We all know that AI progresses at an unprecedented speed, with potential to dramatically disrupt the current social-economic structures. Econ5821, Data Science for Economists, turns out to be a set of skills sitting closely to AI’s firing range.
Before AI, economics students were relatively weak in coding. I thus spent the first few lectures to cover basic coding and advanced coding. Nowadays, vibe coding becomes the norm. I encouraged students to do their works with the assistance of AI. If we can vibe coding with prompts, we would not do it manually. I set the AI policy of this course to be the most open: I allowed any AI with without acknowledgement or restrictions.
Around the New Festival, AI agents’ ability substantially improved. I taught myself the latest agentic AI, and shared with students. In particular, I demonstrated it with the open-source large language models hosted by our department’s DIY cluster, and hooked Openclaw with unlimited free tokens that our department generously provided. Reflected from the teaching evaluation, students liked what I had prepared.
In recent years, there have been a lot of discussions in China about the deteriorating relationship between college teachers and students. Will universities become obsolete? In the time of cyberpunk, the human-to-human interactions is ever more valuable. The following quotation is to be remembered:
道不远人。人之为道而远人，不可以为道。
]]>Every few years, I write a post about the battle of computing languages. I have been a 20-year R user, but I decided to convert to Python in 2025 when I revamped my Data Science course. The transition was smooth.
Computing languages are just languages, and Large Language Models excel in languages. That explains why AI capacity demonstrates its strongest performance in coding tasks, now in the agentic mode. With LLMs at our aides, the difference between computing languages blurs. A few days ago, I tested an AI agent translating one of my full-functioning R packages into a Python replica. In 20 minutes, the job was done, and the agent automatically checked that the two packages produced the same numerical results. The efficiency and accuracy were stunning.
I am still a human. As a native R speaker, honestly, I do not utter Python at the same level of proficiency as R. (As an old-style R speaker, I sometimes feel uncomfortable with the tidyverse dialect of R.) Recently, I asked AI to code a demonstration of some new method that I wanted to learn. With too many self-defined classes, I had a hard time to understand the Python version. I then deleted the Python notebook, restarted a new AI conversation, and requested the agent to provide an R version. It turned out that the R version was much easier (for me) to read and comprehend. With some tests and experiments, it helped me grasp the new method well.
It is a fact that R, as a language developed by and for statisticians, does not ride the wave of AI and machine learning tasks such as language processing, image processing, and so on. The most popular framework for deep learning is pytorch, and it is Python-native. A general programming language, Python is capable in various computer science tasks beyond scientific computing.
I predicted in early 2025 that R would be dominated by Python even in data science. Things change in one year. With the rapid advances of vibe coding, people use natural language for their tasks. Though natural language must be translated by AI into a programming language, it is no longer crucial if the programming language is R or Python. That choice should depend on the following considerations:
Even though I still prefer to teach students in Python, now I do not feel guilty or ashamed to summon my beloved R for my own jobs.
What about MATLAB or STATA? These brothers have no future.
]]>I have been teaching Econ5821 since 2022, when I returned to Hong Kong. The contents of Econ5821 evolved over 10+ years. When I just joined CUHK, there was students’ request in department board meetings that the department should offer more courses to Ph.D.s about programming. Another junior colleague and I volunteered to launch a new one in the spring semester. It was called “Computational Methods in Economics.” It was co-taught for many years until I moved to Georgia Tech. The half (six weeks) from me consisted of programming, computing, and machine learning. My colleague taught dynamic programming in macroeconomics and structural labor. It was a bit ironic that the two instructors didn’t unify the programming languages—mine was R and hers was Matlab.
In 2022 my department’s master of science program had been running for almost a decade. The trend of technological development was unmistakenable: big data and machine learning (The AI tsunami was not there yet). To meet students demand, I re-modeled the previous Ph.D. course into a master-level one, with substantial reduction in the academic contents—those methods only useful in writing research papers. It became more accessible for students with economics and finance background, many of whom had insufficient exposure to coding.
November 2022 will go down into history. This month, OpenAI launched ChatGPT, and it became the most downloaded app instantly. It was able to answer questions, compose poems, draft emails, and write code. It was the most important technological breakthrough so far in this century.
AI would change the landscape of higher education permanently. Some majors, fields, experts, and professors were horrified. University administration was never prepared for such an impact. My employer announced 4 modes of AI adoption, from the most restrictive to no restriction, as Approach 1 to Approach 4. With zero hesitation, Econ5821 adopted Approach 4: “Use is freely permitted without acknowledgement.”
Econ5821 was special in its code-heavy contents, which was intimidating for some students of economics and finance background. The advent of a chatbot that could write code was immediately seen as a positive aide. I kept an open attitude toward AI in its inception. AI has been part of the toolkit since the 2023 spring revamp.
At the beginning, AI’s capacity was limited. Hallucinations popped up as daily jokes in social media. Econ5821 had a middle term exam at that time, with closed-end data collection, data processing, and statistical analysis tasks. I tested the questions in ChatGPT, and I was convinced that AI was unable to do it.
