NCEE0
NATIONAL CENTER FOR
ENVIRONMENTAL ECONOMICS
State Dependence and Long Term Site Capital in a Random
Utility Model of Recreation Demand
D. Matthew Massey and George R. Parsons
Working Paper Series
Working Paper # 07-11
December, 2007
^£0 sU.S. Environmental Protection Agency
^ ^ National Center for Environmental Economics
^ \ 1200 Pennsylvania Avenue, NW (MC 1809)
« Washington, DC 20460
^ http://www.epa.gov/economics
4> r-0
PRO^
-------
State Dependence and Long Term Site Capital in a Random
Utility Model of Recreation Demand
D. Matthew Massey and George R. Parsons
NCEE Working Paper Series
Working Paper # 07-11
December, 2007
DISCLAIMER
The views expressed in this paper are those of the author(s) and do not necessarily represent
those of the U.S. Environmental Protection Agency. In addition, although the research
described in this paper may have been funded entirely or in part by the U.S. Environmental
Protection Agency, it has not been subjected to the Agency's required peer and policy review.
No official Agency endorsement should be inferred.
-------
State Dependence and Long Term Site Capital
in a Random Utility Model of Recreation Demand*
D. Matthew Massey
National Center for Environmental Economics
US Environmental Protecion Agency, Washington, DC 2460
George R. Parsons
College of Marine Studies and Dept. of Economics
University of Delaware, Newark, DE 19716
December 2007
"The views expressed in this paper are those of the author(s) and do not necessarily represent
those of the U.S. Environmental Protection Agency. In addition, although the research described
in this paper may have been funded entirely or in part by the U.S. Environmental Protection
Agency, it has not been subjected to the Agency's required peer and policy review. No official
Agency endorsement should be inferred.
-------
State Dependence and Long Term Site Capital in a Random Utility Model of
Recreation Demand
Abstract
Conventional discrete choice Random Utility Maximization (RUM) models of recreation
demand ignore the influence of knowledge, or site capital, gained over past trips on
current site choice, despite its obvious impact. We develop a partially dynamic RUM
model that incorporates a measure of site capital as an explanatory variable in an effort
to address this shortcoming. To avoid the endogeneity of past and current trip choices,
we estimate an auxiliary instrumental variable regression to purge site capital of its
correlation with the error terms in current site utility. Our instrumental variable
regression gives a fitted value ranging between 0 and 1 for each alternative for each
person - a prediction of whether or not a person visited a site. Results suggest that the
presence of accumulated site capital is an important predictor of current trips, and that
failure to account for site capital will likely lead to underestimates of potential welfare
effects.
Subject Area: Recreation/Travel Demand, Marine/Coastal Zone Resources
Keywords: Site capital, state dependence, beach recreation, travel cost
2
-------
1. Introduction and Background
Conventional discrete choice Random Utility Maximization (RUM) models of
recreation demand ignore the influence of past trips on current site choice.1 Yet, there is
little doubt that past experiences shape a person's utility on future trips. A person
knows more about the characteristics of the sites they have visited in the past - both
characteristics observed and unobserved by the researcher. A person knows more about
the costs of access, best travel routes, best places for parking, and so forth. The time and
search costs needed to plan and access a site visited in the past are no doubt lower than
for a site never visited. Also, because of extra site-specific knowledge a person has less
uncertainty about what a trip to a site will be like (whether positive or negative).
Following this reasoning, failure to account for the effects of knowledge gained during
past visits could easily lead to a model that misrepresents behavior.
The process of past choices influencing current choices has been extensively
examined in a number of disciplines and has variously been dubbed state dependence,
temporal dependence, or habit formation. In his seminal labor market paper Heckman
(1981) defined state dependence as the situation where "past experience has a genuine
behavioral effect in the sense that an otherwise identical individual who did not
experience the event would behave differently." In practice, state dependence can be
difficult to model because of its dynamic nature and the fact that unobserved preference
heterogeneity can lead to spurious state dependencelike outcomes where individuals
repeatedly select the same option. Researchers have predominantly relied on some form
3
-------
of fully or partially dynamic repeated choice models to capture state dependence effects
(Pollak 1970; Rust 1987; Smith 2005).2
Despite its obvious applicability, there have been only a handful of attempts to
account for state dependence in recreation demand models. Those who have attempted
to model the effects of past choices in recreation demand frameworks have motivated
their studies with a number of different assumptions and model structures. One branch
of the literature has attempted to estimate fully dynamic models. Adamowicz (1994) for
example, adapts Pollack's theoretical habit formation model to recreational fishing by
assuming that an individuals recreational opportunities may be viewed as stock of
goods that is consumed and depreciated over time. In each time period individuals
choose whether to consume the available stock or carry some of it over into the next
period. Addressing a similar topic in a very different way, Provencher and Bishop
(1997) adapt Rust's dynamic optimal stopping model of bus engine replacement to
recreational fishing trip demand by assuming that individuals maximize expected daily
utility subject to daily budget constraints (derived from a seasonal budget constraint)
over the course of a season. Expected daily utility is also assumed to include discounted
expected future trip utility conditioned on the current choice. Current choices are
influenced by past choices through a variable measuring the days since an individual's
1 For an assortment of applications of the RUM model to recreation demand see Lin, Adams and Berrens
(1996), Loomis (1995), Parsons, Massey and Tomasi (2000), and Landry and Lui (2007).
2 Fully dynamic models are those models that assume individuals consider both the effects of past decisions
on current decisions and the effects of current decisions on future decisions. Partially dynamic models
generally only consider the effects of past choices on current choices.
4
-------
last trip and through expected catch predictions that are influenced by past trip catch
totals. Both of these studies consider past trips only within a given season.
More recently several researchers have turned to partially dynamic model
structures in order to capture state dependence and preference heterogeneity. Moeltner
and Englin (2004) and Swait et al. (2004) both modify the standard repeated choice logit
to incorporate temporal effects. Swait et al. estimate a meta-utility function made up of
weighted current and past period utilities. These utilities include previous choices and
expected attribute levels constructed of past realizations and current expectations.
