WHEN IS EXPENDITURE "EXOGENOUS" IN SEPARABLE DEMAND MODELS?

Abstract

The separability hypothesis and expenditure as an exogenous variable in a system of conditional demands are analyzed. Expenditure cannot be weakly exogenous in a system of conditional demands specified as functions of the prices of the separable goods and total expenditure on those goods. Furthermore, expenditure is uncorrelated with the residuals of the conditional demand equations only when severe restrictions are satisfied. Therefore, expenditure will seldom be strictly exogenous. Econometric methods are presented for the consistent and efficient estimation of the unknown parameters when expenditures is correlated with the residuals and when it is not.