1. sports
2. fishing

 Joint Estimation of Revealed and Stated Preference Data from the
Alaska Saltwater Sportfishing Economic Survey1
John C. Whitehead
Department of Economics
Appalachian State University
Boone, North Carolina
Daniel K. Lew
Alaska Fisheries Science Center
National Marine Fisheries Service
Seattle, Washington
March 27, 2015
Abstract. We develop econometric models to jointly estimate revealed preference (RP) and
stated preference (SP) models of recreational fishing behavior and preferences using survey data
from Alaska. The RP data are from site choice survey questions and the SP data are from a
choice experiment. Models using only the RP data are likely to estimate the effect of cost on site
selection well but catch per day estimates may not reflect the benefits of the trip as perceived by
anglers. The SP models are likely to estimate the effects of trip characteristics well but may less
attention may be paid to the cost variable. The combination and joint estimation of revealed and
stated preference data seeks to exploit the contrasting strengths of RP and SP data. We find that
there are significant gains in econometric efficiency and differences between RP and SP
willingness to pay estimates are mitigated by joint estimation. The nested logit “trick” model
fails to account for the panel nature of the data and is less preferred to scaled, random parameter
and generalized mixed logit models that account for panel data and scale differences. We find
scale differences across data sources in only one candidate model, the error components mixed
logit. While this model outperformed the standard mixed logit, willingness to pay estimates do
not differ across these two models after adjusting for scale differences.
1
A previous version of this paper was presented at the Society for Benefit-Cost Analysis annual
meeting in Washington, DC, March 2015. The authors thank Trudy Cameron for numerous
comments. Funding for this research was provided by the Alaska Fisheries Science Center,
National Marine Fisheries Service. Opinions expressed are those of the authors and do not reflect
those of NMFS, NOAA, or the U.S. Department of Commerce.
1 Introduction
Under the Halibut Catch Sharing Plan recently adopted by the North Pacific Fisheries
Management Council (Council) and being implemented by NMFS, the Council will begin annual
evaluations of charter sector-specific regulations to manage recreational harvest of Pacific
halibut. The goal of the overall research project is to better understand the demand and value of
saltwater recreational fishing in Alaska, with a primary emphasis on Pacific halibut and its
primary economic substitutes and complements, Pacific salmon. In this paper we develop
econometric models to jointly estimate revealed preference (RP) and stated preference (SP)
models of recreational fishing behavior and preferences using survey data collected by NMFS
(Lew, Lee and Larson 2010). The RP data is site choice behavior and the SP data is from a
choice experiment.
The RP and SP data have been separately analyzed by Lew and Larson (2011, 2012,
2014) and Larson and Lew (2013). The RP models in these publications use travel and time costs
measured by distance to various fishing sites and income data reported in the survey. The
benefits of the trips are measured by catch per day estimated from creel surveys and from
estimates provided by the anglers themselves. The SP models use a total trip cost measure that
does not make explicit travel distance and time cost. Expected catch per day and other attributes
are included in the choice experiment. In this context, the strengths of the RP data are also the
weaknesses of the SP data, and vice versa, so that the RP and SP data should be considered
complementary. The combination and joint estimation of RP and SP data seeks to exploit the
contrasting strengths of RP and SP data while minimizing their weaknesses (Whitehead et al.
2008, Whitehead, Haab and Huang 2011).
2 Data combination can be used to mitigate problems in both RP and SP data. In short, the
RP models are more likely to provide an unbiased estimate the effect of cost on site selection but
catch estimates may not reflect the benefits of the trip as perceived by anglers.2 The SP models
are more likely to estimate unbiased coefficients for trip attributes (including catch) but
hypothetical bias may lead to attribute non-attendance on cost. If less attention is paid to the cost
variable it will be biased downward (in absolute value) leading to upwardly biased willingness to
pay estimates.
Site/species-specific revealed preference catch estimates do not vary across angler and,
therefore, may be highly correlated. Multicollinearity may hinder estimation of unbiased catch
coefficients. Estimation of individual/site specific catch rates is feasible but the data often does
not support estimation (Haab et al. 2012). The SP choice experiment is designed to collect data
on hypothetical behavior with individual variation in catch rates. Also, the revealed preference
data are limited to analyzing behavior in response to a limited range of catch per day variation
across site. The SP choice experiment can be designed to assess variation in attributes beyond the
observed range.
There is much evidence of hypothetical bias of choice experiment data in the
transportation literature (e.g., Hensher 2010, Fifer, Rose and Greaves 2014). Metcalf et al. (2012)
find that total willingness to pay is higher with choice experiment data relative to comparable
contingent valuation data. They scale the willingness to pay estimates from choice experiment
data down by the choice experiment-contingent valuation ratio of total willingness to pay. But,
2
The RP cost will be unbiased under the heroic assumption that the cost variable is not measured
with error.
3 mostly, the environmental economics literature has been silent on this issue. Hypothetical
choices may not reflect budget and time constraints on behavior or data may suffer from
attributed non-attendance. Combining SP data with RP data grounds hypothetical choices with
real choice behavior.