Moeltner and Englin include variables measuring the total number of times a given
option was chosen and the number of consecutive times an option was chosen in order
to capture the state dependence effects. The authors also use a random parameters
(mixed logit) model structure to deal with the unobserved preference heterogeneity that
can lead to spurious state dependence findings.
Not surprisingly, the common finding of all the studies is that the inclusion of
past experiences matters in estimation and welfare results. Two common characteristics
among these studies are (1) a reliance on large panel data sets in which the researcher
knows the order and timing of every decision made (i.e. logbooks or diaries) and (2) a
relatively complicated estimation procedure particularly among the fully dynamic
models. These two issues are important reasons why none of these methodologies have
been fully embraced by practitioners. Recreation demand panel data sets are relatively
rare compared to other survey types because they are more time consuming and
expensive to collect. Previous dynamic models have been so hard to estimate that they
5
-------
usually require assumptions and concessions that substantially reduces their practical
usefulness (Phaneuf and Smith 2004; Swait, Adamowicz and van Bueren 2004).
Furthermore, Adamowicz's results suggest that there is little difference in between fully
and partially dynamic models empirically, bringing into doubt whether the extra
estimation difficulty is even worthwhile.
Although it has not received much attention in the literature to date, researchers
also face the task of defining an appropriate measure of alternative specific experience to
test for state dependence. In many cases, studies have simply used some version of past
trips as a measure of previous experience. The use of past trips is problematic because
past trips are likely correlated with unobserved site characteristics that guided choices in
the past and that are possibly still present for current choices. To isolate state
dependence effects the unobserved correlation must be purged from the measure of past
experience.
To avoid these past problems and complications, we propose an alternative
partially dynamic modeling method that is relatively easy to estimate and requires little
additional data. Similar to previous researchers, we develop a RUM model of site choice
that incorporates information on visits to sites in the past. Following Becker and
Murphy's (1986) terminology we refer to past visits to a site as 'site capital'. Since we use
a dummy variable for whether or a not a person has ever visited a site in a year prior to
the current season as our measure of site capital for a site, we refer to it as 'long term'
site capital. To avoid the endogeneity of past trips with current trip choice, we estimate
an auxiliary instrumental variable regression to purge site capital of its correlation with
6
-------
the error terms in current site utility. Our instrumental variable regression gives a fitted
value ranging between 0 and 1 for each alternative for each person - a prediction of
whether or not a person visited a site or has any site capital at the site. The fitted value,
then, is used in place of the past visit dummy variable and is, in principle, purged of its
correlation with the site utility error terms in the model.
We compare four versions of our RUM model: (1) a basic model that ignores
past trips, (2) a model that incorporates past trips but does not correct for the
endogeneity of site capital, (3) a model that incorporates past trips and corrects for the
endogeneity of site capital using a 'short' instrumental variable regression, and (4) a
model that incorporates past trips and corrects for the endogeneity of site capital using a
'long' instrumental variable regression. By short and long we are referring to the
number of instruments used in the auxiliary regression. The short regression uses a few
key instruments and the long regression uses all appropriate available variables.
Comparing the results using two different instruments allows us to explore the
sensitivity of our results to the choice of instruments. We also estimate all our models
in a random parameters framework in order to account for preference heterogeneity
over the influence of past trips. Lastly, we consider differences in parameter and
welfare estimates across the four models. Our welfare scenarios include the closure of
individual beaches, the closure of groups of contiguous beaches, and the narrowing of
groups of contiguous beaches.
2. Models and Study Design
7
-------
In our Baseline Model individuals have no memory, and the model is described by
the indirect utility functions
where V. is the site utility for a trip to site i on a given choice occasion (z = 1,.. .,62) and
VQ is the utility of doing something other than taking a trip on a given choice occasion.
There are 62 sites in our application. The arguments in the model are trip cost, tc., a
vector of site characteristics, x , and a vector of individual characteristics, y . The site
characteristics are intended to capture aspects of the site that matter to individuals in
selecting a destination and the individual characteristics are intended to capture
characteristics of individuals that help predict their probability of taking a trip. /3 is the
coefficient vector to be estimated. /3 is assumed to vary across the population with the
distribution f(fi \ 0), where 0 contains the parameters of the /3 distribution.3
If the error term £ is assumed to be distributed identically and independently
according to the extreme value distribution, then the probability that a participant
chooses site k on a particular choice occasion is given by the integral of the logit formula
evaluated at all possible values of /3,
V = Btc+Bx+e
/-i \ i ' tc i ' x i i
va = Pyy + e o
exp(^0) + XexP(^)
8
-------
Due to the analytical difficulty of evaluating multiple integrals, simulation is generally
required to obtain results. Equation (2) may be simulated by
(3) =
K r= 1
where R is the number of draws of /3 from /(\0), and V is indirect utility calculated
with draw r of/3 . The simulated probabilities may then be used to construct a simulated
log likelihood function that may be maximized to produce estimates of parameters of
the /3 distribution, 0.
Models 2 through 4 extend the Baseline Model by introducing an individual's long
term site capital as an explanatory variable. In all models, site capital enters the utility
for each site as an alternative specific constant and as an interaction with the vector of
site characteristics. As an alternative specific constant the site capital measure allows
site utility to shift depending on whether an individual has visited that site in the past.
