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ABSTRACT
We investigate the effect of higher house prices or rental costs on family size. We provide a static model of a household's choice of family size assuming constant elasticity of substitution preferences between children, leisure, and other goods, and Cobb–Douglas household production of children using parental time and housing. We then explore the wealth and substitution effects that changing house prices or rental costs have on desired family size. Renters are predicted to have fewer children in response to higher rents. Home owners are predicted to have more children in response to higher house prices only if they have sufficient initial housing and low substitution between family size and other consumption, and fewer children otherwise. Finally, we provide exploratory correlations between the change in lagged house prices or rental costs and the change in number of children born to women using aggregated census units in New Zealand. We find weak negative correlations in both cases.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. Delayed household formation may imply delayed plans to have children.
2. The total fertility rate is defined as the number of children born to a woman, by the end of her reproductive period, if she experienced the current age-specific fertility rates throughout her child-bearing years.
3. The coefficient on the house price variable is negative, while the coefficient on the interaction term is positive and of a greater magnitude than the former.
4. can be thought of as a composite good that excludes children and leisure.
5. The CES utility function assumes that all goods, here including children, are normal goods. It may be objected that there is historical evidence that people have fewer children as incomes increase. However, a driving factor behind the increase in household incomes has been the increase in female labour force participation and women's wages. For simplicity, we have adopted a unitary household wage in our model and do not address this issue. One way to incorporate the possibility that people have fewer children as incomes increase would be to allow for a choice between quantity and (investment-related) ‘quality’ of children (Becker, Citation1960).
6. The household's elasticity of substitution between any pair of the three goods, σ, is defined as .
7. While we do not calculate Cobb–Douglas outcomes, we cover the cases that approach those outcomes from above and below.
8. We recognise that actual household decisions regarding how many children to try for is driven both by women’s and men's opportunity costs of time. However, since our focus is on the effects of housing price or rental costs, we use a unitary wage/household model.
9. When renting is cheaper than owning, the household will sell off all endowed housing. When owning is cheaper than renting, the household may choose to sell off some endowed housing, in which case .
10. In this case where renting is optimal, since any endowed housing is sold.
11. This possibility also holds for the case where owning is optimal, as seen in (Equation20(20) ).
12. The corner solution does not add appreciable insights, but is available from the authors upon request.
13. This rules out ‘big changes’ that reverse the ranking of the two types of housing prices that would result in the household switching from renting to owning, or vice versa.
14. The New Zealand Census is normally held every five years, but the 2011 round was delayed until 2013 due to the Canterbury earthquake of February 2011.
15. At the 2013 Census, there were 2012 ‘area units’ in New Zealand, with an average population of roughly 2000 each. A ‘territorial authority’ is a city council or district council in New Zealand, and is an aggregate of area units. At the 2013 Census, there were 67 territorial authorities in New Zealand, with an average population of roughly 62,600 each.
16. The publicly released census does not report the age groups for females and males separately, and so we control for the proportion of both sexes in the child-bearing age bracket for women.
17. Note that Rent does not control for the quantity (size) or type of residential housing.
18. Goodyear and Fabian (Citation2014) similarly document a divergence in growth of housing prices and rental costs for the Auckland region in particular.
19. The rent component of the CPI (actual rentals for housing) is a subgroup of the ‘housing and household utilities’ group in the CPI. It measures the rent paid by tenants to landlords and comprises three price indices: private and local authority rentals, state rentals, and education accommodation. As of the June 2006 quarter, the rent component had an expenditure weight of 6.87% of the CPI, for which 90% was attributable to private and local authority rentals (Statistics New Zealand, Citation2015, Citationn.d.).
20. For this comparison, we use the QV HPI for ‘all residential’ housing (rather than detached houses only) due to the nature of the rent component of the CPI (the private and local authority rentals index includes apartments, flats, town houses, and houses). The HPI for ‘all residential’ housing takes into account detached houses, flats, and apartments. More about the HPI can be found in Appendix 3.