Parents’ income and children’s school drop-out at 16 in England and Wales: evidence from the 1970 British Cohort Study

Abstract

This paper investigates the effect of parents’ income on children’s drop-out from school at age 16 using data from the 1970 British Cohort Study (BCS70). Unlike previous papers using the same data set, we use a continuous measure of income derived from the grouped income variable available in the BCS70, we employ instrumental variable techniques to address the issue of endogeneity of family income and take account of the potential endogeneity of income response with respect to a child’s education by jointly modelling the school drop-out decision and response to the family income question. Our estimates show the exogeneity of response to the income question with a child’s education and are in line with the previous literature finding a statistically significant small negative effect of family income on school drop-out at 16. On the contrary, other non-pecuniary parental effects, such as parental education and social class, turn out to be both significant and of a sizeable magnitude.

Appendix A1: From grouped to continuous family income

In the BCS70, family income (i.e. parents’ income) is observed in a certain interval on a continuous scale. We want to transform the grouped variable into a continuous one. The procedure has been investigated by Stewart (1983). We summarise here only the main features of the problem and the proposed solution. The latent structure of the model under consideration is given by:

$$ y_i={\bf z_i'}{\varvec \delta}+{\bf p_i'}{\varvec \theta}+\epsilon_i $$

(4)

where y _i is the latent family income of individual i, which falls within a certain interval of the real line (A _k-1, A _k ). ${{{\bf z}_{\bf i}}}$ and ${{\bf p}_{\bf i}}$ are vectors of regressors affecting family income and ${{\varvec \delta}}$ and ${{\varvec \theta}}$ vectors of unknown parameters to be estimated, respectively. ${{\bf z}_{\bf i}}$ represents the variables excluded from the school drop-out equation (i.e. the identifying instruments) that is estimated in a second stage using predicted income from Eq. (4). ε _i ’s are i.i.d. normally distributed random disturbances with zero mean and variance σ² and are assumed to be independent of ${{\bf z}_{\bf i}}$ and ${{\bf p}_{\bf i}}$ .

Ad hoc procedures, such as assigning to each individual the midpoint of her income group, do not in general result in consistent estimates of the parameters ${{\varvec \delta}}$ and ${{\varvec \theta}}$ , while consistent estimates can be obtained by assigning to each observation its conditional expectation:

$$ \hat{y}_i=E(y_i|A_{k-1} < y_i < A_k,z_i)={\bf z_i'}{\varvec \delta}+{\bf p_i'}{\varvec \theta}+\sigma \left[{{\phi(Z_{k-1})-\phi(Z_k)}\over {\Phi(Z_k)-\Phi(Z_{k-1})}} \right] $$

(5)

where ${Z_k=(A_k-{\bf z_i'}{\varvec \delta}-{\bf p_i'}{\varvec \theta})/\sigma}$ and ${\phi(\cdot)}$ and ${\Phi(\cdot)}$ are the standard normal density and cumulative distribution functions.

Stewart (1983) suggests several ways to estimate the parameters of interest ${{\varvec \delta}}$, ${{\varvec \theta}}$ and σ.

In our specific case the parameters are estimated using a maximum likelihood estimator.

After estimating ${{\varvec \delta}}$, ${{\varvec \theta}}$ and σ consistently, it is possible to obtain predicted values for y _i , i.e. a continuous measure of family income.

This measure is used in a second stage for the estimation of the school drop-out equation.