Expanding Bob's OLG Example

Bob had a good OLG exposition of the national debt issue here (if you're coming in this late in the game, you're on your own tracing back links). He was also kind enough to send me the excel file that he used to make the diagram so I could expand it by two examples.

But first I want to make a few points about Bob's post.

1. Gene and I have both pointed this out already, but I want to make it very clear: you have to realize that Bob has not disproved Krugman's point anyway. Add up each row sequentially in Bob's OLG model. All of them add up to 200. There is no burden on future generations in Bob's example. None. He can't get a burden with his model. What he has is individual people (in his case, the last person in the chain - Iris) getting screwed and others benefiting (this is what Paul originally called a "different kettle of fish", and a real problem). But within each period we have the same GDP level. In other word, Bob Murphy's example agrees with Paul Krugman. Bob may have changed his mind but so far he has not offered us a model that supports Bob's decision to change his mind. So why did Bob change his mind? I'm still not sure. He's always welcome back over on our side, though.

2. I will still not get into this in my expansion of Bob's example, but let's also remember what Bob doesn't include: growth and investment. This is not a minor issue, and it strains the extent to which we can really go to these models to tell us something about real life human action. Ask yourself - why in the world would you borrow money without some rate of return? It doesn't make sense. However, I don't fault Nick or Bob over that bit of parsimony because we still have a lot to talk about without it. But you should always keep that in mind.

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OK - new examples. My contention has always been that the burdens in these models are the burdens introduced by the transfers. Debt does not burden any particular generation. What it can do is make different people bear the burden of a policy. That's an important distinction if you're thinking about the impact of debt on GDP. We saw this in Bob's model. Each generation in Bob's model had the exact same income before and after he added debt. However, Iris had a much bigger burden than anyone else in his example. No effect on GDP - big effect on Iris.

To see how debt and transfers interact, I think it's useful to add two numerical examples to what Bob already has. The first two, below, are his (except I change the title of his second example). The third and fourth are mine. The third example considers the case where the government borrows from Old Al to make a transfer to Young Bob. The fourth example introduces the point of Ricardian Equivalence. Let's say we fund Bob Murphy's initial transfer from Young Bob to Old Al with a tax on Young Bob rather than a deficit.

In the third example, then, we have the same financing method but a different transfer.

In the fourth example, we have the same transfer but a different financing method.



First - what doesn't change? One thing that clearly doesn't change is GDP in period 1 through period 9. That is exactly the same in every row, in every scenario.

Point, Krugman (and whoever else is willing to acknowledge they actually do agree with him and he's not some crazy guy stuck in the 1950s).

What does change? The incidence of the burden. In Bob's transfer example, Iris had the highest burden by far, and everyone benefited a little bit as they earned interest over time. In the third example, everyone bears a small burden, Iris bears a slightly smaller burden than she did in Bob's example, and John earns a large benefit. In the fourth example, Al gets a benefit, John bears a burden, and everything else is the same. So while there is no generational burden there are lots of different burdens on different people depending on the scenario.

Point, Krugman (And whoever else is willing to acknowledge they actually do agree with him and he's not some crazy guy stuck in the 1950s).

What causes what does change? What makes the incidence of the burden change in these different examples? Both the nature of the transfer (we know this causes some of the change because we see a difference between example 2 and example 3) and the financing method (we know this causes some of the change because we see a difference between example 2 and example 4). If you want the burden and the benefit to be borne by people living in the future, finance it with deficits. If you want to spread out the costs and the benefits of the deficit differently, change the nature of the transfer (i.e. - note that example 2 gives out a lot of small goodies and then imposes a big cost at the end, while example 3 gives out a lot of small costs and imposes a big benefit at the end).

Point, well, me, because I don't think anyone made this point in the discussion yet.

Where does the burden come from? Unambiguously it comes from the transfer. We have a burden on someone with and without borrowing, after all. One exercise is to add up everyone's lifetime incomes and calculate the deviation of that lifetime income in each example from the baseline (i.e. - example 1). I've done this in the chart below:



We have burdens on people with debt and without debt. If Bob and I had used real numbers rather than intergers for the bond amounts, it would be clear that the total burden in examples 2, 3, and 4 were all the same. Clearly what adds burdens here is the transfer itself, and all debt or tax decisions do is shift the burden around on different people. This is what Krugman said initially. Krugman's point was that if we're thinking about debt and the prospects for growth and the income of future generations, there is no burden on "our children" together.

Bob demonstrates this amply, and I'm just trying to drive the point home. If you still don't get it, add up all of Bob's rows individually yourself and see what income is with and without the debt.

This is very different from how most people think about the national debt. Krugman is right to highlight this and talk about this in the New York Times op-ed page.

Now, what we've learned is that the real costs or benefits are introduced by the nature of whatever it is government is financing. So can we please put this one to rest and get back to things like "is the stimulus a good or bad idea?" without worrying about financing it with deficits (quite) so much?