While we laughed at AI as “too young, to simple, sometimes naive,” AI has been progressing at unprecedented speed, thanks to the scaling law. In 2024, it could handle half of the midterm questions. In 2025, I tested it again with the previous years’ midterm questions, and found the midterm meaningless—I cancelled it.
Three years later, no one doubts that AI has a unique edge and has already revolutionized the way people write code. If you have read this post up to this point, you may reasonably wonder “Why do I still want to enroll in this course?” “Is it a waste of time for me to learn data science?”
I am still teaching it, and I believe it is not a waste of time. As a master’s course, it is an update and enhancement of the economics / finance courses that you learned in your undergraduate study. No matter where you took your undergraduate education, China or USA or somewhere else, undergraduate curriculums are hopelessly outdated. Data science is a direction of economics / finance higher learning that is close to real-world productivity. It exposes you to modern tech toolkit and workflow. It is not about abstract theory, but empirical facts.
In the past, data science had a high wall and deep moat. With the assistance of AI, the entry barrier has been substantially lowered. I envision that in the near future, perhaps 5 years or so, data science becomes part of general education, along with literacy in language, math, and science. At the end of the day, data science is one way to understand the world from a different perspective—the inductive reasoning, in contrast to the deductive reasoning as in standard math and physics.
Even if AI is commonplace, humans must be able to supervise AI and monitor AI. That is, we verify if AI produces what humans intend to produce, and we need to know how to fix issues. If one day AI is so capable that data science is completely automated, humans still need to understand the consequences and implications from AI’s data analysis to make their decisions. Today’s AI is based on large language models, while humans are in the world model. Assuming AI cannot reverse the arrow of time, a human only lives once.
Last week, we witnessed a substantial drop of stock prices of many American software companies. Media attributed it to Anthropic, the company behind Claude Code. Claude Code is the leading AI enterprise of coding agents and assistants. The progress of AI’s coding capacity improves so rapidly that now it starts to trigger an existential crisis of giants such as Adobe, Figma, and Salesforce. The shock spread over to data providers such as Bloomberg and LSEG.
No decent universities are listed in the stock markets, and thus the values of universities are not instantly reflected by investors vote by money. Since the inception of AI, unfortunately, the values of universities all overall the world are declining. It has exposed the sad fact that many skills that are preserved and handed down in the current higher education system indeed have little intrinsic value.
For example, one of the most hated institutions in Chinese Mainland universities is that every student must complete a thesis in order to obtain a degree. A thesis—bachelor’s, master’s, or Ph.D.’s—comes from “research.” However, we can reasonably expect that 95% of undergraduates have no interest and talent for genuine research, and 98% of the theses are a waste of time and printing papers. One of the immediate benefits of AI is that it liberates undergraduates from conducting useless research. AI saves time.
As a university teacher myself, I surely believe and cherish the virtue of higher education. It passes knowledge from Newton, Gauss, and Shannon to the next generation, and contributes new findings and discovery day by day. However, the current system must be revolutionized in view of the impact of automation. The golden days of global higher education are over.
]]>Twenty-plus years ago, I was a finance major. My undergraduate statistic teacher was a small, energetic woman at her forties. She always wore sports shoes when teaching. She covered two estimation methods, one was MLE and the other was the method of moments (MM). MM is too intuitive. It simply uses the sample moments to mimic the population moments. On the other hand, MLE is a conceptual leap. It struck me when I encountered it for the first time. Though it seemed a reasonable way to go, as one definitely doesn’t want to minimize the likelihood or somehow average the likelihood, I had a hard time to immediately appreciate why playing with the likelihood function was a good practice, let alone an optimal approach. There was a non-trivial logic gap to fill to align the parameter of interest with the likelihood function.
It was not until I took graduate-level econometrics that I grasped the (relative) “entropy” at play. Entropy is a deep, grand, and enigmatic building block of the universe. It was first introduced in thermodynamics to describe disorder. von Neumann suggested to Claude Shannon to borrow it because “No one really knows what entropy really is”. The hero of this post, though, is Ronald Fisher, the father of modern statistics. An enthusiastic advocate of MLE, he laid the foundation of MLE in 1922. Fisher also introduced terminologies that remain in use, such as the score and sufficiency. Fisher, obviously, was a pioneer and trailblazer, ahead of Shannon’s work on information theory. Information theory, it turns out, is a cornerstone of modern science far beyond statistics.
