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Incorporating the effect of successfully bagging big game into recreational hunting: An examination of deer, moose and elk hunting
Journal of Forest Economics 28 (2017) 12–17
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Incorporating the effect of successfully bagging big game into recreational hunting: An examination of deer, moose and elk hunting Arwin Pang Department of Accounting, National Chung Hsing University, Taiwan
a r t i c l e
i n f o
Article history: Received 14 November 2016 Accepted 12 April 2017 JEL classification: Q5 Keywords: Structural equations model Hunting demand Bagging probability
a b s t r a c t This analysis aims to quantify the effect that the probability of bagging game will have on the demand for recreational hunting. A two equation structural model has been developed which allows the probability of bagging game to be simultaneously entered into the travel cost model. The basic model is based on a Poisson distribution for the travel cost, and a Negative Binomial distribution is used to deal with the issue of overdispersion. Likelihood ratio tests and non-nested model selection tests have been adopted to choose the model which best fits the data. The results show that a Negative Binomial structural model is the best and the probability of bagging game has a significant effect on the travel cost model. The welfare per hunting day is around $300. ˚ © 2017 Department of Forest Economics, Swedish University of Agricultural Sciences, Umea. Published by Elsevier GmbH. All rights reserved.
Introduction According to the national survey, 12.5 million people 16 years old and older enjoyed hunting a variety of animals within the United States in 2006. Among the hunting games, big game hunting was the most popular type of hunting, such as deer and elk (U.S. Department of the Interior, Fish and Wildlife Service, and U.S. Department of Commerce, U.S. Census Bureau, 2006). Hunting success or harvest was commonly linked to hunter satisfaction. Hendee (1974) first suggested a multiple-satisfaction for hunter. The satisfaction is not solely on bagging game, but more complex elements. This concept recognizes the factors such as enjoying nature, exploring outdoors, adventure, companionship and so on (Hendee, 1974; McCullough and Carmen, 1982; Vaske et al., 1986; Hammitt et al., 1990). However, generally the studies found the harvest is still the strong predictor of hunter satisfaction. Successful hunters reported greater satisfaction than unsuccessful ones. Thus, the importance of maintaining some probability of harvest success to uphold hunter satisfaction is emphasized (Stankey et al., 1973; Decker et al., 1980; Vaske et al., 1982; McCullough and Carmen, 1982; Gigliotti, 2000). There have been numerous studies done by economists to estimate the recreational demand for hunting. Although the literature is rich, it has not paid much attention to hunting success which is recognized in the hunter satisfaction literature. This study attempts to discuss the role of successful bagging in recreational demand
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through hunter satisfaction (utility). We believe besides the pleasure of exploring nature, the successful bagging of game on a hunting or fishing trip also contributes to the hunter’s (or angler’s) utility. Incorporating the hunting success or harvest into the recreational demand for hunting will bridge the gap between the hunting demand and hunter satisfaction. It will also contribute the literature by investigating the significance of harvest success in hunting demand. In literature about fishing demand, there are two ways to understand the role of bagging success. McConnell and Sutinen (1979) developed a bioeconomic model of recreational fishing by assuming that the catch rate is exogenous to private decisions. Greene et al. (1997) and Gillig et al. (2003) also treated catch rate as exogenous when estimating fishing demand. Conversely, some studies no longer assume that catch rate is exogenous in their models. Bockstael and McConnell (1981) introduced a household production function where the catch rate will be affected by exogenous factors like the stock of wildlife and the individual’s experience. This allowed them to model the theoretical interaction between the household’s behavior and public inputs into recreation. McConnell (1979) used a household production function to estimate the empirical value of fish where fish caught per trip is set as a function of the inputs used to catch more fish per trip, the stock density of available fish and the attributes of individual anglers. The 2SLS method is used and the predicted value of fish caught per trip is the instrument variable. McConnell and Strand (1994) instituted an individual catch rate, which is a random variable depending on the density of fish at the site and the characteristics of individual
http://dx.doi.org/10.1016/j.jfe.2017.04.003 ˚ Published by Elsevier GmbH. All rights reserved. 1104-6899/© 2017 Department of Forest Economics, Swedish University of Agricultural Sciences, Umea.
A. Pang / Journal of Forest Economics 28 (2017) 12–17
anglers used in the model, such as hours fished and years of experience. Englin et al. (1997) constructed a two equation structural model that included a total catch function representing angling success within the travel cost model. As for hunting demand, Miller and Michael (1981) studied hunter participation in duck hunting in Mississippi. Hunter success, which is measured by the number of ducks bagged, is included in their model. Creel and Loomis (1990) used truncated Poisson distribution and Negative Binomial count data models to evaluate deer hunting in California. In their model, a dummy variable is included to represent the successful bagging of an animal. They further discussed the confidence intervals for welfare measures in 1991. Lisa and Goodwin (1992) evaluated the demand for hunting trips in Kansas by including the time spent on site in the travel cost method. They concluded that the hunter’s age, investment in hunting equipment, and quality of the site do significantly influence demand. Sarker and Surry (1998) adopted a travel cost method to estimate the demand for and the economic value of recreational moose hunting in Ontario by using 4 alternative count data models (Poisson, Geometric, Negative Binomial type II, and Creel and Loomis). Hansen et al. (1999) developed a multi-site demand model to estimate the demand for pheasant hunting and evaluate the impact of the Conservation Reserve Program on pheasant hunting quality. Cooper (2000) presented two nonparametric approaches and developed one semi-nonparametric count model for travel cost as applied to waterfowl hunting trips for the six national wildlife refuges in California’s San Joaquin Valley. Bennett and Whitten (2003) examined the benefits and costs of duck hunting on wetland conservation. Groothuis (2005) used a linear form travel cost function which includes the number of deer a respondent bagged to estimate the consumer surplus for deer hunting. In addition, there are some other interesting topics related to hunting in the literature. Among them, the regulation of hunting is an important issue that has received much attention. Nickerson (1990) evaluated the demand for regulation of big game hunting for elk and deer in Washington state. Creel and Loomis (1992) developed a Truncated Joint Trip-Bag model which accounts for the effects of bag limits on the behavior of hunters in California. Little et al. (2006) investigated the elk permit lottery demand. Schwabe et al. (2001) studied the value of changes in deer season length in welfare rather than bag limit, which is the traditional method. Wam et al. (2012) used Norwegian grouse hunting data to study the number of permits or the bag size allowed per hunter in sustainable management. Some studies are devoted to hunting license demand (Brown and Connelly, 1994; Loomis et al., 2000; Scrogin et al., 2000; Sun et al., 2005). Milon and Clemmons (1991) evaluated the economic determinants of demand for species variety in wildlife recreation choices. Additionally, the site choices of recreational hunters were also examined (Adamowicz et al., 1997; Newbold and Massey, 2010; Zimmer et al., 2012). From the hunting literature review, although Miller and Michael (1981), Creel and Loomis (1990) and Groothuis (2005) included an exogenous bag variable into their studies, the issue of bagging success in hunting has not drawn as much attention as catching success in fishing. In the United States, hunting of game animals is regulated to ensure the long term viability of hunted wildlife populations. All hunters are required to get licenses to hunt and face bag limits on the number of animals they can take on a single trip or over the length of the season. As mentioned above, these regulations also play an important role in the hunting literature. Although a bagged game attribute will complicate the measurement of demand for hunting and of welfare since it affects hunters’ satisfaction and utility, it should not be neglected. As for the policy of regulation, licenses, tags, permits, and stamps issued in a hunter’s state were included in the hunting demand in this study. Wam et al. (2012)
