# Posts by Tags

## Homothetic theory of the saving rate of the rich

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.

## Necessity of HARA for the concavity of consumption functions

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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.

## Berkeley banning junk food in checkout aisles is nonsense paternalism

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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.

## Inequality on spectral abscissa

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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?

## Fun facts about tennis rule (1)

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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.

## Won tennis tournament

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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.

## GPIF Award

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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.

## Financial lesson from 2020

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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.

## Great Barrington Declaration

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I have just signed the Great Barrington Declaration.

## My unpublished COVID-19 paper is now my most cited paper

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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.

## Berkeley banning junk food in checkout aisles is nonsense paternalism

Published:

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.

## White rice and brown rice

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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.

## Created new website

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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.).

## Miscellnaneous

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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.

## What junior tennis and publishing papers have in common

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

## American Home Shield is fraudulent

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

## Fun drill to improve consistency in tennis

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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.

## Capital and labor income Pareto exponents

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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.

## Paper accepted

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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.

## Paper accepted

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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.

## Full-text articles on ResearchGate

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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.

## Homothetic theory of the saving rate of the rich

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.