one more Nate Silver-related post.
In defense of Barro's research, stock market crashes are usually a leading indicator of a recession or depression. Stocks are priced on expectations of future earnings, so stocks SHOULD drop before the economy actually starts going south.
Stocks fluctuate much more than the magnitude of the recession/depression because equity is at the bottom of the corporate capital structure (A company worth 100, 60 in debt and 40 in equity, if it loses 20% of its value, the debt isn't affected, really, but the equity loses 50% of its value. Similarly, if it gains 20% in value, debt isn't affected but the equity gains 50%. The company's overall value represents the economy, the equity value represents the stock market).
If the economy bottoms at a 5% GDP drop, which is a recession, you would expect a substantially larger stock market drop prior to the recession.
You have a situation were X causes Y, and you can't observe X but you can observe Y. The strength of the causality varies time to time and is difficult to estimate, which is why it was worth Barro's time. If you can estimate the strength of that causality, you can look at what we've seen in the stock market, plug it into Y and reverse engineer to get a sense of X.
I haven't read Barro's paper. Silver is a much better statistician than I am, and if he has objections to the econometric method Barro used and thinks that the prediction is therefore not very useful, that's a fair point. But calling it irrelevant and simplistic ignores the economic intuition underlying Barro's paper.
Again, Silver is a phenomenal statistician, but he's excluded the economic intuition behind Barro's work.
EDIT: I'll point out that I do agree with his very last point - stock market prices have a very large propensity to be irrational for sustained periods of time. Stock markets are an imperfect proxy predictor, not a measuring tool, for economic performance. However, if you pay attention to things like standard deviations and all that, which Barro must have if he predicts a 20% chance of a depression instead of just saying "I don't predict a depression", you can get a rough control for that if you think psychology is in the normal range this time compared to other times of similar stock market crashes.