13
found that selling permits gains profits for the government, but crowding causes a loss of hunter satisfaction. The goal of this study is to investigate the effect of game bagging success on hunting trips. The method is to incorporate the expected probability of bagging game as explanatory variable in estimating the demand for hunting trips which has been absent in the previous literature. This study will employ a structural model to estimate hunting demand with the probability of bagging incorporated. The next section introduces the structural model, which combines the traditional travel cost model and probability of bagging game. The section “Data and results” presents the data and estimated results. The final section concludes the study. Methodology A structural model Travel cost demand function The travel cost method assumes that users try to maximize their utility when choosing a site to visit and that utility is related to socioeconomic characteristics of the consumer and depends on the full cost incurred by it with his/her visit. A typical approach that the individuals increase their utility depending on the number of visits, time spent at the site, characteristics of the site and the quantity of the numeraire. Analytically the maximization problem can be presented as: Max : u(S, r, q)
(1)
where S stands for the numeraire whose price is 1, r represents the number of visits to the recreation site and q is the environmental quality at the site. The maximization of the individual is subject to monetary and time constraints. M + w · tw = S + c · r
(2)
t = tw + (t1 + t2 )r
(3)
where M is exogenous income, which stands for the individual’s demand; w is the wage rate; c is the monetary cost of visiting; t is the time endowment; tw is the time of working; t1 is the time of visiting; t2 is the time spent at the site. The utility maximization problem yields the travel cost demand function (Freeman, 1993). r = r(c, M, q)
(4)
The structural model The structural model is based on the travel cost method in the section “Travel cost demand function” which assumes that hunters try to maximize their utility related to their socioeconomic characteristics and the full cost incurred for their trips. The hunting demand is defined as: Trips = f (TC, X, Z)
(5)
Trips is the number trips taken in a year by hunter; TC is the travel cost; X represents a set of individual characteristics of the hunter; Z is a vector of site characteristics. The probability of bagging is used to obtain the expected probability of success that each hunter has, and is mainly based on measures of personal input and site quality characteristics as per the fishing literature mentioned in the introduction. The model has the following general form: bag = g(X, Z)
(6)
It states that the probability of a bag is linked to a vector of individual characteristics (X) such as hunter experience, skill, and investment in hunting, as well as site quality (Z).
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A. Pang / Journal of Forest Economics 28 (2017) 12–17
Table 1 Descriptive statistics. Variable
Description
Mean
Std. Dev.
Huntday Huntcost Huntbag Age Education Race Income Gender Marriage Huntday2005 License Total Licenses Paid License Holders Region dummy New England Middle Atlantic East North Central West North Central South Atlantic East South Central West South Central Mountain Pacific
The number of hunting days The total amount spent on big game hunting per hunting day Bag or not Years School Years White = 1, Other = 0 Household income Male = 1, Female = 0 Married = 1, Single = 0 The number of days hunting in 2005 The number of hunting licenses owned The number of total licenses issued by hunter’s state The number of paid license holders in hunter’s state
30.58 17.69 0.57 46.08 13.78 0.98 82,451.22 0.96 0.75 23.17 2.21 716,400.30 307,340.80
26.31 54.19 0.50 13.73 2.34 0.15 36,578.52 0.21 0.43 9.63 1.70 628,135.80 251,929.30
0.11 0.08 0.06 0.14 0.23 0.10 0.13 0.07 0.08
0.32 0.28 0.24 0.34 0.42 0.30 0.33 0.26 0.28
Incorporating the expected probability of bagging game into the travel cost demand helps us to evaluate the effect which that probability will have on that demand. The new structural demand is Trips = f (TC, X, Zi , g(X, Z))
taneously is adopted. This joint estimation sums up all likelihood functions from the models to be estimated, treating all variables and all parameters jointly. It has the advantage of avoiding the need for any covariance matrix correction (Murphy and Topel, 1985). The Full Information Maximum Likelihood method is efficient for estimating a joint model. With normally distributed disturbances, the results are efficient among all estimators (Greene, 2000). In the case of the Poisson distribution, the joint estimation likelihood function is:
(7)
Econometric model Since the data for hunting demand follows a count form, count distributions are appealing because they fit the characteristics of the data, being a nonnegative discrete range of values (Creel and Loomis, 1990). The Poisson distribution is one of the most commonly used. It is attractive by being part of the linear exponentials family and keeps a nice robustness that makes the estimators of parameters consistent and asymptotically normal even when the underlying distribution is not strictly Poisson (Gourieroux et al., 1984). A probit link is adopted for the probability of bagging since it has a binary dependent variable which deals with an expected value that lies between 0 and 1 (Greene, 2000). It is related to the normal cumulative density function as it transforms xˇ into the probability associated with its calculated value. For the ith observation, the probit link is defined as i = (xi ˇ)
=
prob
+bi
• • • •
ln
tripsi +
(9)
1 ˛
− ln (tripsi + 1) − ln
i
+bi
prob
· ln(pi ) + (1 − bi
prob
) · ln(1 − pi )
1 ˛
) · ln(1 − pi )
(10)
= exp(xˇ) x: matrix of independent variables bprob : bag reported by hunter p: probability of bag
The first part of the likelihood function is a regular Poisson model of ith observation. The Poisson model is the most basic count travel cost demand. It provides an excellent reference point because it does not contain any shape parameters to be estimated. Although Poisson has many suitable features for our count data estimation and the parameters are unbiased as long as the underlying relationship is linear or exponential, we try to relax the requirement for the mean to equal the variance due to the possible overdispersion issue, because this failure to model heteroscedasticity can lead to a variety of issues. The Negative Binomial is a popular generalization of the Poisson. It can be found by mixing a gamma density with mean 1 and variance 1/˛ with the Poisson. The joint estimation likelihood function of the Negative Binomial distribution is
The represents the cumulative standard normal distribution transformation. A joint estimation where the parameters for the travel cost method and the probability of bagging game are estimated simul-
=
prob
· ln(pi ) + (1 − bi
where
where x is the set of expansionary variables, ˇ is a set of parameters. The log likelihood function relates to the Bernoulli distribution transformation which looks like:
((−i + tripsi · ln i ) − ln(tripsi !))
