准版主moontory和majia20112011吵架的神贴～技术or直觉？

majia20112011

The insight is very deep. At least It lays the foundations for the utility theory. It shows why the transitivity assumption of ordinal preferences is not trivial. It is like the M-M in social choice theory (or, more accurately, M-M is like the Arrow theorem in capital structure) and inspires future research to try to relax the assumptions in Arrow. This is way much much better than some papers which just modify the utility function or introduce more state variables in a workhorse macro model to try to claim that their models produce equity premium that is more close to real data using reasonable risk aversion coefficients. This is the difference between master and engineer. I have no doubt this can only be achieved using technical stuff, just like what Debreu use to establish the Arrow-Debreu equilibrium. They use the techniques for a very good reason.

Here is my understanding which might not be correct: transitivity of ordinal preferences can be violated whenever the number of alternatives is no less than three.

Please tell us the insight of Arrow's impossibility theorem in a few PLAIN sentences.

-- by 会员 moontroy (2011/3/29 12:48:53)

-- by 会员 majia20112011 (2011/3/29 12:56:00)

Tell me the economic insight in this sentence:transitivity of ordinal preferences can be violated whenever the number of alternatives is no less than three.

-- by 会员 moontroy (2011/3/29 13:11:18)

moontroy

Well, this is a good example about idea and technical issue: without any precise definition of plain sentence and intuitive idea, your statement that every great idea(or nobel prize theory) can be stated in several plain sentences is full of confusion and changes all the time. You already change your definition about economics(exclude econometrics is not a very good argument to me, but it seems that you have a pretty strong ideology). And I still can not read any economic insight from the sentence: transitivity of ordinal preferences can be violated whenever the number of alternatives is no less than three. What common sense that everyone knows generates this result? I have learnt that before, but I can not understand your "intuitive explanation", in fact I am quite confused about that statement.
Let me give you a good example of great idea with simple words: search theory
It is costly to wait, but you may find a better job tomorrow.
Given this really plain sentence, it is easy to guess that higher finance aid for jobless people may in fact rise unemployment rate, and there will always unemployment in the market, and also the job allocation maybe inefficient. Even a common people with little economic knowledge can understand them intuitively.

If "transitivity of ordinal preferences can be violated whenever the number of alternatives is no less than three."  is a plain sentences, then why "contract in continuous time can be achieved with martingale representation theorem "  is not a plain and intuitive one?

majia20112011

I do not ever change. From the beginning I am focusing on economic theory not econometrics or theoretical econometrics. I do not deny the importance of important econometrics findings, but they are largely irrelevant to my point. I do not change any of my assumptions or definitions.


This is a good example about how to express certain ideas in plain simple terms. The precision is left to the original paper to find out.  The main reason that I may not give a good explanation about Arrow's theorem is that I took my micro prelims a long-time ago and micro is never my main field, but I think I do give a plain explanation of Kydland and Prescott's work.


Speaking of my understanding of Arrow's theorem, perhaps every student in economics knows the axiomatic representation of preferences and transitivity is one of the assumptions and to most people seems quite intuitive or trivial (or common sense). But what my understanding of what Arrow shows is that this assumption is not as trivial when you consider social choice in a broader context. The easiest way to see Arrow's point is to use a simple voting example as in standard textbooks. Of course, using technical terms is necessary to formally illustrate the point, but to me my statement seems quite plain to students of economics.


Just answer my question: what if the AEA/AFA interview asks you for a 1 or 2 minute summary of your paper? Do you need to tell them you need 5 pages to just give them an intuition and you cannot tell them your idea and intuition without technical details?

Well, this is a good example about idea and technical issue: without any precise definition of plain sentence and intuitive idea, your statement that every great idea(or nobel prize theory) can be stated in several plain sentences is full of confusion and changes all the time. You already change your definition about economics(exclude econometrics is not a very good argument to me, but it seems that you have a pretty strong ideology). And I still can not read any economic insight from the sentence: transitivity of ordinal preferences can be violated whenever the number of alternatives is no less than three. What common sense that everyone knows generates this result? I have learnt that before, but I can not understand your "intuitive explanation", in fact I am quite confused about that statement.
Let me give you a good example of great idea with simple words: search theory
It is costly to wait, but you may find a better job tomorrow.
Given this really plain sentence, it is easy to guess that higher finance aid for jobless people may in fact rise unemployment rate, and there will always unemployment in the market, and also the job allocation maybe inefficient. Even a common people with little economic knowledge can understand them intuitively.

