One more thing about this post. I think I’ve mentioned before that back when I was in grad school I occasionally tutored social science grad students in probability and statistics. I was appalled at how weak their understanding was and it was clear to me that the level of proof required in the social science had already become or would soon become whatever was produced by SPSS (Statistical Package for the Social Sciences, a computer program in common use by social scientists at the time and, for all I know, still used).
Not only has this prediction come true but clearly the standards for everything these days are whatever the tools produce. The standard for a good economics proof is what’s produced by Excel, the standard of a good paper, book, etc. is what’s produced by Word (in mathematics if my eyes do not deceive me it’s still TeX), in presentations it’s PowerPoint.
SPSS is still widely used, though Stata and R are also popular. For the most part, they have been, more or less, converging in terms of the math they can do; R is still the most powerful, but also requires coding.
Having TA’d undergrads on statistical methods, I was shocked to hear a professor basically telling students to throw variables in a model and see what was significant – the opposite of the happy marriage of theory and results that actually constitute proof in the social sciences. Just because software is easy to get running doesn’t mean that it’s easy to use well.
What alarmed me at the time was that the young men and women that I was tutoring had very little grasp of the underlying mathematics. To me that implies no real intuitive sense of what’s going on.
That’s not so bad with simple stuff like standard deviation. With multivariate analysis it can be disastrous. The algorithms that were being used didn’t produce THE correct answer. They produce A correct answer. The students had no idea of how that could be possible.
Social studies claiming to be science does not make them scientific. Social studies should explain why the theory diverge from reality. Interestingly, the Arts have a greater claim to science.
Additional alarming factor: some of the young men and women I tutored are probably heads of departments now.
“To me that implies no real intuitive sense of what’s going on.”
With training in engineering, this is one of the simplist – but most basic , obvious, fundamental etc, yet underappreciated observations.
People, don’t over complicate. Fundamentals matter. And they rarely change. They are, by definition, fundamental.
View your politics through that prism.
When I used to regularly read the various climate change blogs, some of the more credible “skeptics” were statisticians who attacked the statistically-derived conclusions of the climate researchers. Most of their models use proxy data (ice cores, tree rings, etc.) or statistically “extrapolate” from the limited temperature record. Additionally, because various proxies aren’t continuous, researchers graft data together. Obviously, all of that leaves quite a bit of room of precise yet inaccurate conclusions.
Speaking of which, I’m continually amazed at how many people do not understand the difference between precision and accuracy. The notable exceptions are those who regularly shoot firearms and our engineer friends.
@Andy- Most of those “statisticians” struck me as quacks or people picking away to insignificant parts of the data. Since i have a fiend who was a photochemist and one who is a physicist, I have asked them for their opinions since if I am honest I have to admit that the physics is beyond me. They think the studies are pretty good.
Steve
It might be interesting to research whether there is a correlation between political philosophy and mathematical aptitude.
@Steve – What is an insignificant part of the data in a published, peer reviewed article? Some of those “quacks” found actual errors which were corrected – whether they are quacks or not is irrelevant to whether they are right or wrong on the merits. I don’t get why some of those climate scientists were (and remain) so thin-skinned. Criticism is a very normal part of the process. Same goes for economists.
“the standard of a good paper, book, etc. is what’s produced by Word”
Uh, Dave, that’s just plain dumb.
“. I don’t get why some of those climate scientists were (and remain) so thin-skinned.”
I think the laziness of their critics pisses them off. They dont do original research. They wait until years later to ask for data stored on paper and hard to redo, data they had to pay for sometimes. They misrepresent. (How many times have we heard the claim that cooling was predicted?) Maybe they dont like it when told they are in a conspiracy to perpetuate a hoax.
Steve
Steve
Well….not exactly.
A mathematical proof in economics will look like this.
Even in econometrics is not uncommon to see proofs for new tests, and procedures that invoke things like Fatou’s Lemma, the Lebesgue Dominated Convergence Theorem, or the Monotone Convergence Theorem.
