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Overlapping Generations and Economic Modeling

October 19, 2012

About a year ago, there was a huge debate about government debt and the wealth of future generations. I had a great time debating everyone and writing tons of articles, but eventually, the debate staled and people starting talking past one another and it all sort of petered out. Now, the fires have again sputtered to life, and I am drawn like a moth to flame. This debate is really complicated and really subtle. I loved reading Bob Murphy’s piece, which was really the best part of the whole debate, where he summarizes both sides (poor David Brooks). The overlapping generations model is really fun. You really could spend a whole semester on it, or “the dedicated student” could spend one super intense week, as was the case for me.

Here are the paradoxical facts that need to be reconciled:
1. Government debt cannot change real GDP in any single time period.
2. Government debt can be a burden on future generations.

To see how this could happen, consider the following example:
Time period 1: The government borrows $100 from young people (Generation 2) to pay $100 to old people (Generation 1). They promise to pay the young people $110 when they are old.
Time period 2: The government taxes the new generation of young people (Generation 3) $110 to pay Generation 2 $110.

Time period 1: A gets $100, B loses $100.
Time period 2: A dies. B gets $110, C loses $110.

Total GDP is the same as it would have been without the debt, but A gets $100 more, and C gets $110 less. A and B both agree to the law in time period 1, since they both gain from it. Generation C loses, but is not alive to protest the law in the first time period. “We owe it to ourselves” is still true; total GDP does not change. Debt does not allow the government to do anything it could not have otherwise done with a pure tax and transfer program, but it does make the tax and transfer more politically popular by giving generation B a more explicit promise.

Economic Models in General
There are two types of reasoning: inductive and deductive. Economic models are a sort of deductive reasoning. They start with assumptions and simplifications and see what happens and then try to apply the results to the real world. However, like all deductive reasoning, the conclusions are only true by the degree to which the assumptions are true. Even slight changes in the assumptions can lead to dramatically different outcomes for the conclusion of the model. So, the question of “Can I create a model when X happens?” is pretty easy to answer yes. No one is going to be convinced that the real world is a certain way by a model whose assumptions are unrealistic in an important way. A good model can show others *how* you think the world fits together, but can’t convince them *that* the world works a certain way. For that, you need some inductive reasoning.

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