As an interaction term, it allows the coefficients on the site characteristics to differ for
sites with site capital versus those without. Specifically, in models 2 through 4 indirect
utility is specified as
V. = Btc. +ad.+d (B x Yi-fl-d^)(B x.Yi-e.
/ a \ i i tc i i i capt i / \ i / \' no capt i / i
^ '
K = Pyy + £0
3 Because /3 is assumed to vary across the population, it is often written with an n subscript. The participant index n
is supressed in this case in an effort to make interpretation of the remaining notation more straightforward.
cxp(KI)
62 '
cxp(K;)+Xexp(K')
/=1
9
-------
where d = 1 if a person visited site i at some time in their adult life prior to the current
season, and d. = 0 if not. We refer to d. as an individual's long term site capital for site
i. Again, it is long term because it only accounts for the effect of trips in past seasons on
current site choice. It does not account for the effect of trips taken earlier in the current
season on site choice. In this way our model is like McConnell, Strand, and Bockstael
(1990) who consider long terms effects only and unlike Provencher and Bishop (1999),
Adamowicz (1994), and Swait et al (2004) who consider short term effects only. While
the lack of short term considerations is a shortcoming of the model, focusing solely on
long term habit capital greatly reduces the models data requirements. Furthermore, if
preferences are thought to be stable over time, then long and short term preferences
should be good approximations of one another.
We expect a >0, which indicates (all else constant) that sites with site capital
have higher utility than sites without. This implies long term habit formation and is
consistent with McConnell, Strand, and Bockstael (1990). A negative coefficient would
imply variety seeking. We also expect the site characteristics for sites with capital (past
visits) to play a more important role in current site choice than the site characteristics on
sites without capital. Individuals are more knowledgeable about the characteristics at
these sites and hence are more likely to use this information in determining choice over
these sites. For sites without capital, site characteristics are likely to play a smaller role.
For many of these sites, individuals may only have rough guesses about site
10
-------
characteristics. This would imply that /3 have greater explanatory power in the site
choice model than/3
1 no capt
Model 2, or the Exogenous Model, uses our most basic measure of site capital,
which is simply a dummy variable denoting whether or not a person has ever visited a
site in the past. The third and fourth models are identical to the second except that that
they treat the alternative specific site capital measures as endogenous. Accounting for
this endogeneity may be important since past trips (our simple site capital measure in
the Model 2) are likely to be highly correlated with the unobserved characteristics of
current site utility. Or in other words, unobserved characteristics that influence site
choice today were likely to have influenced site choice in the past. A model that ignores
this endogeneity will yield biased and inconsistent parameter estimates and possibly
incorrectly attribute repeated choices to state dependence. Therefore, in the 3rd and 4th
models, we purge the past trip variable of its correlation with current error terms using
an instrumental variables regression.
Following Imbens and Angrist (1994) and Angrist and Rrueger (2001) we
estimate the instrumental variable regression using ordinary least squares. A vector of
site and participant characteristics zin is regressed on responses to the question whether
or not a person has ever visited a site in the past (PASTT). The model may be formally
written,
(5) PASTT = f(zm,
-------
where
-------
(7)W,=^£
D d= 1
ln{exp(F0„) + X-=1exP[^(^ I g)]> ~ln{exP(^o„) + E-=21exP[^(^ I e)]>
where L (< 62) is the number of sites that remain open. We use this formula for all of our
site closure scenarios. Our seasonal measures of loss, reported in a later section, are
simply 240 * Wn, where 240 is the number of choice occasions in the season.
3. Data
In the Fall of 1997, with funding from the National Oceanic and Atmospheric
Administration, we conducted a mail survey of Delaware residents over the age of 16.
Individuals were asked to report their number of trips to 62 ocean beaches in the M id-
Atlantic region since January 1,1997 and to indicate which beaches they had visited in
past years. The beaches included all of New Jersey, Delaware, and Maryland's ocean
beaches. Assateague Island, which is partially in Virginia, was also included. Figure 1
shows the region covered in our analysis and Table 1 provides a list of beaches by name
running from north to south. People were also asked to report household information
such as location of hometown, age, family composition, employment, and so forth.
Individual characteristic summary statistics are presented in Table 2. In our analysis we
consider both participants and non-participants and we focus exclusively on day-trips.
Of the 562 respondents, 397 took at least one day-trip to one of the 62 beaches. The total
number of day-trips taken in the sample was 8034.
For each of the 62 beaches, we gathered the characteristic data listed in Table 2.
We used a variety of resources to compile the data set including travel guides, field
13
-------
trips, interviews with resource managers in Delaware and New Jersey, and geological
maps. The resource managers were particularly helpful; not only in compiling the data
but also in deciding what characteristics are likely to matter to individuals in choosing a
beach. Table 3 reports summary statistics for all site characteristics used in the model.
Table 4 reports summary statistics for the individual characteristics. The average trip
cost to a Delaware beach was about $50 and to a New Jersey beach was about $150. On
average, a person has about 4 beaches with site capital - 10% have zero and 10% have
more than 16. For more detailed descriptions of the data and survey design process see
Massey (2002) and Parsons et al (2000).
4. Estimation Results
We begin by estimating a standard baseline travel-cost RUM model that does not
account for the effects of past trips on current trips. The parameter estimates on the
Baseline Model tell a plausible story and are consistent with our earlier work with these
data (see Parsons et al. (2000) and Parsons and Massey (2002)). As reported in Table 5,
site utility increases with boardwalks, amusements, parks, surfing, park within, and
parking. All are features of beaches that we anticipated would improve the desirability
of the site. Among these, amusements and park within have the highest relative values.
Site utility declines with travel cost, private, narrow, wide, high rise, and facilities.
Private beaches tend to be less desirable for non-residents for day trips due to limited
access. Beaches that are too narrow or too wide are also generally less desirable.
Beaches with high rises (the more developed beaches) tend to have larger overnight and
14
-------
smaller day trip visitation. We also included dummy variables for Atlantic City and
New Jersey to capture their distinct character. Atlantic City, a mecca for gambling and
nightlife in the area, increases site utility in our model. New Jersey reduces site utility.
Both results were expected. Beach length is the only insignificant site characteristic
coefficient, but it does have the anticipated positive sign. The only outcome that ran
counter to our expectations was the negative coefficient on facilities.
