Population aging, health care, and growth

Abstract

This paper constructs a small open two-sector (health care and non-health care) overlapping generations model and investigates how changes in the demand for health care induced by population aging influence the economy’s employment structure and per capita income growth rate. We show that population aging induces a shift in labor from the non-health care sector to the health care sector and lowers the per capita income growth rate. This paper also investigates public policy for child care and demonstrates the existence of an intergenerational conflict between current and future generations concerning public policy on child care.

Appendix

The derivation of $l_{t}^{H}$

By substituting Eq. 3, $w_{t}=\bar{w}A_{t}^{N}$, h _t  = h into Eq. 22, we obtain

$$ z_{t}=\frac{(1-\gamma)R}{1+\phi+p}\frac{(1-\tau_{t-1})}{G_{t-1}^{N}} A_{t}^{H}h. $$

In addition, by substituting Eqs. 7, 10, and 21 and h _t  = h into L _t  = h _t η _t N _t , we obtain

$$ N_{t}h=\frac{1+\phi+p}{1+p-\frac{\theta}{1-\theta}\phi}L_{t}. $$

Moreover, from substituting Eqs. 7, 10, and 21 into Eq. 19, we have

$$ \tau_{t}=\frac{\phi}{1+p}\frac{\theta}{1-\theta}. $$

Using N _t  = n _t − 1(θ)N _t − 1, $z_{t}=\frac{(1-\gamma)R}{1+\phi+p} \frac{(1-\tau_{t-1})}{G_{t-1}^{N}}A_{t}^{H}h$, $N_{t}h=\frac{1+\phi+p}{1+p- \frac{\theta}{1-\theta}\phi}L_{t}$, and $\tau_{t}=\frac{\phi}{1+p}\frac{\theta }{1-\theta}$, Eq. 12 is written as

$$ l_{t}^{H}=\frac{(1-\gamma)R}{n_{t-1}(\theta)}\frac{p}{1+p}\frac{1}{ G_{t-1}^{N}} \equiv l^{H}\left(G_{t-1}^{N},n_{t-1}(\theta)\right). $$

Here, it corresponds to Eq. 23 when θ > 0 and Eq. 15 when θ = 0.