Department of "Huh?" (Eric Zitzewitz Department)
6/21/09 9:53 AM
Grasping Reality with Both Hands The Semi-Daily Journal of Economist Brad DeLong: A Fair, Balanced, Reality-Based, and More than Two-Handed Look at the World J. Bradford DeLong, Department of Economics, U.C. Berkeley #3880, Berkeley, CA 94720-3880; 925 708 0467; delong@econ.berkeley.edu.
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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 http://delong.typepad.com/sdj/2009/06/department-of-huh-eric-zitzewitz-department.html
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Department of "Huh?" (Eric Zitzewitz Department)
6/21/09 9:53 AM
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 http://delong.typepad.com/sdj/2009/06/department-of-huh-eric-zitzewitz-department.html
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Department of "Huh?" (Eric Zitzewitz Department)
6/21/09 9:53 AM
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... rated 4.68 by you and 10 others [? ] You loved this post (
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Krugman vs. Ferguson: Letting the Data Speak (@Freakonomics Blog) Three or Four Mistakes in American Monetary Policy? (@this site) 2 more recommended posts Âť Brad DeLong on June 15, 2009 at 02:23 PM in Economics, Economics: Finance, Economics: Macro | Permalink TrackBack TrackBack URL for this entry: http://www.typepad.com/services/trackback/6a00e551f080038834011570212658970c Listed below are links to weblogs that reference Department of "Huh?" (Eric Zitzewitz Department):
Comments If two people are willing to pay more for something, does it matter if their reasons are contradictory? They aren't obliged to agree with one another to bid against one another. (He thinks it's a Vermeer, and wants it; I think it's really a van Meegeren, and want it.) I know this doesn't affect EZ's argument, but is there really a conflict to resolve? Maybe the ambiguity indicates that long-term interest rates aren't a reliable signal. Where am I mistaken? Posted by: Nathan Myers | June 15, 2009 at 02:39 PM "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." Okay, translate that for me. Do you mean people could be thinking things like: "There's only a 2% that things will be so bad that Treasuries exceed 10% by 01-01-2011, but if so then we'd bloody well better not be selling them!" and "There's only a 2% that things will be so bad that Treasuries exceed 10% by 01-01-2011, but if so then we'd bloody well better be buying them!" Because whenever I forget and call an interest rate curve a probability the quants just sigh and look out the window. Posted by: meno | June 15, 2009 at 02:49 PM It's a betting thing... just because I get $1.00 if a "1" comes up on the dice doesn't mean I'll pay $0.1666 for the privilege of making the bet. Maybe I'll pay $0.12 - but that doesn't mean my subjective probability of a "1" is 0.12, or, perhaps more apropos, that my subjective probability of a 2, 3, 4, 5, or 6 is 88%. http://delong.typepad.com/sdj/2009/06/department-of-huh-eric-zitzewitz-department.html
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Department of "Huh?" (Eric Zitzewitz Department)
6/21/09 9:53 AM
subjective probability of a 2, 3, 4, 5, or 6 is 88%. The interpretation of the graph still holds, though, because there's no reason to believe that over the last few months people suddenly started to care far less about low-inflation events (as opposed to believing they were less probable.) Posted by: John | June 15, 2009 at 03:55 PM Traders are really betting on the output gap. If we rebuild government expecting the economy to restore 6% of GDP, but the real, current output gap comes in at 2% then we will have inflation. Posted by: Mattyoung | June 15, 2009 at 05:28 PM What's so bad about 10% inflation? I mean, if the alternative etc. Posted by: david | June 15, 2009 at 05:56 PM Because history has proven that "normal investors" buying derivatives are necessarily good at predicting the future. And history has also proven that HLI investors buying derivatives with other peoples' money are necessarily motivated to price risk in strict accordance with their superior knowledge at all points along the curve. Too bad those foolish "noise investors" are such idiots, at least compared to people like Larry Summers who have great wisdom and foresight. Posted by: albrt | June 15, 2009 at 08:54 PM Brad, The post you refer to is a follow up post to a post in March that does a similar analysis about the S&P 500. http://freakonomics.blogs.nytimes.com/2009/03/02/quantifying-the-nightmare-scenarios/ In that post (linked to in the post about Treasuries) I make the point about the marginal utility of wealth. The marginal utility of wealth is clearly likely to be different at different levels of the S&P 500, so that is very important to keep in mind when interpreting that analysis. It is less obvious how aggregate wealth will covary with Treasury yields. Perhaps you are right that the ">10% yield" scenario is a higher marginal utility of wealth scenario. High inflation and yields can be consistent with growth too though, so I do not think the sign of the difference is obvious. And I do think you are overstating when you suggest that the marginal utility of wealth is 3.5-7 times higher in that scenario. But it is difficult to know what adjustment to make without knowing how investors expect bonds to covary with other assets (history is arguably not that helpful here) and without knowing what level of risk aversion is reflected in these prices. It's a blog post, not a paper, so I left this level of detail out. The issue though is incorporated by reference to the earlier post -- I am not ignorant of it, as you seem to imply. Eric Zitzewitz Posted by: Eric Zitzewitz | June 16, 2009 at 04:30 AM Brad, One further thought. Perhaps we can follow the advice at the end of my post and settle this dispute civilly "like gentlemen" (as opposed to talking about who wrapped what around what tree). Apart from perhaps differences about the optimal level of technical detail in a blog post and the exact definition of "option implied", our main difference seems to be over E(u'(w)|yield>10%)/E(u'(w)). You think this ratio is 3.5-7, I think it is likely much closer to one than that. Let me propose the following. Let's use the level of the S&P 500 as a proxy for u'(w). You sell me a conditional forward contract. Specifically, you sell me forward a single share of the S&P 500 fund SPY, with settlement at the close on witching day in January 2011 if and only if the 30-year Treasury yield is above 10%. If the Treasury yield is below 10%, the trade is off. This is essentially a bet on E(S&P500|yield>10%). http://delong.typepad.com/sdj/2009/06/department-of-huh-eric-zitzewitz-department.html
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Department of "Huh?" (Eric Zitzewitz Department)
6/21/09 9:53 AM
There's just the matter of the appropriate conditional forward price. You have strong views about this relationship and I don't want to get in the way of your expressing them (credibly). So perhaps a forward price of 50 (corresponding to an S&P level of roughly 500) would be acceptable. Let me know. Eric [The price of 50 is roughly what would be implied by your lower bound of 3.5, a representative investor with a CRRA of 4, and aggregate wealth comoving with Treasuries about half as much in percentage terms as the S&P).]
Posted by: Eric Zitzewitz | June 16, 2009 at 06:09 AM Forget what the graphs mean, isn't there something horribly wrong with the blue line? Those things just aren't supposed to have kinks going down in the middle of the peak, because it inevitably is going to smooth out to a nice graph later. Hedge funds are supposed to go in and fix abnormalities which have a giant 'trade me! trade me!' sign on them. Or were things really so fucked up in february 2009 that massive inefficiencies were remaining open for a while due to illiquidity, counterparty risk, or just plain so much distortion that the hedge funds couldn't chip off the money fast enough? Posted by: Bram Cohen | June 16, 2009 at 08:30 AM
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