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. In the first stage reduced form parameters are obtained through either ordinary least squares or heteroscedastic Tobit estimation, followed by the identification of structural parameters and imposition of cross-equation restrictions using minimum distance techniques. The procedure, which is demonstrated on data from Romania, yields elasticity estimates that lie within an intuitively pleasing range and reveals strong cross-substitution patterns between many commodity groups.