Estimating demand systems with corner solutions: the performance of Tobit-based approaches

Since the introduction of the Tobit framework to perform estimation involving censored dependent variables, practitioners have been facing a clear trade-off between flexibility and theoretical plausibility in modelling consumers’ preferences in the presence of zero consumptions; the Kuhn-Tucker (or virtual price) approach is rigorously based on the economic choice theory but cannot be applied to complex and flexible demand systems, whereas the Tobit-based approach can be applied to any class of demand systems but is deficient in the theoretical foundations on the underlying preferences behind the observed choices. Hence, we assess the performance of three Tobit-based approaches (simple, correlated, and Amemiya-Tobin) and explore the extent of possible biases in elasticity estimates to provide reasonable criteria for model selection. Our analysis concludes that theoretical restrictions implied by the choice theory are essential to the Tobit model and improve its ability to capture the true underlying elasticities and mitigate overrejections. However, the performance of the Tobit models gradually deteriorates as the number of zero consumptions increases; the average rejection rate against the true elasticity values increases substantially as we have more zero consumptions. We illustrate the performance differences among the three Tobit models by applying them to the estimation of demand for fruits and vegetables.