Monday, April 28, 2014

A Brief Intermission

There will be no significant update this week as I devote my free time instead to consumption of "Capital in the 21st Century".  Expect a follow up review next week.

Until then stay safe and rationale.

Sunday, April 20, 2014

Teaching Value

Public education in America is a tricky subject.  Nearly everyone with children would agree that education should be a high priority for tax expenditures.  However, a large portion of the population will never utilize the public education system while they are a tax paying citizen (either due to private options or lack of children).  Additionally, due to widespread unionization teacher's hold a large amount of political power in the United States.  These factors have combined to create a situation where the general feeling is teachers should be better, cost no more and be safe from lay-offs.

Unfortunately, as most reasonable people will recognize, increasing teacher quality without removing the worst teachers or increasing wages is challenging.  What is needed is evidence of the benefits better teachers provide.  Policies could then be enacted based on that evidence to either increase wages or remove the worst teachers. (Please note that removing the worst teachers does not equate to firing them.  Teachers could be incentivized to retire early, or change positions for example.)

Luckily a recent study has provided exactly this evidence.  This study by Chetty et al. tracked how teacher quality (as measured by improvement in test scores) translated into a variety of outcomes later in life.  Better teachers resulted almost universally into better outcomes for students.  Quantitatively, the difference between the bottom 5% of teachers and an average teacher was $250,000 in lifetime wages spread over the classroom annually.  In other words, replacing a poor teacher of 25 students with an average teacher of the same 25 students will result in each student earning an additional $10,000 over the course of their lifetime (Mean present value).

Additional quantitative measures for a one standard deviation in teacher value added include:

  • .82% increased chance to attend college. This is relative to a 37% chance overall. 
  • 1.3% increased annual earnings at age 28.
  • Estimated increase of $39,000 in lifetime earnings per student.(7,000 NPV at age 12).
  • Reduced likelihood of teen pregnancy.
  • Increased retirement plan savings.
All of these factors are indisputable sources of tax revenue or savings which support policies geared towards improving teacher's value added.  Let's set aside any cost savings associated with welfare program utilization rates and examine only the increased tax revenue.  If a students increased earnings have a net present value of $7000, the federal government will get (being extremely conservative) at least $700 of that.  There are approximately fifty million public school students in the United States (source) and a teacher generally instructs twenty-four students at a time. Given these numbers, if teacher value added can be increased by one standard deviation for a cost below eight hundred and fourty billion dollars it would be foolish not to make the expenditure. This would be approximately a 72% increase over existing total state education expenditures.  

If there is one flaw in this study it might be this.  Education may be somewhat of a zero-sum game.  In other words, Jack may get the better job because he had the better teacher.  But that may simply steal the job from Becky.  Thus Jack will certainly benefit, but overall tax revenue may not grow. What is needed is a further study that links this data to productivity gains and economic growth.  This perspective makes it difficult to enact policies from a federal standpoint.  However, at the more local (and state) level it makes the data all the more compelling.  Local schools simply need to out compete their neighbors for the best teachers to reap significant advantages.  Some benefits will be lost to movement out of the locality.  However, the cost to attract better teachers will be significantly less than the cost to improve teachers nationally.  Localities only have to offer slightly higher wages than neighbors. At the national level wages would have to rise significantly to attract more of the working population to the teaching profession. 

While overall national benefits are still a bit unclear, there are some certainties.  Improving teachers significantly improves the future outcomes for students.  Test results are an important metric (although change in test results is better) to judge teachers.  And there are significant gains to be had by pushing for better teachers.  The only question that remains is who is going to start reaping the rewards first.

That's it for this week. Until next time stay safe and rationale. 

Friday, April 11, 2014

Golden Balls

There have been some bizarre game shows over the years.  "Find the Chair" is exactly as entertaining as it sounds, while "Oh Sit!" is a great pun title for televised musical chairs.  But for an economist there's a select few shows which rise above the rest. "The Price is Right", "Deal or no Deal", and "Golden Balls".

American audiences are familiar with the first two shows, but the third is a little known British game show that might as well be taught in game theory courses.

Golden Balls is a simple show of gradual team reduction.  A team begins with four players with one player eliminated each round until two remain.  In the first round twelve balls are drawn from a pool of one hundred. Each ball has an assigned value between ten and seventy-five thousand British pounds.  Four Killer balls are added to the twelve drawn balls and each player randomly receives four balls.

Players then place the balls they receive in two rows. The front row of two balls is visible to all players.  The back row is visible only to the owner of the balls.  Each player then attempts to convince the others that his or her hidden balls are the most valuable (thus making them important to maximizing later winnings). Players then vote to eliminate one of the team members. Round two is played in a similar fashion with each player receiving five balls total.

When the game is narrowed to two players things really get interesting.  Each player takes turns randomly picking one ball from the pool of remaining balls to add to the jackpot and one ball to eliminate from the pool.  If a Killer ball is selected to be added to the jackpot then the jackpot is divided by ten. This process is repeated five times in order to establish the size of the jackpot. I've glossed over a few minor details in the interest of brevity but the bottom line is high value balls are good, Killer balls are bad, and the game ends with two contestants going head to head.

