Overlapping generations model
Encyclopedia
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:
The concept of an OLG model was inspired by Irving Fisher
's monograph The Theory of Interest. Notable improvements were published by Maurice Allais
in 1947, Paul Samuelson
in 1958, and Peter Diamond
in 1965.
gives necessary and sufficient conditions for when an OLG competitive equilibrium allocation is inefficient.
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."
. A two-sector OLG model was developed by Oded Galor
.
Unlike the Ramsey growth model
the steady state level of capital need not be unique. 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
".
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
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.
- MoneyMoneyMoney is any object or record that is generally accepted as payment for goods and services and repayment of debts in a given country or socio-economic context. The main functions of money are distinguished as: a medium of exchange; a unit of account; a store of value; and, occasionally in the past,...
endures for multiple periods. - Individuals must consume in all periods, and their lifetime utilityUtilityIn economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
is a function of consumptionConsumption (economics)Consumption is a common concept in economics, and gives rise to derived concepts such as consumer debt. Generally, consumption is defined in part by comparison to production. But the precise definition can vary because different schools of economists define production quite differently...
in all periods.
The concept of an OLG model was inspired by Irving Fisher
Irving Fisher
Irving Fisher was an American economist, inventor, and health campaigner, and one of the earliest American neoclassical economists, though his later work on debt deflation often regarded as belonging instead to the Post-Keynesian school.Fisher made important contributions to utility theory and...
's monograph The Theory of Interest. Notable improvements were published by Maurice Allais
Maurice Allais
Maurice Félix Charles Allais was a French economist, and was the 1988 winner of the Nobel Memorial Prize in Economics "for his pioneering contributions to the theory of markets and efficient utilization of resources."...
in 1947, Paul Samuelson
Paul Samuelson
Paul Anthony Samuelson was an American economist, and the first American to win the Nobel Memorial Prize in Economic Sciences. The Swedish Royal Academies stated, when awarding the prize, that he "has done more than any other contemporary economist to raise the level of scientific analysis in...
in 1958, and Peter Diamond
Peter Diamond
Peter Diamond was an English actor who had trained at the Royal Academy of Dramatic Art and remembered as a stuntman on television or film....
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 Nt . 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 incomeIncomeIncome is the consumption and savings opportunity gained by an entity within a specified time frame, which is generally expressed in monetary terms. However, for households and individuals, "income is the sum of all the wages, salaries, profits, interests payments, rents and other forms of earnings...
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 CriterionCass criterion
The Cass Criterion is a central result in theory of overlapping generations models in economics. It is named after David Cass.A major feature which sets overlapping generations models in economics apart from the standard model with a finite number of infinitely lived individuals is that the First...
gives necessary and sufficient conditions for when an OLG competitive equilibrium allocation is inefficient.
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
Golden Rule savings rate
In economics, the Golden Rule savings rate is the rate of savings which maximizes steady state level or growth of consumption , as for example in the Solow growth model...
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 DiamondPeter Diamond
Peter Diamond was an English actor who had trained at the Royal Academy of Dramatic Art and remembered as a stuntman on television or film....
. A two-sector OLG model was developed by Oded Galor
Oded Galor
-Work:Galor has made significant contributions to the study of income distribution and economic growth, the transition from stagnation to growth, and human evolution and economic development...
.
Unlike the Ramsey growth model
Ramsey growth model
The Ramsey–Cass–Koopmans model or the Ramsey growth model is a neo-classical model of economic growth based primarily on the work of the economist and mathematician Frank P. Ramsey, with significant extensions by David Cass and Tjalling Koopmans...
the steady state level of capital need not be unique. 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
Dynamic efficiency
Dynamic efficiency is a term in economics, which refers to an economy that appropriately balances short run concerns with concerns in the long run . Through dynamic efficiency, such an economy is able to further improve efficiency over time...
".