]]>英华是浙江富阳人，通过自己的勤奋努力一步一个脚印，从浙江农村走到北京，又从北京走到纽约。他早我四年从北大CCER毕业，08年我申请出国时，他正在哥伦比亚大学读博。我通过电邮向他咨询过哥大的情况。
我第一次见到英华是在New Haven的师姐家中。一群中国留学生的小party上，他人缘挺好，说话轻声慢语地，很gentle，其它的印象并不深。我从网络上知道更多他的想法。那时候的网络还有原创写作，他和几个志同道合的CCER同学一起写作一个名为“旁观组”的博客，用通俗易懂的语言讨论社会现象背后的经济学原理。
我和英华更深的接触发生在2014年初我找工作的时候。英华当时在法国图卢兹大学担任助理教授。图卢兹大学邀请我去做 job talk，这是我第一次去法国。面对可能的机会，我希望更多地了解当地的生活和工作情况，于是又和他联系。Job talk 当天他约了和我 in-person meeting，次日又自掏腰包请我吃了一顿法国大餐—当地大餐也不比美国便宜。看得出来，他喜欢法国的生活，在餐厅熟练地用法语点餐，挥洒自如。
然而数年之后他没有留在法国，辗转去了休斯顿的Rice University。2019年我去Rice做seminar，他正在巴黎访问，看到系里有关我seminar的邮件，向我表示歉意不能出席，并祝我顺利。这是我们最后的通信。
我和英华的个人接触不多，但是我一直关注他的工作。他的研究以微观理论为基础，把结构方程与计量方法相结合。他的研究重点是匹配。匹配问题在现实中有很多例子，最常见的是学生和学校的匹配，还有人体器官(特别是肾脏)捐赠人和被捐赠人的匹配。匹配问题多年来积累了不少微观理论，但是纯微观理论不提供量化证据、不具有可操作性。近年来，数据越来越多，给出了一些定量结果，为实践中的机制设计提供了可能。他正是这方面研究的先锋。
然而，在当今的学术界，开创性的研究往往面临着巨大的风险。英华一开始的发表并不顺利，在学术界摸爬滚打多年之后才渐渐受到同行的认可，杀出一条血路，近年来一系列成果见刊于所谓的经济学五大顶级期刊。这些期刊上的论文，每篇都要经过无数遍打磨，蹉跎岁月；而他2012有关北京中学和学生匹配的原创论文，也就是他当年的 job market paper，到今天仍然还没有发表。
英华是CCER毕业生中第一个真正将微观经济理论、计量经济理论和实证研究完整结合起来并做出成绩的。最庸俗地讲，他挑战成功了80%的五大期刊，是至今所有CCER毕业生的最高纪录。本来他的学术研究正渐入佳境，不曾想天妒英才。
我之所以关注英华的研究，是因为我在读博期间也曾试图向结构模型计量这一方向发展。后来我发现自己能力有限，翻不过这大山，走不出这长夜。我由衷地钦佩那些手持火炬，在崎岖暗夜中前行的孤勇者。
人生无常。那些无法挽回的失落让我们更加珍惜当下的日子。2014年，我确定了工作地点之后向英华报告了我的去向。他给我的回信，有安慰，有鼓励： “Congratulations! That’s a quite nice outcome. Besides, our career is a marathon, and I’m sure you will prove yourself in a few years.”
是的，our career is a marathon。师兄，你不能在前面再领跑一程了吗？
2024-8-10 中国香港
]]>耶鲁大学来自中国学生的博士生人数不多。我们在耶鲁有生活上的交集。晓宏待人真诚，和他相处没有距离感。我们都住在耶鲁大学的Whitehall研究生宿舍，这是优先分配给已婚博士生的恬静小社区。因为对家乡共同的想念，我们偶尔聚餐，比如我在晓宏家吃过饺子，晓宏在我家吃过火锅。萧瑟的秋冬时节，我们经常在饭后散步时不期而遇。我还记得那时陈朗正怀着身孕，晓宏在冷风中小心翼翼陪着散步的场景。
我和晓宏同一年从耶鲁毕业，他去了新加坡国立大学，我来了香港。我听说社会学的学术职位比经济学少。对于来自东亚的新晋博士，能够在亚洲顶尖的新加坡国立大学任职是了不起的成绩；我的一个同样攻读耶鲁社会学博士的韩国朋友就非常羡慕晓宏。
那些年我每年都去新加坡。有一次晓宏得知我在狮城，主动邀请我去游览国大，特别是带我参观了国大的经济系。晓宏和我在国大共进午餐，期间他聊起他的学术话题，说他对党尤为感兴趣，收集了历史上大量的人物资料和和履历用在他的研究。我提起经济学研究中有做中国官员的晋升锦标赛，而他研究的是党早期的发展，类似考古工作，我当时没有多想。
那时候陈朗已经来到香港理工大学任教，两人经常新加坡香港两边跑，为航空公司做贡献。我说你们这样累不累？要不要想办法团聚？他笑了笑说有机会就去香港。然后他问我，你在香港待了好几年了，知不知道什么是“吹水”？我说我真不知道。晓宏认真的给我解释了，吹水就是粤语里面侃大山的意思。想必他在香港结识了学术上志同道合的朋友，经常在一起高谈阔论，也就是吹水。
2018晓宏真的来到香港岭南大学任教，我由衷的为他全家团聚而感到高兴。有一天，他突然给我打电话，说正巧在中文大学，问我是否在家。于是，他和陈朗来我家中小坐了片刻，就匆匆告别。不曾想，这是竟是我们最后一次见面。
我知道晓宏关心中国社会的发展。香港的优势是能身处中国，近距离观测中国。2019年香港风雨飘摇的时候，我得知晓宏即将离开香港，去美国密歇根大学任教。相比香港相对容易的晋升条件，密歇根大学是更有挑战，也是发挥更大影响的学术平台。我钦佩晓宏对于学术追求，这印证了他理想主义。
