# **1. Introduction**

Population aging is an inevitable consequence of the demographic transition. Economic behavior and macroeconomic outcomes change both systematically and endogenously with aging. Therefore, aging countries are bound to experience pressure on fiscal sustainability, while saving and investment are risking falling short of what is needed to keep capital accumulation, wealth, and welfare at desirable levels.

Sufficient saving is important for an economy in order to generate a high income per capita. Population aging has two direct effects on saving: First, aging is traditionally believed to reduce aggregate saving rates because the fraction of people that are “prime” savers will decrease and the dis-saving fraction will increase as implied by the life-cycle hypothesis (LCH) by Modigliani (1966, 1970), Modigliani and Brumberg (1954a,b). This effect will lead to lower economic growth (Solow, 1956; Lee, 1994; Lee and Mason, 2007; Weil, 1997). Second, increasing life expectancy is the other important component of population aging and will lead to a higher saving rate as people anticipate a longer retirement period to be financed partly by private saving (Jorgensen and Jensen, 2010). These two effects consequently have an offsetting impact on saving — and thus on growth.

To further point out the complexity of this issue, what if age-specific saving rates do not decline in old age as posited by LCH? There may be desire to leave bequests (Kotlikoff and Summers, 1981, 1988; De Nardi, et al. (2009), or for elderly to share their pension income with cohabitating children (Barro, 1974). There are a large number of possible indirect effects of aging on saving. For example, when fewer workers must finance a growing number of elderly receiving public pensions, tax rates might create distortions that lead to lower demand for leisure and, thus, positive endogenous effects on the intensity of labor supply. Alternatively, the intensity of labor supply might fall when statutory retirement ages are often increased as a policy response to aging and people experience their lifetime leisure falling. Furthermore, the way in which the Brazilian government decides to finance the inevitably increasing costs for social security and health will also have major implications for the behavioral responses of Brazilians. So, the behavioral dynamics of saving are not only endogenous to aging but also to government financing policies.

The macroeconomic implications of population aging in Brazil are analyzed in this paper using three alternative yet complementary methodologies. First, the international and Brazil-specific _econometric evidence_ on the aging-saving transmission channel is analyzed. Second, a _partial equilibrium_ model is developed to exploit the rich household data on exogenous age-specific saving rates in Brazil. Third, as partial equilibrium analyses do not take into account the potentially endogenous behavioral responses to aging (Acemoglu, 2010) a _general equilibrium_ model is finally presented. Simulations are performed for different scenarios of income inequality and government policies, and the implications for key macroeconomic aggregates, such as saving, wealth, and welfare, are analyzed and discussed in light of the advantages and disadvantages of the different models.

The main findings of the three complementary analyses are the following. In relation to the _econometric evidence_ for Brazil, a higher saving rate is found to lead to higher income growth. This is an empirically well-established relationship for most countries. What is more controversial is the econometric finding that an increase in the old-age dependency ratio has, so far, led to an increase in the private saving rate — suggesting that aging may lead to higher growth in the future due to higher saving rates. The econometric evidence is paired with a literature review that places Brazil in international context regarding the relationship between population dynamics and saving — revealing that Brazil is not the only developing country that has experienced such unexpected dynamics (Chawla, Betcherman, and Banerji, 2007). Ultimately, there is no econometric evidence suggesting that an increasing old-age dependency ratio has led to reductions in saving and growth.

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