While there have been a number of RP/SP joint estimation applications in other
literatures and the SP choice experiment literature in environmental economics has exploded, we
know of only four applications in environmental economics that combine RP and SP choice
experiment data. Adamowicz, Louviere, and Williams (1994) present the first application of
RP/SP joint estimation using choice experiments in the environmental economics literature. They
find that the RP data are limited due to collinearity and the SP data are prone to hypothetical
bias. Adamowicz, et al. (1997) present an application to moose hunting with a focus on a
comparison of RP-SP models with objective or subjective characteristics of the choices. They
conclude that the RP-SP model with subjective characteristics outperforms the other models,
suggesting that RP models are limited by the lack of subjective measurement of choice attributes.
Using the Adamowicz et al. data, von Haefen and Phaneuf (2008) extend the model with
observed and unobserved preference heterogeneity. They reject the hypothesis of consistency
between the RP and SP (i.e., equality of coefficients across data sources) and illustrate how
sensitivity analysis can be used to account for the inconsistency. Abildtrup, Olsen and Stenger
(2015) estimate forest recreation choices with a mixed logit error components model. They find
significant hypothetical bias in the choice experiment data.
In the next section we describe the models available for RP and SP data combination.
These include the nested logit “trick,” the mixed logit error components model and the
4 generalized mixed logit model. Then we describe the data. Since the survey was not specifically
designed for joint estimation we use manipulate the RP and SP data in order to create a parallel
data set. Then we present the results including sensitivity analysis for some of the choices made
in the data manipulation process. Finally, we offer some conclusions and directions for future
research.
Models
Random utility theory is the basis for recreational fishing models involving joint estimation of
RP and SP discrete choices,
,
(1)
where
′
is the utility angler i receives from fishing alternative j, i = 1, …, I, j = 1, …, J,
is the systematic portion of utility,
is a vector of parameters,
is a vector of variables
specific to the choice (e.g., travel cost, catch), and ε is the random error. Given the unobserved
elements of utility, we consider the probability of individual i choosing alternative j is
;∀ ∈
(2)
.
The multinomial logit model assumes the error terms in (2) are independent and identically
distributed (iid) extreme value (also known as Gumbel) variates and takes the form:
(3)
,
∑
5 where μ is a scale parameter (that cannot be identified in a typical discrete choice setting and is
thus implicitly set equal to one). In the multinomial logit model, the model parameters describing
site choice, , are assumed to be constant across individuals, indicating homogeneous response
to site characteristics. In contrast, the mixed logit model adds additional flexibility to the site
choice model by allowing for preference heterogeneity (Train 2003). For MXL, we assume that
individual angler preferences differ randomly according to a specified distribution, f(ß), such that
the unconditional site choice probability takes the form:
(4)
.
∑
In application, (4) does not have a closed form solution so estimation of the parameters requires
simulation of the integral. See Train (2003) for a detailed description of the mixed logit model.
A number of discrete choice models have been developed in order to appropriately
combine discrete choice RP and SP data. A naïve approach simply stacks the data and employs
standard logit models. When RP or SP data are estimated separately the scale parameter in the
multinomial logit is arbitrarily set equal to one. When RP and SP data are stacked and estimated
jointly, it is common for the error terms that result from the different data to have unequal
variance leading to unequal scale parameters (Swait and Louviere 1993). It is typical, but not
automatic, for the SP data to have a higher variance due, perhaps, to the unfamiliarity of the
choice task. The difference in the scale parameter will cause the MNL coefficients to differ
across RP and SP data sets. In this case the RP coefficient estimates will be larger than the SP
coefficient estimates indicating that the characteristics of the SP choices have an unduly large
effect on each choice, relative to the RP data.
6 The relative scale factor in a stacked data set can be estimated as described by Hensher
and Bradley (1993), Hensher, Rose and Greene (2005) and Whitehead (2011). The so-called
nested logit “trick” involves creating a choice situation for each RP (SP) observation that
counterfactually also includes the SP (RP) alternatives. The model is then estimated as a nested
logit with the inclusive value for the RP branch set equal to one. The SP alternatives are
estimated in individual branches but with the inclusive value for each branch constrained to be
equal. The variance of the RP nest is constrained equal to one while the variance of the SP
alternatives is allowed to diverge from one. The nested logit model scales the SP coefficients so
that the RP and SP data can be combined and jointly estimated. Each variance of the error term
is an inverse function of the individual scale factor (Swait and Louiviere 1993). When the scale
parameter for the RP data is set equal to one the nested logit model will estimate the relative
scale factor for the SP data as the inclusive value for the SP data. The SP data is then
appropriately scaled and the coefficients can be estimated jointly.
The nested logit “trick” assumes that the stacked RP and SP observations from each
angler are independent (Hensher, Rose and Greene 2008). Mixed logit discrete choice models
acknowledge the panel nature of the data, allow correlation across choices for each angler and
are capable of estimating scale parameters. Brownstone, Bunch and Train (2000) and Greene and
Hensher (2007) develop a mixed logit error components model where scale is estimated as the
standard deviation of alternative specific SP random coefficients where the mean effect is set
equal to zero. The scale parameter is estimated by included alternative specific constants for the
SP alternatives with zero mean and free variance. The scale parameter is inversely proportional
7 to the estimated variance. Hensher (2008) and Börjesson (2008) provide examples of its
estimation in the RP/SP context.
