A problem in household composition

Distinction made between household‐persons and household‐markers 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.

Key words:

• Leslie model
• household composition
• household growth
• population growth
• fertility
• nonnegative matrices

Notes

Thanks are due to Nico Keilman and to two anonymous referees of this Journal for their valuable comments on previous versions of this paper. Support of the Social Sciences and Humanities Research Council of Canada (Grant 410–91–2000) for this study is gratefully acknowledged.