Paper: arXiv 2305.08268

Authors: Tomohiro Hirano, Alexis Akira Toda

Abstract

Asset price bubbles are situations where asset prices exceed the fundamental values defined by the present value of dividends. This paper presents a conceptually new perspective: the necessity of bubbles. We establish the Bubble Necessity Theorem in a plausible general class of economic models: with faster long-run economic growth ($G$) than dividend growth ($G_d$) and counterfactual long-run autarky interest rate ($R$) below dividend growth, all equilibria are bubbly with non-negligible bubble sizes relative to the economy. This bubble necessity condition naturally arises in economies with sufficiently strong savings motives and multiple factors or sectors with uneven productivity growth.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a highly novel theoretical framework proving the mathematical necessity of asset price bubbles under specific macroeconomic conditions. While it demonstrates strong mathematical rigor through theoretical modeling, it relies entirely on conceptual economic proofs with minimal empirical backtesting or data validation.

Research Flowchart

  flowchart TD
    A["Research Question: Are asset price bubbles<br>inevitable in certain economic environments?"] --> B["Inputs: Economic Growth (G), Dividend Growth (G_d),<br>Autarky Interest Rate (R)"]
    B --> C["Model Assumptions: Strong savings motives &<br>uneven multi-sector productivity growth"]
    C --> D["Theoretical Analysis: Compare long-run rates<br>under condition R < G_d < G"]
    D --> E["Core Outcome: Bubble Necessity Theorem"]
    E --> F["Key Finding: All equilibria are bubbly<br>with non-negligible bubble sizes"]