Left behind: intergenerational transmission of human capital in the midst of HIV/AIDS

Abstract

This paper provides evidence on how adverse health conditions affect the transfer of human capital from one generation to the next. We explore the differential exposure to HIV/AIDS epidemic in sub-Saharan Africa as a substantial health shock to both household and community environment. We utilize the recent rounds of the Demographic and Health Surveys for 11 countries in sub-Saharan Africa. First, we find that an additional year of maternal education leads to a 0.37-year increase in children’s years of schooling in the developing economies in sub-Saharan Africa. Second, our results show that mother’s HIV status has substantial detrimental effects on inheritability of human capital. We find that the association between infected mothers’ and their children’s human capital is 30 % less than the general population. Finally, focusing only on noninfected mothers and their children, we show that HIV prevalence in the community also impairs the intergenerational human capital transfers even if mother is HIV negative. The findings of this paper are particularly distressing for these already poor, HIV-torn countries as in the future they will have even lower overall level of human capital due to the epidemic.

Appendix: Derivation of the model

All assumptions and parameters are explained in the theoretical framework section. The utility-maximizing household maximizes the present discounted value of income of parents and the children as follows:

$$ \mathop\mathrm{max}\nolimits_{s_{c}}\int_0^{T} e^{-\delta t}ye^{\gamma s_\textrm{p}} p(t) dt + \int_{s_\textrm{c}}^T e^{-\delta t}ye^{\gamma s_\textrm{c}} q(t) dt $$

where the present discounted value of parents’ income is

$$ Yp (p(t))= \int_0^{T} e^{-\delta t}ye^{\gamma s_\textrm{p}} p(t) dt $$

and the present discounted value of children’s income is

$$ Yc (q(t))= \int_{s_\textrm{c}}^T e^{-\delta t}ye^{\gamma s_\textrm{c}} q(t) dt. $$

Hence,

$$ q(t)= e^{-\int_{0}^t\mu(z)dz}= e^{-mt}. $$

Table 10 DHS data

Table 11 Importance of paternal education

Table 12 Effect of father’s HIV status on inheritability of human capital

Then, the schooling decision for children is as follows:

$$ \begin{array}{rll} &&{\kern-6pt} \max\nolimits_{s_\textrm{c}}\int_{s_\textrm{c}}^{T}e^{-\delta t}\: y\: e^{\gamma s_\textrm{c}}\: e^{-mt} dt\\ &&\Longrightarrow ye^{\gamma s_\textrm{c}}\left[-\frac{1}{(\delta+m)}e^{-(\delta+m) t}\biggr|_{s_\textrm{c}}^{T}\right]=ye^{\gamma s_\textrm{c}}\left[-\frac{1}{(\delta+m)}\left(e^{-(\delta+m) T}-e^{-(\delta+m) s_\textrm{c}}\right)\right] \end{array} $$

$$ F=\left[\frac{ye^{\gamma s_\textrm{c}}}{(\delta+m)}\left(e^{-(\delta+m) s_\textrm{c}}-e^{-(\delta+m) T}\right)\right]. $$

For the optimal level of children’s schooling,

$$ \frac{\partial F}{\partial s_\textrm{c}}=0 $$

$$ \frac{\partial F}{\partial s_\textrm{c}}=\gamma\left(e^{-(\delta+m)s_\textrm{c}}-e^{-(\delta+m)T}\right)-(\delta+m)e^{-(\delta+m)s_\textrm{c}}=0 $$

$$ (\gamma-\delta-m)e^{-(\delta+m)s_\textrm{c}}=\delta e^{-(\delta+m)T} $$

$$ e^{(\delta+m)s_\textrm{c}}=\left(\frac{\gamma-\delta-m}{\gamma}\right)e^{(\delta+m)T}, $$

when we take the log of both sides, we get the optimal level of schooling for the children’s generation:

$$ s_\textrm{c}^{\ast}=Tln\left(\frac{\gamma-\delta-m}{\gamma}\right) $$

which yields $\frac {ds_\textrm{c}}{dm} < 0$ and $\frac {ds_\textrm{c}}{dq(t)} > 0$. This suggests that children get more schooling when the probability of survival increases. Hence, children’s survival probability at age t, q(t), decreases both with parents’ HIV infection and HIV prevalence in the community; therefore

$$ \frac {ds_\textrm{c}}{d\textrm{HIVparents}} < 0\; and \; \frac {ds_\textrm{c}}{d\textrm{HIVcommunity}} < 0 $$