Recent micro-simulation studies of the demand for electricity by residences have attempted to model jointly the demand for appliance and the demand for electricity by appliance. Within this context it becomes important to test the statistical exogeneity of appliance dummy variables typically included in demand for electricity equations. If, as the theory would suggest, the demand for durables and their use are related decisions by the consumer, specifications which ignore this fact will lead to biased and inconsistent estimates of price and income elasticities. The present paper attempts to test this bias using a subsample of the 1975 survey of 3249 households carried out by the Washington Center for Metropolitan Studies (WCMS) for the Federal Energy Administration. We discuss and derive a unified model of the demand for consumer durables and the derived demand for electricity. To determine the magnitude of the bias resulting from estimating a unit electricity consumption (UEC) equation by ordinary least squares when unobserved factors influence both choice of appliances and intensity of use, we introduce and estimate a joint water-heat space-heat choice model, and conclude with the consistent estimation and specification of demand for electricity equations.