also contains the RP model, SP model,
and CM models.9 Generally, the pattern of preferences across the attributes is similar as
that estimated by unweighted model. In the RP model, even though, the estimated results
show some different directions of the attributes on preferences when compared to those
in unweighted RP model, the differences among these coefficients are not many;
especially travel cost, boat ramp, flushtoilet with shower, and water clarity. When the
estimated results between the RP and SP models are compared, most coefficients of these
two models have similar patterns of preferences across the attributes. In addition, some
coefficients of these two models are more similar than those estimated by unweighted
model such as travel cost and flushtoilet with shower. In the case of CM model, the
coefficients of travel cost and boat ramp are very similar as those from RP model, which
is the same pattern as unweighted model. For the relative scale parameter, it reveals that
the variances of RP and SP data may be different because it is significantly less than one.
However, the test of equality of parameter vectors of these two data after taking into
account the difference in variances also reveals that the coefficient vectors between RP
and SP data are still significantly different (]? 66.42, ^_ 9 .10
9
The SP model in this set is the same as that in unweighted model because each SP question is still
considered as one choice set.
10
The same test is also conducted when we estimate thirty estimate samples. We found that this test shows
the coefficients vectors of RP and SP data are statistically indifferent for one third of estimate samples,
while we found none in unweighted model.
29
The estimate results of the CM model also show that even when the RP data is
weighted by trip proportion, the pattern of parameter estimates is similar to those from
unweighted model in terms of both sign of coefficients and the effect of each attribute.
This may be due to the fact that on average each respondent visits just about two lakes.
Hence, on average the effect of weighting each RP choice set by trip proportion does not
have much effect on parameter estimation.
Model Performance: Prediction Tests
The results of aggregate actual trip and hypothetical trip predictions of unweighted model
from RP and SP representative holdout samples are represented in Table 2.3. The results
of ten lakes are selected due to space limitations. Starting with the RP holdout sample,
the prediction results show that the CM model and the RP model provide similar
prediction results, and they seem likely to over predict for popular lakes such as Fort
Gibson lake, Hefner lake, and Tenkiller lake. However, for lakes with less than 50 trips
total in the sample, the performances of these two models clearly improve. In case of the
SP model, its prediction performance is generally poorer than that from the CM and the
RP model, especially for lakes with total trip less than 100. Turning now to the SP
holdout sample, in each SP holdout sample, the hypothetical trip numbers are calculated
by summing the total actual trip numbers of the lake most visited by each respondent
with the addition trip numbers specified by each respondent under the hypothetical
scenario. The performances of each model seem likely to be similar for prediction this
holdout sample.
30
For the aggregate actual trip and hypothetical trip predictions of the weighted
model, Table 2.4 reports the prediction results from the same representative holdout
samples as Table 2.3. Generally, the results are similar as those represented in Table 2.3.
The CM and RP models tend to overpredict trips for popular lakes, but they provide
better prediction performances for lakes with total trip numbers less than 50. For the SP
holdout sample, the prediction performances of these three models are similar.
Furthermore, the prediction results of these models seem likely to be better than those
from the unweighted model. However, the predictive ability tests, which are the
aggregate level test and the individual level test, could provide clearer information which
models provide superior prediction than the results of trip predictions reported in Table
2.3 and table 2.4.
The results of predictive ability tests for RP and SP holdout samples of
unweighted models are represented in Table 2.5. Starting with the RP holdout sample, the
RMSE shows that the CM model has the lowest error prediction (69.122), while the SP
model shows poor performance for the actual behavior prediction, resulting in about eight
times higher error predictions than CM model. In addition, the mean rank test clearly
shows that the CM model provides the superior predictive performance for almost all RP
holdout samples. In the same manner for the individual level prediction tests, the overall
correlation coefficient, W , and the individual correlation coefficient, WY, suggest that the
CM model generates the best predictive ability, which results in the highest W (0.094) and
WY (0.220) values. The mean rank also strictly confirms that the CM model clearly
dominates RP and SP models for almost RP holdout samples.
31
In the case of SP holdout sample, the SP model turns to provide the best
prediction performance for aggregate level test (RMSE = 221.734), while the CM model
generates the second best predictive ability for this holdout sample. The mean rank also
shows that the SP model provides the best aggregate level predictive ability among thirty
sets of SP holdout samples. However, the story is totally opposite for individual level
prediction tests. The CM model turns to be the best model in term of predictive
performance for individual level prediction. The CM model generates the highest W and
WY values, which are 0.392 and 0.976, respectively. Furthermore, for the W test, the mean
rank values also show that the CM model dominates the RP and SP models for almost SP
holdout samples. It also completely dominates RP and SP models in every SP holdout
samples for WY test.
The predictive ability tests for the weighted models were also conducted. The
results of these tests are represented in table 2.6. The predictive ability for RP holdout
sample of each model is similar to the unweighted models. Namely, the CM model still
dominates RP and SP models in both aggregate level test and individual level tests. The
aggregate prediction error of CM model is lower than that from other two models. In
addition, the mean rank clearly shows that the CM model provides the most superior
aggregate prediction for almost RP holdout sample. In the case of individual level tests,
the mean rank confirms the individual predictive performance of CM model is preferred
to RP and SP models for both W and WY tests.
The results of predictive ability of these models in terms of forecasting the future
behavior (SP holdout sample) are mixed. The SP model still provides the best aggregate
level prediction in this case, while the prediction performance of CM and RP models are
32
similar. However, the CM model becomes the best model for individual level prediction.
For W test, the CM model provides the highest correlation, and also has the smallest mean
rank. In the similar manner, the CM model completely dominates other models in case of
WY test for all SP holdout sample due to the mean rank result.
Discussion and Conclusion
This study finds interesting results in several ways. First, we expected that if the
likelihood ratio test rejects combining the RP and SP data, the predictive ability of CM
model should be poorer than that from RP and SP models. However, generally, the
predictive ability of the CM model actually outperforms RP and SP models in both RP
and SP holdout samples. In case of RP holdout sample, the CM model provides superior
predictive ability over RP and SP models in both aggregate and individual level tests.
Even though in the case of SP holdout sample, the CM model is not the best model for
aggregate trip prediction, it clearly dominates other models in case of individual level
tests.
In addition, the predictive ability results reveal it is not always true that model
based on actual behavior data would predicts well just actual behavior. It could also
provide superior predictive ability for the future behavior. This is found by the empirical
results from RP and SP models. Given the CM model as the best model for prediction,
the RP model clearly outperforms SP model in almost prediction cases. For the RP
holdout sample, the RP model absolutely dominates the SP model for all tests.
Interestingly, in the case of SP holdout sample, even though the aggregate predictive
33
level of RP model is poorer than that from the SP model, it clearly provides higher
predictive performance than SP model in case of individual level test.
However, this does not mean that we can only rely on the RP model, which relies
only on actual behavior data, to predict recreationists’ behavior due to changes in site
management, because the SP data could also provide useful information beyond the
current market situation, which could improve the reliability of the model predictive
performance. This statement is confirmed by the empirical results that the CM models in
both unweighted and weighted cases generate the best predictive performance over the
RP and SP models individually.
In conclusion, this study investigation about the predictive ability of combined
model’s ability to predict both actual behavior and future behavior sheds light on the fact
that the combined model (CM) provides the most accurate predictive performance over
the individual models. This is due to the fact that the CM model contains both actual
behavior (RP data) and future behavior (SP data) information, which offsets the
weaknesses of prediction by the individual data sets. The changes in lake recreationist’s
behavior due to the future changes of lake management that are not currently available in
the market can be captured by the SP data. In addition, the model’s parameters are not
distorted by hypothetical bias because they still rely on real behavior data (RP data). As a
result, the CM model would be the best model for prediction both actual and future
behavior.
