Asterisks of Gall(?)

One of the biggest news items in the last week was the release of the Mitchell Report, which investigated the prevalence of steroid use in Major League Baseball. Pretty much everyone has had something to add to the discussion on performance enhancing drugs. I've been following the story as it develops and had some scattered comments of my own (unfortunately, grading lots of tests and finishing up for the semester prevents me from putting this in the usual essay format):

1) The Blame Game - People have been quick to vilify some of the players named in the Mitchell report as cheaters. For some of the bigger names, such as Roger Clemens, the buzz surrounds whether or not they should be inducted to the Baseball Hall of Fame or not. I am having a tougher time burning effigies of these players. Why? Because they aren't the real culprits behind baseball's "steroid era."

Here is my take. Suspicion of widespread use of steroids and other drugs was growing as early as the late 1980s and early 1990s. Major League Baseball did not take any steps as far as stringent testing and penalties until over a decade later. In the meantime, the use of performance enhancers likely lead to increases in wages and length of tenure for the average player. Given the low level of deterrence and potentially large expected benefits, players went for steroids and HGH, their preferences for health and discount rates notwithstanding. Perhaps there were even externalities from usage: a single player or groups of players performing better and accruing higher wage earnings likely upped the ante for everyone else to performance better, further tipping the cost/benefit balance over to usage.

In any case, the MLB did nothing for a really long time. Not only that, post the strike induced lock-out in the early 1990s, the game was essentially "saved" in the eyes of paying fans by the steroid induced home run chase in the summer of 1998. The MLB's inaction and their packaging of the game in terms of increased power hitting and speed likely created the right kind of incentives to induce the marginal player into trying to get the extra boost.

2) Asterisks - Putting asterisks on records held by suspected users of performance enhancing drugs seems like a difficult proposition to me. If the Mitchell Report is indeed the tip of the iceberg, and use of agents like anabolic steroids and HGH was (and is) widespread, it is hard to distinguish between "legit" and "cheater-induced" records and probably unwise to try and do so. Rather, interpretation of statistics should be left up to discerning fans.

Still like asterisks? Given the discussion in (1), try this one: MLB*.

3) "Steroids don't help you ______" - Some players and analysts claim that performance enhancing drugs do not really help you become a better baseball player. Two supporting arguments are generally cited. First, steroids and HGH do not help you develop the mechanics to hit a ball, work a pitch count, etc. Second, many of the players named in the Mitchell Report are scrubs - steroids didn't help them hit 50 home runs or clock 95 on their fastball.

Regarding the first point, here is a quote from Ken Caminiti (just one of a brilliant collection in http://www.baseballssteroidera.com):

"The stronger you get, the more relaxed you get. You feel good. You just let it fly. If you don't feel good, you try so hard to make something happen. You grip the bat harder and swing harder and that's when you tighten up. But you get that edge when you feel strong. That's the way I felt. I felt strong, like I could just try to meet the ball and -- wham! -- it's going to go 1,000 mph. Man, I felt good. I'd think, Damn, this pitcher's in trouble and I'd crush the ball 450 feet with almost no effort. It's all about getting an edge."

The second argument is really easy to deconstruct: we simply do not know how these players would have done had they not use steroids (assuming the allegations are true). The scrubs on the list may have never even made it to the major leagues without the extra jolt. Steroids likely provide a boost to players sitting at any level on the baseball skill distribution: they don't have to make you an all-star, but they may make you slightly better than you were before. In a competitive industry, this might be all the edge you need.

4) "The game of baseball has been denigrated" - Can anyone honestly tell me that this scandal, involving individuals cheating in order to perform better, is worse than the 1919 White Sox scandal and the match fixing scandal in international cricket where, in both cases, teams intentionally threw games? Sports have weathered these storms in the past. Baseball will be always popular and its heroes will come and go, steroids or not.

