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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.

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About me

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** Published:**

These days I mostly play competitive tennis, so my opponents usually have sufficient understandings of the rules and we do not get into disputes. However, debates and disputes sometimes occur in recreational play, which could be annoying. So in a series of posts, let me talk about some rules that could be overlooked by recreational players. The official rules can be found in the “Friend at Court” here.

** Published:**

My paper “Capital and Labor Income Pareto Exponents across Time and Space” got accepted at Review of Income and Wealth. I have long felt that in the discussion of inequality, people often don’t make the distinction between income and wealth. In this paper we (my coauthor Tjeerd de Vries and I) estimate the Pareto exponents for capital and labor income separately for as many countries/years as possible. Using 475 country-year observations, we find that the median capital and labor income Pareto exponents are 1.46 and 3.35 respectively, so capital income (hence wealth) is more unequal than labor income. This conclusion is not surprising at all, but the point of the paper is to provide a systematic analysis, which was lacking in the earlier literature.

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My paper “Asymptotic Linearity of Consumption Functions and Computational Efficiency” with Qingyin Ma got accepted at Journal of Mathematical Economics. The main result is that when the marginal utility function is regularly varying (behave like a power function), the consumption function in optimal savings problem becomes asymptotically linear and we characterize the asymptotic slopes. Initially this paper was part of a bigger project with Ma & Toda (2021), but we split the paper in two to keep them focused and at manageable lengths. The JET paper treats only the case with CRRA (constant relative risk aversion) utility but has an economic application. The JME paper assumes regular variation plus some technical condition and discusses computational efficiency.

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I played the San Diego District Championship NTRP 3.5 men’s singles over the last two weekends, and I won the final 6-1, 6-7(5-7), 7-5.

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My paper “Perov’s Contraction Principle and Dynamic Programming with Stochastic Discounting” got accepted at Operations Research Letters. I found a generalization of Banach’s contraction mapping theorem when I was studying a certain dynamic programming problem with stochstic discounting. It turned out that the fixed point theorem was due to Perov (1964) but I thought the application was interesting, so I wrote a short paper.

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In tennis, a pusher is a player who can consistently hit the ball back inside the opponent’s court. They have good footwork and run to every ball. Michael Chang and Rafael Nadal are legendary professional players that have perfected this valuable skill.

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I have been playing tennis and publishing papers long enough that I have found something in common.

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I have been a customer of American Home Shield, a home warranty company, for a few years until today.

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I have been a recreational tennis player for 6 or 7 years. Since fall 2020, I have started to play some matches. (You can see my statistics here.) After starting to play competitively, I have read a lot about tennis strategies because obviously it is more fun to win than to lose. I soon learned (both from theory and experience) that one of the easiest ways to improve your match results is to be more consistent, that is, to reduce unforced errors. So I have been paying attention to consistency and my games have improved.

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I don’t remember when I opened a ResearchGate account; I guess I did so to increase the visibility of my research. I don’t really use their service, but I find it annoying that I get requests to upload full-text articles. This is a waste of time because most of my papers are available online as working paper versions. (These days I upload my working papers exclusively to arXiv.) So I decided to write a short document stating that all of my papers are linked from my personal website (and provided the link), and uploaded it as a full-text article.

** Published:**

It is a great honor to announce that I have been awarded the 4th Government Pension Investment Fund (GPIF) Finance Award under the auspices of Ministry of Health, Labor and Welfare and Ministry of Education, Culture, Sports, Science and Technology in Japan. I am very happy that my research has been recognized.

** Published:**

My paper “A Theory of the Saving Rate of the Rich” was accepted at Journal of Economic Theory. I started this project in early 2020. Initially, the paper was about rigorously establishing the asymptotic linearity of policy functions when preferences are homothetic and the constraint is asymptotically homogeneous of degree 1. This is not surprising but the proof is difficult. As we worked on the proof, we (my coauthor and I) discovered that the asymptotic slope of the policy function can be zero, which was surprising. When the asymptotic marginal propensity to consume (MPC) is zero, an infinitely wealthy agent saves 100% of the wealth, which can explain the empirical puzzle that wealthy people save a lot although it seems unnecessary. So instead of focusing on just a mathematical fact, we decided to frame the paper as a new theory of the saving rate of the rich.

** Published:**

I have been investing for over 20 years. After learning about the capital asset pricing model and the mutual fund theorem and reading “A Random Walk Down Wall Street” and “Stocks for the Long Run”, I have been more or less consistently investing in low-cost index ETFs such as VTI and VXUS. This allowed me to stay in the market during the bottom in March 2009 and not to miss the bull market since then despite some of my colleagues advising me that stocks are overpriced. My kids’ 529 funds have grown about 3 times in nominal value. I have been maxing out my 403b, 457b, and Roth IRA contributions and joking I could retire if I choose to. Based on theory and experience, I preach the importance of passive investing to students in my finance class.

** Published:**

My paper “Necessity of Hyperbolic Absolute Risk Aversion for the Concavity of Consumption Functions” was accepted at Journal of Mathematical Economics. The publication process was quite efficient. I came up with the idea in late September 2020 and wrote a short paper. After getting rejected from a different journal, I sent to JME. I am very happy that it came out in less than three months after I have started the project. Journals in economics tend to be very slow in the review process, perhaps because many papers tend to be long and unfocused. We should all write concise and focused papers.

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I have just signed the Great Barrington Declaration.

