Self selectivity in censored discrete continuous choice: the empirical implications of alternative correction formulae

In modelling the relationship between a discrete choice (eg, of vehicle type) and a continuous choice (eg, vehicle utilisation) one typically observes the level of the continuous dependent variable of only the chosen discrete alternative. The absence of data on the level of consumption of the non chosen alternatives is a potential source of selectivity bias. In many contexts it is invalid to assume that the level of consumption is independent of the technology of a consumer durable; for example the amount of use of an old four cylinder vehicle is likely to be less, ceteris paribus, than that of a new eight cylinder vehicle. Failure to recognise the endogeneity of unobserved influences on vehicle choice in the utilisation decision will contribute to erroneous predictions. There exist many procedures for correcting for selectivity so that predictions of usage levels of non chosen alternatives can be obtained if one wishes to include usage as an influence on vehicle choice, or if one wants to apply the usage model to obtain usage predictions on any vehicle type. In this paper we identify the main sources of self selectivity, motivate the problem with an example, and introduce correction formulae that are easy to implement and generalise to polychotomous choice. We assess the empirical implications of the alternative formulae in the context of household vehicle type choice and level of use. The data is drawn from the first wave of a panel data set of 1436 households in the Sydney metropolitan area (a).