A scaled multinomial logit model is one in which individual scale parameters are
estimated. In effect, the model estimates a different coefficient vector for each individual in the
sample (Hensher 2012). The generalized mixed logit model can be used so that individual scale
and preference heterogeneity can be accounted for (Fiebeg, et al. 2009). First, consider the basic
∆
mixed logit model which involves individual specific coefficient estimates,
where
~
is a vector of individual characteristics, Δ is a vector of parameters,
Γ ,
is the error term,
0,1 and Γ is the lower triangular Cholesky matrix. A mixed logit model with unobserved
preference heterogeneity results when Δ is equal to zero. The basic conditional logit model
results when Δ and Γ are both equal to zero. Greene and Hensher (2010) show that the mixed
logit parameter estimates can be individually scaled:
∆
(5)
where
′
,
1
is the mean variance,
Γ
are parameters,
characteristics, is the coefficient on the unobserved scale heterogeneity,
are individual
, and 0
1 is a
weighting varialbe. The scaled multinomial logit model in heterogeneous scale with a data
source shift can be estimated when Δ and Γ are both equal to zero and ′
, where SP
is equal to one for the stated preference data source and zero otherwise (Hensher 2012).
The independently estimated RP and SP models and jointly estimated RP/SP models can
be used to estimate a willingness-to-pay for changes in the non-cost attributes. Haab and
McConnell (2002) show that the marginal willingness-to-pay for a change in catch for each
8 fishing trip is
, where
is the functional form of the change in the catch rate
being evaluated which can be nonlinear (i.e., diminishing in catch). Since the coefficient on
travel cost is in the denominator of the willingness to pay function, it plays a large role in value
determination. Hypothetical bias in SP cost coefficients will lead to bias in willingness to pay for
catch.
All of these models are estimated with NLOGIT software (Greene, 2012, Chang and
Lusk 2011). In the next section we estimate each of these models but efforts to estimate the SP
scale parameter with a scaled MNL and generalized mixed logit models failed (these results are
available upon request).
Data
A 2007 survey of Alaska saltwater anglers collected information on saltwater fishing
participation, effort, and preferences of resident and non-resident anglers over the 2006 fishing
season. The survey was administered to three groups of anglers for which separate survey
instruments were developed: non-residents, residents of Southeast Alaska, and all other Alaska
residents. Lew, Lee and Larson (2010) describe the development, content, and structure of the
three survey versions, their implementation, and a summary of the data.
In this study we focus on the southeast Alaska resident data. The southeast Alaska RP
data were analyzed separately in Larson and Lew (2013). Using a repeated mixed logit model the
authors show how multiple sources of catch data, creel and survey, could be used in the same
model and weighted to provide improved value estimates. The southeast Alaska SP data were
9 analyzed separately in Lew and Larson (2014). The authors focused on the relationship between
catch and keep and catch and release rates.
In this study we focus on a sample of southeast Alaska resident anglers who took a trip to
a southeast Alaska fishing site and also answered each of four stated preference questions. We
use a sample size of n = 204. There is a preponderance of nonusers in the n = 398 sample and the
no RP trip option makes combining data less informative (e.g., the no trip option dummy
variable is strongly positive in the RP data). Only considering users in this exercise puts an
emphasis on the gains from combining data from an intercept sample. This type of data
combination will be most informative to other recreation demand choice experiment models that
can be combined with surveys of on-site users.
In order to combine data, it is recommended to have the same number of observations so
that neither data source dominates in estimation. There are four SP observations (i.e., trip
preferences) and 2245 RP observations (i.e., trips) in the data. There are at least two approaches
to generating four RP observations: (1) we could use the 10 site data and stack the same choices
four times ignoring of the total number of trips taken by the angler or (2) randomly select two or
three other sites to combine with the observed choice. Both of these were attempted with option
(2) eventually preferred. Reducing the choice set in this way is not expected to affect willingness
to pay estimates (Whitehead and Haab 1999).
First, we consider whether a model with a choice set of two or three alternatives is
preferred. We compare a repeated RP model with 10 sites and all trips, a typical trip RP model
with 10 sites, a typical trip RP model with 2 sites and a typical trip RP model with 3 sites. The
10 typical trip is equal to one if the site has the maximum number of trips:
max
1 for
and 0 otherwise. There are four ties in the data. In this case the typical trip site was
chosen randomly by the computer. The distribution of typical trips is very similar to the
distribution of total trips (Table 1).
In order to develop an RP data set we randomly choose one and two non-chosen sites for
inclusion in the model. We estimate single period multinomial logit models and find similar
results. The travel cost coefficients are negative and statistically significant in both models.
Importantly, the magnitude of the travel cost coefficient is similar across models. The pattern of
catch coefficients is also similar with only king salmon being statistically significant. Given
these similarities we begin this exercise with the 2 site model.