5) What to do now? - One the one hand, the Mitchell Report suggests stringent testing, harsher penalties and player education to stem the use of performance enhancing drugs in baseball. On the other hand, some analysts argue that it is impossible for testers to keep up with innovations in performance enhancers. After all, existing tests still cannot detect "the cream" and "the clear," substances Barry Bonds is suspected to have used. In fact, Marion Jones, who admitted using these products never tested positive, covering over 160 tests in sum. In this situation, these observers argue that legalizing these agents in the game and regulating their use with physician oversight might be a better way to go in terms of player health and leveling the playing field.

I'm not sure where I stand on this one, though I think I would lean towards trying to rid the sport of performance enhancing drugs. For one thing, I'm not really convinced by the "arms race" argument against more stringency. Following Gary Becker's seminal analysis on crime, suppose that the average player will use steroids if the expected benefits outweigh the expected costs. In this framework, expected costs are equal to the probability of being caught * the value of the costs themselves. Those who think we'll never catch steroid users believe the probabilities will be too low to give any bite to the costs. On the other hand, increasing penalties, publicly "outing" suspected users, and introducing uncertainty into Hall of Fame chances may jack up the costs enough to outweigh the lack of change in the probability. After all, do you think many players or managers are going to try and pull a Pete Rose now given all that he has been through? Social norms and pressure can be powerful and perhaps more stringency, then, could be a good policy to go with.

A thoughtful post by The Sports Economist provides more arguments for "cleaning up" baseball. One of the more interesting thoughts in that piece, which was alluded to earlier here, is that steroid use by a given MLB player has externalities: others will want to use it in order to compete and this will be true all the way down the pipeline. Where it becomes dangerous is at the level of younger people, who do not possess the resources to have a personal trainer monitor their use. This could have adverse health consequences both in the short and long run.

There is some evidence of noteworthy use of steroids in high school. This piece in JAMA suggests that almost 7% of high school senior athletes have used anabolic steroids. Of these, many started on their regimens as early as junior high. 7% seems like a pretty big number to me. What would be nice to have are figures relating likely steroid-driven adverse health events among this group and information on why these kids decided to initiate such regimens. That way we could get a sense of the extent to which externalities are operative in steroid use.

When Bad Inference Happens to Good People

I turned on ESPN yesterday night for some pre-game analysis on the Houston Texans-Denver Broncos contest. I wasn't paying too much attention until I heard the following statement: "One of Houston's keys to victory tonight is to give Ron Dayne 20-25 carries."

I did a double take. Ron Dayne? An NFL journeyman with decent size, but limited speed, who is best utilized in a platoon of running backs? It turns out that the analyst was basing his comment on the following fact: the Texans are 4-1 in the past two seasons when Ron Dayne gets more than 20 carries.

This is another example of people confusing correlation for causation. There are two (or maybe more) explanations for the Ron Dayne tidbit:

1) Ron Dayne is a game changing talent who, if given the ball, will more often than not win the contest for you.

2) Ron Dayne getting 20 carries or so is a symptom of things working right offensively for the Texans. When the Texans are firing on all cylinders, Dayne's rushing opportunities and totals may reflect the fact that linebackers and safeties are playing off the line of scrimmage and drop back into coverage, allowing Dayne to get his 5-10 yard runs, or that offensive line play is so dominant that Dayne is able to run clear through the woods.

I think the second explanation is probably the more likely one. After all, can you imagine a defensive coordinator thinking before a game, "wow, we need to get 8 in the box to stop Ron Dayne"? Ron Dayne is a good player, but he's not LaDainian Tomlinson or even Frank Gore - the 2007 version.

In any case, this innocuous episode reflects the danger of attributing causal stories to what are only correlations. Unfortunately, fates of entire policies have hinged on bad inference, that too in arenas less trivial than professional sports.

Time Inconsistency, Parking Tickets and Health Care

The New Haven police gifted me a parking ticket a couple weeks back. The payment scheme for the ticket works something like this: it's $15 if you pay it within two weeks or so, $30 if within four weeks and $60 thereafter. I still haven't paid my ticket, so I am looking at about $30 right now.

Am I just completely insane? Why didn't I pay my ticket on time? I could have saved at least 15 bucks. Well, as it turns out, I always did (and still do) intend to pay it sooner rather than later. But getting an envelope, writing a check and sending the thing out was (and is) kind of annoying process to me. Every day I would say, "I'll do it tomorrow."

