The theoretical model of Gaertner (1974) and Pollak (1976) for the interdependence of preferences in the Linear Expenditure System is estimated for a cross-section of households. The interdependence of consumption of different households has implications for the stochastic structure of the model and for the identifiability of its parameters. Both aspects are dealt with. The empirical results indicate a significant role played by the interdependence of preferences. One of its implications is that predictions of the effects of changes in a household's exogenous variables differ according to whether the exogenous variable only changes for this household or for all households jointly.