Monday, November 5, 2012

Debt enriches the future?

My latest salvo in the ongoing war at Free Advice.
Here it is. I hope the formatting is decent:
Can a debt *enrich* the future? By Bob's criteria it can.
Let's look at the example of Apple Atol, just a few miles from Apple Island where their policies differ.
In period 1 govt borrows 1  at 100% from young A for old Z.

In period 2 govt borrows 2  at 100% from young B and pays off the loan to old A.
In period 3 govt borrows 4  at 100% from young C and pays off the loan to old B.
In period 4 govt borrows 8  at 100% from young D and pays off the loan to old C.

In period 5 govt borrows 16 at 100% from young E and pays off the loan to old D.
At this point the Atol switches policies to get a steady state. There are many ways to do this.
Govt can tax the youngster 8 and borrow from the youngster 8 at 100%, or borrow from the youngster 16 at 0%.
Let's use the latter.
In period 6 govt borrows 16  at 0% from young F and pays off the loan to old E.

In period 7 govt borrows 16  at 0% from young G and pays off the loan to old F.

In period 8 govt borrows 16  at 0% from young H and pays off the loan to old G.
I lack Bob's mad table skills but let me show the resulting data
oq 100 yz 100
oz 101 ya 99
oa 102 yb 98
ob 104 yc 96
oc 108 yd 92
od 116 ye 84
oe 116 yf 84
of 116 yg 84
oh 116 yi 84

Now let's do Bob's diagonal sums.
Everyone ends up with at least 200, and some end up with more than 200. C gets 204.
The future, by Bob's critria, has been enriched.
A few other things to note. This example runs on pure debt, not defaults and not taxes, but there are several ways to produce such examples.
Old Z is better off too, no-one is harmed.
By the Krugmanite criteria, the Atol is not enriched.

For style points, the govt can just destroy the apple it borrows from ya.
Then the chart changes to "oz 100 ya 99"
That leaves Z out of the windfall, but the Bob-defined enrichment still works with no-one losing out *even with an apple destroyed*.
By the Krugmanite criteria the style points apple destruction impoverishes the present, without aiding the future. Broken windows anyone?

I suggest this example shows Bob's crtiteria are wonky, and that the limits of integration are inappropriate.


  1. Bob's OLG model was never presented as a "this is what will necessarily happen" kind of model. It was always intended to be a counter-example to the universal claim that debt NEVER impoverishes people in the future.

    Here, you are just changing some of the assumptions, such as the taxes and timing and whatnot, to arrive at a scenario where debt leads to people in the future being enriched.

    Your example doesn't show Bob's criteria are "wonky". It only shows that Bob's model is not the only mathematically possible model. But that's not a big deal, because his model is a possible future as well.

  2. Frank would never voluntarily agree to go from (100, 100) to (84, 116) with any preferences that value "consumption smoothing," or what is also called diminishing marginal utility within each period. In other words, the government wouldn't be able to roll over its debt at 0% interest.