This is what is called time (or dynamic) inconsistency. The basic idea is that one's current self and one's future self (say tomorrow, or next month) have differing ideas on what actions should be taken (present or future). This is more than a theoretical construct: its a pretty big deal in health economics. An example (taken from the above linked wikipedia page):

Each day smokers face a dynamic inconsistency: their best plan is to enjoy smoking today, but to quit tomorrow in order to get health benefits. However, the next day, the plan is the same; enjoy smoking today and quit tomorrow. This goes on, and they never give up, even though they plan to, hence the inconsistency.

You can easily see how this behavior is important in understanding other health behaviors, such as dieting and other weight loss efforts or perhaps even going to the doctor to get some anomaly checked.

If time inconsistency is a strong barrier to self-motivated health efforts, how does one get around this? Yale economist Dean Karlan and law professor Ian Ayres think they have an answer. The two have recently started a company called StickK. Here is the basic idea:

The company will have a Web site offering individuals hoping to reach a goal — anything from sticking to a diet to learning to ride a unicycle — legally binding contracts where they will pay a set dollar amount to charity if they fail in their endeavor.

The author of the book "The Undercover Economist," Tim Harford, is testing out StickK's methodology. He has paid a $1,000 so-called contract bond to the company, and has promised to donate 10% of this deposit to charity if he fails to complete 200 push-ups and 200 sit-ups every week.

"When I signed up to do this, I thought to myself, the contract bond isn't going to matter at all; what's relevant is that I've made the psychological commitment to do these press-ups and sit-ups," he said. "I was completely wrong. There's absolutely no way I would have done these press-ups and sit-ups for the past six weeks had it not been for the commitment bond."

I'm really curious to see a) how many people choose to enter binding contracts and b) how effective these are for the average consumer.

In the meantime, I think I'll pay my parking ticket...tomorrow.

Fashion Show Economics

I watched the Victoria's Secret fashion show a few nights ago. It was just fantastic. Here are a few interesting tidbits I picked up:

1) Heidi Klum is a good singer.

2) Only B-list celebrities appeared to be interested in actually showing up to the event. Ryan Seacrest? The Spice Girls? VS is offering this two day only promotion where any purchase of $60 dollars or more gets you a free Spice Girls CD. A neat little study for an undergraduate or intro stats class: using discontinuities in the sales promotion to identify causal effects, does the prospect of a Spice Girls CD induce more people to shop and buy at the store? Does it move the marginal $56 purchaser to buy the extra item that puts her over the top?

My priors tend towards the null on this one.

3) The most interesting feature of the show were the model biopics. Many of the models were discovered when they were 12-14 years old. I find that really amazing. How much certainty is there in forecasting whether a 13 year old will turn out to be a supermodel or not? I'm not sure where you can get data on this question, especially given the obvious selection bias - for every Selita Ebanks or Adriana Lima, there are probably 100s of others that you don't observe that don't make it.

To get around this, I thought about the compositional change in the popular clique between 7th and 12th grade in high school. The popular clique in any school is generally comprised of the "hot people," and is generally superficial enough to kick out people who move from hot to not as well as embrace people who move in the other direction. I estimate that about 68% of the popular clique in 7th grade continued to be popular in 12th grade. This larger inter-grade correlation can be explained by persistence in looks and social status as well as the bond of friendship, though its hard to pin down the relative contributions of these factors.

Even so, I think making predictions about a 13 year old is still really difficult. Of course there has to be some science to it: some people have a comparative advantage in discovering models and make a career out of doing so. Indeed, there are a lot of industry specific skills that are either innate or learned. If you've watched America's Top Model, it's easy to get a sense of this: Tyra and the other judges rate the contestants on a vector of different characteristics, where some of the elements are obvious and others not so much.

But at the end of the day, you just never know. A pharmaceutical company, for example, mines through a myriad of candidate molecules, finds the ones that are bioactive, and pushes those forward for further testing. The vast majority of these new chemical entities or compounds will fail, either to be refined or scrapped altogether. But some do make it, and the incentives are such that its worth pushing forward and leaving no stone unturned. After all, the next molecule you find might be worth billions.

