Alexis Akira Toda

Alexis Akira Toda

Mathematical economist

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Migration to Japan works only for lower-middle-class Americans

2 minute read

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I often see posts about Americans moving to Japan for affordability and other reasons, such as food and culture. It is true that life in Japan is quite affordable these days, perhaps due to the weak yen and over three decades of economic stagnation. I sometimes dream about living in Japan after I retire.

住所と相続税

less than 1 minute read

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最近、Geminiに「引退後はどこに住んだらいいか、税制の観点から説明してほしい」みたいなことを聞いたら、目から鱗の情報を教えてくれた。

Capital One Quicksilver 0% intro APR (4)

less than 1 minute read

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In my post, I mentioned that I have been happy with the Capital One Quicksilver Card because it offered 0% intro APR for 15 months (and the card has no annual fee and gives 1.5% cash back on all purchases).

During the 0% APR period, I racked up nearly $30,000 of credit card debt. By doing so, my credit score went down from around 835 to 795. However, I paid off the debt last week before the end of the 0% APR period. A few days later, my credit score went back to 835. Now that the 0% APR period is over and the credit card offers only 1.5% cash back on everything (less than 2% with my Fidelity card), I contacted Capital One to switch from Quicksilver to Savor, which offers 3% cash back on dining and bakeries.

I highly recommend the card to anybody. If you open an account by clicking this link, you will receive an extra sign-up bonus.

Crowded airport lounges

1 minute read

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I often visit airport lounges, and a common experience is that they are crowded.

Income inequality at UCSD economics, 2024

less than 1 minute read

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The University of California compensation data for 2024 is now published. I have updated the data set for my paper and rerun the regressions. For readers interested in predicting their salaries, the 2024 prediction equation is \[\log y = 12.20 -0.0096T + 0.0051N_\textrm{pub} + 0.0201N_\textrm{top5} + 0.2181D_\textrm{tenure} + 0.2601D_\text{full}, \] where \(y\) is the 9-month salary, \(T\) is the number of years elapsed since obtaining Ph.D., \(N_\textrm{pub}\) is the cumulative number of peer-reviewed research articles, \(N_\textrm{top5}\) is the cumulative number of top 5 publications, and \(D_\textrm{tenure}, D_\textrm{full}\) are dummy variables for tenure and full professor.

Credit card for grocery shopping

1 minute read

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One key principle for saving money is to cut costs in a category with a high share of expenditures.

Nissan Leaf after 7 years (3)

2 minute read

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In this post and this post, I discussed my ordeal of getting the battery of the Nissan Leaf replaced. This matter was resolved in September 2023, but since I have never posted an update, here it is.

529 qualified expenses

less than 1 minute read

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I opened 529 accounts for my kids about 15 years ago. Their nominal balances have grown by about 200% over this period. (Actually, this is something that I regret. I enrolled in targeted date funds without thinking too much. Investment returns have suffered since 2020 because the portfolio’s bond share increased and inflation was high. I should have invested 100% in stocks instead.)

Is it worth keeping the Marriott Bonvoy Boundless Card?

2 minute read

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As I occasionally use Marriott, a few years ago I got the Marriott Bonvoy Boundless Card because it was offering a welcome bonus. I won’t go into details, but the basic structure is that the annual fee is $95 and the benefits are 6 Marriott Bonvoy points per dollar spent on Marriott stays and an annual Free Night Award (worth up to 35,000 Marriott Bonvoy points). The value of a Marriott Bonvoy point is about 0.8 cents. (Regardless of the credit card use, Marriott Bonvoy members earn an additional 10 points per dollar spent on stays. As an automatic Gold Member with the American Express Platinum Card, I get a 25% bonus, so 10 points become 12.5 points. But these points are not included in the above calculation because they are independent of the credit card.)

Tracking spending

1 minute read

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In this post, I mentioned that Fidelity Full View provides account syncing for Fidelity customers. Dividing spending into categories, it also presents a pie chart of spending. The picture below is my own example; I erased the specific amounts and kept only the percentages. In general, to save money, it is best to focus on spending categories with large shares, which in my case are home, children, food, travel, etc.

Tracking cash flow

1 minute read

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In this post, I mentioned that I tracked every single penny of my spending from 2008 to 2022, but I stopped because there was little room left to improve my behavior, and the opportunity cost of keeping track of everything was too high. During this period, I tracked my income and expenditures by manually entering items in an app and using (now discontinued) Mint.com.

Capital One Quicksilver 0% intro APR (3)

less than 1 minute read

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In my post, I mentioned that I have been happy with the Capital One Quicksilver Card because it offered 0% intro APR for 15 months (and the card has no annual fee and gives 1.5% cash back on all purchases).

I referred my wife to open an account, and we both received the referral bonus. But what has been truly great is the targeted deals through Capital One Shopping. We are now remodelling our two bathrooms that are over 20 years old. As my wife has been searching for fixtures, she has started receiving targeted deals from Home Depot, Lowe’s, Bed Bath & Beyond, etc., often offering 15% cash back. Furthermore, the timing of our remodelling coincided with Black Friday/Cyber Week sales (of course, intentionally), so we often get an additional 20% off from the merchants. Overall, I think we saved a few thousand dollars by optimizing credit card use.

I highly recommend the card to anybody. If you open an account by clicking this link, you will receive an extra sign-up bonus.

Saving taxes through UTMA accounts

less than 1 minute read

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While studying how to legally save on taxes, I realized the following trick.

  1. Transfer appreciated stocks to your child’s UTMA (Uniform Transfers to Minors Act) custodial account.
  2. Sell the stock while keeping the capital gains within $1,350.
  3. Use the fund in whatever way you like.

This procedure completely avoids capital gains tax (15% at my tax bracket). The reason is that the standard deduction for a child is $1,350, so as long as income is below that amount, there is no need to file or pay taxes.

