## Department of "Huh?" (Eric Zitzewitz Department)

Justin Wolfers gives the keys to the freakonomicsmobile to Eric Zitzewitz:

Krugman vs. Ferguson: Letting the Data Speak:

Why Have Long-Term Interest Rates Risen?There’s no debating that long-term interest rates on government debt have risen. But there’s a pretty fierce debate about what it means. Harvard historian Niall Ferguson interprets this as indicating that the bond market is worried about the U.S. deficit and the prospect of inflation. Princeton economist Paul Krugman thinks it indicates that worries about deflation have eased. It’s a high-stakes debate: Professor Ferguson is arguing that the stimulus package has counterproductively stimulated inflation fears, while Professor Krugman thinks the stimulus has worked as intended by reducing the likelihood of deflation. In fact, Krugman has argued for another dose of fiscal stimulus.So who is right?... Resolving their debate requires measuring the likelihood of different inflation scenarios. Let’s do it. The graph below plots the probability of different outcomes for the yield on 25-year Treasuries on two different dates — late February and the end of last week.... The blue line shows that there was a lot of uncertainty about future Treasury yields in February, including a very large chance of very low interest rates, as in Krugman’s deflation scenario. But the green line shows that this deflation risk appears to have receded. In fact, the recent increase in Treasury yields is almost entirely due to a reduction in the probability of the deflationary (low nominal interest rates) scenario. Score this round for Krugman...

OK. Zitzewitz is out of the driveway and the car is still running. He has, how ever, run over the mailbox and crushed it into smithereens. The graph should, I think, say not "Option-Implied Probability Distribution" but instead "Risk-Neutral Option Pricing-Implied Probability Distribution." But the car is still rolling down the street because Zitzewitz does say--correctly--that Krugman is right and Ferguson is wrong: rates have risen because the fear of deflation has ebbed and not because the fear of inflation has grown (in fact, he claims the fear of inflation is less than it was in February).

But then Zitzewitz wraps the freakanomicsmobile around a tree:

While Ferguson wrongly diagnosed the cause of the rise in interest rates, he is right that the markets are spooked about the risk of an inflationary breakout. There’s about a 7 percent chance that 25-year interest rates will exceed 10 percent.... This is a fairly extreme scenario: long-term interest rates have not been above 10 percent since inflation was tamed in the mid-1980’s. So there’s a chance that Professor Ferguson may be right about the broader issue: now that deflationary worries seem to have eased, it might be time to start turning the fiscal policy battleship around...

No, no, and no. It is not that the market thinks that there is a 7% chance that the 25-year Treasury nominal rate will exceed 10% in January 2011. Rather, the probability that the 25-year Treasury will exceed 10% in Jaunary 2011 times the scaled marginal utility factor for how much you fear Treasury rates above 10% together equal .07 when you normalize values so that the sum over the entire probability distribution of the scaled marginal utility factors is equal to one. (I know that that is totally incomprehensible, but that does make sense.)

The chance that 25-year Treasury rates will be above 10% in January 2011 is more like 1% or maybe 2%: it is not 7%.

To say that there is a 7% chance that the 25-year Treasury rate will be above 10% in only 19 months is to say something bizarrely misleading.

Someone please call AAA...