I'm guessing there's a parallel to supermodels. As a model finder or agency, you don't know if your 13 year old will turn into John Abraham (the Indian one, not the guy on the Jets), on the one hand, or Atheendar Venkataramani, on the other. But you take the risk, and if it is indeed the former case, there are huge returns to be had. And, for a time, those returns might be increasing in the earlier you find the next great supermodel. Indeed, just as competitive forces push Merck and Pfizer into random jungles looking for even more random plants, the modeling industry probably evolved on a margin where those who moved first in finding younger and younger prospects were able to gain a leg up on their rivals.

The Deep Structure of the Universe? (Some Friday Fun)

I went to an interesting talk last week on why individuals don't choose to buy long-term care insurance. While the speaker did not have an answer to that question just yet (it's a work in progress), she did have a lot to say on the use of qualitative methods as a set up for and complement to statistical methods. In the past I've made fun of qualitative work as a "be all, end all" strategy in attacking a given research question ("its not representative," "it takes forever to do," "I don't believe things if there is no math or hard data," etc). But I do agree that qualitative work can help give direction to statistical analysis and aid in the interpretation of sempirical results.

Anyway, in explaining the mechanics behind the qualitative methodology, the speaker pointed out how sampling in qualitative methodology essentially obeys the law of diminishing returns (called the saturation principle, here). Basically, you keep adding to the sample until you stop learning anything new - when the marginal returns to interviewing approach zero. Apparently the majority of qualitative studies saturate somewhere between 25 and 30 subjects/interviewees.

I had a sudden flash of insight when I heard these numbers. The Central Limit Theorem (the big one) posits that the sum of a vector of random variables distributed with finite variance approaches a normal distribution for large values of n. Imagine a really screwed up probability distribution. Draw n numbers from it, and take the sum. Do it over and over and look at the distributions of the sums. Boom! Its looks normal! Its a beautiful result, and the proof is quite elegant, too.

The Central Limit Theorem appears to kick in around n of 30 or so. Thats whyI got so excited about the saturation numbers: its just interesting that two apparently distinct phenomena attain right around the same sample size. Obviously, I could be exhibiting a classical behavioral economics bias and attributing patterns to what are basically unrelated phenomena that just so happen to agree with one another. On the other hand, maybe there is more to it - something fundamental and deep.

Some more: If you like these kind of oddities and puzzles, you should read Fermat's Last Theorem by Simon Singh. It's one of the best books I've read in a long time. Basically it covers the 300+ year history of this annoying and outstanding math problem that kids can understand but adults (including Hall of Famers like Euler) could not solve for several centuries. The beast was laid to rest in 1993 by a Princeton mathematician who spent something like a decade of his life working on this problem and this problem alone. While the problem for a long time looked like some trivial curiousity, the Last Theorem ultimately speaks to some deep connections between branches of mathematics thought to be distinct.

The book is chock full of short biographies of all the mathemeticians who made contributions to solving the problem, interesting nuggets about number theory and the fundamental importance of prime numbers, irrational numbers, etc, and insights into how seemingly trivial mathematics could have mighty big things to say about the natural and physical world. It's a great read, and allows us normal folk to catch a glimpse into the beauty of mathematics.

How Can You Not Love Fantasy Football?

I've copied a recent post from our fantasy league discussion board below. When I realized how ridiculous it would sound to people who aren't part of our league (or are non-participants in fantasy sports in general), I started laughing and couldn't stop. I'm still laughing now.

Just to put it in context, we have twelve teams in our league and six playoff spots. This is the final week of our regular season. Three teams (myself included) have clinched playoff spots and a whopping seven teams, all 6-6, are fighting for the other three.

Here goes:

I don't know if we've ever had a week as exciting as this right before the playoffs. Each of the 6-6 teams could end up in the playoffs.

Homechickens has to win to get the 1st round bye.

Hufflepuff and Bum Bum are playing for the first 1st round bye.

Then it gets really interesting.

