Parental altruism and nest leaving in Europe: evidence from a retrospective survey

Abstract

We use retrospective life-history data from the Survey of Health, Ageing and Retirement in Europe to assess parental altruism through the effect of parental resources and home characteristics on the age at which individuals now aged 50 or more left the nest in 13 countries. We show that the nest leaving age has declined from one cohort to the next and that the tendency has been of a relative decline in leaving one’s parents to start a family and an increase in leaving home to pursue higher education, even if the first pattern was still the most common for the baby-boomers. We test an altruistic model where constrained parents push the child out, where less constrained “proximity altruistic” parents can help the child by providing a home or even, for the richest “active altruists”, help the child leave the nest. Taking into account the endogenous child’s choices of education, we find that most parents helped by being proximity altruists, while some helped their children move out and that the quality of the home had an important influence on the nest leaving age.

Appendix: Derivations of the empirical predictions in Table 1

The child has four possible utility levels depending on the co-residence status and on whether the parent makes a transfer:

$$ \begin{aligned} V^{c} |_{{T^{c} = 0}} & = \alpha \ln Y_{k} + \left( {1 - \alpha } \right)\ln \bar{H} + \left( {1 - \alpha } \right)\ln n^{\delta - 1} \\ V^{c} |_{{T^{c} > 0}} & = \alpha { \ln }(\bar{Y}_{p} + Y_{k} ) + \left( {1 - \alpha } \right){ \ln }\bar{H} + \left( {1 - \alpha } \right){ \ln } n^{\delta - 1} + \alpha { \ln }\left( {\frac{{\beta^{c} \alpha }}{{\gamma + \beta^{c} \alpha }}} \right) \\ V^{i} |_{{T^{i} = 0}} & = \ln Y_{k} + \left( {1 - \alpha } \right)\ln \left( {\frac{1 - \alpha }{{\rho_{k} }}} \right) + \alpha { \ln }\alpha \\ V^{i} |_{{T^{i} > 0}} & = { \ln } (\bar{Y}_{p} + Y_{k} ) + \left( {1 - \alpha } \right)\ln \left( {\frac{1 - \alpha }{{\rho_{k} }}} \right) + { \ln }\left( {\frac{{\beta^{i} }}{{\gamma + \beta^{i} }}} \right) + \alpha { \ln }\alpha \\ \end{aligned} $$

In each case, the child decides whether to leave or not depending on the sign of V ⁱ − V ^c. Then, the partial derivatives of V ⁱ − V ^c give the effect of Y _p , β, n, δ, ρ _k and $\bar{H}$ on the probability of leaving the nest which are summarized in Table 1.

Income effects

• 1. If T ^c > 0 and T ⁱ > 0:

  $$ \frac{{\partial (V^{i} - V^{c} )}}{{\partial Y_{p} }} = \frac{{\partial (V^{i} - V^{c} )}}{{\partial Y_{k} }} = \frac{1 - \alpha }{{\bar{Y}_{p} + Y_{k} }} > 0 $$

  The sign is the same if T ^c = 0 and T ⁱ > 0.

  $$ \frac{{\partial (V^{i} - V^{c} )}}{{\partial \beta^{i} }} = \frac{\gamma }{{\beta^{i} \left( {\gamma + \beta^{i} } \right)}} > 0 $$

• 2. If T ^c > 0 and T ⁱ = 0:

  $$ \begin{aligned} \frac{{\partial (V^{i} - V^{c} )}}{{\partial Y_{p} }} & = - \frac{\alpha }{{\bar{Y}_{p} + Y_{k} }} < 0 \\ \frac{{\partial (V^{i} - V^{c} )}}{{\partial Y_{k} }} & = \frac{{\bar{Y}_{p} + (1 - \alpha )Y_{k} }}{{Y_{k} (\bar{Y}_{p} + Y_{k} )}} > 0 \\ \frac{{\partial (V^{i} - V^{c} )}}{{\partial \beta^{c} }} & = - \frac{\alpha \gamma }{{\beta^{c} \left( {\gamma + \beta^{c} \alpha } \right)}} < 0 \\ \end{aligned} $$

• 3. If T ^c = 0 and T ⁱ = 0:

  $$ \begin{aligned} \frac{{\partial (V^{i} - V^{c} )}}{{\partial Y_{p} }} & = 0 \\ \frac{{\partial (V^{i} - V^{c} )}}{{\partial Y_{k} }} & = \frac{1 - \alpha }{{Y_{k} }} > 0 \\ \end{aligned} $$

Other effects

In all cases:

$$ \begin{aligned} & \frac{{\partial (V^{i} - V^{c} )}}{\partial n} = - \frac{\delta - 1}{n} \, < \, 0 \\ & \frac{{\partial (V^{i} - V^{c} )}}{\partial \delta } = - \left( {1 - \alpha } \right){ \ln }n \, < \, 0 \\ & \frac{{\partial (V^{i} - V^{c} )}}{{\partial \rho_{k} }} \, < \, 0 \\ & \frac{{\partial (V^{i} - V^{c} )}}{{\partial \bar{H}}} - \frac{1 - \alpha }{{\bar{H}}} \, < \, 0 \\ \end{aligned} $$