接下来新冠席卷全球，我和晓宏之间久未联系。有时陈朗在脸书上提起晓宏身体不好，然而我看到网上信息晓宏还在积极参加各种学术活动，想来并无大碍。直到最近数月，情况急转直下，我不由为晓宏担心。但是没想到，他这么快就离开了我们。
从讣告当中，我才知道晓宏原本在北大读的是化学，后来因为浓厚的兴趣转到了社会学专业。那时经济高速发展的中国社会正在经历巨变。站在学理的制高点观察和理解国家的变迁，这一憧憬一定对他构成了不可抗拒的吸引。
我在经济学系。虽然都是社会科学，坦诚地讲，我和晓宏在学术上没有交集；并且我们对有些问题的看法不一样。但我自己的狭隘，不妨碍我去欣赏他的学问。晓宏的研究关注的是社会的巨变。这些问题无法用经济学均衡来刻画，也没有足够多的数据来推断。理解那些很少发生但深刻影响世界的重大社会历史事件以及它们背后的规律，是他追求的圣杯。
晓宏是我的兄长和朋友。他有思想、有抱负、有才华，坚毅勇敢。他太早地离开了；但他永远在我的心中。
2023-12-27
中国香港
]]>2023-04-13
我每年都收到多封本科生的电子邮件，询问有没有机会帮我做研究助理(research assistant)。我和CUHK本科生的合作非常愉快；我自认为是个负责的老师，工资、推荐信没少过。
这几年我对这个事情有了新的认识。虽然科研只适合很少一部分人，可是经济不好的时候，想读研的人越来越多。学生寻找研究助理岗位，攒科研经历，把自己和竞争者区别开来。了解到经济价值之后，就有中介从事这个买卖，把本科生的科研经历变成一个产业。一些高校从业人员奋不顾身，加入这个产业，变成了科研经历的供给方。这些新现象，破坏了培养科研人才梯队的旧有秩序。
我目前的科研工作并不需要大量的人力。最核心的能力，比如发掘问题、数学证明、还有英语写作，我到了博士生的最后阶段才达到国际水准。这些能力都是通过数年辛苦才得来，并不是有人学习一些本科入门课程就能帮上忙的。如果有学生通过短短几年的本科学习，就掌握这些技能，那么其天资远远超过我；应该去更好的学校，找更好的老师指导。
本科生大部分没有自己的的科研想法。有必要明确一下规矩。
2022-01-20
国内读博士靠考试，国外读博士通过申请。经济系的录取过程，和其他理工科的院系不太一样。经济系的博士生，不需要教授通过自己的研究经费来支持。所以，录取谁是全系的决定。
首先，靠谱的经济系网站上都会列出申请的硬件，比如托福成绩，GRE成绩，GPA要求。申请截止之后，系里秘书会先过滤一遍，把不符合硬件要求的申请人删掉，然后将剩下交给博士招生委员会。招生委员会一般由4-5人组成，委员会主席通常是有威望的资深教授。根据申请人数多少，每份申请材料由至少两位教授打分写评语。这里的打分，当然不可避免地有一定主观随意性。但通常每位同学都会申请十几所学校，所以大数定律会起作用。归根结底，用实力说话。
委员会评完之后，将在全系所有长聘轨教授参加的大会上向同事作报告(present)。根据录取的人数限制，从高到低排名次。对于非顶尖的经济系，有一定比例最优秀的申请人可能会有其他学校更好的offer。根据历史数据，委员会预估一个发offer的cut-off line。
假设今年有18个录取名额，委员会可能准备发出24个offers。为了决定把这24个offers发给谁，委员会可能在大会上请同事讨论前36名。前几名，优势明显，大概率没什么争议。20–30的，可上可下。这时候，一两位评审委员会之外的教授意见就可能发挥作用。比如说，教授A说这位排在第27名的同学，是ta的一个认识的同行教授B推荐。教授B非常了解这位同学，说ta的GPA虽然不完美，但学术研究有潜力，又吃苦耐劳。如果这个学生招进来，教授A愿意指导。这样的情形下，录取概率就会增加。
对于远低于录取线的申请者来说，这里面没有灰色空间。就算申请人是某教授的亲人，教授也不可能把ta从第42名弄成第24名。在边际上的申请人，申请材料之外的内部信息有作用。
排名确定之后，24个offers发出去。如果接受的offers少于18个，委员会可以招一个小班而把剩下的名额放在明年，或者用waitlist上的名次按顺序补充。如果发生overshoot，也就是多于18个人接受了offer，那么多出来的名额就从下一年的招生计划中扣掉。
如果同学拿到了offer，那么恭喜你。offer板上钉钉，主动权完全在你手中。如果你有了更好学校的offer，请尽快婉拒你不想去的学校的offer，为其他还在等offer的同学做个好事。
2025-04-29
数学证明是计量经济学理论区分于其他经济学领域最核心的技术。已经发表出来的论文中的证明，是从起点（假设）到终点（结论）的行走过程。这跟走迷宫差不多。证明的技术需要学习；一开始要花时间首先看懂别人是如何走通迷宫，然后体会别人走迷宫的心路历程。初学者以可能以为起点和终点都是固定的，然后去走路。在更高的阶段，起点和终点都由自己定。
一个办法是从结论出发。我知道一些可以行走的路径。比如说工具箱里的大数定律或者中心极限定理。我先就使用这些东西，把结论猜出来。然后回头看在证明的过程中需要哪些假设，再把假设补上。
另一种可能是从假设出发。在一些合理的假设下，能推出些什么东西？太难的结论证不出来，需要知道什么时候停步。
做数学证明是个劳心费神的过程，同时也是很有意思的过程。这当中的酸甜苦辣，只有亲身尝试过才能体会。
