Author Archives: Justin Wolfers

Interpreting the Fed

Here’s a puzzle.

For the first time ever, yesterday at 2pm the Fed released its forecasts for inflation (and other variables) for the next three years.  How should one interpret an inflation forecast for 2010?  Surely this is a statement of what the Fed thinks the “long run” looks like.  Thus, the 2010 inflation forecast – of 1-3/4 percent – is essentially an articulation of the Fed’s inflation target (or at a minimum, its definition of effective price stability).

Now imagine that you are trying to price long-term bonds.  Surely an articulation of the Fed’s inflation target is the most important news all year, if not in several years.  (And surely it is more important than trying to discern whether the short-run forecasts suggest an easing next month, or the month after.)

But markets thought this completely uninteresting.  Take a look at the bond market response:
Of course, markets wouldn’t respond, if they already knew that this is the Fed’s inflation target.  But I’m not so sure this is accurate.  The Philly Fed’s latest Survey of Professional Forecasters suggested  that the expected inflation target was a bit lower (1.6%), and previously Chairman Bernanke had suggested a “comfort zone” of 1-2%

Even if the markets already understood the Fed’s target then surely the announcement of yesterday’s news at least removed substantial uncertainty, which should have – but didn’t – change the risk premium built into the relative pricing of nominal relative to inflation-indexed bonds.

I am left to conclude that markets are either under-reacting to truly important news, or they are truly prescient and already knew the Fed’s inflation target.  My bet is on the former. 

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Publication Bias and the Death Penalty

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The front page of Sunday’s New York Times contained an interesting article reviewing research linking  the death penalty to homicide trends.  Adam Liptak attempts to provide a balanced account of the debate, noting first one set of findings:

According to roughly a dozen recent studies, executions save lives. For each inmate put to death, the studies say, 3 to 18 murders are prevented.

And then my own research:

The death penalty “is applied so rarely that the number of homicides it can plausibly have caused or deterred cannot reliably be disentangled from the large year-to-year changes in the homicide rate caused by other factors,” John J. Donohue III, a law professor at Yale with a doctorate in economics, and Justin Wolfers, an economist at the University of Pennsylvania, wrote in the Stanford Law Review in 2005. “The existing evidence for deterrence,” they concluded, “is surprisingly fragile.”

Surely a dozen studies is itself evidence of robustness.  Why then is then is it that we find these results are fragile?  Two words: Publication bias (also known as the file drawer problem).  Our research revealed that alternative approaches to testing the execution-homicide link can yield a huge array of possible results (positive and negative).  But if only strong pro-deterrent results are reported (and the others remain in the file drawer), this could look misleadingly like there is a pro-deterrent consensus.

It turns out that there are some rather simple tests for publication bias.  Our friends in medicine provide a useful intuition.  Imagine that there are many separate drug trials being considered – some with large samples, some with small samples.  If all results are being reported, then smaller samples should, on average, yield similar estimates to larger samples, albeit with a bit more noise (in both directions).  So the standard error of an estimate should be uncorrelated with the coefficient.  But if researchers only report statistically significant estimates, then they will only report results with t-statistics>2, yielding a strong correlation between standard errors and coefficient estimates.

You can probably guess what we find.

Continue reading "Publication Bias and the Death Penalty" »

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Why I’m Betting on the Red Sox

One of the most pervasive beliefs among sports fans is a belief in "streaks".  I cannot tell you the number of times I have heard sports commentators this week tell us that the Rockies have won 21 of their last 22 games.  And this alone is the reason that I’m betting against the Rockies.

The "hot hand bias" was first documented in a fascinating paper by Tom Gilovich, Robert Vallone and Amos Tversky.  That original paper (available here) is a wonderful read, showing that the widespread belief among basketball fans of a strong "hot hand" is simply false.  That is, today’s streak doesn’t predict tomorrow’s behavior.  I love teaching this paper to my MBA students, simply because they don’t believe it.  The hot hand fallacy is a wake-up to how pervasive bias can be.  A nice example of how sports can yield very convincing teaching metaphors.

A subsequent literature has developed showing that many (most?) of the sports statistics that ESPN loves to share with us, are simply useless as inputs for forecasting the future.  It seems that our brains are a bit too willing to try to find order, even in a world where chaos reigns.  This leads me to believe that most baseball fans are a bit too optimistic that the Rockies’ streak will persist.

Some will protest that subsequent research has found evidence of streakiness in specific sports.  I agree.  But this is beside the point: it is essentially an observation about sports.  What is more relevant here (and no-one has convincingly refuted) is that sports fans tend to believe that streakiness is even stronger

Believe it or not, there is now an entire blog devoted to the hot hand and streakiness in sports – read more here.  Or if you are interested in the performance of streaky baseball teams in the post-season, read this analysis at

(OK, there is one more reason I’m betting on the Red Sox: I went to graduate school in Beantown, and learned to love baseball at Fenway.)

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Is there manipulation in the Hillary Clinton prediction market?

Both Eric Zitzewitz and I have recently noticed some suspicious activity in the InTrade market for whether Hillary Clinton will be elected President, with someone bidding up her odds from about 25 to around 40 (currently hovering at 38).  This just strikes as us too high, relative to her chances of even garnering the nomination (around 51).  And when we saw this mis-pricing, we suggested that manipulation may be at play (see Eric here; my comments here; Robin Hanson here; and Greg Mankiw here).

But Koleman Strumpf isn’t so sure that this is manipulation. Koleman’s main evidence is that the law of one price appears to (roughly) hold across markets, and so the 2008.PRES.CLINTON security is similarly priced on BetFair, and elsewhere.  Of course, this isn’t evidence against manipulation, but it is interesting.  He raised the real possibility that this is a rational market response to some recent developments, although for the life of me, I can’t figure out what development that may be.

At the heart of Koleman’s concern is a question about the burden of proof here. And I have some sympathy for the view that when a market price moves in a direction you don’t expect, one should change one’s expectations, not one’s view of prediction markets.

So here is a simple way to resolve the issue of the burden of proof…  If the current market price is a reflection of available information, then as future information comes in, the market price is as likely to rise as to fall.  So I want to offer Koleman the following bet: If the price of 2008.PRES.CLINTON is higher than 38.3 (the last traded price on Intrade) on June 30, 2007, then I’ll buy him his favorite cigars. And if it is lower, I’ll be waiting for a good bottle of Aussie red.

Of course, we would want to make sure that this friendly wager is, itself, manipulation-proof.  So I’ll suggest we use the volume-weighted average trading price on June 30 to resolve the bet, and not simply the last 11:59pm trade.

So Koleman, do we have a bet? 

And more generally, do we have a useful mechanism for resolving scientific disputes?

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