Monday, January 9, 2012

One more post, for Bob's sake.

Bob doesn't like that I used inheritance in my example three. Fine. If the debate on the national debt turns on the question of inheritance now, that's fine by me because... well... we have fairly ample evidence that inheritance does happen.

I also say "fine" because I hope Bob realizes this was just to highlight the importance of the transfer itself - the initial government transaction - for the result. Bob and Nick specifically chose a debt-financed transfer from young to old. If you had chosen an investment that would have turned out differently, but since we were in an endowment economy I just wanted to flip the direction of the transfer.

My point, Gene's point, Steve's point, and Krugman's point still remains: you cannot find a future time period that is poorer as a result. You can find individuals in the future that are poorer. That's the whole point of debt - pushing the burdens into the future. The thing is, the way you do that is by pushing assets into the future too.

Anyway, if Bob is fine with endowments from nature but not endowments from parents, this gets tricky in a model with two people that only overlap in one period (that forces the direction in which you can make transactions). But perhaps this unannotated three period, three person example will be of interest to people (and if you can't figure out an unannotated version you've probably tired of the discussion by now anyway):

I'm not going to do the utility calculations Bob suggests.

Here in the last period two of the three people are coming out on top, one is bearing a cost. If we had investment instead of a pure endowment economy that one wouldn't have to bear a cost.

Maybe this still doesn't satisfy Bob because one person is still bearing a cost. I'm not sure if I can tweak it anymore - I just did that quickly. I would even be willing to say (until someone proves me wrong) "without inheritance the cost-bearer must be the last person even if there are also benefit-earners in the last period". I'm not entirely sure why that matters. We've always agreed that individuals in the future bear burdens that they otherwise wouldn't as a result of debt. That point was in Krugman's very first post. I don't understand what the significance is of this last person for Bob.

What I hope Bob understands is that in my opinion, he was making Krugman's point even with his own example 1 and 2. And it's not just my opinion - that's what Gene and Steve were telling him too.


  1. Daniel,

    I appreciate your willingness to put so much into this debate. You and I clearly are the MVPs for Team Krugman and Team Rowe, respectively.

    However, let me note something ironic here:

    (1) You claimed there's nothing really about debt going on here, because you could (you claimed) use my own framework to show deficit financing being used to make the earlier generations lose at the expense of the later generations.

    (2) Gene thought this was a game-winner. He said on his blog of your result, "Game, Set, and Match" when linking to your result.

    (3) Before looking at your example, in my head I tried to figure out how your claimed result could be possible. I couldn't make it work.

    (4) I looked at your result and saw it relied on inheritances, which are not in my model and so make things really tricky, because now we can't easily check if someone is made better or worse, since we don't know how much they care about the next generation's consumption etc. So I asked if you could do it over, without inheritances, and by specifying an actual utility function so we can literally check the math to see if your example works.

    (5) If I'm understanding you in this post, you are saying, "No, so far I can't get it to work Bob, but I still think it probably does."

    (6) Last point: If you and Gene are saying debt per se has nothing to do about hurting future generations, and indeed we can use debt financing to hurt the present generation while helping future generations (that is indeed a great point, and Gene would be right that it would be decisive if it's right), then why did you write this:

    You can find individuals in the future that are poorer. That's the whole point of debt - pushing the burdens into the future.

    Do you see the problem? On the one hand, Nick and I are being called naive for thinking debt somehow hurts people down the road, and then you come back and say, "Duh, of course debt hurts people down the road."

    Anyway, if you can come up with an actual numerical example with a utility function to show me people in the present being hurt while people in the future gain through deficit financing, I would love to see it. I think it might be impossible though, at least in the framework I've been using.

  2. Hey Daniel, I've been thinking a bit more about this and I'm pretty sure it is impossible, in the framework I was using. So if you think it's possible in a more general framework, it would be interesting for us to try to figure out which of my restrictive assumptions is driving the result. However, I don't think it's my assumption that there is no altruism, because you're right that we can just make a person live for three periods and that effectively is like the person in my original model caring about the next generation (but not his grandkids). So, since I don't think you can get your result in my model, I'm thinking you can't get it with my-model-plus-altruism-for-descendants.

