Paper: arXiv 2411.07674

Authors: Ngoc-Sang Pham

Abstract

We prove that a two-cycle equilibrium in a general equilibrium model with infinitely-lived agents (GEILA) constitutes an equilibrium in an overlapping generations (OLG) model. Conversely, an equilibrium in an OLG model that satisfies additional conditions is part of an equilibrium in a GEILA model. Our framework, which includes three assets (physical capital, a Lucas tree, and fiat money), encompasses both exchange and production economies. As an application, we demonstrate that equilibrium indeterminacy and rational asset price bubbles can arise not only in OLG models but also in GEILA models.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical bridge between GEILA and OLG frameworks using complex general equilibrium dynamics and transversality conditions. However, as a purely theoretical micro-founded macroeconomic paper, it lacks empirical data, backtesting, or statistical validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Map Equilibrium Relationship<br>Between GEILA & OLG Models] --> B[Model Framework Setup:<br>Exchange & Production Economies]
    
    B --> C["Assets Included:<br>1. Physical Capital<br>2. Lucas Tree<br>3. Fiat Money"]
    
    C --> D[Equilibrium Mapping & Mathematical Proofs]
    
    D --> E[Direction 1: GEILA 2-Cycle Equilibrium<br>&#8594; OLG Equilibrium]
    D --> F[Direction 2: OLG Equilibrium + Conditions<br>&#8594; GEILA Equilibrium]
    
    E --> G[Key Outcomes: Indeterminacy & Rational Asset<br>Price Bubbles Proven in GEILA Models]
    F --> G

Cited References (46)

  1. To Bubble or Not to Bubble: Asset Price Dynamics and Optimality in OLG Economies — → 2508.03230
  2. Comment on ‘Asset Bubbles and Overlapping Generations’ by Jean Tirole (2025) — link
  3. Global Characterization of Equilibria in Tirole’s (1985) Model with a Dividend-Paying Asset (2025) — link
  4. Rational Bubbles Attached to Real Assets (2024) — link
  5. Bubble economics (2023) — link
  6. Bubble Necessity Theorem — → 2305.08268
  7. Real indeterminacy and dynamics of asset price bubbles in general equilibrium (2019) — link
  8. The Indeterminacy Agenda in Macroeconomics (2019)
and 38 more
  1. Intertemporal equilibrium with heterogeneous agents, endogenous dividends and collateral constraints (2018) — link
  2. Financial bubbles and capital accumulation in altruistic economies (2018) — link
  3. The Macroeconomics of Rational Bubbles: A User’s Guide (2018) — link
  4. Asset bubbles and efficiency in a generalized two-sector model (2017) — link
  5. Rational land and housing bubbles in infinite-horizon economies (2016) — link
  6. Intertemporal equilibrium with financial asset and physical capital (2015) — link
  7. On Ramsey equilibrium: capital ownership pattern and inefficiency (2013) — link
  8. Bubbles, Financial Crises, and Systemic Risk (2012) — link
  9. Myopia and monetary equilibria (2010) — link
  10. Cass transversality condition and sequential asset bubbles (2004) — link
  11. Intergenerational Altruism and Neoclassical Growth Models (2004) — link
  12. A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations (2002) — link
  13. Asset price bubbles in Arrow-Debreu and sequential equilibrium (2000) — link
  14. A simple proof of Ekeland and Scheinkman’s result on the necessity of a transversality condition (2000) — link
  15. Overlapping Generations or Infinitely-Lived Agents: Intergenerational Altruism and the Economics of Global Warming (1997) — link
  16. Bubbles and constraints on debt accumulation (1992) — link
  17. Co-existence of a representative agent type equilibrium with a non-representative agent type equilibrium (1992) — link
  18. On The Possibility of Price Decreasing Bubbles (1990) — link
  19. Confidence and the Real Value of Money in an Overlapping Generations Economy (1987) — link
  20. Stationary sunspot equilibria in a finance constrained economy (1986) — link
  21. Transversality Conditions for Some Infinite Horizon Discrete Time Optimization Problems (1986) — link
  22. ASSET BUBBLES AND OVERLAPPING GENERATIONS (1985) — link
  23. Observational equivalence of the overlapping generations and the discounted dynamic programming frameworks for one-sector growth (1985) — link
  24. On the Possibility of Speculation under Rational Expectations (1982) — link
  25. Equilibrium in dynamic models with an infinity of agents (1981) — link
  26. ASSET PRICES IN AN EXCHANGE ECONOMY (1978) — link
  27. Are Government Bonds Net Wealth? (1974) — link
  28. EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY (1954) — link
  29. Introduction to economic theory of bubbles ✩ (2014)
  30. Comparative Statics and Perfect Foresight in Infinite Horizon Economies (2008)
  31. Incomplete Markets (2007) — link
  32. Equilibrium Dynamics with Many Agents (2006) — link
  33. Rational asset pricing bubbles (1997) — link
  34. Observational equivalence of the overlapping-generations and the cash-in-advance economies (1987) — link
  35. Comparative Statics and Perfect Foresight in Infinite Horizon Economies (1985) — link
  36. 2025b. Rational bubbles on dividend-paying assets: a comment on Tirole (1985)
  37. The optimal quantity of money (1980)
    1. Asset Prices with Overlapping Generations and Capital Accumulation: Tirole (1985) Revisited

2 of 46 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.