Tomoaki Nakatani1* and Kazuo Sato2
The aim of this paper is to extend the truncated and endogenously stratified Poisson and negative binomial models to three alternative discrete distributions, namely the generalized Poisson, geometric and Borel distributions. Our primary intention here is to demonstrate how the improper treatments of the data generate divergent outcomes by applying those results to the recreation trip data surveyed from the visitors to an indigenous horse park in Japan. Our empirical application shows that failure to account for overdispersion, truncation and endogenous stratification leads to substantial changes in parameter estimates and their standard errors. The parameter on the travel cost tends to be underestimated in absolute value in the standard setups. This induces serious overestimation of the economic benefit that the recreation site offers to the society. Even when the endogenous stratification is incorporated, ignoring the overdispersion estimates the per capita per trip consumer surplus over 7 times larger than the one obtained under the endogenous stratification and overdispersion.
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