economic implications over generational periods of 20 years; i.e. over the period 2010 to 2030 and 2030 to 2050. The projections are based on 20-year projections in population growth and life expectancy (UN Population Division).

# **_General Equilibrium Implications of Population Aging_**

The overall structure of the general equilibrium model encompasses demographics, households, firms, and government. Since aging, broadly speaking, consist of two elements: (i) lower population growth due to reductions in fertility; and (ii) changes in life expectancy due to reductions in mortality, they should be considered as a joint demographic development in any general equilibrium analysis on the economic implications of aging. There are differential economic implications of these two demographic changes, however, and it important to distinguish these in order to identify what drives the aggregate results of the general equilibrium analysis.

_Economic implications of lower fertility and, thus, lower population growth:_ The general equilibrium implications of an isolated drop in the population growth rate — which changes the age-structure of the population over the demographic transition and lead to future aging—is that the capital-labor ratio increases and makes labor a more scarce production factor. This may cause factor prices to change, with upward pressure on wage rates and a downward influence on the return to capital.

A reduction in the population growth rate may also lead to transitory changes in saving behavior as well as labor supply decisions in which case the capital-labor ratio may change even further and amplify the direct effect originating fewer workers. This effect on saving rates is not present in the simulation of saving rates in the partial equilibrium analysis. Importantly, this effect partly leads to the potential _second demographic dividend_ , which was found to be positive for Brazil (Mason, 2010).

As a result, the population dynamics that originate from low mortality and fertility endogenously leads to increased saving as the dependency ratio reaches its lowest level. This is due to a higher weighted average of the saving rate due to more people in the working age who have high saving rates and fewer young and elderly who often have lower saving rates. Increased capital accumulation is the implication of this development, which contributes to a second demographic dividend and, at least theoretically, a higher per capita income.

Additional dynamics appear when the government manages systems related to the population structure — in particular pay-as-you-go (PAYG) pensions systems but also health and education systems. Furthermore, Weil (2006) finds that the distortion created by taxes needed to fund PAYG pension systems is a key channel through which a higher dependency ratio affects aggregate output and welfare.<sup>9</sup> In cases where the government decides that pensions or health benefits should be held constant, fewer workers must finance the benefits for more retirees. This leads to fiscal partial equilibrium effects counteracting the higher wages that workers receive due to the aforementioned general equilibrium effects.

If the model includes more features (such as, for example, human capital, and intra-household bequest dynamics) the aggregate effect of changes in population growth will become more difficult to

> 9 There is a large body of literature on the subject of demographic change and viability of social security arrangements (see e.g. Auerbach and Lee, 2001; Campbell and Feldstein, 2001; and Cutler et al., 1990), but this is not the focus of here.

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