Theil's theory of rational random errors is sufficient for strict exogeneity of group expenditure in separable demand models. Generalized rational random errors is necessary and sufficient for strict exogeneity of group expenditure. A simple, robust, asymptotically normal t-test of this hypothesis is derived based on the generalized method of moments. An application to per capita annual U.S. food demand in the 20th century strongly rejects exogeneity of food expenditure in a model that in all other respects is highly compatible with the data set and with the implications of economic theory.