title: On the relationship between household composition and population age distribution.
abstract: 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.
authors.affiliation: a      School of Urban and Regional Planning   ,  University of Waterloo   ,  Waterloo ,  Ontario ,    Canada.
authors.forename: A
authors.initials: A
authors.lastname: Akkerman