    Incidentally, here's a sketch of a proof in my world:

    ==> In period 1, if the government runs a deficit, then it must be borrowing from Young Bob to pay Old Al. (If it tried to borrow from Old Al, it would fail, because Old Al won't be around in period 2 to collect.)
    ==> But if the government doesn't throw away apples, that means Old Al benefits from the deficit in period 1.
    ==> Thus we can't even get off the ground. There is no way in my model that deficit financing in period 1 can hurt the people in the first generation.

    Ha! As I was typing up this comment, the answer came to me. I think you will appreciate it Daniel, since it's pretty neat, and I wouldn't have thought of it without your input. (I.e. you should be proud that your efforts have helped to make another cool thing pop out of this debate.) But, Gene will be in a pickle, because it will make the exact opposite point of what he wanted. I.e. if he thought your observation was "Game Set Match" then he is in trouble since I'm going to show the opposite.

    Let me give you (and Gene) a hint, before I write this up at my blog. (I might not get to it today.) Yes, you and Gene are certainly right that the government can impoverish early generations at the expense of later ones, through tax and transfer. But, the government can't mimic the outcome through *deficit* financing. Instead, it can mimic it through... (Can you guess?)

    Here's another hint: Start by having the government tax Old Al 50 apples in period 1. Then figure out how the government would "distribute" the proceeds such that only the last 5 people benefit. It's not by the government borrowing money, I'll tell you that much...

  3. Hey there, it's me again. I didn't have time to fill it all out, but yeah, you can (for example) tax Old Al 64 apples in period 1, and the government lends them to Young Bob at a NEGATIVE 50% interest rate.

    Then in period 2, Old Bob pays the government back 32 apples, which it lends to Young Christy at -50%. etc.

    Because of the very low interest rate, the people who roll the surplus over benefit in utility terms.

    In the period when the surplus has dwindled down to 1 apple, the government just hands it over to the young person at that point. So, by using a budget surplus, the government hurts Old Al and enriches subsequent people.

    (You would have to go into fractional apples if you wanted to get all the way down to John in period 9.)

  4. Daniel,

    You still don't get it. Simply astonishing. You wrote:

    "you cannot find a future time period that is poorer as a result. You can find individuals in the future that are poorer"

    If what you wrote were really true (or, to be more precise, had anything other than a trivial truth across an aggregate since this is, in fact a condition set by the Rowe/Murphy model itself), the burden could be undone across the future time period without transferring that burden, or any part of it, to any one else within the time period, or to anyone in a subsequent time period. This is quite literally impossible to do since, at any instant in time after the initial reallocation event, when the burden becomes realized as such (as a tax or as a default of any kind), it is then a past event (someone in period 8 ate the loaned apples from Iris). For example, Iris in period 8 cannot ever be made whole in period 9, nor can Iris within the period of time 8-9 be made whole without making someone else in period 9 or later worse off.

    Let me try one last time. The laymen's understanding of the burden of debt incurred today is exactly right (Krugman was exactly wrong)- costs are being pushed onto a future generation/s of peoples. Those people may or may not be alive today, but they will surely exist, and the burden they will bear cannot be completely fixed by any possible actions made in the future. All that could be done is to spread that burden (see Murphy's last example) over more people, or put it all on the most narrow group (the last people to buy the bond chain started in period 1) so that any subsequent generation is again indifferent to the events of period 1.

    You claim that Krugman understood all of this, but I don't the evidence is anywhere close to supporting your assertion. If he had understood it, then it is isn't possible to explain why he added the caveats about the internal vs external debt and the balance of payments that American's receive. When he added those caveats, it was an attempt to foreclose the objection that it mattered who owed what to whom across national borders, but doesn't matter within them (thus Americans could "owe it to themselves"). However, the Rowe/Murphy OLG model clearly shows that American's can't owe it to themselves- some will bear the burden, others will not (but won't benefit either, in this model!), and the future, at any point in time, can't change this because it is an event in the past.

  5. I could continue this and denounce your ignorance of the issues too, Yancy, but I'm really sick of arguing like this and getting told I haven't furnished arguments, links, or references that I have.

    Everything's on record, so I don't really need to.

    Have a good day.


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