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).