i
(8)
i = yi ln i + (1 − yi ) ln(1 − i )
+
1 ln ˛
1 ˛
·
1 (1/˛) + i
+ tripsi ln(i ((1/˛) + i ))
(11)
A. Pang / Journal of Forest Economics 28 (2017) 12–17
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Table 2 Estimated results. Poisson
Constant Huntcost Age Education Race Household Income (in 1000) Gender Married Pacific Total Licenses (in 1,000,000)
II
I
II
4.1039*** (0.8534) −0.0058** (0.0023) 0.0009 (0.0049) −0.0570** (0.0227) −0.1757 (0.5777) 0.0000 (0.0018) 0.3014 (0.3830) −0.1954 (0.1467) −0.4057** (0.1723) 0.0052 (0.1083)
2.7230** (1.0896) −0.0063*** (0.0024) 0.0008 (0.0048) −0.0623*** (0.0235) −0.3638 (0.5631) 0.0001 (0.0017) 0.3414 (0.3569) −0.1566 (0.1483) −0.4857*** (0.1579) −0.0243 (0.0934) 0.2816** (0.1102) 1.7856* (1.1455) 0.4814*** (0.0462)
3.8320*** (0.5783) −0.0032*** (0.0007) 0.0012 (0.0046) −0.0612*** (0.0224) 0.0495 (0.3114) −0.0002 (0.0016) 0.3158 (0.3350) −0.1318 (0.1359) −0.3585** (0.1625) 0.0332 (0.0971)
2.0500*** (0.5309) −0.0033*** (0.0013) 0.0045 (0.0033) −0.0552** (0.0257) −0.0191 (0.2426) 0.0004 (0.0014) −0.2424 (0.2082) −0.1589 (0.1186) −0.3619* (0.2417) −0.1008 (0.0888) 0.2673** (0.1080) 4.1059*** (0.6141) 0.4077*** (0.0496)
Huntbag Prob(Huntbag) Alpha Probit Constant
−0.5311* (0.6414) 0.0011* (0.0067) 0.4985 (0.4966) 0.0148* (0.0095) −0.0848* (0.0548) 0.0009 (0.0037)
Age Gender Huntday License Paid License Holder (in 10,000)
Log Likelihood LR test
Negative Binomial
I
−2116.7 346.4***
−2289.9
−0.5313 (0.5815) 0.0011 (0.0072) 0.4987 (0.4391) 0.0148* (0.0101) −0.0848* (0.0567) 0.0009 (0.0036) −876.77 238.8***
−996.17
*
Significant at the 15% level. Significant at the 5% level. *** Significant at the 1% level. Heteroscedasticity-consistent (robust) standard errors are reported in parentheses. **
where ˛ is the overdispersion parameter and estimated from the data. The expectation is that relaxing the equivalence between the mean and variance will result in improved efficiency. The optimization is to find the parameters which maximize the joint estimation likelihood function. Newton’s method for maximum likelihood estimation is used. For Poisson and Negative Binomial distributions, both the basic travel cost model and the structural model are estimated in this study. In the basic travel cost model, the bag probability reported by hunter is included. While in the structural model, the probability of bagging produced by the probit part is entered into the basic travel cost function as equation (7). Data and results The data set used in this study is the 2006 National Survey of Fishing, Hunting, and Wildlife-Associated Recreation by U.S. Fish and Wildlife Service. The Survey was carried out by the U.S. Census Bureau in two phases. In the first phase 85,000 households nationwide were interviewed by telephone in April 2006. The screener questionnaire was about demographic information of the house-
hold members and attempted to find out which members of the household had fished, hunted, or watched wildlife in 2005, and would likely engage in those activities in the future. The second phase includes three detailed telephone interviews about the activities and expenditures. The respondents were at least 16 years old. In total, 21,938 anglers and hunters were surveyed. The dependent variable in travel cost demand is the number of hunting days (Huntday) in 2006 instead of hunting trips mentioned in section 2 since a trip could be varying in length. Here, a hunting trip refers to big game hunting which is for deer, elk or moose. The first explanatory variable in the travel cost demand model is the travel cost of a hunting day (Huntcost) which is the total amount a hunter spent on big hunting tips in 2006 over the number of hunting days. The other explanatory variables include the demographic variables Age measured in years, and Education measured in school years, Race (White = 1, Other = 0), Income which is the mean value of income per interval of the questionnaire, Gender (Male = 1, Female = 0), Marriage (Married = 1, Single = 0), Total Licenses is the number of licenses, tags, permits and stamps issued in the hunter’s state, a region dummy – Pacific and Huntbag (Yes = 1, No = 0). Totally there are 205 observations used in this study.
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A. Pang / Journal of Forest Economics 28 (2017) 12–17
On the probability of bagging, the dependent variable is Huntbag which is whether the hunter has bagged game or not on a hunt in 2006. The explanatory variables are Age; Gender; Huntday, the number of days the hunter hunted during 2005; License, the number of hunting licenses the hunter owned in 2006; and Paid License Holder, the number of paid license holders of hunter’s state. The descriptive statistics are reported in Table 1. The estimated results for the two distribution models are displayed in Table 2. For both models, a basic model (I) and a structural model (II) are estimated. For all models, the intercept terms are positive. The travel cost (Huntcost) coefficients are negative and significant at the 1% level, showing a downward sloping demand curve as expected. For the socioeconomic variables, the negatively significant coefficients on Education show that people with less school years take more hunting days. Race, Household income and Married have an insignificant effect on hunting days in models. The total number of licenses, tags, permits, and stamps in a hunter’s state has an insignificant negative effect on hunting days in the model II. Pacific includes states of Alaska, California, Hawaii, Oregon, and Washington where people engaged in less hunting activities in the survey. These states also issue fewer licenses in the national hunting license report, which has a negative effect on hunting days. The results of model I and II are quite consistent in the travel cost demand except Gender with switching signs in Negative Binomial model. This result indicates that it is present both in travel cost demand and the probability of bagging game. The net effect includes the direct effect on travel cost and the indirect effect through the probability of bagging game. Huntbag has a positive effect on hunting days in both basic models. The coefficients of Prob(Huntbag) in structural model II are always positive and significant which indicates that not only does the expected probability of bagging game have a positive impact on the utility of a hunting day, but that the likelihood of bagging also influences the number of days positively. It should be noted that the magnitude of coefficients on Prob(Huntbag) are much larger than on Huntbag. The results for bagging probability are consistent. In Poisson model, the positive significant coefficient of Age shows that an older hunter has a higher probability to bag an animal. More skilled and experienced hunters who spent more days hunting have a higher probability of bagging in both distribution models. Hunters with more licenses don’t assure the good luck on bagging. The number of paid licenses in a hunter’s state has negative impact on hunting days, but they are not statistically significant. The likelihood ratio (LR) test results in Table 2 show the econometric specification that best fits the data between the basic and structural model for each distribution model. These results show that model II is better than model I. A non-nested model selection test (Vuong, 1989; Englin and Lambert, 1995) is used to select the best distribution among different specifications. This test is a two-step procedure. In the first step, the sample variance of the log likelihood ratio is compared to the critical value from a multivariate distribution to decide whether the null hypothesis that two conditional models are distinguishable is rejected or accepted. If the null hypothesis is rejected the second step applies a directional test to indicate either that one model dominates the other or that neither model is preferred. The results of the first step show that the null hypothesis is rejected. The test statistics of the second step is −7.4596, significantly shows that Negative Binomial model II is better than Poisson model II. In addition, the significant coefficient of the dispersion effect (˛) in the Negative Binomial model also supports this finding. These two pair-wise comparisons of model selection indicate a strong preference for Negative Binomial model II. Consumer surplus represents the difference between the maximum that consumers would be willing to pay for a good and what
