Testing for Overdispersion in Truncated Count Data Recreation Demand Functions

Abstract

Recreation demand functions specify the relationship between the number of trips a recreationist takes to a recreation site in a given time period and the cost of the trip. The dependent variable in these recreation demand functions is a non-negative integer, which suggests the use of an estimator based on a count data distribution. Additionally, because much of the data for estimating recreation demand functions are obtained through the use of on-site samples, an estimator which accounts for truncation is called for. Current research has addressed these issues by employing truncated count data estimators. Some of these estimators, however, are subject to problems of overdispersion. As in standard regression analysis, it is desirable to test the adequacy of the fitted count data model and to examine whether a specific deficiency of any initially entertained count model can be removed by progression to a less restrictive model. Prior research in this area has not adequately addressed this issue. Hence, in the present research, score tests for overdispersion are presented and discussed. The usefulness of such tests for recreation demand modelling are illustrated through an empirical recreation boating example. The results indicate that overdispersion can have significant effects on consumer surplus estimates. The importance of these tests and the ease with which they can be implemented gives credence to their routine application in future cases where truncated count data recreation demand functions are estimated.