34
Table 2.1 Descriptive Statistics of Attribute Level and Variables Used
Variable Definition Mean
Travel cost U.S dollar (round trip) 182.47
Number of boat ramp 3.27
Availability of campsite
No campsite 1 if no campsite, 0 otherwise 31.57%
Campsite 1 if site has campsite, 0 otherwise 66.22%
Campsite with electricity 1 if site has campsite with electricity, 0 otherwise 57.54%
Availability of restroom
No restroom 1 for no restroom, 0 otherwise 17.35%
Portable toilet 1 if site has portable toilet, 0 otherwise 55.98%
Restroom with flush toilet 1 if site has restroom with flush toilet, 0 otherwise 39.41%
Restroom with flush toilet
and shower
1 if site has restroom with flush toilet with shower,
0 otherwise
49.25%
Lodge 1 if site has lodge, 0 otherwise 7.41%
Water clarity Secchi disk depth measured in foot 2.81
Major lake 1 if major lake, 0 otherwise 15.33%
Lake location
Northeast region 1 if located in Northeast region, 0 otherwise 39.00%
Southeast region 1 if located in Southeast region, 0 otherwise 30.33%
Southwest region 1 if locate in Southwest region, 0 otherwise 13.00%
Northwest region 1 if located in Northwest region, 0 otherwise 18.78%
Note: Region is geographically indicated by bounds of I40 and I35, which divide Oklahoma into four
regions.
35
Table 2.2. Parameter Estimates for Unweighted and Weighted Models of Oklahoma
Lake Site Choice Models
Variable
Unweighted Model Weighted Model
CM RP SP CM RP SP
Travel Cost 0.011***
(0.000)
0.011***
(0.000)
0.017***
(0.000)
0.013***
(0.000)
0.013***
(0.000)
0.017***
(0.000)
Boat Ramp 0.009***
(0.006)
0.009***
(0.009)
0.209**
(0.012)
0.011**
(0.048)
0.010***
(0.009)
0.209**
(0.012)
Campsite 0.024
(0.757)
0.176
(0.503)
0.740***
(0.002)
0.047
(0.593)
0.085
(0.503)
0.740***
(0.002)
Campsite with
Electricity
0.063
(0.401)
0.694
(0.108)
0.904***
(0.000)
0.122
(0.153)
0.660
(0.108)
0.904***
(0.000)
PortaPotties 0.277***
(0.000)
0.076
(0.446)
0.241
(0.440)
0.367***
(0.000)
0.087
(0.446)
0.241
(0.440)
FlushToilet 0.008
(0.909)
0.005
(0.960)
0.933***
(0.000)
0.022
(0.796)
0.077
(0.960)
0.933***
(0.000)
FlushToilet with
Shower
0.321***
(0.001)
1.347***
(0.000)
1.243***
(0.000)
0.267***
(0.007)
1.315***
(0.000)
1.243***
(0.000)
Lodge 0.016
(0.802)
0.444***
(0.001)
0.255
(0.180)
0.001
(0.991)
0.507***
(0.001)
0.255
(0.180)
Water Clarity 0.060***
(0.002)
0.119***
(0.000)
0.171**
(0.045)
0.036
(0.158)
0.116***
(0.000)
0.171**
(0.045)
Major Lake a 1.637***
(0.000)
1.431***
(0.000)
1.836***
(0.000)
1.623***
(0.000)
North East Region 0.505***
(0.009)
0.597***
(0.002)
0.384
(0.207)
0.489***
(0.002)
South East Region 0.352*
(0.085)
0.468**
(0.024)
0.184
(0.568)
0.368**
(0.024)
South West
Region
0.063
(0.781)
0.249
(0.283)
0.344
(0.358)
0.105
(0.283)
SP Intercept b 2.164***
(0.000)
2.164***
(0.000)
Relative Scale
Parameter
0.454***
(0.000)
0.474***
(0.000)
No. of choices 27300 26208 1092 27300 26208 1092
Loglikelihood 2412.958 2040.308 327.953 1086.879 725.711 327.953
Notes: ***, **, and * indicate significant level at 1%, 5%, and 10%, respectively. Numbers in parentheses
are pvalue.
a Lakes with surface area bigger than 5,000 acres are coded to 1 and 0 otherwise.
b This intercept represent a dummy variable that equal 1 for option neither A or B and 0 otherwise.
36
Table 2.3. An Example of Trip Predictions for the Unweighted Models for RP and SP Holdout Samples
RP Holdout Sample
Model Fort Gibson Hefner Tenkiller Hudson Boomer Arcadia Wes Watkins Canton Atoka Broken Bow
Total Predicted Trips
CM 911.8 94.1 180.4 92.9 25.0 31.5 25.2 34.7 3.2 12.3
RP 1329.2 100.3 176.9 82.9 21.6 36.3 23.0 29.2 2.6 26.4
SP 441.9 2.5 23.5 0.9 1.8 31.6 13.1 20.0 0.1 0.9
Total Actual Trips
288 149 57 49 41 35 34 27 22 12
SP Holdout Sample
Model Fort Gibson Eufaula Copan Wes Watkins Canton Hefner Thunderbird Sooner Oologah Okmulgee
Total Predicted Trips
CM 2932.3 615.4 59.5 63.6 32.8 81.6 38.0 15.7 21.2 10.5
RP 2958.8 589.0 43.4 53.8 31.9 60.2 45.3 13.0 16.7 9.3
SP 2540.6 713.4 28.8 49.7 41.3 53.4 50.4 5.7 15.0 7.1
Total Hypothetical Trips
460 136 80 61 40 34 24 20 14 8
37
Table 2.4. An Example of Trip Predictions for the Weighted Models for RP and SP Holdout Samples
RP Holdout Sample
Model Fort Gibson Hefner Tenkiller Hudson Boomer Arcadia Wes Watkins Canton Atoka Broken Bow
Total Predicted Trip
CM 1041.1 80.1 197.3 89.8 21.4 30.2 24.0 49.8 2.4 10.3
RP 1827.6 91.7 207.1 85.4 13.3 32.0 23.9 38.0 2.5 31.0
SP 441.9 2.5 23.5 0.9 1.8 31.6 13.1 20.0 0.1 0.9
Total Actual Trip
288 149 57 49 41 35 34 27 22 12
SP Holdout Sample
Model Fort Gibson Eufaula Copan Wes Watkins Canton Hefner Thunderbird Sooner Oologah Okmulgee
Total Predicted Trip
CM 2928.9 636.6 62.8 62.8 33.8 85.3 38.4 16.3 21.8 10.7
RP 2840.3 603.0 45.8 51.4 32.1 62.7 45.4 12.3 17.0 10.1
SP 2540.6 713.4 28.8 49.7 41.3 53.4 50.4 5.7 15.0 7.1
Total Hypothetical Trip
460 136 80 61 40 34 24 20 14 8
38
Table 2.5. Results of the Predictive Ability Tests over Thirty Sets of Unweighted Models and RP and SP Holdout Samples
RP Holdout Sample SP Holdout Sample
Model RMSE W WY RMSE W WY
Mean Value of Statistics
(MinimumMaximum)
CM 69.122
(45.67593.732)
0.094
(0.0320.168)
0.220
(0.1710.269)
256.538
(77.818438.441)
0.392
(0.1690.816)
0.976
(0.9710.985)
RP 97.939
(67.041151.430)
0.086
(0.0240.162)
0.202
(0.1470.257)
263.683
(71.399461.949)
0.374
(0.1450.726)
0.928
(0.8820.960)
SP 593.277
(44.143732.080)
0.021
(0.0010.194)
0.048
(0.0160.260)
221.734
(44.973398.646)
0.283
(0.1190.587)
0.890
(0.8470.920)
Mean Rank
CM 1.033 1.033 1.033 2.133 1.267 1.000
RP 2.033 2.033 2.033 2.567 1.800 2.100
SP 2.933 2.933 2.933 1.300 2.933 2.900
39
Table 2.6. Results of the Predictive Ability Tests over Thirty Sets of Weighted Models and RP and SP Holdout Samples
RP Holdout Sample SP Holdout Sample
Model RMSE W WY RMSE W WY
Mean Value of Statistics
(MinimumMaximum)
CM 79.390
(51.50499.771)
0.094
(0.0320.164)
0.218
(0.1680.258)
257.407
(80.680441.387)
0.391
(0.1710.808)
0.973
(0.9670.986)
RP 121.966
(83.311180.018)
0.084
(0.0210.151)
0.198
(0.1430.245)
261.970
(71.399449.895)
0.370
(0.1470.740)
0.921
(0.8360.965)
SP 593.277
(44.143732.080)
0.021
(0.0010.194)
0.048
(0.0160.260)
221.734
(44.973398.646)
0.283
(0.1190.587)
0.890
(0.8470.920)
Mean Rank
CM 1.033 1.067 1.067 2.167 1.333 1.000
RP 2.033 2.000 2.000 2.433 1.733 2.200
SP 2.933 2.933 2.933 1.400 2.933 2.800
40
CHAPTER III
VALUING LAKE RECREATIONAL DEMAND: THE CASE OF
TWOSTEP APPROACH WITH TAKING INTO ACCOUNT
POTENTIAL LAKE USERS
Introduction
When people decide to take recreational trips, they consider where they want to go and
how many times to go. In recent years, many studies focusing on recreational demand
have usually applied conditional logit models to study site choice selection. The
conditional logit model explains well which sites will be visited by recreationists, but it
does not explain how many trips will be taken. The latter issue becomes important
because when the quality of amenities in recreational sites changes; both the site selected
and the trip numbers will be affected. Count models, such as poisson and negative
binomial models, can be used to explain changes in the trip numbers due to changes in
destination quality, but they cannot verify the changes in site substitution across
recreational sites. Due to the weakness of these models in terms of inability to explain