The SP site choice data is adapted from a contingent ranking exercise where respondents
are asked for their most preferred and least preferred of three alternatives. The first two
alternatives (A, B) are fishing trips that vary over fishing mode, fishing days, target species,
daily bag limit, actual catch and size, and cost per trip. Catch levels are truncated where the
actual catch exceeds the daily bag limit. Alternative C is the no trip alternative. We assume that
respondents would choose the fishing site that they rate as their most preferred. We delete cases
whose choices are ambiguous. Less than 10% of the anglers prefer no trip across the four choice
occasions. Anglers choose equally across alternatives A and B.
Results
The multinomial logit RP site selection models are presented in Table 2. We present three
models, the repeated trip model including all 2245 trips across 10 sites, the typical trip model
11 across 10 sites and the typical trip model across two sites. The travel cost coefficient is negative
and statistically significant in each model with the z-statistic falling as the number of trips and
alternatives fall. The coefficient for king salmon is positive and statistically significant in each
model with the same pattern of efficiency. The coefficient on halibut is not statistically
significant in any model. The coefficient on silver salmon is only statistically significant in the
total trips model. The pattern of willingness to pay estimates is similar across models with king
salmon valued highest. Notably, willingness to pay for halibut is not statistically significant in
any of the revealed preference models.
Given that our primary interest is in improving SP models by including RP data in the
estimation, we begin our investigation with the simplest data available and consider a two RP
alternative data situation. In order to develop RP data for combining with the SP data we
randomly select a non-chosen fishing site four times. These four alternatives are each paired with
the chosen site and stacked to create a RP panel. The SP panel consists of SP choices for
respondents who answered each of the four questions. The RP and SP multinomial logit (MNL)
results are in Table 3.
The RP model has statistically significant travel cost, king and silver salmon catch
coefficients. The halibut coefficient remains statistically insignificant. The SP model has a
negative travel cost coefficient but it is an order of magnitude lower (in absolute value) and
estimated much less efficiently relative the RP coefficient. This suggests that anglers pay less
attention to the trip cost in the hypothetical questions relative to their actual behavior. In contrast,
the catch coefficients are each statistically significant in the SP model and their magnitudes are
lower. The silver salmon coefficient and the no trip option coefficient is negative.
12 Next, the data are stacked and jointly estimated. Several gains from joint estimation are
observed. Each of the coefficients are estimated more efficiently due to the simple fact that there
are more observations. One might think that the jointly estimated willingness to pay estimates
will fall in between independently estimated estimates. But, if the SP data breaks collinearity
across alternatives in the RP data then this naïve expectation will not be observed. The
willingness to pay estimate for halibut falls in between the RP and SP estimates and is
statistically significant. Willingness to pay for halibut and king salmon are not statistically
different. The king salmon willingness to pay estimate falls below both RP and SP estimates.
Silver salmon willingness to pay is in between RP and SP estimates and is not statistically
significant.
The nested logit “trick” results are similar to the naïve stacked model but there are subtle
differences. Each of the coefficient estimates are statistically significant. The SP data dominates
in estimation of in estimation of the each of the coefficients. The travel cost coefficient is
increased in absolute value but the catch coefficients are lower than both the RP and SP model
coefficients. Both of these effects lead to lower willingness to pay estimates. The silver salmon
coefficient is negative and statistically significant with the SP data dominant. Willingness to pay
estimates for halibut and king salmon are lower when compared to the naïve stacked model.
The SP scale parameter is greater than and statistically different from one which indicates
greater variance in the SP data. The magnitude of the scale parameter is very similar to the scale
parameters from two case studies in Whitehead (2011). In contrast, the scale parameter from a
nested logit “trick” model with RP data including all 10 of the RP sites stacked four times is an
order of magnitude greater (these results are available upon request). This suggests that there is
13 extreme heteroskedasicity in SP data when compared to RP data after stacking of uniform RP
choices with additional alternatives, perhaps artificially introducing less randomness in the RP
data. The choice of only 2 alternatives in the RP data is strengthened by this result but sensitivity
analysis is needed. For example, increasing non-chosen alternatives greater to be greater than 2,
but less than 10, may increase the efficiency and accuracy of the RP data while not introducing
artificial non-randomness across choices.
We next apply the scaled, mixed and generalized mixed logit models to the SP data and
then apply the same models to the RP-SP with and without scale effects to determine gains from
joint estimation. The mixed logit is specified with triangular distributions for the catch variables
(Hensher and Greene 2003). In this case the limits of the distribution are equal to the mean and
the standard errors of the limits are equal to the standard errors of the coefficients. The
generalized mixed logit model is estimated with the gamma weighting parameter set to one.
When the model is estimated with gamma freely estimated it is greater than one which violates
the theory (Fiebig et al. 2010). In these models the no trip option is parameterized by interacting
the no trip alternative specific constant with income and fishing experience.
