Theoretical and Empirical Advantages of Truncated Count Data Estimators for Analysis of Deer Hunting in California

Abstract

Truncated Poisson and truncated negative binomial count data models, as well as standard count data models, OLS, nonlinear normal, and truncated nonlinear normal MLE were used to estimate demand for deer hunting in California. The truncated count data estimators and their properties are reviewed. A large sample (N = 2223) allowed random segmenting of the data into specification, estimation, and out‐of‐sample prediction portions. Statistics of interest are therefore unbiased by the specification search, and the prediction results allow comparison of the statistical models' robustness. The new estimators are found to be more appropriate for estimating and predicting demand and social benefits than the alternative estimators based on a variety of criteria.

An estimate of the recreational value of the Agulhas Plain, South Africa, with special reference to the value of plant biodiversity

“…Trips are a count data variable, which is usually Poisson distributed, meaning that a small number of people visit quite frequently while most visit rarely. However, since survey data almost never meet Poisson's stringent requirement of the mean being equal to the variance, a Poisson regression produces biased and inconsistent coefficients (Creel & Loomis, 1990;Grogger & Carson, 1991). The mean equals variance requirement of Poisson is relaxed in the negative binomial regression by including a parameter alpha to capture the degree of over dispersal in the sample (Martínez-Espiñeira & Amoaka-Tuffour, 2008).…”

“…In practice, the price of substitute sites was not universally included in the literature. Some studies omitted it for good reason; for example, once a license for hunting at a specific site had been purchased, the site no longer had relevant substitutes (Creel & Loomis, 1990). Other studies omitted the price of substitute sites for convenience (Rosenthal, 1987;Common et al, 1997;Garrod & Willis, 1999;Liston-Heyes & Heyes, 1999).…”

“…In travel-cost modelling, consumer surplus was defined as the integral of the trip demand function between an individual's travel-cost expenditure and a choke price, where the number of visits per annum demanded is "choked" to zero by excessive distance to the site (Eglin & Shonkwiler, 1995;Bellù & Cistulli, 1997;Markandya et al, 2002). For count data models, consumer surplus per visit was calculated as 1/β TC (Creel & Loomis, 1990). A further concern has been raised in the literature, that the Marshallian consumer surplus is strictly inappropriate where the empirical income effect is positive (Ziemer, Musser & Hill, 1980;Carr & Mendelsohn, 2003), but in practice this is of little concern, as measurement errors in the demand function are likely to be far larger than the difference between the Marshallian and Hicksian consumer surplus values (Eglin & Shonkwiler, 1995;Campbell & Brown, 2003).…”

“…Over the last twenty years, individual travel cost models have emerged as the preferred way of measuring the use value of recreational sites (Creel & Loomis, 1990;Freeman, 1993;Eglin & Shonkwiler, 1995;Gurmu & Trivedi, 1996;Garrod & Willis, 1999;Ward & Beal, 2000;Shrestha, Seidl & Moraes, 2002;Martínez-Espiñeira & AmoakaTuffour, 2008).…”

Fundamentals of estimating the net benefits of ecosystem preservation: the case of the Salton Sea

“…Results suggested that the annual net present value for camping at this park alone was nearly $40 million. Other recent analyses include valuing hiking in National Forests in Colorado and Montana (Hesseln et al, 2004), canoeing in Canada (Hellerstein, 1991), hunting in California (Creel & Loomis, 1990), Chinook Salmon sport fishing in Alaska (Layman et al, 1996), and ecotourism and wildlife viewing in Costa Rica, and Kenya (Menkhaus & Lober, 1996;Navrud & Mungatana, 1994). This method could similarly be employed to value the flow of recreation services from the Salton Sea.…”