The individual characteristic data in the Baseline Model shows that no-trip utility
increases with working from home, working part time, and retirement. Conversely, the
probability of taking a trip rises with having kids, having flexible work hours, being a
student, or being a volunteer. The coefficients on these variables were statistically
significantly different from zero in all cases except kids under 10.
Due to the large number of parameters in the estimated models, we only allow
two parameters to be random in our mixed logit estimation: no-trip constant and site
capital.4 Site capital is not included in the baseline model and interestingly, the no-trip
constant's estimated deviation is not statistically significant. This was counter to our
expectation that there might be considerable unobserved heterogeneity over taking a
trip versus not taking a trip.
Next we extend the Baseline model by estimating three new versions of the model
that incorporate three different measures of site capital. Model 2 uses the most basic site
4 When we allow more parameters to be free in our repeated logit setting with no-trip included as a choice,
we continually ran into convergence and singularity problems. Limiting the model to a few site
characteristics or restricting the model to be site choice only without participation helped, but we felt the
sacrifice here in terms of a useful model for policy applications was too high. In the trade off between
adding unobserved heterogeneity and having a richer behavioral model (with more observed site
15
-------
capital measure, which is simply a dummy variable indicating whether or not a person
has ever visited a site in a previous season. While conceptually appealing and easily
implemented in practice, past trip choices are likely to be correlated with current trip
choices thereby creating an endogeneity problem. To deal with this endogeneity, Model
3 and Model 4 utilize measures of site capital calculated from instrumental variable
regressions. In each model, a set of instruments is used to predict past trip visitation (as
measured by the past trip dummy from Model 2). As shown in Table 6, the two
measures differ by the number of instruments used in estimation. This follows Becker
and Murphy (1986). Model 3 only includes a short set of instruments, none of which
appear in the Baseline RUM model, while Model 4 includes a long set comprised of the
short set plus the explanatory variables used to predict trips in the Baseline RUM model.
Results of the instrumental variable regressions are plausible and relatively consistent
across the two models for the instruments they share. The exception is the distance
variable which, as expected, losses size, significance, and even changes sign when trip
cost is included in the long regression. Each measure of site capital is then incorporated
into a separate modified version of the Baseline model as a regressor. Model 2 uses the
exogenous past visit dummy variable, Model 3 utilizes the endogenous short instrument,
and Model 4 uses the endogenous long instrument.
An ideal instrument is one that is correlated with site capital (or taking a trip to a
site in the past) but uncorrelated with the current site utility error term. While far from
perfect, our set of four variables are plausible - distance to a beach, age, owning a
characteristics, participation, and splitting the sites with and without site capital into two separate groups),
16
-------
vacation home near the beach, and income. Vacation home is probably the weakest on
this list as a pure instrument since choice of site and choice of a location to own a beach
home may be governed by similar excluded attributes. As is conventional we also
include all the regressors from the original model in the long version instrumental
variable regression.
The three site capital RUM models tell much the same story as the Baseline Model,
however, they do provide significant support to the hypothesis that site capital
accumulated on past trips does affect current choices. As we expected the coefficients
on sites without site capital have much less explanatory power than the coefficients on
sites with site capital - notice the number coefficients with unexpected signs and
without statistical significance on the sites without site capital. This stands to reason as
people have little experience over the sites they have not visited in the past and hence
are less able to base current site choice on site characteristics. On the other hand, for
sites they have visited in the past, site characteristics are well known and play an
important role in current site choice.
This dynamic may be seen in sign changes that several variables undergo when
separated into visited and unvisited sites. For example, in the Baseline Model, private
beaches reduce average utility, but when site capital is accounted for private beaches
actually increase utility in previously visited sites. Similarly, New Jersey beaches
decrease utility in the Baseline model while they increase utility if they have been
previously visited. Going in the other direction, beach length is insignificant in the
we opted for the latter.
17
-------
basic model, but strongly positive and significant for unvisited beaches. Surfing also
makes a noticeable shift in sign and is significant. The results certainly suggest that
beachgoers treat the characteristics of sites visited in the past differently from sites never
visited in making current site choices — a reasonable and expected result.
Also as expected, in all versions of the site capital model, the site capital
coefficient is positive and significant indicating habit formation for site choice.
Surprisingly though, all the models predict very little deviation in site capital
preferences. The lack of deviation suggests a fair degree of unobserved homogeneity
among beach goers and that few, if any, beachgoers in the data set are variety seekers.
To make direct comparisons across the models, we calculate the implicit prices
for each coefficient in each model. In discrete choice models, absolute values across
models are not comparable, but values relative to a common coefficient (in our case
price) are comparable. These ratios also can be interpreted as implicit prices for the
attributes - the value an attribute holds assuming a person is constrained to visit the site.
As Table 7 shows the implicit prices fluctuate significantly at times across the four
models. Results also show that the endogenous site capital models (Models 3 and 4)
predict that site capital is one to one and a half times more valuable than the exogenous
site capital (Model 2). This rather sizeable increase in the value of site capital between
the exogenous and endogenous models indicates a fair degree of correction for
endogeneity.
Finally, it is important to note that the trip cost coefficient, which plays a major
role in valuation as the marginal utility of income in the denominator of equations (6)
18
-------
and (7), declines once the corrected site capital variable is included in the models -
compare Models 1&2 versus Models 3 &4. This implies that trip cost plays a less
important role in site choice than conventional models would suggest — trip cost, in
effect, is picking up some site capital effects in conventional models. Once included in
the model and corrected, we see the trip cost coefficient fall. This will lead to larger
welfare estimates in the site capital versions of the model in the next section.
5. Welfare Estimates
With a few exceptions, travel-cost random utility models are estimated for the
purpose of valuing site access or changes in site characteristics. With this in mind, we
consider how welfare measures (presented in Table 7) vary across our models. We
consider four welfare scenarios: the loss of a group of sites, the loss of beach width, the
loss of a few selected single sites, and the loss of site capital.