they actually pay. The usual integration under the ordinary demand function has a per hunting day which is −1/ˇHuntcost . The variance of consumer surplus per hunting day estimates can be calculated as (Englin and Shonkwiler, 1995): Var
1 ˇ
=
S2 S4 +2 6 4 ˇ ˇ
(12)
where S denotes the standard error of ˇ. These calculations can therefore give the welfare for hunters with the Negative Binomial structural model. The consumer surplus per big game hunting day is around 301.26 dollars with standard error $14.98. When the probability of bagging is increased by 1% for each hunter, the expected hunting days will be increased from 30.45 to 31.73, the consumer surplus per hunting day is raised by $384 which is −1/ˇHuntcost · (31.73 − 30.45). The successful bagging of an animal not only brings the hunter satisfaction but also the economic value of the animal itself. Conclusion Typically a hunter’s utility is not only derived from the trip itself but also the successful bagging of game. However, little attention has been paid to the issue that bagging an animal brings hunter satisfaction. This study incorporates the probability of bagging game into the travel cost demand model. The probability of bagging game plays a more significant role in the basic travel cost model than just including the variable Huntbag. From the coefficients in the results, this role appears to be ten times greater. Also, the LR test confirms that the structural model is more suitable than the traditional travel cost model. It also indicates that a positive relationship between the expected probability of bagging game and the number of hunting days taken exists. Those hunters with a higher probability of bagging take more hunting days. In the model specification, the LR test shows that the structural model is better than the basic model. In addition, quantifying the effect that the probability of bagging game has over recreational hunting demand can help the welfare of a hunting day be estimated more accurately. In earlier studies, Creel and Loomis (1990) found that consumer surplus per trip was $36–172 for deer hunting in California depending on statistical models. Offenbach and Goodwin (1994) suggested that Kansas hunters’ benefits were about $218 per trip. Sarker and Surry (1998) estimated the benefits for per moose hunting trip were $210–252 (these values have been converted to 2006 dollars). Our estimation based on the Negative Binomial structural model for per big game hunting day is around $300. Big game hunting has always been regulated by the number of licenses, lottery participation, and general and individual bag limits to sustain wildlife populations. However, the regulations might jeopardize hunters’ satisfaction and participation. For policy recommendations, the results show that licenses, tags, permits and stamps issued in a hunter’s state does not significantly affect the hunting days taken by the hunter. A hunter may not always hunt only in his own state but the report shows that those licenses are mostly held by residents. This reveals the regulation does not result in a crowd effect while it also brings substantial revenue to the state. Thus the policy maker could keep the sustainability when issuing licenses, tags, permits and stamps. On the other hand, the number of licenses a hunter bought doesn’t gain the success of bagging an animal. Hunting success mainly depends on a hunter’s experience. The welfare estimation in this study can help improve decision making for the sustainability of hunted wildlife populations. A hunting day brings around $300 of satisfaction to a hunter. This welfare is based on Negative Binomial model II since the two pair-wise comparisons of model selection indicate a strong support. The significant dispersion parameter also shows the favorability of this model over the Poisson model.
A. Pang / Journal of Forest Economics 28 (2017) 12–17
This study does not cover site attributes since the data comes from national surveys and the regional classification is problematic. The site choice of hunters has also not been taken into consideration. In the future, narrowing down the area might be a good idea and could provide more information. The structural model of combing the traditional travel cost model and the probability of bagging could be applied to many kinds of activities as long as the probability enters into the consumer’s utility function. Acknowledgement The author appreciates the financial support from the Ministry of Science and Technology at Taiwan (NSC 102-2410-H-035-006). References Adamowicz, W., Swait, J., Boxall, P., Louviere, J., Williams, M., 1997. Perceptions versus objective measures of environmental quality in combined revealed and stated preference models of environmental valuation. J. Environ. Econ. Manag. 32 (1), 65–84. Bennett, J., Whitten, S., 2003. Duck hunting and wetland conservation: compromise or synergy? Can. J. Agric. Econ. 51, 161–173. Bockstael, N.E., McConnell, K.E., 1981. Theory and estimation of the household production function for wildlife recreation. J. Environ. Econ. Manag. 8, 199–214. Brown, T.L., Connelly, N.A., 1994. Predicting demand for big game and small game hunting licenses: the New York experience. Wildl. Soc. Bull. (1973–2006) 22 (2), 172–178. Creel, M.D., Loomis, J.B., 1990. Theoretical and empirical advantages of truncated count data estimators for analysis of deer hunting in California. Am. J. Agric. Econ. 72 (2), 434–441. Creel, M.D., Loomis, J.B., 1992. Modeling hunting demand in the presence of a bag limit, with tests of alternative specifications. J. Environ. Econ. Manag. 22, 99–113. Cooper, J.C., 2000. Nonparametric and semi-nonparametric recreational demand analysis. Am. J. Agric. Econ. 82, 451–462. Decker, D.J., Brown, T.J., Gutierrez, R.J., 1980. Further insights into the multiple-satisfactions approach for hunter management. Wildl. Soc. Bull. 8, 323–331. Englin, J., Lambert, D., 1995. measuring angling quality in count data models of recreational fishing: a non-nested test of three approaches. Environ. Resour. Econ. 6, 389–399. Englin, J., Shonkwiler, J.S., 1995. Modelling recreation demand in the presence of unobservable travel costs: toward a travel price model. J. Environ. Econ. Manag. 29, 368–377. Englin, J., Lambert, D., Shaw, W.D., 1997. A structural equations approach to modeling consumptive recreation demand. J. Environ. Econ. Manag. 33, 33–43. Freeman III, A.M., 1993. The Measurement of Environmental and Resource Values. Resources for the Future, Washington, D.C. Gigliotti, L.M., 2000. A classification scheme to better understand satisfaction of Black Hills deer hunters: the role of harvest success. Hum. Dimens. Wildl. 5, 32–51. Gillig, D., Woodward, R., Ozuna Jr., T., Griffin, W.L., 2003. Joint estimation of revealed and stated preference data: an application to recreational red snapper valuation. Agric. Resour. Econ. Rev. 32 (2), 209–221. Gourieroux, C., Monford, A., Trognon, A., 1984. Pseudo maximum likelihood methods: application to Poisson models. Econometrica 52, 701–720. Greene, G., Moss, C.B., Spreen, T.H., 1997. Demand for recreational fishing in Tampa Bay, Florida: a random utility approach. Mar. Resour. Econ. 12, 293–305. Greene, W.H., 2000. Econometric Analysis, 4th ed. McGraw-Hill, New York. Groothuis, P.A., 2005. Benefit transfer: a comparison of approaches. Growth Change 36 (4), 551–564.
