Overlapping generations model

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For the population genetics model, see Overlapping generations.

An overlapping generations model, abbreviated to OLG model, is a type of economic model in which agents live a finite length of time and live long enough to endure into at least one period of the next generation's lives.

The concept of an OLG model was devised by Maurice Allais in 1947 and popularized by Paul Samuelson in 1958 as a way of simplifing monetary economics and macroeconomic models. OLG models can have varying characteristics depending on the subject of study, but most models share several key elements:

individuals receive an endowment of goods at birth
goods cannot endure for more than one period
money endures for multiple periods
individuals must consume in all periods, and their lifetime utility is a function of consumption in all periods

[edit] Basic OLG model

The most basic OLG model has the following characteristics:

Individuals live for two periods; in the first period of life, they are referred to as the Young. In the second period of life, they are referred to as the Old.
A number of individuals is born in every period. The specific number born in a given period is denoted as N_t . For example, N₁ denotes individuals born in period 1.
The economy begins in period 1. In period 1, there is a group of people who are already old. They are referred to as the initial old. They can be denoted as N₀ .
There is only one good in this economy, and it cannot endure for more than one period.
Each individual receives a fixed endowment of this good at birth. This endowment is denoted as y. This endowment of goods can also be thought of as an endowment of labor that the individual uses to work and create a real income equal to the value of good y produced. Under this framework, individuals only work during the young phase of their life.

[edit] Notation

Very often, one of the problem economists find in write an OLG model is referred to the notation. All the variables of an OLG model should contain two information: the chronological time t, and the generation τ. Greek letter τ indicates the period of time when the generation was born. For instance, if we refer to the variable consumption (c), then the right way to write the variable in an OLG model is c^τ_t, which should be read as the consumption at time t of the generation τ (that was born at time t). This generation overlaps with other generations. For instance, in an economy divided into young (generation τ born at time t) and old (generation τ-1 born at time t-1), at time t the consumption of the groups will be written as c^τ_t for the young and c^τ-1_t for the old.

[edit] Characteristics of the OLG model

Two important aspects of the OLG model are that, unlike in the Ramsey growth model the steady state level of capital need not be unique nor efficient. Essentially, because there is an infinite number of agents in the economy (over time) there is no prior restriction on the differential equation that relates the capital stock to investment (note that the First welfare theorem requires that there be a finite number of consumers in an economy). Hence, multiple equilibria, even a continuum of them, are possible. Furthemore, it is possible that 'over saving' can occur - a situation which could be improved upon by a social planner. Since there is an infinite number of generations, a social planner could transfer some consumption from one generation to the previous one, compensate the first generation with a transfer from the next and so on, into infinity. However, certain restrictions on the underlying technology of production and consumer tastes can ensure that the steady state level of saving corresponds to the Golden Rule savings rate of the Solow growth model and thus guarantee intertemporal efficiency. Along the same lines, most empirical research on the subject has noted that oversaving does not seem to be a major problem in the real world.