The most important and striking result is certainly the finding that failure to
account for site capital leads to lower welfare estimates. In almost all cases in, the
Baseline model, which does not account for individuals' accumulated site capital,
predicts the smallest welfare effects of all the estimated models. If people have little or
no site capital for a given site or sites, as is the case with the least visited sites in the
choice set, then the baseline and site capital models return very similar welfare
estimates. However, as the level of accumulated site capital increases for a given site,
the baseline and site capital models' welfare estimates begin to diverge. At the extreme,
19
-------
the site capital models' welfare estimates for the loss of the most visited beaches range
from roughly one and a third to two times larger than the baseline model.
The second main result that emerges from the welfare results is that failure to
account for endogeneity in the site capital measure also will lead to smaller welfare
estimates. In almost all cases, the Exogenous Model (Model 2) predicts smaller welfare
effects than the two Endogenous Models (3 and 4). It is also obvious from the results that
the choice of site capital instruments can have a significant effect on welfare results. The
Endogenous Short Model (Model 3) returns the largest welfare predictions in every case.
While consistently larger than the Baseline Model estimates, the Endogenous Long Model's
welfare effects are actually closer in magnitude to the Exogenous Model than they are to
the Endogenous Short Model.
The results appear to be driven by two factors. As noted above, the coefficient
estimate on trip cost is lower in the site capital models implying that models without site
capital inadvertently attribute too much explanatory power to trip cost. Indeed, people
overwhelmingly tend to visit closer sites, but when site capital is accounted for we see
that much of this actually is due to people having visited close sites in the past. Hence,
some of the trips to nearby sites are due, at least in part, to site capital. Second, the
coefficient on the site capital term is large in relative terms and increases the utility at
sites with already high utility. This, in turn, increases the expected utility of taking a trip
to beaches with high site capital relative to other beaches and gives higher welfare losses
when the sites are lost or narrowed.
20
-------
The results also indicate that accumulated site capital is valuable. To measure
this value, we estimate a welfare scenario in which we assume that all participants
"loose" their accumulated site capital. We find that site capital values range from the
mid $600's up to the mid $900's per person.
6. Comments, Caveats, and Conclusions
One of the most attractive features of our application is that it is relatively simple
to implement compared to previous attempts at modeling state dependence. The past
trip information used in the model is easily gathered by a mail or phone survey of the
general population. It is not too taxing for individual's to remember whether or not they
visited a site in the past. So, it is a rather simple adjustment to make to our conventional
models, and it appears to matter significantly.
On the downside, our measure of site capital does not account for intensity. For
example, our measure treats a site with one trip taken 10 years ago the same a site with
20 trips taken over the past two years. There are a number of ways to improve the
measure. For example, one might use the number of past trips to a site, or the number of
past years visiting the site, and/or weight recent years more heavily, or even account for
quality of the past experience (was site i a beach the person liked or disliked?). Each of
these requires information that is more difficult to recall than simply whether or not you
have visited the site in the past.
Our measure also fails to account for forward-looking behavior and for any
adjustments that may take place over time that may affect the computation of welfare.
21
-------
With forward-looking behavior individuals are viewed as making investments in site
capital when they visit a site today. That investment can be used as site capital on future
visits to a site, thereby raising future trip utility. If a person visits a site that becomes a
favorite, its site utility might increase considerably. We ignore this dynamic completely
in our myopic model. Although, as noted, there has been little evidence of forward-
looking or variety seeking behavior in past studies. Also, in the computation of welfare
when sites are closed or narrowed, people may find themselves visiting new sites and
thereby developing new found site capital. This should work to dampen welfare loses
of site closures over time. Our model ignores this dynamic as well and it would seem to
be fertile ground for future research in improving models with a dynamic element.
Most importantly, our results suggest that failure to account for past visits and
accumulated site capital will likely lead to underestimates of potential welfare effects.
Additional research is required to determine whether or not our result will hold in other
applications, but intuition and theory suggest they will. Future research may also want
investigate ways to formalize the selection of instruments used to purge endogeneity
from the past trip variable. The results of this study suggest that estimates are sensitive
to instrument choice. Indeed, the validity of the results hinges on the credibility of the
instruments successfully purging the endogeneity of past trips. Nevertheless, the model
presented in this paper is a substantial improvement over previous models that ignore
site capital entirely.