2021-12-30
怎样才能有好的idea？我觉得，做研究是知识深度和广度积累的过程。如果知识涉猎很多而没有深度，博而不专，无法突破他人。如果知识没有宽度，只对一个小领域研究很透，一直做下去，边际收益也会递减。长方形的面积等于长乘以宽。作为研究者，两个维度都重要，缺一不可。《论语》说，“学而不思则罔，思而不学则殆”，是同样的道理。
讲讲我的亲身经历。经济学博士要毕业的时候，工作市场论文(job market paper, JMP)是展示自己最重要的成果。博士毕业前一年，我还在为JMP题目苦苦挣扎。阅读文献是读博士的重要环节；我会把文章存下来备查。那一年的寒假，找不到题目的我，随手翻看电脑上的保存的文件。我偶然打开一个PDF，只有5页，然而灵光闪烁。这个小notes没有署名，我寻思，这是谁写的呢？过了半分钟，我才意识到，这原来是过去的我写的。博士生二年级的时候，上完一门统计系的课，我写下这个想法。当时我试图去证明，但是做不出来。计量理论研究最重要是要获得做证明的能力。我资质不高，没有大量练习和思考的积累，这能力不会凭空产生。博士生二年级时候我能力不够。等到博士最后一年，重新拾起这个尘封的idea, 花两个月的时间，顺利地把证明做出来了。这篇文章后来发表在这里。
这段经历说明，光有想法是不够的，需要技术才能实现想法。
]]>微观经济学的原理，相对而言是比较普遍性的道理，不受国家的限制。相反，宏观经济学问题，严重依赖国家的制度背景。比如，曼昆的教材讲了很多美联储如何运作。对中国学生而言，更重要的是要知道中国的货币体系、国有银行体系如何运作。同时，经济学是实证的科学。曼昆书中的数据，全部以美国为出发点来讨论经济增长、财富分配和不平等；中国当然是外国，是重要的贸易伙伴。认真的学生完成这门课之后，了解很多美国的事实，但是对中国却一无所知。这是误人子弟。
我支持建设我国的经济学教材体系。然而，事实是，我国经济学学者研究水平参差不齐，在世界学术界受到同行认可的权威更是凤毛麟角。这时候，应该由谁来决定由哪些个人或者团队来编写教材？抑或由市场来决定?
我读本科的时候，惊奇地发现，有写学术平平的老师，动不动也写本教材。后来才明白，这些教材无非是评职称的敲门砖；并不是因为某某教授成为了这个领域的领军人物，受到责任感的感召，要为大家把知识系统地呈现出来。我国大学系统的这些弊病，不仅浪费了老师的时间，更浪费了学生的时间。老师自己教课，年复一年，倒也无所谓；而学生的学习机会通常只有一次。
以计量经济学为例，方法本身不分国界，比如说渐进理论在哪个国家都一样。近些年有一些有实际问题导向的方法运用创新，在教学中应该提及原始的出发点，让学生体会这些创新的激动人心之处。广泛流行的计量方法，在中国肯定也有人采用；应该让学生了解方法如何运用到中国的实际问题之中。关键还是教师要提高自己的业务水平。
]]>2022-01-10
作为高等教育从业人员，我的日常是做研究和教课。今天讲讲教课的事情。自从我读研开始，陆陆续续接触过四本高级计量教材。我简要说说每本书的侧重点，然后推荐其中一本。
William Greene的Econometrics Analysis是我读硕士时老师推荐的阅读教材。当时在国内很流行。Greene是NYU Stern的应用计量经济学家，已经多年没有发新的计量理论论文。这本书最出彩的地方是它的数学附录，讲得全，适合本科到研究生的数学衔接。
我那时自学主要看Fumio Hayashi的Econometrics，花了不少时间钻研。这本书体系比Greene完整，建模上用GMM一以贯之。内容更有深度，比如推导了非稳定时间序列的渐进分布。现在来看，这本书出版于2000年，之后再也没有更新，有的内容难免过时。Hayashi的主要学术成就在宏观研究，也不是做计量理论的。
Jeffrey Wooldridge的Econometric Analysis of Cross Section and Panel Data在国内也很流行，简直是微观实证同行的必引经典。作者的太太是劳动经济学家，书里用了不少他自己家的例子。内容在面板数据线性、非线性模型回归，方差聚集等问题上比较深入。然而，参数微观计量不是我的菜。我去Michigan State做过两次seminars，没好意思作者说，这教材读不下去。
我读博士的时候，Bruce Hansen的整本教材只有不到200页。经过作者年复一年的扩展、修改、补充，2021年已经发展到两卷本。第一卷Probability and Statistics for Economist 400页，第二卷Econometrics 1000页。我个人喜欢Hansen的风格。知识体系最新，覆盖面最广。一上来就讲，线性回归只是一种对条件期望的逼近，经典高斯马尔可夫假设没有实用性，超越传统教材。在广度上，覆盖横截面回归，时间序列，面板数据，非参数半参数回归，机器学习。在深度上，重要结论有完整证明，理论工具一直讲到经验过程(empirical process)。课本内容再向前一步，便是理论前沿。
Hansen的书是时代的里程碑，是目前最好的计量经济学理论教材。作者为学术传播无私奉献，将两卷书放到网上供免费下载。然而，即便如此，由于内容新、广、深，窃以为该书未必会流行。
学通一本书就够了。Hansen是我师兄，必须捧个场。我教课用的讲义，根据这两卷本发展而来，是几个重要章节的精华简本。同样自由下载哦。