The travel cost coefficient is negative and statistically significant in each model, although
it is only weakly significant in the scaled MNL model. Halibut and king salmon coefficients are
positive and statistically significant in each model. The silver salmon coefficient is statistically
significant in the generalized mixed logit model. Angler participation increases with income and
fishing experience in the random parameters and generalized mixed logit model. The tau
coefficient on the scale parameter is statistically significant in the scaled MNL and generalized
mixed logit models, indicating heterogeneity in the scale parameter. The mean of the scale
14 parameter (i.e., sigma) is equal to one in the scaled and generalized mixed logit models but each
individual scale parameter is not positive as required by theory (Fiebig et al. 2010).
Willingness to pay estimates are larger than in all previous models. The generalized
mixed logit willingness to pay estimates are more than twice as great as those from the scaled
MNL and mixed logit models. The value of halibut catch is greater than the value of king salmon
catch but the differences are not statistically significant. The value of silver salmon catch is only
statistically significant in the generalized mixed logit model.
The jointly estimated models are in Table 6. Again, several gains from joint estimation
are observed. Coefficients are estimated more efficiently and the silver salmon coefficient is
positive and statistically significant in each model. The travel cost coefficient is negative and
(strongly) statistically significant in each model. Other results are similar to the SP models.
Angler participation increases with income and fishing experience and the tau coefficient on the
scale parameter is statistically significant. The mean of the scale parameter is equal to one in the
scaled and generalized mixed logit models but each individual scale parameter is not positive,
making these results questionable.
The error components model contains scale parameters for each SP alternative. The two
trip alternatives have standard deviation estimates that are not statistically different from one,
indicating no heteroskedasticity. The standard deviation for the no trip option is large and
statistically different from one. This indicates heteroskedasticity in the no trip option, but since
there is not a no trip option in the RP data, this may not be an issue.
15 In contrast to the SP data results, the willingness to pay for catch is consistent across
three of the four models. Willingness to pay for halibut and king salmon is between $41 and $49
in the scaled and mixed logit models. Willingness to pay for silver salmon is statistically lower
but consistently positive across each model. The willingness to pay estimates in the generalized
mixed logit model are larger than the others and follow the same pattern across species as in the
RP data.
Conclusions
This study finds that there are significant gains to jointly estimating RP recreation trip and SP
choice experiment data. There are significant gains in econometric efficiency and differences
between RP and SP willingness to pay estimates are mitigated by joint estimation. The only
model where the SP scale parameter made a significant difference was in the nested logit “trick”
model. This model fails to account for the panel nature of the data and is less preferred to scaled
and random parameter models that account for panel data and scale differences. With these data
we found scale differences across data sources in only one candidate model, the error
components mixed logit. While this model outperformed the standard random parameter model,
there is little statistical evidence of scale differences and willingness to pay estimates did not
differ across these two models.
These results should not be directly compared to the Lew and Larson papers since our
interpretation of the data differs. The Alaska sportfishing survey was not designed to collect data
for RP and SP joint estimation. In order to appropriately combine the data we made a number of
data decisions that could lead to differences in separate RP and SP analyses. Nevertheless, the
16 data handling decisions made here are not invalid; i.e., the separate RP and SP analyses in this
study are different, but valid, approaches to obtaining willingness to pay values.
These results raise questions about much of the SP choice experiment literature in
environmental economics. Even with the attention accorded to the Adamowicz, Louviere, and
Williams (1994) seminal contribution (over 1200 cites on Google Scholar), the choice
experiment literature has proceeded with little to no attention paid to its similarities to RP data3.
This is in stark contrast to the contingent valuation and contingent behavior literatures which
have spent considerable time comparing and jointly estimating RP and SP data (Carson et al.
1996, Whitehead, Haab and Huang 2011).
The lack of attention to this issue may be due to the fact that many choice experiments
are not designed as behavioral surveys. With the southeast Alaska data we assumed that a
ranking of the “best” trip would be a chosen trip. Many other choice experiments are designed to
elicit non-behavioral preferences and elicit nonuse values for which there is no behavioral trace.
Our results suggest that choice experiment survey design should pay more attention to their
behavioral counterparts and that choice experiments should receive more scrutiny than seems to
be the case4.
While these results are promising they should only be considered as preliminary. In our
models we have simplified the data to (1) focus on variables that are contained in both the RP
See Araña and León (2013) for one counter-example in the environmental economics literature.
See Krucien, Gafni, and Pelletier‐Fleury (2014), Lancsar and Swait (2014) and Fifer, Simon,
Rose, and Greaves (2014) for discussion in the health and transportation literatures. 4
Also, Crastes and Mahieu (2014) find that choice experiments take 62% less time to publication
compared to contingent valuation papers. 3
17 and SP data (travel cost and catch) and (2) assess the simplest RP choice scenarios. Considering
(1), it is not necessary for the RP and SP coefficients vectors to contain the same elements. In
fact, it is typical for RP data sets to have some variables that do not vary or are unobserved
across individuals. In this case, the SP data must be used to identify the effect of the variable on
the choices (e.g., fish size). Also, SP choice experiments may be difficult to design some
attributes that are relatively easy to estimate with RP data (e.g., time cost). Future work with
these data will include additional attributes from the SP survey and time cost variables from the
RP data (Larson and Lew, 2014). Considering (2), future work with these data should investigate
the most appropriate number of RP alternative in the panel data and include the full sample size
(including nonusers from the RP data, n = 398).