changes in trip numbers and site substitution, some researchers have developed linked
41
site selection models to explain the site selection and number of trips taken by
recreationists (Feather et al., 1995; Hausman et al., 1995; Parsons and Kealy, 1995;
Parsons et al., 1999). The linked site selection model is based on a two stage estimation.
The first stage is site allocation model, and the second stage is the trip number model.
The previously mentioned studies of linked site selection models rely on actual behavior,
revealed preferences, using information from individuals who actually participated in
recreational activities. However, no previous studies have accounted for people who may
participate in the future if the quality of recreational sites improves in a way that induces
them to take a visit a site even if they had taken no trips before. Ignoring the recreation of
potential participants may distort the total benefit gained, in terms of per choice occasion
welfare and the number of trips taken, as a result of the quality improvement because the
benefits of some individuals are uncounted.
Combining the revealed preference (RP) and stated preference (SP) data reduces
the bias from missing potential recreationists who opt in because the SP data can ask
hypothetical questions with quality changes to both survey recreational participants or
nonrecreational participants. This allows us to measure the recreation benefits in terms
of increases in numbers of trips taken and per choice occasion with also taking into
account the potential new recreationist enticed by improving site quality. Another benefit
gained by combining the RP and SP data is the reduction in bias in the estimators, which
comes from when respondents are not familiar with the potential site qualities beyond the
current situation from SP questions. This anchors the hypothetical behavior (SP) with
actual behavior (RP).
42
However, the standard error obtained from second stage model does not take into
account error that appears when generating the predictor from first stage model. This
would result in downward biased standard error in the second stage model, which leads to
an incorrect hypothetical test. To deal with this problem, the bootstrap technique is
applied to calculate robust standard errors for the second stage model. Applying this
method using the combined RP and SP data to estimate demand for recreation results in
two benefits. First of all, the benefit gained from quality improvements in terms of
changing the site selection and numbers of trips taken can be calculated while taking into
account potential participants. The second benefit is that the twostep estimation with
standard error correction approach provides corrected standard errors, so reliable
statistical tests can be imposed.
The data used in this study comes from a statewide survey of Oklahoma lake
recreation conducted in Fall 2007. The survey contains both RP and SP data questions.
The discrete choice analysis, SP data, provides information on potential behavior of
increased or decreased visitation due to quality improvements and changes in price.
Because the survey was designed to give visitation changes with potential quality
improvements in the stated preference survey, the two step estimation is possible. By
combining the RP and SP data of both current and potential lake users, this study propose
an estimation method to estimate recreation benefits from site quality improvement that
takes into account site allocation, numbers of trips taken, and potential lake recreationists.
43
Theory Discussion
Consider an individual’s demand, shown by Figure 3.1, to take trips to recreational site ,
1, 2,…, `, which depends on the price and quality of site . Improvement of a site’s
quality leads to a forward shift of demand, resulting in an increase in numbers of trip
taken, given the price constant. From figure 1, when the quality of recreational site is
improved from ab to a;, the individual may decide to take T; trips. c
a; represents the
demand shift resulting from the site’s quality improvement. In this case, the consumer
surplus gained from site’s quality improvement is shown by area d.
In addition, when the site quality is improved, new participants who have never
participated in recreation activity at the original quality level may visit the recreational
site. These individuals are called as potential recreationists.11 This situation can be
represented by figure 3.2. Before the site’s quality improvement, at the price "b the
potential recreationist’s demand for trip is zero. However, after an improvement in the
site’s quality to a;, he or she might decide to take Te; trips, and consumer surplus gained
by this individual is area f.12
From these two figures the total consumer surplus gained from current and
potential lake recreationists is represented by area a plus b. These two figures also
provide the intuition that if the potential recreationists are ignored, the consumer surplus
11 There is another group of individuals who would not participate in recreation at any price or quality.
These individuals do not participate in recreation for reasons such as health and preference, so they do not
receive any consumer surplus (Grogger and Carson, 1991; Haab and McConnell, 1996; Whitehead et al.
2000).
12
We expect that the numbers of trips taken by potential recreationists after a site’s quality improvement
should be less than that of the current users.
44
gained from quality improvement should be downward biased because their benefits
gained are ignored.
Data Description
Data used in this study were collected by a mail survey entitled, “Oklahoma Lake Use”
(2007) which included information to estimate the travel cost method and a discrete
choice experiment. Data on travel distances and lake characteristics were compiled from
GIS maps from Oklahoma Water Resource Board (OWRB), which was created by
Caneday and Jordan (2003), lake websites, and phone interviews with lake managers.
The survey was mailed to 2,000 individuals, who were randomly chosen, in every
county of Oklahoma during fall 2007. A random sample was obtained from Survey
Sampling Inc, Fairfield CT stratified across 6 regions of Oklahoma. The survey was first
distributed during the last week of September 2007 by mail. Standard Dillman procedures
were used to get the highest possible response rate (Dillman, 2000). Two weeks after the
survey was mailed; the postcard reminder was mailed to people who had not responded.
Then, two weeks later, the follow up survey with cover letter was mailed individuals who
had not replied to the survey. As a result, 401 surveys out of 2000 were returned. One
hundred and twenty one of them were incomplete and unusable surveys, and allowing for
150 undeliverable surveys due to no forwarding addresses, the net response rate was
15.14 percent.13 Descriptive statistics of attribute levels and variables used are given in
13
An unusable survey is a survey that the respondents report as never visiting lake before and also selected
choice C (want to do as they stated in RP question) in discrete choice questions indicating no preferences
for change.
45
Table 2.1. Since revealed and stated preferences data are used, the survey was designed
to obtain both types of data.