22
-------
M11 >- Atlantic Region
Figure 1
23
-------
Table 1: Mid-Atlantic Beaches from North to South
New Jersey: North Shores
1. Sandy Hook
2. Sea Bright
3. Monmouth Beach
4. Long Branch
5. Deal
6. Asbury Park
7. Ocean Grove
8. Bradley Beach
9. Avon-by-the-Sea
10. Belmar
11. Spring Lake
12. Sea Girt
13. Manasquan
New Jersey: Barnegat Peninsula
14. Point Pleasant Beach
15. Bay Head
16. Mantoloking
17. Normandy Beach
18. Chadwick Beach
19. Ocean Beach
20. Lavallette
21. Ortley Beach
22. Seaside Heights
23. Seaside Park
24. Island Beach State Park
New Jersey: Long Beach Island
25. Barnegat Light
26. Loveladies
27. Harvey Cedars
28. Surf City
29. Ship Bottom
30. Long Beach
31. Beach Haven
32. Holgate
New Jersey: Atlantic City Area
33. Brigantine
34. Atlantic City
35. Ventnor
36. Margate
37 Longport
New Jersey: South Shore
38. Ocean City
39. Strathmere
40. Sea Isle City
41. Avalon
42. Stone Harbor
43. North Wildwood
44. Wildwood
45. Wildwood Crest
46. Cape May
Delaware:
47. Cape Henlopen State Park
48. North Shores
49. Henlopen Acres
50. Rehoboth Beach
51. Dewey Beach
52. Indian Beach
53. Delaware Seashore State Park
54. North Bethany Beaches
55. Bethany Beach
56. Sea Colony
57. Middlesex Beach
58. South Bethany Beach
59. Fenwick Island State Park
60. Fenwick Island
Maryland/Virginia
61. Ocean City, MD
62. Assateague Island
24
-------
Table 2: Explanatory Variables
SITE CHARACTERISTICS:
Trip Cost
Length
Narrow
Wide
Park
High Rise
Private
Park Within
Boardwalk
Amusements
Surfing
Facilities
Parking
Atlantic City
New Jersey
Travel cost (includes tolls, beach fees, transit costs, and parking
fees) + time costs (.333 • (income / 2080) • travel time )
Length of beach in miles
Beach width from dune toe to berm less than 75 feet (1 if yes, 0 if
no)
Beach width from dune toe to berm greater than 200 feet (1 if yes,
0 if no)
State park, federal park, or wildlife refuge (1 if yes, 0 if no)
Highly developed (1 if yes, 0 if no)
Private or limited access (1 if yes, 0 if no)
Part of the beach is a park area (1 if yes, 0 if no)
Boardwalk with shops and attractions present (1 if yes, 0 if no)
Amusement park, rides, or games available or nearby the beach
(1 if yes, 0 if no)
Recognized as a good location for surfing (1 if yes, 0 if no)
Facilities such as bathrooms, showers, and food available on or
just off the beach (1 if yes, 0 if no)
Presence of adequate parking near beach (1 if yes, 0 if no)
Beach in Atlantic City, NJ (1 if yes, 0 if no)
Beach located in New Jersey (1 if yes, 0 if no)
INDIVIDUAL CHARACTERISTICS:
Kids Under 10
Kids Between 10-16
Work Part Time
Work at Home
Volunteer
Flexible Time
Retired
Student
Number of children under the age of 10
Number of children between 10 and 16 years old
Work part time (1 if yes, 0 if no)
Work at home (1 if yes, 0 if no)
Volunteer (1 if yes, 0 if no)
Flexible work schedule (1 if yes, 0 if no)
Retired (1 if yes, 0 if no)
Student (1 if yes, 0 if no)
25
-------
Table 3: Explanatory Variable Summary Statistics for Beach Characteristics*
Delaware, Maryland, and
All Beaches
Virginia Beaches
(47 beaches)
(16 beaches)
Continuous Variable Mean Values and Ranees
Trip Cost* (1997$)
$49.49
$122.04
(0.00 to 184.76)
(0.00 to 310.85)
Length (Miles)
1.20 miles
1.86 miles
(0.40 to 22.00)
(0.40 to 22.00)
Percentage of Beaches With Each Characteristic
Narrow
6.3%
14.5%
Wide
18.8%
24.2%
Park
25.00%
9.7%
High Rise
6.3%
24.2%
Private
37.5%
25.8%
Park Within
0.0%
14.5%
Boardwalk
6.3%
37.1%
Amusements
12.5%
12.9%
Surfing
43.8%
35.5%
Facilities
50.0%
38.7%
Parking
43.8%
45.2%
Atlantic City
0.0%
1.6%
New Jersey
0.0%
74.2%
f Calculated over 562 people
for eachbeach in the choice set.
26
-------
Table 4: Explanatory Variable Summary Statistics for
Individual Characteristics
Continuous Variable Mean Values and Ranges
Kids Under 10 .41 kids
(0 to 6)
Kids Between 10-16 .28 kids
(0 to 4)
Percentage of Individuals with Each Characteristic
Work Part Time 10.1%
Work at Home 6.4%
Volunteer 3.2%
Flexible Time 18.5%
Retired 24.6%
Student 5.0%
27
-------
Table 5: Estimation Results
MODEL 1:
Baseline Model
MODEL 2:
Exogenous
Model
MODEL 3:
Endogenous
Model w/ Short
IV
MODEL 4:
Endogenous
Model w/ Short
IV
SITE CHARACTERISTICS
Trip Cost
-0.0378 (64.97)
-0.0324 (59.10)
-0.0206 (30.39)
-0.0287 (51.49)
Site Capital ( OC in equation 4)
Site Capital (Mean)
Site Capital (Deviation)
3.460 (16.73)
0.089 (0.90)
5.281 (23.73)
0.653 (2.40)
6.058 (25.80)
0.151 (.087)
Sites with Capital ( j3 . in equation 4)
Length
Narrow
0.002
(0.04)
-0.025
(0.67)
-0.084
(2.20)
-0.321 (8.25)
-0.256
(3.02)
0.129
(1.42)
-0.294
(3.20)