18 References
Abildtrup, Jens, Søren Bøye Olsen, and Anne Stenger. "Combining RP and SP data while
accounting for large choice sets and travel mode–an application to forest recreation." Journal of
Environmental Economics and Policy ahead-of-print (2014): 1-25.
Adamowicz, W., Louviere, J. and Williams, M. (1994) Combining revealed and stated
preference methods for valuing environmental amenities, Journal of Environmental Economics
and Management, 26: 271-292.
Adamowicz, W., Swait, J., Boxall, P., Louviere, J., and Williams, M. (1997) Perceptions versus
objective measures of environmental quality in combined revealed and stated preference models
of environmental valuation, Journal of Environmental Economics and Management, 32: 65-84.
Araña, Jorge E., and Carmelo J. León. "Dynamic hypothetical bias in discrete choice
experiments: Evidence from measuring the impact of corporate social responsibility on
consumers demand." Ecological Economics 87 (2013): 53-61.
Börjesson, Maria. "Joint RP–SP data in a mixed logit analysis of trip timing decisions."
Transportation Research Part E: Logistics and Transportation Review 44, no. 6 (2008): 10251038.
Brownstone, David, David S. Bunch, and Kenneth Train. "Joint mixed logit models of stated and
revealed preferences for alternative-fuel vehicles." Transportation Research Part B:
Methodological 34, no. 5 (2000): 315-338.
19 Carson, Richard T., Nicholas E. Flores, Kerry M. Martin, and Jennifer L. Wright. "Contingent
valuation and revealed preference methodologies: comparing the estimates for quasi-public
goods." Land economics (1996): 80-99.
Chang, Jae Bong, and Jayson L. Lusk. "Mixed logit models: accuracy and software choice."
Journal of Applied Econometrics 26.1 (2011): 167-172.
Crastes, Romain, and Pierre-Alexandre Mahieu. "Contingent valuation versus choice
experiments: a meta-analysis application exploring the determinants of the time for publication
acceptance." Economics Bulletin 34, no. 3 (2014): 1575-1599.
Fiebig, Denzil G., Michael P. Keane, Jordan Louviere, and Nada Wasi. "The generalized
multinomial logit model: accounting for scale and coefficient heterogeneity." Marketing Science
29, no. 3 (2010): 393-421.
Fifer, Simon, John Rose, and Stephen Greaves. "Hypothetical bias in Stated Choice
Experiments: Is it a problem? And if so, how do we deal with it?" Transportation research part
A: policy and practice 61 (2014): 164-177.
Greene, William H., NLOGIT 5.0, Econometric Software, Plainview NY (2012).
Greene, William H., and David A. Hensher. "Heteroscedastic control for random coefficients and
error components in mixed logit." Transportation Research Part E: Logistics and Transportation
Review 43, no. 5 (2007): 610-623.
20 Greene, William H., and David A. Hensher. "Does scale heterogeneity across individuals matter?
An empirical assessment of alternative logit models." Transportation 37, no. 3 (2010): 413-428.
Haab, Timothy, Robert Hicks, Kurt Schnier, and John C. Whitehead. "Angler heterogeneity and
the species-specific demand for marine recreational fishing." Marine Resource Economics 27,
no. 3 (2012): 229-251.
Hensher, David A. "Empirical approaches to combining revealed and stated preference data:
some recent developments with reference to urban mode choice." Research in Transportation
Economics 23, no. 1 (2008): 23-29.
Hensher, David A. "Accounting for scale heterogeneity within and between pooled data
sources." Transportation Research Part A: Policy and Practice 46, no. 3 (2012): 480-486.
Hensher, David A. "Hypothetical bias, choice experiments and willingness to pay."
Transportation Research Part B: Methodological 44, no. 6 (2010): 735-752.
Hensher, David A., and Mark Bradley. "Using stated response choice data to enrich revealed
preference discrete choice models." Marketing Letters 4, no. 2 (1993): 139-151.
Hensher, David A., and William H. Greene. "The mixed logit model: the state of practice."
Transportation 30, no. 2 (2003): 133-176.
Hensher, David A., John M. Rose, and William H. Greene (2005) Applied Choice Analysis: A
Primer, Cambridge.
21 Hensher, David A., John M. Rose, and William H. Greene. "Combining RP and SP data: biases
in using the nested logit ‘trick’–contrasts with flexible mixed logit incorporating panel and scale
effects." Journal of Transport Geography 16, no. 2 (2008): 126-133.
Krucien, Nicolas, Amiram Gafni, and Nathalie Pelletier‐Fleury. "Empirical testing of the
external validity of a discrete choice experiment to determine preferred treatment option: The
case of sleep apnea," Health economics (2014).
Lancsar, Emily, and Joffre Swait. "Reconceptualising the External Validity of Discrete Choice
Experiments." PharmacoEconomics (2014): 1-15.
Larson, Douglas M., and Daniel K. Lew. "How Do Harvest Rates Affect Angler Trip Patterns?"
Marine Resource Economics 28, no. 2 (2013): 155-173.
