Alexis Akira Toda

Alexis Akira Toda

Mathematical economist

Nonexistence of Rational Bubbles in Miao and Wang (2018)

2 minute read

Published:

Jianjun Miao of Boston University and Pengfei Wang of Peking University 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; 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, there are 74 papers that are mainly about 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, where 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 to reach a better and mutual understanding about bubbles, and that the science of bubbles will prosper forever, without ever imploding.

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Income inequality at UCSD economics, 2023

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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

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

Backdoor Roth

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

I haven’t been paying attention much, but there are income limits for traditional and Roth IRA. 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 employer, I can no longer contribute to Roth. However, there is a legal loophole called backdoor Roth. All you need is to contribute to a traditional IRA (which is not tax deductible due to the income limit but this is irrelevant) and then do a Roth conversion. This way, anybody can contribute to 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, for this year there is a problem because I have already contributed to Roth 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 traditional 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 resource, I added sufficient cash to hit the $7,000 annual contribution limit right away so that 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 something new about money tips, but I spent a few hours of my time 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

Published:

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.