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.

Additional information

Notes on contributors

A. Akkerman

Thanks are extended to Joseph E. DiSanto, Calvin Goldscheider, Lionel Needleman and Ross T. Newkirk for valuable comments and discussions on the topic of household composition.