Homogeneity and endogeneity in systems of demand equations

In estimating systems of demand equations one of the right-hand-side explanatory variables, expenditure, may be endogenous in the sense that it is correlated with the equation error. If the assumption of homogeneity of degree zero in prices and nominal income is imposed on the system, it turns out it is still possible to estimate the parameters of the system even when expenditure is endogenous. The estimation procedure is simple requiring just one additional ordinary least squares regression. The paper also demostrates that a model in which homogeneity is tested with expenditure assumed exogenous is exactly equivalent to a model in which the exogeneity of expenditure is tested with homogeneity imposed. Previous tests of demand systems which have rejected the homogeneity postulate might therefore be reinterpreted instead as rejecting the hypothesis of exogeneity of expenditure with homogeneity of degree zero in prices and nominal income taken as given.