I wish I had known about this trick earlier, but it’s better to learn about it later than never. As I have substantial shares of VTI that I bought in 2010 for $60 per share but are now valued at around $335, I transferred a few shares to my kids’ UTMA accounts and sold them. Turning appreciated stocks into cash is almost alchemy.

Round trip between San Diego and Atlanta

less than 1 minute read

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I often fly between San Diego and Atlanta, usually with Delta (because there are more flight options than Alaska, which also offers direct flights between SAN and ATL). As I was looking to book my next trips, I noticed that flight tickets got much more expensive, often over $600 round-trip with Delta (main cabin). After playing around with various searches, I realized that if I book a round trip from Atlanta instead of from San Diego, the price drops by 25% or more. I am not sure why, but maybe it’s because if I book from Atlanta and the trip is over the weekend, the booking system may classify me as a (price-elastic) leisure traveller. By using Alaska instead of Delta, the price often drops below $300 round-trip. Although I have achieved gold status with Delta, since Alaska is much cheaper and also offers status match, I will likely switch to Alaska.

Econ Journal Watch goes LaTeX

less than 1 minute read

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Great news. Starting from the September 2025 issue, Econ Journal Watch publishes papers typeset in LaTeX.

For years, I have been begging the editorial board of EJW to accept LaTeX submissions. This summer, I attempted to submit a comment to urge EJW to accept LaTeX submissions, but to my surprise, I was told EJW was working to transition to LaTeX over the summer, so the point of my comment became moot. The call for papers does not appear to have been updated yet, but we will see whether they officially announce that they welcome LaTeX submissions.

American Express increased annual fee of Platinum Card to $895

3 minute read

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American Express increased the annual fee of the Platinum Card from $695 to $895.

In this post last year, I discussed my love-hate relationship with the American Express Platinum Card. When I opened the account many years ago, I recall that the annual fee was $450. Then it increased to $550 and then to $695. Now it’s $895. It has reached a point where I need to reconsider whether it is worth keeping the card. (See also this opinion.)

The card offers various credits, but most are things I won’t use or are redundant.

  • $400 Resy credit ($100 quarterly): Most of the restaurants that I go to anyway (Asian food) are not in Resy. To me, it makes the most sense to use Resy restaurants for business (for which I get reimbursed) and get the credit, but optimizing is a mental burden.
  • $600 Hotel credit ($300 semiannually): This is for Fine Hotels + Resorts or Hotel Collection, and you need to stay for two nights. Most hotels are expensive. If I can use it for business trips (for which I get reimbursed), it is worth it, but I won’t stay at these hotels for personal trips.
  • The American Express Global Lounge Collection: This is a benefit I have valued in the past (to get free food, drinks, and space at airports, especially Centurion Lounges). But now that I have achieved Delta Gold status (I also have One World Emerald status), its value has declined relatively.
  • $200 Uber credit: This is useful when I travel. During the off-season, I have to use it for Uber Eats. (Uber Eats is overpriced to begin with, so I usually order one Indian curry for pick up on Uber Eats and then order extra stuff at the restaurant directly.)
  • $120 Uber One Credit ($10 monthly): The cost of Uber One is $9.99 per month, so essentially it’s free. I have just signed up for this service, so I will see whether it’s useful.
  • $300 Digital Entertainment Credit ($25 monthly): This is useless. I don’t use these kinds of services.
  • $200 Airline Fee Credit: I use it for Delta, and in the past, it helped me cover change fees or upgrades. But it’s not really necessary.
  • $209 CLEAR Plus credit: CLEAR used to be useful for skipping the security line at the airport. But TSA Precheck has improved (with digital ID, etc.), and I no longer see value in CLEAR.
  • Hilton Honors Gold Status: You get free breakfast for two people, but I rarely stay at Hilton.
  • Marriott Bonvoy Gold Elite Status: I have a different Marriott card, so this is redundant.
  • Leaders Club Sterling Status from The Leading Hotels of the World: I have never heard of this hotel chain.
  • Fee Credit for Global Entry or TSA PreCheck: This is useful, but I have two other cards that provide the same benefit, so it is redundant. (I can use it for family members, though.)
  • $300 Lululemon credit ($75 quarterly): My wife and daughter buy stuff at Lululemon sometimes, so it could be useful.
  • $100 Saks Fifth Avenue credit ($50 semiannually): I won’t shop at Saks unless there is this credit. I just buy minimal stuff, like underwear, when it’s on sale.
  • $200 Oura Ring credit: I don’t know what this crap is.
  • Walmart+ Monthly Membership credit ($12.95 monthly): I don’t use it.

I didn’t list all the benefits and credits, but the rest are less important. My membership renewal is next May, so I still have time to think about it.

Slavery descendants to get preference for college admission if bill approved

less than 1 minute read

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This is utterly absurd. The California Assembly Bill 7 states

This bill would state that the California State University, the University of California, independent institutions of higher education, and private postsecondary educational institutions may consider providing a preference in admissions to an applicant who is a descendant of slavery, as defined, to the extent it does not conflict with federal law.

As a classical liberal, I believe that whether you should be admitted to college or not depends only on your merit, and who your ancestors were has no relevance. Besides, how do you even verify whether one of your ancestors was a slave?

The radical left has often promoted discrimination under the name of DEI. This one has the same intention, though it is carefully worded (“may consider providing a preference […] to the extent it does not conflict with federal law”) so as not to be legally binding.

Econ Journal Watch comment leads to retraction

1 minute read

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Econ Journal Watch (EJW) is one of my favorite journals, which publishes critical comments. I have published one myself.

While browsing past issues of EJW, I came across this comment, which documents that the 2017 Accounting Review article of Bird and Karolyi reports exactly identical numbers in all 11 tables as the 2015 working paper version, despite the fact that the authors switched the main specification and the robustness check between the working paper version and the published version. To this comment, Bird and Karolyi replied

we identified a potentially confusing description of our methodology, which was introduced during the final iteration of copy editing at The Accounting Review. This description conflicted with our correct and clear description of our methodology elsewhere in the published version of the paper.