2022-01-17
接着上次讲教材，这次谈谈研究生计量经济学入门课教学的内容和目标。
设计一门课，是个最优化问题。上课的时间有限。境外大学学期短，通常只有12-14周教学时间，必须权衡覆盖面广度和内容的深度。
这门课最关键的是线性回归。把最小二乘法(OLS)理解透彻之后，我们就发现其实线性的广义矩方法(GMM)就是它的一个拓展。而各种非线性回归的理论性质探讨，无非是在最优值点做线性展开，忽略更小的高阶项，让在局部返回线性状态。归根结底，线性问题在数学上容易处理。而对非线性问题，我们尽量用线性问题去逼近。
我的课程安排大致这么几块内容：
如果经典分布假设被违反，就需要用到大样本理论。 大样本理论有两大支柱，大数定律和中心极限定理。通常本科学得皮毛，需要花点时间加深。 通过一些转换工具，大数定律可以用来证明OLS的相合性，中心极限定理可以用来证明OLS的渐进正态性。 有了渐进正态性，就可以做Wald, Lagrangian multiplier test, likelihood ratio test统计推断。 接下来是OLS这套理论的应用。
Diff-in-diff, 面板数据固定效应和随机效应模型，是OLS的直接使用。 有内生性？两阶段最小二乘法(2SLS)就是把OLS的理论重新来一遍。 到这里，上课时间已经用完。让人略感安慰的是，把这些内容学通了，2/3的经济学实证论文基本可以看懂。如果以后做实证，就依据自己的领域逐步精进。做宏观的，学些时间序列技术；做微观的，学些因果推断技术；都不难。如果要做计量理论，这么点是远远不够的，万里长征才开始了第一步。
至于什么是因果？什么是概率？如何拒绝或接受假说？它们是哲学问题，没有标准答案。有人说(经济)理论假说就有因果，有人说可控实验才有因果。概率是两大学派数百年的争论。接受或拒绝是两类错误的权衡，常用的操作并非金科玉律。这门课提供一些角度去思考这些深层次问题。
2022-01-27
之前讲了教材和课程内容，今天接着讲讲数学基础。
除了世界领先的几个经济学博士项目之外，做经济学微观和宏观理论学生数量并不多。现在经济学的领域和话题越分越细，同时数据越来越丰富，大部分博士的毕业论文以实证问题为主。研究生阶段的第一门高级计量经济学为实证工作打基础。然而，这个基础课的基础是数学。
高级计量经济学其实涉及到的经济学内容并不多。相反，它是是本科数学的总结和深入。数学基础是从本科入学开始的历练过程。到研究生阶段再回头补，有点晚。
我读本科的时候，经济学、金融学的课程，基本上是水课。只有三门数学课是实打实的课程，不含糊。我虽然考分都不错，但是当时没发现它们有什么用。特别是线性代数中行列式，秩，特征值、特征向量等概念，在本科的经济学学习中，几乎没有任何用处。好像这门课纯粹是测验智力，到了毕业我也没明白为什么要学线性代数，
到了研究生计量的多元回归，我才发现线性代数的基础性作用。微积分和概率论也同样重要。比如，线性回归就是一个求解最小值的过程，需要用到微积分当中最优化的一阶条件来求解析解，二阶条件验证最小值。还有就是极限的概念，因为渐近理论全部依赖于样本量趋近于无穷大想象世界。概率论和数理统计的使用场景，更是无处不在。比如说我们用它来导出在正态分布下，线性回归的有限样本性质。高级计量的理论部分是微积分、线性代数和概率统计的混合使用。
2022-02-04
理想很丰满，现实很骨感。开始读博士的时候，人人都立志要成为理论大师。读到毕业的时候，大部分人变成了跑回归的。当年剑桥的大师们徜徉在康河的柔波里，身旁是河畔的金柳和波光里的艳影。现如今，研究人员都挤在一个小屋子面对IDE，是社会科学领域的程序员。
博士资格考试是需要数学的。如果考挂，就没有然后了。
微观理论要用到一些实分析的内容； 宏观需要一点常微分方程； 计量需要的知识，我已经在上文写过。 归根结底，学好本科的微积分、线性代数、概率论三件套，能应付90%的任务。其他各种更高级的数学工具，只对考完博士资格之后在相应理论领域继续深耕的人士有帮助。
然而，理论教职的需求太小，使得博士生只有少数做理论。大部分经济学博士考完资格考试，就把之前的数学忘得差不多，留下安身立命的本领是跑回归。造成这样的资源错配，因为经济学课程更新速度过慢，跟不上时代的节奏。
从二战之后到1990年代，是经济学理论的黄金时期。现在是数据和故事为王。经济学研究不可避免的从知识密集型向劳动和资源密集型转变，这是经济学研究越来越内卷的根本原因。鼓吹要把数学学得多好才能把经济学学好的人，是在误导初学者。
将回归跑出精彩的人有的，我就有幸认识几位。然而，相对于这个群体的庞大基数而言，是凤毛麟角。
如果你是无畏的时代逆行者，虽然前路漫长崎岖，然而无限风光在险峰
]]>Dear all,
I am looking forward to meeting you next Friday morning in Econ5121A. I have uploaded the latest syllabus onto Blackboard. You can find it under “Course Content”. Hansen’s free textbook “Econometrics” will remain the primary text this year.
