Tuesday, October 16, 2012

Sort of an obvious point...

[UPDATE: I just realized I used U=ln(X) instead of U=sqrt(X), which is what Bob originally specified... and I stupidly deleted the excel file and don't have time to redo it now. I don't think it should change any of the conclusions - only the numbers. But if someone wants to double check that, be my guest]

...but perhaps still worth making.

Bob Murphy tries to bolster Nick Rowe's case here with his OLG table. It does not demonstrate at all that future national income is hurt by debt. Quite the opposite. It does demonstrate what everybody always said - debt has distributional effects. It also shows that when you make young people pay in the future the benefits that old people enjoy in the present and then kick that can faster than your income grows... people in the future do worse than people in the present. Go figure.

But how are we supposed to feel about this?

When we compare generations, one thing that economists are usually careful about doing but Bob did not to do (to simplify things) is discount the future. So at period 1, if we assume the discount rate equals the interest rate (we have no depreciation in these apple trees, so that's reasonable) and otherwise assume Bob's additive natural log utility function, what do you get?:

A slight preference against debt transfers.


It's entirely driven by the consumption smoothing preference.

That's fair enough. But what if old people in this model had income of 50 and young people had income of 150? That's why we do Social Security, is it not?

Then you'd have a preference for transfers financed by debt sitting at period 1, again, because of a desire for consumption smoothing over the life-cycle.


  1. Daniel:

    1. The log vs sqrt U function won't make any important difference. Diminishing MU matters, but both have that.

    2. "It does not demonstrate at all that future national income is hurt by debt. Quite the opposite."

    Of course it doesn't. By assumption. Because it's a *counterexample* to those who claim that future generations are worse off only if future national income is hurt.

    3. Your table lost me a bit, on the "names" thing.

    4. If the social planner discounts future utility, I could rig an example in which deficits make current generations better off and future generations worse off *and the social planner likes deficits precisely because they do that*! Because he doesn't care about future generations as much as current generations.

    5. Normally, we don't discount future utilities by the interest rate. We discount future utilities by the rate of time preference proper, not the marginal rate of time preference.

  2. Nick:

    I'm inclined to agree with you, but only in part.

    Normally, we wouldn't pay 100% interest when 1.523% interest would increase Bob's utility. If the government announced a tax on the old sufficient to cover the interest on a 3-apple debt at a rate which makes each generation indifferent to the debt, then the government could roll over the debt forever, and the cost in utility to each generation is equivalent to something like a loss of 1/40th of an apple per year.

    This is, of course, completely consistent with your argument that the interest is the problem, not the debt. But then again, Daniel is completely correct when he says this loss is in consumption smoothing. If the government simply taxed the young three apples and gave to the old, the loss would be precisely the same, but with zero debt.

    Not bad for an example where the endowments and preferences are totally rigged to show a burden.

  3. Daniel, please show me where Krugman or Baker ever said, "Future national income can't be hurt by debt, but every single American in the future might be made poorer."

    1. As I've pointed out a couple times now, Krugman repeatedly referenced GDP (that's why I keep making this point). I also repeatedly noted that Baker uses mushier language than Krugman and for that reason I like what Krugman has said on it better.


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