Out of curiosity, I checked the original published article, and the publisher simply states

The authors acknowledged that the published version of their article misstates the use of CRSP-based index membership in the main specifications and Russell-based index membership data as a robustness test. […] However, the authors were unable to provide the original data and code requested by the publisher that reproduce the findings, as shown in the article’s tables, supporting this assertion. Accordingly, the article has been retracted.

I am glad to know that some journals do the right thing.

Number of articles on arXiv

1 minute read

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Since 2017 or 2018, I have only posted my working papers on arXiv because it is free, open to anyone (they need a referral for initial submission, though), users can download the source file, and version control is straightforward. I see no value in SSRN, though it still seems popular among economists. An added bonus of arXiv is that if you use Overleaf, there is an option to submit to arXiv, so the submission process is (mostly) painless.

Out of curiosity, I wanted to know how many articles arXiv publishes by year and field. It was easy to get these statistics. For instance, for economics, you can go to https://arxiv.org/archive/econ and click “Article statistics by year”.

The graph below shows the number of articles in mathematics (math), computer science (cs), physics (physics), statistics (stat), and economics (econ). Here are a few observations.

  • Mathematics, physics, and statistics seem to have a common trend.
  • Computer science was not special until around 2004, but since then, the number of articles has grown much faster than in other fields.
  • Economics is still very small but is growing more rapidly than other fields (except computer science).
  • There seems to be a slight increase in the number of articles in 2020, likely because people had more time to do research during the pandemic or because it became popular to write papers on COVID.

Number of arXiv articles

Capital One Quicksilver 0% intro APR (2)

less than 1 minute read

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In my post, I mentioned I opened the Capital One Quicksilver Card because it offered 0% intro APR for 15 months (and the card has no annual fee and gives 1.5% cash back on all purchases).

I have been using the card for about half a year, and so far I am very happy with it. In particular, I paid my federal and state income taxes using the card, so I essentially deferred the tax payment by one year, interest-free. (The IRS charges a 1.75% fee for paying taxes with a credit card, but because the card gives 1.5% cash back, it is nearly offset.) I highly recommend the card to anybody. If you open an account by clicking this link, you will receive an extra sign-up bonus.

On illegal immigrants

1 minute read

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If a person enters my house without my permission, I suppose I have the right to ask them to leave, and if they refuse, I may force them to leave. By analogy, if a person crosses the border into a country without the government’s permission, I suppose the government has the right to ask the person to leave, and if they refuse, they may force them to leave. Therefore, I see no problem with some governments cracking down on illegal immigration and attempts to deport illegal immigrants (although there may be exceptions on an individual basis, for example, children who were taken to the country by their illegal immigrant parents and grew up for quite some time, losing ties to their country of birth). It is just common sense, following from the fundamental principle of a liberal society that honors property rights. A corollary of this argument is that I do not understand why some people (typically the radical left or whatever they are called) organize protests against the crackdown on illegal immigration.

夏目漱石全集

less than 1 minute read

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だいぶ前の話になるけど、アトランタへの通勤の時間を有効に使おうと思って、Amazon Kindleで夏目漱石全集を2ドルだか3ドルで買った。主要作品は文庫本で持っているけど、マイナーな作品も読めてとてもよかった。

Is WTN necessary?

3 minute read

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Among amateur tennis players, including high school and college players, I think it is fair to say that UTR (Universal Tennis Rating) is the number that we look at to measure the skill level. UTR rates tennis players on a scale of 1 to 16.5, with higher numbers indicating a higher skill level. According to the Wikipedia page, UTR was developed by a private company in 2008 to evaluate junior players.

The case for flat tax

4 minute read

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My tax situation in 2024 was very complicated due to a job change, a move, and a Roth conversion, among other factors. While filing for taxes, I studied part of the tax code. I discuss my thoughts here.

Baby Steps Millionaires (2)

6 minute read

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In my article yesterday, I discussed the book Baby Steps Millionaires by Dave Ramsey. This book presents many real-world examples of ordinary people achieving financial independence (“millionaire” status) through hard work, discipline, and consistent investing. These stories are all inspiring.

Baby Steps Millionaires (1)

6 minute read

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This weekend, I read Baby Steps Millionaires by Dave Ramsey. I came across this book because a Google Feed article on personal finance recommended it. I could have clicked “Buy Now” on Amazon ($18 or so), but I found it in a local library’s catalog, so I went to the library to borrow the book. As I discussed in my article on frugal habits, if I account for the opportunity cost of spending 20 minutes to visit the library, it does not make economic sense. But to me, visiting the library is part of leisure, so it is justified.

Yield on UCSD pension

1 minute read

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As I was preparing to file taxes, I paid some attention to my UCSD pension balance. When I quit UCSD last year, I left the pension there rather than cashing it out. It occurred to me to evaluate the pension’s yield, so I made some calculations.

The Algebra of Wealth

2 minute read

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I recently read The Algebra of Wealth by Scott Galloway. An article about it came up in my Google Feed, and the book looked interesting, so I borrowed it from the library. (I could have clicked “Buy Now” on Amazon as it costs less than $20, and I could have used my research fund, but I am frugal.)

My frugal habits

9 minute read

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Living a frugal life is one of the most important means to achieve financial independence. In this post, I will discuss tips for frugality.

The Richest Man in Babylon

3 minute read

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Over the winter break, I read The Richest Man in Babylon, which is a 1926 classic on personal finance. I have read it a few times before, but it is entertaining enough to read once every few years. I highly recommend it to anyone interested in personal finance. But let me mention that the book is more philosophical or theoretical than practical, and to succeed in personal finance, it is important to augment abstract knowledge with practical tips, such as understanding the tax code.

Farewell, Citibank

1 minute read

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As part of my annual financial review, I closed my Citibank checking account, which I have had since coming to the U.S. in 2008.