Larson, Douglas M., and Daniel K. Lew. "The Opportunity Cost of Travel Time as a Noisy
Wage Fraction." American Journal of Agricultural Economics 96, no. 2 (2014): 420-437.
Lew, D. K., J. Lee, and D. M. Larson. 2010. Saltwater sportfishing in Alaska: A summary and
description of the Alaska saltwater sportfishing economic survey, 2007. U.S. Dep. Commer.,
NOAA Tech. Memo.
Lew, Daniel K., and Douglas M. Larson. "Economic Values for Saltwater Sport Fishing in
Alaska: A Stated Preference Analysis." North American Journal of Fisheries Management 32,
no. 4 (2012): 745-759.
22 Lew, Daniel K., and Douglas M. Larson. "Is a fish in hand worth two in the sea? Evidence from
a stated preference study." Fisheries Research 157 (2014): 124-135.
Swait, Joffre, and Jordan Louviere. "The role of the scale parameter in the estimation and
comparison of multinomial logit models." Journal of Marketing Research (1993): 305-314.
von Haefen, R.F. and Phaneuf, D.J. (2008) Identifying demand parameters in the presence of
unobservables: a combined revealed and stated preference approach, Journal of Environmental
Economics and Management 56:19-32.
Whitehead, John, “Multiple choice discrete data joint estimation,” Chapter 6 in Whitehead, John,
Tim Haab, and Ju-chin Huang, eds. Preference Data for Environmental Valuation: Combining
Revealed and Stated Approaches. Vol. 31. Routledge, 2011.
Whitehead, John C., and Timothy C. Haab. "Southeast marine recreational fishery statistical
survey: distance and catch based choice sets." Marine Resource Economics 14, no. 4 (1999):
283-298.
Whitehead, John, Tim Haab, and Ju-chin Huang, eds. Preference Data for Environmental
Valuation: Combining Revealed and Stated Approaches. Vol. 31. Routledge, 2011.
Whitehead, John C., Subhrendu K. Pattanayak, George L. Van Houtven, and Brett R. Gelso.
"Combining revealed and stated preference data to estimate the nonmarket value of ecological
services: an assessment of the state of the science." Journal of Economic Surveys 22, no. 5
(2008): 872-908. 23 Table 1. Revealed Preference Trips
Total
Typical
Site
Sum
%
Sum
%
1
46
1.9%
4
2.0%
2
76
3.1%
8
3.9%
3
997
41.1%
87
42.6%
4
9
0.4%
2
1.0%
5
407
16.8%
30
14.7%
6
120
4.9%
13
6.4%
7
250
10.3%
18
8.8%
8
397
16.4%
31
15.2%
9
78
3.2%
9
4.4%
10
45
1.9%
2
1.0%
24 Table 2. Revealed Preference Conditional Logit Models
RP - Total Trips
RP - Typical Trip
RP - Typical Trip
Coeff. S.E.
z
Coeff. S.E.
z
Coeff. S.E.
z
Travel cost
-0.05 0.00 -43.14 -0.05 0.00 -12.46 -0.06 0.01 -5.08
Halibut
-0.12 0.18 -0.65
0.47
0.61
0.76
0.80
1.39 0.57
King salmon
7.74 0.30 25.79
7.93
1.05
7.52
7.91
2.75 2.88
Silver salmon 1.35 0.14 9.57
0.61
0.49
1.25
0.83
1.12 0.74
Cases
204
204
204
Trips
2245
204
204
Alternatives
10
10
2
Time Periods
1
1
1
Willingness to pay for one additional fish
WTP S.E.
z
WTP
S.E.
z
WTP
S.E.
z
-2.50 3.89 -0.64
9.10 11.65 0.78
12.40 21.35 0.58
Halibut
167.96 5.86 28.68 154.32 18.26 8.45 123.14 39.54 3.11
King salmon
29.35 3.40 8.65
11.95 10.06 1.19
12.95 17.68 0.73
Silver salmon
25 Travel cost
Halibut
King salmon
Silver salmon
No trip
Scale
Cases
Time Periods
Log-Likelihood
AIC
Halibut
King salmon
Silver salmon
Table 3. Multinomial Logit Models
RP - MNL
SP - MNL
RPSP – Naïve
Coeff. S.E.
z
Coeff. S.E.
z
Coeff. S.E.
z
-0.059 0.006 -10.730 -0.005 0.001 -3.480 -0.020 0.001 -20.250
0.969 0.748 1.300 0.409 0.071 5.720 0.659 0.077 8.590
7.428 1.306 5.690 0.340 0.067 5.040 0.594 0.076 7.830
1.142 0.553 2.060 -0.078 0.039 -2.000 0.037 0.040 0.910
-1.543 0.169 -9.140 -2.497 0.158 -15.810
204
4
-92.69
193.4
WTP
S.E.