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Recently, my working paper Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact has surpassed my JEBO paper in terms of citation counts, and has become my most cited paper. My COVID-19 paper is one of the very first written by an economist on this topic, and it appeared in the first issue of the working paper series Covid Economics. Although I am no longer working on this paper since the situation with COVID-19 has been changing too quickly (especially when I wrote the paper in March 2020) to keep up with, I am glad that this paper has made some impact. In fact, it was featured in VoxEU and Fortune articles.

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As a long-time California resident, I am very well aware of all those government red tapes. But the recent move of the city of Berkeley to ban placing junk food and beverages at checkout ailes is completely nonsense.

`$$...`

, `\[...`

, and `\begin{equation*}...`

** Published:**

I have been using \(\LaTeX\) for over 20 years now. When I write a displayed equation without numbering on a single line, I have been using `$$...$$`

because it was simple. I didn’t understand why some people use `\[...\]`

, because the latter takes more time to type and is not necessarily easy to read. Today I read this article and learned that `$$...$$`

is incorrect. From now on, I will switch to `\begin{equation*}...\end{equation*}`

because it is easy to read and we can add equation numbering by deleting `*`

if we change our mind.

** Published:**

I have recently read the article “Why Mathematicians Should Stop Naming Things After Each Other”. The same logic seems to apply to economics.

** Published:**

Let \(A, B\) be square (complex) matrices such that \(|B| \le A\). Then it is well known that \(\rho(B) \le \rho(|B|) \le \rho(A)\), where \(\rho\) denotes the spectral radius (largest absolute value of all eigenvalues). See, for example, Theorem 8.4.5 of Horn and Johnson (2013). In my recent paper with Brendan Beare and Won-Ki Seo, we needed to use the spectral abscissa (largest real part of all eigenvalues) instead of the spectral radius. By analogy, we can make the following conjecture: if \(A, B\) are square complex matrices such that \(\mathrm{Re} b_{nn} \le a_{nn}\) for all \(n\) and \(|b_{nn’}| \le a_{nn’}\) for all \(n \neq n’\), then is it true that \(\zeta(B) \le \zeta(A)\), where \(\zeta\) denotes the spectral abscissa?

** Published:**

There is a restaurant called “The Bistro” on UCSD campus. Although I don’t like this restaurant because it’s basically a fusion American Asian place, sometimes I have to eat there when we take seminar speakers for lunch. Once I ordered some fried cod (neither quite fish and chips nor tempura). On the menu it said the dish comes with brown rice, so I asked the server to substitute white rice for brown rice. (Although I don’t have statistics to quote, I would say most Japanese people eat white rice - only those that are health-conscious and opinionated eat brown rice, though obviously the latter is healthier.) When the dish arrived, I was stunned that the rice, though white, was sushi rice (i.e., vinegared rice). I asked the server to bring proper white rice but she didn’t know the difference. Since then, whenever I organize the seminar lunch, I choose a different place.

** Published:**

I have created a new website. I have been using Google Sites to create my old website. I like the classic Google Sites because it allows the user to take control of the structure by programming in html. However, the new Google Sites no longer have this feature, and since the classic Google Sites will be discontinued in 2021, I had to do something else. After a bit of Google search, I found this template, which is exactly what I wanted (ability to take full control, free, no advertisements, etc.).

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Advices on applying to economics Ph.D. programs

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List of my coauthors

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Email writing tips for undergraduate students

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Resources on LaTeX

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My policy for writing letters of recommendation

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Places that I have visited

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Short description of portfolio item number 1

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Short description of portfolio item number 2

Published in *Journal 1*, 2009

This paper is about the number 1. The number 2 is left for future work.

Recommended citation: Your Name, You. (2009). "Paper Title Number 1." *Journal 1*. 1(1). __http://academicpages.github.io/files/paper1.pdf__

Published in *Journal 1*, 2010

This paper is about the number 2. The number 3 is left for future work.

Recommended citation: Your Name, You. (2010). "Paper Title Number 2." *Journal 1*. 1(2). __http://academicpages.github.io/files/paper2.pdf__

Published in *Journal 1*, 2015

This paper is about the number 3. The number 4 is left for future work.

Recommended citation: Your Name, You. (2015). "Paper Title Number 3." *Journal 1*. 1(3). __http://academicpages.github.io/files/paper3.pdf__

** Published:**

This is a description of your talk, which is a markdown files that can be all markdown-ified like any other post. Yay markdown!

** Published:**

This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field.

Undergraduate, *UCSD*, 2015

This course covers some topics in operations research, such as convex analysis, nonlinear programming, and dynamic programming. I do not currently teach this course.

Graduate, *UCSD*, 2016

This course trains third year Ph.D. students to conduct research, write papers, and make presentations.

Graduate, *UCSD*, 2017

This course covers topics in finance theory. I do not currently teach this course.

Undergraduate/Graduate, *UCSD*, 2020

This course covers the classical Arrow-Debreu theory of general equilibrium. The undergraduate course (Econ 113) meets 3 hours per week for 10 weeks and covers about 2/3 of the lecure note. The graduate course (Econ 200B) meets 3 hours per week for 5 weeks and covers the entire lecture note.

Undergraduate, *UCSD*, 2020

This course covers some some institutional details on the financial markets, bond pricing (including duration analysis), optimal portfolio problem, mutual fund theorem, Capital Asset Pricing Model, and option pricing (including bounds on option prices, suboptimality of early exercise of American call options, put-call parity, and binomial option pricing).

Graduate, *UCSD*, 2021

This course covers mathematical topics that are essential for economics, very quickly but rigorously.