Intergenerational Linkages, Uncertain Lifetime and Educational and Health Expenditures

Empirical evidence suggests a positive correlation between health and educational outcomes at the aggregate level. However, both inter and intra-country data suggest that these variables may not always be monotonically increasing in income, pointing towards household income as a possible mitigating factor in the relationship between health and education expenditures and outcomes. We develop an overlapping generations model where agents spend their childhood studying, undertake expenditures to educate their offspring and health expenditures to improve their own longevity in adult age, and spend old age in retirement. Our model is characterised by two equilibria. In one equilibrium, longevity enhancing health expenditure is an inferior good, resulting in agents substituting health expenditures in favour of education expenditures on offspring as their income increases. In the other equilibrium, health expenditure is a normal good, but for incomes below a certain level, an increase in income causes agents to raise health expenditures whilst lowering education expenditures on offspring, while for incomes above this level all expenditures are increasing in income. These results suggest that the relationship between parental longevity and offspring’s human capital depends on income and whether agents consider longevity enhancing health expenditure to be an inferior or normal good. Dynamics of the model show that the economy could either achieve unbounded growth or converge towards a lower bound of income in the long run.