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Hammitt, W.E., McDonald, C.D., Patterson, M.E., 1990. Determinants of multiple satisfaction for deer hunting. Wildl. Soc. Bull. 18, 331–337. Hansen, L., Feather, P., Shank, D., 1999. Valuation of agriculture’s multi-site environmental impacts: an application to pheasant hunting. Agric. Resour. Econ. Rev. 28 (2), 199–207. Hendee, J.C., 1974. A multiple-satisfaction approach to game management. Wildl. Soc. Bull. 2, 104–113. Lisa, A.O., Goodwin, B.K., 1992. Travel-cost analysis of the demand for hunting trips in Kansas. Appl. Econ. Perspect. Policy 16 (1), 55–61. Little, J.M., Grimsrud, K.M., Champ, P.A., Berrens, R.P., 2006. Investigation of stated and revealed preferences for an elk hunting raffle. Land Econ. 82 (4), 623–640. Loomis, J., Pierce, C., Manfredo, M., 2000. Using the demand for hunting licences to evaluate contingent valuation estimates of willingness to pay. Appl. Econ. Lett. 7 (7), 435–438. McConnell, K.E., 1979. Values of marine recreational fishing: measurement and impact of measurement. Am. J. Agric. Econ. 61 (5), 921–925. McConnell, K.E., Sutinen, J.G., 1979. Bioeconomic models of marine recreational fishing. J. Environ. Econ. Manag. 6, 127–139. with contributions by Valdes, S. and Weninger, Q.RMcConnell, K.E., Strand, I.E., 1994. The Economic Value of Mid and South Atlantic Sportfishing, vol. II. University of Maryland. McCullough, D.R., Carmen, W.J., 1982. Management goals for deer hunter satisfaction. Wildl. Soc. Bull. 10, 49–52. Milon, J.W., Clemmons, R., 1991. Hunters’ demand for species variety. Land Econ. 67 (4), 401–412. Miller, J.R., Michael, J.H., 1981. Determinants of hunter participation: duck hunting in the Mississippi Flyway. Am. J. Agric. Econ. 63 (4), 677–684. Murphy, K.M., Topel, R.H., 1985. Estimation and inference in two-step econometric models. J. Econ. Bus. Stat. 3 (4), 370–379. Nickerson, P.H., 1990. Demand for the regulation of recreation: the case of elk and deer hunting in Washington state. Land Econ. 66 (4), 437–447. Newbold, S.C., Massey, D.M., 2010. Recreation demand estimation and valuation in spatially connected systems. Resour. Energy Econ. 32 (2), 222–240. Offenbach, L.A., Goodwin, B.K., 1994. Travel-cost analysis of the demand for hunting trips in Kansas. Rev. Agric. Econ., 55–61. Sarker, R., Surry, Y., 1998. Economics value of big game hunting: the case of moose hunting in Ontario. J. For. Econ. 4 (1), 29–60. Scrogin, D., Berrens, R.P., Bohara, A.K., 2000. Policy changes and the demand for lottery-related big game hunting licenses. J. Agric. Resour. Econ. 25 (2), 501–519. Schwabe, K.A., Schuhmann, P.W., Boyd, R., Doroodian, K., 2001. The value of changes in deer season length: an application of the nested multinomial logit model. Environ. Resour. Econ. 19 (2), 131–147. Stankey, G.H., Lucas, R.C., Ream, R.R., 1973. Relationships between hunting success and satisfaction. In: Transactions of the North American Wildlife Conference, vol. 38., pp. 235–242. Sun, L., van Kooten, G.C., Voss, G.M., 2005. Demand for wildlife hunting in British Columbia. Can. J. Agric. Econ. 53, 25–46. U.S. Department of the Interior, Fish and Wildlife Service, and U.S. Department of Commerce, U.S. Census Bureau, 2006. 2006 National Survey of Fishing, Hunting, and Wildlife-Associated Recreation. Vaske, J.J., Donnelly, M.P., Heberlein, T.A., Shelby, B., 1982. Differences in reported satisfaction ratings by consumptive and nonconsumptive recreationists. J. Leis. Res. 14, 195–206. Vaske, J.J., Fedler, A.J., Graefe, A.R., 1986. Multiple determinants of satisfaction from a specific waterfowl hunting trip. Leis. Sci. 8, 149–166. Vuong, Q., 1989. Likelihood ratio tests for model selection and nonnested hypotheses. Econometrica 57, 307–333. Wam, H.K., Pedersen, H.C., Hjeljord, O., 2012. Balancing hunting regulations and hunter satisfaction: an integrated biosocioeconomic model to aid in sustainable management. Ecol. Econ. 79, 89–96. Zimmer, N.M., Boxall, P.C., Adamowicz, W.L., 2012. The impacts of chronic wasting disease and its management on recreational hunters. Can. J. Agric. Econ. 60 (1), 71–92.
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Journal of Forest Economics journal homepage: www.elsevier.com/locate/jfe
Incorporating the effect of successfully bagging big game into recreational hunting: An examination of deer, moose and elk hunting Arwin Pang Department of Accounting, National Chung Hsing University, Taiwan
a r t i c l e
i n f o
Article history: Received 14 November 2016 Accepted 12 April 2017 JEL classification: Q5 Keywords: Structural equations model Hunting demand Bagging probability
a b s t r a c t This analysis aims to quantify the effect that the probability of bagging game will have on the demand for recreational hunting. A two equation structural model has been developed which allows the probability of bagging game to be simultaneously entered into the travel cost model. The basic model is based on a Poisson distribution for the travel cost, and a Negative Binomial distribution is used to deal with the issue of overdispersion. Likelihood ratio tests and non-nested model selection tests have been adopted to choose the model which best fits the data. The results show that a Negative Binomial structural model is the best and the probability of bagging game has a significant effect on the travel cost model. The welfare per hunting day is around $300. ˚ © 2017 Department of Forest Economics, Swedish University of Agricultural Sciences, Umea. Published by Elsevier GmbH. All rights reserved.
Introduction According to the national survey, 12.5 million people 16 years old and older enjoyed hunting a variety of animals within the United States in 2006. Among the hunting games, big game hunting was the most popular type of hunting, such as deer and elk (U.S. Department of the Interior, Fish and Wildlife Service, and U.S. Department of Commerce, U.S. Census Bureau, 2006). Hunting success or harvest was commonly linked to hunter satisfaction. Hendee (1974) first suggested a multiple-satisfaction for hunter. The satisfaction is not solely on bagging game, but more complex elements. This concept recognizes the factors such as enjoying nature, exploring outdoors, adventure, companionship and so on (Hendee, 1974; McCullough and Carmen, 1982; Vaske et al., 1986; Hammitt et al., 1990). However, generally the studies found the harvest is still the strong predictor of hunter satisfaction. Successful hunters reported greater satisfaction than unsuccessful ones. Thus, the importance of maintaining some probability of harvest success to uphold hunter satisfaction is emphasized (Stankey et al., 1973; Decker et al., 1980; Vaske et al., 1982; McCullough and Carmen, 1982; Gigliotti, 2000). There have been numerous studies done by economists to estimate the recreational demand for hunting. Although the literature is rich, it has not paid much attention to hunting success which is recognized in the hunter satisfaction literature. This study attempts to discuss the role of successful bagging in recreational demand
E-mail address: [email protected]
through hunter satisfaction (utility). We believe besides the pleasure of exploring nature, the successful bagging of game on a hunting or fishing trip also contributes to the hunter’s (or angler’s) utility. Incorporating the hunting success or harvest into the recreational demand for hunting will bridge the gap between the hunting demand and hunter satisfaction. It will also contribute the literature by investigating the significance of harvest success in hunting demand. In literature about fishing demand, there are two ways to understand the role of bagging success. McConnell and Sutinen (1979) developed a bioeconomic model of recreational fishing by assuming that the catch rate is exogenous to private decisions. Greene et al. (1997) and Gillig et al. (2003) also treated catch rate as exogenous when estimating fishing demand. Conversely, some studies no longer assume that catch rate is exogenous in their models. Bockstael and McConnell (1981) introduced a household production function where the catch rate will be affected by exogenous factors like the stock of wildlife and the individual’s experience. This allowed them to model the theoretical interaction between the household’s behavior and public inputs into recreation. McConnell (1979) used a household production function to estimate the empirical value of fish where fish caught per trip is set as a function of the inputs used to catch more fish per trip, the stock density of available fish and the attributes of individual anglers. The 2SLS method is used and the predicted value of fish caught per trip is the instrument variable. McConnell and Strand (1994) instituted an individual catch rate, which is a random variable depending on the density of fish at the site and the characteristics of individual
http://dx.doi.org/10.1016/j.jfe.2017.04.003 ˚ Published by Elsevier GmbH. All rights reserved. 1104-6899/© 2017 Department of Forest Economics, Swedish University of Agricultural Sciences, Umea.
