Noah smackdown watch: Bayesian updating edition

Either I manage to stay on most people's good sides, or most people just don't care about me that much, but for whatever reason, Noah smackdown attempts are rare. But today, J. Bradford DeLong has delivered a smackdown on Yours Truly. Last year I wrote a qualified defense regarding John Cochrane's warning of inflation, saying that basically, well, these things are hard to call. If there's a 1% chance of a catastrophic hyperinflation and a 99% chance of a continued economic stagnation, is it right to say that inflation is "the danger"? Brad says no:

Naughty, naughty Noah!... 

When you say something is "the danger", you are saying that other things are not dangers. "The". Definite article. You are saying that there is one and only one danger... 

And if other things are in fact dangers? Then the fact that you did not say that "the danger" would arrive by a date certain does not rescue you. You are wrong in your dismissal of those other things as not dangers. 

You can plead hyperbole--that you did not mean that this was really the only danger but that it was the only significant danger, or the only truly worrisome danger, and that it was the only worrisome or significant danger. 

But then, when asked about what actually happened, and whether your dangers was in fact the only worrisome or significant behavior, all you can then do is say something like: "LOOK! HALLEY'S COMET!!" 

I still say that while it is true that predictions and scenarios are not necessarily forecasts, a willingness to mark your beliefs to market is the first virtue of a wannabe academic. 

I say a failure to mark your beliefs to market is a fatal vice for anybody who wants to be taken as an intellectual.

As the wannabe academic in question, I think I'm fairly willing to mark my beliefs to market. But my own beliefs didn't really enter that much into my earlier post.

But how about Cochrane's beliefs, and terminology?

Suppose that you decide that A) a catastrophic hyperinflation is the worst feasible scenario (which seems reasonable, given that the U.S. borrows in our own currency), and that B) there is a 1% chance of that happening, and that C) 1% multiplied by the cost of (A) is considerably greater than 99% multiplied be the cost of a continued grinding stagnation. In that case, I think you're justified in saying that inflation is "the" danger. Yes, as Brad says, you're being hyperbolic, but the phrase "the danger right now" is common enough that I'm not going to lose any sleep over it.

So how about marking beliefs to market? With very unlikely events, this is hard to do. Suppose you believe that you have a 1% chance every year of getting shot. Suppose three years go by and you don't get shot. Well, even if your prior belief was correct, there was a 97% of that outcome happening. So you're not going to update your belief very much. 

So that, I think, is why I didn't get on Cochrane's case about the inflation warning, the way I got on, say, Steve Williamson's case for his 2012 prediction of imminent inflation.

If all this sounds like excuse-making, well, it is. It's difficult to go back and read something you wrote in the past and try to figure out if it was dumb or not, because there is always the nagging feeling that you must have had some good reason to write what you wrote. So here I am reading my earlier post and wondering what I was thinking. 

I think I was thinking something like this:

Before the 2008 crisis, many people were worried about a dollar crisis, in which China would decide to sell off dollar assets, triggering a flood of selling that raised interest rates. Those who worried about that danger included Brad DeLong (see also here). A spike in interest rates would tempt the Fed to engage in extreme monetary easing or even finance the deficit directly, which many theories predict would lead to inflation.

I think that this is probably what I thought Cochrane had in mind when I read this:

Our danger now is a run on Treasury debt.  It's not just can the Fed soak this stuff back up again, but can it soak this enormous amount of debt back up again when people don't want either money or Treasury bills or anything labeled "U.S. Government."  The danger is not 1932; the danger is Argentina, a massive run from Treasury debt.

Now, that scenario is not at all what happened in 2008, causing many of the people who had worried about it - including Brad DeLong - to issue mea culpas. But just because a dollar crisis didn't happen in 2008 doesn't mean that it wasn't possible in 2012. It is not even necessarily true that what happned in 2012 proved that a dollar crisis was significantly less likely in 2012 - remember the example of the 1% chance of getting shot. 

So I was probably thinking in those terms. I was probably thinking "Cochrane thinks that the dollar crisis scenario is still a danger. That seems unlikely to me given that it hasn't happened already, but maybe Cochrane sees things differently for reasons I don't understand. And maybe he's talking about small-probability events with catastrophic consequences, and that's why he calls it 'the danger' while not noticeably changing his belief in this regard."

At least, that's what I think I was thinking...

Update: On Twitter, Brad pointed out that an "Argentina" outcome probably isn't so bad that we should consider a 1% chance of it to be "the big danger". Actually, my instincts agree with that. But since the dollar is the world's reserve currency, I think it quite likely that a dollar crisis would be a much worse calamity than a run on the Argentine peso.