Cost-benefit analysis of credit cards

5 minute read

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As year-end approaches, I downloaded the transaction history for my credit cards to analyze the costs and benefits.

Syllabus template

less than 1 minute read

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As I prepare for my first teaching assignments at Emory, I have started by creating a syllabus template. My department provided a Word template, but it wasn’t exactly to my taste, so I wrote a \(\LaTeX\) template here. The version titled syllabus_template.tex follows the basic structure of the Emory economics template, and the version titled syllabus_template_toda.tex adds some of my information that I use across all my courses. A few comments:

Income inequality at UCSD economics, 2023

less than 1 minute read

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The compensation at University of California has just published the figures for 2023. I have updated the data set for my paper and run regressions. In case readers are interested in predicting their salaries, the prediction equation in 2023 is \[\log y = 12.12 -0.0100T + 0.0052N_\textrm{pub} + 0.0204N_\textrm{top5} + 0.2485D_\textrm{assoc} + 0.5048D_\text{full}, \] where \(y\) is the 9-month salary, \(T\) is the number of years elapsed since obtaining Ph.D., \(N_\textrm{pub}\) is the cumulative number of peer-reviewed research articles, \(N_\textrm{top5}\) is the cumulative number of top 5 publications, and \(D_\textrm{assoc}, D_\textrm{full}\) are dummy variables for associate and full professors.

Comparing taxable, traditional, and Roth accounts

2 minute read

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Three years ago, I wrote a blog post in which I mentioned that I stopped (strictly speaking, significantly reduced) contributing to 403(b) and 457(b) retirement savings plans because I could no longer afford it.

Nonexistence of Rational Bubbles in Miao and Wang (2018)

2 minute read

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Jianjun Miao and Pengfei Wang published a paper titled “Asset Bubbles and Credit Constraints” at American Economic Review in 2018. In their abstract, they state that they “provide a theory of rational stock price

bubbles”. For those who are not familiar with the economic theory of bubbles, “rational bubble” means that the asset price (denoted by \(P\)) exceeds its fundamental value (denoted by \(V\)) defined by the present value of dividends, so \(P>V\), in a model in which agents are rational.

Most papers in the rational bubble literature assume that the asset pays no dividends, because there are known difficulties with positive dividends. (I can talk about this more, but it is technical, so I refer the reader to my JME review article with Tomohiro Hirano, especially Section 3.4.) Miao and Wang’s paper is ambitious because they claim to attach a rational bubble to a dividend-paying asset. For instance, in their literature review, they state

Some studies (e.g., Scheinkman and Weiss 1986; Kocherlakota 1992, 2008; [Santos

and Woodford 1997](https://doi.org/10.2307/2171812); Hellwig and Lorenzoni 2009) have found that infinite-horizon models of endowment economies with borrowing constraints can generate rational bubbles. Unlike this literature, our paper analyzes a production economy with stock price bubbles attached to productive firms.

Here, the cited papers are all rational bubble models. Subsequent papers by the authors also advertise Miao and Wang (2018) as a rational bubble model. For example, Footnote 4 of Dong, Miao, and Wang (2020) states

Introducing dividends or rents will complicate our analysis without changing our key insights. See Miao and Wang (2018) and Miao, Wang, and Xu (2015) for models of rational bubbles attached to assets with dividends or rents.

In a recent working paper by Tomohiro and I titled “Rational Bubbles: A Clarification”, we mathematically proved the nonexistence of rational bubbles in the model of Miao and Wang (2018). In other words, \(P=V\) in their model.

It seems that there is a widespread misunderstanding in the literature. According to our systematic literature search detailed in the paper, 74 papers focus on the theory of bubbles and cite Miao and Wang (2018) as a paper on bubbles. Among those 74 papers, 68 cite Miao and Wang (2018) as a rational bubble model specifically. As proved in our paper, the model of Miao and Wang (2018) is not a rational bubble model. It is an asset pricing model with multiple equilibria, in which the high- or low-stock price equilibrium is selected based on agents’ self-fulfilling expectations. In both equilibria, the stock price reflects fundamentals. I hope that our paper will help foster a better, mutual understanding of bubbles and that the science of bubbles will prosper forever, without ever imploding.

Backdoor Roth

2 minute read

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I have been investing in a Roth IRA. Currently, the contribution limit is $7,000/year.

I haven’t been paying attention much, but there are income limits for traditional and Roth IRAs. For traditional, married couples filing jointly cannot deduct contributions if their modified adjusted gross income (MAGI) is above $136,000. For Roth, married couples filing jointly cannot contribute if their MAGI is above $240,000.

Because I recently got a raise by changing employers, I can no longer contribute to a Roth. However, there is a legal loophole known as the backdoor Roth. All you need to do is contribute to a traditional IRA (which is not tax-deductible due to the income limit, but that is irrelevant), then do a Roth conversion. This way, anybody can contribute to a Roth regardless of their income. So from next year on, I can simply contribute $7,000 of cash to my traditional IRA account, do a Roth conversion, and invest the funds in whatever way I like.

However, this year there is a problem because I have already contributed to a Roth IRA before I knew I would exceed the income limit. I did a bit of research and found this article. Reading it, I did the following.

  1. First, I recharacterized this year’s Roth contributions to traditional.
  2. Then, I contributed cash to a traditional IRA to hit the annual contribution limit.
  3. Finally, I converted all funds from traditional to Roth.

The idea is that, by recharacterizing my existing Roth contributions to traditional, it’s as if I contributed to traditional in the first place. To save my mental resources, I added enough cash to hit the $7,000 annual contribution limit right away, so I can forget about it for this year. Because the existing contributions to Roth had capital gains, by recharacterizing to traditional, I will have to pay capital gains taxes. This TurboTax article explains how to handle taxes.

It’s fun to learn new money tips, but I spent a few hours doing so. Since the income limit for Roth is not binding due to the backdoor Roth loophole, it would make more sense for the government to simply eliminate the income limit for Roth altogether. And if there is no income limit for Roth, there should be no limit for traditional either. Our lives will be much simpler that way.