A. Pang / Journal of Forest Economics 28 (2017) 12–17
anglers used in the model, such as hours fished and years of experience. Englin et al. (1997) constructed a two equation structural model that included a total catch function representing angling success within the travel cost model. As for hunting demand, Miller and Michael (1981) studied hunter participation in duck hunting in Mississippi. Hunter success, which is measured by the number of ducks bagged, is included in their model. Creel and Loomis (1990) used truncated Poisson distribution and Negative Binomial count data models to evaluate deer hunting in California. In their model, a dummy variable is included to represent the successful bagging of an animal. They further discussed the confidence intervals for welfare measures in 1991. Lisa and Goodwin (1992) evaluated the demand for hunting trips in Kansas by including the time spent on site in the travel cost method. They concluded that the hunter’s age, investment in hunting equipment, and quality of the site do significantly influence demand. Sarker and Surry (1998) adopted a travel cost method to estimate the demand for and the economic value of recreational moose hunting in Ontario by using 4 alternative count data models (Poisson, Geometric, Negative Binomial type II, and Creel and Loomis). Hansen et al. (1999) developed a multi-site demand model to estimate the demand for pheasant hunting and evaluate the impact of the Conservation Reserve Program on pheasant hunting quality. Cooper (2000) presented two nonparametric approaches and developed one semi-nonparametric count model for travel cost as applied to waterfowl hunting trips for the six national wildlife refuges in California’s San Joaquin Valley. Bennett and Whitten (2003) examined the benefits and costs of duck hunting on wetland conservation. Groothuis (2005) used a linear form travel cost function which includes the number of deer a respondent bagged to estimate the consumer surplus for deer hunting. In addition, there are some other interesting topics related to hunting in the literature. Among them, the regulation of hunting is an important issue that has received much attention. Nickerson (1990) evaluated the demand for regulation of big game hunting for elk and deer in Washington state. Creel and Loomis (1992) developed a Truncated Joint Trip-Bag model which accounts for the effects of bag limits on the behavior of hunters in California. Little et al. (2006) investigated the elk permit lottery demand. Schwabe et al. (2001) studied the value of changes in deer season length in welfare rather than bag limit, which is the traditional method. Wam et al. (2012) used Norwegian grouse hunting data to study the number of permits or the bag size allowed per hunter in sustainable management. Some studies are devoted to hunting license demand (Brown and Connelly, 1994; Loomis et al., 2000; Scrogin et al., 2000; Sun et al., 2005). Milon and Clemmons (1991) evaluated the economic determinants of demand for species variety in wildlife recreation choices. Additionally, the site choices of recreational hunters were also examined (Adamowicz et al., 1997; Newbold and Massey, 2010; Zimmer et al., 2012). From the hunting literature review, although Miller and Michael (1981), Creel and Loomis (1990) and Groothuis (2005) included an exogenous bag variable into their studies, the issue of bagging success in hunting has not drawn as much attention as catching success in fishing. In the United States, hunting of game animals is regulated to ensure the long term viability of hunted wildlife populations. All hunters are required to get licenses to hunt and face bag limits on the number of animals they can take on a single trip or over the length of the season. As mentioned above, these regulations also play an important role in the hunting literature. Although a bagged game attribute will complicate the measurement of demand for hunting and of welfare since it affects hunters’ satisfaction and utility, it should not be neglected. As for the policy of regulation, licenses, tags, permits, and stamps issued in a hunter’s state were included in the hunting demand in this study. Wam et al. (2012)
13
found that selling permits gains profits for the government, but crowding causes a loss of hunter satisfaction. The goal of this study is to investigate the effect of game bagging success on hunting trips. The method is to incorporate the expected probability of bagging game as explanatory variable in estimating the demand for hunting trips which has been absent in the previous literature. This study will employ a structural model to estimate hunting demand with the probability of bagging incorporated. The next section introduces the structural model, which combines the traditional travel cost model and probability of bagging game. The section “Data and results” presents the data and estimated results. The final section concludes the study. Methodology A structural model Travel cost demand function The travel cost method assumes that users try to maximize their utility when choosing a site to visit and that utility is related to socioeconomic characteristics of the consumer and depends on the full cost incurred by it with his/her visit. A typical approach that the individuals increase their utility depending on the number of visits, time spent at the site, characteristics of the site and the quantity of the numeraire. Analytically the maximization problem can be presented as: Max : u(S, r, q)
(1)
where S stands for the numeraire whose price is 1, r represents the number of visits to the recreation site and q is the environmental quality at the site. The maximization of the individual is subject to monetary and time constraints. M + w · tw = S + c · r
(2)
t = tw + (t1 + t2 )r
(3)
where M is exogenous income, which stands for the individual’s demand; w is the wage rate; c is the monetary cost of visiting; t is the time endowment; tw is the time of working; t1 is the time of visiting; t2 is the time spent at the site. The utility maximization problem yields the travel cost demand function (Freeman, 1993). r = r(c, M, q)
(4)
The structural model The structural model is based on the travel cost method in the section “Travel cost demand function” which assumes that hunters try to maximize their utility related to their socioeconomic characteristics and the full cost incurred for their trips. The hunting demand is defined as: Trips = f (TC, X, Z)
(5)
Trips is the number trips taken in a year by hunter; TC is the travel cost; X represents a set of individual characteristics of the hunter; Z is a vector of site characteristics. The probability of bagging is used to obtain the expected probability of success that each hunter has, and is mainly based on measures of personal input and site quality characteristics as per the fishing literature mentioned in the introduction. The model has the following general form: bag = g(X, Z)
(6)
It states that the probability of a bag is linked to a vector of individual characteristics (X) such as hunter experience, skill, and investment in hunting, as well as site quality (Z).
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A. Pang / Journal of Forest Economics 28 (2017) 12–17
Table 1 Descriptive statistics. Variable
Description
Mean
Std. Dev.