If you are getting rusty on calculus and linear algebra, I suggest that you review them by yourself. Students from Department of Economics have taken the math camp recently, but I don’t know the arrangement those from other departments. As you can expect, graduate-level econometrics will be math intensive.
Today is September 1, a day with fun or bitter memory throughout your school years. Anyway, I hope you enjoy this last weekend before the new semester—another new semester in your life. I will see you soon.
Dear all,
It was nice meeting you. I hope that you have a better idea about our course after the lecture. I wish I were granted of two semesters to build up the foundation of statistics and the superstructure of econometrics. However, only one semester is at our disposal. This is a typical problem we economists are faced with: constrained optimization.
What I went over today was 6-hours of lecture in the summer. These mathematical apparatus may appear alien at the first glance if you have never taken real analysis or measure theory, but you don’t have to worry too much. Each person has his or her style in approaching an empirical problem. After all, econometrics is not mathematics, although I believe the marginal utility of a healthy dose of mathematics remains positive at your current stage.
Dear all,
I hope it does not disappoint you too much that the conditional mean model or the linear projection model is motivated from a prediction perspective, rather than a romantic causal model. Today’s lecture is a full-flavor blend of calculus, linear algebra and probability, for which your sweat and toil in ruminating over undergraduate mathematics will be rewarded.
Teaching Econ5121A reminds me of my path. It sends me back to the golden autumn in 2005, when I was a first-year postgraduate student in Peking University. My confidence was smashed by microeconomics and macroeconomics but econometrics surfaced as my last refuge. I had aspired to become a financial economist, whereas I was reborn from ash as an econometric theorist.
I understand that few of you would pick econometrics as your research concentration. Even so, reading and exercising are essential training for you to conjure your colorful economic insight from dry data. With the looming super typhoon at Hong Kong’s horizon, may I gently ask you to retire home and peruse the following tasks.
This year’s Econ5121A has an experimental part: the IPython notebook embedded with code snippets. It is new in my teaching. The first live code demonstration was useful, though I experienced a short moment of faith collapse. I knew the law of large numbers is mathematically true, but what I saw was in dramatic contrast to the theory’s prediction: something must have been compromised. I was unaware of my omission of the chi-square distribution’s degree of freedom until a student helped me out—thank you. Presenting in front of an audience is different from debugging alone in my office.
Also new is assignment submission in this course. I hope the homework can give you better understanding of the course materials. One cannot master mathematics without exercises, and the same applies to econometrics. We will continue with this practice. Could you please do the following this week?
Dear all,
After a few weeks, you may have noticed that econometric theory differs from the paradigm of microeconomics and macroeconomics. No assumption so far is about human behavior. Instead, they are concerned about the physical mechanism of data generation. You may have wondered if you run into a wrong classroom of mathematical statistics. Unfortunately, your impression will not be altered until the last few lectures when we cover instrumental variable and endogeneity. It is safe to say that econometric theory is a branch of applied mathematics. One student asked me “What does econometrics research look like?” This question can be answered by pulling out any issue of the Journal of Econometrics or Econometric Theory. Look at the papers therein. I bet the proofs will be much longer than the section about economics.
This week witnessed a grand live show in pure mathematics: Sir Michael Atiyah claimed that he had proved the Riemann hypothesis, one of the most important unsolved mathematical questions. In 1859, Riemann conjectured that all nontrivial solutions to the Euler-Riemann zeta function zeta(s) = 0 have their real part equal to 1/2. This hypothesis has been verified by computer for trillions of zero points, but there is not yet a proof. Based on such overwhelming evidence, all statisticians, even those skeptical Bayesians, would believe almost certain that the Riemann hypothesis is true. In this regard, is a proof of the Riemann hypothesis, at its face value, really that relevant?