Theoretical economics will make use of things like Kakutani’s fixed point theorem, discuss demand as upper-hemi continuous correspondences, or look at things like bordered Hessians.
Now, for empirical economics things get much less…precise. It is not uncommon to see the highest priests that teach the bright young minds go into their offices and become the gravest of sinners in terms of statistical modelling. And even excluding the instances of things like cherry picking the data or searching for the best specification and then pretending like the previous 50 regression models didn’t exist…publishing one’s data and statistical package code is always a good idea. Honest mistakes can happen or things can get over looked.
I think you and I are thinking of completely different critics.
Interesting that one of those critics weighs in on the R&R paper.
@Steve
Too bad these guys don’t know much about mathematics. The economy is a chaotic system. In mathematical terms the problem is of the form np-complete – no conceivable computer can solve it, even given infinite time. An amazing number of problems are of this form.
Roy
“It might be interesting to research whether there is a correlation between political philosophy and mathematical aptitude.”
All my mathematician friends are left-wing.
“It might be interesting to research whether there is a correlation between political philosophy and mathematical aptitude.â€
Let me expand a bit because implicit in that is a certain naiveté about the world and about people. I’m going to mention a name here that will probably be unfamiliar to most (maybe Steve V. or Ice has heard of this man). Gottlob Frege was a German mathematician-logician who lived from about the middle of the 19th century until the early 1920s. The importance of Frege cannot be overstated. He is the father of modern mathematical logic and in a fundamental way, the father of much of modern Anglo-American philosophy. (It was Frege who told Wittgenstein to go to Cambridge and study logic and philosophy with Russell.) Michael Dummett was an English philosopher who wrote the definitive intellectual biography of Frege. In his preface to that book, Dummett wrote that he was shocked when going through Frege’s papers to discover that Frege was an anti-semite. When I read that I was mildly shocked that Dummett was shocked. Not because there are traces of anti-semitism in Frege’s writings, but because you can tell absolutely nothing about Frege’s political opinions from reading his works on logic and philosophy. For all one can tell from his writings, he could have been a Crypto-Druid. Dummett brought the same kind of naiveté to his research on Frege that is reflected in what I quoted from Roy — the idea that because someone is highly trained in mathematics and logic this means that in he or she will be correct in their politics (where correct = “thinks like I do”). That is silly and pernicious nonsense.
He was also influential in the philosophy of language.
Back in college and grad school I think I must have taken more mathematical logic courses than could probably be imagined.
My experience has been that mathematicians are predisposed to be pretty left wing, engineers are frequently pragmatists. The political leanings of people in different fields also tend to vary over time. When I took economics courses, a lot of my profs were pretty Marxist. Not so common now. My impression is that economics has sort of swung towards libertarianism.
@Roy Lofquist,
Heh, I thought of Steve McIntyre when I first read an article on Reinhart and Rogoff. The one thing Reinhart and Rogoff have done that sets them apart from Mann et. al. is that they released their data and the excel code. Still, it looks like the tipping point arguments have just taken huge hit.
Many economists have come to appreciate the importance of incentives and information and that the government is not that good at either. Also add on the rise of public choice are of economics that deals with rent seeking.
As I think I’ve mentioned before in 2+ years of econ classes, I don’t think I heard the word “incentive” once. Did hear a lot about taxes, though.
Of course, the term “rent-seeking” hadn’t even been coined when I took economics. People did it; there just wasn’t a word for it.
SPSS is taught at a number of the different faculties in Canada as well. It seems a little bit dated, but is probably easier to use for some of the students who may not be mathematically inclined in the first place.
@Steve & Dave,
I should have said “engineering aptitude” rather than mathematical. The mathematicians I have known are just plain weird – not a generalist amongst them. Got their own little worlds they live in.
As to economists – they try to attack the problem with tools totally unsuited to the job. There are no tools for dealing with chaotic systems with discontinuous parameters. Engineers are successful because they stay well away from those beasties.
Methinks the best training for an economist would be history studies and then learning how to dig a staight ditch – it’s a lot harder than it looks.
Roy