-0.294 (3.23)
Wide
-0.836
(16.01)
-0.550
(10.14)
-0.614
(11.36)
-0.697 (12.96)
Park
0.556
(3.76)
0.503
(2.86)
0.649
(3.54)
0.632 (3.53)
High Rise
-0.476
(7.28)
-0.562
(7.86)
-0.731
(9.81)
-0.962 (13.09)
Private
-0.669
(11.18)
-0.369
(5.82)
0.121
(1.91)
0.500 (7.76)
Park Within
1.549
(14.27)
0.647
(5.68)
0.739
(6.39)
0.759 (6.57)
Boardwalk
0.612
(4.48)
0.532
(3.21)
0.747
(4.31)
0.538 (3.18)
Amusements
1.491
(26.99)
1.007
(17.64)
1.267
(22.14)
0.132 (1.83)
Surfing
0.818
(17.24)
0.574
(10.92)
1.050
(19.76)
0.930 (17.66)
Facilities
-0.308
(3.08)
-0.292
(2.50)
-0.392
(3.28)
-0.256 (2.19)
Parking
0.412
(3.13)
0.200
(1.24)
0.386
(2.29)
0.247 (1.50)
Atlantic City
1.590
(12.71)
0.375
(2.86)
0.604
(4.56)
-0.634 (4.59)
New Jersey
-1.351
(14.67)
0.011
(0.11)
0.136
(1.32)
2.282 (17.79)
Sites without Capital ( f5no capt in equation 4)
Length
Narrow
0.615
(4.27)
1.376
(9.28)
1.150
(7.66)
0.723
(1.94)
1.622
(3.68)
1.869
(4.60)
Wide
0.582
(2.14)
0.517
(1.97)
0.608
(2.30)
Park
-2.641
(4.47)
-3.736
(6.64)
-3.905
(6.79)
High Rise
-1.169
(3.82)
-0.873
(2.91)
-1.062
(3.50)
Private
-1.429
(4.73)
-4.021
(17.31)
-3.603
(15.66)
Park Within
-0.187
(0.61)
-0.445
(1.16)
-0.432
(1.49)
Boardwalk
-0.157
(0.40)
-0.242
(0.65)
-0.492
(1.29)
Amusements
0.011
(0.04)
-0.913
(3.14)
-2.077
(6.82)
Surfing
-0.460
(1.86)
-2.717
(14.03)
-2.900
(14.74)
Facilities
1.378
(3.75)
0.972
(2.44)
1.020
(2.52)
Parking
-0.131
(0.33)
-1.284
(3.18)
-1.335
(3.25)
Atlantic City
1.272
(2.53)
1.637
(2.69)
1.320
(2.68)
New Jersey
-0.215
(0.94)
-2.585
(10.58)
-0.650
(2.42)
28
-------
Individual Characteristics
Constant (Mean)
4.924 (70.29)
7.408
(35.62)
7.039
(58.65)
7.390 (55.79)
Constant (Deviaiton)
0.199 (1.20)
-0.059
(0.70)
-0.046
(0.53)
-0.040 (0.48)
Kids Under 10
-0.037 (1.13)
0.020
(0.70)
-0.062
(2.15)
0.027 (0.93)
Kides Between 10-16
-0.170 (5.70)
-0.152
(5.08)
-0.204
(6.72)
-0.269 (8.83)
Flexible Work Hours
-0.170 (3.71)
0.034
(0.71)
-0.034
(0.69)
-0.015 (0.31)
Part Time Work
0.126 (2.48)
0.0950
(1.75)
0.042
(0.76)
-0.104 (1.88)
Work at Home
0.895 (11.09)
0.919
(11.55)
0.828
(10.28)
0.633 (7.81)
Volunteer
-0.382 (6.04)
-0.111
(1.80)
-0.031
(0.50)
0.270 (4.25)
Student
-0.633 (12.77)
-0.493
(9.83)
-0.921
(17.53)
-0.561 (11.22)
Retired
0.422 (8.24)
0.333
(6.23)
0.472
(8.75)
0.181 (3.36)
Log Likelihood
-0.344361
-0.315677
-0.315488
-0.315524
29
-------
Table 6: Instrumental Variable Regression Results
DEFINITION
SHORT
MODEL
LONG MODEL
Distance
Distance from home
residence to beach in miles
-0.0027 (60.67)
0.0001 (0.47)
Log(age)
Log of age of respondent
0.1146 (66.21)
0.1072 (45.84)
Income
Household Income of
respondent (1997$)
0.0008 (9.75)
0.0013 (12.32)
Vacation Home
1 if respondent owns a
second home on a Mid-
Atlantic Beach
0.1341(8.31)
0.1034 (7.017)
Trip Cost
See Table 2
-0.0011 (10.20)
Length
-
0.0409(11.24)
Boardwalk
-
0.0343 (5.02)
Amusements
-
0.1840(19.89)
Private
-
-0.0632 (9.84)
Park
-
0.0038 (0.29)
Wide
-
0.0143 (2.23)
Narrow
-
0.0048 (0.74)
Atlantic City
-
0.1804 (9.71)
Surfing
-
0.0127 (2.41)
High Rrise
-
0.0317 (4.56)
Park Within
-
0.0185 (2.41)
Facilities
-
-0.0116(1.44)
Parking
-
0.0135 (1.69)
New Jersey
-
-0.3180 (37.45)
Kids Under 10
-
0.0099 (3.71)
Kids Between 10-16
-
-0.0052(1.56)
Part Time
-
-0.0214 (3.01)
Retire
-
-0.0396 (6.23)
Flexible Work
-
0.0272 (4.71)
Student
-
0.0578 (6.07)
Volunteer
-
0.0522 (4.51)
Work at Home
See Table 2
-
-0.0269 (2.99)
R-SQUARED
0.138
0.293
30
-------
Table 7: Implicit Prices for Site Characteristics
MODEL 1:
Baseline Model
MODEL 2:
Exogenous
Model
MODEL 3:
Endogenous
Model w/ Short
IV
MODEL 4:
Endogenous
Model w/ Long
IV
Site Capital
Site Capital (Mean)
Site Capital (Deviation)
Sites with Capital
Length 0.04
Narrow -6.76
Wide -22.11
Park 14.71
High Rise -12.60
Private -17.70
Park Within 40.98
Boardwalk 16.19
Amusements 39.44
Surfing 21.64
Facilities -8.16
Parking 10.89
Atlantic City 42.07
New Jersey -35.73
Sites without Capital
Length
Narrow
Wide
Park
High Rise
Private
Park Within
Boardwalk
Amusements
Surfing
Facilities
Parking
Atlantic City
New Jersey
106.78 256.36 211.08
2.74 31.68 5.26
-0.77 -4.08 -11.19
3.97 -14.25 -10.24
-16.96 -29.83 -24.29
15.54 31.52 22.01
-17.36 -35.46 -33.52
-11.38 5.87 17.43
19.98 35.85 26.45
16.43 36.24 18.75
31.08 61.48 4.58
17.70 50.99 32.39
-9.02 -19.03 -8.92
6.18 18.73 8.60
11.57 29.34 -22.09
0.35 6.61 79.52
18.97 66.80 40.07
22.32 78.72 65.12
17.97 25.09 21.18
-81.51 -181.36 -136.07
-36.08 -42.39 -37.01
-44.10 -195.18 -125.55
-5.76 -21.62 -15.03
-4.83 -11.75 -17.13
0.35 -44.33 -72.37
-14.19 -131.90 -101.04
42.54 47.20 35.55
-4.05 -62.33 -46.51
39.25 79.44 46.00
