Simulation, numerical approximation and closed forms for joint discrete continuous models with an application to household vehicle ownership and use

Integrated models for multiple decision variables, not necessarily from the same family, are becoming possible thanks to the advances in econometrics and in the estimation techniques. Recently, probit type models have been proposed to model joint decisions for the flexibility offered by the multivariate normal to capture correlations across the different dependent variables. Ordered probit models are in general preferred to unordered probit for the saving in computational costs deriving from the closed mathematical form of the choice probabilities. In this study, we compare results obtained from unordered probit models estimated with simulation and numerical computation to those obtained from ordered discrete–continuous probit. The analysis is performed on household decisions concerning vehicle holding and mileage travelled and using data extracted from the 2009 National Household Travel Survey. Estimation results show that discrete–continuous unordered probit are superior to ordered structures in terms of goodness of fit, but produce comparable results when applied to predict behavioral changes. Model applications for policy analysis also reveal that income and density only affects marginally vehicle holding decisions and annual miles driven, while driving cost has a more significant effect on annual household mileage.