While you enjoy one more holiday thanks to Chairman Mao’s timely announcement at the Gate of Heavenly Peace, may I gently ask you to complete some mundane readings and exercises not as fascinating as mathematicians’ 160-year pursuit of the solutions to the zeta function?
Dear all,
Asymptotic theory is a leap of faith from our secular finite-sample real world to the sacred infinity-sample utopia. It is also a leap of mathematical apparatus involving sequences, limits and series (无穷级数)—those in the “advanced” category. The quest of of understanding series has led to many amusing problems, such as the summation of all natural numbers equals, for which both Leonhard Euler (1707-1783) and Srinivasa Ramanujan (1887–1920) independently came up with the seemingly nonsense answer -1/12.
Dear all,
Asymptotic theory is the foundation of modern statistics as well as econometrics. Our two lectures only scratch the very surface of the theory: we introduced the definition of modes of convergence, the statements of law of large numbers and central limit theorem of the simplest forms, and applied them to study the behavior of the OLS estimator. Numerous hours is your essential investment to be a licensed wizard or witch in asymptopia.
—————–华丽的分割线—————–
As you may be aware of, this year’s Nobel Prize of Economics is awarded to Paul Romer and William Nordhaus. I know the latter tall and quiet gentleman in person. I knew him as early as when I was a freshman in Zhejiang University: I spent a lot of time in the cold and wet winter that year reading the Chinese translated version of Economics by Paul Samuelson and William Nordhaus, and this book embarked my journey in economics. When I met Nordhaus for the first time in 2008 as a first-year Ph.D. student at Yale, I expressed my sincere appreciation to him as one of his millions of readers. I stammered a bit, as I got too nervous in front of him—just imagine that a boy worshiped Cristiano Ronaldo one day enrolled into the Youth Academy of Juventus and had an opportunity to say hello to his idol!
In the following years, I didn’t have much interaction with Nordhaus. He is at senior age, and his research about environmental policy and climate change is of enormous importance but not mainstream. While every time I saw him, I was impressed by his gentle style, his neatly combed gray hair, and his unmistakable smile. The last time that I talked to him was in New Haven Train Station in January 2014. He was the President of American Economic Association (AEA) at that time, and he took a train to Philadelphia, Pennsylvania to address to the annual AEA meeting. It happened that I boarded the same train to the same conference—not as the AEA President but as a hopeful job market candidate. Fortunately or unfortunately, that conference knocked me to Hong Kong, and it ended the story between the giant and little me.
Dear all,
Our TA said that you did better than expected in the midterm. I believe this is a treatment effect. It is the first time that we assign reading and exercises on both textbooks. The exam questions tend to be easy if you invest enough hours.
Today we covered hypothesis testing, one of the fundamental tasks in statistics to quantify the uncertainty from random sampling. As I have exposed the inconvenience of the frequentist framework in decision making, perhaps I will also give an example next week on how Bayesian deals with such a problem.
Dear all,
Today I happily introduced Bayesian inference, for the first time in Econ5121A. I personally like the theoretical beauty of the Bayesian idea very much, although I keep working on frequentist asymptotic theory in my research papers in order to have them published.
We also had an early radioactive exposure of machine learning. Machine learning will become mainstream in econometrics, and old dogmas will be swept into the ash heap of history.
Dear all,
Panel data, no doubt, is an important topic of tremendous practical relevance. However, in terms of theory it does not have much to offer, at least at the entry level. The most widely used fixed effect model and the random effect models are special cases of OLS that we have covered. Our selected textbooks have very brief treatment of panel data. Therefore, this week only reading but no exercise is assigned.
Dear all,
Starting from the topic of endogeneity, econometrics diverges from statistics. Econometricians assume existence of IV in theoretical papers (see, for example, Shi, 2016). In single-equation empirical works, researchers rarely possess a convincing exclusive IV. Those few successful examples are based on institutional background, which is case-by-case and can hardly be generalized to other scenarios.
In some applied fields without well-framed theory, too much time has been wasted in the attack against endogeneity and the hunt for instruments. As Starchurski correctly points out (p.342), “The best solution [to endogeneity] is better modeling.” In multiple-equation models, often time instruments are naturally generated (see, for example, Ross and Shi, 2018) within the system. In other words, the economics makes it clear the source of endogeneity as well as the whereabouts of instruments. This is the approach I personally prefer.
Dear all,
It was great to talk to a few of you during the Graduate Party on Friday afternoon. I was glad to learn that my class was easier than microeconomics and macroeconomics.
The ultimate goal of Econ5121A is to make you understand applied econometric techniques by yourselves. That is why I assign reading and exercises ahead of my teaching this week as well as in last week. Given our coverage, you should be able to read the empirical part of most applied papers that use linear models, and you know how to do your own regression analysis.
If you are interested in working on econometric theory, then there is a long march to go. For a theorist, the ultimate goal is to be able to create new theoretical results by yourselves—for example, prove consistency and asymptotic normality for a new estimator that you propose. Our training at Econ5121A is insufficient for this purpose. However, with intelligence, diligence and perseverance, nothing is impossible.
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