Huntday Huntcost Huntbag Age Education Race Income Gender Marriage Huntday2005 License Total Licenses Paid License Holders Region dummy New England Middle Atlantic East North Central West North Central South Atlantic East South Central West South Central Mountain Pacific
The number of hunting days The total amount spent on big game hunting per hunting day Bag or not Years School Years White = 1, Other = 0 Household income Male = 1, Female = 0 Married = 1, Single = 0 The number of days hunting in 2005 The number of hunting licenses owned The number of total licenses issued by hunter’s state The number of paid license holders in hunter’s state
30.58 17.69 0.57 46.08 13.78 0.98 82,451.22 0.96 0.75 23.17 2.21 716,400.30 307,340.80
26.31 54.19 0.50 13.73 2.34 0.15 36,578.52 0.21 0.43 9.63 1.70 628,135.80 251,929.30
0.11 0.08 0.06 0.14 0.23 0.10 0.13 0.07 0.08
0.32 0.28 0.24 0.34 0.42 0.30 0.33 0.26 0.28
Incorporating the expected probability of bagging game into the travel cost demand helps us to evaluate the effect which that probability will have on that demand. The new structural demand is Trips = f (TC, X, Zi , g(X, Z))
taneously is adopted. This joint estimation sums up all likelihood functions from the models to be estimated, treating all variables and all parameters jointly. It has the advantage of avoiding the need for any covariance matrix correction (Murphy and Topel, 1985). The Full Information Maximum Likelihood method is efficient for estimating a joint model. With normally distributed disturbances, the results are efficient among all estimators (Greene, 2000). In the case of the Poisson distribution, the joint estimation likelihood function is:
(7)
Econometric model Since the data for hunting demand follows a count form, count distributions are appealing because they fit the characteristics of the data, being a nonnegative discrete range of values (Creel and Loomis, 1990). The Poisson distribution is one of the most commonly used. It is attractive by being part of the linear exponentials family and keeps a nice robustness that makes the estimators of parameters consistent and asymptotically normal even when the underlying distribution is not strictly Poisson (Gourieroux et al., 1984). A probit link is adopted for the probability of bagging since it has a binary dependent variable which deals with an expected value that lies between 0 and 1 (Greene, 2000). It is related to the normal cumulative density function as it transforms xˇ into the probability associated with its calculated value. For the ith observation, the probit link is defined as i = (xi ˇ)
=
prob
+bi
• • • •
ln
tripsi +
(9)
1 ˛
− ln (tripsi + 1) − ln
i
+bi
prob
· ln(pi ) + (1 − bi
prob
) · ln(1 − pi )
1 ˛
) · ln(1 − pi )
(10)
= exp(xˇ) x: matrix of independent variables bprob : bag reported by hunter p: probability of bag
The first part of the likelihood function is a regular Poisson model of ith observation. The Poisson model is the most basic count travel cost demand. It provides an excellent reference point because it does not contain any shape parameters to be estimated. Although Poisson has many suitable features for our count data estimation and the parameters are unbiased as long as the underlying relationship is linear or exponential, we try to relax the requirement for the mean to equal the variance due to the possible overdispersion issue, because this failure to model heteroscedasticity can lead to a variety of issues. The Negative Binomial is a popular generalization of the Poisson. It can be found by mixing a gamma density with mean 1 and variance 1/˛ with the Poisson. The joint estimation likelihood function of the Negative Binomial distribution is
The represents the cumulative standard normal distribution transformation. A joint estimation where the parameters for the travel cost method and the probability of bagging game are estimated simul-
=
prob
· ln(pi ) + (1 − bi
where
where x is the set of expansionary variables, ˇ is a set of parameters. The log likelihood function relates to the Bernoulli distribution transformation which looks like:
((−i + tripsi · ln i ) − ln(tripsi !))
i
(8)
i = yi ln i + (1 − yi ) ln(1 − i )
+
1 ln ˛
1 ˛
·
1 (1/˛) + i
+ tripsi ln(i ((1/˛) + i ))
(11)
A. Pang / Journal of Forest Economics 28 (2017) 12–17
15
Table 2 Estimated results. Poisson
Constant Huntcost Age Education Race Household Income (in 1000) Gender Married Pacific Total Licenses (in 1,000,000)
II
I
II
4.1039*** (0.8534) −0.0058** (0.0023) 0.0009 (0.0049) −0.0570** (0.0227) −0.1757 (0.5777) 0.0000 (0.0018) 0.3014 (0.3830) −0.1954 (0.1467) −0.4057** (0.1723) 0.0052 (0.1083)
2.7230** (1.0896) −0.0063*** (0.0024) 0.0008 (0.0048) −0.0623*** (0.0235) −0.3638 (0.5631) 0.0001 (0.0017) 0.3414 (0.3569) −0.1566 (0.1483) −0.4857*** (0.1579) −0.0243 (0.0934) 0.2816** (0.1102) 1.7856* (1.1455) 0.4814*** (0.0462)
3.8320*** (0.5783) −0.0032*** (0.0007) 0.0012 (0.0046) −0.0612*** (0.0224) 0.0495 (0.3114) −0.0002 (0.0016) 0.3158 (0.3350) −0.1318 (0.1359) −0.3585** (0.1625) 0.0332 (0.0971)
2.0500*** (0.5309) −0.0033*** (0.0013) 0.0045 (0.0033) −0.0552** (0.0257) −0.0191 (0.2426) 0.0004 (0.0014) −0.2424 (0.2082) −0.1589 (0.1186) −0.3619* (0.2417) −0.1008 (0.0888) 0.2673** (0.1080) 4.1059*** (0.6141) 0.4077*** (0.0496)
Huntbag Prob(Huntbag) Alpha Probit Constant
−0.5311* (0.6414) 0.0011* (0.0067) 0.4985 (0.4966) 0.0148* (0.0095) −0.0848* (0.0548) 0.0009 (0.0037)
Age Gender Huntday License Paid License Holder (in 10,000)
Log Likelihood LR test
Negative Binomial
I
−2116.7 346.4***
−2289.9
−0.5313 (0.5815) 0.0011 (0.0072) 0.4987 (0.4391) 0.0148* (0.0101) −0.0848* (0.0567) 0.0009 (0.0036) −876.77 238.8***
−996.17
*
Significant at the 15% level. Significant at the 5% level. *** Significant at the 1% level. Heteroscedasticity-consistent (robust) standard errors are reported in parentheses. **
where ˛ is the overdispersion parameter and estimated from the data. The expectation is that relaxing the equivalence between the mean and variance will result in improved efficiency. The optimization is to find the parameters which maximize the joint estimation likelihood function. Newton’s method for maximum likelihood estimation is used. For Poisson and Negative Binomial distributions, both the basic travel cost model and the structural model are estimated in this study. In the basic travel cost model, the bag probability reported by hunter is included. While in the structural model, the probability of bagging produced by the probit part is entered into the basic travel cost function as equation (7). Data and results The data set used in this study is the 2006 National Survey of Fishing, Hunting, and Wildlife-Associated Recreation by U.S. Fish and Wildlife Service. The Survey was carried out by the U.S. Census Bureau in two phases. In the first phase 85,000 households nationwide were interviewed by telephone in April 2006. The screener questionnaire was about demographic information of the house-
hold members and attempted to find out which members of the household had fished, hunted, or watched wildlife in 2005, and would likely engage in those activities in the future. The second phase includes three detailed telephone interviews about the activities and expenditures. The respondents were at least 16 years old. In total, 21,938 anglers and hunters were surveyed. The dependent variable in travel cost demand is the number of hunting days (Huntday) in 2006 instead of hunting trips mentioned in section 2 since a trip could be varying in length. Here, a hunting trip refers to big game hunting which is for deer, elk or moose. The first explanatory variable in the travel cost demand model is the travel cost of a hunting day (Huntcost) which is the total amount a hunter spent on big hunting tips in 2006 over the number of hunting days. The other explanatory variables include the demographic variables Age measured in years, and Education measured in school years, Race (White = 1, Other = 0), Income which is the mean value of income per interval of the questionnaire, Gender (Male = 1, Female = 0), Marriage (Married = 1, Single = 0), Total Licenses is the number of licenses, tags, permits and stamps issued in the hunter’s state, a region dummy – Pacific and Huntbag (Yes = 1, No = 0). Totally there are 205 observations used in this study.
