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On the relationship between household composition and population age distribution
1a School of Urban and Regional Planning , University of Waterloo , Waterloo , Ontario , Canada.
Population Studies
|November 15, 2011
Summary
This study introduces the household composition matrix, a tool for understanding population and household structures. It reveals a direct link between average household fertility and the youngest population age group.
Area of Science:
- Demography
- Mathematical Sociology
- Population Studies
Background:
- Household composition and population age distribution are key demographic variables.
- Existing models analyze these distributions separately.
- A unified algebraic framework is needed for integrated analysis.
Purpose of the Study:
- To present the household composition matrix as a linear transformation.
- To demonstrate its application in linking household and population age distributions.
- To derive a relationship between household fertility and youngest age group size.
Main Methods:
- Utilizing the household composition matrix for algebraic analysis.
- Interpreting the matrix's first row as average household fertility rates.
- Deriving a mathematical relationship using matrix algebra and population vectors.
Main Results:
- The household composition matrix linearly transforms household head age distribution to population age distribution.
- The first row of the matrix represents average household fertility.
- A derived formula links household fertility to the size of the youngest age group.
Conclusions:
- The household composition matrix provides a unified approach to population and household projection.
- This method facilitates simultaneous projection of population and households.
- The findings are suitable for computational applications with standard age groups.
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