## February 03, 2004

This is a (humorous) comment I posted I while back in Brad Delong's website. As a mathematician you might find it amusing. The somewhat humorous example below, is not quite the same thing as Enron accounting tricks, but the general principle of debt shifting is. (What was shifted around to "LMJ" and "LMJ1" in the case of Enron were financial assets with different variances)

Hilbert's Hotel and the Bush Administration's financial strategy (or BUSH'S BANK). Let me begin by a simple proposition in Financial mathematics which is well known, elementary but worth repeating: (pardon the AMS LaTex). PV denotes the present value operator on a stream of income. Assumption: discrete time parametrized by N. Any stream of income $\bar{Y}$ with $V = PV(\bar{Y},r)$ and such
that $Y_t = 0$ for $t \geq n$ can be achieved by borrowing, buying and selling annuities at each period $t \leq n$ and having no holdings or debts for $t>n$.
Proof: We can easily reduce this to the case of $V=0$. The strategy is as follows. For $t = 0$ borrow $Y_0$ to provide the desired payment at time $0$ . At $t=1$, borrow $(1+r) Y_0 + Y_1$ to pay back the principal and accumulated interest of the first loan and to provide the desired payment $Y_1$. At time $t=n$ payback

(1+r)^n Y_0 + \cdots + (1+r) Y_{n-1} + Y_n =
(1+r)^{-n} \sum_{t=0}^n Y_t (1+r)^{-t}
= PV(\bar{Y},r)

Note $Y_n = 0$ and since $PV(\bar{Y},r) = 0$ by hypothesis, no new loans are needed.
IMPORTANT REMARK:
Note that if we no longer assume that debts are zeroed out at time n,then no condition on the present value is necessary. You can start with 0, and using the strategy of borrowing accumulating larger and larger deficits, you can live it up giving yourself an arbitrarily large income stream.
This is a financial variant of the principle of Hilbert's infinite-room hotel.
We should rename this to BUSH'S BANK

If a debtor is able to find creditors to unboundedly accept its debt, then it also has the ability to shift its debt burden off to infinity. In the finite real world obviously, something will constrain debt divergence and eventually lead to a collapse somewhere, sometime. But this little financial trick does have a political purpose: debt-shifting. That is it succesfully shifts the point of debt collapse either to a remote point in the future or to some other remote creditor. It is a time version of a Ponzi scheme. Note that in the case of our debt, the creditors that are taking up the debt are to a large extent asian nations, including the chinese. What is
extremely worrying to me is that shifting the debt collapse to the chinese will allow the Bush admin (or some subsequent Bush-like admin) to use all the political cards against the chinese: The race card, the language card, the "democracy" card, the WMD card and the unfair competitor card. Am I being too paranoid? Am I taking Richard Perle too seriously?

The comment would be humorous if the real life consequences weren't so scary. Luckily I'm used to reading LaTeX as is. Thanks for your comment.

The comments to this entry are closed.