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A. Pang / Journal of Forest Economics 28 (2017) 12–17
On the probability of bagging, the dependent variable is Huntbag which is whether the hunter has bagged game or not on a hunt in 2006. The explanatory variables are Age; Gender; Huntday, the number of days the hunter hunted during 2005; License, the number of hunting licenses the hunter owned in 2006; and Paid License Holder, the number of paid license holders of hunter’s state. The descriptive statistics are reported in Table 1. The estimated results for the two distribution models are displayed in Table 2. For both models, a basic model (I) and a structural model (II) are estimated. For all models, the intercept terms are positive. The travel cost (Huntcost) coefficients are negative and significant at the 1% level, showing a downward sloping demand curve as expected. For the socioeconomic variables, the negatively significant coefficients on Education show that people with less school years take more hunting days. Race, Household income and Married have an insignificant effect on hunting days in models. The total number of licenses, tags, permits, and stamps in a hunter’s state has an insignificant negative effect on hunting days in the model II. Pacific includes states of Alaska, California, Hawaii, Oregon, and Washington where people engaged in less hunting activities in the survey. These states also issue fewer licenses in the national hunting license report, which has a negative effect on hunting days. The results of model I and II are quite consistent in the travel cost demand except Gender with switching signs in Negative Binomial model. This result indicates that it is present both in travel cost demand and the probability of bagging game. The net effect includes the direct effect on travel cost and the indirect effect through the probability of bagging game. Huntbag has a positive effect on hunting days in both basic models. The coefficients of Prob(Huntbag) in structural model II are always positive and significant which indicates that not only does the expected probability of bagging game have a positive impact on the utility of a hunting day, but that the likelihood of bagging also influences the number of days positively. It should be noted that the magnitude of coefficients on Prob(Huntbag) are much larger than on Huntbag. The results for bagging probability are consistent. In Poisson model, the positive significant coefficient of Age shows that an older hunter has a higher probability to bag an animal. More skilled and experienced hunters who spent more days hunting have a higher probability of bagging in both distribution models. Hunters with more licenses don’t assure the good luck on bagging. The number of paid licenses in a hunter’s state has negative impact on hunting days, but they are not statistically significant. The likelihood ratio (LR) test results in Table 2 show the econometric specification that best fits the data between the basic and structural model for each distribution model. These results show that model II is better than model I. A non-nested model selection test (Vuong, 1989; Englin and Lambert, 1995) is used to select the best distribution among different specifications. This test is a two-step procedure. In the first step, the sample variance of the log likelihood ratio is compared to the critical value from a multivariate distribution to decide whether the null hypothesis that two conditional models are distinguishable is rejected or accepted. If the null hypothesis is rejected the second step applies a directional test to indicate either that one model dominates the other or that neither model is preferred. The results of the first step show that the null hypothesis is rejected. The test statistics of the second step is −7.4596, significantly shows that Negative Binomial model II is better than Poisson model II. In addition, the significant coefficient of the dispersion effect (˛) in the Negative Binomial model also supports this finding. These two pair-wise comparisons of model selection indicate a strong preference for Negative Binomial model II. Consumer surplus represents the difference between the maximum that consumers would be willing to pay for a good and what
they actually pay. The usual integration under the ordinary demand function has a per hunting day which is −1/ˇHuntcost . The variance of consumer surplus per hunting day estimates can be calculated as (Englin and Shonkwiler, 1995): Var
1 ˇ
=
S2 S4 +2 6 4 ˇ ˇ
(12)
where S denotes the standard error of ˇ. These calculations can therefore give the welfare for hunters with the Negative Binomial structural model. The consumer surplus per big game hunting day is around 301.26 dollars with standard error $14.98. When the probability of bagging is increased by 1% for each hunter, the expected hunting days will be increased from 30.45 to 31.73, the consumer surplus per hunting day is raised by $384 which is −1/ˇHuntcost · (31.73 − 30.45). The successful bagging of an animal not only brings the hunter satisfaction but also the economic value of the animal itself. Conclusion Typically a hunter’s utility is not only derived from the trip itself but also the successful bagging of game. However, little attention has been paid to the issue that bagging an animal brings hunter satisfaction. This study incorporates the probability of bagging game into the travel cost demand model. The probability of bagging game plays a more significant role in the basic travel cost model than just including the variable Huntbag. From the coefficients in the results, this role appears to be ten times greater. Also, the LR test confirms that the structural model is more suitable than the traditional travel cost model. It also indicates that a positive relationship between the expected probability of bagging game and the number of hunting days taken exists. Those hunters with a higher probability of bagging take more hunting days. In the model specification, the LR test shows that the structural model is better than the basic model. In addition, quantifying the effect that the probability of bagging game has over recreational hunting demand can help the welfare of a hunting day be estimated more accurately. In earlier studies, Creel and Loomis (1990) found that consumer surplus per trip was $36–172 for deer hunting in California depending on statistical models. Offenbach and Goodwin (1994) suggested that Kansas hunters’ benefits were about $218 per trip. Sarker and Surry (1998) estimated the benefits for per moose hunting trip were $210–252 (these values have been converted to 2006 dollars). Our estimation based on the Negative Binomial structural model for per big game hunting day is around $300. Big game hunting has always been regulated by the number of licenses, lottery participation, and general and individual bag limits to sustain wildlife populations. However, the regulations might jeopardize hunters’ satisfaction and participation. For policy recommendations, the results show that licenses, tags, permits and stamps issued in a hunter’s state does not significantly affect the hunting days taken by the hunter. A hunter may not always hunt only in his own state but the report shows that those licenses are mostly held by residents. This reveals the regulation does not result in a crowd effect while it also brings substantial revenue to the state. Thus the policy maker could keep the sustainability when issuing licenses, tags, permits and stamps. On the other hand, the number of licenses a hunter bought doesn’t gain the success of bagging an animal. Hunting success mainly depends on a hunter’s experience. The welfare estimation in this study can help improve decision making for the sustainability of hunted wildlife populations. A hunting day brings around $300 of satisfaction to a hunter. This welfare is based on Negative Binomial model II since the two pair-wise comparisons of model selection indicate a strong support. The significant dispersion parameter also shows the favorability of this model over the Poisson model.
A. Pang / Journal of Forest Economics 28 (2017) 12–17
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