Category Archives: Math and Statistics

On the use of math in economics…

As I prepare my course in managerial economics, I have tried to put myself in my students’ shoes and ask why all the math?  This is a particularly relevant question because my students are enrolled in Baylor’s executive MBA program, and they (quite understandably) have no interest in becoming professional economists. 

In his recent blog entry entitled “Mathematics and Economics”, Paul Krugman notes, among other things, that “Math in economics can be extremely useful”, and that math can serve an essential analytic function by helping to clarify one’s thoughts.  Some other samplings from the economics blogosphere include the following observations:

  1. Greg Mankiw (cf. http://gregmankiw.blogspot.com/2006/09/why-aspiring-economists-need-math.html) notes, among other things, that “Math is good training for the mind. It makes you a more rigorous thinker.”
  2. Jason DeBacker (cf. http://www.econosseur.com/2009/02/why-economists-use-so-much-math.html) makes the following observations: “Math provides a common language for economic thought”, and “Math helps to quantify tradeoffs.”  He also notes that “Using math puts in plain sight the assumptions that lie behind a model and the mechanisms at work in the model”, which is consistent with Professor Krugman’s observation noted above.

However, I am also reminded of the famous quote “it is better to be vaguely right than precisely wrong” which is commonly (and incorrectly) attributed to the famous economist John Maynard Keynes. (For what it’s worth, O’Donnell (2006) notes (see p. 403, footnote 14) that “This saying so aptly captures a strand in Keynes’s thought that he is frequently, but wrongly, treated as its author”; apparently, the original source for this memorable quote was a contemporary of Keynes by the name of Wildon Carr (see Shove (1942: 323)). 

References

O’Donnell, R., 2006, “Keynes’s Principles of Writing (Innovative) Economics,” Economic Record 82 (259), 396-407.

Shove, G.F. (1942), “The Place of Marshall’s Principles in the Development of Economic Theory,” Economic Journal, 52 (208), 294–329.

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On the "science" behind the International Gymnastics Federation’s tie-breaking rules

I was interested to learn today that in spite of the fact that the American gymnast Nastia Liukin and the Chinese gymnast He Kexin both posted scores of 16.725 for their uneven bars performances in the Beijing Olympics, He was awarded the gold medal whereas Liukin received the silver medal. Apparently ties were allowed in Olympic gymnastics until 2000; in such cases, both athletes would be awarded the same medal type. However, since 2000, the International Olympic Committee (IOC) has adopted so-called “tiebreaker” rules conceived of by the International Gymnastics Federation (FIG) which effectively penalize the athlete who receives the least consistent, or most highly variable set of scores across 6 judges.

The technical details concerning the actual algorithm used by FIG are provided here. For starters, the highest and lowest scores provided by 6 judges are tossed out so the “execution” score is based upon the average of the remaining four scores. Effectively, the data are “winsorized”, presumably for the purpose of discounting the effects of overly generous and overly miserly judges. Once this calculation has been made, then the first tie-break calculation requires throwing out the highest and lowest deductions from a perfect”execution score of 10 and then averaging the remaining four deductions. If there is a tie after the first tie-break (as there was in this case), then the rules call for a second tie-break in which the highest remaining deduction is thrown out, leaving a total of 3 of the original 6 deductions to averaged. When this calculation was performed, He had an average deduction of .933 versus Liukin’s .966. Liukin lost primarily because after the second pass, she had a higher average deduction among the remaining three judges. He won because her average deduction from 10 by the 3 remaining judges was lower than it was for Liukin.

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On the "science" behind the International Gymnastics Federation's tie-breaking rules

provided here. For starters, the highest and lowest scores provided by 6 judges are tossed out so the “execution” score is based upon the average of the remaining four scores. Effectively, the data are “winsorized”, presumably for the purpose of discounting the effects of overly generous and overly miserly judges. Once this calculation has been made, then the first tie-break calculation requires throwing out the highest and lowest deductions from a perfect”execution score of 10 and then averaging the remaining four deductions. If there is a tie after the first tie-break (as there was in this case), then the rules call for a second tie-break in which the highest remaining deduction is thrown out, leaving a total of 3 of the original 6 deductions to averaged. When this calculation was performed, He had an average deduction of .933 versus Liukin’s .966. Liukin lost primarily because after the second pass, she had a higher average deduction among the remaining three judges. He won because her average deduction from 10 by the 3 remaining judges was lower than it was for Liukin.]]>

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Fooled by Randomness quote

I really like the following quote from Fooled by Randomness (pp. 55-56): “Things are always obvious after the fact… It has to do with the way that our mind handles historical information. When you look at the past, the past will always be deterministic, since only one single observation took place.”

This describes well a common error that is made all too often, by the news media in particular. News reporting often involves studying risky phenomena after the fact; i.e., after a disaster has already occurred. Journalists are highly susceptible to this particular aspect of being fooled by randomness. Often their analysis only makes sense if one had the luxury of perfect foresight.

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