Demographics in demand systems

Household composition can be expected to affect the allocation of household expen-diture among goods, at the very least because of economies of scale as household size increases and because different people have different needs (adults versus children, for example). Specifying demographic effects correctly in demand analysis is important both in order to estimate correct price and expenditure elasticities and for the purpose of making household welfare comparisons. A common way of including demographics is as a function that scales total expenditure, and to make this scaling function indepen-dent of the level of total expenditure. A popular method in the parametric estimation of demand systems is to estimate share equations that are quadratic in the logarithm of total expenditure, but there is also a substantial literature on the semi-parametric estimation of Engel curves. We employ some of these semi-parametric techniques to show that, for some goods, further terms are likely to be required in the Engel curve addition to quadratic terms. We use this to identify the parameters of a scaling function that varies with total expenditure.