How much public debt is sufficient?

In Why public debt is a good thing, Syll quotes Krugman:

Believe it or not, many economists argue that the economy needs a sufficient amount of public debt out there to function well. And how much is sufficient? Maybe more than we currently have. That is, there’s a reasonable argument to be made that part of what ails the world economy right now is that governments aren’t deep enough in debt.

I'd say that is true, far as it goes, but it doesn't go far enough. "Maybe more than we currently have" doesn't answer the question. Nor does it offer a rule of thumb you can use to figure out an answer.

The question Krugman asks is: How much public debt is sufficient? The rule of thumb answer is: It depends on the level of private debt. When the "private debt to public debt" ratio is high, the cost of private debt interferes with economic growth. To improve growth in that environment, the Federal debt must rise rapidly -- more rapidly than private debt. This happened in our economy between 1981 and 1994:

Graph #1: Private Non-Financial Debt relative to the Gross Federal Debt

It took a long time, because the increase in public debt is a foundation upon which private debt can grow. The increase in Federal debt lowers the ratio, but also allows private debt to grow, which raises the ratio.

If you want to reduce the private-to-public debt ratio, it is a mistake to focus on public debt alone. It is necessary to discourage the growth of private debt, at least when private debt is high. Preferably, always.