Farewell, UCSD

3 minute read

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As I have already announced on my website, I am resigning from UCSD. Today is my last day. I have been employed for 11 years, so I have bittersweet feelings for sure.

Trip to Japan

2 minute read

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I have just returned from a 10-day trip to Japan. During this short stay, I visited the Ikaho hot spring, did some sightseeing in Tokyo with my family, and gave talks at Waseda University and the University of Tokyo.

Website updated

less than 1 minute read

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After spending several days, I significantly updated my website. Below is a list of the main changes.

  • Previously, there was a “Research” page that I created manually. But it was tedious to list all papers in a consistent style (e.g., journal names in bold, coauthors in italics, etc.), so I automated it.
  • I omitted publication information except the journal name and year, because I don’t think they are very important, and one can easily find them by clicking the link to the published paper.
  • I searched for all my paper drafts on my computer and added slides whenever I found them.
  • I merged “Conference proceedings” with “Other publications” because I don’t see a reason to keep proceedings as a separate section, given that I don’t have many.

Talks

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Maybe it is not the best use of my time, but I created a “Talks” page, which lists past and future talks and presentations. After spending all afternoon tweaking the code, I came up with something satisfactory. For now, I included only talks in 2023 and 2024, but I might add past ones.

Nissan Leaf after 7 years (2)

less than 1 minute read

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I have been waiting almost 9 months for the replacement battery for my 2016 Nissan Leaf, and the delay is extremely frustrating.

Nissan Leaf after 7 years (1)

3 minute read

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In 2016, I purchased a Nissan Leaf. Given the technological progress in electric vehicles, it’s almost a joke now, but it had a 30kWh battery with around 110 miles of range. Including everything (tax, registration, etc.), it cost 42,647 dollars. My employer subsidized $10,000, and I received a $7,500 federal tax credit, so at that time, I thought it was not a bad deal. 110 miles of range seemed enough for daily chores, and for road trips, we had been renting a gas-powered vehicle. This was our only vehicle in the household until 2020, when we bought a Tesla Model Y.

biblatex

1 minute read

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For managing bibliographies for my papers, I have been using the natbib package with bibtex for a long time.

Pitfall of electric bike

2 minute read

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When I moved from Connecticut to San Diego in 2013, one thing I paid attention to when searching for a house was finding one within a reasonable distance from work. I knew that San Diego had nice weather and commuting by bicycle was feasible. So to save money and get some exercise, I cut the number of vehicles in my household from two to one and bought an electric bike to commute. (In 2020, I went back to two vehicles because we could no longer keep up with only one vehicle to manage kids’ activities.)

Investment and taxation

3 minute read

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Since I started working in 2013, I haven’t given much thought to investing. Because I know that investing in an index fund is the theoretically right thing to do and I do not like paying taxes, in addition to participating in my employer’s mandatory defined benefit retirement plan, I have just been maxing out investments in 403(b), 457(b), and Roth IRA (all invested in low-cost index funds).

Optimal use of sabbatical credit

1 minute read

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This post is completely boring for outsiders. I am just writing this down so that I do not forget.

Disabling Canvas Inbox

1 minute read

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My university uses Canvas for instructional purposes. Canvas has a feature called “Inbox” that lets you send messages. I have long thought this functionality not only useless but even harmful. This is because I ignore everything sent to Canvas Inbox, but students who are unaware that I do not use it may send me messages that get ignored and then complain. Since I was unable to find information on how to disable Canvas Inbox, I contacted the university’s technical support.

Fun facts about tennis rule (3)

3 minute read

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These days, I mostly play competitive tennis, so my opponents usually have a good understanding 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.

Fun facts about tennis rule (2)

1 minute read

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These days, I mostly play competitive tennis, so my opponents usually have a good understanding 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.

Fun facts about tennis rule (1)

3 minute read

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These days, I mostly play competitive tennis, so my opponents usually have a good understanding 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.

Capital and labor income Pareto exponents

1 minute read

Published:

My paper “Capital and Labor Income Pareto Exponents across Time and Space” was accepted for publication in Review of Income and Wealth. I have long felt that in discussions of inequality, people often fail to distinguish 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

less than 1 minute read

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

Paper accepted

less than 1 minute read

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

Good pusher, bad pusher

2 minute read

Published:

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 who have perfected this valuable skill.

American Home Shield is fraudulent

7 minute read

Published:

I have been a customer of American Home Shield, a home warranty company, for a few years until today. This company is the worst business I have ever dealt with, I would say worse than the California Department of Motor Vehicles.

Full-text articles on ResearchGate

less than 1 minute read

Published:

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.

GPIF Award

less than 1 minute read

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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.

Homothetic theory of the saving rate of the rich

1 minute read

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.

Financial lesson from 2020

1 minute read

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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 after reading “A Random Walk Down Wall Street” and “Stocks for the Long Run”, I have been 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 miss the bull market since then, despite some of my colleagues advising me that stocks were overpriced. My kids’ 529 funds have grown about 3 times in nominal value. I have been maxing out my 403(b), 457(b), and Roth IRA contributions, and joking that 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.

Necessity of HARA for the concavity of consumption functions

less than 1 minute read

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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 being rejected by another journal, I submitted to JME. I am very happy that it came out in less than three months after I started the project. Journals in economics tend to be very slow in the review process, perhaps because many papers are long and unfocused. We should all write concise and focused papers.

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

1 minute read

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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.

Difference between $$..., \[..., and \begin{equation*}...

less than 1 minute read

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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 \[...\], since the latter takes longer to type and isn’t 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.

Inequality on spectral abscissa

1 minute read

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?