Harmonica and FightingIrish control their own destiny and are into the playoffs with a win.

Regal, Detroit, Drunken, and Buckeye are also competing with each other for points scored this week b/c they are all within 40 pts. of each other.

dags needs to win and have DetroitLions4eva lose to make the playoffs.

It's pretty cool b/c everyone has something to play for.

Cheer for my team!

Obesity in Developing Countries? Part II

More on the association between early life circumstances and later obesity. Check out this new working paper by Anne Case and Alicia Menendez on gender differences in obesity in South Africa. Here is the abstract (emphasis mine):

Globally, men and women face markedly different risks of obesity. In all but of handful of (primarily Western European) countries, obesity is more prevalent among women than men. In this paper, we examine several potential explanations for this phenomenon. We analyze differences between men and women in reports and effects of the proximate causes of obesity -- physical exertion and food intake -- and the underlying causes of obesity -- childhood and adult poverty, depression, and attitudes about obesity. We evaluate the evidence for each explanation using data collected in an African township outside of Cape Town. Three factors explain the greater obesity rates we find among women. Women who were nutritionally deprived as children are significantly more likely to be obese as adults, while men who were deprived as children face no greater risk. In addition, women of higher adult socioeconomic status are significantly more likely to be obese, which is not true for men. These two factors can fully explain the difference in obesity rates we find in our sample. Finally (and more speculatively), women's perceptions of an 'ideal' female body are larger than men's perceptions of the 'ideal' male body, and individuals with larger 'ideal' body images are significantly more likely to be obese.

Root for the Underdog of the Season!

For the last nine years, I've been playing Yahoo! Fantasy Football with the same group of college and high school buddies. In this time span, I've only been to the playoffs in four times and have yet to win a single playoff game. I fielded my best team in 2002, destroying the opposition to go 10-3 and finish regular season number one. Then, in the flameout of all flameouts, I lost each of my three playoff games and finished in 6th place.

Basically, as the "owner" of my team, I would fire myself as GM and Coach. I might as well set up the team and outsource all the decision making to someone who knows better.

Anyway, this season, with two games left in the regular season, I am sitting in second place at 8-3, having scored more points that each of the teams below me, and just five points off the pace of the first place squad. I've clinched a playoff spot, and I am hoping to win it all.

I think you should root for my team this year, especially because since my squad is the kind of underdog everyone would want to root for. Here is why:

1) I've overcome adversity at multiple points this season - I lost Ronnie Brown, who was an early season fantasy hoss, for the year, Jevon Walker for most of the season, and David Gerrard for a crucial four game stretch. Despite this, I keep winning. I attribute this to my unusually good waiver wire strategies (see 3).

2) My squad is made up of a lot of cast-offs and feel good stories - For example, my starting QBs are Jeff Garcia, a journeyman, elderly statesman, and David Gerrard, who wasn't even supposed to start when I drafted him. My backup QB is Vinny Testerverde, a guy my father remembers seeing play when he was in grad school. My second starting RB is Jesse Chatman, Ronnie Brown's replacement in Miami who kept getting kicked off of his past teams for being overweight. My defense was drawn entirely off the waiver wire (I missed the live draft when I was in South Africa). Finally, even my lovable uber-star, the incomparable LaDanian Tomlinson, is having an off year (by his standards, anyway).

3) The owner really needs this win - My college roommate, a three or four time champion, keeps pointing out how I've historically sucked at fantasy. In the past, other owners have criticized admittedly stupid roster moves I've made (for every mid season trade for Larry Johnson, I've drafted rookie WRs in the fourth round). I need to win both to earn respect and to offset what has been a ridiculously dry semester of research.

Also, did I mention that I haven't won a playoff game in nine years? There is only one way to describe that: hapless.

4) Finally, my team is named Hufflepuff's Cup, in honor of the kind but ultimately unremarkable Hogwarts House. Its funny how my team has turned out to be just like them: no stars, just solid performers who put their hearts and bodies on the line for me every week. How can you root against a team like that!?

So, for the next five weeks, root for Hufflepuff's Cup. It's like cheering for Rocky or those Chak De India girls: its a tough ride but, in the end, I think you'll be glad you stuck with 'em.