If "transitivity of ordinal preferences can be violated whenever the number of alternatives is no less than three."  is a plain sentences, then why "contract in continuous time can be achieved with martingale representation theorem "  is not a plain and intuitive one?

-- by 会员 moontroy (2011/3/29 16:03:43)

moontroy

Before I mention econometrics, you never exclude that field in your argument(and you continuous arguments like ALL nobel price thoery, which with no doubt include many econometrics theory), I don't know how could you state "you never change", maybe you have different definition of economics in your mind, but that is absolutely not a common knowledge. Please give me a clear definition of "insight". If insight, as you argued in the Arrow's case, is just a statement of a theorem, then almost every technical paper can also get some plain and short statement, like "continuous time contract behaves similar to static contract but with existing time", is that a economic insight, or a result? You don't need to tell me that "transitivity is non trivial", it is interpretation of and what we learn from the result, not the economics insight(or you have a somewhat different definition of insight).

Thanks for your AEA/AFA case, but there are plenty of alternative theory to explain it.  For a school which may interview 30-40 people in 2 days, the most efficient way is a short interview to ruled out most of those interviewees, and then investigate those candidates in flyout. I assume you have attended many job talks, and I assume you may have seen many cases that some candidate with very promising abstract(or first 5 minutes presentation), and states a very interesting result but end up with dull and trivial logic.  These cases happened again again and again simply because people usually only states the interesting result and very general idea(like coordination problem, or market friction) in the interview, which make people have no clue to really judge their paper. Those papers often have a quite interesting title or result, but is in fact trivial or with ridiculous assumptions, they appears "insightful" in first 1 or 2 minutes.

majia20112011

By default, I exclude econometrics. Just count how many econometrics Nobel Prize in the past, but if you want to stick to those trivial details, I just want to say again that econometrics is excluded in the discussion and I am not going to mention this again.




By insight, what I mean is thoughts of truly ingenuity that nobody else in the past have ever thought about it and this both questions our usual intuition or our understanding of economics and spurs a new field of economic research. Arrow's result is insightful because it challenges the way we think and it is EXACTLY because interpretation of it that triggers a new field of research and numerous follow-up papers. If you just treat any result LITERALLY as what the theorem states, then I have nothing else to say. You can say with the same logic that first and second welfare theorems are just theorems and interpretations of them don't count as insights. However, it is the striking interpretations of the welfare theorems that lead to the school of free-market economics. If you just take the theorem LITERALLY, they are just two theorems. Some technical papers are exactly what you have mentioned, with nice technique-generated theorems but no interpretation that would lead to big economic insight. I am not familiar with Sannikov's work but if his work is purely introduce a methodology that solves the continuous time principal-agent problem, then this paper is of limited insight compared with the original discrete time or even single period principal-agent models. Lucas always says, you need  to justify why you use dynamic models. if dynamic models do not provide any additional economic insight beyond static models, why bother use it?  So I believe Sannikov's work must have something additional beyond methodology, i.e., it must be that there is economics in his paper, not merely mathematics.


Give a nice summary of your work is necessary but not sufficient condition to get good fly outs and it is not limited to AEA/AFA conference but to your fly outs, to your 30-minute talk with faculty members. Even in your 90-minute presentation, to be honest, most people will just focus for 10-15 minutes and then they will not be that focused. That's not what I have said, but a big name person's word. Therefore, you need to summarize your work nicely in the first 10-15 minutes, show people what is the economics in your paper, why is it important and interesting and how does it help us better understand the ECONOMICS not the MATHEMATICS. You need solid models to support your summary, but if you cannot say explicitly in the first couple of minutes what is your ECONOMIC contribution, your model can be very beautiful and technical but you are not going to get a good chance of impressing the audience.