-6.64 -125.50 -22.65
31
-------
Table 8: Beach Closure Seasonal Welfare Loss Per Person (1997 Dollars)
Baseline
Model
(1)
(2)
EXOGENOUS
Site Capital Models
(3) (4)
ENODGENOUS ENDOGENOUS w/
W/ SHORT LIST LONG LIST
Loss of Sites: Multiple Beaches
All Delmarva: Cape Henlopen St. Park
DE to Assateague Island VA
$443.81
$657.43
$1035.19
$735.56
All Delaware:
374.90
567.70
893.38
633.77
Northern Delaware Beaches: Cape
Henlopen St. Park, North Shores, Henlopen
Acres, Rehoboth Beach, Dewey Beach, and
Indian Beach
255.72
383.53
619.58
437.92
Southern Delaware Beaches:
Delaware Seashore St. Park, North Bethany
Beaches, Bethany Beach, Sea Colony,
Middlesex Beach, South Bethany Beach,
Fenwick Island St. Park, and Fenwick Island
111.96
168.97
250.12
178.91
All New Jersey Beaches:
25.88
36.11
58.87
39.33
Loss of Sites: Most Popular Beaches
Rehoboth, DE:
125.46
162.28
260.89
185.02
Ocean City, MD:
50.72
60.26
97.63
70.26
Cape Henlopen, DE:
55.99
84.83
148.45
104.44
Loss of Sites: Least Popular Beaches
Ortley, NJ:
0.19
0.06
0.04
0.03
Chadwick, NJ:
0.05
0.03
0.03
0.02
Normandy, NJ:
0.03
0.04
0.04
0.03
Beach Erosion: All Beaches Reduced to Narrow
All Delaware:
30.19
74.38
106.82
70.74
Northern Delaware Beaches:
24.97
22.56
62.53
44.77
Southern Delaware Beaches:
55.33
96.57
170.23
116.10
Site Capital:
Site Capital (d)
664.25
940.35
735.84
32
-------
References
Adamowicz, W. (1994). "Habit Formation and Variety Seeking in a Discrete Choice
Model of Recreation Demand." Journal of Agricultural and Resource Economics 19(1):
19-31.
Angrist, J. D. and A. B. Rrueger (2001). "Instrumental Variables and the Search for
Identification: From Supply and Demand to Natural Experiments." Tournal of Economic
Perspectives 15(4): 69-85.
Becker, G. S. and K. M. Murphy (1986). A Theory of Rational Addiction. University of
Chicago, George G. Stigler Center for Study of Economy and State Working Paper.
Chicago
Heckman, J. J. (1981). Heterogeneity and State Dependence. Studies in Labor Markets. S.
Rosen. Chicago, IL, University of Chicago Press
Imbens, G. W. and J. D. Angrist (1994). "Identification and Estimation of Local Average
Treatment Effects." Econometrica 62(2): 467-475.
Landry, C. E. and H. Lui (2007). A Semi-Parametric Estimator for Revealed and Stated
Preference Data: An Application to Recreational Beach Visitation. East Carolina
University Working Paper
Lin, P.-C., R. M. Adams and R. P. Berrens (1996). "Welfare Effects of Fishery Policies:
Native American Treaty Rights and Recreational Salmon Fishing." Tournal of
Agricultural and Resource Economics 21(2): 213-276.
Loomis, J. (1995). "Four Models for Determining Environmental Quality Effects on
Recreation Demand and Regional Economics." Ecological Economics 12: 55-68.
Massey, D. M. (2002). Heterogeneous Preferences in Random Utility Models of
Recreation Demand. Department of Economics. Newark, DE, University of Delaware
McConnell, K. E., I. E. Strand and N. E. Bockstael (1990). "Habit Formation and the
Demand for Recreation: Issues and a Case Study." Advances in Applied Microeconomics
5: 217-235.
Moeltner, K. and J. Englin (2004). "Choice Behavior Under Time-Variant Quality: State
Dependence Versus "Play-It-by-Ear" in Selecting Ski Resorts." Tournal of Business and
Economic Statistics 22(2): 214-224.
Parsons, G. R. and D. M. Massey (2002). A Random Utility Model of Beach Recreation.
The New Economics of Outdoor Recreation. N. Hanley, D. Shaw and R. E. Wright.
Northampton, MA, Edward Elgar
33
-------
Parsons, G. R., D. M. Massey and T. Tomasi (2000). "Familiar and Favorite Sites in a
Random Utility Model of Beach Recreation." Marine Resource Economics 14: 299-315.
Phaneuf, D. J. and V. K. Smith (2004). Recreation Demand Models. Handbook of
Environmental Economics. K. Maler and J. Vincent
Pollak, R. A. (1970). "Habit Formation and Dynamic Demand Functions." The Journal of
Political Economy 78(4): 745-763.
Provencher, B. and R. Bishop (1997). "An Estimable Dynamic Model of Recreation
Behavior with an Application to Great Lakes Angling." Journal of Environmental
Economics and Management 33(1): 107-127.
Rust, J. (1987). "Optimal Replacement of GMC Bus Engines: An Empirical Model of
Harold Zurcher." Econometrica 55(5)
Smith, M. D. (2005). "State Dependence and Heterogeneity in Fishing Location Choice."
Journal of Environmental Economics and Management 50(2): 319-340.
Swait, J., W. Adamowicz and M. van Bueren (2004). "Choice and temporal welfare
impacts: incorporating history into discrete choice models." Journal of Environmental
Economics and Management47(1): 94-116.
34
------- |