Revealed Preference Data
Respondents were asked to report their visitation patterns for singleday trips to 144
public lakes in Oklahoma in 2007.14 They were also asked to report their activities at the
lakes, as well as the features of lakes that were important to them. In order to obtain the
effect of water quality on lake recreation demand, water clarity was used as the proxy for
water quality. Water clarity data was gathered from the Beneficial Use Monitoring
Program (BUMP) database of OWRB (Beneficial Use Monitoring Program Report,
2007).1 Other amenity data were collected for each lake including the types and numbers
of restrooms, docks, campsites and boat ramps, etc. These amenity data were collected
from the lake websites and/ or by phone interview. TransCAD software was used to
calculate the distance from each ZIP code to 144 lakes via roads by assuming that
respondents selected to travel by shortest path (TransCAD, 2008). Then, the distances
were expressed as round trip travel cost, which was combined with outofpocket
expenditure and opportunity cost of time.2
Stated Preference Data
The survey solicited SP data. Each respondent faced two discrete choice sets which
presented possible alternative lake recreational opportunities at differing lake amenity
levels and distance. These choice sets were orthogonally designed with quality and
14 The survey also provides choice for people who have never visited lake before. Even though, these
people have never visited lake before, they are also asked to answer the discrete choice questions.
46
amenity improvements at a lake similar to the lake respondents most often visited (which
they indicated in the RP portion of the same survey). The SP questions elicited visitors’
preferences for lake characteristics, including availability of lake amenities and distance.
Six measurable attributes associated with lake recreation experiences of either 2 or 6
levels were determined (Table 1.1). This created 4 3 2 6 2,304 possible
combinations. Each combination was then randomly paired with another combination
(Lusk and Norwood, 2005). The third option was stated as the respondent’s most
frequently visited lake as given in the revealed preference data.
Each respondent was asked to answer two experimental choice questions. Each of
them contains two options of hypothetical lakes (Figure 1.1). Because some attributes of
the SP questions such as the number of boat ramps, water clarity, and distance, were
asked as a quality improvement, i.e. and increase in amenities, the information from lakes
that were most visited by each respondent was used as the base information to adjust the
levels of those attributes to be the same as RP data. For example, if Tenkiller Lake was
the lake most visited by a respondent, the number of boat ramps in SP question was
added by the actual number of boat ramps in Tenkiller Lake. Moreover, the SP questions
also asked the number of trips respondents would take given the lake they choose in the
discrete choice question. This allows us to determine the number of trips they would take
under a hypothetical situation.
47
Empirical Model
The Site Choice Selection
An individual’ decision to visit lakes is modeled using the random utility model. The idea
of random utility model is that an individual would visit lake if his/ her utility gained
from visiting lake is higher than or equal that from either other lakes or not visit any
lakes;
3.1 #g , " & h i#gi , "i &; `
where is the utility of visiting site and i is the utility of visiting any other site in
choice set , which also includes the option to not visit any lakes. Also, g and " are
the vector of lake quality and cost of visiting lake, respectively. Let us assume that the
indirect utility function consists of two components, which are an observed component
( , and an unobserved component ( . The probability of visiting site is
3.2 2W
Pr# h i i; ` &
The observed component would be observed by either respondent’s actual
behavior or from the hypothetical responses in which the attributes are arguments. If the
distribution of the stochastic component is independently and identically distributed (IID)
according to Gumbel random variable, the probability of choosing choice among those
available in choice set can be expressed in closed form as
3.3 2W
exp
$
Σi() exp#$ i&
48
where $ is scale parameter. Commonly, in the case of a single set of data, the scale
parameter cannot be identified, so it is usually set equal to 1. However, for at least two
data sets pooled together, the scale parameter can be identified.
In this study, two data sets, the current lake user data and the potential lake user
data, are pooled together. In addition, each data set also contains two types of data, which
are RP and SP data. Therefore, differences of variances between data sets and also
between types of data are possible. Three scale parameters to capture these differences
are constructed. The first scale parameter calibrates the difference of variances between
the current and potential lake user data by normalizing the scale parameter of current lake
user data to 1. The second scale parameter captures the differences of variances between
RP and SP data of current lake user data set by setting the scale parameter of RP data
equal to 1. The differences between RP and SP data for potential lake user data sets are
also possible, so the third scale parameter is constructed to clarify these differences by
normalizing the scale parameter of RP data to unity. To show how scale parameters are
allowed to vary, the variables for equation (3.3) is rewritten as
3.4 2W/no
exp
$no
Σi() exp#$no i&
Equation (3.4) represents the probability of choosing site of individual 1 for trip
scenarios pY, where p is current lake user data or potential lake user data, and q
represents RP or SP data. The log likelihood function to be maximized then becomes
3.5 * s s 2W/no
/(9 no(<o
49
However, in the current lake user RP data, each respondent can visit more than
one site in each choice set provided in the questionnaire. This may create an
overweighting problem for the RP observations since other RP and SP data are
considered as one choice set and each respondent provides one response in each choice
set. To solve this problem, equation (3.5) is weighted by weighting current lake user RP
data by the trip proportions, and these proportions also add up to one over each RP choice
set (Adamowicz et al., 1997; Haener et al., 2001). For example, if some respondents
visited three different lakes, those three lakes will be weighted by one third and the rest
of lakes are weighted by zero. By weighting the data in this manner, all observations are
given equal weight.
The Number of Trips Taken Model
In addition to the decision to choose lakes to visit, respondents also decide how many
trips they would take given the current and hypothetical lake attribute’s quality. To create
the trip number model and linked site choice selection model, the models in this study is
followed the Hausman et al. (1995). The linkage between the site choice selection model
and trip number model is calculated by dividing expected utility from visiting each lake
(calculated from site choice selection model) by the absolute value of the travel cost
coefficient from the site choice selection model. This variable reflects the per trip
consumer surplus from visiting each lake.15 Later, this variable is called a per trip
consumer surplus.16 17
15
Hausman et al. (1995) claimed that by using the per trip consumer surplus in the secondstage model,
their linked model is theoretical consistency with twostage budgeting process. However, Smith (1997) and
Herriges et al. (1999) argued that this consistency would only hold in cases where extremely assumptions
are maintained. Herriges et al. also suggest that a KuhnTucker model may be better in case of utility
50
The trips to a lake are given as count data, so a count model such as poisson
model or negative binomial model is appropriate. Because each data set for each
respondent contains more than one choice of lake, the random effects model is employed
to take into account the heterogeneity among individuals. Assume that T no/, the number
of trips taken to lake by individual 1 in a particular trip scenario pY, is draw from the
Poisson distribution with mean t no/
3.6 Pr
T no/ u no/
exp
Ut no/ t no/
v5wo6
u no/!
where
u no/ 0, 1, 2,…; p current and potential lake user data;q RP and SP data.
t no/ depends on the per trip consumer surplus, demographics of respondents, and lake
activities and is as follows
3.7 01t no/ 01$ no/ / no/ / / /
no/ is the per trip consumer surplus of individual 1 taking trip to lake in trip
scenario pY; / is a vector of respondents demographics; / is a vector of activities at
lake of individual 1; / is the random effect for individual 1. The variable / allows
trip variation across individuals that cannot be explained by independent variables. The
estimate parameters are , , and . The distribution of trips u no/ can be either poisson
distribution or negative binomial distribution depending on its mean and variance. If
mean and variance are equal, the poisson distribution is appropriate. However, if
consistency but the estimation is difficult, especially in the case of a large number of available recreational
sites.
16
In the Hausman et al. (1995) paper, they reversed sign of this variable to the negative and called it as
price index. However, to prevent confusion, we prefer to use it as the per trip consumer surplus.
17 This consumer surplus is based on the assumption of indifference in Willing bounds, which means that
the areas under Marshallian demand curves are as close of the more exact areas under Hicksian demand
curves (Haab and McConell, 2002).