White rice and brown rice

less than 1 minute read

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There is a restaurant called “The Bistro” on the 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 to lunch. Once I ordered some fried cod (neither quite fish and chips nor tempura). On the menu, it said the dish came with brown rice, so I asked the server to substitute white 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

less than 1 minute read

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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 lets users 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 find another solution. 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.).

misc

Discretization

Published:

Methods and code for discretizing probability distributions and stochastic processes.

About this website

Published:

Notes on how this website is structured, maintained, and published.

My research philosophy

Published:

Personal principles for choosing problems, collaborating, and doing research.

Travel

Published:

A personal guide to favorite places and a record of countries and territories visited.

LaTeX

Published:

LaTeX resources, templates, packages, and workflows I use.

How to get rich

Published:

Practical principles for building wealth through saving, investing, and career choices.

Coauthors

Published:

A record of my coauthors and collaborative research.

Tax-saving tips

Published:

Practical notes on legally reducing taxes in the United States.

other

Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact Permalink

Published:

After returning from my UK trip in early March 2020, just a few days before the closure of the border, I got interested in COVID-19, like many of us. I played around with some models and I derived a system of differential equations that turned out to be identical to the Kermack & McKendrick (1927) susceptible-infected-recovered (SIR) model. I searched the literature and found the closed-form solution by Harko et al. (2014). At that time, little was known about COVID-19, so I decided to estimate the epidemiological parameters from data to predict the epidemic dynamics.

Visualizing the Contraction Mapping Theorem Permalink

Published:

After my 2022 ECMA paper got accepted in January 2022, I got burnt out. I stopped doing research and spent most of my time playing tennis. I became a captain of a USTA 7.0 mixed doubles team (I had just become 4.0), and my wife and I recruited strong players, organized practices, and advanced to sectionals twice. In one of the Southern California sectionals, we narrowly lost in the semifinal.

My coauthor Jim Rauch was the recruitment chair when I got hired at UCSD in 2013. He was also the department chair from 2013 to 2016, so I had a lot of interaction with him. When we chatted in June 2022, he mentioned he was interested in a project to animate the contraction mapping theorem to help build intuition. We knew it had zero career benefit but it sounded fun, so I wrote up some pedagogical material and Matlab codes and Jim made the video.

We tried to publish this in journals on economic education but we got desk-rejected each time and the paper became dormant. Later, I was asked to review a paper at Qeios. Because I had never heard of that journal, I thought it was a predatory journal, but upon inspection its business model seemed interesting: they publish anything, but reviews are open and (to prevent abuse) not anonymous. So we posted our paper there, and we are happy that our paper and video have been well received.

Convergence of value functions

‘Ergodicity Economics’ is Pseudoscience Permalink

Published:

In May 2023, I read something about Ergodicity Economics, and I thought it was a completely nonsense pseudoscience promoted by failed self-proclaimed physicists. Although it had zero career benefit, to contribute to the public good to prevent the spread of pseudoscience, I spent a few days writing this critique. The paper got desk-rejected from Physical Review Letters, Physical Review E, and Chaos and became dormant. After my pleasant experience at Qeios, I published the paper there.

Essential Mathematics for Economics Permalink

Published:

I taught math camp at the UCSD economics PhD program from 2015 to 2023. A publisher noticed that I have been posting my lecture notes at my website and solicited its publication as a book. I completely rewrote my notes from 2023 to 2024. I think this is the best textbook on “Mathematics for Economics” out there.

portfolio

publications

Radii of the Inscribed and Escribed Spheres of a Simplex Permalink

Published in International Journal of Geometry, 2014

(Mathematics) High-dimensional generalization of the fact that the sum of the reciprocals of the radii of escribed circles of a triangle equals the reciprocal of the radius of the inscribed circle; obtained those results in 1998 when I was freshman.

👍Discretizing Nonlinear, Non-Gaussian Markov Processes with Exact Conditional Moments Permalink

Published in Quantitative Economics, 2017

After working on the maximum entropy discretization method in Tanaka & Toda (2013, 2015), in 2014 I wanted to apply the method for discretizing Markov processes. Because I had neither sufficient programming skills nor knowledge of potential applications, I asked my colleague Johannes Wieland if he knew a good graduate student to work with, and he referred me to Leland. At that time, Leland was working on the estimation of nonlinear state space models using discretization (which later became his job market paper), so our interests aligned. Leland played an instrumental role for this project such as suggesting discretizing the conditional distributions, coding, and finding interesting applications. We owe Craig Burnside for suggesting using a closed-form asset pricing model to evaluate solution accuracy, and Jim Hamilton for suggesting avoiding simulations entirely.

We initially submitted this paper to Econometrica. We had two positive and two negataive reports, and one of the negative one complained about the possibility of matching higher order moments, which we pointed out in a footnote but did not implement out of laziness. I regret that maybe if we did it from the beginning, we might have been able to publish this paper at Econometrica. When we sent the paper to QE, we exercised the option to transfer Econometrica reports, and the review process was painless.

I believe the discretization method in this paper is still the best in the literature and has been applied in many papers by other researchers. Please see my discretization page for up-to-date files.

👍The Equity Premium and the One Percent Permalink

Published in The Review of Financial Studies, 2020

👍(Finance, Theory, Empirical) In general equilibrium model with heterogeneous risk aversion and/or beliefs, the wealth distribution predicts excess stock returns, which we confirm in data using estate tax rate change as instrument.

👍A Theory of the Saving Rate of the Rich Permalink

Published in Journal of Economic Theory, 2021

👍(Theory, Macro) Prove asymptotic linearity of policy functions when preferences are homothetic; show that asymptotic marginal propensities to consume can be zero, implying a large saving rate of the rich.

