A problem in household composition

"Distinction made between household-persons and household-markers [the person who identifies the family or household as a unit] is formalized in the notion of nested populations. This leads to an extension of the Leslie model into a formulation of growth for both population and households. The extended model involves the matrix presentation of household composition where ratios of household-persons who are age 0, per household-marker, function as surrogate values for fertility rates. The extended model describes change over time in the distribution of population by age, and in the distribution of households by age of household-marker, or household-head. The model involves the inversion of a nonnegative matrix, and is feasible only if it yields, projected over time, nonnegative entries in vectors representing distribution of population by age, and distribution of household-heads by age. Conditions for the feasibility of the extended model are discussed, and a sufficient condition for feasibility over a single interval is identified." (SUMMARY IN FRE)     

Trajectories of Fertility and Household Composition in the Demographic Profile of the Czech Republic

The household composition matrix is a representation of the demographic structure of households, specific to age groups of household members and household heads. As such, the matrix reflects also the environmental conditions, housing in particular, that mould households' demographic structure. By specifically depicting the presence of children in households, household composition could be viewed as gauging fertility within the context of housing conditions. This stance is examined in an application to Czech census data for the year 1991, at the commencement of an intense process of socio-economic transformation that accompanied the collapse of communism across Eastern Europe. Within this process, housing had an inadvertent impact upon the structure of households in general, and upon fertility decline in particular. By using the standard matrix representation of household composition, correspondence between trajectories of age-specific fertility and household composition emerge throughout the Czech Republic. This correspondence illustrates the potential household composition analysis carries for fertility measurement and estimation in rapidly changing economic environments.     

On the relationship between household composition and population age distribution

Summary Composition of households by age of head and by age of other household members has recently been presented in a convenient algebraic expression, the household composition matrix. It has been shown that this matrix operates as a linear transformation from the vector of household distribution by age of head to the vector of population age distribution. A further analysis will show that the first row of the matrix may be interpreted as representing a vector of average household fertility rates. If the linear relationship between household and population distributions is fully implemented, then a relationship between household fertility and the size of the youngest age group can be derived. If w is the population age distribution and w (1) is the number of persons in the youngest age group, then: where α is the first row of the household composition matrix with its first element eliminated, C is the household composition matrix with its first row and first column eliminated, and Ψ is the vector w with its first element, w (1) eliminated. Extension of this result will enable simultaneous projection of population and households, suitable for computer application to conventional five-year age groups.