## Thursday, May 06, 2004

### Borrowing Forever

Suppose I were to keep a diary. And suppose that for every two days I live, I write about one day of my life in my diary. Then, when I die, I will have written about one-half of my life.

Suppose an immortal deity were to keep a diary and also takes two days to write about each day of his existence. How much of his life will he end up chronicling? All of it! Because he will write about each day N on days 2N and 2N+1. There are no days that he won't write about.

The difference between the time limited and the forever applies to borrowing as well. If I borrow more than I pay off every year of my life, when I die there will be, by definition, unpaid debt that will never be paid and at that point my estate would be bankrupt (if not before). However, it's not quite the same for a government. If the U.S. government borrowed four percent of GDP each year forever, and the U.S. economy grew four percent each year, also forever, would the total government debt:
(a) Spiral out of control causing the government to go bankrupt; or
(b) Asymptotically approach 1.04 times GDP and level off?
The answer is (b). In other words, the government can borrow forever, and as long as there is some growth, the total debt as a fraction of GDP will approach some constant level. 1.04 times GDP might be a bit high, but if the deficit were only 2% on average, the total debt level would be 0.52 times GDP, a pretty manageable value. Higher growth reduces the level further. Inflation (i.e., higher nominal growth) reduces it further.

Indeed, that is why Social Security and Medicare dwarf deficits when considering future government liabilities. As long as there's growth, deficits today matter little in 50 years.

Also, even this year's deficit doesn't look like it will be as bad as first expected. According to the Washington Post, Federal Deficit Likely to Narrow by \$100 Billion:
Smaller-than-expected tax refunds and rising individual tax receipts will pare back federal borrowing significantly for the first half of this year and could reduce the \$521 billion deficit projected for the fiscal year by as much as \$100 billion, Treasury and congressional budget officials said yesterday...
U.S. government deficits are way down on my list of worries at the moment.