why age structure determines the need of invesment of money by goverment
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A dynamic model of the age structure:
Economists have long recognized the need to incorporate age heterogeneity into macroeconomic analysis. Samuelson (1958) and Diamond (1965) developed economic-demographic models in which agents progressed through a discrete set
of ages. Overlapping generations (OLG) models of this type have been used extensively in the economic growth literature. OLG growth models typically assume a two- or three-period lifecourse, which allows for a relatively clean analysis of fertility and old-age dependency. However, periods within such models represent long spans of time in the real world (e.g., 20 to 30 years). More important, most models do not allow for variability in the time spent in each phase of life.
We develop here a somewhat stylized continuous-time model that borrows both from the traditional OLG framework and from the “model of perpetual youth” by Blanchard (1985). Given our interest in economic dependency, we model the lifecycle as a progression through a series of stages of economic life rather than conceptualizing it as a series of ages. Most individuals follow a pattern whereby they are first dependent on their parents, then work for some amount of time, and then retire. Accordingly, we divide the population into three groups: AY(t) is the stock of young people who have never worked at time t; AM(t) is the stock of people in their working years; and AO(t) is the stock of people who once worked but are retired by time t.
To focus on the dynamics of the age structure, we assume that output is produced solely by labor, which is supplied inelastically by people in their working years. The total pool of resources available for consumption is:
Ω(t) = W(t)AM(t), (1)
where W(t) is the prevailing wage at time t. A system of transfers from the working supports the young and the elderly. As a result, we focus on the youth and old-age dependency ratios:
y(t)=AY(t)AM(t)ando(t)=AO(t)AM(t).
In the remainder of this section, we establish various properties of the equations governing the evolution of the dependency ratios, which provide the basis for our model’s dynamical system.
Economists have long recognized the need to incorporate age heterogeneity into macroeconomic analysis. Samuelson (1958) and Diamond (1965) developed economic-demographic models in which agents progressed through a discrete set
of ages. Overlapping generations (OLG) models of this type have been used extensively in the economic growth literature. OLG growth models typically assume a two- or three-period lifecourse, which allows for a relatively clean analysis of fertility and old-age dependency. However, periods within such models represent long spans of time in the real world (e.g., 20 to 30 years). More important, most models do not allow for variability in the time spent in each phase of life.
We develop here a somewhat stylized continuous-time model that borrows both from the traditional OLG framework and from the “model of perpetual youth” by Blanchard (1985). Given our interest in economic dependency, we model the lifecycle as a progression through a series of stages of economic life rather than conceptualizing it as a series of ages. Most individuals follow a pattern whereby they are first dependent on their parents, then work for some amount of time, and then retire. Accordingly, we divide the population into three groups: AY(t) is the stock of young people who have never worked at time t; AM(t) is the stock of people in their working years; and AO(t) is the stock of people who once worked but are retired by time t.
To focus on the dynamics of the age structure, we assume that output is produced solely by labor, which is supplied inelastically by people in their working years. The total pool of resources available for consumption is:
Ω(t) = W(t)AM(t), (1)
where W(t) is the prevailing wage at time t. A system of transfers from the working supports the young and the elderly. As a result, we focus on the youth and old-age dependency ratios:
y(t)=AY(t)AM(t)ando(t)=AO(t)AM(t).
In the remainder of this section, we establish various properties of the equations governing the evolution of the dependency ratios, which provide the basis for our model’s dynamical system.
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