Testing the Normality Assumption in the Sample Selection Model with an Application to Travel Demand

In this paper we introduce a test for the normality assumption in the sample selection model. The test is based on a generalization of a semi-nonparametric maximum likelihood method. In this estimation method, the distribution of the error terms is approximated by a Hermite series, with normality as a special case. Because all parameters of the model are estimated both under normality and in the more general specification, we can test for normality using the likelihood ratio approach. This test has reasonable power as is shown by a simulation study. Finally, we apply the generalized semi-nonparametric maximum likelihood estimation method and the normality test to a model of car ownership and car use. The assumption of normal distributed error terms is rejected and we provide estimates of the sample selection model that are consistent