曼昆. (2006). "经济和数学" 系列文章（来自其个人博客）

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收藏 2012-05-21

（一个好的标题确实很重要，需要学习）

以下为曼昆同志在blogspot的博客文章，谈了一些自己求学、教学和写作教科书的经历，也涉及到经济学学习、研究和实务中的数学问题。如果他自己已经表达过对问题的看法，我们就不要强为其作注。

如果您点击链接之后浏览受阻，请向下翻页阅读转载。

2楼：Tuesday, May 23, 2006
外链：Advice for Aspiring Economists

3楼：Wednesday, May 24, 2006
外链：Which math courses?

4楼：Thursday, June 01, 2006
外链：Love Econ, Bad at Math

5楼：Tuesday, June 20, 2006
外链：An engineer seeks career advice

6楼：Friday, September 15, 2006
外链：Why Aspiring Economists Need Math

7楼：Wednesday, March 28, 2007
外链：My Life as a Student

人尽其能，物尽其用。直接浏览会遇阻隔，依次张贴在回复中了。

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WangLuoxuan

2012-5-21 21:03:55

Tuesday, May 23, 2006
Advice for Aspiring Economists
A student from abroad emails the following question:

Do you have some hints for me, how to become a good economist?

Here is some advice for, say, an undergraduate considering a career as an economist.

1. Take as many math and statistics courses as you can stomach.

2. Choose your economics courses from professors who are passionate about the field and care about teaching. Ignore the particular topics covered when choosing courses. All parts of economics can be made interesting, or deadly dull, depending on the instructor.

3. Use your summers to experience economics from different perspectives. Spend one working as a research assistant for a professor, one working in a policy job in government, and one working in the private sector.

4. Read economics for fun in your spare time. To get you started, here is a list of recommended readings.

5. Follow economics news. The best weekly is The Economist. The best daily is the Wall Street Journal.

6. If you are at a research university, attend the economic research seminars at your school about once a week. You may not understand the discussions at first, because they may seem too technical, but you will pick up more than you know, and eventually you’ll be giving the seminar yourself.

You may find some other useful tidbits in this paper of mine.

Updates: Here is some advice from Susan Athey about applying to grad school in economics. And here are the criteria a top economics PhD program uses in determining admissions.

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WangLuoxuan

2012-5-21 21:04:31

Wednesday, May 24, 2006
Which math courses?
In response to my previous post offering advice to aspiring economists, a student emails me:

Since the time allocation is limited, I can take only some math courses and the problem is that I am not sure which courses are most important for a successful economist and which course I should take first. Can you possibly suggest for me a list of math courses that a typical economics student should take step by step?

Here is one plan of action:

Calculus
Linear Algebra
Multivariable Calculus
Real Analysis
Probability Theory
Mathematical Statistics
Game Theory
Differential Equations

There is, of course, some flexibility about the order of courses. Check the prerequisites at your school to figure out the right sequencing.

Let me also recommend a book if you need a crash course for catch up or review: Mathematics for Economists by Carl P. Simon and Lawrence Blume.

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WangLuoxuan

2012-5-21 21:05:17

Thursday, June 01, 2006
Love Econ, Bad at Math
A student emails me seeking advice. To paraphrase a long letter, he asks:

I love economics and my economics courses, but I struggle with my math courses and am not doing particularly well in them. What graduate school and career path would be right for me?

I have met Harvard students with similar questions. This spring I talked with a Harvard senior who, because of a weak math background, was rejected by every econ PhD program to which he applied. At the same time, he had a strong academic record overall and was accepted by several of the very best law schools.

There are two possible paths for such a person.

1. Make extra effort to get a stronger foundation before applying to a PhD program in economics. One possibility is to spend a year or two at a master's program, such as the one at the LSE. Although one can go directly from an undergrad degree to a PhD program (such as Harvard's), some students get a master's degree first, and that background gives them a leg up when they start a PhD.

2. Stay involved in economics but through a different channel than graduate school in economics. Many people involved in economic policy are trained as lawyers rather than economists. Two examples that come to mind are Gene Sperling and Brink Lindsey. I don't know anything about their math backgrounds, but I imagine that a person could follow their admirable career paths without having studied all the math you need for an econ PhD. There are many areas of law that are filled with economic analysis, such as tax and antitrust. A person who loves economics can find many courses that would interest him in law school. (The same could be said about schools of business and public policy).

To decide which of these two paths is right for you, you have to look hard at your own tastes and aptitudes to figure out your comparative advantage.

I spent 1 1/2 years in the early 1980s as a student at Harvard Law School, and I think I could have forged a happy career with a law degree instead of a PhD. In the end, I decided that my comparative advantage was in economics rather than law, so I suspended my law studies. But I can always go back and finish the law degree if this economics thing doesn't work out for me.

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WangLuoxuan

2012-5-21 21:06:11

Tuesday, June 20, 2006
An engineer seeks career advice
A graduate student in engineering emails me to ask for some advice about his educational plans:

Hi Dr. Mankiw,

I've been reading your blog for a while now, and since you seem to be so wonderful about responding to email asking for comments and advice, I thought I'd give this a try especially after reading your post about how you ended up as an economist and not a lawyer.

I'm an engineering student, currently one year into graduate studies. I suppose I was one of those people who applied to grad school "by default," without thinking enough about what it was I really wanted to do with my life. One semester in, I realized I'd made a big mistake, that although I was still interested in academic research, engineering wasn't for me. I almost quit, but decided to stay with it until I either finished a Masters or decided what else to do. So right now (to the unfortunate detriment of my thesis research) I'm looking at a few other options.

