Friday, January 06, 2012

Clarifying My Point on Rowe's Model

I think I can express more clearly what is wrong with Rowe's model.  At the start, the government increases consumption by borrowing, and people eat 100 more apples.

But from whom did the government borrow the apples? It can't be foreigners: Rowe has assumed a closed economy. It can't be from savings: Rowe has assumed no saving. Rowe has the government "borrowing" apples from the ether. If he didn't, it would be clear that, in a closed economy, for the government to increase someone's consumption by 100 apples, it must reduce someone else by 100. And there would be no net consumption gain in generation 1.

At the end, the government taxes apples away to pay off the loan. But to whom does it pay off the loan? Not foreigners -- see above. It taxes away the apples, but "pays them back" to the ether.

And that's how Rowe achieves his result: if he showed the borrowing coming from someone, the there's be no net consumption gain in period 1, and if he showed the loan being paid off to someone in period N, there'd be no net consumption loss.

In the comments on the previous edition of this post, Rowe seems to be saying that cohort A is literally eating the apples of cohort C. Well, if this were possible, then obviously the model would work. But forget economics: the apple crop of two generations hence is simply not physically available for us to eat today. That is not a physically possible form of borrowing.

UPDATE: OK, Rowe has clarified what he is claiming in the comments. I don't think I was nuts to interpret him as I did, given the paragraph I quoted, but if you read his comment, then you will see what he really was getting at.

But now, what I believe his model shows is that if the government makes transfer payments from the young to the old, the old will benefit at the expense of the young. I will now model the same result with no borrowing: update soon.


  1. Gene: "I think I can express more clearly what is wrong with Rowe's model. At the start, the government increases consumption by borrowing, and people eat 100 more apples."

    Nope. I didn't say that.

    The number of apples produced each period is a constant. And total consumption of apples in any period equals total production in the same period, and must be constant too. But cohort A can eat more apples in its lifetime if A eats some of B's apples when A is old and B is young. Then B gets repaid by eating some of C's apples when B is old and C is young.

  2. OK, when you say this:

    "Suppose the government makes a transfer of 100 apples to the current cohort, financed by borrowing. Does that create a burden on future generations? Yes or no? B or NB?"

    That seemed to be what you were saying. But I will go through the argument again, since I assume that if you don't think that is what you were saying, then that isn't what you were saying!

  3. OK, as I said, I don't think my interpretation of the paragraph I quoted was nuts, but I now see what you meant. I will post my own model in response soon.

  4. @Nick Rowe: So, I must be even less sophisticated than you - which from the little digs and asides in your post, apparently makes me an even better person - but there's some stuff here I just don't get.

    1. At the beginning you say your model economy has no real growth. Later you say, "debt is increasing faster than GDP." But with no real growth, isn't GDP static?

    2. We only had the one bond for 100 apples that keeps getting rolled over, didn't we? So, right at that moment, debt increases faster than GDP - infinitely faster. But after that, we just see the same debt being rolled over several times. So how come, after that initial bond issue, debt:GDP isn't static, since both are flat?

    3. Why does Cohort A want to eat more apples? What good does it do them?