Thanksgiving: A Good Time to Think About Obesity

Related to my earlier post, I just came a recent article about the driving forces behind obesity in the developed world. Here is a link to a non-technical summary of the paper (a link to the actual article is nested within) and here is nice analytic piece by the Healthcare Economist.

The major take home point is that most (over 90%) of the increase in obesity seems to be driven by the fact that people are eating more now than before. The authors of the paper contend that the other side of the equation, decreased caloric expenditure, is quantitatively less important, though still non-trivial.

The main question then is: why are people consuming more calories? The theories out there to explain this generally fall into two categories:

1) high monetary and opportunity costs of healthy foods relative to unhealthy foods (the proliferation of fast food joints, putative effects of US agricultural subsidies, etc)
2) lower costs of calories in general due to improvements in agricultural technology

I don't know if anyone has really been able to assess the relative (or even absolute) importance of these explanations in the data. I do know that obesity is a scorching hot area of research and that the coming years should provide us with a slew of new research evidence for us to feast on. A good example: a new working paper assessing the fast food joint-obesity link.

In the meantime, Happy Thanksgiving and enjoy the inevitable feast!

Obesity in Developing Countries?

I'm doing some research on nutrition, child health and public programs in Mexico and, in the process of looking for a paper, came across this interesting article in JAMA about obesity among the Mexican poor. It turns out that obesity rates among the poor in Mexico rival those in the United States (obesity rates in general have followed a similar trend to the US, with large increases occurring between the 1980s and 1990s). This is especially interesting given that poor Mexicans live in conditions similar to the developing world, where obesity is only common among the upper strata of the population (though this is starting to change; exs: rural India and China). Doubly interesting is the growing phenomenon of young children who are both stunted and overweight, an interesting paradox of early life deprivation, on the one hand, and excess on the other.

Causes for the rapid increase in Mexican obesity are likely similar to those in the U.S.: changes in technology and policy that alter the balance between caloric input and output. For example, this paper notes that increasingly sedentary lifestyles and changes in diet are likely largely responsible for increased fattening. While I'm not sure if anyone has really stepped in and done some kind of accounting exercise or decomposition trying to explain time-trends in Mexican obesity, this doesn't seem to be a bad conjecture to make given the evidence.

We know from the United States that the poor are much more susceptible to these secular trends: healthy food appears to be a normal good, fast foods inferior, and exercise a luxury good. At least from what I can gather from the Mexican evidence, this is likely to be the case south of the border, as well. But are there reasons, external to basic economic theory, that might explain why the poor tend to be more obese?

There are some interesting biological theories that suggest that individuals who are deprived of nutrition while in the womb but exposed to relative abundance thereafter are more likely to become obese, diabetic, and develop cardiovascular disease. The idea is that fetus' adapt to scarcity, which results in permanent metabolic/endocrine changes. While these changes are advantageous in scarcity, the might actually be maladaptive in situations of relative abundance. Some evidence supporting this theory in (laboratory) animal and human populations can be found on pp 44-45 of this very thorough survey on the economics of health and socioeconomic status in developing countries (a must read for all interested in health and development as an area of research).

So tying this back to poverty: poor individuals are either more likely to be born in situations of deprivation or, in the case of economy wide shocks, unable to smooth their consumption so as to prevent under-investments in their kids during the fetal period and early childhood years. Faced with falling (unhealthy) food prices and secular changes in the level of human activity, if the biology behind the aforementioned theory is sound, these individuals might be doubly affected in terms of developing metabolic and cardiovascular conditions. Notice that the theory would also explain the stunted/overweight kids: stunting is a result of the fetal adaptation to scarcity, and overweight the result of exposure to abundance.

While some work on the Dutch and Chinese famines support this hypothesis (see the previous link), I am not aware of any other work looking the interaction between early life conditions/endowments and secular changes in technology. As a result, and since the marginal cost of adding this on as a project is low (I am using a well-suited Mexican dataset for another purpose, anyway), I've decided to have a go at the theory and see what I find. I'll keep you posted.