Once the jackpot is established each contestant receives one final pair of golden balls. One ball says "split" and the other says "steal".  The contestants converse for a time (attempting to convince the other of their trustworthiness) and then choose a ball. Both players balls are revealed and one of three outcomes plays out.

If both contestants select split then everyone wins. The contestants split the jackpot evenly.  If one contestant chooses split and the other chooses steal than the stealer gets the entire jackpot.  If both contestants select steal than no one receives anything.

It's possible you may recognize this as a modification of the classic prisoner's dilemma.  Cooperation benefits everyone, but defection benefits one person more than cooperation would as long as the other doesn't defect as well.  Of course if both defect the outcome is unfortunate for everyone.

Interestingly, most shows end with at least one player choosing to steal.  It's easy to attribute this selfish play to simple greed.  However, interviews conducted with participants seem to indicate that isn't the case.  Most players claim that they choose to steal not because they wanted the money all to themselves, but rather because they feared being made a fool of by the opposing player.  The fact that fear of betrayal or public embarrassment seemingly supersedes desire for considerable monetary gain is an interesting motivational indicator.  Of course, it's also quite possible that this is a post hoc rationalization by players to justify themselves as more than simply greedy.

One player in particular stands out as having beaten the Golden Balls system.  Nick Corrigan found himself in the final two showdown with his teammate.  When the time came to convince the other that he would split Nick took another approach.  He insisted that when the time came, he would select the "steal" ball.  Nick claimed that he was going to steal and after the show he would split the money with the opposing player.

At first everyone was shocked.  The players argued at length. His opposition implored him, "Why not just both choose split and share the money?" But Nick was resolute, he would select the steal ball.

It seems like a ridiculous plan.  After all, nothing compels Nick to split the money after the show.  But look at it from his opponents perspective. If Nick is going to choose steal what choices are there?  Go along with him and choose split, hoping he'll make good on his promise.  Or choose steal and certainly get nothing.  There is no fear of betrayal, no public humiliation. Everyone knows what Nick is going to do. The choice for his opponent is simply to hope for something or guarantee nothing.

Eventually, after a long and heated debate Nick's opponent gave in and agreed to select the split ball.  True to his word when the balls were revealed it showed "Split". Nick however was not quite so honest. Not one, but two balls read "Split". Both players win and everyone walks away happy.  Interestingly, in the post game interview Nick's opponent revealed his planned strategy. He said he'd planned to steal 100%.

That's all for this week. Until next time stay safe and rationale.

Tuesday, April 1, 2014

Flashy Magically Rendered Images (fMRI)

All credit to Pete Etchells for the following article.

A new study has raised new questions about how MRI scanners work in the quest to understand the brain. The research, led by Professor Brian Trecox and a team of international researchers, used a brand new technique to assess fluctuations in the performance of brain scanners as they were being used during a series of basic experiments. The results are due to appear in the Journal of Knowledge in Neuroscience: Generallater today.
“Most people think that we know a lot about how MRI scanners actually work. The truth is, we don’t,” says Trecox. “We’ve even been misleading the public about the name – we made up functional Magnetic Resonance Imaging in 1983 because it sounded scientific and technical. fMRI really stands for flashy, Magically Rendered Images. So we thought: why not put an MRI scanner in an MRI scanner, and figure out what’s going on inside?” To do this, Trecox and his team built a giant imaging machine – thought to be the world’s largest – using funds from a Kickstarter campaign and a local bake sale. They then took a series of scans of standard-sized MRI scanners while they were repeatedly switched on and off, in one of the largest and most robust neuroscience studies of its type.
“We tested six different MRI scanners,” says Eric Salmon, a PhD student involved in the project. “We found activation in an area called insular cortex in four of the six machines when they were switched on,” he added. In humans, the insular cortex has previously been implicated in a wide range of functions, including consciousness and self-awareness. According to Trecox and his team, activation in this area has never been found in imaging machines before. While Salmon acknowledged that the results should be treated with caution – research assistants were found asleep in at least two of the machines – the results nevertheless provide a potentially huge step in our understanding of the tools we use to research the brain.
However, some researchers are skeptical of the findings. Professor Stephen Magenter, Professor of Image Processing at Yate University, UK, is a vocal critic of the statistical analyses that Trecox used. “They just used felt tip pens to highlight and extend the areas they were interested in,” he alleges, adding that he would never colour outside the lines. In response to these claims, Salmon says that this study was one of the most advanced of its kind. “All of our analyses were digital,” he notes. “We used MS paint wherever possible.”
The findings raise interesting questions about how fMRI techniques should be used from now on. “If there’s a possibility that MRI machines are showing some sort of rudimentary self-awareness, then we really need to explore this further,” says Trecox. He adds: “One way to do this is to look at what’s happening in our giant scanner, and for that, we’re going to need a bigger machine.”

Of course April Fool's. Hopefully everyone finds it as amusing as I did.  Until next time stay safe and rationale.