In this paper we derive a joint continuous/censored demand system suitable for the analysis of commodity demand relationships using panel data. Unobserved heterogeneity is controlled for using a correlated random effects specification and a Generalized Method of Moments framework used to estimate the model in two stages. While relatively small differences in elasticity estimates are found between a flexible specification and one that restricts the relationship between the random effect and budget shares to be time invariant, larger differences are observed between the most flexible random effects model and a pooled cross sectional estimator. The results suggest the limited ability of such estimators to control for preference heterogeneity and unit value endogeneity leads to parameter bias.