16.31 12.33
124.99 19.78
19.21 9.37
z
1.32
6.32
2.05
204
204
4
8
-726.35
-978.45
1462.7
1966.9
Willingness to pay for one additional fish
WTP S.E.
z
WTP S.E.
z
89.77 26.62 3.37 32.78 3.59
9.12
74.62 23.49 3.18 29.56 3.73
7.93
-17.04 10.56 -1.61
1.82
1.99
0.92
26 RPSP -"NL Trick"
Coeff. S.E.
z
-0.015 0.001 -18.330
0.332 0.067 4.930
0.202 0.061 3.290
-0.083 0.039 -2.120
-3.213 0.266 -12.090
1.359 0.091 14.880
204
8
-2211.39
4434.80
WTP
22.80
13.85
-5.73
S.E.
4.41
4.19
2.70
z
5.17
3.31
-2.12
Table 4. Stated Preference Data Models
Scaled Multinomial Logit Random Parameters Logit Generalized Mixed Logit
Coeff.
S.E.
z
Coeff.
S.E.
z
Coeff. S.E.
z
Halibut
0.873 0.395 2.210
0.529
0.084 6.320
1.869 0.310 6.040
King salmon
0.753 0.360 2.090
0.444
0.080 5.510
1.832 0.383 4.790
Silver salmon
-0.046 0.070 -0.660 -0.046 0.040 -1.140 0.190 0.099 1.910
Travel cost
-0.008 0.005 -1.700 -0.004 0.001 -3.020 -0.007 0.002 -3.840
No trip x income
-0.051 0.044 -1.150 -0.012 0.002 -4.810 -0.015 0.003 -5.260
No trip x experience -0.081 0.083 -0.980 -0.017 0.007 -2.340 -0.014 0.008 -1.780
Halibut_SD
0.529
0.084 6.320
1.869 0.310 6.040
King salmon_SD
0.444
0.080 5.510
1.832 0.383 4.790
Silver salmon_SD
0.046
0.040 1.140
0.190 0.099 1.910
Tau
1.413 0.422 3.350
1.609 0.075 21.400
Gamma
1.000 fixed
Scale SD
1.005
0.909
Sigma SD
2.529
2.051
Cases
204
204
204
Time Periods
4
4
4
Willingness to pay for one additional fish
WTP
S.E.
z
WTP
S.E.
z
WTP
S.E.
z
Halibut
111.57 34.45
3.23
132.60 42.17
3.14
285.17 77.17
3.70
King salmon
96.26 32.50
2.96
111.22 36.17
3.07
279.48 75.47
3.70
Silver salmon
-5.87
8.45
-0.69
-11.51 11.72
-0.98
28.94 14.51
1.99
27 Halibut
King salmon
Silver salmon
Travel cost
No trip x income
No trip x
experience
Halibut_SD
King salmon_SD
Silver salmon_SD
SP Alt1 SD
SP Alt2 SD
SP No trip SD
Tau
Gamma
Sigma mean
Sigma SD
Cases
Periods
LL1
LL0
Chi-squared
AIC
McFadden's R2
Table 4. Revealed and Stated Preference Data Models
Scaled Multinomial
Random Parameters
Random Parameters Logit Logit
Logit
ECM
Coeff.
S.E.
z
Coeff. S.E.
z
Coeff.
S.E.
z
1.233 0.220 5.610 0.937 0.097 9.710
1.009
0.113
8.920
1.189 0.237 5.020 1.034 0.120 8.590
1.091
0.138
7.940
0.113 0.071 1.600 0.161 0.046 3.480
0.149
0.051
2.930
-0.029 0.005 -6.30 -0.021 0.001 -19.17
-0.024
0.001 -18.100
-0.037 0.009 -4.17 -0.020 0.003 -7.410
-0.080
0.018
-4.410
-0.054
0.019
-2.890
0.820
0.141
5.810
1.00
0.98
204
8
-990.30
-1792.94
1605.28
1994.60
0.45
-0.029
0.937
1.034
0.161
0.008
0.097
0.120
0.046
-3.730
9.710
8.590
3.480
0.043
0.113
0.138
0.051
0.362
0.509
1.368
-2.430
8.920
7.940
2.930
1.130
0.590
5.120
-0.030
2.038
2.764
0.517
1.251
1.000
204
204
8
8
-973.88
-862.56
-1792.94
-1792.94
1638.11
1860.75
1959.80
1743.10
0.46
0.52
Willingness to pay for one additional fish
28 -0.105
1.009
1.091
0.149
0.408
0.302
7.002
Generalized Mixed
Logit
Coeff. S.E.
z
2.038 0.255 8.000
2.764 0.334 8.270
0.517 0.094 5.510
-0.026 0.001 -17.72
-0.027 0.003 -8.35
0.009
0.255
0.334
0.094
-3.370
8.000
8.270
5.510
0.062 20.240
fixed
0.956
1.500
204
8
-922.60
-1792.94
1740.66
1859.20
0.49
Halibut
King salmon
Silver salmon
WTP
43.24
41.70
3.97
S.E.
4.24
4.68
2.33
z
10.20
8.91
1.70
WTP
43.84
48.37
7.52
S.E.
4.04
5.09
2.09
z
10.84
9.50
3.60
29 WTP
41.59
44.98
13.92
S.E.
4.13
5.04
1.14
z
10.07
8.93
12.16
WTP
78.06
105.87
19.80
S.E.
8.56
11.07
3.28
z
9.11
9.56
6.04