Before I mention econometrics, you never exclude that field in your argument(and you continuous arguments like ALL nobel price thoery, which with no doubt include many econometrics theory), I don't know how could you state "you never change", maybe you have different definition of economics in your mind, but that is absolutely not a common knowledge. Please give me a clear definition of "insight". If insight, as you argued in the Arrow's case, is just a statement of a theorem, then almost every technical paper can also get some plain and short statement, like "continuous time contract behaves similar to static contract but with existing time", is that a economic insight, or a result? You don't need to tell me that "transitivity is non trivial", it is interpretation of and what we learn from the result, not the economics insight(or you have a somewhat different definition of insight).

Thanks for your AEA/AFA case, but there are plenty of alternative theory to explain it.  For a school which may interview 30-40 people in 2 days, the most efficient way is a short interview to ruled out most of those interviewees, and then investigate those candidates in flyout. I assume you have attended many job talks, and I assume you may have seen many cases that some candidate with very promising abstract(or first 5 minutes presentation), and states a very interesting result but end up with dull and trivial logic.  These cases happened again again and again simply because people usually only states the interesting result and very general idea(like coordination problem, or market friction) in the interview, which make people have no clue to really judge their paper. Those papers often have a quite interesting title or result, but is in fact trivial or with ridiculous assumptions, they appears "insightful" in first 1 or 2 minutes.

-- by 会员 moontroy (2011/3/30 0:55:29)

moontroy

Apparently we have quite different default definition of economics and economics insight, so I will not continue the discussion. I agree your idea in your definition, but I would not say technical issue is a second order factor, that is too strong is unfair to many excellent work. Again, no offense, just a debate to make things clear.

majia20112011

Sure, let's just rephrase the debate.


My point is that technical issue is a second factor. The main logic is that we are talking about economics (- econometrics) not mathematics or physics. In mathematics or physics, it may well be the case that the more technical, the better. However, for economics when we are writing papers, we are telling an economic story to our audience of economists or soon-to-be economists. Therefore, the story itself is very important. You can have nice models, complex algebra. But if you cannot tell a compelling and interesting economic story out of your model, then what is the point of writing such a model?  Let's use topology as an example. You can have a topological space with very great and beautiful properties. But what if eventually it turns out that the only topological space that can satisfy these properties are the topological space generated by the empty set? Pure technical papers without a good economic story to tell is, in my opinion, a topological space generated by the empty set.


My second argument is that economics (-econometrics again) is mostly an applied subject. Again it comes from the fact that economics is a social science and the purpose of economics is to answer social questions. Therefore, economics is not a subject that has the mission to provide technical tools. Put that in a different way, the most important talent for doing models in economics is to identify questions or issues that are economically interesting and important and think of how to model that in a clear and elegant way that best addresses the question or issue. If you need complex technical tools, then just go and get it. That's why I say this is a second-order issue. Whenever you need it, learn and pick it up. But if you have no such talent in identifying what question or issue that is important, although you are armed with lots of technical tools, you do not know where to shoot with your arms. Don't you agree knowing where to shoot is the first-order importance?

Apparently we have quite different default definition of economics and economics insight, so I will not continue the discussion. I agree your idea in your definition, but I would not say technical issue is a second order factor, that is too strong is unfair to many excellent work. Again, no offense, just a debate to make things clear.

-- by 会员 moontroy (2011/3/30 3:56:18)

moontroy

It seems we also have quite different understandings about mathematics and physics, and I will keep silent on your statements about researches. That is fine, we need some different opinion to think those problem throughly, thanks for your input anyway

BusFin

"In mathematics or physics, it may well be the case that the more technical, the better."

Let me tell you, this is absolutely not the case. Don't judge other fields like that if you have no research experience or exposure to those solid sciences.
Though I agree with what you intend to stress (intuition, insights, blabla), I don't like your strong attitude toward other things/people. Most mathematicians and physicists I have so far interacted with are very humble people.

byeade

Comparative agree with your point of view