51
variance exceeds mean, overdispersion, the negative binomial distribution is preferred.
This will be tested in the estimation process.
To combine current and potential lake user data sets, for which each data set
contains RP and SP data, structural changes in trip demand between these data may exist.
Hence, we create dummy variables to account these structural changes. The first dummy
variable, which captures the structural change between current and potential lake users, is
set equal to 1 if the observation comes from potential lake user, and equal to 0 otherwise.
This dummy variable captures the parallel demand shift between current and potential
lake users. In addition to the difference between current and potential lake user data, each
data set also contains RP and SP data, so the structural changes among these data may be
possible. Therefore, another set of dummy variables are created. The first dummy
variable of this set is the SP dummy variable, which is set equal to 1 if the data is SP and
0 otherwise. In addition, the SP data of potential lake user may be different from that of
current lake user. To account for the structural change between these two data, the second
dummy variable of this set is included to the model by interacting the SP dummy variable
with potential lake user dummy variable.
In addition, differences in data sets may also affect the slope of demand for trips.
Hence, each dummy variable is multiplied by the per trip consumer surplus to capture
this effect. The demand for a lake recreation model that allows us to pool the RP and SP
data of current and potential lake recreationists together is derived by adding and
interacting these dummy variables into the mean t no/. The modified trip demand model
can be shown as follows
52
3.8 01t no/ 01$ no/ /
no/ / / ;c; ?c?
c; c?
c; no/
c? no/
c; c? no/ /
where c; and c? are the potential lake user dummy variable and the SP dummy variable,
respectively.
Including these dummy variables with their interaction effects requires us to test
several hypotheses. The first hypothesis to be tested is that if there is no structural change
at all between current lake and potential lake user’s data sets, then ; 0. The
second hypothesis is that it is possible that the structural changes in trip demand are
parallel shifts so that ; 0 and 0. Besides the structural change between current
and potential lake users, it is also possible that the structural changes between RP and SP
data may occur. Hence, the hypothesis ? 0 is also tested for both parallel and
slope changes between RP and SP data. On the same manner, if only the parallel shift
occurs then ? 0 and 0. The final set of hypotheses to be tested is the SP data of
potential lake user. These tests test for the structural changes between entire SP data and
the SP data of potential lake user. If there is no structural change between these two data
sets, 0. If structural change is just parallel shift, then 0 and 0.
However, the standard errors estimated from the second step model, trip taken model, are
incorrect because they do not take into account the errors from first step model, site
choice selection model. Ignoring this problem would result in wrong hypothetical test
results.
Two approaches can deal with this problem of incorrect standard errors in the trip
numbers model. The first is the Full Information Maximum Likelihood (FIML) approach.
53
The second is a twostep approach. The FIML would yield consistent estimators and
asymptotically correct estimates of standard errors for secondstep model, the number of
trips taken model, in this study only if the joint distribution of errors between first and
second steps models is defined correctly. However, previous research shows that
sometime it is difficult to identify the appropriate joint distribution of errors (Hubbell et
al., 2000; Greene, 2003; Starbuck et al., 2004). Twostep approach, on the other hand,
does not require jointdensity function for the errors, and it would also yield the
consistent estimates of secondstep model parameters. However, the standard errors of
the secondstep model are miscalculated because the errors occurred in the firststep
model are not taken into account in the secondstep model. This problem causes incorrect
statistical tests. Murphy and Topel (1985) developed a standard error correction approach
that can provide corrected standard error for secondstep model. However, it is difficult
to implement, especially for panel data models (Martina and Neha, 2007). As shown by
Petrin and Train (2002), Pinar and Train (2003), and Martina and Neha, (2007) a
bootstrap technique can substitute for the MurphyTopel method to correct the standard
errors in the second step model, so this technique is applied to correct the standard error
in the second step model.
Welfare Estimation
From the twostage approach presented above, the welfare changes from lake quality
improvement that take into account per choice welfare change and change in trip
numbers can be calculated. When the quality of a lake is improved, the per trip consumer
surplus, which is measured from the site choice selection model, for each lake also
changes. Since the consumer surplus reveals the per choice (also per trip) welfare
54
changes due to the quality improvement, it also impacts the number of trips taken,
changes in consumer surplus calculated from the difference of trip taken before and after
quality improvement could reflect the welfare changes that account for per trip welfare
and number of trip taken changes (Hausman et al. 1995; Parsons et al. 1999). The
measurement of this welfare change can be represented as follows18
3. 9 Δ exp
Z
)<
)<
/ ^
;
T; U Tb
where Z is the vector of variables in the number of trip model, shown in equation (3.8);
; and b are the consumer surplus after and before lake quality improvement,
respectively. T; and Tb are the predicted trip numbers after and before lake quality
improvement, respectively.19
In addition to make this welfare calculation results strong, welfare analysis
proposed by Bockstael et al. (1987) is also applied, which can be employed with the twostage
model presented above (Parsons et al., 1999).20 This welfare analysis starts with
calculating per trip welfare changes measured from site choice selection model, which
can be shown as follows21
18
This welfare measurement is based on the assumption of small income effect, which makes the Hicksian
demand function for trips is approximately the same as the Marshallian demand function represented by
equation (3.8) (Hausman et al. 1995).
19 In case of potential lake user, the predicted trip number before lake quality improvement, Tb, is set to
zero.
20
They found that the welfares estimated from Hausman et al. (1995) and Bockstael et al. (1987) methods
were similar.
21
This formulation assumes the marginal utility of income is constant, so the Marshallian demand is
approximately equal to the Hicksian demand.
55
3.10 Δ , U
1
; U b
where is the coefficient of travel cost from site choice selection model and ; and b
are the expected maximum utilities after and before lake quality changes, which are also
calculated from site choice selection model.
Equation (3.10) is then multiplied by the average of predicted trip numbers before
and after lake quality improvement, which are estimated from the count model, equation
(3.8). The welfare change that include changes of per choice occasion welfare and
number of trips is
3.11 Δ ,
T; Tb
2
Δ ,
To compare the welfare measurement between the combined RP and SP model
that includes both current and potential lake users and the combined RP and SP model
using only current lake users, the set of combined current lake user RP and SP models are
also employed. For this case, the first stage model contains only the relative scale
parameter between RP and SP current lake user data. In addition, only the current lake
user RP/SP dummy variable and its interaction with consumer surplus shown in (3.8) are
included in the second stage model.
Estimation Results
The first stage estimation results are shown in Table 3.2. The FCP model is the first stage
model of the combining current and potential lake user case, while the FCO is the first
stage model of the current lake user only case. Starting with the FCP model, most of
56
coefficients in this model are consistent with theory and previous lake recreation studies.
Lakes located closer to an individual’s home have a higher chance of being visited than
those further away. In addition, lakes with higher quantity amenities such as numbers of
boat ramps, availability of flush toilets and flush toilets with showers seems to attract
lake recreationists more than those with fewer of these amenities. Lakes with higher
water clarity are also preferred by lake recreationists. For the unique variables of the RP
data, the variable, type of lake, reveals that major lakes, which have water surface area
more than 5,000 acres, are also preferred by lake users. However, the comparison
between regional variables and the no visits to lake(s) option, which is selected by all
potential lake recreationists in RP question, reveals the “no visit” option provides higher
utility than visiting a lake option represented by the lake region locations. This surprise
result is shown by the negative sign and significant level of North East (NE), South East
(SE), South West (SW), and North West (NW) variables. It may be due to the fact that
the no visit choice is uniformly chosen by all potential lake users, while the region
variables, specified by lake locations, are not uniformly selected by current lake
recreationists. This may result in insignificant impact of region factor on choosing lake to
visit, shown by similar coefficient values of each region variable. This will be
investigated in the first stage model of the current lake user only case (FCO model).
