So, in this debate with commenters over stock returns vs. GDP growth, I may have to concede.

The ratio of stock prices to GDP is P/Y. Assuming no dividends, that means that P/Y has to increase for stock returns to exceed GDP growth.

I write P/Y = (P/E)(E/Y) where E is earnings. In a steady state, E/Y is constant.

My intuition was that P/E cannot grow indefinitely. If P/E is constant and E/Y is constant, then P/Y is constant. Which would make my claim, that stock returns cannot exceed GDP growth, a theorem.

But my intuition that P/E cannot grow indefinitely is not necessarily true. My intuition treats P/E as the inverse of an interest rate, and when P/E goes to infinity, the interest rate goes to zero. I worry that my intuition is based on a more complex world, in which implicitly there are other securities with positive real interest rates.

I think I can imagine P/E rising indefinitely. The machine costs $100 today. It earns $1. So now it is worth $101. If I bought it for $100, I can sell it for $101 and spend the $1. Then next year, the person who bought it for $101 can sell it for $102. And so on.

There is still something quasi-Ponzi about this. Suppose that GDP is $200. That means that in one hundred years the price of the machine is going to be more than GDP.

In any case, the commenters who have been telling me that it is possible for stock returns to exceed GDP growth forever have convinced me that my basic proof does not work.