While studying macroeconomics during my degrees I always had
unanswered question on my mind. Why students are taught unrealistic models? The
criticism arises about the realism and simplicity of economic models which are
presenting in macroeconomics classes to students. Many models are
criticized for being unrealistic, but I understood that if realism is added to
the model they become too complex. For me OLG model seems much
more realistic and simple at first glance. The most unambiguous
side of the model is that time does not have the beginning and the end as it is
assumed in many other models. Time goes forever and it is scientifically
proven. Samuelson rediscovered this model in 1958. The model is formulated in
such a way that individuals
live for two periods. In the first period of life they are referred to as a
young and in the second period of life they are referred to as the old. The
second generation (young generation (t)) at time T=1 gives something (money,
capital and etc.) to the first generation (old generation (t-1)) at time T=1,
and when they get old (first generation (t)) at time T=2 then the third
generation (young generation (t+1)) could give something to the second
generation who are currently old at time T=2. Let’s simplify this puzzle and
say that YOUNGS are CONSTANTLY making gifts to OLDS.
This model is mostly based on the common
knowledge. Common knowledge of event A of households H
is the circumstance when all households know A, moreover they all
know that they know A, they all know that they all know that they
know A, and so on. There is well known theorem by Aumman which emphasizes
that two rational people with common knowledge of each other's
beliefs cannot agree to disagree (never disagrees). If you
thought time was going to come to an end the last young generation knowing that
they were the last generation then they would refuse to give money to old
because they were not going to get anything back when there were old. If
everyone is rational and there are common knowledge that the world is going to
end nobody would ever participate in the social security scheme.
What is Overlapping Poor Generations model
OLPG?
Now,
I adapt this model in case of poor households. If at time T=1, when first
generation born in a poor family and respectively h/she is poor, h/she is not
able to make a gift to another generation which is old at time T=1, so previous
generation (t-1) is not supported. Model assumes that people are rational under
common knowledge, so OLG model will be modified to OLPG as follows;
At time T=1 first generation has 3 apple and at time T=2
first generation is old and has apples from the previous period T=1, which is
personal income accumulated from saving. To survive at T=2, h/she has to use
his saving. Moreover he has common knowledge, knowing that at time T=2 second
generation who are young is not able to give gift to him/her. So under these
circumstances generations are overlapping but not their incomes, personal
incomes are independent from each other’s. This is a specific case, when we are
speaking about poor generations. We know that poverty is a cycle and it expands
over generation. There is no end of the chain, since generation 1 saves only in
purpose to consume.
The OLPG model has the following characteristics:
- Saving (t) =Investment (t) =Consumption (t+1)
- Consumption (C) plus saving (S) is equal to disposable income (DI)
- DI = Personal Income (PI) – Taxed Personal Income = PI for Poor People
- Taxed personal income is around zero for poor people
- C +S=PI
- C (t+1) = S(t)
- PI (3 Apples) = Consume 2 Apples + Save 1 Apple > Young (at time T=1)
- PI (3 Apples) = Consume 1 Apple > Old (at time T=2)
Graph 1. Example of OLPG model
Author's own elaboration
Graph 1 shows that generation lasts when they are young and old.
So let’s say we are at time T=1, there is young and old generations. Young generation has 3 apples (household consumes 2 and save 1 because under
common knowledge h/she knows that at time T=2 second generation who are young
at that period will not endow them) and old ones have just 1 apple.
Young households are incredible well off. They are working and more productive.
But on the other hand, when they are old and retired and feeble they don’t have
very much.
Summing up, I basically modified OLG model to OLPG, in the
specific case when households are poor and their utility maximization is saving
oriented (in baseline model of OLG, households maximize their utility based on
how much they consume today plus discounted future consumption). Poverty is
mostly transferred from one to another generation. Many studies figured out that it is very hard to lift out of poverty if
you were born into it (Moore, 2001; Heslop and Gorman, 2002; Bird,
2007).
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