To combine the RP and SP data from current lake user and potential lake user, the
relative scale parameters that take into account the differences in variances of these data
are estimated. Sigma1 represents the relative scale parameter of current lake user data and
potential lake user data, while Sigma2 and Sigma3 represent the relative scale parameters
of RP and SP data of current lake user and potential lake user, respectively. The estimate
57
results confirm the differences in variances of these data sets due to the statistical
significance of the coefficients on Sigma1, Sigma2, and Sigma3.22
Turning now to the FCO model, generally the pattern of preference across
attributes of FCO model is similar as that estimated by FCP model. Namely, most of
coefficients have the same signs and are also significant like the FCP model. However,
the size of coefficients in FCO model is generally bigger than those obtained from FCP
model. This could imply that the current lake users may be more sensitive to changes in
lake attributes than potential lake users. Because the FCO model contains only RP and SP
data of current lake users, only one relative scale parameter is estimated. The value of the
relative scale parameter in this case is also statistically significant, which confirms the
difference in variances of current lake user RP and SP data.23 Because this model
contains only data from current lake user, the NE, SE, and SW locations are compared to
the NW location. The result is interested, which is no regional variables are statistical
significant. This confirms the expectation in FCP model that region factor may not be the
key factor for current lake recreationists to make their visiting decision.
After estimating the first stage models, then using each respondent origin with
current lake condition (RP data) and hypothetical lake condition in discrete choice
question (SP data), the per trip consumer surplus for each lake obtained by each
respondent is computed. This per trip consumer surplus is used as a linkage variable
between site choice selection model and the number of trips taken model. Other
22
We also test for the equality of parameter vectors of these data sets after taking into account the relative
scale parameters. The test reveals that the coefficient vectors among these data sets are significantly
different
]? 130.587, ^_ 9 .
23 We also conduct the same test as we did for the FCP model. Similarly, the test reveals that the coefficient
vectors between RP and SP data of current lake user are significantly different
]? 25.477, ^_ 9 .
58
explanatory variables included in the random effects negative binomial model are the
activity engaged in at the lake, income, and dummy variables that capture the structural
changes among these data sets.24
Table 3.3 represents the estimation results of number of trip taken models for both
combining current and potential lake users and only current lake user data sets. Starting at
the combined current and potential lake user data set, two models are estimated, SCP1
and SCP2. The SCP1 is the most general model, in which the intercepts and slopes of
demand for trip are allowed to vary across current and potential lake users as well as their
RP and SP versions. The coefficient of per trip consumer surplus has the expected sign
and is statistically significant.
Only fishing, swimming, and picnicking activities seem to have significant
impact on the numbers of trip taken, while other activities reported in the table may have
no effect on the numbers of trip taken.25 Only individuals who have annual income higher
than $60,000 tend to significantly take more trip than those who have annual income less
than $60,000.
Then to test whether the current and potential lake user’s data represent the same
underlying behavior, the hypothesis that ; ? 0 is tested. The test reveals that these
coefficients are jointly significantly different from zero
]? 46.25, ^_ 2),
suggesting that the trip demand of potential lake users is different from that of current
lake user. However, individual tests show that the structural change may be just parallel
24
We run descriptive statistics to check whether the mean and variance are equal. The descriptive statistics
clearly present that variance exceeds mean, so the random effect negative binomial is preferred for our
data.
25
Activities in lakes reported in the table are compared to other activities.
59
shift only due to the statistically insignificance of ?. As expected, due to the negative
sign of ;, at the same level of lake quality, potential lake users seem likely to take fewer
trips than current lake users. A similar test between RP and SP data sets is also
conducted. This test tests whether the SP data represent the same trip demand model as
the RP data, 0. The result is also similar to the previous test. Namely, the joint
test reveals the structural change between these two data sets
]? 90.84, ^_ 2 , and
both and are individually statistically significant, indicating that both intercept and
slope structural changes may exist between RP and SP data. The final test conducted for
this model is whether the trip demand model of SP data of potential lake user is different
from that of entire SP data. This test tests whether 0. Similar to the previous
tests, this joint test shows that the structural changes of SP data of potential lake user
may also occur
]? 6.50, ^_ 2 . However, this structural change may be just a
parallel shift only thanks to insignificant of .
Based on these test results, a model without interaction between Pot_ dummy and
Cons surplus and between Pot_dummy*SP dummy and Cons surplus is estimated.
However, the entire SP trip demand is allowed to shift and change shape with the
interaction variable. This model is shown as SCP2 in Table 3.3. In addition, all
coefficients of these variables, which capture the differences among trip demand behavior
of current and potential lake users, are statistically significant. As expected, the
coefficient of Pot_ dummy is still negative as in SCP1 model, indicating that potential
lake user would take fewer trips than current lake user given the same lake quality. The
SP dummy and Pot_dummy*SP dummy variables indicate similar behavior of current and
potential lake users. These variables show that current and potential lake users tend to
60
take more trips when they answer the SP question. This is not surprise results because
choices in the SP question have at least one lake’s amenity improved from its current
condition.
From the significance of these variables, the current and potential lake user’s data,
which each contains RP and SP data, can be combined after the structural changes
between them are calibrated. For other variables, as can be seen, most of their signs and
statistical significance change only slightly when compared to the SCP1 model.
Therefore, the estimated results of this model are not discussed again.
To compare the welfare changes from improving lake quality improvement, a
demand for trip model with current lake users only is also estimated. The estimation
result of this model is represented by SCO column in Table 3.3. Most of coefficients have
similar pattern as those from SCP2 model. However, the size of coefficient is generally
larger than those obtained from SCP2 model. The coefficient of Cons surplus variable,
for example, is 0.011, which is significantly larger than that of SCP2 model, 0.005. This
confirms that the difference in trip demands between current and potential lake users
exists. In addition,a joint test result clearly indicates the difference underlying behavior
between RP and SP data of current lake user
]? 1450.99, ^_ 2 . Individual level
tests also confirm the parallel shift and slope change of SP behavior of current lake user.
From the SCP2 and SCO models results, the demand for trips is different among
current and potential lake users and also for their RP and SP data. The changes in demand
for trips are mixed. The demand for trips changes in both parallel shift and slope change
for current lake user, while only parallel shift exists for the potential lake user.
61
Welfare Measures
After having the estimates results from both site choice selection model and numbers of
trip taken model, these results is used to calculate the welfare changes due to an increase
in 1 foot of water clarity. Two sets of welfare changes are estimated. The first set is the
mean per trip welfare, which is calculated from the site choice model. The second set is
the annual welfare, which is calculated from the trip demand model. Starting with the
mean per trip welfare, Table 3.4 contains two sets of results, the combined current and
potential lake users and current lake user only. In addition, each set has the welfare
measures for two conditions; current lake condition and an increase in 1 foot of water
clarity. The sample mean of lake condition is used to calculate welfare estimates in case
of current lake condition. For an increase in 1 foot of water clarity case, water clarity
attribute is increased to1 foot above the current mean value, while other attributes are the
same as current lake conditions. The differences in welfare estimates between minor lake
and major lake are also allowed. The results clearly show that the per trip welfare
estimates from a model that combines current and potential lake users are significantly
larger than those from current lake users only. As expected, major lake is valued higher
than minor lake in both cases. In addition, improving water clarity by an increase in 1
foot of water visibility would increase per trip (per choice) welfare about $10 to $13 per
trip ($2007 USD).
Turning now to the annual welfare estimates, to calculate the annual welfare
changes from an increase in 1 foot of water clarity for these two data sets, the means per
trip consumer surplus in Table 3.4 are plugged in to the SCP2 and SCO model to
62
calculate the predicted trip numbers of current water clarity and improving water clarity
conditions.