I've always been interested in economics, and I'm beginning to think it might be the right fit for me. I believe I naturally think like an economist, and I have a very strong math and stats background to go with my interest. I've also done a lot of reading on the subject (including your wonderful macro textbook). The only problem is I have absolutely no formal education in economics--not even a single course, since I thought the first year economics courses I had the prerequisites for in undergrad seemed a little too basic to spend my precious electives on.

Do you have any advice for someone like me who wants to transition into graduate studies in economics from another field?

Keep up the great blogging,
[name withheld]

In your situation, I would recommend applying directly to graduate schools in economics. As an engineer, you have the necessary background in math and statistics. If you have done as much econ reading as you say, my guess is that admissions committees will forgive you for not having taken formal economics courses.

Admissions committees for econ PhD programs are often more forgiving of a weak econ background than a weak math background. That might seem odd, but it is easily explained. As economists, we think we can help you catch up if you need help in econ. After all, econ grad school is all about studying econ. But if you have a weak math background, you will start behind and have a harder time catching up.

Another option, instead of applying directly to an econ PhD program, is to apply to a master's program, such as that at the LSE. With a master's under your belt, a subsequent application to PhD programs will look stronger.

I have met several students in the Harvard econ PhD program with stories like yours. They were "refugees" from technical fields like engineering and physics who discovered late in life their interest in economics. It was not too late for them to switch, and it is probably not too late for you. Your education may end up taking a year or two longer than it would have if you had figured out your interests earlier, but that is a small cost to pay compared with the cost of ending up in the wrong field.

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WangLuoxuan

2012-5-21 21:06:53

Friday, September 15, 2006
Why Aspiring Economists Need Math
A student emails me a question about the use of math in economics:

Dear Dr. Mankiw,

Hi, I am an undergraduate student studying economics in Michigan. I have recently become a big fan of your blog. I found your "Advice for Students" very helpful to professional economist-wannabes like me, and especially, those considering graduate study in economics. Your suggestion on math preparation for undergrads landed me on one simple question: "Do economists really use all that math?"

I was wondering if you could tell me how closely math and the works of professional economists at international organizations, such as World Bank and IMF, are related?

I look forward to your answer. Thank you in advance!

Best Regards,
[name withheld]

A student who wants to pursue a career in policy-related economics is advised to go to the best graduate school he or she can get into. The best graduate schools will expect to see a lot of math on your undergraduate transcript, so you need to take it. But will you use a lot of differential equations and real analysis once you land that dream job in a policy organization? No, you won't.

That raises the question: Why do we academics want students that have taken a lot of math? There are several reasons:

1. Every economist needs to have a solid foundation in the basics of economic theory and econometrics, even if you are not going to be either a theorist or an econometrician. You cannot get this solid foundation without understanding the language of mathematics that these fields use.

2. Occasionally, you will need math in your job. In particular, even as a policy economist, you need to be able to read the academic literature to figure out what research ideas have policy relevance. That literature uses a lot of math, so you will need to be equipped with mathematical tools to read it intelligently.

3. Math is good training for the mind. It makes you a more rigorous thinker.

4. Your math courses are one long IQ test. We use math courses to figure out who is really smart.

5. Economics graduate programs are more oriented to training students for academic research than for policy jobs. Although many econ PhDs go on to policy work, all of us teaching in graduate programs are, by definition, academics. Some academics take a few years off to experience the policy world, as I did not long ago, but many academics have no idea what that world is like. When we enter the classroom, we teach what we know. (I am not claiming this is optimal, just reality.) So math plays a larger role in graduate classes than it does in many jobs that PhD economists hold.

Is it possible that admissions committees for econ PhD programs are excessively fond of mathematics on student transcripts? Perhaps. That is something I might argue with my colleagues about if I were ever put on the admissions committee. But a student cannot change that. The fact is, if you are thinking about a PhD program in economics, you are advised to take math courses until it hurts.

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WangLuoxuan

2012-5-21 21:07:43

Wednesday, March 28, 2007
My Life as a Student

A reader of the blog writes:

Prof Mankiw,

Just to let you know, I'm a big fan of yours and some of your work has inspired me to pursue a career in Economics. I just have one question for you - that may seem silly, but hey, - your educational background is very impressive - but did you ever struggle with any of the courses you studied as a student?

Sometimes, an academic life can be a struggle, can't it? Or do you find it all fun?

Thanks for reading this. I know you are very busy so I'll understand if you don't reply. You are an inspiration.

[name withheld]

As a student, I had the most trouble with three kinds of courses:

1. Those that required motor skills. I was solidly in the bottom quartile of my junior high school and high school classes in shop, typing, and physical education (but somehow I managed to become captain of my high school fencing team).

2. Those that required good memorization skills. Languages in particular were a weak point in my academic career, mostly because I had trouble learning the large quantity of new vocabulary words.

3. Those that required large quantities of reading. I have always been a slow reader. This was a particular handicap when I was a law school student.

But the most difficult time for me was when I had to accept the limits of my mathematical abilities. Math was my strongest subject in high school. I got an 800 on the math SAT, won the high school math prize, and didn't really feel like I was working hard at it. I thought I was hot s***. But then I got to Princeton and met people who were really good at math, the kind who become serious mathematicians, and I began to see the limits of my aptitude in math. I took some hard math courses there and did okay at them, but I was far from the top of the class.

Many econ grad students at Harvard, maybe most, are stronger in math than I am. In recent years, some of my coauthors (such as Ricardo Reis and Matthew Weinzierl) have been Harvard students with strong technical skills. My comparative advantage in the coauthorial quid pro quo is based on experience, intuition, writing skills, and a pretty good nose for interesting questions.

One of the nice things about being a professor is that you can specialize in those things you are best at, and you can find collaborators that compensate for your weaknesses. In other words, being a professor is a lot easier than being a student.