👍Determination of Pareto Exponents in Economic Models Driven by Markov Multiplicative Processes Permalink

Published in Econometrica, 2022

To obtain the double power law result in my 2014 JET paper, I assumed some conditional independence (which rules out persistent heterogeneity) and took the continuous-time limit, which was not entirely satisfactory. In those days, all power law results in economics relied on the IID assumption, which is clearly unrealistic. Around Footnote 13, Gabaix (1999) states

Tail Behavior of Stopped Lévy Processes with Markov Modulation Permalink

Published in Econometric Theory, 2022

This is a follow up paper of Beare & Toda (2022), where we characterize the tail behavior of Markov-modulated Lévy processes that are stopped at state-dependent Poisson rates. In 2018, Brendan gave the project to Won-Ki, who was his student. I joined Won-Ki’s dissertation committee to advise on this project, and we essentially translated the discrete-time results in Beare & Toda (2022) to continuous-time. The CARA-Huggett economy example in Section 4 was recycled from an earlier version of Beare & Toda (2022).

👍Optimal Epidemic Control in Equilibrium with Imperfect Testing and Enforcement Permalink

Published in Journal of Economic Theory, 2022

👍(Theory) Study a behavioral SIR model with imperfect testing and government enforcement and show that equilibrium action is approximately static efficient in the sense that the laissez faire equilibrium allocation is close to the optimal short-term lockdown policy, implying that short-term lockdown policies are redundant.

Capital and Labor Income Pareto Exponents across Time and Space Permalink

Published in Review of Income and Wealth, 2022

(Power law, Empirical) Estimate capital and labor income Pareto exponents across 475 country-year observations and document that capital income inequality is higher than labor income inequality (median Pareto exponents 1.46 and 3.35 respectively) and the two inequalities are uncorrelated, suggesting importance of distinguishing the two.

👍Bubble Economics Permalink

Published in Journal of Mathematical Economics, 2024

👍(Theory, Macro, Finance) Self-contained review of the theory of asset price bubbles.

👍Bubble Necessity Theorem Permalink

Published in Journal of Political Economy, 2025

In the fall of 2022, Tomohiro Hirano, Ryo Jinnai, and I studied a model in which the interaction between idiosyncratic investment risk, leverage, and the presence of a dividend-paying asset in fixed supply affects asset prices. Tomohiro and Ryo had already worked on asset price bubbles including Hirano and Yanagawa (2017) and Guerron-Quintana, Hirano, and Jinnai (2023), whereas it was a new topic for me. This collaboration led to the working paper of Hirano, Jinnai, and Toda (2023) “Necessity of Rational Asset Price Bubbles in Two-Sector Growth Economies”, which we posted to arXiv in November 2022.

We submitted the paper to Econometrica in January 2023. It was rejected on May 5, 2023. We had three reports. The first report, written by an expert, was on the fence but found the example of nonexistence of fundamental equilibrium (Proposition 2.2) “extremely surprising” and stated that

[the] interesting contribution of the paper is … to show that there might be settings where equilibria without bubbles do not exist.

The second report was likely written by a quantitative macroeconomist, declined to evaluate the theoretical contributions, and recommended rejection, while acknowledging that

What’s more of a surprise, is that under some conditions, we necessarily go to \(R=G\).

The third report was written by an expert and provided many comments. One of them was

Miao and Wang (2018, AER) … also study models of bubbles attached to assets with positive dividends/rents

and another was

I am not convinced by one of the main result of the paper that an equilibrium with rational asset price bubbles exists but equilibria with asset prices equal to fundamental values do not,

though this referee did not point out any specific mathematical error.

Three days later, on May 8, 2023, Jianjun Miao sent an email to me, in which he disclosed that he was the third referee at Econometrica.

Email from Miao

In case it is difficult to read, I quote it here.

I know you have a paper with Tomohiro and Ryo just got rejected at ECMA. You may guess that I am one of the referees. I am very interested in topics on asset bubbles and your paper. One main issue of your paper is that I do not think your proofs of nonexistence of fundamental equilibria in your examples are convincing. Your proofs only focus on one type of trading strategies as detailed in my report. In other words, you essentially prove that an equilibrium with that type of trading strategy does not exist, but there may exist fundamental equilibrium with other trading strategies. I know you are a serious theorist and good at math. Hope you understand my point. I am also happy to have more discussions on this point from a pure academic perspective.

Another minor issue is that your paper does not fairly cite the literature, especially my related work. I know Tomohiro well and invited him to several conferences and a BU seminar too. It seems that he always avoids citing most of my papers. In contrast I always cite his related papers. I told him this issue before as I treat him and you as friends and allies. But it seems that he is quite stubborn.

The part “other trading strategies” is a bit strange, as our example employed a two-period overlapping generations model in which the unique portfolio choice in equilibrium is that the old sell the entire asset and the young buy the entire asset (which is necessarily true by market clearing). After this exchange, I offered to explain the proof in a Zoom meeting with Miao, but he insisted that a fundamental equilibrium (an equilibrium with \(P=V\)) always exists and was not willing to listen.

At this point, Tomohiro and I were not yet aware of the issues with Miao and Wang (2018) discussed in our clarification paper (subsequently published at Econ Journal Watch) or this post, but we were encouraged by the first referee’s reaction of “extremely surprising”, so we decided to write a new paper to establish the robustness of the nonexistence of fundamental equilibria. We worked intensively for a week and posted a new working paper “Bubble Necessity Theorem” to arXiv on May 14.

After polishing, we submitted this paper to Econometrica on June 21, 2023, this time attaching a cover letter detailing the conflict of interest with Miao. This paper was desk-rejected without any feedback from the editor: you can see the decision letter here.

Being worried if the cover letter was the cause of rejection, we then submitted the paper to Journal of Political Economy without a cover letter. Fortunately, we received a revision request on September 5, 2023 with three positive reports. After several revisions, the paper was accepted on April 23, 2024 and was published in 2025.

We will keep fighting for scientific integrity.

Toward Bubble Clarity: A Comment on Miao and Wang Permalink

Published in Econ Journal Watch, 2025

In the fall of 2022, Tomohiro Hirano, Ryo Jinnai, and I studied a model in which the interaction between idiosyncratic investment risk, leverage, and the presence of a dividend-paying asset in fixed supply affects asset prices. This collaboration led to the working paper of Hirano, Jinnai, and Toda (2023) “Necessity of Rational Asset Price Bubbles in Two-Sector Growth Economies”, which we posted to arXiv in November 2022.