These results are represented by Table 3.5. Starting with the SCP2 model, there
are two sets of predicted trips number for improving water clarity, which are the
predicted trip numbers of current and potential lake users. Each set also contains minor
and major lakes predicted trip numbers. The predicted trip numbers of current lake user
are predicted using per trip consumer surplus of an increase in 1 foot of water clarity and
per trip consumer surplus of current water clarity. When the water clarity is improved by
1 foot of water visibility, the predicted trip numbers of minor and major lakes are 2.495
and 5.805, respectively. In case of current water clarity, the predicted trip numbers of
minor and major are 2.372 and 5.518. This results in 0.123 and 0.287 increase in trip
numbers for minor and major lakes of current lake user due to an increase in 1 foot of
water clarity. These changes of trip numbers are then used to calculate the annual welfare
changes due to an increase in water clarity. The HLM is the Hausman et al. (1995)
welfare measure shown in equation 3.9, while BHK is the Bockstael et al. (1987) welfare
measure represented in equation 3.11. For the minor lake, the HLM and BHK give very
similar results of annual welfare changes, which is about $25. Similarly, these two
welfare measures techniques also provide almost the same results for major lake, which
yields an increase in annual welfare about $58. The similarity of welfare results
calculated from these two techniques was also found by Parson et al. (1999).
In case of potential lake user, because they have not had experience visiting these
lakes before and this information was not shown in the survey, so we assume that types
of lake would not affect their visiting decision. From this reason, the predicted trip
63
numbers of minor and major lakes for potential lake user are restricted the same by
dropping the coefficient of major lake out from trip calculation. The predicted trip
number of potential lake users is then calculated by using the same per trip consumer
surplus as current lake user case, but calibrating the predicted trip number by the
coefficient of Pot_ dummy variable, ;. This ends up with the trip number about 0.378
for potential lake user after the water quality improved by 1 foot increase of water
visibility. Because the trip numbers at current water clarity is zero for potential lake user,
this predicted trip number is used as the change in trip numbers. In contrast to the current
lake user’s case, the HLM and BHK techniques provide significant different welfare
change results. The annual welfare change from HLM technique is about $77, while that
from BHK technique is just $4.
Changes in trip numbers and annual welfare by using only current lake
recreationist data are also calculated. The model used to estimate trip numbers in this
case is SCO model. The pattern to estimate the predicted trip numbers is similar as that
from the combined current and potential lake user’s case. Namely, the per trip consumer
surplus of an increase in 1 foot of water clarity and current water clarity are calculated
from the FCO model. These two consumer surpluses then are included in the SCO model
to calculate the predicted trip number after and before the water clarity change. The
predicted trip numbers in case of an increase in 1 foot of water clarity are 0.127 for minor
lake and 0.301 for major lake. The final trip calculation of SCO model is the predicted
trip for current water clarity. The predicted trip numbers are 0.114 and 0.270 for minor
and major lakes, respectively. Then these predicted trip numbers are used to calculate the
seasonal welfare changes by HLM and BHK techniques. The results are surprising in
64
which the welfare changes are very small in both techniques, which are about $1 and $3
for minor and major lakes. This may be due to the small amount of consumer surplus
generated from the first stage model, which results in the very small predicted trip
numbers as well as their changes after the lake clarity improvement.
As expected, per trip and annual welfares calculated from the combined current
and potential lake recreationist’s model are generally larger than those from current lake
recreationist model. Per trip welfares calculated from the combined model are generally
almost three times larger than those from the current lake user model. Similarly, the
combined model also significantly generates larger annual welfare changes than those
from the current lake user model, even in case of potential lake users. In addition, the
most important benefit of the combined model may be the fact that it can capture the
welfare gained from the potential lake user after the lake water clarity improvement. This
would prevent the downward bias of the total welfare estimation due to ignoring the
benefit gained of potential lake users who could become participants when the lake
quality is improved. However, the potential lake user’s welfare estimates could be biased
in either downward or upward directions if the potential lake users do not react to quality
improvement as they state in survey questions.
Conclusions
This paper shows how the current and potential lake user’s data, which each contains
revealed and stated preferences data, can be combined to use in the linked site choice
model, which could measure the annual welfare changes due to changes in recreational
site amenities. The stated preference data allows estimating welfare changes beyond the
range of historical and current quality variation. This study also states that new lake users
65
attracted by improving in lake quality should be included in estimating recreation
demands because some nonparticipants could become participants when the higher lake
quality is introduced. Failure to include participants who become participants after the
site quality improves results in biases in welfare estimation.
The empirical models suggest that structural change between current and potential
lake user for trip demand exists. In addition, the structural change of trip demand also
occurs among revealed and stated preference data of current and potential lake users. A
significant shift and change in the shape of trip demand occurs for the current lake user,
while only a significant shift in demand for trips exists for potential lake user. In addition
to compare the annual welfare changes due to the lake quality improvement, the linked
site choice selection model with current lake user data only is also estimated. The
empirical results are similar as those from the combined current and potential lake user
model in which the demand for trip shifts and changes in shape between RP and SP data.
These models then are used to calculate the welfare changes due to an increase of
1 foot of water clarity. The annual welfare changes calculated from the combined model
are significantly larger than those obtained from the current lake user model even in case
of potential lake user. In addition, the combined model can also capture the annual
welfare change from the potential lake user, which cannot be generated by the current
lake user model. This would be the most benefit generated by the combined model and
this also shows that ignoring potential participants results in a downward bias of annual
welfare measures because the benefits gained by potential participants are ignored.
66
In term of policy implications, only an increase in 1 foot of water visibility may
not be enough to attract Oklahoman potential lake users to take trips to lakes because the
predicted trip number from this improvement is actually lower than 1. To attract them, an
increase in water clarity more than 1 foot and/ or improvement of other lake amenities
such as restroom with flush toilet and shower might entice potential lake users to
participate in lakebased recreation activities.
Even though, the model could verify the behavior of potential lake user as well as
their welfare changes due to lake quality improvement, to predict their trip numbers and
calculate the welfare changes, this study assume that the potential lake users would
behave as they answer in the survey questions when the lake quality is improved. The
welfare estimates from this study could be biased in either downward or upward
directions if the potential lake users do not react to quality improvement as they state in
survey questions, i.e. there is hypothetical bias. Therefore, future research should
investigate this issue (Norwood et al., 2007). One way to do is to collect data from these
participants by stated preference questions with predictable quality changes. Then
collecting the revealed behavior of these participants again after the quality changes
happen. A comparison of stated behavior before the quality change with revealed
behavior after the quality change would provide some evidence whether potential lake
users really react to the site quality changes as they state in the survey.
