Overlapping generations model

For the topic in population genetics, 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.

All OLG 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.

The concept of an OLG model was inspired by Irving Fisher's monograph The Theory of Interest.^[1] Notable improvements were published by Maurice Allais in 1947, Paul Samuelson in 1958, and Peter Diamond in 1965.

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.

Characteristics of a Pure-Exchange OLG model

Two important aspects of the OLG model are that the steady state equilibrium 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. The Cass Criterion gives necessary and sufficient conditions for when an OLG competitive equilibrium allocation is inefficient.^[2]

Furthermore, 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.

A third fundamental contribution of OLG models is that they justify existence of money as a medium of exchange. In an OLG model, money is a welfare-improving "innovation."

Characteristics of OLG models with Production

A OLG model with an aggregate neoclassical production was constructed by Peter Diamond.^[3] A two-sector OLG model was developed by Oded Galor.^[4]

Unlike the Ramsey growth model the steady state level of capital need not be unique.^[5] Moreover, as demonstrated by Diamond (1965), the steady-state level of the capital labor ratio need not be efficient which is termed as "dynamic inefficiency".

See also

• Peter A. Diamond
• Karl Shell
• Macroeconomic model

References

1. ^ Aliprantis, Brown & Burkinshaw (1988, p. 229):

   Aliprantis, Charalambos D.; Brown, Donald J.; Burkinshaw, Owen (April 1988). "5 The overlapping generations model (pp. 229–271)". Existence and optimality of competitive equilibria (1990 student ed.). Berlin: Springer-Verlag. pp. xii+284. ISBN 3-540-52866-0. MR1075992. 

2. ^ Cass, David (1972), "On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization", Journal of Economic Theory 4 (2): 200–223, doi:10.1016/0022-0531(72)90149-4 
3. ^ Diamond, Peter (1965), "National Debt in a Neoclassical Growth Model", American Economic Review 55: 1126–1150 
4. ^ Galor, Oded (1992), "A Two-Sector Overlapping-Generations Model: A Global Characterization of the Dynamical System", Econometrica 60 (6): 1351–1386, doi:10.2307/2951525 
5. ^ Galor, Oded; Ryder, Harl E. (1989), "Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital", Journal of Economic Theory 49 (2): 360–375, doi:10.1016/0022-0531(89)90088-4