👍Unbalanced Growth and Land Overvaluation Permalink

Published in Proceedings of the National Academy of Sciences, 2025

This is my fourth paper on rational bubbles. The first paper is “Necessity of Rational Asset Price Bubbles in Two-Sector Growth Economies”, which we posted on arXiv in December 2022. (The paper is still unpublished and its title has changed a few times, though we expanded the example in Section 2.2.1 as an independent paper and published at JPE.) The second paper is “Equilibrium Selection in Pure Bubble Models by Dividend Injection”, which we posted on arXiv in March 2023 and still unpublished. The third paper is “Housing Bubbles with Phase Transition”, which we also posted on arXiv in March 2023 and still unpublished.

When we initially discovered the necessity of bubbles (i.e., bubbles inevitably emerge under some conditions), the example was based on an endowment economy with growth and constant dividends. After discovering this example, I became interested in applications. Because land and housing are typical assets on which bubbles often arise (at least in the casual sense), I worked on several models that could generate endogenous dividends. After some trial and error, I realized that the elasticity of substitution (either in the utility function of the production function) plays an important role: once we remove the knife-edge restriction of elasticity being exactly equal to 1 (Cobb-Douglas), the economy and dividends grow at different rates (unbalanced growth), which generates bubbles under a low interest rate condition. This paper emerged from this idea: empirical evidence suggests that the elasticity of substitution between land and non-land factors exceeds 1, so when the economy grows, land rents do not grow as fast and generates a land bubble.

We submitted the paper to American Economic Review in July 2023. We got rejected in October 2023 with one positive report, one on the fence, and one negative. Around that time, we got an R&R from JPE for the necessity paper, so we thought it more advantageous to wait until JPE accepts the paper to have a better reputation. Therefore, we let the paper be dormant for a year, and I used this paper as my job market paper when I was on the market in Fall 2023. After JPE accepted our paper, we revised the unbalanced growth paper. Because some AER referees asked for more empirical work, which we don’t have any expertise, we shortened the paper and submitted to American Economic review: Insights in August 2024. We got rejected in November 2024 with just one, one-page report.

At that point we had too many pending projects, and we had no intention of bloating the paper with empirical work or extensions, so we decided to submit the paper to Proceedings of the National Academy of Sciences in November 2024, which is a top science journal. (And being a science journal, papers are much more concise than those in economics journals. An added benefit of PNAS is that you can suggest 6 potential reviewers and 3 you would like to exclude from reviewing, so we can suggest true experts and avoid people with conflicts of interest.) We received a minor R&R with two positive reports in December 2024 and got accepted shortly after we resubmitted in February 2025. I have been submitting hundreds of papers to different journals, but science journals provide far better experience than economics journals.

Incentivizing Hidden Types in Secretary Problem Permalink

Published in International Journal of Game Theory, 2025

In the academic year 2021, Longjian (then undergraduate student at Peking University) visited UCSD for an exchange program. He asked me if he could take the first year PhD microeconomics. Normally I don’t allow undergraduate students to take PhD classes, because almost all precedents failed to keep up with the coursework. However, looking at Longjian’s CV and academic transcript, I realized that he had taken many advanced math courses and excelled in all of them, so I took the chance and allowed him to take the course. He ended up in the top quarter of the PhD cohort, so his performance was impressive.

Land Bubbles Despite Non-Vanishing Rents Permalink

Published in Economics Letters, 2025

In any rational bubble model with a dividend-paying asset, the dividend yield (dividend to price ratio) must converge to zero in the long run (see, for instance, Lemma 1 of my JPE paper). Some people have a strong belief that the dividend yield should be stationary and reject the idea of rational bubbles on this basis.

Pareto’s Limits: Improving Inequality Estimates in America, 1917–1965 Permalink

Published in Cliometrica, 2026

I owe a great deal to coauthor Vincent Geloso for this paper. Vincent has written a series of papers that improve the top income share estimates. In 2023 he found my paper on nonparametric density estimation from tabulated summary data and suggested that we apply the method to estimate top income shares from tax returns data. At that time, the literature used Piketty’s Pareto interpolation method, which was ad hoc.

👍Comment on ‘Asset Bubbles and Overlapping Generations’ by Jean Tirole Permalink

Published in Econometrica, 2026

My coauthor Tomohiro introduced me to the theory of asset price bubbles, and we began working together in the summer of 2022. Until then, I knew nothing about the literature. By the fall of 2023, we had written many papers that we considered groundbreaking. In 2025, one of these papers, “Bubble Necessity Theorem”, was published at Journal of Political Economy, and another, “Unbalanced Growth and Land Overvaluation”, was published at Proceedings of the National Academy of Sciences. In the fall of 2023, we wrote a review article on rational bubbles, which was published at Journal of Mathematical Economics in 2024.

Reducible Markov Modulation, Pole Order, and Tail Behavior in Random Growth Models Permalink

Published in Journal of Applied Probability, 2026

This is a follow up paper of Beare & Toda (2022) and Beare, Seo, & Toda (2022), where we characterize the tail behavior of stopped Markov additive processes in discrete- and continuous-time, respectively. In these papers, we assumed that the transition probability matrix of the Markov chain is irreducible. While writing the latter paper, in 2021 I obtained a complete characterization of the tail behavior even if the transition probability matrix is reducible. However, the argument was complicated, so we saved the result for another paper. Subsequently, Brendan discovered a connection to the Rothblum index theorem.

talks

teaching

Operations Research (Econ 172B)

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.

Advanced Financial Markets (Econ 433)

Undergraduate, Emory, 2025

This course studies personal finance, 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). The course requires good analytical skills (basic calculus and probability/statistics). To solve numerical examples, we will learn programming in Matlab, although no prior knowledge is necessary.

wp