Letters to Students (2018)

Notes: When I taught Econ5121A in the fall semester of 2018, I wrote 12 weekly letters to students. In 2024—five years later, I shared these historical messages to keep a record of teaching and common experience with students. These messages have been edited by removing the mentioning of reading, exercises, and exams.

Sep 1, 2018

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.

Sep 7, 2018

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.

Sep 15, 2018

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.

Sep 22, 2018

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?

Sep 28, 2018

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?

Oct 6, 2018

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.

Oct 12, 2018

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.

Oct 26, 2018

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.

Nov 2, 2018

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.

Nov 10, 2018

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.

Nov 17, 2018

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.

Nov 23, 2018

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.