👍Comment on ‘Asset Bubbles and Overlapping Generations’

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.

While studying the literature and writing the JME review article, we realized that Tirole’s classic 1985 paper on asset price bubbles had some issues. Thus, on p. 9 of the review article, we wrote

Proposition 1(c) of Tirole (1985) recognizes the possibility that bubbles are necessary for equilibrium existence if the interest rate without bubbles is negative. Although he gives some explanations on p. 1506 in the sentence starting with “The intuition behind this fact roughly runs as follows’’, he did not necessarily provide a formal proof.

Furthermore, on p. 127 of our JPE paper, we wrote

Theorem 3 is different from proposition 1(c) of Tirole (1985) because Tirole imposes several high-level assumptions without providing examples satisfying them, assumes a constant dividend growth rate, and does not rule out asymptotically bubbleless equilibria.

We thought such statements were sufficient to highlight the marginal contribution of our papers relative to Tirole (1985). However, subsequently, we received criticisms from anonymous reviewers of our other papers, such as

Tirole (1985) has already done this. […] The paper is just a derivative of Tirole (1985) with small twists. The authors themselves also have several closely related papers. One of them is published in JPE. They all have the same idea with small twists. This submission is just a derivative.

It seems that there are people who are either unable or unwilling to read papers.

The analysis of Tirole (1985)’s model in Section V.A of Hirano and Toda (2025) was incomplete because it assumed logarithmic utility and relied on an assumption on an endogenous object, which I have not been happy with. By coincidence, Ngoc-Sang Pham read my JPE paper and got interested in clarifying the issues in Tirole (1985), so we decided to work together. We thus wrote “Asset Prices with Overlapping Generations and Capital Accumulation: Tirole (1985) Revisited”, posted to arXiv in January 2025, and submitted to Econometrica. This paper was rejected, but we were invited to resubmit a comment focusing on Proposition 1(c) of Tirole (1985). Long story short, Proposition 1(c) of Tirole (1985) is incorrect (as stated) because we have a counterexample. However, Theorem 1 of our comment restores the result under the additional assumptions that initial capital is not too small and dividends are not too large.