Empirical investigations into the expenditure and time allocation decisions of households usually allow the variation in demographic characteristics across households, in particular the number and ages of dependent children, to affect these decisions. The motivation for allowing such demographic effects is two-fold. First, it permits the researcher to pool observations from households with differing demographic characteristics. Secondly, it has been argued that it allows the researcher to construct an index, normally called an equivalence scale, to show the (full) income required by a household with some given composition to attain the same level of utility as some reference household, and hence permits comparisons of welfare levels across households. There are two areas of controversy surrounding this literature which directly relate to its two sources of motivation. First, what is the appropriate demographic specification? Second, can the estimated parameters be used to undertake welfare comparisons? A series of demand studies, including Barten (1964), Blundell (1980), Blundell and Walker (1982), Gorman (1976), Muellbauer (1974, 1977), Hurd and Pencavel (1981), Pollak and Wales (1978, 1981), and Ray (1983), have attempted to answer the first problem by considering the current allocation of goods, and in some cases household time, conditional on demographic structure. This literature treats demographic variables as exogenous whereas, in contrast, the neoclassical fertility literature (see for example the contributions in Schultz (1973)) treats the numbers and ages of children as endogenous nonmarket goods within a lifecycle optimising framework. The second problem has been raised by Pollak and Wales (1979) who argue convincingly, whether household composition is the result of endogenous decisions or not, it is impossible to compare the welfare of households with different compositions using the results of empirical demand analysis since market decisions do not reveal how the households feel about the presence or absence of children. Thus estimated equivalence scales are necessarily based on the households' preferences conditional on their demographic compositions. The object of this paper is to suggest a new approach to the problem of demographic specification and to show that this approach both highlights the problem of making welfare comparisons and, at least in part, resolves it.