67
Table 3.1 Descriptive Statistics of Attribute Level and Variables Used
Variable Definition Mean
Travel cost U.S dollar (round trip) 177.94
Number of boat ramp 3.31
Availability of campsite
No campsite 1 if no campsite, 0 otherwise 31.36%
Campsite 1 if site has campsite, 0 otherwise 65.92%
Campsite with electricity 1 if site has campsite with electricity, 0 otherwise 57.25%
Availability of restroom
No restroom 1 for no restroom, 0 otherwise 17.23%
Portable toilets 1 if site has portapotties toilet, 0 otherwise 55.94%
Restroom with flush toilet
1 if site has restroom with flush toilet, 0
otherwise 39.40%
Restroom with flush toilet
and shower
1 if site has restroom with flush toilet with
shower, 0 otherwise
49.06%
Lodge 1 if site has a lodge, 0 otherwise 7.41%
Water clarity Secchi disk depth measured in foot 2.75
Major lake 1 if major lake, 0 otherwise 15.27%
Lake location
Northeast region 1 if located in Northeast region, 0 otherwise 37.84%
Southeast region 1 if located in Southeast region, 0 otherwise 29.21%
Southwest region 1 if located in Southwest region, 0 otherwise 11.95%
Northwest region 1 if located in Northwest region, 0 otherwise 16.60%
Consumer surplus 622.16
Activity in lake
Fishing 1 if fishing, 0 otherwise 57.54%
Boating 1 if boating, 0 otherwise 46.40%
Sightseeing 1 if sightseeing, 0 otherwise 41.82%
Picnicking 1 if picnicking, 0 otherwise 43.18%
Swimming 1 if swimming, 0 otherwise 42.42%
Yearly Income
< 20000 1 if yearly income less than 20000, 0 otherwise 8.23%
2000039999 1 if yearly income between 2000039999, 0
otherwise
29.30%
4000059999 1 if yearly income between 4000059999, 0
otherwise
21.08%
6000099999 1 if yearly income between 6000099999, 0
otherwise
25.73%
> 100000 1 if yearly income higher than 100000, 0
otherwise
15.65%
Potential lake user 1 if potential lake user, 0 otherwise 41.85%
Note: Region is geographically indicated by bounds of I40 and I35, which divide Oklahoma into four
regions.
68
Table 3.2. First Stage Model Results of FCP and FCO Models
Variable FCP FCO
Travel cost 0.005***
(0.001)
0.012***
(0.001)
Boat ramp 0.006
(0.004)
0.012**
(0.005)
Campsite 0.179***
(0.048)
0.166
(0.108)
Campsite with electric 0.181***
(0.047)
0.281***
(0.106)
Portapotties 0.022
(0.053)
0.213*
(0.114)
Restroom with flush toilet 0.261***
(0.052)
0.191*
(0.102)
Restroom with flush toilet and shower 0.343***
(0.060)
0.495***
(0.124)
Lodge 0.012*
(0.006)
0.195*
(0.100)
Water clarity 0.054***
(0.016)
0.128***
(0.031)
Major lake 1.141***
(0.124)
1.554***
(0.175)
NE 3.160***
(0.228)
0.438
(0.311)
SE 3.434***
(0.253)
0.226
(0.331)
SW 3.333***
(0.258)
0.385
(0.396)
NW 3.771***
(0.298)
SP ASC 0.351***
(0.066)
0.680***
(0.150)
Sigma1 0.309***
(0.030)
Sigma2 0.236***
(0.038)
0.544***
(0.094)
Sigma3 0.918***
(0.233)
Log likelihood 1387.762 1030.523
No. of Observation 42178 26400
Note: *** and * indicate significant level at 1% and 10%, respectively. Sigma1 refers to the relative scale
parameter of current and potential lake user data. Sigma2 refers to the relative scale parameter of RP and
SP data of current lake users. Sigma3 refers to the relative scale parameter of RP and SP data of potential
lake users.
69
Table 3.3. Second Stage Model Results of SCP1, SCP2, and SCO Models
Variable SCP1 SCP2 SCO
Cons surplus 0.005***
(0.000)
0.005***
(0.000)
0.011***
(0.001)
Activities in lake
Fishing 0.179***
(0.064)
0.176***
(0.064)
0.242***
(0.075)
Boating 0.054
(0.058)
0.053
(0.059)
0.093
(0.069)
Sightseeing 0.090
(0.059)
0.090
(0.059)
0.099
(0.069)
Picnicking 0.119**
(0.060)
0.117*
(0.060)
0.010
(0.072)
Swimming 0.113*
(0.065)
0.112*
(0.065)
0.049
(0.073)
Income
2000039999 0.031
(0.103)
0.028
(0.104)
0.012
(0.137)
400059999 0.120
(0.111)
0.118
(0.111)
0.143
(0.139)
6000099999 0.313***
(0.111)
0.309***
(0.112)
0.396**
(0.134)
> 100000 0.344***
(0.126)
0.345***
(0.126)
0.421***
(0.148)
Pot_ dummy
; 1.544***
(0.399)
1.887***
(0.269)
Cons Surplus*Pot_dummy
? 0.001
(0.001)
SP dummy ( 0.425***
(0.106)
0.399***
(0.103)
3.150***
(0.084)
Cons Surplus*SP dummy
0.002***
(0.000)
0.002***
(0.000)
0.008***
(0.001)
Pot_dummy*SP dummy
0.935**
(0.431)
1.456***
(0.271)
Cons Surplus*Pot_dummy*SP
dummy
0.003
(0.002)
Constant 2.690***
(0.161)
2.655***
(0.161)
5.473***
(0.168)
Log likelihood 5953.249 5955.395 4946.629
No. of Observation 42718 42718 26400
LR test 29.150*** 29.18*** 19.460***
Note: ***, **, and * indicate significant level at 1%, 5%, and 10%, respectively. Numbers in parentheses
are standard errors, which are calculated by 1,000 bootstrap repetitions. LR test tests which models
between random effect negative binomial model and pooled negative binomial model is appropriate. The
null hypothesis is the pooled negative binomial is preferred.
70
Table 3.4. Mean Pertrip Welfare Estimate for FCP and FCO Models
Water clarity Minor lake SE Major lake SE
FCP (Current and potential lake users)
Current condition $133.478
($62.849$204.107)
36.036 $304.956
($202.414$407.497)
52.318
1 foot increase $143.766
($70.439$217.093)
37.412 $315.244
($210.438$420.049)
53.473
FCO (Current lake user only)
Current condition $21.932
($25.820$69.684)
24.364 $104.511
($44.227$164.795)
30.758
1 foot increase $32.422
($17.972$82.816)
25.712 $115.001
($52.307$177.695)
31.987
Note: The numbers in parentheses indicate the 95% confidence intervals of pertrip welfare, which are
calculated using the Delta method.
71
Table 3.5. Mean Annual Welfare Estimates and Changes in Trips due to an Increase
in 1 foot of Water Visibility for SCP2 and SCO Models
Water clarity Minor lake SE Major lake SE
SCP2 (Current and potential lake users data combined)
Current user
Change in mean trips 0.123 0.287
Change in welfare
HLM (equation 3.9) $25.034
($22.979$27.090)
1.049 $ 58.240
($53.457$63.022)
2.440
BHK (equation 3.11) $25.040
($10.980$39.099)
7.173 $58.252
($25.545$90.961)
16.688
Potential user
Change in mean trips 0.378 0.879
Change in welfare
HLM (equation 3.9) $76.822
($70.513$83.131)
3.219 $ 178.719
($164.043$193.396)
7.488
BHK (equation 3.11) $3.891
($1.706$6.077)
1.115 $9.053
($3.970$14.137)
2.594
SCO (Current lake user data only)
Change in mean trips 0.013 0.031
Change in welfare
HLM (equation 3.9) $1.262
($1.105$1.419)
0.080 $2.998
($2.625$3.371)
0.190
BHK (equation 3.11) $1.264
($0.667$1.860)
0.304 $3.001
($1.585$4.417)
0.722
Note: The numbers in parentheses indicate the 95% confidence intervals of pertrip welfare, which are
calculated using the Delta method. HLM and BHK represent the Hausman et al. and Bockstael et al. annual
welfare measures, respectively.
72
Figure 3.1. Trip Demand for Current Recreationists at Current and Improved Site’s
Quality
73
Figure 3.2. Trip Demand for Potential Recreationists at Current and Improved
Site’s Quality
74
CHAPTER IV
ESTIMATING DEMAND FOR URBAN FISHERIES
MANAGEMENT: AN ILLUSTRATOPM OF
CONJOINT ANALYSIS AS A TOOL
FOR FISHERIES MANAGERS
Introduction
As the population becomes increasingly urbanized across the United States, angling
participation and fishing license sales have declined (U.S. Fish an