In most applications of complete systems of demand functions to national accounts data it is implicitly assumed that the demand functions are identified. For post-war Sweden this is not an altogether good assumption because due to rent control there was an excess demand for housing. In this paper the linear expenditure system is modified to include a supply function for housing. Supply is simply assumed to be a function of excess demand. The model is estimated by the maxi mum likelihood method and the results are compared to those obtained for the ordinary linear expenditure system.